- #1
rook_b
Homework Statement
Let A be the area of a circle of radius r that is changing with respect to time. If dr/dt is constant, is dA/dt constant? Explain.
Homework Equations
A = 2(pi)r^2
dA/dt = 2(pi)(r)*dr/dt
The Attempt at a Solution
I can't decide. You see if dr/dt is constant and multiplied by 2(pi) then dA/dt must be constant. But, r, what is r? It must be that 'r' is a function of time, I think. Or, r is an initial value that grows as the rate dr/dt. A constant rate times a constant should yield a constant rate, but multiplied by a variable it will yield a variable rate. I hate r.
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