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.
