is and we feel that we're here and we have an opportunity to select some of the greatest talent to take a look at this challenge that we have to help give us quite an amazing museum and really tackle this changing of the experience at the Alamo. The heart of this is the management committee which is made up of the city of San Antonio myself, Shoe Scully at the Alamo in Downey which is Jean Powell and Ramona Bass and the general land office which is Hector Vaillet and Brian Preston will be moving this along with the citizens of Israe committee we've committed that the plan will be moving forward and work with the citizens of Israe committee to help inform a lot of the elements of the plan the final approval will come to HDRC of course she will be informing THC on that. Okay, thank you. With the streets closed how is the entry going to be managed and has that been worked out yet have you heard about a limited of maybe three entry points or maybe six during the evening some sort of gates or walls has that been worked out yet or is that further design up? Yeah, there's still more design work to do what I can say is that we don't know what that formal entry looks like because it's part of the museum visitor center design which we hope to begin here very soon. What we know is that it's not going to be a simple doorway or a term style it's obviously what we want is to create a very dramatic sense of arrival to truly orient people it's, I'm using words straight out of the vision value principle our goal is to change that experience that is there today which is really an experience that is lacking a sense of place sense of orientation and so as we move forward with the plan we expect a very a sense of arrival that I think is what we call a formal entry point now the two access points are also there in addition when needed this is about changing the experience for those that are visiting the site and we expect more people to come to the site and so our goals in the design are to make sure that we're meeting what we expect to be an influx of visitors to the site both local and those that are visiting San Antonio so it's difficult to tell you exactly what it looks like but it's about getting people oriented on the site and we can say it's getting quite grand thank you I do have a couple of questions on the lease if the citizens decided that we don't like what the GLO is doing and they all pick up the phone and stop by our council people's offices and say we don't like something about it whatever it is how they're managing it and when the city doesn't like how they're managing it maybe you guys and the city managers say they're just managing whatever what are the potential remedies how does Iroh work out I'll let the city attorney handle that I think we wrote some of those predictions we've included in the lease a pretty robust dispute resolution process what I have found in terms of agreements like this which long term and you have pretty complex issues it's best to build in the dispute resolution process that identifies issues early on the management committee will do that and then there's an elevation process that if issues don't get resolved they get elevated ultimately though there's not agreement we can go to the courts we do have remedies for the city if the GLO is not complying with the lease terms those are depending on what the breach is of the lease the remedies are key to what the ultimate breach of the lease is going up to termination but I will tell you it's a high hurdle to get to termination we hope we never have to get there but it's there and the example I used earlier is for example if the GLO tries to build an amusement park I'm exaggerating obviously we have clearly the right to terminate the leases they're not complying with the elbow plan I noticed in the lease it sounds like the city asked for control or for certain days can that be amended as things can be decided there's other days of significance or there's a in fact we built that in as the flexibility as new days and in fact as based on data obviously we don't know a lot now until it's actually implemented and once we actually get data on entry in terms of timing and everything there's flexibility in there to adjust those thank you speaking of data one of my other questions I know we saw the traffic study in the video but I was wondering was there any studies on the peak pedestrian traffic in front of the animal over the last two and a half three years we've done multiple pedestrian studies direction of access peak hours of access and so we understand today clearly in the summer spring break it's a whole different story than it is maybe out there today so we have a complete picture of the pedestrians and where they're coming and it did inform the plan that you see in front of you okay that's pretty much the base of my question that's important to make sure that we do include the Native American industry that's in the animal and the civil rights issues that we heard today those are also important and you know it looks like everybody in the city cares deeply about the animal and we all have our members so some of the people here today obviously their ancestors and their family has shared blood in other words have more recent memories you know I myself have marched into the parade in front of there and I remember my niece and nephew came and we you know and went in front and took our picture so I can understand the emotional attachment we have to this historic site and I think that's part of the reason we need to treat it as such as historical as I wonder what it would be today if in the like 1800's early 1900's the entire site of the animals treated as it should be instead of sold off in pieces and live sometimes literally picked by brick so I wonder what it would be today that's it thank you Charlie you commissioning understand I appreciate again the passion that's behind what we're doing here today I'm going to just speak about my experiences my family and I enjoy the historical travel I can tell you you've been to Mount Vernon Fort Sumter in Charleston, Gettysburg Pearl Harbor, the National Mall and one of the experiences that we really enjoy is kind of the place setting, the place of arrival we don't have that experience at the Alamo and so when you arrive at it it's really this diminutive building in the middle of downtown and you don't have that sense I think the plan here twice to establish that sense of arrival I think it is very important for what the historical traveler the historical traveler and what I'd like to ask is kind of the you assume itself and we talked about the building but what about the artifacts that's in the building what are those being sports funds are those at risk to not assembling and being able to share the story of the Alamo if we don't proceed with some type of building to exhibit the exhibits can everybody speak to that staff well actually you're speaking to the heart of what the cooperative agreement was all about in 2014 the city began a process on its own to start the Alamo positive and this one mistake came in and asked a partner along with the Alamo and the Alamo and what we see is this is an opportunity to make this one place right now because of the way it is it is subdivided we have different elements of the project so the idea is to yes make sure that we are unifying everything it is part of the guiding principles to make sure that we are being thoughtful about all the elements so that we can begin to tell the story a story that will be institutionalized by a museum and protect the tangible artifacts but also help to recover a lot of the stories as was expressed we want to make sure that we are uncovering all those layers telling all the stories and telling a complete history at the Alamo your testimony today also about the source of funding from the state can you speak to the source of funding both private and public the security of those funds are available and also beyond funding for the maintenance of the Alamo the city of San Antonio has allocated about $38 million towards this project the state of Texas so far has allocated $106 million and the rest will come in $200 million plus from private donations and as you can see the city's investment is $38 million to what we think will be a half a billion dollar investment on the site with incalculable economic benefits to the area to the property itself and to your point about creating a sustainable model that allows us to capture the footprint and run a site that is going to be well funded and last for many years to come because we have taken a look at all the elements that can help capture some of those revenues and resources so that we can express that history thank you very much I am really excited about this I am from Mexico my accent from many other countries as well I am used to going around the world and I think one of the commissioners mentioned this is our chance to show the world the real Alamo you are all very emotional with the Alamo and I feel like that's what we need and how we are we are not giving it the respect it deserves we are going there to get Araspa and take a picture in front of it we are not going inside there is not much to see by building this museum and bringing the original artifacts from there actually making it a central entrance go see it and not only the church and the facade everything else that is around this plaza we are actually going to be able to show more the cemetery being there actually you all have more access saying that you have more close family to the cenotaph you have access to it 24-7 I think we all are on that section and also when I say nobody mentions the torture friendship you are getting with respect that it deserves yes it is very hard to go there and actually take a picture and that represents the mighty commission I would just like to reiterate to the city staff some of them have been here a very late they have been working all day long to the representatives for each of our visitors and to the public they have been here very focused and earnest and articulate in their concerns I just want to make a few comments I am actually a very enthusiastic supporter of the master plan I have some very great concerns about some aspects and unfortunately those are aspects that are sort of beyond our control I think somewhere by zombie or by the dynamics of the city and state law and Texas I understand that is a dynamic that is very delicate and that it has been a very challenging road over time one of my concerns I actually had to do more with the management of the site over time there is some discussion about that and I have read very carefully through the lease agreement and also through the package that was given to us and there are two precedents that were shown in the package one of which I visited but don't have a lot of knowledge about how it is managed the other one I know quite a bit about the management of public forward that is the independence mall and in that case and actually I understand in both cases neither one of those historic sites are managed in a way in which they were anticipated and so I think that we need to be very careful in how we proceed with the implementation of the lease and the plan because sometimes there is unforeseen events going on and it has been mentioned the Secretary of Interior's standards there was ID 4 that was mentioned earlier in the conservation site very well crafted letter but there is also concepts of reversibility that need to be taken into account if you do things that are irreversible what do you do going back to independence mall for a second it came out of the sea beautiful movement the sea started in the 1950s but really didn't get going until the mid 50s and that was a high water mark for urban renewal and in a very hard hand-handed hand-fisted way hundreds of millions were removed from the three blocks of the center of the most historic part of Philadelphia a very narrow interpretation of the site they left only one building other than Independence Hall and the flanking buildings and it was the Quaker's meeting house because it fell within the 18th century narrative of the site that they wanted to have constructed there now I mention that because then in the 2000s something called 9-11 came along and there was a very reactionary attempt to lock down the entire site to help protect it and that's what I got involved in we got to examine things like blast radiuses and backpack bombs and things like that that were pre-arounds to be imagined but also as they were constructing more in Orleans master plan they came across the footings of the slave quarters at the President's house and this happened to coincide with the entrance to the new visitor's center that was envisioned there so I mention these things because when we look at these sites that have complex histories sometimes complex things come up as we dig into them and we've got to be really careful that we're not doing things that are irreversible and so I'm very concerned and unfortunately I'm not so certain what kind of leverage we have on this but very concerned about our swath of buildings being treated in a much more like an urban renewal kind of way just cleared away and we lose an essential portion of the history the continuum of history of the site so I don't have a solution for that I hope maybe we can craft something in our in our motions here that might earnestly implore that the GLO listen to the professional experience of the THC staff and treat those buildings with the property they deserve Thank you My hand Yes, I'm going to share in Davidson the statement that if the state has the property, certain property then the state can charge people for what is now a free area and someone addressed that I'm sorry, can you repeat the question? Yes, sharing Davidson brought up the point that areas around the Palomar are now free and if the state takes ownership they have ownership of it they may decide to have events where people will be charged again they're not taking ownership of the site it's a lease agreement remains the owner of the site and regarding special events I think that that would be up to the museum itself if the state is holding special events on site that's something that they have heard me over but the site itself is always going to remain free I think the question specifically was on 603 and we clarified with the GLO it was drafted to try to address as the councilman said special events or occasional events where there may be parts of the plaza where it would be for a private event we've already talked to the GLO and we'll clarify that in the lease it wasn't intended to be one where there was a fee it was meant to address those situations where you might have a special event or occasion where you might charge a fee thank you could someone put a picture on the screen to show the area which is really under the control of the state and will be closed off during certain hours but the rest of the area will be open to the public I think I may repeat the question you're saying so after hours there's portions that will be closed off their own by the state of Texas can't hear you what of this area that we are considering tonight will always be open to the public the plaza itself will always remain open there the church which currently is shut down at night church and long barracks will be protected overnight and so will the museum now the plaza itself if you look over there you see there's a dotted line almost right up against the long barracks you see the dotted line jogs in a little bit from that little line that's the portion that will be closed off to protect the two existing artifacts everything else in the plaza will be open put something on the pointer up to that and albino please we don't have a laser pointer just use the mouse can you see the mouse you can walk on price well okay so with the pointer on that line are you saying that everything to the so called right is open to the public or not that will be closed that is owned by the state of texas that includes the gardens the long barracks and the church that is correct like it is today so after hours the gardens and long barracks and the church that area essentially is closed down from the public okay and everything to the so called left is open at all times to the public non-museum hours it's completely open during museum hours you have a formal entry but you do always have 24-7 access well as soon as you go into the museum then you can go anywhere on the left hand side that is correct for free you don't have to pay to get into the one entrance that would be open no you don't have to pay thank you junior most of my questions have actually been answered at this stage going through our purview of police agreement and the road closure so at this time I would like to just thank staff for everything they've done this fantastic presentation today and a ton of information actually took quite a while to review and read and understand thank you Gene for your traffic analysis and the moving pictures pretty awesome thank you everyone for coming tonight and speaking and what's in your opinion and your passion for being here my like I said most of my questions have been answered I do have a couple lingering ones one is the lease agreement finalized is that the final language as I said there's one modification we've already talked with GLO but it will be finalized before the council votes on it next week but I would say that what you have in front of you is pretty much the lease with some potential clarifications such as the one on the potential charging of a fee for occasional rents I think that's easy clarification it clearly says that they shall not charge and they shall not allow vendors lease or anything like that correct pretty clear to me and I think I miss part of this conversation but the GLO today currently operates the animal so as we move forward if this plan comes to fruition the way it is operated isn't going to be dramatically changed from the way it's being operated today that is correct what happens when the lease is over I mean it's 100 years from now but what happens oh it is at the end of the lease there is an option to purchase by the GLO it has to be at market price and it has to be approved by the city and if they do not exercise the option to purchase the land goes back to the city it's a lease so not only does the land go back anything that's on it goes back to the city in the process we'll work building the Crocker Building I know there's a lot of questions as to how that's all going to be how that's going to be how the museum will be put in there and those buildings will be re-purposed what is the process for that the outside is going to be left the same and the inside there's going to be some conversation on how to make them fit together because they're different floor plates and architecture and whatnot how is that moving forward the 35 talented respondents to the RFQ that's exactly what we're going to be working with them on what we hope we get is some opportunity to discuss what available technologies can provide some answers but this is about a creative process allowing the talented individuals to process in a thoughtful way we want to do everything we can to incorporate these buildings as part of the design but it's hard for us to give you an answer about how that design is going to be done we don't want to be prescriptive about it I guess the city and the geo-order have input as to what the consultants are coming up with it's going to be kind of a round table kind of discussions on how it all comes we're doing that right now it's going to be a process of short listing of 35 entrance to the RFQ and we'll be discussing that through the existing process the process that's got us here today which is the citizen advisory committee the management committee and the executive committee that have really been about bringing a lot of people together a diverse group of individuals to provide input insight about what we're doing with this entire project that continues we're moving forward together on that we think that this process has been an incredibly thoughtful process that has got us to this point we intend to continue that thank you very much that's all my questions we have a question from Commissioner Wolfe thank you everybody for hanging with us I feel like we're in the home stretch I wanted to say we're getting there but obviously we're all here important to all of us so thank you for hanging in there we've all had a lot of presentations and I think that thank you again for all of the input I think this is a very compassionate, very considerate, very collaborative plan I think we've considered the employers, the employees special interest groups tourists, local school groups residents community groups and all the stakeholders my perspective is about the access and I know we've talked about the street access and managed access the street access I drive 3-4 times a week and I'm always worried about hitting somebody I go very very slow there because people step off that curb it's right there I have no problem closing the street simply because I want it to be a revered space and I don't want us to drive over what should be an honored space on the other hand I take an educator lens because that is my background and understanding that telling a story is a scaffolding experience I do however like most of us I think are conflicted when we talk about barriers and I do oppose a barrier that limits any reasonable access but you have to start somewhere when you're talking about an educational experience again that's the lens that I'm using I want physical conditions that elevate the experience but I think one of the things that we've been briefed on a couple of times is what those barriers may or may not look like or could you explain to us a little bit about some of the considerations of those barriers that have been discussed to this point and that's my point of view Thank you for the question and so as a reminder in May of 2017 we were looking at the glass walls that had barriers and they were from 8 to 14 feet and now we've taken those glass walls down and we do have barriers but we're calling them from railings they have yet to be designed we think they'll be about 42 inches in height around a historic mission plaza and it could be a landscape barrier it could be a metal barrier those have yet to be designed and those will be things that the management committee will be working on throughout the next couple of months and that'll come back to the HRC and Commissioner and Commissioner Peck I did want to add that you're correct that the GLO they do own the church in the long barric and the garden but they contract with the Alamo Trust to manage the actual Alamo just the church in the long barric Thank you very much Mr. Commissioner my comments were and I appreciate the public's input and I appreciate the staff the City and all the commissions and I think it's an outstanding job I did approach this with a very skeptical eye I was concerned about why do I do anything at all and it is as my fellow commissioners have pointed out in all those who travel there's something lost in the experience of visiting the Alamo and I do agree with the comment that the senate has does tell the story because there's not any other place that does tell the story and the reason to move it I think is a very strong one in that it can be relocated and still be respectful and what I didn't like is one of the initial comments that the senate needed to be removed because it was out of scale and I thought that's very much akin to complaining that a flagpole is tall and pointy and for visitors that are there they have nothing other than to do then kind of hang out and walk over to the senate and it's beautiful and I really enjoy it it's one of the things I love about working downtown and I too travel Alamo street almost every day and I walk past there and I talk with people it's a beautiful space and so I think the initiative and the impulse of this is like a change to enhance an experience to tell the story that there is room for improvement here and as my planning Commissioner Kelleport said this development has been a hazard over the years so here's a chance to get it right and do it better and conceptually I was very much skeptical of the access I've been reassured and I've sat through several presentations and I've seen it develop and I've seen those presenting take input and revise and redirect and improve on what has been presented so far this idea that I was opposed to of a single entry point it seemed rather constricting it's a concept of access to an axis where you enter on a church where you enter a site where that is to make a place and to begin an experience and my view of the historic buildings if you walk in front of them you can see just about 8 feet in front of the facade where the walls of the Alamo used to be and my view is if it's too close there's no need to demolish the buildings can be relocated a lot of the buildings on Commerce Street were relocated in 1950s on the street wire the Alamo National Bank was moved 15 feet just with manpower we have much more better technology now so there's things that can be done and I think overall the concept of making this a better place to tell the story is all around well done and I appreciate the efforts Commissioner Brenson Thank you Commissioner everyone for asking these questions as far as what is going on there seems to be a lot of questions not answered we have a lot of questions here today and commenting on some of these things that we have interpretation seems very vague of what is actually being done so I do have a question as far as the transportation study is there also any real data done or anything that we can show community or what we have? Well as we move forward with the plan as you see today you have a concept plan and then when you go from concept you go to schematic and as you do that you take all those studies and put them together and then we come forward with the final plan you combine the pedestrian information with the traffic information the landscape design along the streets and those are the next steps that we will do in the plan and combine all of that information So as you are saying there is still not enough information to say give enough people what they need to know about locking off roads only making a pedestrian even though we are suggesting that and also changing the mobility around the outcome You were asking I thought specifically about pedestrians it is just like all of the plan because the design team hasn't selected the rail it hasn't selected the type of surface in the plaza the type of trees where the trees will go so the exact pedestrian plan the exact sidewalk plans those have not been worked out yet that's the next step in the plan Thank you As far as the lease Thank you that was all As far as the lease is concerned I would like I guess the clarification maybe not just for me but others the year lease I guess what was 25 Do you have a quote there as far as what it is specifically How long the lease is the term of the lease is 50 initial term of 50 years which can be extended for two additional 25 year periods Was there any mention of a third party that I heard earlier about the addition in there After the expiration After the expiration of any term GLO has an option to purchase at market price but again the city has to approve that and at the end of any if they don't extend the lease or at the end of the second term extended term then the lease terminates and the property goes back to the city Thank you Is there still a representative from the conservation society here Susan? Yes Yes As it says in your letter about the third paragraph down equally concerning are the lease terms Could you elaborate on that It says equally concerning on the lease terms which will require all admins to pass through a single entrance term That's Patty's We do have a concern with the single entry And why is that? I think it's managing people I think most of this was done to manage people and you have access I think if people were allowed to go in and you didn't have the one access there but they were allowed to go in then you could roam through the plaza like you can now You still would have the option to go to the museum but there's just the focus on the world class museum for the one entry And as it also says here extensive discussion and design regarding the mission period from 1836 How do you think that would be compromised or not enhanced? I'm sorry That's the last paragraph on your letter Sorry she spedied hers We've been discussing this for some time We really wanted just to be sure There's been so much focus all along about the mission period the battle and not coming forward The plaza has a long history and also the history that we talked about with the Woolworth building that we think is very important Those buildings are important I hate to point back on the buildings but they really are important and it is one of those things that once they're gone they're gone You can redo the streets you have to redo everything but not the building and so much of the buildings and the rest of the plaza has to do with the history So to us it's important not to stick plaque up there and say just what here are the lunch counters but to have the building and have things that represent the rest of the history around the plaza and not just the battle The battle is important but there is so much more in your case as far as what's important as well so that you're able to tell the entire story is important And are you in partnership still with the daughters? No I am a daughter but we are not in partnership and we do stand-along on our statements Alright I believe we have a question down to Gina Bortnaz Mr. Chairman I'd like to follow up on my previous comment I know that there's been a lot of thought and effort and energy put into this design and I appreciate everyone at all I would just like to see a little bit more detail before considering the constant for consensual approval I do have a question about the museum At the on-site meeting recently at the Castle of Trevino you mentioned the possibility of including the Hyatt Garage and I wonder if that's still a consideration Yeah, we're always looking for opportunities and that is something that's ongoing that's not solidified just yet so we hope to see that be a part of the project potentially but it's like any other piece of this project is as people learn more and more about the work that's happening at the Alamo we're seeing more and more workers come in and join us for this potential project I think the conclusion of that facility would take some of the pressure off the demolition of the historic buildings and also the sale down on potentially and I would say we've never stated that our goal in any way is to demolish those buildings whatsoever and incorporate them and it is part of our vision and guiding principles to tell all the stories at the Alamo My apologies to the planning commission and one of the commissioners often made a questioning and I do apologize for that I think we're all getting laid trying to see each other but please do continue and again my apologies Thank you Laura is also asking the questions as far as the community is concerned at Alamo Dixon can you come up please citizen representation of your wife and the daughters and moving them to the senate how is that important to you as far as where it is now to where it will be located what the idea is the senate has in terms of the original agreements between the United States the city designated where it was going to be and it in my viewpoint they made the right decision it is where it should be and I think it should be calculated Thank you very much I'm just in my opinion as well moving this in a time that is almost in my personal kind of life it's like moving the Washington Monument and how the police don't know yet it's not a big deal here in Alamo but it's also talking about moving trees and also walking things yes they are to the right we have a picture up above and it's closed as it is now I would just like a little bit more detail as far as pedestrian safety mobility things that say that's the next step that says if you've already approved something and have sold this lot it's already going forward with something that a lot of information is not being carried over from police to maybe public meetings and also obviously a lot of people in this room have questions thank you for your participation and everything that you all have done here and for sitting this long and doing this I would like to hear more from the community as far as people and all different ages and it's great to have these technical questions but also I'd like to know more technicalities and everything to the specific because there are a lot of loopholes that's kind of first in my actual contest I would just like to remind members of the planning commission that our purview is the street closure tender lease agreement and nothing else so when you're considering for your vote only take those two items into consideration we're not responsible for the senate to have for the other ages it's actually the first three bullets on the agenda and when you're already to make a motion you'll put the agenda back up there so you'll see it we have one more commission on this and comments from the ACRC great thanks everybody for your comments today everybody on both sides I feel like it's very passionate about moving this project in the right direction and the way it's best for the city we've heard a lot of discussion about detail and you know that are very important to move forward historically and as an architect I feel like the comments that have been made about where we are and this process is accurate I mean we are very much on the we're not even to the schematic design yet we're in that conceptual pre-schematic phase where we're trying to uncover all of the problems and we're trying to do our research to get the data where we can make that decision the best design possible I've seen the list of the selected designers that have put their hat in for this project and it's really impressive it's world class people who base their living off of being sensitive to these issues and making decisions that are best for the entire city so I think that says a lot to me about the way that this group is approaching this project and it gives me a little bit of comfort on the next steps and on the details that we can see in the future today we're basically giving them permission to move forward with design on some of these concepts and to kind of cover some of the detail and I think that that's really important the research that we've done regarding the restructuring of the senate staff you know again the parade routes capturing back some of this sacred space for our civilians and for the citizens of San Antonio I think it's critical capturing that place and making it a place you know again it's not captured it's not even not by the city it's becoming its own place again and I think that's really important so I thank you all for your comments it's made an impression on me to get to the next round of these discussions and to ask more questions and to be very sensitive to the things that you guys are wanting more information on and more data on so I just wanted to say thank you to the commissioners as well thank you thank you I want to thank everyone who's here to stay so long and committed to this I appreciate everyone's comments I especially want to thank staff and everyone that's been involved I'm sure it wasn't just a couple of years in the making I'm sure it was several years in the making and I appreciate everyone's input and all of the commissioners as well I have a question for I guess the city attorney with respect to the lease terms I assume a defined term of animal plan will be its intent is as amended correct I assume the animal plan consists of construction plans and designs that will come later on correct I mean it's based on the current animal plan but it does envision that that animal plan will evolve as the details are added on once we get into past concept and into the studies and design elements it does allow for that flexibility okay and I assume you all may have discussed this or at least documented this that neither I don't want to say neither the city but the GLO will claim any kind of sovereign immunity from any breaches or damages against the GLO no that's why it's structured as a lease that's a good question I'm not sure it is a lease Commissioner Garcia can we bring the slide up with the I guess the after hours access points I have a little question of Commissioner Cosh just was asking so the dash line represents what area would be closed out to the public after hours and I can totally understand I wanted to protect the animal and the long variants and we've already heard the story of the rock star doing things doing there but how close and how will we be able to still experience those buildings and are we going to still be able to enjoy the little photographs or is it a case where you don't have to be tipping tone over a privacy fence and that kind of thing? No in fact it's pretty much what you experienced today and so the idea is to make sure that the artifacts which are going to be undergoing a very significant amount of rehabilitation study next month that is a critical part of this plan currently the site the church and long variants are protected at night people can walk up take a picture and that will exist in this plan as well so that line basically represents essentially what is there today Okay because it looks like it's quite a bit of weight in the chapel and it's been a while since so that's why I'm kind of wondering It's right up against the long variants It's right up against the long variants but I'm just saying on the chapel portion the postcard version of the Alamo I notice there's quite a bit of distance There's a long piece that's there and we can I think we can demonstrate that you're pretty much right there right in front of the church but that as close as people can So I'm going to take the question Excuse me Can you today stand at night in front of the church or you have to go where the lawn I can't step on the lawn today but can you go past that point to the door Not at night You can't do that at night You have to stand with the lawn on your back and the church in the back and the distance of the door and the mess Thank you Walk up the door Now if you can Thank you One question on actions but it still seems to be hard for others I understand during museum hours we'll have that one access As I'm speaking out loud it does make sense again that you get the story and you go to the middle and go to the end and so we're directing and we're unlike again in Boston unlike the freedom fair we start anywhere and I'm kind of lost and I'm not getting a story like it probably should have but so I think that's our purpose and intent If we do get the numbers and the crowd and we do see people waiting is that not an easy fix in the future to add an additional access or two or three because we already do have additional access points after hours Yes, again it's also outlining the lease in terms of the goal of online is to not have any weight loss I mean that is not part of the plan and certainly not part of the successful direction of the museum So what we intend to do is create a formal entry that is robust that is going to address all those concerns that are going to be doing all the studies necessary working with the preeminent design team to help address those issues We have built in two additional access points we feel that those are definitely enough of course around the entire site I mean it's quite porous outside the museum First I'd like to thank everybody for being here I'll be real brief I'd like to specifically thank the staff for keeping the commissioners very well informed on this in the weeks prior and answering many of our questions ahead of this so a lot of what's happening here are reiterating the questions and I have one very specific question that hasn't come up and that has to do with the Paseo del Alamo and any structures that would be associated with the visitor center and the museum that would occur over the Paseo del Alamo that piece of property and would call them the first two of these here so you isn't correct Well it's a combination of both because we anticipate using the museum slash visitor center as a way to connect us down to the river level and so it is it's kind of a combination of two That would likely be an element that we would have a chance to comment on That is correct I would like, I mean this is like our co-commissioner this is the beginning of a very good decision I implore you all to involve your next generation you're all talking about who you descend from and I don't see any young person that are talking on you or like as the next generation which will be the generation that actually enjoys this so I don't want to make an instance I just wanted to tell you They got school They know where they come from They know the stories They don't know where they come from Okay No further questions from the Planning Commission I guess at this point in time I will close the public hearing from the Planning Commission portion of this meeting I said it earlier and I just want to reiterate that while I'm getting ready to ask for a motion on this item so while you're considering how you're going to vote please remember that you're only voting on the cat if you could put it up you're only voting on the closure the repurposing of the road and the lease agreement the rest of the stuff that we discussed today is not going to the Planning Commission to base your vote on that Some motion do I have to read off the reader Yes if you could Question 2 Approve the closing, vacating and abandoning sections of right away located on Alamo Street Alamo Plaza and Houston Street The restriction of right away located on Alamo Plaza Alamo Street, Blum Street Crockett Street and East Houston Street Pedestrian and emergency vehicle use only The execution of a master lease agreement with the Texas General Land Office for Property Located in the Historic Alamo Mission Bookprint and Property Required for the Development and Management of the proposed Alamo Museum Conceptual Approval of the Treatment That's all I will second the motion Okay, so we have a motion for approval by Commissioner Gonzalez We have a second by Commissioner Christopher Garcia Commissioner Cedarola Yes Commissioner Gonzalez Yes Commissioner Christopher Garcia Yes Commissioner Zuna Yes Commissioner Kostik I think we have is fine I still have concerns about the lease agreement and what concerns me the most is there's no assurance that those three commercial buildings will be preserved That's right So there's no discussion, we just need to know whether you abstain, yes or no I want you to put down why I'm abstaining, thank you Commissioner Brunson Chairwoman Brunson Close the HDRC portion and we will be seeking a motion Mr. Chairman I move to conceptually approve the treatment of the historic Mission San Antonio de Vallejo Plaza site and general design concepts to conceptually approve the treatment of public garadaway including Eastern Street to the East and the last historic Mission Bookprint and Crawford Street, Bloom Street and the last historic Mission Bookprint to conceptually approve the alterations to the percentage of Alamo and Maverick block areas to include the new street level connection to the Soya Street and alterations to the torture friendship area to include a new connection to the river wall and the final approval to dismantle, repair and reassemble the Santa Fe in Alamo Plaza at the approximate location of the existing landscape and the second commissioners will be a role called Commissioner Fish Commissioner Wolfe Commissioner Bustamante Commissioner Carpenter Commissioner Group Commissioner Bowman Commissioner Lafoun Commissioner Vargas Commissioner Borrino Borrino, I'm sorry, Borrino That's okay because my students from South Texas are going to be Borrino and I'm getting used to it So anyway, I am going to go Yes, Mr. Chairman prior to you all adjourned I would like to move for a resolution I would like to move for a resolution that it be resolved that as the river building blocks and palace theater are historically important and necessary to keep understanding of Alamo Plaza is the sense of the commission that these buildings should be preserved at Alamo Plaza in the design of the river motion in a second There's always a favor sitting by Mr. Chairman as opposed to saying so then motion passed Mr. Chairman, please refrain from talking there's still meeting going on Excuse me Committee members, the resolution which is put forth is not agenda it isn't something that you can make a motion for and actually pass You can I think you've made it very clear that you want that entry into the minutes and that can be captured that way Thank you Okay at this point is 9.43 and I am closing the planning commission portion of this meeting and I am closing the commission motion we are adjourned


How's it going everyone Caleb here with Leighton sports cards next night? We have a three-box prism football break number 39 random team style Launch the link in the chat for you for the results. Let's get right to it. Thanks again so much for joining Like I said guys personals are full likely overfill Sam will begin as many done as he likely as he possibly can tonight Yeah, he'll be he'll be grinding through him for you guys Palmer tremble.  There to 225 and Matt Ryan green scope auto for the Atlanta falcons to 75 There you go 75 Josh was out so you there. Don't join Randy and Vaughn in the band club Panic time says Mike. I know that's a lie Tony hyper on the James white hype Jalen hurts. I know that's just a straight line Yeah, Mike is not Zach Wilson base rookie there he is Jets Dio orange James Harrison the 249 Jalen waddle nice purple power to 49 boom Great card What a start to the break What a start to the break there you go dolphins nice waddle the 49 It was close, I know it was close Aziz Adafi Another purple power this time. It's miles Garrett grounds To what break Proplexer base cards, I think they're semi fohoco the world series more recently Jalen dart in there to 99 bucks Silver Devonte Adams all out sheep shots Vaughn sheep shots Sheep shots That's fine Dazz Amonra, St. Brown We got a Jordan booked Brooks there red wave the 149 and a silver Jimmy G. Here we go. Here we go Kevin Byard hunter long Kyle Pitts base Big Ben there to 199 and a silver Jolt Isman Whatever like you know what I mean. Yeah, it's like so long ago now T law on the base How about a manga Kyler Murray boom Wow, what did I say? You did call that one That's all Sam on the call out there Vaughn B. Vaughn Wow nice to me How about that Vaughn good job Vaughn gray one will maggot good stuff fireworks delve and cook Vaughn B What a hit what a hit Niko Collins on the hyper to 175 silver Lamar Right Joshua Yes, they yep Ian book scour neck To 225 Marshall Falk any merchant T law Yeah Some cool stuff just a couple of break spots Cornell Paul Jared Dopes power of breaks 275 Mark Brunel and a silver Jalen waddle. There he is One pack guys two boxes to go Peyton Turner assente Samuel It's a purple Jordan Lewis Purple the 125 Derek Henry brilliance Yeah, this has been a waddle loaded break as well. Yeah, wait who made it over your dawn Joshua You're done not starting the all-star game I Think it's showing right Felton, I'm pretty sure it is Tyler Hague be there on the purple cracked ice to 225 Josh Allen brilliance Yeah, it's just because of his pitching as well. There's no way. Oh, Tony's not gonna start the all-star game He's gonna win the MVP Chris Evans Phillips orange Andy Dalton the 249 and a silver rookie auto of Ian book Nice one there. I don't know. I think he'll still win the MVP. Maybe he could I could be wrong Stokes Micah Parsons Chase Claypool for the Steelers to 25 on the Navy digital camo and a hype Justin Herbert's I Hear you've gone. Yeah, just as like a hitter Marshall jr. There we got Elijah Mitchell on the hyper Silver Blake Martinez I Hear you phone his pitching just is you know, it adds so much to his value Jalen waddle on the base rookie Morrig We got a purple Marquise Colston to 125 silver Curtis Martin Trace sermon And Jalen camp red wave Ronald Jones to 149 silver Adam Thielen. That's what I mean Vaughn. Yeah, it does It does people want to see him in the all-star game. Yeah, Seth Williams Ty Hilton that time to 199 and a break CD is he is He is kind of the face of the league in some if you ask some people that is gain. Well Herbert's Spencer. Yes, and a Pete Warner to 225 Jordan Lewis silver And guys, thanks again so much remember we are all sold out this evening really appreciate that first her quity pay Greg Russo purple cracked iced area slay and Fireworks Aaron Jones. Hey, he's Invicta What's that six? Look at these characters coming in, right? Hey, he's Invicta. How are you? No, I'm a Davis Ambrie Thomas Forest don't know he's not forest Montez sweat to 99 silver Adolfi away Yeah, I know some Victor. I know Yeah, he did have the thunder for two of them. It's up six How's it going six? I'm already Rogers count trash base Vernon Hargraves hyper to 175 and emergent Sri Lantz Okay, see twice one giddy Yeah, I know I know Jonu Smith Shuba to real cox to 60 and silver TJ who Schminzata auto Here he is Bengals. I didn't collect boxes today Caleb gathered the boxes today. I did not touch any box. I did not get any box from the back. So all of your Frustrations Caleb. Oh, no. Oh, no Well, good thing you didn't smell my name, right? So we're all good We're all good Good luck everyone. Hey, thanks six. I'm in the clear. He said Lane we got a one-of-one of Vonte Maddox What was the other big actual hit? Oh, we just got a manga Kyler Murray to 249 Elvin Kamara Ridley Yeah, I don't even know how you came up with that you must have been really typing getting out your frustration Typing was absolutely going at it Cornell Powell semi Fajoco there on the crack dice to 99 and a silver taste of hill auto Saints You got both the QBs Plus one breaker haste At times they can be pretty swift. Yes, Peyton Turner 75 Devonte Parker emergent Mack Jones Rip a lot of base heavy stuff on gaming Pulled Zach Wilson champ ticket contenders out of the 49. Yeah, that was nice out of the contenders mixer Well, I mean to be fair Lane, it's an avante max, but it's a one-of-one, but it's just not the player, you know Paramin so hype hyper pyramid to 175 silver auto Sri Lans There you go Is that good enough for you Lane? 49ers Congrats John P You go John, let's go man.  You're right Tony Franks Charles Woodson to 225 and a hyper or excuse me a purple power fireworks Justin Herbert's to 49 purple power there nice one Take that on the purple power. I'm still financially recovering from the one-on-one Raven Zach Wilson Dio, Noah Gray there to 199 Silver Jerry Judy. Here we go. Here we go Daniel Jones Aziz and Adafi Jake the snake to 249 Silver Russell Wilson There he is Yes, KP, but it might be a little bit difficult on that one because there were still about half colors So, I don't know exactly how that one's gonna go over, but yes, KP That's kind of what I mentioned in the video as well step on digs there on the cracked ice to 99 silver Pat Pete's It was a one-of-one Ray Lewis at Reed Ray Lewis shield at Reed and Jamal Lewis laundry tag with Wallace six here funny Dazz Amon rubbys Stuck to it hype Jerry Judy 15 Yeah, that's your five dollars is Yeah, yeah Jarvis Landry Hunter long Kyle Pitts on the base Quitty pay orange to 249 and silver Kaleis Campbell Sam Croft of cheese on that card Geez bands one-of-one Shelly Avanti Maddox to 149 new recruits Najee Mike Vic Ian book teal a base There he is James white to 225 and a silver deserts Patrick. Thank you all. Let's do a quick recap here appreciate very much That's number 39 three boxer pick your excuse me random team prism Silver Taysum Hill TJ who spins up in book and Matt Ryan to 75 on the autos Magdottos Tre Lantz silver Jalen waddle the 49 and the manga Kyler Murray Appreciate it guys. Thanks again so much. Hope you enjoyed the break flawless up the next this evening


What's up guys and welcome to trendy updates up our SPM birds now onto the trending news today is Michael Magoha who is the son of the late former CES George Magoha and of course he did pay a very beautiful tribute to his father and the lessons that he learned from his father kwebun takua na pitiya this lessons that he said that his father taught him with all his 36 years because Michael is 36 years now nteza kupiti aijambola kwanza mbalo Michael alieza kusema is his father was always a phone call away and this means when he needed him or wanted his assistance he was always there that means George Magoha was always there for his family and he says it doesn't matter whether he was a CES whether he was a surgeon he was always there na ilo nijambola mbalo Michael alieza kutadya kusuba bayake of course anasema kuna oto aneza kumuliza how do you handle your father is very strict we also the late professor George Magoha was a non-nansens napundo Michael alieza kusema he always saw a happy man a happy person nini mkimona pale yukom kali sana ieya li kwa naona babake was a very happy person and of course Michael was getting a little bit you know emotional during this attribute session lakin alieza kua sure watu that don't worry amuke amuke and that is what he kept on saying and lesson number two that he learned from his father is family is the most important thing you never know when you have a time na naeza kusema ya kwanba babake alijua hilo and that is why he was able to spend time with his family always he knew it na kama mna jua ya kwanba professor george magoha alieza kuita bibi mtoto na bibi amtutua ke during his last moment and of course had a conversation with him and told them that he this time is over alafudembo latatu ambalo micho ameza kusema he learned from his father is he always did what he had to do of course he was a solution solver and we saw that even when he was a professor of ncs of education tulieza kuna that he was indeed a solution solver and he says that is what his dad did he did what he had to do of course and he says that he was waiting for his retire ya nini kitu ambacho babake alijua hilo liza ah when am i going to retire na naeza kusema that every time akima liza kazi moja he gets appointed on the other so his retirement really got never really get to come quite early of course he says that his father wanted him to know that he is the standard and i used to always he wanted he is him to know he says that his father wanted him to know that he is the standard and he should never compare himself to anyone and this is something micho says that he has always lived by kwaivu micho alene liya kusema kitu ambacho ataeza kukimis or rather just luck in his life is the hope that his father was bringing because he was the real hope in his life he always had something to look up to and talk to every single time and they were very close according to micho magoha of course anaeza pio kumalizia palia kisema he always spent time with his mentees yani profesor the late always spent time with people ambaya li kua meza kusa kua sa idea no he says be human and spend time with people that is what he said and clearly you can see he was a good you know a person that spent time with his family as well and also the people that he used to mentor and of course the son of george magoha micho during his tibit has been able to say to honor his father's george magoha memory is keep it simple and do what you are supposed to do when you are supposed to do it very simple and that is what we are going to be learning from the late profesor george magoha according to his son micho magoha of course after that he thanked the people and of course viewing later he hopes to make friends with people who see them who came to see them send their father and that was it from micho's tribut and we wish the family all the very best as they go through this hard time from right here from espion bars we say rest in peace profesor george magoha


Hello all welcome to the problem-solving session on important topics this particular session is basically meant for the J main and some J advance concepts So those who have joined in the chat Those who have joined in the session, please type in your names in the chat box Hello all good morning So without much delay, let us get started with the first problem of the day So here we have a question if one lies between the roots of this equation and Box x represents the greatest integer less than equal to x then the greatest integer function of 4 mod x by mod x square plus 16 whole to the power of m is equal to Is equal to which of the following options? So all good morning to you all please feel free to type in your response in the chat box Hello, Dipanjini Yes, guys any response? No idea All right So guys first of all if you look at this quadratic expression this quality expression has got the coefficient of y square as 1 That means it is a graph of a parabola which opens upwards Okay, it opens upwards Okay, and one lies between the roots. So if one lies between the roots Let's say x y equal to one lies between the roots It means the value of this function. Let's say I call this as y.  Can you see the screen now?  How does it help us? Now all of these quantities that you see that is x mod x square 16 etc. These are all positive quantities. These are all positive quantities. So can I say arithmetic mean? greater than geometric mean if I apply I can say x square mod x square plus 16 by 2 would be greater than equal to 16 mod x square under root right Which means mod x square plus 16 would be greater than 4 mod x which implies 4 mod x by x square mod x square plus 16 will be less than equal to half Will be less than equal to half, right? Now if this is less than equal to half We are also aware that this will this will be a positive term as well. That means it will lie somewhere between 0 and half correct and If I raise it by a power which is greater than 2 If I raise both sides with a power which is greater than 2 Okay, then can I say this term this term would be still Lying somewhere between 0 and half because any fraction if you raise to a power which is greater than 1 It will still become smaller That means gif of this Gif of this expression would always be equal to 0 because it's a value which is somewhere between 0 and half Is that clear So of course Shruti was correct. She was the first one to answer this Option a will be correct in this case again, this has to strike to you this has to strike to you and How does it strike to you the presence of 16 and 4? mod x square and mod x Is that clear any question regarding this? Alright, so moving on to the second question Second question says the pair of state lines joining origin to the point of intersection of these two circles Yes, guys Any progress made on this? So you would have all learned the process of homogenization So homogenization is the process where let's say you have been given any curve and there's any line and You want to find out the pair of straight lines connecting this with the origin Okay, so when you want to find the pair of these two straight lines connecting the point of intersection of two curves by a line Okay, so here the question is find the pair of straight line joining origin to the points of intersection of these two circles So can I say the point of interest the line of intersection? The the line connecting the points of intersection of these two circles would be its common chord correct, so What are the equation of a common chord of? Circle whose equation is s dash equal to 0 and s double dash equal to 0 You can I say common chord will be nothing but s dash minus s double dash equal to 0 correct So when you subtract these two equations you will end up getting two gx plus fi To gx plus fi equal to minus of a square is Equal to minus of a square correct So let's say this is our line to gx plus Fy is equal to minus of a square right, and let us homogenize this with the Equation of the circle x square plus y square is equal to a square Okay So what I'll do next is I'll write a square into One square Okay, and instead of one square. I will write two gx plus two fy by Minus a square guys. Can you see the screen? Can you see the screen now? This which is four times gx plus gx plus fy Whole square by a to the power four Okay So when I replace it back over here what I will get is x square plus y square is equal to a square times four gx plus fy square By a to the power four So a square and it this will get cancelled off and you can simplify it as a square Can you see now? Okay, so finally this is what we get which is actually a square X square plus y square minus four gx plus fy whole square equal to zero Which is actually your option number B, which is correct. Sorry because of the constant power cut and all You may be facing some problem right now, but I think it's really fine in some time Right. So guys, please remember the concept of homogenization which actually helps you to find the Equation of the pair of lines connecting the intersection of a line and a curve of second-degree equation Homogenization doesn't work if the curve is having a General equation higher than degree two. So let's move on to the Third question today This question has been picked up from a 3d geometry the equation of a plane through the intersection of these two planes and parallel to this line So this is the Unsymmetrical or you can call it as asymmetrical form of the equation of a line. So when two planes are given basically the The line formed by the intersection of these two planes is written as the equation of two separate planes Which is called the asymmetrical form option C What about others? All right, so I think it's the easy question So a plane passing through the Intersection of these two planes and parallel to this line Please guys note that when y is zero and x is zero. It's saying that it's your x-axis right So So the equation of the desired plane will be this Now the equation is the equation of this plane is giving you a family member that we are looking for which is parallel to the x-axis That means the direction cosines of this plane directed direction cosines of the Norman to this plane will be Perpendicular to the direction cosines of x-axis So it's something like this. This is your plane and this is your x-axis Okay, so the Norman from the plane will be perpendicular to the x-axis so First of all grouping the terms containing Now we have one into a plus lambda a dash Plus zero into b plus lambda b dash Plus zero into c plus lambda c dash should be equal to zero Which means a plus lambda a dash is equal to zero, which means lambda comes out to be minus a by a dash Right, is that fine guys? Is this clear? So putting these values over here, why is it giving me zero everywhere and parallel to this line? Okay Lambda is correct guys, right? So when you put it back over here, I'll get the equation as ax plus by plus cz plus d Minus a by a dash a dash X b dash y Yes, yes, yes, that's what I'm wondering why there's no extra Yeah So you would realize that when you multiply with a dash throughout you will be getting something like this So why term will a x-dash term will totally vanish. You'll have a dash b minus a b dash Y plus z term will become a dash c minus a c dash Plus a dash d minus a d dash equal to zero So I think which option is matching with this Option number c is matching with this option number c is correct. So guys, let's move on to the fourth question Shweta, it is not telling you it is greater than that. It is telling you it is greater than equal to that Please read the question carefully. All right, so let's check here again as You rightly said this term Should always be greater than equal to this right So W plus x plus y plus z will always be greater than four times W x y z to the power of one by four Today's whole side to the power of four So it'll become two fifty six W x y z Now here it is the opposite way round. So here it is given. This is greater than equal to this. So This will only be possible if the equality holds true Right and aim will be equal to GM only when the quantities are all equal That means W x y z will all be equal to each other In other words if I use this equation If I use this equation, I will get 815 24 Let's say x or y or w whatever you want to take. This is equal to 24 So each one of them is going to be one. So w equal to x plus equal to y equal to z will all be equal to one Correct. Now using this you have to construct this new equation which of course will be one plus one which is two t square x into y will be again one t and And under root of four, which is two equal to zero Okay, and I have to find the nature of the roots of this equation So the nature of the roots of the equation will have to find the discriminant which is b square minus four ac Which is one minus four into two into two which is definitely negative Which means? Which means this particular equation has imaginary roots So option C is correct over here. Is that fine guys? So let us move on to the next question, which is the fixed question Alright, so Shweta said one Kushal says four Anybody else? Kushal, can you send me the snapshot of your working on my personal chat? So we have a parabola over here. Let's say I draw this parabola Y square is equal to 4x and a chord is drawn from a point P 1 comma t Okay, so which cuts the parabola at points a and b and it's given to us that P a into bb is 3 mod t Then we have to find the maximum value of it So what I will do is I will use the distance form of the line. So let's say This is at a distance of r from a P So I can write it as x minus 1 by cos theta Is equal to y minus t by sine theta is equal to r Okay So I can write clearly x as r cos theta plus 1 and y as r sine theta plus t Now since x and y that is this point x and y would lie on the parabola This would satisfy the equation of the parabola Y square is equal to 4x right So Y square Equal to 4x Y square is equal to 4x So let me simplify this it gives you r square sine square theta plus 2rt sine theta plus t square is Equal to 4r cos theta plus 4 which is going to be r square sine square theta plus r times 2t sine theta Minus 4 cos theta Plus t square minus 4 equal to 0 now we know for sure that there are two values of r possible So one will be let's say r1 and the other one will be let's say r2 So r1 and r2 would be the roots of this equation. So the roots of this equation would be r1 and r2 So the product of the two roots would be nothing but t square by 4 minus sine square theta And we'll take a mod over here. It just in case, you know, this becomes negative And this is equal to 3 mod t This is equal to 3 mod t which means This expression is equal to mod of sine square theta and we all know mod of sine square theta will be less than zero Sorry, it will be less than one So this expression will always be less than equal to okay Which means mod of t square minus 4 will always be less than equal to 3 mod t so we can write this as This and it is factorizable as so t lies between minus 1 and 4 T lies between minus 1 and 4 So if t lies between minus 1 and 4, the maximum value of t will be 4 So the maximum value of t will be 4. So yes, Kushal was correct Any question with respect to this guys? Please let me know. Is it clear? Please type CLR If it is clear. So let's move on to the next question That's question number 6 Sure, I'll go over the solution once again See first of all, what did I do is I use the distance form of the equation of a line? So let's say a line passing through P has the equation x minus 1 by cos theta y minus t by sine theta equal to r This is called the distance form of a line. This is called the distance form of a line. Okay So I've got my x and y in terms of theta r and t and then I use the fact that x and y would be these meeting points, right? So that would satisfy this parabola So when I got When I substituted x and y in the equation of a parabola, I got a quadratic in R and This quadratic in R has roots r1 and r2 Correct. What is given to us is pA into pB. pA into bB is actually r1 into r2 That is the product of the roots. Product of the root is C by A. This is your A This is your C So C by A. C by A will be this t square by 4 by sine square theta. That will be equal to 3 mod t Then I found sine square theta a mod is equal to this and we all know sine square theta The greatest value is 1. So this will be always be less than 1 I got an inequality. I solved the inequality and I got the maximum value of t as 4 Is it clear to you Shruti now? It's okay. No problem. Second option. Okay. What about others? Okay, option a Okay, anybody else I need at least okay psi s and d All right, so let's discuss this First of all, we need to find out the integral 0 to pi by 2 So for that you divide by cos square both the sides So we'll have secant square x dx and we'll have a square a b square tan square x And now take your tan x st So it becomes 0 to infinity dT by a square plus b square t square Taking your tan x st So secant square x dx will become dt So this will become 1 by b square 0 to infinity dt by t square a square by b square So this will be 1 by a 1 by a tan inverse of t by a okay It's going to be 1 by a b and this is going to be when you put the limits This is going to be pi by 2. So that's pi by 2 a b So pi by 2 a b is given to you as pi by 16, which means a b is equal to 8 Which means a b is equal to 8 Now, we know the minimum value of this is minus under root a square plus b square. Okay So a square plus b square by 2 will always be greater than under root of a b That means a square plus b square by 2 will always be greater than under root of 8 Sorry under root of a square b square. Yeah, sorry. So that will become Just root 8. Okay. So I can say a square plus b square will always be greater than 16 So under root of this will always be greater than this So a square plus b square under root will always be greater than 4. So the minimum value of this will be Minus under root a square plus b square, which is minus of 4. So which is going to be this So your option number a becomes correct So only Shweta gave the right answer over here. So guys read the question very very carefully I think this was an easy question. However, I should not have wasted time doing all these things as a serious Esperance, you are supposed to remember the result of this 5 by 2 a b Because this is so common integral that comes in your school exam as well. Is that fine any questions? All right, so I'll move on to the next question then question number seven any idea guys It's given that f of x is a quadratic expression x square minus a x plus b a is an odd positive integer and the roots of this equation are two distinct prime numbers If a plus b is 35 find the value of this expression Yeah, it's an integer. The answer will be an integer, but it's not an integer type All right, so let's discuss this A is an odd positive integer and the roots of this are two distinct prime numbers Okay, so let's say the two prime numbers are p and q So some of the root should be equal to a Correct and since these two are prime numbers These two are prime numbers and a is coming out to be odd Now prime numbers are normally known to be odd Right, but two odd numbers will never add to give you an odd number Correct, but two odd numbers will never add to give you an odd number Correct that means one of the prime numbers have to be even and the only even prime number is two correct The only even prime number is right So if one of the roots is two I Can always put this in two so f2 would be equal to zero which implies four minus two a plus b should be equal to zero That means two a minus b should be equal to four and a plus b is equal to 35 So three a is 39. So a is 13 So if a is 13 b has to be 22 correct, that means the quadratic expression f of x is x square minus 13 x Plus 22 equal to zero not equal to zero equal. This is equal to this Okay, so you can also factorize this as x minus 2 into x x plus 2 into x minus No, I don't think so it will be factorizable. Yeah minus 2 and minus 11 So this will be x minus 2 and x minus 11 This is your f of x correct Now what is f1? So let's figure it out f1 f1 would be 1 minus 2 by 1 minus 11 which is going to be minus 1 into minus 10, which is 10 F2 would be zero itself Similarly f3 would come out to be or you can treat this as a summation process You can treat this as a summation process because we cannot sit and literally count them up so I Can treat this as if you are trying to sum up You're trying to sum up x square minus 13 x plus 22 summation from x equal to 1 till 10 which is going to be N into n plus 1 into 2 n plus 1 which is by 6 minus 13 into Summation of this will be 10 into 11 by 2 plus 22 into 10 Okay, this multiplied with f of 10. So let me calculate this first. So this will be 2 7 This 5 so is 35 into 5 35 385 minus 55 into 11 in fact, I can simplify this here itself This will be 55 into 7. This will be 55 into 13 and this will be 55 into 4 so that will give you 55 into 7 plus 4 minus 13 which is going to be minus of 55 into minus of 2 which is minus 110 and what will be f of 10 f of 10 will be 10 minus 2 by 10 minus 1 11 which is going to be again minus of 1 minus of 8 right so my result would be Minus 110 into minus 8 which is plus 880 Which is plus 880. So absolutely correct. So those who answer 880. I think the first one to answer it was Maishnavi So moving on So this is a question which has been picked up from properties of triangles If O is the circum circle circum center of the triangle ABC and R1 R2 R3 are the radii of the circum circles of the triangle O, B, C, O, C, A and O, A, B respectively Then we have to find this expression Yes, any response from anyone? Not getting Okay So you guys first let us understand. Let's say this is a circle and we have these sites as a BNC okay The question is R1 is the radius of the circum circle of O, B, C So O, B, C, what is that? What is the formula for circum circles? Circum circle formula is ABC by 4 delta right So now let us under let us consider that let the area of Triangle O, B, C, B, delta 1 Okay So can I say R1 will be equal to ABC ABC for this will be R square a by 4 delta 1 Okay, that means a by R1 a by R1 will be 4 delta 1 by R2 Correct Similarly, similarly I can say B by R2 will be what? 4 delta 2 by R square and C by R3 will be 4 delta 3 by R square Okay Now when you add them that is a by R1, B by R2, C by R3 You are adding 4 R square delta 1 plus delta 2 plus delta 3 and The sum of all these delta is actually delta so it becomes 4 delta by R square right and again Delta is what? Delta is ABC by 4R So place it over here. So 4 times ABC by 4R into R square 4 4 gets cancelled You get ABC by R cube which is option number B is correct Option number B is correct guys properties of triangle you need to visit again I think the formulas have slipped out of your mind Okay, however, they're very easy. This is very easy concept. So now we can take a small break over here Let's have a small break and On the other side of the break We'll resume with more problems and we'll resume at 1145 a.m. All right, so let's resume back. Yeah, so let's take up this problem the ninth problem. Yes, guys Any response? Yeah, any response guys, please feel free to type it in the chat box This is a basic question on limits that you can expect See I use your common sense definitely if X is sending to 1 by alpha, you know that your denominator is going to be 0 right and Looking at your options. Your answer is not infinity means your numerator should also be 0 that means somehow This cubic equation should have one of its roots as 1 by alpha correct now clearly the product clearly you can see that if you put X as minus 1 it's going to be Satisfying it right it's going to be satisfying it. So other route is going to be minus 1 as well right and The product of the root is minus b by a c by minus d by a so let's say the other root is unknown to me Let's say beta.  Can you take it from here since we have known the roots for this now? So the roots are known for this Can you proceed from here on all right? So alpha is already given to us as the root Okay, so don't need to waste time during in doing this So this was not necessary So assume like this question this part of the question was not necessary So this let's say even if it is not given to you in the question You should be still be able to solve it.  Yes option number D is correct So option number D becomes correct overlay. Okay guys. I was expecting that he would solve these kind of problems And these are basic concepts which come out from limits, okay Moving on to the next question question number 10 for the day Just a hint you can use integration by parts over here. This is easy to integrate you can call this as V You can call this as you Minus one. Okay. No minus one is not the answer. Yeah That's not real. Yeah, that's not real for x greater than pi by 4. All right, so let's try this problem out I'll apply integration by parts over here Treating this as my u And treating this as my v.  I'll just write it as sine x Plus 1 by 2 root cos x cos 2x into sine 2x Right the rest of the parts. I'll copy it as such now. Let us focus on simplifying this part So this will become integration of cot x I will have sine x a root of cos 2x Plus sine 2x by Cos x under root of cos 2x Whole into under root of cos 2x no doubt so far. So This time I'm copying as such So next what I'll do I'll write this as cos x by sine x. So that becomes integral of Cos x under root of cos 2x and this is sine 2 sine x Cos x so when it multiplies to Cos x by sine x it becomes 2 cos square x So here I'll get Minus 2 cos square x How can you further simplify this any idea? This is actually a huge problem. It would easily take around 10 to 15 minutes add and subtract one in the numerator, okay? How does that help? We can use integration by parts again in the third last step I think from here on we can simplify this we have to just simplify and try to try to bring out some terms Which are you know that can be integrable. So Okay, so let's see what happens when we add and subtract one. Okay, so Shweta is suggesting to add and subtract one to cos square x becomes cos 2x. Okay, so let's try doing this add and subtract one Okay, so let's try this out cos x under root of cos 2x and This becomes cos 2x Plus one then it becomes cos x under root cos 2x plus cos 2x so it becomes integral of one plus one by Cos x under root cos 2x plus cos 2x Yeah, now after that what to do No idea, right Okay, so after that we can just try out some you know conversion into a cos so Let's multiply cos x on top so it becomes cos square x and the root of cos 2x plus Cos x cos 2x Is this helping us out? Can we use x interval condition to evaluate the integral guys here? We have a this integral to solve So let's not bother about x right now. Let's treat it as an indefinite integrals to solve So we'll do one thing will try this out later on meanwhile. We'll move on with the other problem So we'll come back to this problem because I think some Integration step is something which we have to use over here So let us look into this question. Meanwhile, we'll come back to this So here we have a question where f of x is given as this cubic equation where a b c d are real and 3 b square is less than c squared This is an increasing function and g of x G of x is 8 times f dash x plus b times Double derivative of f of x plus c square and capital g of x is the integral of gt from alpha to x Now we have to comment about the nature of capital g of x More than one option may be correct in this So this question says f of x is this cubic equation and g of x is this so let us find g of x first So it's a times the derivative of this which is 3 a x square 2 b x plus c plus b times double derivative which is going to be a 6 a x plus 2 b and Plus c square so it's going to be 3 a square x square plus 2 a b and 6 a b which is 8 a b x and 2 b square Plus c square plus a c Okay Now let us first find the nature of g of x first of all g of x has its coefficient of x square as positive So this is positive Let's talk about the discriminant. Discriminant is b square b square minus 4 a C Okay Let us simplify this to a certain extent. I can take 4 a square common for sure So I'll have 16 b square 4 a square is gone. So minus 6 b square Minus 3 c square Minus 3 ac yeah So that will become 4 a square or 10 b square minus 3 c square minus 3 ac Okay Next we have also given that f of x has f of x is this expression and a b c d are real okay a b c d are real means The derivative of this function must have So let's find a derivative of this function f of x first which is going to be 3 a x square plus 2 b x plus c Okay, if this function is an increasing function means this term should always be positive Correct if this term is always positive means a should be always positive and the discriminant over here that is 4 b square minus 4 ac which is 12 ac should always be negative that means b square should always be less than 3 ac correct So b square should always be less than 3 ac. So can I write this expression to be less than? Instead of 10 b square Sorry instead of ac I can write this term as b square itself So I replace 3 ac term with b square because I wanted to come to this expression since b square is less than 3 ac Minus 3 ac will be greater than B square will be greater than minus 3 ac So what I did I I replace my b square with or replace my minus b square with or 3 ac with minus b square Okay Which means this expression for a square? This will become 9 b square minus 3 c square which is Take 3 out so 3 into 4 a square This will be 3 square minus c square So is it clear what I've done So after this step when I replace 3 ac with b square this this quantity becomes lesser than this because b square is lesser than 3 ac so you are instead of subtracting a higher quantity you are subtracting a lower quantity So the resultant expression should be higher than the previous one correct so that implies 12 a square 3 b square minus c square and we know that 3 b square is lesser than 3 b square is lesser than c square. So this is going to be a negative term This is going to be a negative term. This is going to be a positive term So this entire quantity is going to be less than zero that means Discriminate determinant of g dash x is less than zero means g of x is always positive Correct, so if g of x is always positive For a x all belonging to our what I can I commend about capital g of x which is actually integral of Which is actually integral of G of t dt from alpha to x So let me just use Leibniz rule over here differentiate it you get g of x and since g of x is always positive It implies g dash x will also be positive. That means g of x is an increasing function G of x is an increasing function So I think option number b is definitely correct But if option b is correct d will also be correct because increasing function. It has to be a one-one function as well Is that fine guys any question? This is a typical j advance level question. Is that fine alright? So moving on to the 12th question So next question in front of you is a vector question a is given to you b is given to you And x1 x2 x3 can take only values from minus 3 to 2 number of possible vectors b says that a and b are mutually perpendicular Okay, 1918 What about the others? Okay, so Most people are getting 19 and 18 only Alright, so let's discuss this So when you do a dot b You get x1 plus x2 plus x3 correct So when you take the dot product of these two vectors you get x1 plus x2 plus x3 and this should be zero Okay Now you have to choose Such values of x1 x2 x3 says that you get zero and you have only these many options Okay, so can I use multinomial theorem over here? Can I use multinomial theorem here? That means can I use the fact that I need to get the I need to get the Coefficient of x to the power zero in this That means I need to get the coefficient of 1 plus x plus x square plus x cube plus x4 plus x5 By x cube to the power of 3 I need to get the coefficient of x to the power zero in this Right in other words, I need to get the coefficient of x to the power nine in this Because in the denominator, I'll get x to the power nine right So if I'm able to find the coefficient of x to the power nine from this my job will be done Correct. Now. This is a gp This is a gp Whose first term is one common difference is x. So basically I'm looking for coefficient of x to the power nine in this That means coefficient of x to the power nine in this expression Now this can be only be written till 1 minus x to the power six because other terms will exceed x to the power nine So let me stop here And this will be infinitely, you know begin number. Okay, so this is like 1 minus x to the power 1 minus x to the power Minus n right which we know is expanded as 1 plus nx Plus n n plus 1 by 2 factorial x square and so on Okay, now I'll hand pick up terms from here. So first of all, I need the x to the power nine term from here So what are terms are required from here x to the power nine term? What is x to the power three term?  That's actually n plus r minus 1 cr So remember n over here is 3 And r for this is 9 So coefficient of x to the power 9 would be what coefficient of x to the power 9 would be 9 plus 3 minus 1 which is 11 c 9 Okay So this will be 11 c 9 Coefficient of x to the power 3 will be Coefficient of x to the power 3 will be 3 plus 3 minus 1 c 3 which is going to be 5 c 3 So this is 5 c 3 So your final answer will be 1 into x to the power 9 which is 11 c 9 Okay Oh one mistake. I mean this should be 3 over here. I'm sorry. Yeah So the other coefficient will be minus 3 into x to the power 3 coefficient which is 5 c 3 So swetha is asking had it been x 1 plus 3 x 2 plus x 3 equal to 0 Then what will be the change in the multinomial theorem? See in that case, uh, what I will do for x 2. I will always I will always cube all those all those terms Are you getting it just for the middle expression x 2 I will be using the powers like see whatever is the value of x 2 that will always make it three times So it can take values like minus 9 minus 6 Minus 3 0 so that those terms I will be using it Why because x 2 can take values which are minus 3 minus 2 minus 2 minus 1 0 1 2 So 3 x 2 will take triple those values correct So for the middle term For the other terms I would write this For the other terms I would be writing this But for the middle term I would be writing x to the power minus 9 x to the power minus 6 Etc till x to the power. Sorry. This will be plus 2 got it swetha right So, chalo will complete this question over here By the way, this was not required So we'll complete the question over here. So 11 c 9 11 c 9. Let's calculate its 10 11 into 10 By 2 minus 3 into 10, which is this So that's going to be 55 minus 30 55 minus 30 means Answer will be 25 So none of you could get it right So moving on to the next problem This is a question from ellipse So the question is the equation of the family of ellipse is given to you then the locus of the extremities of the latter spectrum You have to find the locus of the extremities of the latter sector I wrote it on the device itself Any response guys for this So first of all your a square is equal to cos square alpha Correct and b square is sin square alpha. So we know that This is equal to 1 But we also know that a square is b square is a square 1 minus c square Now, why we know this because in the interval 0 to pi by 4, this will be at a higher level than this So a would be greater than b So the formula will be b square is a square 1 minus e square correct That means a square plus a square 1 minus e square is equal to 1 So 2 a square Minus 1 is a square e square Now, what is the extremities of the latter sector? What is the extremities of the latter sector? In an ellipse So if you draw an ellipse What would be the extremities of the latter sector? Can I say it's a a comma b square by And minus a sorry a comma minus b square by This will be minus a comma b square by a and minus a comma minus b square by Is that okay? Any question so far? So, uh, I can say safely that x could be Plus minus a e and y could be plus minus b square by Right. That means x could be plus minus under root 2 a square minus 1 and y will be Plus minus now b square is from here. I can say b square is 1 minus a square So this is 1 minus a square by Okay Now from these two I have to try to eliminate my a I have to try to eliminate my a Okay, so what I'll do is I'll write x square as 2 a square minus 1 so x square plus 1 is 2 a square Correct from here. I can say Uh Y square is 1 minus a square whole square by a square correct So replacing a square with x square plus 1 by 2 in both the positions So replacing it over here. I get y square is equal to 1 minus a square whole square By a square So let's let's bring the a square on top. So it becomes x square plus 1 by 2 So that becomes x square plus 1 y square by 2 is equal to this becomes 1 minus x square whole square by 4 So this 2 and this 2 gets cancelled. So it becomes 2 x square plus 1 y square 1 minus x square whole square So your option number option number option number B becomes correct Option number B becomes correct. So guys, uh Only I think the integration question is left for us to be solved So I would request you all to try it again. Okay. Well, we may have done some silly mistakes or some errors over here but, uh, please check this and Treat this as a homework question Okay, and try to solve this Sure Shweta, I'll just repeat the last part as well see once I got the Once I got x equal to a plus minus a and y equal to plus minus a I try to get everything in terms of a So plus minus a from here is nothing but plus minus under root 2 a square minus 1 So this is your x This is your y Correct. So x square is this y square is this So here I made a is is something which I assumed so a is a parameter I don't want any parameter to occur in my final answer. So I replace a in terms of x and put it back in the other equation Okay, so a square is this and I put it in in this equation of y square And then I simplified it and I got my final answer. Is that clear Shweta? So request you all to complete that integration problem and please post the solution on the group if you have found it Okay Read that as homework Any exams you have on monday or exams are over Oh practicals are left. Okay. So all right guys Thank you so much for coming online Okay over and out from my side. Bye. Bye And best of luck for your practicals