SOLUTION: y varies directly as x and inversely as the square of z calculator. y = 32 when x = 114 and z = 6. find y when x = 3 and z = 6

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Question 1063818: y varies directly as x and inversely as the square of z calculator. y = 32 when x = 114 and z = 6. find y when x = 3 and z = 6
Found 3 solutions by mananth, greenestamps, josgarithmetic:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
y varies directly as x and inversely as the square of z calculator. y = 32 when x = 114 and z = 6. find y when x = 3 and z = 6

+y+++%28alpha%29+++%28x%2Fz%5E2%29


+y+=+k+%28x%2Fz%5E2%29



32=k%28+114%2F36%29
k = (32*36)/114= 10.1052

y = 10.1052*(3/36)= 0.8421

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The other tutor goes to a lot of unnecessary work to get a decimal approximation of the answer.

From the given set of data to the new one, the value of z does not change, so the only change in the value of y is due to the change in the value of x.

y varies directly as x, so when the value of x changes by a factor of 3/114 = 1/38 the value of y changes by a factor of 1/38.

ANSWER: 32(1/38) = 32/38 = 16/19

Convert that to a decimal approximation if required or desired... but the answer in fraction form is exact.


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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y varies directly as x and inversely as the square of z cross%28calculator%29.
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k, variation constant
y=k%28x%2Fz%5E2%29
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yz%5E2=kx
k=%28yz%5E2%29%2Fx

You were then given some values to find what is k value.
k=32%286%5E2%29%2F114
k=32%2836%2F114%29
or better to try
k=%282%2A2%2A2%2A2%2A2%2A2%5E2%2A3%5E2%29%2F%282%2A3%2A19%29
k=%2832%2A6%29%2F19
k=192%2F19--------which might be how you want it;

highlight_green%28y=%28192%2F19%29%28x%2Fz%5E2%29%29-------your variation model.