SOLUTION: Given that T=2(PIE SYMBOL) open SQUAREROOT L/g rearrange the formulea to express g in terms of T, pie and L

Question 1190456: Given that T=2(PIE SYMBOL) open SQUAREROOT L/g
rearrange the formulea to express g in terms of T, pie and L
Found 2 solutions by Theo, Alan3354:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
equation is:
T = 2 * pi * sqrt(L/g)
divide both sides of the equation by 2 * pi to get:
T / (2 * pi) = sqrt(L/g)
square both sides of the equation to get:
(T / (2 * pi))^2 = L/g
multiply both sides of the equation by g and divide both sides of the equation by (T / (2 * pi))^2 to get:
g = L / ((T / (2 * pi))^2)
this can be simplified to:
g = (L * 4 * pi^2 / T^2

this can be confirmed by randomly assigning a value to g and L.
i chose 64 for L and 16 for g.
i get:
T = 2 * pi * sqrt(L/g) = 2 * pi * sqrt(64/16) = 2 * pi * sqrt(4) = 4 * pi.
the value of T is equal to 4 * pi.

when T = 4 * pi and L = 64, then:
g = L / ((T / (2 * pi))^2) becomes:
g = 64 / ((4 * pi / (2 * pi))^2 which becomes:
g = 64 / 4 which becomes:
g = 16.

since we had originally assigned 16 to g, this confirms the unsimplified formula is correct, given that T = 4 * pi and L = 64.

when T = 4 I pi and L = 64, then:
g = (L * 4 * pi^2 / T^2 bcomes:
g = (64 * 4 * pi^2) / (4 * pi)^2 which becomes:
g = 256 * pi^2 / (16 * pi^2) which becomes:
g = 256 / 16 which becomes:
g = 16.

since we had originally assigned 16 to g, this confirms the simplified formula is correct, given that T = 4 * pi and L = 64.

you can use either the unsimplified formula or the simplified formula.
if they want the answer simplified, then use the simplified formula.

let me know if you have any questions.
theo

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
No PIE in math unless it's a pie chart.
Use the Greek letter pi.
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