2. A ladder 25 feet long is leaning against a wall.
If the foot of the ladder is being pulled away from
the bottom of the wall at a rate of 14 ft/sec, at what
rate is the top of the ladder moving down the wall
when it is 7 feet above the ground?
dy = ­ 48 ft/sec
dt

4. A hot air balloon is being inflated at a rate of 16 cu ft/sec
At what rate is the radius increasing when r = 2 ft
dV = 16
dt V= 4 r3
3
dr = 1 ft/sec
dt

5. Two automobiles start from a point A at the
same time. One travels west at 8 km/hr, the
other travels north at 45 km/hr. How fast is the
distance between them increasing 3 hours after
they start? 91.41 km/hr

6. The length of a rectangle is decreasing at the rate
of 2 cm/sec while the width is increasing at the
rate of 2 cm/sec. When L = 12 and W = 2,
find the rate of change of
0
a) the area
b) the perimeter 0
c) the length of the diagonal ­ 1.64 cm/sec

7. The length of a rectangle is decreasing at the rate
of 2 cm/sec while the width is increasing at the
rate of 2 cm/sec. When L = 12 and W = 2,
find the rate of change of
b) the perimeter
­ 1.64 cm/sec

8. The length of a rectangle is decreasing at the rate
of 2 cm/sec while the width is increasing at the
rate of 2 cm/sec. When L = 12 and W = 2,
find the rate of change of
c) the length of the diagonal
­ 1.64 cm/sec

9. Exercise 4.6
Questions 1 ­ 11