Math 125-103
Fall 2012
Quiz 22, Oct. 24
Carter
Name
1. Compute the derivative:
y = Arcsec(2s + 1)
Solution.
2
p
.
|2s + 1| (2s + 1)2 − 1
y0 =
2. Water runs into a conical tank at the rate of 9 ft.3 /min. The tank stands vertex down and
has a height of 10 feet and a base radius of 5 feet. How fast is the water level rising when the
water is 6 feet deep?
Solution.
• Let V denote the volume of water in the tank.
5
• Let r denote the radius of the water.
• Let h denote the height of the water.
• Given
• Find
dV
dt
dh
dt |h=6 .
h
As the figure indicates,
r
5
= .
h
10
Thus
r=
The volume of a cone is
V =
We have
V =
Thus
Solve for
So
h
.
2
π 2
r h.
3
π h 2
π 3
( ) h=
h .
3 2
3·4
dV
π dh
= h2 .
dt
4 dt
dh
dt :
r
10
= 9 ft.3 /min.
4 dV
dh
= dt2 .
dt
πh
dh
4·9
1
|h=6 =
= .
2
dt
π6
π