retaining wall, because retaining wall is a very important structure in geotechnical engineering. So, to retain the soil, so you have to build the structure for this type of retaining wall. So, there are different types of retaining wall and we will discuss about various type of retaining wall, how to choose the dimension and what are the different factor of safety that we have to consider during the design of retaining wall. Then those things will be discussed in this class. So, first I will discuss about the different types of retaining wall. So, first the types of retaining wall, so first one is our gravity retaining wall, we can go for this type of arrangement, this is ground surface and this is, so this type is filling material. Now, depending upon its weight, we will get the stability for this type of gravity retaining wall and this is constructed for PCC plane cement concrete, we will not use any reinforcement for this type of retaining wall and this is not economical for large height. If the retaining wall height is very large, then this type of retaining wall is not very economical, but and then the next one is is semi gravity retaining wall, this type of retaining wall and this is ground surface, this is the retaining wall where the size of retaining wall is slightly reduced compared to the gravity retaining wall by providing small amount of reinforcement in the back face side. So, we can say that this gravity retaining wall, the most of the stability is given by the weight of this retaining wall and here reinforcement is not used. So, that is why we need, we have to use a very huge size of retaining wall, but in semi gravity retaining wall, the size of this retaining wall as compared to the gravity retaining wall is slightly reduced, is reduced by providing a small amount of reinforcement in the face of this retaining wall. So, this is reinforcement that is used and this is the filling material this side. Now, third type of retaining wall is cantilever retaining wall. Now, this type of retaining wall which is made of PCC plane cement concrete. So, this is the ground surface. Now, this type of retaining wall which is made by RCC reinforcement concrete and where these are the reinforcements and which is suitable for a height of 6 to 8 meter, suitable for a height of 6 to 8 meter. So, this and the next one another type of retaining wall is that is counter fort retaining wall. This is the retaining structure and this is the longitudinal side and where with some interval this counter forts are used. So, these are called counter forts and this is now this type of reinforced, this type of retaining wall the providing the use of this counter fort is to reduce the shear force and the bending moment in the vertical stream of the slab. So, this portion is called the stream of the retaining wall. So, this counter forts are reduced to this counter fort are used to reduce the shear force and bending moment which is induced in the vertical stream of the retaining wall or this and the base slab also. This is the base slab. So, to reduce the shear force and bending moment of this base slab and the stream this retaining counter forts are used. This counter forts are used with certain intervals. Now, economical for if the retaining wall height if this is the height of the retaining wall. Now, if height is more than 6 to 8 meter then this type of retaining wall is very suitable and this counter forts are used on the backfill side because this is our backfill side. So, this counter forts are used in the backfill side. So, these are the four different types of retaining walls. So, first one is gravity retaining wall where this most of the stability is getting from the weight of the retaining wall and where this we are using the plain cement concrete PCC. Then the next one is semi gravity retaining wall where the size of the gravity retaining wall is reduced by providing the small amount of the reinforcement. And the third one is counter fort retaining wall cantilever retaining wall where the RCC reinforced cement concrete is used for that type of retaining wall. Now, this cantilever retaining wall is suitable for the 6 to 8 meter height. Now, if a height of the retaining wall is more than 6 to 8 meter then you have to go for this counter fort retaining wall to provide the counter fort which is used to reduce the bending moment and shear force which is induced in the vertical stream and the base of the slab. And these counter forts are provided at the backfill side. Now, we have to design to these different types of retaining wall. So, first we will go for this gravity retaining wall and then before we go for the gravity retaining wall you should know what are the different types of factor safety you have to determine. What are the checks you have to do for this design of this retaining wall? First suppose if this is a typical section of a retaining wall say where this one is the backfill site and this is ground surface and this is foundation. So, this is our backfill site.  So, this retaining wall has to retain this soil pressure. So, that means the soil will give the lateral pressure on this retaining wall. So, now if I go through the free body diagram of this retaining wall structure. So these are the if this is the center of this retaining wall or if this is b by 2 this one also b by 2. So, total width is b and if this is the height of the retaining wall h then first this active earth pressure that will act at this is p a active earth pressure that will act at h by 3 distance from the base of this retaining wall because this and then similarly when we know that this retaining wall if it is move in this direction then this phase will be active earth pressure. Similarly, this soil this portion below the foundation soil this soil will also provide a lateral pressure in the opposite opposite to the p a. So, that is the opposite to the movement of this retaining wall. So, that means here act one passive earth pressure that will act. So, this is a passive earth pressure p p. So, this is and this one is the toe of the retaining wall. So, this passive earth pressure also act suppose this is the depth of the or the portion of the base of the retaining wall is at a depth of d from the foundation soil and where this soil will provide applied a passive earth pressure and this soil will apply active earth pressure. And now if we go for the reaction force for this base of the retaining wall. So, this because this weight of the retaining wall. So, that will act in this direction this is the weight self weight of the retaining wall that will act. Now, this is this reaction will act in this direction if I take the two components of this reaction R. Suppose this is this reaction is R and if we take the two components this is R H dash and this one R V dash. So, now this distance from the toe of this reaction force is say X bar and from the centre this one say E. So, now what are the forces that we will consider. So, that means we consider the active earth pressure we will consider the passive earth pressure we will consider the self weight of this retaining wall for the gravity retaining wall later on when you go for the cantilever retaining wall then for different theories you have to consider the weight of the soil also. So, this weight will act in the downward direction this active earth pressure will act from this direction and the passive earth pressure will act in the opposite direction. So, there is a friction that will act in between the base of the foundation or retaining wall and the soil. So, that means then this for this vertical and horizontal force. So, there is a two basically vertical and horizontal force then there is a reaction that will develop at the base of the foundation. So, if I take the two components of this reaction R one is R H dash one is R V dash. Now, say this R is acting as a distance of X bar from the toe of the retaining wall and so then that point of this reaction force is also at a distance of E from the center of the of the of the retaining wall. So, now if I go for this equilibrium condition say say R V dash is equal to W. So, that means this R V dash that is equal to the W this vertical components equal to this W another one this R H dash that is equal to this R H dash is equal to P A minus P P. Now, if I neglect this P P because this portion of force if I neglect this P P because this portion of force if I neglect because as this P P is very small compared to this P A and this P P will also provide additional safety for this retaining wall. So, if I neglect this P P and consider only P A by neglecting P P then R H dash will be equal to P A. Now, another condition we have to take moment from the with the respect to toe and that moment should be 0 for equilibrium condition if I take moment from the toe and this will be 0. So, we can write that R V dash into X bar that is equal to W and if W is acting at a distance of A or this acting at X distance of A from the toe of the retaining walls and this is W into A then minus P A into H by 3 as we are neglecting the P P. So, we can write that X bar is equal to W A minus P A into H by 3 divided by R V dash. So, we can write this all if we can write in the general form then W A that is the summation of all moment which is giving the resistance because this weight is actually giving the resistance and this P A is trying to overturn this retaining wall. So, it is pushing from this side and trying to overturn this retaining wall and this weight of the retaining wall basically providing the resistance. So, that moment is resistive moment minus summation of the overturning moment or M O and divided by all force of the vertical force. So, these are the vertical force. So, that means we can calculate the X bar in the summation of resistive moment minus summation of overturning moment divided by summation of vertical force. So, now we can write that our E eccentricity is equal to B by 2 minus X by. So, once we get we determine also we this X by by using this expression. So, we can determine the E value also by B by 2 minus X bar. Now, based on that what are the different stability checks that we will consider the first one is that there is a sliding between if I take this photographs here. So, there is a sliding between the soil and the retaining wall base. So, that means it may fail because of the sliding if I if the sliding is if the friction force is not enough in this base and of the retaining wall and the soil then there is a possibility of sliding. So, that sliding have to prevent. Now, sliding force that means for that means for no sliding condition we have to check the factor of safety. So, factor of safety F s for the no sliding condition the sliding force is a resisted by this vertical force into the coefficient of friction. So, this r v dash and mu and the sliding force is this is this is a possibility of slide because of this r h force. So, that is r h dash. So, where we can write that mu is the coefficient of friction between base of the wall and soil or you can write that is equal to tan delta. Now, in this case this factor safety should be equal to 1.5. So, that will give the no sliding condition. So, next one is overturning no overturning condition. That means this because of this force because of this p a force it will overturn this retaining wall and this weight will resist this overturning force. So, we have to no overturning condition that means we if we consider the first factor safety for no overturning condition that is the summation of m r divided by summation of m r o overturning. So, where summation of m r is sum of all resisting moment about 2 and summation of m o is sum of all overturning moment. So, for this previous case if I get the factor of safety for overturning case f a o or factor of safety for sliding f a s then f o that will give us for this previous case w a divided by p a into h by 3. And that should be also greater than 1.52. So, that is why we have to no overturning 2. So, next check that we have to do that for the bearing capacity check. So, that means next check is no bearing capacity failure. So, no bearing capacity failure means if the base soil or foundation soil is very poor then we have to check then there is a possibility that that soil will fail because of as the vertical load is coming on that soil.  Now, for that purpose we have to calculate the stress p max of the soil that will give us the r v dash all the summation of vertical force divided by width of the retaining wall into 1 plus 6 e divided by b. And or the p mean the minimum 1 is r v dash divided by b 1 minus 6 e divided by b. But here as we are considering the maximum stress so we work as taking this p max. And now for the factor of safety for bearing capacity failure that will be q n a divided by p max where q n a is equal to the allowable bearing pressure or this and this f s this should be greater than equal to 3. So, that means this soil pressure that it can take it can able to take and divided by p max so that we will get this factor of safety. Then first check fourth check that no tension failure no tension condition that totally depends on suppose if I get this is our base of the retaining wall. So, this stress distribution as we will go for this p max and p mean. So, you may get this type of distribution for the stress this stress distribution at the base of the retaining wall you may get this type of stress distribution this is p mean and this is p max. Now there is a possibility that we may get this type of distribution also where this will if this is positive then this will give us this p mean this is p max. So, this will give us the tension condition so, this will give you the negative stress was that will give us the tension condition. So, we have to avoid this no tension condition if this type of situation arises then you have to avoid this no tension condition and for the no tension condition it is occur when if a is greater than equal to b by 6. So, if e is less than b by 6 then this we have to redesign the dimension of the retaining wall to avoid the no tension to avoid the tension developed in the base of the retaining wall. So, for the no tension condition this e should be equal to greater than b by 6. So, these are the four checks we have to do during the design of retaining wall first we have to decide the rough step why if I go for the design of this retaining structure first we have to roughly decide the dimension of the retaining wall by based on the provided guidelines. Then we have to first see whether this retaining wall is safe against sliding and bearing or not if it is safe then you have to go for whether the this no tension condition is occurred or not then finally, you have to go for the bearing pressure calculation. So, all these four conditions if satisfy then we can decide. So, this dimension will provide for the retaining structure. Now, next one that for the other this checks addition to this checks what are the different other design criteria or guidelines. So, first we will go for the gravity retaining wall. Suppose, this is the retaining wall this is gravity retaining wall and this is the ground surface which is inclined at angle i with the horizontal surface this is our vertical stream. Now, provided guidelines suppose this is the existing soil and this is the back field. Now, this say is the depth of the retaining wall T and then for this if I consider the vertical line along the this face then you will give the this height of the retaining wall is H say. So, this is say height of the retaining wall H. Now, for the guideline which is provided that this top portion take around 0.3 meter or 300 millimeter. Now, this slope is 1 is 230. Now, this height of this base that is taken as H by 10. Now, with this guideline is we can consider 2 third of H. And this portion this extended portion is taken H by 6. Now, if I join this line with this extreme point and if this angle is alpha and this angle is eta then and what are the forces that will act. So, this is the weight of the concrete W c and this is weight of the soil you can consider. So, if I go that d value this d is at least 0.6 meter we have to provide this d value at least 0.6 meter. Now, as base width this base width of the retaining wall. So, base width we can consider 0.5 H to 0.7 H in between 0.5 H to 0.7. Now, this earth pressure that will act. So, now this earth pressure diagram if I consider this earth pressure. So, this earth pressure act this will act P a for this soil and here we also act the passive earth pressure this is active earth pressure. So, if we consider neglect this passive earth pressure. So, this earth pressure can be calculated either ranking formula or Coulomb's theory. Now, for this rankings theory if I consider this earth pressure can be computed either by rankings theory or by Coulomb's theory. Now, for rankings theory the shear zone should not pass through the stream. That means that this line is the extreme line of this condition if this line is passing through this stream then that is not acceptable if I consider the ranking theory. So, to satisfy that condition in this angle we can calculate this is 45 degree plus i by 2 minus phi dash by 2 phi is the friction angle minus sin inverse sin i divided by sin phi dash. Similarly alpha is equal to 45 degree plus i by 2 minus i by 2 plus sin inverse sin i divided by sin phi dash. So, now if i is equal to 0 then alpha is equal to 45 degree plus phi dash by 2 minus i by 2 minus i by 2. So, first you have to check whether this line is if I consider the ranking theory you have to consider check whether this line is passing through the stream or not. So, this for the shear zone this line should not be passed through this stream. So, this is the extreme point. Now, there is a few things that you have to clarify that if I consider suppose this is the retaining wall and we can use the rankings theory. Now, if I use the rankings theory suppose this is the two if I consider the same retaining wall. So, if I this is our foundation this is the ground circle this is backfill side. So, then we first we if I use the first case we use the rankings theory and next one if I use the Coulomb's theory. So, the same retaining wall if I consider for the Coulomb's theory for the different the forces that you have to consider that again if I join this point. So, this is alpha. So, here alpha as i is equal to 0 alpha will be 45 degree plus phi by 2 and then this angle. So now, this P a will act here. Now, this is our base now for the Coulomb's theory as we know this if I draw a vertical line or perpendicular line. So, this is 90 degree perpendicular line the face of this side of the retaining wall then P a will act with an angle delta of the vertical line. So, this perpendicular line P a will act with an angle delta whereas, in case of rankings theory it will act with the parallel to this backfill side size. If it is the angle is i then it will act with an angle of i whereas, it will act with parallel to this. So, here also this is the surface ground surface in parallel to ground surface. Now, what are the forces that we will consider this here the weight of concrete that we will consider again this is also the ground surface. Here the weight of this concrete we will consider in additional to that we will consider the weight of this soil also between this area. So, that means here we are not considering the weight of this soil here we are considering the weight of this soil and weight of this concrete also. But here this will act parallel to this ground surface here it will act perpendicular line with making an angle delta where delta is the friction angle between the soil and wall. So, delta is the interface angle between soil and the wall. So, these two things we have to remember when if we use the two different theories for this analysis part. Now, next one for the semi gravity retaining wall for the gravity we have discussed about different types of loading condition. Now, semi gravity retaining wall where this base width is slightly smaller as compared to the gravity one and rest of the design process are same. Now, next one you will go for the cantilever retaining wall design. So, for the cantilever retaining wall. So, for the cantilever retaining wall suppose this is the particular cantilever retaining wall. So, this is the ground surface in the backfill size which is making an angle i again. Now, this is the d depth of the retaining wall and this one is the h height of the retaining wall. Now, again if I consider the ranking expression then if we join this line this will give you the h and if I join the vertical line. Now this is the earth pressure distribution. So, this p a will act which parallel to the ground line and now the recommendation this as this top portion is 0.3 meter. Now, this angle is again 1 by 30. Now, this h this height of the base with the thickness of this base is 0.1 h this is 0.1 h. Now, this distance is also 0.3 meter. Now, this is 0.1 h this one this at the this t t junction this thickness is also recommended 0.1 h and this one is two-third of h roughly or this base width is two-third of h or 0.5 h to 0.7 h. Now, similarly thickness of this side is also is taken at it is either 0.1 h or h by 12 to h by 8. So, that means it is in between that is h by 10 this is considered here. So, either this is average value of this two is 0.1 h, but this range is h by. So, these are the guidelines to starting the to choose the initial dimension of the this retaining wall. So, now this one is this distance we can first choose then we will consider the weight. So, these are different weights first we will consider we will consider weight of concrete we will consider weight of soil if I take the ranking expressions. Now, for this condition what are the factor of safety we will choose for this type of retaining wall that first one that we will consider the factor of safety factor of safety against this is sliding. So, this factor of safety that will give us the total vertical force for the sliding into tan delta or delta 1. So, where this delta or delta dash where delta dash is the interface angle between the base of wall and soil. So, this is the interface of wall and soil. So, this is the interface friction angle between the base of wall and the soil. So, this is the summation of v into tan delta plus this if this total width is b. So, this base width is b b into c 2 c 2 is the cohesion as the base soil plus this p p if I consider the passive force p p that is also acting here. So, if I consider p p is the passive force. So, that will give you the base friction angle divided by p h or the p a that is horizontal force. So, that means this force this p p will act here this is the passive resistance that will act. So, p p b where b is the base width and c 2 is the cohesion of soil or foundation soil. So, there is two types of soil one is foundation soil where the retaining wall is resting another is backfill soil. So, c 2 is the cohesion of the foundation soil. So, that means the summation of all the forces into the friction angle divided by b into c 2 divided by p p this passive resistance plus this is plus b c 2 plus p p and divided by p a. So, this is for the sliding force that we can consider for this type of analysis. Now, if I consider the total free body diagram or the total forces of this type of retaining wall then this is the vertical portion. So, this is the retaining wall on this angle which is making an angle I this is ground surface. Now, for this edge so this is our active pressure that will act. So, with an angle I so p active with an angle I this is for the backfill soil. The next for this type of soil where this backfill soil generally this is a phi type of soil that means cohesion is not considered as a c phi type of soil and if it is a base soil if it is a c phi type of soil then you will get this type of distribution of the soil pressure. So, this is our c type of soil. Now, here we will consider this passive pressure and this is the reaction force that will act in the base in this form that is p min and this is p max. So, this reaction will act in this form. So, that will give you this is p min p max. Now, to calculate the weight suppose this for this top portion this will give us c 2 c root k p and for this bottom portion and this p p 1 that will act at a distance of d by 3 this is p p if this distance is d. So, this will give us c 2 c root k p and for this p p we can divide this part into two different portion one this is p p. So, one is p p 1 and another one for this one is p p 2. So, this is p p 2 that will act at a distance of d by 2. So, now finally, if I consider this stress again if I draw here. So, this is the passive force distribution for this portion so this is the d depth of the this foundation soil and then this stress value is 2 c 2 root k p and this value is k p gamma 2 d plus 2 c 2 root k p where k p is the coefficient of passive earth pressure and gamma 2 is the unit weight of the base soil. So, here this base soil. So, there is we can say the dimension this is the c 1 cohesion of the and phi 1 and this is gamma 1. Similarly, here also c 2 phi 2 gamma 2 most of the cases this c 1 is 0 for the black field. So, this c 1 is 0 for the black field and this c 1 is 0 for the black field case. So, this is the if I consider these forces. So, these are the pressure that will act. So, if I take the two parts one is this is p p 1 which is acting this is triangle at a distance of d by 3 from the base another is acting is p p 2 this is p p 2 which is acting as a distance of d by 2 from the base. So finally, so we can first we have to determine the stress of this triangle portion which is acting as a distance of d by 2 and then this stress of this rectangular portion which is acting as distance of d by 2 from the base. Then suddenly if we add these two stress then we will get the total passive force that is acting p p for this portion and then we can acting we can determine the point of application. So, suppose the if the h bar or d bar is the point of application of this passive force that we can determine that p p 1 into d by 3 plus p p 2 into d by 2 divided by p p 1 plus p p 2. So, total force so in this way first you have to calculate p p 1 from this triangular force this triangle that because we know the stresses at this edge and this edge and then p p 2 for this rectangular portion then we can determine d b bar. And this this stress p p p max and p min we can determine by using the previous expression then p a also calculate for the passive active force that is acting. So, now for the weight calculation we can divide this retaining wall into different section. Suppose so first we can consider this is the first section this is section 2 this is section 3 this is section 4 this is section 5. So, this 1 2 3 4 5. So, all these sections we can divide and you can take and then separately we can determine the weight of every section. And then finally, we can determine the factor of safety against the sliding overturning then bearing capacity and all those things. Now when we calculate this p a then we can calculate this p p p a value then p a this force will give us that half into gamma into h square into k a where h gamma is the unit weight of the soil h is the height of the retaining wall. Suppose this is the height of the retaining wall and k a is the active coefficient of active earth pressure. Now this coefficient of active earth pressure for the Rankine's and the Coulomb's there are different expressions are given. So, for the Rankine's theory if I use the Rankine's theory then this k a is equal to cos i into cos i minus root over h into cos i minus root cos square i minus cos square phi dash then divided by cos i plus root over cos square i minus cos square phi dash.  Thus if i is equal to 0 then k a for the Rankine's case is 1 minus sin phi dash 1 plus sin phi dash and k p is just reversed 1 plus sin phi dash 1 minus sin phi dash. Now if I use the Coulomb's theory then you will get that k a is equal to for the case of Coulomb's theory k a is equal to suppose if this is our say retaining wall and here this force is acting here draw a perpendicular line is acting angle delta. So, and this is our horizontal line and this is our horizontal line and if this angle is beta say this angle is beta this is acting a delta is horizontal line and this angle will give us that 90 degree minus beta. Now here this is the value now for this type of k a will get by this expression that sin square beta plus phi dash. Now this is sin square beta sin beta minus delta then 1 plus root over sin phi dash plus delta into sin phi dash into sin phi dash into sin phi dash minus i divided by sin beta minus delta into sin beta plus i and total this is square for C 0 condition. Now similarly for the k p that will calculate by sin square beta minus phi dash divided by sin square beta sin beta plus delta 1 plus root over sin phi dash plus delta sin phi dash plus i sin beta plus delta sin beta plus i sin beta plus i sin beta plus then total square. So, by this way we can determine the passive and active coefficient of earth pressure for Rankine's theory and for Coulomb's theory if we use different condition. So, in the next class I will discuss about the different and solve a few problems to show that how to design design means to determine the dimension of the retaining wall by considering the different factor safety for sliding overturning bearing and no tension condition and to choose a proper dimension of the retaining wall. Thank you.


The High Court of the Federal Capital Territory on Monday refused to vacate an interim order which restrained the National Chairman of the Labour Party, Julio Saburi, the National Secretary of Hajj Farouk Ibrahim and two others from parading themselves as leaders of the party. We would analyze that today on the breakfast. As the under-17 Africa Cup of Nations AFKON draws nearer, Golden Eagle's coach Ndukau Badi is working relentlessly with his technical team to put together a squad that will make Nigeria proud. We have a sports analyst to give us some insight on this this morning. Also don't forget we would also be analyzing the big stories on the newspapers today. Welcome to the breakfast. My name is Nyam Gul Aghaji. I'll be joined later on by Kofi Battels but right now I'd just like to say it's a pleasure having you on the show this morning. Well there are so many things that are coming up. We look at the social media and we see a lot of things that we some some of them are very heart wrenching. Some of them are gladdening. Some of them are just there looking at us and in the days of social media that is what we get. Sometimes we get the stories that look so good but they are not true. For this one is true a black teen Raphael shot for accidentally going to the wrong house to pick up his siblings. Wrong house to pick up his siblings and this was the guy who very young boy who needed to pick some some of his sisters from a place and because the numbering was almost the same and he made a mistake and went to a white neighborhood and somebody didn't take it very well and so he was shot and it was not just a mistake. The problem was that after he was shot the person who shot him came out and then made sure that he was shot again and that made the second time but we're lucky or he was lucky that he didn't die. In fact as we speak now he is recuperating in his home. He has left the hospital right now and he's feeling a little bit better but what does that speak to us. It's in America that I wonder who really are the Americans and what level the racism is in America. It's in America that we have everybody else being labeled something about where he comes from is in America we see Mexican Americans. We don't see Mexican UK or Mexican Europeans. It's in America we see African American. It's in America even the people that are indigenous Americans are labeled also who really are the Americans and who are the owners of America that people will have this kind of behavior and it's still existing in the 21st century and it's really really heartbreaking that people who have been there to build America to make it great as great as it is now just because of that color they're still being labeled as the people that should never be associated with. Anytime some of the whites see the black people what comes to their mind is criminality, it's drugs, it's armed robbery, it's killings, it's a lot of other things and they just don't want to mix with them and some of them even feel that they are of the lower species and should never be seen as equals so this thing happened and then we also have seen in a new photo that a 16-year-old Raf Yal has appeared to be able to sit up now on the bench and in the photo that we are seeing on the screen now he's sitting with attorney Lee Merritt according to an Instagram post on Wednesday from an activist and a family spokesperson shown King and they say that his home and looks great. Raf is walking, walking miracle with a head of steel okay I like that that's what King wrote in the post which Merritt reposted had the bullet hit his head a fraction of an inch in any other direction he would probably be dead right now his shadow to be back in court on June 1 we do hear that the shooter has turned himself in and we don't know how that is going to turn out we've seen that there are a lot of other people who killed black Africans or black Americans in in that place and they just got a slap on the wrist and there are people who did lower or smaller or yeah crimes that you would not call you cannot put in the same place with others that they've done for instance the people that killed Floyd in the way black and they did what they did I'm not sure they were going to have sentencing for years they're going to just have live imprisonment or they're going to face other things that are even worse than that while the charges have been filed this remains an active investigation according to the prosecutors in a statement and according to them and I quote we are continuing to work with law enforcement to gather any and all evidence available in this case okay so let's see how it goes we're hoping that the needful will be done but it shouldn't always be that when a black is involved in any crime that is being committed I like the black is the victim people have to carry placards before the law enforcement will have to do what they need to do I mean racism is bad enough but when it is so bad that it has to cost the life of another person is even worse and I don't know why America that preaches equality preaches so many other things and to make them look good will still have things like this happening in that climb and funny enough that is the place we call Sena climbs how sane is a Sena climb I really don't know okay we also have another issue the federal executive council has approved 1.5 trillion Naira road projects across 11 states in some papers it is in billions but here is 1.5 trillion Naira the minister of works and housing Babatundi Fashola has said over 700 kilometers of road spreading across 11 states in the country would soon be completed he disclosed this while briefing state House correspondence on the outcome of the meeting of the federal executive council FEC on Wednesday in Abuja the meeting was presided over by vice president Yamiro Shimbajor Fashola said over 1.5 trillion Naira would be spent on the projects by the Nigerian national petroleum company limited NNPC according to him the states where the roads are cited include a do Delta Kano Kaduna Bernu and Adamawa also the minister of labor and employment to Chris Giger said the council approved the second phase of the electronic Nigeria social insurance trust fund which will enable concessionaries to upgrade infrastructure the sum of 15 billion Naira the minister of state for budget and national planning claims Agba said the FEC has approved the sum of 3.4 billion Naira for the procurement of a surveillance aircraft for the use of the Nigerian custom service and what a lot of people are just wondering is why now why these things are very lofty this money being voted for all these things they are very good but why did they not come up a few a few weeks back a few months back a few years back or something okay was it on the drawing board we've seen in Nigeria that even if even if it's the same party handing over to the next there is no guarantee that there's going to be continuity the next government the next administration coming in will have a very very neck breaking burden or in debt to pay and now that these things are being done did they give the incoming administration room to suggest some things to have input and they suggest only in the decisions that it took now because they are going to be the ones to implement we just saw on the papers today that even the field subsidy removal there's no specific date that has been set and all that so that means no proper plan was done before the announcement was made so now that this money is being voted for all the things that they are going to do how much is the budget how is the next administration going to take it where they're involved in the planning for all this we they have like a less than 40 days to get to that point where they are going to leave this administration that is so on the 29th of May hopefully we're going to have a new administration and this humongous amount of money is being voted to do the projects that we do not know if they are going to come into fruition even the ones that were supposed to be done in by this administration have not been completed right now there's still terrible traffic for instance because work is being done on the lego seabird on expressway that we were promised was going to be completed long before now we do hope that there's not going to be friction we do hope that there's going to be seamless transition into the next government we do hope that the next government will do well to continue with whatever plan that this administration has had we do hope that they were carried along when they were taking all these decisions but there's so much to talk about especially when we get to where we're going to be reviewing the newspaper dailies for today because there's so many things that we are going to see in the papers so in case you didn't have the opportunity to read the papers or you're not on the social media or which is most unlikely anyway but we're going to have analysts that will be looking at those things critically enough to give insight to what is really happening beyond just the headlines once again i'd like to say welcome to the program today and we have another story a trending story we're not taking a break just yet twitter has commenced removal of all legacy verification checkmarks also referred to as badges recall that Elon Musk had mentioned his plan to make twitter have a subscription-based package for users as early as during the acquisition process of the micro blogging platform as at the time of sharing this post thousands of accounts including that of co-founder and former CEO of twitter jack dosi have been impacted we also have the account of somebody like philippo bean who is the special assistant to the vice president on new media who has been impacted as well fortunately someone like philippo bean has what is like the nearest or the best well let it not be like i am trying to advertise it but we have people who have home built home grown if you may things that can replace twitter so maybe it's high time we'll begin to look at home solutions to all the things that we need so we have a macro blogging side which is twitter but we have some others in Nigeria that can also do the job of twitter with a minimum wage of 30 000 naira per month approximately 100 000 sorry 1000 naira a day it will require six days of work to be able to afford twitter blue subscription in Nigeria in fact more than one day six days of work because twitter blue subscription is equivalent to one hours work in the us and uk because of what they earn but it's not the same thing because it's above 6000 naira so if a thousand naira per day that means you're eating into the seventh day to be able to subscribe to twitter and get your blue chip or something to subscribe it costs a total of 6342 naira well 6342.02 naira per month that is 66 302 naira 54 cobble a year that is equivalent to 11 dollars a month and 114.99 dollars a year so nigera strength chart dot com is about the best alternative to twitter like i said and verification of the blue tick is still 100 free so why not we begin to look at home grown solutions to our problems we can also reach the world by using what Nigerians are doing and let's consider you know encouraging people who are Nigerians who can do what we find outside this should not be the case of going to France to buy pizza that can be done in Ojua legba or to buy a car that can be done by innocent motors for instance and all that let's promote our own people well we will just take a short break and when we return we hope to look at the headlines of our dailies and see what can be said about that stay with us


Hello and welcome to the session. My name is Asha and I shall be helping you with the following question which says, in each of the following exercise 10 to 20, find the equation for the LF that satisfies the given condition. 18th is B is equal to 3, C is equal to 4 and centre at the origin and 4 chi on the x axis. So let's start with the solution and here we are given that B is equal to 3, C is equal to 4 and centre is at the origin 4 chi on the x axis. Now here we are given that focus is on the x axis. So this implies that the major axis is along the x axis and thus the standard equation of an LF given by x square upon a square plus y square upon b square is equal to 1 where a is the length of semi minor sorry major axis and B is the length of semi minor axis and for this standard equation the 4 chi is given by plus minus C comma 0 and C which is the distance of focus from the centre is given by a square minus b square. Now here we are given the values of b and c. So I am substituting the value of b and c in this equation let us find out a. So we have C as 4 is equal to root over a square minus b is 3 so we have 3 square. Squaring both sides we have 16 is equal to a square minus 9 or a square is equal to 16 plus 9 which is equal to 25. Therefore we have a square is equal to 25 and b square is b is given to us as 3 so we have 3 square is equal to 9. Now let us substitute a square is equal to 25 and b square is equal to 9 and the standard equation to get the equation of an LF which we are required to find so we have x square upon 25 plus y square upon 9 is equal to 1 as the equation of an LF for a given condition. The answer is the equation of an LF where b is equal to 3, c is equal to 4 and centre is at the original focus, y on the x axis is given by x square upon 25 plus y square upon 9 is equal to 1. So this completes the session hope you have understood it take care and have a good day.