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yashar806
 2 years ago
Best ResponseYou've already chosen the best response.0I have attached the question

yashar806
 2 years ago
Best ResponseYou've already chosen the best response.0yes, could you explain it ?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1ok first off z is 4, so lets forget z and replace it by 4

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1the volume of the first tube, the one with side \(x\) is \(4\times (\frac{1}{4}x)^2\)

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1because your entire length is \(x\) and you are folding it in to a square so the side of the square is \(\frac{1}{4}x\)

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1and therefore the area of the square is \((\frac{1}{4}x)^2=\frac{x^2}{16}\) and since \(z=4\) the volume is \(4\times \frac{x^2}{16}=\frac{x^2}{4}\)

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1the volume of the second one is easy, since \(z=4\) it is just \(y\)

yashar806
 2 years ago
Best ResponseYou've already chosen the best response.0then we add them togther?

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1now we use the fact that \(x+y=8\) and so \(y=8x\)

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1now we add them together, because now we have an expression for the volume in one variable it will be \[V(x)=\frac{x^2}{4}+8x\]

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1now if this is a calculus question you can take the derivative, set it equal to zero and solve if not, you can say the vertex is at \(\frac{b}{2a}\) with \(a=\frac{1}{4}\) and \(b=1\)

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1ok good this has a min at the vertex, and i guess a max at the end point of the interval, so be careful about what that is

satellite73
 2 years ago
Best ResponseYou've already chosen the best response.1i guess it is \([0,8]\) since \(x\) must be in there somewhere

yashar806
 2 years ago
Best ResponseYou've already chosen the best response.0Hi just quick question, why we need interval there? how did you know that there should be an inteval?
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