SOLUTION: 1.X,Y and Z are such that X varies directly as Z and inversely as the cube root of Y. If X=8,Y=27 and Z=4, find, i.an expression of X in terms of Y and Z. ii.the value of Y when

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Question 1124147: 1.X,Y and Z are such that X varies directly as Z and inversely as the cube root of Y.
If X=8,Y=27 and Z=4, find,
i.an expression of X in terms of Y and Z.
ii.the value of Y when X=12 and Z=10.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

1.X,Y and Z are such that X varies directly as Z and inversely as the cube root of Y.
If X=8,Y=27 and Z=4, find,
i.an expression of X in terms of Y and Z.
X=kZ%2Froot%283%2CY%29
8=k%2A4%2Froot%283%2C27%29
8root%283%2C3%5E3%29=4k
%288%2A3%29%2F4=k
k=4%2A3
k=12



ii.the value of Y when X=12 and Z=10.

X=kZ%2Froot%283%2CY%29
12=%2812%2A10%29%2Froot%283%2CY%29
12root%283%2CY%29=%2812%2A10%29
root%283%2CY%29=%28cross%2812%29%2A10%29%2Fcross%2812%29
root%283%2CY%29=10...cube both sides
%28root%283%2CY%29%29%5E3=10%5E3
Y=1000