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Point) For cach vaie ot Ine hnclon h(I,v)A(Ar15) nas & mlnimum vahue m(A)Find m(X) m(^) (Use Ine Ielter L for A Yuui CXDtsiun(6i For Mich Vlutm( A) Ine Largesl ...

Question

Point) For cach vaie ot Ine hnclon h(I,v)A(Ar15) nas & mlnimum vahue m(A)Find m(X) m(^) (Use Ine Ielter L for A Yuui CXDtsiun(6i For Mich Vlutm( A) Ine Largesl and whal - Lhat IAXIINUMmarimum m(A)Find tne M-nimim vaille ot f(z,y) MIIMum $v? subyeci Io the constraint-melnooLanrano muruplers and Ealuaie(Pow ara inese. [Ernn relaled o Iesult i part (0)?

point) For cach vaie ot Ine hnclon h(I,v) A(Ar 15) nas & mlnimum vahue m(A) Find m(X) m(^) (Use Ine Ielter L for A Yuui CXDtsiun (6i For Mich Vlut m( A) Ine Largesl and whal - Lhat IAXIINUM marimum m(A) Find tne M-nimim vaille ot f(z,y) MIIMum $ v? subyeci Io the constraint- melnoo Lanrano muruplers and Ealuaie (Pow ara inese. [Ernn relaled o Iesult i part (0)?



Answers

HIV Infection The time interval between a person's initial infection with HIV and that person's eventual development of AIDS symptoms is an important issue. The method of infection with HIV affects the time interval before AIDS develops. One study of HIV patients who were infected by intravenous drug use found that 17$\%$ of the patients had AIDS after 4 years, and 33$\%$ had developed the disease after 7 years. The relationship between the time interval and the percentage of patients with AlDS can be modeled accurately with a linear equation. Source: Epidemiologic Review.
(a) Write a linear equation $y=m t+b$ that models these data, using the ordered pairs $(4,0.17)$ and $(7,0.33) .$
(b) Use your equation from part (a) to predict the number of years before half of these patients will have AIDS.

Hey, it's Claire so enumerated here. So for part A, you could see that the graf from the graph we could see that the curve is Kong cave up. So Kong Cave What word for part B on the derivative represents a slope of the curve in that interval. So age of tea, it's equal to each too. We're two to honesty. One we're gonna fine. So let's exist here. Number of infected people open people. And then this is R H prime. So for the year, these are all gonna be in 19 since 1982 done number effective people were 80. This was 0.11 095 for 29 seven lin for 1983 upper eighties three for any five you knew since seven movie means. And then we'll start here. 89 90 91. And then here we have 300 700 1500 2500 3500 4500 6000. Some day, 200 in 9000. This is 0.201 653 a 76 mine eyes this 760.40 3124 nine Bye. Or a six This is 0.5 036 5233 by three for 2500 it's 25000.5033 987 for 93 then for 3500 it's point find 032 090 589 and for 4500 it's 45000.754 37 66 251 We're 6000. It's 60000.60321 289 one says a 9.531 for 7200 its 72000.9 zero for 068 30 74 for Part C. We know that from Part A, we felt the slope of detention to the curve is always increasing, and the curve is. Khan gave up. But when we calculate the second derivative, we see that it's only Conch Eve, up from 1982 to 84 in 1987 and 89 to 91 its downward when it's 1985 to 86 in 1988 because the second derivative here becomes negative. So Kong Cave up. See you for 1982 to 84 87. I'll just put the last two days. Since they're all starts from 19 1989 to 91 you're in Kong Cave downward 1985 to 86 80.

In this problem during the Diagram 1st. So just look at it carefully. The diagram looks something like this which I am drawing here. So this is the diagram here. The value it X. And in this side empties working tense and I think he reached T. This english tita, this english tita. This length is Elway to Similarly in this side Lee length is L x two. So late. The point or decent by a distance X. This is point. Oh now from the condition of the Liberian point. Oh I can write to T. Scientific is equal to empty. Also I can write the value of Z. Is equal to MG by To sign a treaty to which is equal to empty by two. X. Underwood held by two. Holy squared plus X square. They didn't be question #1 on further simplification. I can write E. Bye bye. D. By two. Holy square is called to side is equal to E. Capitally. So finally the value of P. Is equal to E. Capitally by the square by for rated vacation number two. In addition to it, I can also write the value of is equal to And that would L x two. Holy square plus X squared minus L. Y. To buy held by two Which is equal to under Hood. one Flash 2 weeks by hell. Holy square minus one. This is the question number three. So from equation 123 I can write the value acs minus X by understood 1-plus 2 eggs by L. Holy squared is equal to MG. L. By by E. D squired as the value of axes very smaller than L. So finally, I can write four X cube by. Too early. Square is equal to MG N by pi E d. Square. So access equal to L mg by two pi. It is square hole to the power one by three, which is equal to 2.5 centimeter is the answer.

So the question here says that um in 2006, um we essentially want to calculate a model for HIV. So in 2006 we have um 40 million people that were infected with HIV. And at the rate at that particular time it was 4.3 million people per year here. So M p y s million per year. And um for a here it wants us to utilize this rate here, which is 4.3 million per year and calculate a formula for the model um to calculate how many people are infected with HIV x years after 2006. So we can model this by saying F of X. Which is essentially just a notation for the function is equal to four three X. Where on 4.3 is gonna be a constant and it's the rate at which essentially something goes up. So every year after, we're going to get 4.3 more and more and more, And we have to add this to 40 as we're using this population here 40 million as a base rate whereby we already know there's 40 million infected at that time. So essentially this is gonna be the formula that we have um for be here, it wants us to estimate the number of people who have been infected by the year of 2012. So we know that as this particular case is gonna be the year of 2006, we essentially need to plug in X. Is equal to six in order to get um 2000 and 12. So F. Of X here is going to be equal to 4.3 times six plus 40. And that's gonna give us a value of 65.8 million people. And that's the answer to a Russian.

We have a vector valued function are of tea e to the negative to T I Plus Co. Scient, E J Post three. Cy Inti. Okay, and it's passing through the 0.110 Um, we need to figure out the value of tea that corresponds to when it's passing through that point. So let's go ahead and equate the first the first component of this point with the first component of our. So we hav e to the negative to t is equal to one, and this implies that T equals zero. Okay, let's go ahead and now calculate the derivative of our That's negative to e to the negative to t I plus Negative scientist E J Plus three co sign T K. Now let's go ahead and calculate the derivative of our at zero. We have negative to I plus zero j plus three k. So we are now set up to be able to write down a vector equation for a line. So this is going to be negative to 03 krone rise by t passing through 110 So this is the equation for the for the line, and we want to know, At what point does this tinge it Line passed through the X Y plane. That is, where does it pass through? Excuse me. Not the X y, but the y Z plane. Okay. And in particular in the y Z plane, we know that the X equals zero, and that's how we're going to figure this out. Let's go ahead and set the X components to the perimeter rised line V equal to zero. So we have negative to t plus one. That's the X component of the is being set equal to zero because it's passing through the Y Z plane that tells us that t must equal one half. Now let's go ahead and calculate what V is at one half, and that's going to tell us the point that it passes through what it's passing through the Y Z plane so have negative to 03 times one half +110 This gives us 013 house, and that's it that supported passes through


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