Page 80 - How To Solve Word Problems In Calculus

When z = 50,

2
2
50 = x + 30 2
2
2500 = x + 900
2
x = 1600
x = 40

Substituting the appropriate values,

dx
50(−2) = 40
dt
dx −100 5
= =−
dt 40 2
1
The speed of the fish is 2 /2 ft/sec. The negative rate indicates that
x is shrinking. (The fish is moving toward the bridge.)
7.

h
r

dV dh
Given: = 10 Find: when h = 5.
dt dt
The volume of a cone is related to its height and radius by the
π 2 1
equation V = r h. Since h = r , it follows that r = 2h,so
3 2
π
2
V = (2h) h
3
4π
= h 3
3

Differentiating with respect to t,

dV 2 dh
= 4πh
dt dt
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