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The period
T (in seconds) of a pendulum is given by
T=2pisqrt(((L)/( 32))), where
L stands for the length (in feet) of the pendulum
pi=3.14, and the period is 12.56 seconds, what is the length?
The length of the pendulum is
qquad feet.

The period $T$ (in seconds) of a pendulum is given by $T=2\pi\sqrt{\left(\frac{L}{32}\right)}$ , where $L$ stands for the length (in feet) of the pendulum $\pi=3.14$ , and the period is $12.56$ seconds, what is the length? The length of the pendulum is $\square$ feet.

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Simplify radical expressions with variables II

Full solution

Q. The period

T

(in seconds) of a pendulum is given by

T=2\pi\sqrt{\left(\frac{L}{32}\right)}

, where

L

stands for the length (in feet) of the pendulum

\pi=3.14

, and the period is

12.56

seconds, what is the length? The length of the pendulum is

\square

feet.

Use Pendulum Period Formula: First, we need to use the formula for the period of a pendulum, $T = 2\pi \cdot \sqrt{L / 32}$ . Given $T = 12.56$ seconds and $\pi = 3.14$ , we need to solve for $L$ .
Substitute Values: Substitute the values into the formula: $12.56 = 2 \times 3.14 \times \sqrt{L / 32}$ .
Simplify Equation: Simplify the equation: $12.56 = 6.28 \times \sqrt{\frac{L}{32}}$ .
Isolate Variable: Isolate $\sqrt{\frac{L}{32}}$ : $\sqrt{\frac{L}{32}} = \frac{12.56}{6.28}$ .
Calculate Square: Calculate the division: $\sqrt{\frac{L}{32}} = 2$ .
Remove Square Root: Square both sides to remove the square root: $(\sqrt{L / 32})^2 = 2^2$ .
Solve for L: Simplify the squaring: $L / 32 = 4$ .
Calculate Multiplication: Solve for $L$ : $L = 4 \times 32$ .
Calculate Multiplication: Solve for $L$ : $L = 4 \times 32$ . Calculate the multiplication: $L = 128$ .

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