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4 comments:
Having a little bit of trouble simplifying from this point on number 21:
dy/dx = x^2(4x((2xV-x^2)/x^4) + 2x(4x(V/x^2))
Harrison, I don't know why your derivative is so complicated. I assume it is the derivative of the Surface area function, which is A=x^2 + 4xh. Then if you replaced the h with the volume function equation you should still just get the sum of two power functions. So, I don't know where such a elaborate derivative comes from.
I dont know if this is a stupid question but for 32 Im having some serious trouble trying to decide how to start. So far I have 4 different equations, but I'm not really sure where to go from here. I have:
hypotenuse(of town1)= sqrt(1+x^2)
hypotenuse(of town2)= sqrt(16+(4-x)^2)
Area(of town1)=x/2
Area(of town2)=.5(4-x)(4)
I feel like these might not even be the right equations that I need...help please
(sorry its kind of late)
Kelsey, you have a good start. See, all you are concerned with is minimizing the distance from each town to the pumping station. Thus that quantity will be the sum of the two hypotenuses. Then you'll have an equation. Your two hypotenuse equations look fine. As for your area equations, I'm not sure you'll need to be concerned with area in this problem.
Also, exercise some caution with the derivative when you get to that. Try to break it down and show all steps to avoid small errors in the algebra.
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