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Once a week you babysit your neighbor's toddler after school, usually going to a local playground. You notice that each swing on the swing set takes nearly the same amount of time, about 2.7 seconds. Use the pendulum formula below to find out how long the swing is. round your answer to the tenths place.
T= 2pie *square root* L/32

A. 1.8 feet
B. 37 feet
C. 5.9 feet
D. 5.4 feet

Respuesta :

Rearrange the formula  to isolate the variable L. 

Divide both sides by 2pi to get: 

 

Square both sides to get: 


 

Multiply both sides by 32 to get: 

 

Finally, substitute in 3.1 in place of T and calculate L.
JeanaShupp

Answer: C. 5.9 feet

Step-by-step explanation:

Given: Time : 2.7 seconds

The given pendulum formula :

[tex]T=2\pi\sqrt{\dfrac{L}{32}}[/tex]

To find the length of the swing , substitute the value of T = 2.7 in the above formula , we get

[tex]2.7=2\pi\sqrt{\dfrac{L}{32}}\\\\\Rightarrow\ \sqrt{\dfrac{L}{32}}=\dfrac{2.7}{2(3.14)}=0.429936\approx0.43\\\\\Rightarrow\ \sqrt{\dfrac{L}{32}}\approx0.43[/tex]

Squaring on both the sides, we get

[tex]\dfrac{L}{32}=(0.43)^2\\\\\Rightarrow\dfrac{L}{32}=0.1849[/tex]

Multiplying 32 on both sides, we get

[tex]L=0.1849\times32=5.9168\approx5.9[/tex]

Hence, the length of the pendulum = 5.9 feet.

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