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Q2 Let Z be the function given implicitly 2 =x2z2 +y2 +2 = 3xy 0z Then at x = 0 ,y = 1 is worth dx a) 3 b) 2 c) - 1 d) 0...

Question

Q2 Let Z be the function given implicitly 2 =x2z2 +y2 +2 = 3xy 0z Then at x = 0 ,y = 1 is worth dx a) 3 b) 2 c) - 1 d) 0

Q2 Let Z be the function given implicitly 2 =x2z2 +y2 +2 = 3xy 0z Then at x = 0 ,y = 1 is worth dx a) 3 b) 2 c) - 1 d) 0



Answers

$\begin{array}{ll} & \text { (1) } \int-2 x+y+4 z=3 \\ \text { Consider the system: } & \text { (2) }\left\{\begin{array}{l}x-y+2 z=1 \\ \text { (3) } x+y-3 z=2\end{array}\right.\end{array}$ a. What is the result if equation 1 and equation 2 are added? b. What is the result if equation 2 and equation 3 are added? c. What variable was eliminated in the steps performed in parts (a) and (b)?

So. Question number eight from less than 12.2. Um, has a three variable three equation system, and it's a three part question. Question eight a. Says what is the result if equation one and equation to are added so Equation one negative two X plus y plus four z equals three. An equation to X minus y plus two z equals one. Well, I want you to notice that in equation number one, you have a positive why and an equation. Number two. You have a negative Why. So what happens when those two equations are added is that the train to erase that line is that the why variables are eliminated y variables are eliminated. So what is the results? If those two equations are added together? Well, the result ISS negative two x plus x gives me a negative x positive. Why negative? Why those cancel out four Z plus choosy is six Z and three plus one is four. So this is question eight. A. Let's look at question. A B. Question eight b says what is the result if equation to an equation, three are added, so you'll notice an equation to you have that negative? Why and an equation. Three. You have a positive Why So those are going to be eliminated? A positive X plus Another X gives you two x The wise again were eliminated to Z minus three z is negative Z and one plus two equals three. So this is the result. If equations two and three are added together and then question eight C says Well, what variable was eliminated in the steps that were performed in part A and B Well, what variable did we eliminate? We eliminated the Y variable we eliminated? No, why variable and that's it.

Execution we have to solve the double integration that is eyes equals 0-1. An integration 022 This is X squared plus Y square the X Dy. Now this can be written as 0 to one. The X into 0-2. Disease X squared plus Y squared B Y. Now first of all I'm going to solve this integration So this will come out to be Integration 0-1. This is access square wife plus Y que by three and the limited from 0 to 2 and this is the X. Now I can say this bill comes out to be integration 0-1. Now put the value of limit of why you're so this can be Kuwaiti square Last eight x 3. Yes. Now I'm going to again integrate with respect to X. So we will get disease Integration 0- one. Sorry this bill comes out to be this is to execute by three plus air tax by three and the limited from 0 to 1. Now put this limit and we will get this is to buy three plus eight by three and This will comes out to be 10 x three. So this is our answer for this revolution and for that option, C. Is the correct choice. Thank you.

The execution we have to solve the triple integration. That is integration from 0 to 3. Integration from 0 to 2. And integration from 0 to 1 X plus Y plus get into dx dy desert. So first of all I'm going to integrate it with respect to their so this can be written as 0 to 3. This is D X 022 This is for D Y and 0 to 1. This is this will come out to be X squared plus Y. Jed plus jerry square by two and the limited from 0 to 1. Now I'm putting this limit here. So I will get this is integration from 0 to 3 D X. And this is integration from 0 to 2. This will comes out to be X. Y. Sorry, this will be not one year. This is just because I'm integrating it with respect to gender. Now this will come out to be X plus Y plus. This is one x 2. Do I. Now I'm going to integrate it with respect to Y. So this is 0-3. And this will come out to be X. Y. Plus. This is why square by two plus Y. Two. And the limited from 0 to 2. And this is D. X. Now for the limit of white here. So we will get this is integration 0 to 3. This is two X plus two plus one dx. Now integrate with respect to works and finally we will get disease axis square plus two. X. Plus. Sorry this is two X plus X. And the limit is from 0 to 3. Now put the limit and we will get disease X squared plus three X. 0-3. So this will comes out to be 9-plus 3 into 3 0. So we can say that finally we will get disease 18. So this is the answer for this given to shin. And for that option is the correct choice. Thank you.

In this problem we are given 3Z is equal That -4 models. Models of three Z is equal to the models of the F -4 and we know that is equal to X plus II to buy. So let us first find trees. It so it equals three X plus I don't three way And then we need to find said -4. So explain this item of I -4 and collecting real animation. Eri paths we have x minus four plus I have by now we need models of trees. So models of trees. It is equal square root three X square last three way square. That is square root nine x square last night. My square Also we need models of Zed -4. So that is square root of X -4 sq. Let's Play Square. If we simplify X -4 Whole Square we have x square minus eight X plus 16 plus y squared. And these two things are equal. So we have square root nine x square plus nine by square is equal to square root off X Square -8 plus 16 less waste. Now to get rid of the square let us square both sides. So if we square the square roots they get eliminated and we are left with nine X square plus nine by square is equal to x square minus eight. Last 16 less waste. Now. Now let this isolate the constant tone. So we have nine x square minus x square Plus nine by Square minus y squared plus a tax equals 16 adding like terms we have each X square plus eight. Y squared blessed take is equal to 16. Now all the terms are divisible by eight, so we have x squared plus Y square. Classic equals oh and we need to find the value of this expression only, so our answer is two or option. See


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