SOLUTION: Imagine a rope wrapped around Earth at the equator (Earth's circumference C). Then think of adding d feet to the rope's length so it can now circle Earth at a distance h feet abov

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Question 170681: Imagine a rope wrapped around Earth at the equator (Earth's circumference C). Then think of adding d feet to the rope's length so it can now circle Earth at a distance h feet above the equator at all points. Length of rope = C + d
Write an equation to model this situation.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Imagine a rope wrapped around Earth at the equator (Earth's circumference C). Then think of adding d feet to the rope's length so it can now circle Earth at a distance h feet above the equator at all points. Length of rope = C + d
Write an equation to model this situation.
:
2*pi*r = C
and
2*pi*(r+h) = C+d
:
Substitute (2*pi*r) for C
2*pi*(r+h) = 2*pi*r + d
:
Multiply what's inside the brackets
(2*pi*r) + (2*pi*h) = (2*pi*r) + d
:
Subtract (2*pi*r) from both sides
2*pi*h = d; the equation to find d
:
Divide both sides by 2pi
h = d%2F%28%282pi%29%29; the equation to find h