Page 79 - How To Solve Word Problems In Calculus

dz
100 = 100
dt
dz
= 1
dt
The hypotenuse is growing at the rate of 1 cm/min.

(b) 1
A = xy
2

dA 1 dy dx
= x + y
dt 2 dt dt
As in part (a) after 2 minutes x = 80 cm and y = 60 cm.

dA 1
= [80 · (−5) + 60 · 5]
dt 2
=−50

2
The area is decreasing at the rate of 50 cm /min.
6.

z 30'

x
Fish
dz dx
Given: =−2 Find: when z = 50
dt dt

From the theorem of Pythagoras,
2
2
z = x + 30 2
Differentiating,

dz dx
2z = 2x + 0
dt dt
dz dx
z = x
dt dt
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