Quandaries and Queries


Name: ladymei

I have a question about calculus:
The width x of a rectangle is decreasing at 3 cm/s,
and its length y is increasing at 5 cm/s. At what rate
is its area A changing when x=10 and y=15?

I used the equation x(dx/dt)y(dy/dt)=A(dA/dt), where t
is time. I plugged in 10 for x, 15 for y, -3 for
dx/dt, 5 for dy/dt, and 150 for A, but it didn't work.
However, I don't know whether my equation is correctly
set up or not. Could you please show me how to set up
the equation for this problem? Thanks.




If x is the width of a rectangle and y is its length then the area A is given by

A = x y

Since the length and width are changing with time you can think of x, y and A as functions of time. Thus,

A(t) = x(t) y(t)

This is the expression you need to differentiate, with respect to t, to find an expression for the rate at which the area is changing. Differentiation with respect to t gives,

 dA(t)/dt = x(t)  dy(t)/dtdx(t)/dt y(t)



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