SOLUTION: The period T, in seconds, of a pendulum of length L, in feet, may be approximated using the formula T = 2•pi•sqrt{L/32} For part B, express your answer both as a squ

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: The period T, in seconds, of a pendulum of length L, in feet, may be approximated using the formula T = 2•pi•sqrt{L/32} For part B, express your answer both as a squ      Log On

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Question 1208653: The period T, in seconds, of a pendulum of length L, in feet, may be approximated using the formula

T = 2•pi•sqrt{L/32}

For part B, express your answer both as a square root and as a decimal.

A. Solve the given formula for L.

B. Find the period T of a pendulum whose length is 8 inches.

For part B, 8 inches must be converted to feet before substituting into the given formula.
You say?
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
a)
Note that we want to isolate the term that has L. Dividing both sides by 2pi gives sqrt%28L%2F32%29=T%2F%282pi%29. Squaring both sides gives L%2F32=T%5E2%2F%284pi%5E2%29. Finally, multiplying both sides by 32 gives L=8T%5E2%2Fpi%5E2.
b)
There are 12 inches in a foot, so 8 inches is equal to 8/12 feet, or 2/3 feet. Plugging that in for L gives T=2pi%2Asqrt%28%282%2F3%29%2F32%29=2pi%2Asqrt%281%2F48%29=pi%2Fsqrt%2812%29. Simplifying and rationalizing gives T=pi%2Asqrt%283%29%2F6. Expressing this as a decimal gives 0.906899682... The answer is irrational, and so round it as necessary.