Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.9 - Related Rates - 3.9 Exercises: 21

Answer

$\frac{db}{dt} = -1.6 cm/min$

Work Step by Step

$A = \frac{1}{2} bh$ $100 = \frac{1}{2} b(10)$ $100 = 5b$ $b = 20cm$ $A = \frac{1}{2} bh$ $\frac{dA}{dt} = \frac{1}{2}(h \times \frac{db}{dt} + b \times \frac{dh}{dt})$ $2 = \frac{1}{2}(10 \times \frac{db}{dt} + 20(1))$ $2 = \frac{1}{2}(10 \times \frac{db}{dt} + 20)$ $2 = 5\times\frac{db}{dt} + 10$ $2-10 = 5\times\frac{db}{dt}$ $8 = 5\times\frac{db}{dt}$ Solve for $\frac{db}{dt}$: $\frac{8}{5} = \frac{db}{dt}$ $\frac{db}{dt} = -1.6 cm/min$
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