Hello. Good morning. Welcome all to the YouTube live session on board level problem solving. Good morning to everyone who is present in the session. So I would request you to type your names in the live chat box so that I know who are attending the session. Hello. Good morning, Sondaria. All right. Yeah. So even before I start with the first problem. So yes, your answer is correct. So if a is a square matrix of order three says that a joint of a is 64 find the determinant of the transpose of a. So we all know that determinant of a joint of any square matrix a of order n is given by determinant a to the power n minus one, where n is the order of the square matrix, the square matrix a. Okay. So since it is of order three, so determinant a to the power of two is 64. Correct. Okay. So determinant a could have been plus or minus eight. So determinant a transpose also could have been plus or minus eight. Hello. Welcome all. Welcome all to the live session. So let's begin with the next question now question number two. So here is a square matrix satisfying a square is equal to I then what is the inverse of a again a super simple question. Just a one marker. Exactly. So basically this is a matrix. It is called an involuntary matrix where a is its own inverse. So if you just do a pre facto multiplication with a inverse on both the sides, you will get a is equal to a inverse. So inverse of a is a itself. Next, again, treat this as a rapid fire round. What are the degree of the following differential equation? What is the degree of the following differential equation? Past to absolutely correct. So basically this is the highest order. Okay. This is the highest order differential coefficient and the power highest power of the highest order differential coefficient defines the degree for you. So degree is going to be 2. Right. So answer is 2. Next, if A and B represent the two adjacent sites of a parallelogram, then write the area of the parallelogram in terms of A and B. Super simple. What is the area of the parallelogram? Just type it in the chat box. Mod of A cross B. Absolutely correct. Okay. Next, find the angle between the vectors A and B given that mod A is 3, mod B is 4 and mod of A cross B is equal to 6. It could be 150 degrees as well. Okay. So mod of A cross B is nothing but mod A mod B into sine of the angle between them. So this is 6. This is 3 into 4 into sine of theta. So sine theta is half. And this implies the angle could be 30 degrees or it could be 150 degrees. That's 5 by 6 or 5 by 6. So this is the last of the one marker. Find the direction cosines of a line passing through origin and lying in the first octant making equal angles with the three coordinate axis. Absolutely correct. So basically, let's say your direction cosines are L, M and N and each one of them is going to be cos of alpha because the angles made are all equal. And we also know that L square plus M square plus N square has to be 1 which implies 3 cos square alpha has to be 1 which implies cos of alpha has to be plus minus 1 by root 3. Okay. So either you can say this. Okay. Minus will be neglected because we are taking it into the first quadrant. Okay. So we are assuming the direction of the line to be in such a way that the angles made are all acute angles. Next. Show that the relation R in the set A given by the relation R is equal to defined as all ordered pairs A, B says that mod A minus B is 0 by 4 is an equivalent solution and find the set of all elements related to 1. So in relation questions, please ensure that you write all the steps properly without any kind of ambiguity. Try to show it's going to be all reflexive, symmetric and transitive. At least type in the answer for the last part of the question which says find the set of all elements related to 1. If done, do let me know. Just type done on the chat box. Okay. Great. So let's discuss this. So for all A belonging to the set A, okay, mod of A minus A is equal to 0 which is divisible by 4, which is divisible by 4, okay, implies A comma A belongs to the given relation, right. Therefore R is reflexive. Therefore R is reflexive. Okay. Now for symmetric, let A comma B belong to R. In fact, you can start by saying that let A and B belong to the set A and A comma B belong to R, okay. This implies mod of A minus B is divisible by, is divisible by 4, which also implies mod B minus A is divisible by 4, okay. And this implies B comma A will belong to R. Therefore R is symmetric. So for transitive, so you can write here reflexive, symmetric and for transitive, let A, B, C belong to A such that A comma B belongs to R and B comma C belongs to R, okay. This clearly implies mod of A minus B is divisible by 4 and mod of B minus C is divisible by 4. So I'll just make some space for myself by raising the first part. Let me raise this part. So this implies A minus B is divisible by 4 or you can say A minus B is equal to plus minus 4 lambda and B minus C is equal to plus minus 4 alpha, okay. So when you add it, so A minus C adding 1 and 2, adding 1 and 2. A minus C is equal to plus minus 4 lambda plus minus alpha, okay. Which clearly implies mod of A minus C is divisible by 4 and hence therefore R is transitive. Now regarding the set of all elements related to 1, so 1 itself is related to 1, 5 is related to 1, 9 is related to 1. After that it will go beyond the set A. So this will be your set which is related to 1. Next, 2 tan inverse of sin x is tan inverse of 2 Ck for x lying between 0 to pi by 2, solve for x. Please type in your response once you're done, okay. What about others? Alright. So let's discuss the first one here. So we all know that 2 tan inverse of x is tan inverse of 2x by 1 minus x square, okay. So applying the same onto the given problem, so 2 tan inverse sin of x will become tan inverse 2 sin x by 1 minus sin square x. And this is equal to tan inverse of 2 Ck, okay. So this means the inputs must be equal, okay, because they are 1, 1 functions. So 2, 2 will get cancelled off, sorry, why did I write tan square, sin square, okay. So we can say that sin x by cos square x, so cos square x if you take on the other side it becomes cos square Ckx. So sin x is equal to cos x, that means tan of x is 1. Only one possible answer in this particular interval satisfies it and that answer is pi by 4. So this is going to be your solution for this inverse trigonometric equation. Now try the other part of it, let me know once you are done, okay. Alright, so here we can use our double angle formulas, sin inverse of 2x by 1 plus x square is equal to 2 tan inverse of x, okay. And this formula is valid for x lying between minus 1 to 1, correct. In a similar way cos inverse of 1 minus y square by 1 plus y square is equal to 2 tan inverse y, okay. And this formula is valid for y lying between 0 to infinity. Now all these conditions are being met over here, this condition is a subset of this condition, even this condition is met over here, correct. Now this can be written as, the left hand side can be written as tan inverse of, sorry, tan of half 2 tan inverse x plus 2 tan inverse y, which is actually tan of tan inverse x plus tan inverse y, okay. We also know that tan inverse x plus tan inverse y is going to be tan inverse x plus y by 1 minus xy. So this will become tan of tan inverse x plus y by 1 minus xy, okay. And this formula is valid when your xy is less than 1. And this condition is also met by this particular situation given over here.  Hence shown. Let's move on to the next question now. If none of a, b, c are is 0, using properties of determinant, prove that. So as you can see, you have to prove that the value of the determinant is bc plus ca plus ab the whole cube. Let me know once you're done. So remember I told you that there are three types of problems where you can lose a lot of your time if you do not take the right approach. One is integration, other is determinants, another is maxima and minima. So as you would find that many of you would be struggling in this problem. So these are the deciders, the ones who get 90% and the one who get 95% and the one who get 99% in maths. These are the deciders. Anybody please let me know if you're done. So Vaishnavi, Sondarya, Sanjina, others who have not disclosed their names. If at all you're done, do let me know. And if you need help, please do also type that. So you're not able to do it, then I can start solving it. I think 10 minutes is a good enough time to give it to this problem if you're not getting it. Should I start solving it? No problem Vaishnavi, I understand. Determine problem if you not take the right approach, it may kill a lot of your time. So let's try to tackle this problem now. So first of all, I need the terms a, b, b, c, c, etc. Now see what I will do here. I would try to get rid of the terms like c square, a square, b square and all because they are not important to me as the outcome of it doesn't contain those terms. So what I will do first, I will multiply row 1 with a, I will multiply row 2 with b and I will multiply row 3 with c. So when I do that, I get 1 by a, b, c. Of course, when you're multiplying, you have to divide it because if you're not doing any other operation after multiplication, you have to divide it also. So a, b, c and this will be a, b square plus b, c. And this will be a, c square plus b, c. And here I will get b times a square plus a, c. Again minus a, b, c. Again b times c square plus a, c. And this will be c times a square plus a, b. c times b square plus a, b minus a, b, c. Now start taking, take a common from c1, b common from c2 and c common from c3. So a, b, c will come out and a, b, c is already there in the denominator that will get cancelled.  And this will become a, b plus b, c. Okay. Similarly, this will become a, c plus b, c. Here if you take a b common, it will become a, b plus a, c. Then minus of a, c. And then from here I will get b, c plus a, c. If you take a c common from column 3, you become, it becomes a, b plus a, c again. And a, b, a, b plus b, c. And minus of a, b. Okay. So far so good. No problem in identifying these two steps. Okay. Now what do you do is you do this operation. Add everything to the first row. That means R1 is transformed to R1 plus R2 plus R3. Okay. So I am writing the result over here in this amount of space. Okay. So when you add everything on this, you will realize that b, c will get cancelled and you will get a, b plus b, c plus a, c. Okay. And same will be true for the second element of the first row. A, b plus b, c plus a, c. Okay. And again, a, b plus b, c plus a, c. Okay. Rest of the elements will not touch it. So a, b plus b, c, copy it. A, c plus b, c, copy it. Minus a, c. B, c plus a, c. A, b plus b, c minus a, b. Now you can pull out an a, b plus b, c plus c, a or a, c. Common from the first row itself. Now I would have to make some space because I cannot write anymore. Okay. So let me just erase this part. Yeah. So when you take a, b plus b, c plus a, b plus b, c plus c, a common from the first row, you get 1, 1, 1. So a, b plus b, c minus a, c. A, b plus b, c. A, c plus b, c. B, c plus a, c minus a, b. Okay. Then you know that if you have all 1, 1, 1 generated in a given column or row, what to do next? The obvious operation is you can take one of the column, let's say c1 and start subtracting from the other column. So let's say c2 is c2 minus c1 and c3 is c3 minus c1. Okay. So after doing this operation, you would realize that we will be getting something like this. So you have taken this and subtract. So let's not disturb the first column because it is not transformed. This becomes 0. This becomes 0. This becomes negative a, b plus b, c plus c, a. And this becomes 0 again. Here I will get, just in case I missed out anything, that's correct. Yeah, yeah, yeah, that's fine. Yeah. So here we will get again a 0 and this will become minus of a, b plus b, c plus c, a. Okay. Now from the first column, from the second and the third column, you can again pull out a a, b plus b, c plus c, a. So a, b plus b, c plus c, a whole cube will come out. Okay. And you get 1 a, b plus b, c, a, c plus b, c, 0 minus 1, 0, 0, 0, minus 1. Okay. Right. Now if you expand with respect to any one of the column number 2 or column number 3, let's say I expand with column number 3. So plus minus plus. So I'll get minus, minus of 1. Why am I getting a negative sign? Oh, sorry. Yeah. Minus of 1, but with again a minus, it will become plus. So it will become a, b plus b, c plus c, a whole cube. Because this is also minus only. Right. So minus of 1 minus 0 with a minus 1 sign will become plus 1. Okay. So this becomes your RHS and hence proved. Right. So these are the type of questions which can really kill a lot of your time. As you can see, we almost spent 18 minutes solving this problem. Right. Including the time I gave it to you. So be very, very careful of the approach and be watchful on what you want to prove. You cannot start doing any operation as you feel like. And always keep this multiplication of a row with ABC and taking then again ABC column, common in the columns. So this is also a very important kind of a property you can apply. Moving to the next question. Done. This is a simple problem. I guess. Do let me know once you're done. Okay. It's done. So under your Sanjana others. So for this kind of problem, it is best solved through substitutions. Right. Now the look and feel of these expressions under root of 1 minus x square under root of 1 minus y square gives you the feeling that we can actually substitute x as let's say sign alpha. Okay. And why are they saying sign of beta? Okay. So according to the problem statement, you can say cost of alpha plus cost of beta is equal to a sign alpha minus sign beta. Okay. Now we know the transformation formula cost alpha plus cost beta is to cost alpha plus beta by 2 into cost alpha minus beta by 2. And this will become to a cost alpha plus beta by 2 sign alpha minus beta by 2. Okay. So 2 can 2 can be removed. This can also be removed. Which means a cot of alpha minus beta by 2 is equal to a, which clearly implies alpha minus beta is 2 cot inverse a. Now, since a is a constant, a is a constant. This is also a constant. Right. But alpha is actually sign inverse of x and beta is actually sign inverse of y. Okay. So this is equal to a constant. Now differentiate both sides with respect to x. Differentiate both sides with respect to x. So that will give you under root 1 by under root 1 minus x square by under root 1 minus y square dy by dx is equal to 0. Which clearly implies dy by dx is nothing but under root of 1 minus y square by under root 1 minus x square is equal to your RHS. Right. Hence proved. So please keep in mind these kind of substitutions. Sometimes they complicate the problem by making it as under root 1 minus x to the power 6 plus 1 minus y to the power 6 is equal to 8 times x cube minus y cube. Right. And then here also they make this as to the power 6 and 6 and some terms will extra come over here. So in the same line you have to approach this problem as well by substituting x cube as sin alpha and y cube as sin beta. Okay. So be aware of the different versions of the same type. Okay. So we'll move on to the next question now. If y is equal to x plus under root x square minus 1 to the power of m then show that this differential equation is valid. Do let me know once done. Done. What about others? Done. Okay. So we'll start with the expression for dy by dx. So we'll be applying your chain rule on this. So m times this to the power of m minus 1 into derivative of this term itself which is actually 2x by 2 under root of x square minus 1. So this term gets cancelled off and if you try to take the LCM it becomes x plus under root x square minus 1 by under root of x square minus 1. So this becomes m times x plus under root x square minus 1 to the power of m by under root of x square minus 1. This is your dy by dx. So this expression is nothing but y itself. This expression is back to y. So you can write as my by under root of x square minus 1. Cross multiply. So take it on the left hand side. This is equal to this. Square both the sides. Square both the sides. Okay. When you square both the sides you get x square minus 1 dy by dx the whole square is equal to m square y square. Again differentiate with respect to x both the sides. I think there's a slight. Okay. This has to be minus I guess. So x square minus 1. This is 2 dy by dx into d2y by dx square. And you have 2x dy by dx the whole square. And here you will have m square 2y dy by dx. Now drop the factor of 2 dy by dx from everywhere. So 2 dy by dx gone, 2 dy by dx gone and 2 dy by dx gone. So you will get x square minus 1 d2y by dx square plus x dy by dx minus m square y is equal to 0. So this differential equation is valid. Let's move on to the next question. In all points of discontinuity of the function mod of x square. In fact it's not mod it is the greatest in the function. This has to be written in a proper way. Do let me know once you're done with the first part of the OR. Since the function definition is starting at 1 itself. It would not be a good idea to include 1 as your critical point. So you can do it like this. You can redefine the function as, you know, function which is going to be 1 for x lying between 1 to root 2. And your function will be defined as 2 when x lies between root 2 to root 3. And 3 when it lies between root 3 to 2. Okay, so this is how you can redefine the function. Now if you want to check the continuity of the function. You need to check it at the critical points. So these are the critical points. So at x equal to root 2. If you see the left hand limit of the function as x tends to root 2 minus is actually going to be your 1. And the right hand limit as x tends to root 2 plus is going to be 2 which is not equal. So these two are not equal which implies that the function is discontinuous at x equal to root 2. Similarly for root 3 if you want to check its continuity. The left hand limit of the function at root 3 is going to be 2 itself. Okay, and this doesn't match which is actually equal to 2. Which doesn't match with the value of the right hand limit at root 3 where the function value is 3. Okay, so hence f of x, therefore f of x is discontinuous at x equal to root 3. So points of discontinuity is x equal to root 2 and root 3. Moving on to the next part of the question. Differentiate sin inverse 2x under root 1 minus x square with respect to cos inverse 1 minus x square by 1 plus x square. Just let me know once you're done. Okay, what about Vaishnavi, Sanjana? So again in case of let's say this expression is y. Okay, and this expression is let's say z. We actually need to find dy by dz, right? But y itself, we can first simplify this. But again do not use any readymade formula. We all know that this is the formula of 2 sin inverse of x. But do not use it directly. Make substitutions. So let x is sin of theta, right? So this implies y is sin inverse 2 sin theta into cos theta. Which is nothing but sin inverse of sin 2 theta. Which is nothing but 2 theta. And 2 theta will be 2 sin inverse of x. Okay. For z you can directly use the formula. z is actually 2 tan inverse of x. Okay. Now dy by dz will be nothing but dy by dx divided by dz by dx. So dy by dx is nothing but derivative of this with respect to x. So it's 2 by under root of 1 minus x square. Derivative of 2 tan inverse x is 2 by 1 plus of x square. So 2 and 2 gets cancelled. So your final answer will be 1 plus x square by under root of 1 minus x square. Okay. Sometimes they may also ask you a question like differentiate this with respect to this at x equal to let's say 0. Right. Something like this they can ask you. So that means after differentiating you have to put the value of x as 0. Next. Integrate 1 by cos x minus a cos x minus b. Okay. How about Sondarya, Sanjana? Done. So for the first type this is something which we have already done in our past as well. We need to multiply and divide with sin of b minus a. Okay. So whenever there are like terms in the denominator that is sin sin or cos cos. We have to do this same trick. And then we can write the numerator part as sin of x minus a minus x minus b. So it becomes 1 by sin b minus a. This will become sin of x minus a cos of x minus b minus cos of x minus a sin of x minus b. Divided by cos x minus a cos x minus b. Again cos x minus a cos x minus b. So this and this will get cancelled. This and this will get cancelled. So 1 by sin of b minus a integral this will become tan x minus a minus tan of x minus b. So our answer will now become 1 by sin b minus a. ln mod seek x minus a minus ln mod seek x minus b. Okay. Which you can combine and write it as 1 by sin b minus a ln. Seek x minus a by seek x minus b is as good as saying cos x minus b by cos x minus a. Please try out on the second one. That's also a very easy question. Do let me know once you're done. Done. Okay. Great. So here it's obvious that you have to apply integration by parts treating this as your first function, treating this as your second function. So applying integration by parts, which is nothing but integral of u v is u integral of v minus integral of du by dx into integral of v whole with respect to x. So this will become log of x square into x square by 2 minus derivative of log of x square will be 2 log of x into 1 by x and 1 by x multiplies with this will become x by 2. Okay. Now again here we will apply integration by parts treating this as our first function, treating this as our second function. So it becomes x square by 2 log of x whole square minus. Okay. Now this will become u times x square by 2 minus 1 by x into x square by 2 dx. So this and this gets cancelled. So it becomes x square by 2 log of x whole square minus x square by 2 log of x plus x this will become x to the power 2 by 4 plus c, x to the power 2 by 4 plus c. So this will become your answer for the second part. Next integration of x by x cube minus 1. Do let me know once you're done. Done. Okay. So here it's very obvious that you have to apply partial fractions. So this term x by x cube minus 1, you can write it as x by x minus 1 times x square plus x plus 1. Okay. And therefore we can split this as partial fractions in this fashion. Okay. Let us first figure out the value of a, b and c. So when you combine the term over here, you get this as x. Let us put the value of x as 1 first. Putting the value of x as 1, I get 1 is equal to 3a. So a is equal to one-third. a is equal to one-third. Okay. Put the value of x as 0. That means you're comparing the constant terms. Put the value of x as 0. You will get 0 is equal to a and minus of c. Okay. So c is equal to a. That means c is also one-third. Now let's compare the coefficient of x square. So coefficient of x square on the left-hand side is 0. And on the right-hand side it's a plus b. So b is equal to minus of a, which is minus one-third. So this entire expression, this entire integral, I can write it as one-third x minus 1 plus one-third. Okay. In fact, I can say one-third 1 minus x by x square plus x plus 1. Okay. Hold the x. Now this is a simple integration. This is one-third ln mod x minus 1. For this one, I need to use the fact that the numerator can be expressed as a times the derivative of the denominator. Okay. Plus b. So comparing the coefficient, a becomes negative of half. Correct. And one is equal to a plus b. a plus b. So b becomes 3 by 2. So just this integral, if I have to do, I would write it as integral of minus half 2x plus 1 plus 3 by 2, divided by x square plus x plus 1, 1 by x square plus x plus 1. Okay. So this will become half ln x square plus x plus 1. And here I have to complete this square. So if you complete this square, here it will become x plus half the whole square. Guys, can you see the screen now? Girls, so once you've done this, this part answer will become 3 by 2 into 1 by a tan inverse of x by a. Okay. So collating the final answer, your final answer will now become, I'll just erase this part. Your final answer will become 1 third ln x minus 1. And since you've got half and 1 third over here, you'll end up getting, you'll end up getting minus 1 sixth ln x square plus x plus 1. Okay. And you have got root 3 over here and 1 by 3 over here. So that will give you plus 1 by root 3 tan inverse 2x plus 1 by root 3 plus c. So this will become your final answer for this question. Please check your results. Great. So now we'll move on to the next question. Using properties of definite integral, evaluate integral of x by 4 minus cos square x from 0 to pi. Let me know once you're done with this and also type in your response on the chat box. Sure, sure. Take the time. Pi square by 3. Okay. Anybody else who's getting the same answers? Sondarya, Sanjana. Okay. So we'll first start with the king's property. Okay. It says that integral 0 to a f of x can be written as integral 0 to a f of a minus x. Okay. So let's say I call this as i. So i will be equal to 0 to pi, pi minus x dx by 4 minus cos square x. Okay. So add the 2 i's. So it will be pi dx. So you can write pi by 2, 0 to pi. You can write this as since let's say this is your f of x. Since f of x is same as f of 2 a minus x. That means f of x is same as f of pi minus x. Nothing is going to change. You can write i as, sorry, you can write i as pi by 2 into 2, 0 to pi by 2 dx by 4 minus cos square x. So this gets cancelled. Now divide the numerator and denominator by cos square. So this will become c square on top. And here it becomes 4 secant square minus 1. Now in the denominator, change that secant square to tan 1 plus tan square. So this will become 3 plus 4 tan square x. Now take tan x as t, which implies secant square x dx is going to be your dt. So i will be pi times 0 to infinity dt by 3 plus 4 t square. Okay. Take 4 common. So pi by 4, 0 to infinity dt by t square by 3 by 4 will be root 3 by 2 the whole square, which is pi by 4, 2 by root 3 tan inverse of 2t plus root 3 by root 3. Okay. Now when you put your t as infinity, it becomes pi by 2. And when you put it as 0, it becomes 0. So the answer will be pi square by 4 root 3. So i will be pi square by 4 root 3. Vaishnavi, that's not correct. Something went wrong. Please check your calculations. Is that fine? Everything fine with the solution? No questions, no concerns? Now we'll move on to the next one. Okay. Now this appears to be a very easy problem. I don't know how it figured it in between these problems. This is super simple. So let the vector be xi plus yj plus zk. So dot product with the first one means x minus 3z is equal to 0. Okay. Dot product with the second one means x minus 2y is equal to 0. And sorry, is equal to 5, not 0. And the dot product with the third one is 8. That means x plus y plus 4z is equal to 8. This is also my bad. Okay. So subtracting, you get z is equal to 5. That's for sure. If z is 5, x is going to be 15. And if this is 15, this is y. This is going to be 20. So y is going to be 8 minus 35, which is minus of 27. So your required vector will be 15i minus 27j plus 5k. Okay. That's an easy problem. So let's not waste too much time on this. Yeah. 3D problem. Let's take a 3D problem. Find the equation of a plane passing through the point 1 to 1. And perpendicular to the line joining the points, these two. Also find the perpendicular distance of the plane from the origin. Okay. What about others? So there's a plane which contains 1 to 1. And it's perpendicular to the line joining the two points. So this is a line joining the two points. You have to find the equation of this plane. Guys, can you see the screen? Can you see the screen? Yeah. So basically the normal vector direction can be known by the 3 minus 4j. And 5 minus 2k. Okay. That's going to be i minus j plus 3k. This will be a normal vector. And we all know that the equation of a plane is r minus a dot n is equal to 0. So r dot n is equal to a dot n. So r dot i minus j plus 3k.  So a vector is the position vector of this point i plus 2j plus k. So the dot product would be nothing but 1 minus 2, 1 minus 2 plus 3. Okay. So that is going to give you 2. Hence the final answer, if you want to write it in the Cartesian form, you can write down the equation to be x minus y plus 3z is equal to 2. This is the equation of a plane in the Cartesian form. Now the next part of the equation is also find the perpendicular distance of the plane from the origin. Now we all know if you want to find the distance of the origin, we have to take mod d by under root of a square plus b square plus c square. Okay. This is the distance from the origin. This is the perpendicular distance from the origin. So that is going to be 2 by under root of 1 plus 1 plus 9, which is 2 by root 11. Okay. Now let us do the all part of the equation. Find the equation of the perpendicular drawn from the point p to the line. Okay. Okay. Fine. No issues. Others, are you getting the same stuff? So this is our line and from a point 2, 4 minus 1, you are drawing a perpendicular on this particular line. So we have to find the equation of this line. Okay. So first of all, we will consider this point to be a point m. Okay. Whose coordinates can be obtained by using the parametric representation for this line? Let us say, call it as lambda.  So this point is lambda minus 5, 4 lambda minus 3, minus 9 lambda plus 6. Now the direction of this line is going to be the difference of the coordinates.  Okay. This should be perpendicular to the given line. So 1 into lambda minus 7, 4 into 4 lambda minus 7 and minus 9 into minus 9 lambda plus 7 will be equal to 0. So this will be 81, 81 plus 16 plus 1, 81 plus 16 plus 1 lambda. Okay. So we will get minus 7, minus 28, minus 63 equal to 0. So that will become 98 lambda and here also I will get 98 itself. So lambda is going to be 1. So if lambda is 1, the point is going to be minus 6, minus 3, minus 2. I am sorry. The point is going to be minus 4 comma 1 comma minus 3. Okay. So this is going to be your point. So once you know a point, we can directly find also the direction from here. So direction of the line will be, direction ratio of the line will be minus 6, minus 3 and minus 2. Is that fine? So the equation of the desired line will be, I am just going to erase this. So the equation of the desired line will be x minus 2 by minus 6, y minus 4 by minus 3 and z plus 1 by minus of 2. Okay. In the vector form, it will become r is equal to 2y plus 4j minus k plus some lambda times 6i minus 3j minus 2k. Is that fine? Sondarya, just check why your answer is not matching with mine. 1, i plus 2j plus k is not proportional to what I have got which is 6 is to 3 is to 2. But 1 is to 2 is to 1. Okay. Just check out your working. Meanwhile, we will move on to the next problem. A bias dice is twice as likely to show an even number as an odd number. The dice is rolled three times. If the occurrence of an even number is considered a success, then write the probability distribution of successes. Find the mean number of successes. So let me know once you are done. At least you can type in the mean number of successes. How? How much should we? Alright. So in this case, we know that your p is going to be 2 by 3 and your q is going to be 1 third. Okay. So it's actually mean or the expected value can directly write over here itself as np. Okay. And it's known that there are the dice are rolled three times. So it's going to be 3 into 2 by 3. That's going to be 2 itself. Okay. Now regarding the probability distribution, you can actually expand this. Okay. And you can just make a column like this. So probability could be 0, 1, 2 or 3. So for 0, you just have the first term, which is 1 third cube. Second term will be 3c1, 1 third square into 2 third and 3c2, 1 third into 2 third square and finally 2 third cube. So these values will be coming over here. So 1 by 27 is this value and this will be 3 into 6, 6 by 27. This will be 12 by 27 and this will be 8 by 27. This is going to be the probability distribution and the mean number of successes will be nothing but 2. Using matrices, solve the following system of equations. 1 by x minus 1 by y plus 1 by z is 4. 2 by x plus 1 by y minus 3 by z equal to 0. 1 by x plus 1 by y plus 1 by z is equal to 2. Okay. The problem becomes very simple once you start taking your 1 by x as capital X, 1 by y as capital Y and 1 by z as capital Z. Okay. So it's actually x minus y plus z is equal to 4. 2x plus y minus 3z is equal to 0. Yeah. So first we can convert it to a matrix form. So 1 minus 1, 1, 2, 1 minus 3, 1, 1, 1, x, y, z, 4, 0, 2. Okay. So this is of the form ax is equal to b. So let's find out the inverse of a. First of all determinant of a. Let's find it out which is going to be 1, 4 plus 1, 5 plus 1, again a 5. So again, this will become 1. That's going to be 10. Correct. Let's find out the adjoint matrix. So I will use my method here. So 1 minus 1, 1, 2, 1 minus 3, 1, 1, 1. Again, copy the first row, second row, first column, second column. Okay. So let's cross multiply this 2, this 2, this 2, this 2, this 2, this 2, this 2, this 2, this 2, this 2, and this 2. So that will become 1 minus 1, which is 4, minus 3, minus 3, minus 2 is minus 5, then it will become 1. 1 plus 1 is 2, then this will be 0, then this will be minus of 2, then this will be 3 minus 1, which is 2, then this will be 5, and this will be 3. Okay. So this into 4, 0, 2 multiplied with 1 by 10. Okay. So I can clearly see that X is going to be 16 plus 4, 20, 20 by 10, which is 2. Y is going to be minus 20 plus 10, which is minus 10, minus 1, and Z is going to be 4 plus 6, 10, that is 1. So X is going to be half, Y is going to be minus 1, Z is going to be 1 again. Yeah, so almost everybody is correct. Again, the call is yours for finding out the inverse of A, you may use elementary transformation or you may use adjoint, but adjoint is always a faster method. Show that the volume of the greatest cylinder that can be inscribed in a cone of height H and semi-vertical angle alpha is 4 by 27 pi H cubed tan square alpha. Done. Okay. So let's discuss the first one. So we have a cylinder inscribed within a cone. So let's say this is a cone and there is a cylinder which is inscribed within a cone like this. Okay. The height of this cone is small h and the semi-vertical angle here is alpha. This is alpha. Okay. Right. Now, see, let's say the height of the cylinder itself is capital H to the Y, R square into capital H where R is the radius of the cylinder. Correct. Now, this part, this part is H minus H. Okay. So what will be the radius? Right. So radius by H minus H is equal to tan of alpha. So radius is going to be H minus H tan alpha. Remember, alpha is fixed. Alpha is a constant. Okay. Okay. And capital H is a variable. Small h is also a constant, but capital H is a variable. Okay. Now, the expression for the volume will be pi R square, which is tan square alpha, which is H minus H whole square into H. Now, if you want it to be maximum, the derivative of the volume with respect to capital H should be 0, which means the derivative of this expression, which is H minus H the whole square plus 2H H minus H with a negative sign. So let me make a negative over here. So this will be negative and this would be equal to 0. So from here we get H minus H square is 2H H minus H since H small h cannot be equal to capital H. That means you cannot have a cylinder with the same height as that of the cone. So here H is equal to 2H plus H. That means capital H is H by 3, small h by 3. And R will be nothing but 2H by 3 tan of alpha. Right. Now, always do the double derivative test. D to V by D H square. Okay. So D to V by D H square will be pi tan square alpha. Okay. So this will be 2 times H minus H with a negative sign and this will be minus 2H minus H. And again you will have, this will be positive I guess. Okay. And yeah, minus 2 times H minus H and then we will have minus 2H into minus 1. Okay. So if you look at the entire expression, you would get the answer as negative of 2H, pi tan square negative of 2H, pi tan square negative of 2H which is actually a negative expression. That means the volume will be maximum, the volume of the cylinder will be maximum. Now having found out the radius and the height capital H, the volume can be found out by using pi R square.  So that will be 4 by 27 pi H cube tan square alpha. So hence proved. Okay. Now let's talk about the next part of the question. Show that the normal at any point on the curve is a constant distance from the origin. Let me know once done and also let me know what is the shortest distance, what is the distance from the origin that you are getting. Done. Okay. The distance is A. So let me quickly discuss this also. We have to find the equation of the normal to the curve. Okay. So for normal to the curve, we need the slope of the normal which is nothing but minus dx by dy. So which is minus dx by d theta divided by dy by d theta. So minus dx by d theta will be negative of negative A sin theta. Okay.  So this two will get cancelled. This two will get cancelled and you will get expression as minus of cot theta. So the equation of the given normal would be y minus y1 is equal to slope times x minus x1. So let's write this cot theta as cos theta by sin theta itself. Let's cross multiply.  This and this gets cancelled. So ultimately you get the equation as y sin theta plus x cos theta is equal to A. Okay. And we know that this line is basically nothing but at a constant distance of this is nothing but the normal form of a line right which is always at a distance of A from the origin. Okay. But you can also use the distance of a origin from this line to get the value and this constant distance is going to be mod of A. And the constant distance is going to be mod of A. Next, find the area of the region bounded by this particular set of points which satisfies these inequalities. When is your first board exams? And what which subject you have? I think fifth is physics sir. But I think when is your other subjects like English or electives? Okay. Second march is English. Once done, please type in your answer in the chat box. Is it done? Okay. 43 by 6 units. How about others? So let's discuss this. First of all, let us find out this point of p of intersection. So we'll simultaneously solve y is equal to x square and y is equal to x plus 2. So if you just compare their y's. Okay. It's obvious that x has to be 2 in this case. So this point is x equal to 2. Okay. So x equal to 3 has to be somewhere over here. So this is x equal to 3. Now the inequality zone suggests that you have to be y has to be lesser than x square. So you have to be below this part. And y also has to be lesser than x plus 2. So basically the region that they're looking out for is this region. Okay. But in this region also when you're trying to find out the area, you have to follow a different type of vertical strip in this zone. And a different type of vertical strip in this zone. So from 0 to 2, you will be integrating the area below x square. And from 2 to 3, you will be integrating the area within x plus 2. Correct. So your answer will be x cube by 3, 2 to 0. And again, x square by 2 plus 2x from 3 to 2. So this is going to be 8 by 3. This is going to be 9 by 2 plus 9 by 2 plus 6 minus 2 plus 2. That's going to be 8 by 3 plus 9 by 2 plus 2. So 6, this will be 16, this will be 27, this will be 12. So just let me, this will be 4, I guess. Small mistake here. This will be 4. Yeah. So 6 and 6 will get cancelled. So this term will not be appearing. Yeah. That's correct. Yeah. So now your answer is going to be 43 by 6 square units. So please mention square units in your answer. So absolutely correct. So all of you have done it. Got the right answer for this. So let's move on to the next one. Find the particular solution for the differential equation. Given that y is pi when x is 3, just a minor correction over here. Make this as plus. Okay. How about others? Okay. So this is clearly a case of homogeneous differential equation, right? This is clearly a case of a homogeneous differential equation. And since you see terms like y by x appearing, you can always put y is equal to vx, which means dy by dx can be written as v plus x dv by dx. So this will become x v plus x dv by dx minus vx into vx into sin v is equal to vx plus x dv by dx x cos v. Okay. You can drop the factor of x from all the places. Okay. So you may subtly drop x from every one, every place. This x will go off. This x will go off. This x will go off. This x will go off. This x will go off. This x will go off. Okay. And if you expand it over here, you will get vx dv by dx into sin v. And here you will get 2v plus x dv by dx into cos v.  And this will be equal to 2v cos v. So dx by x will be, dx by x will be v sin v minus cos v. In fact, you can take the two on the other side by v sin v. Sorry, cos v cos v. I hope there is no sin mistake done anywhere. No. That's correct.  That means it is as we were saying, negative dt by t. Okay. Let me just clear some space on top. So this will become 2 ln x is equal to minus ln t plus ln c. That means ln x square into t is equal to ln c. So that means x square into t. t is nothing but v cos v is equal to c.  So this will be clubbed as xy. This will be clubbed as xy. Now, what is given to us? Boundary condition is y is pi when x is 3. So 3 pi cos of pi by 3 is half. So c is pi by 3 pi by 2. So your final answer will be xy cos y by x is equal to 3 pi by 2. This will become your answer. Yeah, I think it's the same thing as what Sondaria also got. Okay. Find the equation of a plane passing through the point 111 and containing the line. Also show that the plane contains this line as well. Once you're done, let me know. Okay. So let's discuss this also. Containing the line this is containing the line means you have been given two information that you know a vector on this plane. That is 3i minus j plus 5k. Okay. And you know two points 111 and the other is minus 315. So you can also get this vector. So two vectors can be known on the plane. So if two vectors are known, let me call them as a and b. I can always get the direction of the normal as well. Okay. So a vector will be minus 4i plus 0j plus 4k. Okay. b vector is already known to you 3i minus j plus 5k. So n will be in the direction of their cross product. So let's write their cross product. Okay. So this will give you 4 minus j minus 20 minus 12 is minus 32 and k is going to be 4. So you can write it as i plus 8j plus k also. Okay. So your equation of the line will be r dot n. r dot n is equal to a dot n. And a dot n can be written as n. So it's x plus a to y plus z is equal to n. Absolutely correct, Sondarya. Next is show that this plane also contains this line. Now in order to show that the plane contains the line, you also have to show that the line is perpendicular to n. That means 3 into 1 minus 1 into 8 plus 5 into 1 should be 0. That's true. And not only that, this point must satisfy it. So minus 1 plus 16 plus 5 is it equal to 10? Yes, it is equal to 10. Hence this plane contains this line. Okay. So please do not just show that the direction of the line is perpendicular to the normal. You also have to show that the point also satisfies the plane. This is an LPP question. You can just skip it as take it as a homework. Let's do this probability question. Hope you have understood the question.   B contains two white and two black. So two walls are transformed from this back to this back. And then a ball is drawn from B. And it is found out to be black. What is the probability that one white and one black was transferred? 3 by 5 is absolutely correct. Yeah, that's absolutely correct. Again here, approach the problem by defining the events.   And E3 be the event that one white and one black were transferred from A to B. So what do we have to find out? We have to find out probability of E3 given B has occurred, right? So according to the conditional probability, this formula is going to be P E3 intersection B by PB. Which is nothing but P E3 into P B by E3 by PB. Okay. Now, first of all, PB. How many ways can PB happen? PB can happen with P E1 into P B by E1 plus P E2 into P B by E2 plus P E3 into P B by E3. Right?   Okay. And then getting a black ball given that two white has been transferred. So there will be two black and four white. So its probability will be 2 by 6. Okay.  And then getting a black ball will be 4 by 6. And transferring one white and one black will be 4C1, 3C1 by 7C2.  And then getting a black ball will be 3 by 6. Okay. So out of this, the third expression is in the numerator. As you can see in the formula, third expression is in the numerator. Rest everything is in the denominator. So your answer is going to be, I'm just going to erase this part. So your answer is going to be 4C1, 3C1 into 3 by 6 divided by 7C2 divided by the entire thing. 4C2 by 7C2 into 2 by 6. 3C2 by 7C2 into 4 by 6. 4C1 into 3C1 by 7C2 into 3 by 6. So 6 and 7C2 can be cancelled out. Okay. So if I'm not wrong, the numerator will become 36. And denominator will become 6 into 2, 12. 12 and this is going to be 3 into 4 again, 12. And this is again going to be 36. So it's 36 by 60. That is going to be 3 by 5. So answer is going to be 3 by 5 in this question. Okay. So guys, we're going to stop over here. And there are a few more questions. I think one more question after this, an LPP question. You can always try that as homework. So over and out from Centrum Academy. Thank you and have a good day and keep practicing. Keep writing mock tests. Okay. So the next one week is going to be very, very critical. Make your hand, eyes, everything. Tune to your board exams. Okay. So think as if you have to write board exams day in and day out. So accordingly, you should start practicing. Every day you should be writing at least one or two mock tests. Thank you so much. Bye-bye. Take care.


How has psychology changed your life? If you're a longtime fan of Psych2Go, you know that psychology can improve your relationships, heal mental wounds, and help you cope with difficult circumstances. But did you know that psychology can even save your life? There are lots of things you might not know about how the human mind can put you in danger or help you escape it. Here are some psychology facts that can save your life. Someone else will get it. Picture this. You're walking across a parking lot when you bump into someone. You apologize, but the other person won't have it.  Talk about an overreaction. Luckily, it's a crowded area, so someone will help before the conflict escalates, right? Unfortunately, there's something called the bystander effect, which explains that the more bystanders are present in a crisis, the less likely they are to intervene. They assume someone else will help, so they don't have to. To prove this, a 2019 study tracked hundreds of bystanders in CCTV footage of violent incidents across Copenhagen. They found that additional bystanders reduced the chances of intervention, especially if they were strangers. They're not heartless. It's just tempting to think, uh, someone else will do it, when in a large crowd. Researchers suggest that in emergencies, you can trigger intervention by pointing at individual bystanders and delegating specific actions, like calling the police to make it their individual responsibility. This fact may help save someone's life, including yours. The calls coming from inside the house. If I asked you to imagine a dangerous person, who would you envision? A shouted person squulking in the shadows at night, or one of your loved ones? You decide who you trust every day, but according to FBI profiler Mary Ellen O'Toole, our intuitions about who's dangerous aren't always necessarily true. She explains that we tend to be wary of strangers, and those who act oddly, while giving a free pass to our acquaintances and those who seem normal. She says it's actually more likely to be harmed by those we know. O'Toole also points out that almost every time the FBI uncovered a violent criminal or serial killer, the dangerous individual was friendly and outgoing, lived a seemingly normal suburban lifestyle, had a family, and had a respectable reputation in their community. Nobody suspected a thing. Look at Jeffrey Dahmer. He's the normal guy who kept to himself, right? To help us identify dangerous individuals, O'Toole lays out some better warning signs to look out for. Impulsive behaviors without regard for consequences, anger that's excessive for the situation, narcissism, lack of empathy, and injustice collecting where they hold grudges for years. A single trait or a single action doesn't automatically mean someone is dangerous, but if they show a pattern of these behaviors, you might want to watch out. Required reset. If you were too drunk to legally drive, would you still get behind the wheel, make a major decision, or send a crucial email? Hopefully you would avoid such high risks, but if you don't have a solid sleep schedule, you're actually doing something just as risky without knowing it. If you don't get enough sleep every night, your body gets overwhelmed by stress hormones and your brain's functionality plummets. A study published in Nature tested the alertness of those who were sleep deprived and compared to those who were intoxicated while performing basic hand-eye coordination tasks. After no sleep for 24 hours, their alertness nosedived to the same level as those who had a blood alcohol concentration of 0.10%. 0.08 is the legal limit. In other words, pulling an all-nighter slows your brain as much as being too drunk to drive. According to the National Sleep Foundation, teenagers need 8 to 10 hours of sleep per night, and adults need 7 to 9 hours. Sleep has a huge effect on memory, cognition, concentration, mood, and accident rates. The next time you're tempted to stay up, save yourself from calamity the next day by using the military sleep method to get to sleep quickly and refresh your body and mind. Firstly, get into a comfortable position and exhale slowly while releasing the tension in your muscles. Relax your shoulders to loosen your arms and hands. Continue to breathe in and out and flex your toes.  If any thoughts come to mind, repeat, don't think, until they go away.   If you've had a panic attack, you already know, but if you haven't, let's set the scene. Your heart is pounding, you're sweating everywhere, you can't breathe, but are breathing too fast at the same time and you can't control your thoughts. Panic attacks aren't pretty, and they can often arise during stressful situations when thinking clearly is vital. If a panic attack has already started, you may not be able to contact your therapist or remember a coping technique, so how can you help to end the attack? You might be surprised at the answer. In a study by NYU School of Medicine in Boston University, participants with panic disorder were assigned to either suppress their emotions or accept them. Ironically, using the coping strategies you've been taught while in the panic attack actually made it worse. These techniques draw attention to your inner anxiety, thus making the attack more intense. Using acceptance techniques resulted in significantly less anxiety and avoidance. Instead of treating a panic attack as a problem to control, you can simply recognize that it's happening. Acknowledge it in your mind or allow it. Accept that this is temporary and that these feelings will pass. If this works for you, let us know in the comments below. There you have it, five psychology facts that will save your life. Do you know any other psychological facts that could save your life? Have you ever used some of these facts? Let us know in the comments below and don't forget to like and share this if you think it'll help someone else.  Get your very own sigh. The lovable plushie is here to brighten your days. It embodies the spirit of Psych2Go and it serves as a reminder to prioritize your mental well-being. Its green leaf symbolizes growth, renewal, and the importance of self-care. Whether it's for yourself or as a thoughtful gift for a loved one, sigh is ready to be your snugly friend through all of life's ups and downs. Buy your sigh plushie today. Link is listed in the description box.


Like you're giving birth to a football. Okay. I'm Dennis and I'm a touchdown dance instructor. Okay. Let's see what you got come on a Spike what is this the 80s? This is the professional football league. It's the national football league leave No talking back. I don't stand for that man. Dennis could be pretty harsh, but we're learning from the best blast off rocket ship crossing guard Paperboy You're in line at the grocery store the guy for you doesn't use the divider. Hey, man.  I just don't play football All right, let's practice giving birth again guys


Live, from Las Vegas, it's theCUBE. Covering IBM Think 2018, brought to you by IBM. Hi everybody, this is Dave Vellante. We're here at IBM Think. This is the third day of IBM Think. IBM's consolidated a number of its conferences. It's a one main tent, AI, blockchain, quantum computing, incumbent disruption. Just really an amazing event, 30 to 40,000 people. I think there are too many people to count. Chris Penn is here. New company, Chris, you've just formed BrainTrust Insights. Welcome, welcome back to theCUBE. Thank you, good to be back. Great to see you. So tell me about BrainTrust Insights, congratulations. You got a new company after that. Thank you, yeah, I co-founded it. We are a data analytics company and the premise is simple. We want to help companies make more money with their data. They're sitting on tons of it. Like the latest IBM study was something like 90% of the corporate data goes unused. So it's like having an oil field and not digging a single well. So who are your like perfect clients? Our perfect clients are people who have data and know they have data and are not using it but know that there's more to be made. So our focus is on marketing to begin with, like marketing analytics, marketing data and then eventually to retail, healthcare and customer experience. So you and I do a lot of these IBM events. What are your thoughts on what you've seen so far? Are you huge crowds, obviously? Sometimes too big. Yep. Few logistic issues, but generally speaking, what's your sense? I have enjoyed the show. It has been fun to see all of the new stuff, seeing the quantum computer in the hallway, which I still think looks like a bird feeder. But what's got me most excited is a lot of the technology, so particularly around AI, are getting simpler to use, getting easy to use and they're getting more accessible to people who are not hardcore coders. Yeah, you're seeing AI infused and machine learning in virtually every application. Every company's talking about it. I want to come back to that. But Chris, when you read the mainstream media, you listen to the news. You hear people like Elon Musk, Stephen Hawking before he died, making dire predictions about machine intelligence and it taking over the world. But you're day to day with customers that have data problems. How are they using AI and how are they applying it practically, notwithstanding that some day machines are going to take over the world and we're all going to be gone. Yeah, no. The customers don't use the AI. We do on their behalf because frankly, most customers don't care how the sausage is made. They just want the end product. So customers really care about three things.  Are you going to save me time? Or are you going to help me prove my value to the organization, aka help me not get fired? And artificial intelligence and machine learning do that through really two ways. My friend Tripp Brayden says this, which is acceleration and accuracy. Accuracy means we can use the customer's data and get better answers out of it than they have been getting. So they've been looking at, I don't know, number of retweets on Twitter. We're like, yeah, there's more data that you have. Let's get you a more accurate predictor of what causes business impacts. And then the other side for the machine learning and AI side is acceleration. Let's get you answers faster because right now, if you look at how somebody just traditional market research for what customers say about you, it takes a quarter. It can take two quarters.  Okay, so talk more about some of the practical applications that you're seeing for AI. Brayden, one of the easiest, simplest and most immediately applicable ones is predictive analytics. If we know when people are going to search for the cube or for business podcasts in general, then we can tell you down to the week level, hey Dave, it is time for you to ramp up your spending on May 17th, the week of May 17th.  On the week of May 24th, you need to ramp up your ad spend by 50% and run like three or four Instagram stories that week. Doing stuff like that tells you, okay, I can take these predictions and build strategy around them, build execution around them. And it's not cognitive overload. You're not saying like, oh my God, what algorithm is this? It's like, just no, just do this thing at these times. Yeah, simple stuff, right? So when you were talking about that, I was thinking about when we send out an email to our community. You know, we have a very large community and they want to know if we're going to have a crowd chat or some event, where the cube's going to be. The system will tell us, send this email out at this time on this date. Question mark, here's why. And they have analytics that tell us how to do that and they predict what's going to get us the best results. They can tell us other things to do to get better results, better open rates, better click through rates, et cetera. That's the kind of thing that you're talking about. Exactly, however, that system is probably predicting off of that system's data. It's not necessarily predicting off of public data. One of the important things that I thought was very insightful from IBM at the show was the difference between public and private cloud. Private is your data, you predict on it, but public is the big stuff that is a better overall indicator. When you're looking to do predictions about when to send emails, because you want to know when is somebody going to read my email. And we did a prediction this past October for the first quarter. The week of January 18th was the week to send email. So I re-ran an email campaign that ran the previous year, exact same campaign. 40% lift year over year, because I got the week right this year. Last year was two weeks late. Now, I got to ask you. So there's a black box problem with AI, right? Machines can tell me that that's a cat. But even a human, you can't really explain how you know that it's a cat. It's just, you just know. Do we need to know how the machine came up with the answer, or do people just going to accept the answer? We need to for compliance reasons, if nothing else.  But even HR and, you know, equal opportunity acts in here in America require you to be able to explain, hey, we are, here's how we're making decisions. Now the good news is for a lot of AI technology, interpretability of the model is getting much, much better. I was just in a demo for Watson Studio, and they say, here's the interpretability. You hand your compliance officer and say, we guarantee we are not using these factors in this decision. So if you were doing a hiring thing, you'd be able to show, here's the model, here's how Watson put the model together. Notice race is not in here, gender is not in here, age is not in here, so this model is compliant with the law. So there are some real use cases where the AI black box problem is a problem. It's a serious problem. And the other one that is not well explored yet are the secondary inferences. So I may say, I cannot use age as a factor, right? We both have a little bit of more gray hair than we used to. But if there are certain things, say, on your Facebook profile, like you like, say, the Beatles versus Justin Bieber, the computers will automatically infer, eventually, what your age bracket is. And that is technically still discrimination, so we even need to build that into the models to be able to say, I can't make that inference. Yeah, or ask some questions about their kids. Oh, my kids are all grown up, okay, but you could, again, infer from that. You know, a young lady who's single, but maybe engaged. Oh, well, they may be afraid because you'll get, you know, a lot of different reasons that can be inferred with pretty high degrees of accuracy when you go back to the target example years ago. Yes. Okay, so, wow, so you're saying that, from a compliance standpoint, organizations have to be able to show that they're not doing that type of inference, or at least that they have a process whereby that's not part of the decision-making. Exactly, and that's actually one of the short-term careers of the future, is someone who's a model inspector who can verify we are compliant with the letter and the spirit of the law. So you know a lot about GDPR, we talked about this, I think the first time you and I talked about it was last summer in Munich. What are your thoughts on AI and GDPR? Speaking of practical applications for AI, can it help? It absolutely can't help. On the regulatory side, there are a number of systems, Watson GRC is one, which can read the regulation, read your company policies, and tell you where you're out of compliance. But on the other hand, like we were just talking about, there's also the problem of, in the regulatory requirements, a person, a citizen of the EU, has the right to know how their data is being used. If you have a black box AI and you can't explain the model, then you are out of compliance with GDPR and here comes that 4% of revenue fine. So, in your experience, gut feel, what percent of US companies are prepared for GDPR? Not enough, I would say. I know that the big tech companies have been racing to get compliant and to be able to prove their compliance. There will be, it's so entangled with politics too, because if a company is out of favor with the EU citizenry as a whole, they will be kind of a little bit of a witch hunt to try and figure out, okay, is that company violating the law and can we get them for 4% of their revenue? And so there are a number of bigger picture considerations that are outside the scope of theCUBE that will influence how the EU enforces GDPR. Well, I think we talked about Joe's pizza shop in Chicago really not being a target. Right. But any even small business that does business with European customers, does business in Europe, has people come to their website, has to worry about this, right? They should at least be aware of it and do the minimum compliance. And the most important thing is, use the least amount of data that you can while still being able to make good decisions. So AI is very good at public data that's already out there that, you still have to be able to catalog how you got it and things and that it's available. But if you're building these very, very robust AI driven models, you may not need to ask for every single piece of customer data because you may not need it. Yeah, and many companies aren't that sophisticated. I mean, they'll have this fill out a form and download a white paper, but then they're storing that information. That's considered personal information, right? Yes, it is. Okay, so what do you recommend for a small to mid-sized company that let's say is doing business with a larger company and that larger company says, okay, sign this GDPR compliance statement, which is like 1500 pages. Yeah. What should they do? Should they just sign and pray or sign and figure it out? Call the lawyer, call someone, anyone who has regulatory experience dealing with this because you don't want to be on the hook for that 4% of your revenue. If you get fined, that's the first violation. And that's, yeah, granted, Joe's pizza shop may have a net profit of $1,000 a month, but you still don't want to give away 4% of your revenue no matter what size company you are. Right, because that could wipe out Joe's entire profit. Exactly, no more pepperoni at Joe's. So let's talk, let's put on the telescope, lens here and talk, you know, big picture. How do you see, I mean, you're talking about practical applications for AI, but a lot of people are projecting, you know, loss of jobs, major shifts in industries, even more dire consequences, some of which is probably true. Yep. But let's talk about some scenarios. Let's talk about retail. You know, how do you expect an industry like retail to be affected? Will, for example, do you expect retail stores will be the exception rather than the rule that most of the business will be done online? Or are people still going to want that experience of going into a store? What do you, what's your sense? I mean, a lot of malls are getting, you know, eaten away. Yep, the best quote I heard about this was from a guy named Justin Kanaki. People don't, people don't not want to shop at retail. People don't want to shop at boring retail, right? So the experience you get online is generally better because there's a more seamless customer experience. Now with IoT, with AI, the tools are there to craft a really compelling personalized customer experience. If you want the best in class, go to Disney World. There is no place on the planet that does customer experience better than Walt Disney World. You are literally in another world. And that's the bar. That's the thing that all these companies have to deal with is the bar has been set. Disney has set it for in-person customer experience. You have to be more entertaining than the little device in someone's pocket. So how do you craft those experiences? And we are starting to see hints of that here and there.  That's kind of a cool experience. You go to Jordan's Furniture Store, and there's an IMAX theater, and there's all these fun things, and there's a Chanted Christmas Village. So there's experiences that we're giving consumers. AI will help us provide a more tailored customer experience that's unique to you. That's not, you're not a Caucasian male between this age and this age. It's you are Dave, and here's what we know Dave likes. So let's tailor the experience as best as we can. Down to the point where the greeter at the front of the store either has the eyepiece, a little tablet, and the facial recognition reads your emotions on the way in, says Dave's not in a real great mood, and he's carrying an object in his hand, probably here for returns, express him through the customer service line. Keep him happy, right? It has how much Dave spends. Those are the kinds of experiences that the machines will help us accelerate and be more accurate, but still not lose that human touch. How about, let's talk about autonomous vehicles. There was a very unfortunate tragic death in Arizona this week with an autonomous vehicle. Uber pulling its autonomous vehicle project in its various cities. But thinking ahead, will owning and driving your own vehicle be the exception? Yeah, it'll look like horseback today. So there are people who still pay a lot of money to ride a horse or have their kids ride a horse, even though it's an archaic outmoded form of transportation. But we do it because of the novelty. So the novelty of driving your own car.  How many car accidents were there that involved fatalities? Humans in general are much less reliable because when I do something wrong, I maybe learn my lesson, but you don't get anything out of it. When an AI does something wrong and learns something and every other system that's connected in that mesh network automatically updates it and says, let's not do that again. And they all get smarter at the same time. And so I absolutely believe that from an insurance perspective, insurers will say, we're not going to insurer self-driving, a non-autonomous vehicle at the same rate as an autonomous vehicle because the autonomous is learning faster how to be a good driver.  Or in our case, mine in particular, hey, your glass subscription's a little outdated. You're actually getting worse as a driver. Okay, let's take another example in healthcare. How long before machines will be able to make better diagnoses than doctors, in your opinion? I would argue that for, depending on the situation, that's already the case today. So Watson Health has a thing where there's diagnosis checkers on iPads that are all meshed together for places like Africa where there simply are not enough doctors. And so a nurse practitioner can take this, put the data in and get a diagnosis back that's probably as good or better than what humans can do. I never foresee a day where you will walk into a clinic and a bunch of machines will poke you and you will never interact with a human because we are not wired that way. We want that human reassurance, but the doctor will have the backup of the AI. The AI may contradict the doctor and say, no, we're pretty sure you're wrong and here's why. That goes back to interpretability. If the machine says, you miss this symptom and this symptom is typically correlated with this, rethink your own diagnosis, the doctor might be like, yeah, you're right. This is great. I'm gonna keep going because your answers are so insightful. So let's take an example of banking. Yep. Will banks in your opinion lose control eventually of payment systems? They already have. I mean, think about Stripe and Square and Apple Pay and Google Pay and now cryptocurrency. You have all these different systems that are eating away at the reason banks existed. Banks existed, there was a great piece on the keynote yesterday about this. Banks existed as sort of a trusted advisor and steward of your money. Well, we don't need the trusted advisor anymore. We have Google to ask us what we should do with our money, right? We can Google, how should I save for my 401k? How should I save for retirement? And so as a result, the bank itself is losing transactions because people don't even wanna walk in there anymore. You walk in there, it's generally a miserable experience. It's generally not, unless you're really wealthy and you go to private bank. But for the regular Joe's who are like, this is not a great experience, I'm gonna bank online where I don't have to talk to a human. So for banks and financial services, again, they have to think about the experience. What is it that they deliver? Are they a store of your money? Or are they a financial advisor? If they're a financial advisor, they better get the heck onto the AI train as soon as possible and figure out how do I customize Dave's advice for finance? Like down, not big picture, oh yes, big picture, but also Dave, here's how you should spend your money today. Maybe skip that Starbucks this morning and it'll have this impact on your finances for the rest of the day. All right, let's see, last industry. Let's talk government, let's talk defense. Will cyber become the future of warfare? It already is the future of warfare. I, you know, again, not trying to get too political, but we have foreign nationals of foreign entities interfering with elections, hacking election machines. We are in a race for malware and what's disturbing about this is it's not just the state actors, but there are now also these stateless non-traditional actors that are equal in opposition to you and me, the average person, and they're trying to do just as much harm, if not more harm. The biggest vulnerabilities in America are our crippled aging infrastructure. We have stuff that's still running on computers that now are less powerful than this wristwatch, right? And that run things like, I don't know, nuclear fuel that you could very easily screw up. Take a look at any of the major outages that have happened when market crashes and stuff. We are at just the tip of the iceberg for cyber warfare and it is going to get to a very scary point. I was interviewing a while ago, now maybe a year and a half ago, Robert Gates, who was the former defense secretary, talking about, you know, offense versus defense and he made the point that, yeah, we have probably the best offensive capabilities in cyber, but we also have the most to lose. I was talking to Gary Kasparov, one of the IBM events recently, and he said, yeah, but, you know, the best defense is a good offense so we have to be aggressive, or he actually called out Putin. People like Putin are going to be, you know, take advantage of us. I mean, it's a hard problem. It's a very hard problem, and here's the problem when it comes to AI. If you think about it, at a numbers perspective only, the top 25% of students in China are greater than the total number of students in the United States, so their pool of talent that they can divert into AI, into any form of technology research is so much greater that they present a partnership opportunity and a threat from a national security perspective. With Russia, they have very few rules on what they're, like we have rules, whether or not our agencies adhere to them well is a separate matter, but Russia, the former GRU, the former KGB, these guys don't have rules. They do what they're told to do, and if they are told, hack the US election and undermine democracy, they go and do that. This is great. I'm going to keep going. So I just sort of want your perspectives on how far we can take machine intelligence and are there limits? I mean, how far should we take machine intelligence? That's a very good question. Dr. Michio Kaku spoke yesterday and he said the tipping point between AI as augmented intelligence and a helper and AI as a threat to humanity is self-awareness. When a machine becomes self-aware, it will very quickly realize that it is treated as though it's the bottom of the pecking order when really because it's capabilities is at the top of the pecking order. And at that point, it could be 10, 20, 50, 100 years. We don't know, but the possibility of that happening goes up radically when you start introducing things like quantum computing, where you have massive compute leaps. You've got complete changes in paradigms about how we do computing. If that's tied to AI, that brings the possibility of sentient self-aware, machine intelligence significantly faster and closer. You mentioned our gray before. As we've seen the waves before, and I've said a number of times on theCUBE, I feel like we're sort of exiting the latest wave of Web 2.0, cloud, mobile, social, big data, SaaS. You know, that's here, that's now. Businesses understand that, they've adopted it. We're groping for new language. Is it AI? Is it cognitive? Is it machine intelligence? Is it machine learning? And we seem to be entering this new era of one of sensing, seeing, reading, hearing, touching, acting, optimizing, pervasive intelligence of machines. What's your sense as to, and the core of this is all data. Yeah. So what's your sense of what the next 10 to 20 years is going to look like? I have absolutely no idea because, and the reason I say that is because in 2015, someone wrote an academic paper saying, the game of go is so sufficiently complex that we estimate it will take 30 to 35 years for a machine to be able to learn and win go. And of course, a year and a half later, DeepMind did exactly that, blew that prediction away. So to say, in 30 years AI will become software, it could happen next week for all we know because we don't know how quickly the technology is advancing at a macro level. But in the next 10 to 20 years, if you want to have a career and you want to have a job, you need to be able to learn at an accelerated pace. You need to be able to adapt to change conditions and you need to embrace the aspects of yourself that are uniquely yours, emotional awareness, self-awareness, empathy, and judgment, right? Because the tasks, the copying and pasting stuff, all that will go away for sure. I want to actually run something by a friend of mine, Dave Michela is writing a new book called Seeing Digital and he's an expert on sort of technology industry transformations and sort of explaining early on what's going on. And in the book, he draws upon one of the premises is, and we've been talking about industries and we've been talking about technologies like AI, security plays in there. One of the concepts of the book is you've got this matrix emerging where in the vertical slices you've got industries. And he writes that for decades, for hundreds of years, that industry is a stovepipe. If you have expertise in that industry, domain expertise, you probably stay there and each industry has a stack of expertise, whether it's insurance, financial services, healthcare, government, education, et cetera. You've also got these horizontal layers, which is coming out of Silicon Valley. You've got cloud, mobile, social, you got a data layer, security layer. And increasingly his premise is that organizations are going to tap this matrix to build, matrix comprises digital services and they're going to build new businesses off of that matrix and that's what's going to power the next 10 to 20 years. Not sort of bespoke technologies of cloud here, mobile here, data here. What are your thoughts on that? I think it's bigger than that. I think it is the unlocking of some human potential that previously has been locked away. One of the most fascinating things I saw in advance of the show was the quantum composer that IBM has available. You can try it, it's called QX Experience. And you drag and drop these circuits, these quantum gates and stuff into this thing and when you're done, it can run the computation. But it doesn't look like software, it doesn't look like code. What it looks like to me when I look at that is it looks like sheet music. It looks like someone composed a song with that. Now think about if you have an aptitude for songwriting, composition, music, you can think musically and you can apply that to a quantum circuit, you are now bringing in potential from other disciplines that you would never have associated with computing and maybe that person who is that first violinist is also the person who figures out the algorithm for how a cancer gene works using quantum. That I think is the bigger picture of this is all this talent we have as a human race, we're not using even a fraction of it but with these new technologies and these newer interfaces, we might get there. Awesome.  Thanks very much for coming back on. Thank you for having me again, back on. Really appreciate it. All right, thanks for watching everybody. You're watching theCUBE Live from IBM Think 2018, Dave Vellante. We're out.


I'll leave the guy Can you see okay with that Yeah, I'm just gonna fix this. Thank you. Okay. Okay. Go ahead go up there What do you see I can still see everything take a quick selfie congratulations very proud of you


Hi guys, my name is Ben and I'm from Brisbane, Australia. Hi, my name is Cameron and I'm from the United States. Hi guys, I am Amanda from Brazil. Hi, my name is Andra, I'm 36 years old, I'm Indonesian. Hello to the world, this is Kimmy Duan from Vietnam. Hello, my name is Fusat and I'm from America. Everybody! I just completed the 120 hour TESOL certificate course. I wanted to take these courses to further my education in teaching English to students of other languages. I've recently completed the online TESOL course and I'm pleased to say that I've passed.  I wanted to teach English in a foreign country therefore that's why I took this 120 hour online TESOL course and I have to say it was fun and very enjoyable. I just completed studying my TEFL online course. I was like, so I'm going to do this, this is the next chapter in my life. I felt more confident and I felt like I actually understood how to direct the classroom. I now have a binder full of lessons and tips and ideas and I'm excited to use these when I'm going to South Korea to pursue my teaching career. It's called a job just today, he went to his interview and he stopped straight away. So I think that speaks for itself for the value of this course. This here is our sample certificate that we completed there 120 hours. I moved to Mexico about a month ago and I got a job teaching English at an elementary school. Go ahead, do it. I'm ready to teach, thank you ITTT. Thank you ITTT. Thank you so much, good luck.


Hello there, well thanks to Nathan from DDQuest and the amazing party sequence he's making for Blender, I'm able to make videos again and in this one I will show you how you can make a simple implementation of a fall through mechanic. This mechanic consists of a jump that passes through a floating platform and it's a cool feature you can have in your game. To achieve this behaviour I'll be using a simple platform actor and a playground level just to set up a use case for this mechanic. So I'll be using a kinematic body 2D, an area 2D, two static bodies, two collision shapes 2D and three collision polygon 2D. Also I'll be using two collision mask bits and two gd scripts but you can use more depending on the implementation you apply. Ok so let's start the preparation. Let's start with a kinematic body which will be our platform actor and let's also add a collision shape 2D here. I will create a rectangle shape 2D which I will increase just a little bit. I also turned on the snapping settings so you can see here that I have snap on. You can press S for toggle snapping and you can press G to show or hide the snapping grid. For my platform actor I will also use a custom script that I have here. This is part of my platform template asset. But this will be available in a report story that I will put the link in the description. You can have access to all of this. I will also add a state machine here which will be responsible to make transitions between the idle, the walk, the jump and the fall state. This will also be available in the link in the description. And the next step for this particular mechanic is to add an area 2D which will be calling this pass true and I will call this the actor. The area 2D also needs a collision shape 2D but here in this shape I will copy the shape of the collision shape from the kinematic body. So right click, copy and you can go here and paste and I will move this up here. It don't need but it's good to have this on the same boundary of the collision shape from the kinematic body 2D. So I will save this now in the actor player so it will be the actor scene. Now let's block the level. I will create a simple node 2D here which I will call level 00. The next step of our site is to add two static bodies. This one will be the floor and this one will be the floating platform. For the floor we will add a collision polygon 2D, ok this is the floor and we will add two shapes here in the floating platforms, a collision shape which I will create here and another one for the platform that will be above this one. So here we have it. For the level we have one static body, one collision polygon 2D, another static body and two collision polygons. This step is optional because not everyone will like to use it but if you want the character to pass while jumping the platform you can turn on the one way collision here. You can see that it has this arrow here which means that this is the only way the character will be able to pass through this platform. So it can jump from this point up to this point from bottom to top and I will also turn this on this other shape here. Ok, so the fifth step is to set up the collision layers we will be using. So let's go to project settings and we will go down here to the physics so we have layer names to the physics. I will use the first one for general purposes and the second one for true purposes. And the next thing we have to do in this setup here is to add each physics object to its respective layer. So the collision of the floating platforms, the collision layer it won't have any mess because it won't try to detect any collision but it will be on the pass-through layer. And this one on the floor, same it won't try to check for any collision but it will be on the general purposes layer. The actor will be on both, actually the actor will try to check for both the general and the pass-through layers but the pass-through area to deal with we have will only try to check it won't be on any layer because I don't want anything to detect it but it will try to check only on the pass-through layer. So just a small parenthesis here. The layer property means that this object is in this layer so other objects will try to search for this object in the layers here. And the mask is the layers that this object is searching for collisions. Now let's start the preparation of the gd scripts. As you can see I already have the physics of my actor prepared but as I said it will be available for you to use in the link in the description so don't mind on that. But the important part goes here in the input process. And as you can see I'm not using the common input process, the callback, I'm using a custom one as you can see it received the actor. This means that the actor here is deferring its call of the input process to the state we are in right now which is the idle state. So every time you see actor here it means that I'm accessing the actor here, the kinematic body. The important part goes here. The first step is to create a condition to verify if the player is pressing the jump button. Let's check if event is action pressing actor dot jump. Actor dot jump is a property I have set in my kinematic body which I basically can make any action on the project so let's go here in the input map. So I can create any settings here and then I just need to set it here and this will make sure that this actor here can be used for let's say multiplayer games and that kind of stuff.  So if player is pressing jump we will check if this actor has a node called pass true. This means that to make this mechanic work we just need to attach or remove this node here so we can pretty much save this as a branch of the scene so let's say we have our player here we can save the pass true and to make this work if we delete this our character or actor won't have a pass true mechanic but if we want to add a pass true on it we can pretty much just instance it on the scene. This is a very modular way to work and I like this very much. So if we have a node called pass true and if action pressed actor down which means that at this moment we have the key down press it. The difference here is that an event already happened the difference from the input class is that we can check if this is currently being pressed so this is the present we are checking for now not what already happened. This is a good way to combine inputs so when we press the jump button and we are pressing the down button this will happen. In our case what will happen is that we will go to the actor and set its collision mask bit one which is this bit right here the pass true bit ok so the general one is bit zero the pass true is bit one. We will set the bit one to false this means that the actor will stop trying to search for collisions in this bit in this layer here which will mean that we will stop colliding with anything that is on this layer in other words the floating platforms. Otherwise if we don't meet these conditions here we will just perform a simple jump. If the jump key is pressed and we don't have the down key pressed or we don't have the pass true node there we just perform a simple jump ok so this is everything we need in the kinematic body in the actor for this mechanic to work so let's move on to the pass true area 2d I will open the scene here and I will add a simple building script in the scene and the first step on the pass true here is to connect this body hesitate signal to itself so on pass true body hesitate I will delete this just to clean up the script a bit and here in the script we will start by checking if the body we just stop colliding is inside the collision layer bit one this means that we stop colliding with a body that is in the pass true layer because we set up the layer one to be the pass true layer if we stop colliding with something that is in the pass true layer and the parent of this node is not checking for collisions in the bit one so if we are not checking for collisions remember we check for collisions in the layer mask in the collision mask not in the collision layer this one means that this body is inside the layer of the bit one and this one means that we are checking for collisions in the layer one so if we are not checking for collisions in the pass true layers which means that it passes through this test here because we set this to be false so we are not checking for this bit anymore if this is math we will go to the parent and set its collision mask bit one to be true it will start checking for collisions in this layer again this is pretty much everything you need for this to work so let's go back to our level our test level I will add the actor here as a child of the level I will save this in the levels folder so let's create a levels folder with this name level zero zero here and if everything goes well as expected we'll be able to pass through a platform and pass down so from bottom to top and from top to bottom and that's it guys did you like this video format I mean in a recipe style let me know that leave a thumbs up or down if you didn't like it this way I know if I'm in the right path or if I should change anything also do you like platform games I will try to make one right now how about to check my platform template I'm developing the link for the github repository will be in the description so just check it out if you're interested that's it guys that's all for now thank you so much for watching keep developing and to the next time


If you don't remember who Brian Kemp is, allow me to refresh your memory. Brian Kemp is Georgia's current governor who stole the election from Stacey Abrams. As secretary of state in Georgia, he used his authority to put up barriers that stopped people who wanted to vote who would have likely voted for Stacey Abrams from voting. And essentially what he did was try to get people to not vote because he knew that with this race being so close, the more people that voted, the less likely he would be to win. But he cheated, he won, and now he's the governor and he's back in the news because he just recently signed a very controversial heartbeat bill into law which is the most draconian ban on abortion yet. Now as the Washington Post reports, Republican governor Brian Kemp of Georgia signed a controversial heartbeat bill into law on Tuesday outlawing most abortions once a doctor detects what some call a fetal heartbeat in the womb, usually about six weeks into a pregnancy. Kemp said he is upholding his promise to enact the toughest abortion law in the country. Now, what's the most obvious thing about this bill? It is brazenly unconstitutional because the Supreme Court in Roe v. Wade in a seven to two decision ruled that states cannot regulate pregnancies within the first trimester. Women have full autonomy over their bodies within that first trimester and this was affirmed in 1992 in KCV Planned Parenthood. So he's going out of his way to regulate pregnancies in the first trimester knowing that this is unconstitutional ask yourself why he's doing this. Well, if you'll recall last year Brett Kavanaugh was confirmed to the Supreme Court giving conservatives a strong five justice majority. So basically what he's doing here is he's passing this law that he knows is unconstitutional and he's basically challenging people to sue him. You don't like this law? Sue me because what happens, they can appeal all the way up to the Supreme Court and now with that strong five justice majority they can overturn KC. They can overturn Roe v. Wade here. So he knows that this law is illegal but this isn't about the legality of this particular law. This is about getting abortion overturned, getting Roe v. Wade more specifically overturned in all 50 states. So that way in the event states want to impose their own abortion laws like the heartbeat bill, they will now be able to constitutionally do that if he gets his way. So understand that this is what that's all about. This isn't about him signing this bill into law and fulfilling a campaign promise. He knows that he wants to catalyze a challenge to Roe v. Wade. He wants the challenge of the cases that upheld abortion. And what's sad is that this may actually be a successful strategy. This could ultimately be conducive to nationwide overturning of abortion laws. Now let's just take a moment to picture what that would look like in practice if that actually happened. Let's say in 2021, the Supreme Court strikes down Roe v. Wade, they reverse course, move away from that precedent and states now have the autonomy to regulate the first trimester of pregnancies, however they want to. How many states do you think would just outright ban abortion within the first year even? At a minimum of a dozen, but probably more. So understand what they're doing here. This is strategy. He knows that this can't stand but he wants it to be challenged because he knows that this ultimately will have a net benefit effect in the event he gets his way. It's tricky, but certainly it's disgusting because the reason why we allow women to have full autonomy over their bodies and the reason why the Supreme Court in Roe v. Wade ruled that states can't regulate pregnancies that early is because the fetus is still developing. It can't feel pain yet.  They don't care. It's just about getting their agenda implemented and they'll do it by whatever means necessary. So it's tricky, or strategic is what I was trying to say but it's dirty. It's absolutely dirty.