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Answer :
Answer:
0.16 inches per second
Step-by-step explanation:
The vertical height of the pole in inches can be modeled at time t by the expression y=7-4t. The horizontal distance of the end from the wall can be found using the Pythagorean theorem. We want the derivative of that horizontal distance at t=0.
Setup
x² +y² = 176² . . . . . . Pythagorean relation
x² = 176² -y² = 176² -(7 -4t)² . . . . . . substitute time function for y
x² = 30976 -(49 -56t +16t²) . . . . . . expand
x = √(30927 +56t -16t²) . . . . . . . . . square root
Solution
The rate of change of x, the distance of the end from the wall, is the derivative of x with respect to t:
[tex]x'=\dfrac{56-32t}{2\sqrt{30927+56t-16t^2}}[/tex]
At t=0, this is ...
x'(0) = 28/√30927 ≈ 0.159217
The bottom of the pole is moving away from the wall at the rate of 0.16 inches per second.
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