The formula T=2π√L/480 can be used to find the period (T in seconds, the time it takes a pendulum to complete one cycle) of a pendulum that is L cm long.
(a)Rewrite this formula using rational exponents. Don't forget to rationalize the denominator.
(b)Solve the formula for L.
Thanks Henry and bobpursley for replying. Now the question makes sense :-)
(a) To rewrite the formula using rational exponents, we can express the square root (√) as a fractional exponent (1/2). Rationalizing the denominator involves eliminating any radical (square root) in the denominator.
The given formula is: T = 2π√(L/480)
To rewrite it with rational exponents, we express the square root as a fractional exponent:
T = 2π((L/480)^(1/2))
Now, let's rationalize the denominator by multiplying both the numerator and denominator by the radical conjugate (√(480)):
T = 2π((L/480)^(1/2) * (√480)/(√480))
Simplifying further, we get:
T = 2π((L * √480)/(480 * (√480))) or
T = 2π((L * √480)/(480√480))
(b) To solve the formula for L, we need to isolate L on one side of the equation:
T = 2π((L * √480)/(480√480))
Multiply both sides of the equation by (480√480):
T * (480√480) = 2π * (L * √480)
Simplifying, we get:
L * √480 = (T * 480√480)/(2π)
Now, we divide both sides of the equation by √480:
L = ((T * 480√480)/(2π))/√480
Simplifying further, we get:
L = (T * 480)/(2π)
I think you mistyped 980
T=2PI (L/980)^.5
to solve for L, square both sides first.
a. T = 2pi*sqrt(L/980).
Square both sides:
T^2 = 4(pi)^2(L/980).
b. Multiply both sides by 980/4(pi)^2:
980T^2/4(pi)^2 = L.