5 Steps to a 5 AP Calculus AB 2019 - William Ma

MA 3972-MA-Book April 11, 2018 14:46

180 STEP 4. Review the Knowledge You Need to Score High

r

4

h

10

Figure 9.1-2

Thus, you can reduce the equation to one variable:

V=

1

3

π

(

2 h

5

) 2

h=

4

75

πh^3.

Step 4: Differentiate both sides of the equation with respect tot.

dV

dt

=

4

75

π(3)h^2

dh

dt

=

4

25

πh^2

dh

dt

Step 5: Substitute known values.

2 =

4

25

πh^2

dh

dt

;

dh

dt

=

(

25

2

)

1

πh^2

m/min

Evaluating

dh

dt

ath=5;

dh

dt

∣∣

∣∣

h= 5

=

(

25

2

)

1

π(5)^2

m/min

=

1

2 π

m/min.

Step 6: Thus, the water level is rising at

1

2 π

m/min when the water is 5 m high.

Shadow Problem

A light on the ground 100 feet from a building is shining at a 6-foot-tall man walking away

from the light and toward the building at the rate of 4 ft/sec. How fast is his shadow on the

building becoming shorter when he is 40 feet from the building? (See Figure 9.1-3.)

100 ft

Building

Light 6 ft

Figure 9.1-3