Question

Related Rates Calculus Question
A square plate is cooling and contracting at a rate of 3cm^2/sec. How fast is the length of an edge decreasing when the area of the plate is 12cm^2?

Answer 1

do they give you an equation to use? I think area of a square is A = xy? height x width or length x width? I forget. Use that equation and differentiate the whole thing w/ respect to time.
If it is A = xy
differentiate to get dA/dt = x(dx/dt) + y(dy/dt) <--- product rule

plug in your knowns, use algebra to rearrange and find your unknown.

Answer 2

I believe that the area of a square is A=S^2? because squares have the same sides throughout? im not really sure

Answer 3

Differentiate to get:
\[\frac{ dA }{ dt }= 2s(\frac{ ds }{ dt })\]

Answer 4

Sorry im getting myself confused now. When I see cooling, I think of newtons law of cooling, partial differentials.

Answer 5

oh, its ok, i am solving it right now, may you please check my work afterwards? thank you :)

Answer 6

fa sho

Answer 7

oh wait if the area of the plane is 12cm^2, how do I find the sides?

Answer 8

2 sides means you multiply it by two. Assuming they are of equal length.

Answer 9

so \[\sqrt{12}\]

Answer 10

Area of Square:
A = x² = √ 12
-> x = 2√3
Thus:
-3 = 2 * 2√3 dx/dt
Can you solve for dx/dt now?

Answer 11

hahaha! i was wrong its -sqrt3/4

Answer 12

thank you :)