Saturday, January 31, 2015

Single Variable Calculus, Chapter 3, 3.8, Section 3.8, Problem 20

At what rate is the boat approachng the dock when it is 8m from the dock?
Illustration:







Required: dxdt when x=8m

Solution:

By using Pythagorean Theorem we have,

z2=12+x2 Equation 1

taking the derivative with respect to time


\cancel2zdzdt=\cancel2xdxdtdxdt=zxdzdtEquation 2


We can get the value of z by substituting x=8 in equation 1


z2=12+x2z2=12+82z=65m


Now, using equation 2 to solve for the unknown


dxdt=658(1)dxdt=658m/s


This means that the boat is approaching the dock at a rate of 658m/s when the boat is 8m from the dock.

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