Question 1018075: Given that u^2 is directly proportional to cube of w.find the value of w when u=27,if u=8 when u=8.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the general formula for direct variation is y = kx
when y = u^2 and x = w^3, this formula becomes u^2 = k * w^3
when u = 8 and w = 8,m this formula becomes 8^2 = k * 8^3.
solve for k to get k = 8^2 / 8^3 = 1/8.
when u = 27 and k = 1/8, the formula becomes 27^2 = 1/8 * w^3
multiply both sides of this equation by 8 to get 27^2 * 8 = w^3
take the cube root of each side of this equation to get cube root of (27^2 * 8) = cube root of (w^3).
simplify to get cube root of (27^2 * 8) = w.
this can be expressed as cube root of (27 * 27 * 8)
since cube root of 27 is 3 and cube root of 8 is 2, this becomes:
cube root of (3^3 * 3^3 * 2^3) which can then be expressed as cube root of (3^3) * cube root of (3^3) * cube root of (2^3) which can then be expressed as 3 * 3 * 2 which is equal to 18.
the cube root of (27^2 * 8) is equal to 18.
you can use your calculator to confirm.
when u = 27, w is equal to 18.
you get u^2 = k * w^3 becomes 27^2 = 1/8 * 18^3 which becomes 729 = 5832 / 8 which becomes 729 = 729.
this ocnfirms the solution is good.
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