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.
| dy |
| dt |
=
(b) If
dy/dt = 2,
find
dx/dt
when
x = 12.
| dx |
| dt |
=
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