Question

A screen saver displays the outline of a 3 cm by 2 cm rectangle and then expands the rectangle in such a way that the 2 cm side is exanpanding at the rate of 4 cm/sec and the proportions of the rectangle never change. How fast is the area of the rectangle increasing when its dimensions are 12 cm by 8 cm?

Answer 1

This is a linearization problem.
A = uv
dA/dt = u (dv/dt) + v(du/dt)
du/dt=4 cm/s.
dv/dt =4*(3/2)=6 cm/s (aspect ratio does not change)
When u=8, v=12, then
dA/dt = (8*6 + 12*4) cm^2/s
= 96 cm^2/s

Answer 2

o thx my teacher vhasnt really explained those yet

Answer 3

But was it done in a way you could understand?
If not, we have to try another way of doing it.

Answer 4

i dont get uv

Answer 5

u, v represent the sizes of the screen at time t, i.e. u=u(t), v=v(t).