SOLUTION: if w is jointly proportional to the cube of x and to the cube root of y, and w=336 when x=2 and y=216, then A.) find a general formula to describe the relationship (use fractional

Algebra ->  Volume -> SOLUTION: if w is jointly proportional to the cube of x and to the cube root of y, and w=336 when x=2 and y=216, then A.) find a general formula to describe the relationship (use fractional      Log On


   

Question 475789: if w is jointly proportional to the cube of x and to the cube root of y, and w=336 when x=2 and y=216, then
A.) find a general formula to describe the relationship (use fractional exponents rather than radicals, if necessary) and
B.) use the formula to find w when x=8 and y=8. Round your answer to 2 decimal places, if necessary.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
if w is jointly proportional to the cube of x and to the cube root of y, and w=336 when x=2 and y=216, then
:
A.) find a general formula to describe the relationship (use fractional exponents rather than radicals, if necessary)
Let k = constant of the variation
w = x%5E3%2Ay%5E%281%2F3%29%2Ak
w=336 when x=2 and y=216,
2%5E3%2A216%5E%281%2F3%29%2Ak = 336
8 * 6 * k = 336
48k = 336
k = 336%2F48
k = 7
the formula
w = 7%2Ax%5E3%2Ay%5E%281%2F3%29
:
:
and
B.) use the formula to find w when x=8 and y=8.
w = 7%2A8%5E3%2A8%5E%281%2F3%29
w = 7 * 512 * 2
w = 7168