the formula $t = 2pisqrt{\frac{l}{32}}$ relates the time, $t$, in seconds for a pendulum with the length…

the formula $t = 2pisqrt{\frac{l}{32}}$ relates the time, $t$, in seconds for a pendulum with the length, $l$, in feet, to make one full swing back and forth. what is the length of a pendulum that makes one full swing in 2.2 seconds? use 3.14 for $pi$.\n2 feet\n4 feet\n11 feet\n19 feet

the formula $t = 2pisqrt{\frac{l}{32}}$ relates the time, $t$, in seconds for a pendulum with the length, $l$, in feet, to make one full swing back and forth. what is the length of a pendulum that makes one full swing in 2.2 seconds? use 3.14 for $pi$.\n2 feet\n4 feet\n11 feet\n19 feet

Answer

Explanation:

Step1: Substitute given values into formula

Given $T = 2.2$ and $\pi=3.14$, the formula $T = 2\pi\sqrt{\frac{L}{32}}$ becomes $2.2=2\times3.14\sqrt{\frac{L}{32}}$.

Step2: Simplify the right - hand side

$2\times3.14 = 6.28$, so the equation is $2.2 = 6.28\sqrt{\frac{L}{32}}$. Then $\sqrt{\frac{L}{32}}=\frac{2.2}{6.28}\approx0.35$.

Step3: Square both sides

$(\sqrt{\frac{L}{32}})^2=(0.35)^2$, which gives $\frac{L}{32}= 0.1225$.

Step4: Solve for L

Multiply both sides by 32: $L=0.1225\times32 = 3.92\approx4$.

Answer:

4 feet