Page 77 - How To Solve Word Problems In Calculus

After 2 hours, x = 2 × 25 = 50 and y = 2 × 45 = 90. It follows
√ √
2 2 2
that z = 140 + 70 = 24,500 and z = 24,500 = 70 5.
√ dz
70 5 = (50 + 90)(25 + 45)
dt
√ dz
70 5 = 9800
dt

dz 9800 140 √
= √ = √ = 28 5 km/h
dt 70 5 5

4.
Second base

90
y
90 − x First base

x 90

Home
dx dy
Given: = 20 Find: when x = 50
dt dt
2
2
2
From the diagram, 90 + (90 − x) = y .
Differentiating,

dx dy
0 + 2(90 − x) − = 2y
dt dt
dx dy
− (90 − x) = y
dt dt

When x = 50,

2
2
90 + (90 − 50) = y 2
8100 + 1600 = y 2
√ √
y = 9700 = 10 97
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