# rates of change

1- Each side of a square is increasing at a rate of 6 cm/s. At what rate is the area of the square increasing when the area of the square is 49 cm2?

cm2/s .

2_ This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

The length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of 8 cm/s. When the length is 14 cm and the width is 12 cm, how fast is the area of the rectangle increasing?

Using A = lw, we have

3-

A cylindrical tank with radius 7 m is being filled with water at a rate of 3 m3/min. How fast is the height of the water increasing?

in m/min ??

4-

Suppose

y = 2x + 1

, where x and y are functions of t.

(a) If dx/dt = 3,

find

dy/dt

when

x = 4.

dydt

=

(b) If

dy/dt = 2,

find

dx/dt

when

x = 12.

dxdt

=

5-Two sides of a triangle have lengths 13 m and 16 m. The angle between them is increasing at a rate of 2°/min. How fast is the length of the third side increasing when the angle between the sides of fixed length is 60°? (Round your answer to three decimal places.)

m/min