I have been given an assignment by my teacher, only I can't answer 3 of the questions.(adsbygoogle = window.adsbygoogle || []).push({});

1) A rectangle is expanding so that its length is always three times its width. The perimetre of the rectangle is increasing at a rate of 12cm/minute. Find the rate of increase in area of the rectangle when the perimetre is 80cm.

Here's what I have:

3x=y 2x+2y=80, Area=xy

2x+2(3x)=80

x=10, y=30, dP/dt = 12 dA/dt=?

If I take the derivative of a=xy, I need to know the derivative of x and y. But I am not given these. I do not know how to find these.

2) A rectangular area of 3200m^2 is to be fenced off. Two opposite sides will use fencing costing $2/metre, and the remaining sides will use fencing that costs $8/metre. Find the dimensions of the rectangle with the least costs.

3200=xy

y=3200/x

P=2x+2y

P=2x+2(3200/x)

P=2x+6400/x

P=2x+6400(x^-1)

Then I am stuck =(

3) A wooden chest is rectangular in shape with its length along the fron twice as its width. The top, front, and two sides of the chest are made of oak; the back and bottom are made from pine. Oak costs three times as much as pine. Find the dimensions that minimize of the cost of the chest if the volume is 0.25m^2.

I have no idea where to start. I know that V=xyh and x=2y, so V=2(y^2)h

Thanks for all your help! =D If this is in the wrong section, please move it.

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# Homework Help: Calculus - Derivatives and Applications

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