The rate of variable reactangle is increasing at rate of 60 cm square / second . The length of the reactangle is always equal to the square of the breadth.At what rate the length is increasing at the instant where the breadth is 4cm?
Let the breadth (width ?) be x
then the length = x^2
area = width*length = x(x^2) = x^3
d(area)/dt = 3x^2 dx/dt
given: d(area)/dt = 60
find d(length)/dt when x = 4
60 = 3(16) dx/dt
dx/dt = 5/4
length = x^2
d(length)/dt = 2x dx/dt, so when x = 4
d(length)/dt = 2(4)(5/4) = 10
I skipped the units for convenience's sake, so
d(length)/dt = 10 cm/s