Question

if x varies inversely as the cube of y when y=2 and the value of x = 81 what will be the value of y when x= 3
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Answer 1

SOLUTION

GIVEN

x varies inversely as the cube of y when y = 2 and the value of x = 81

TO DETERMINE

The value of y when x = 3

EVALUATION

Here it is given that x varies inversely as the cube of y

$\displaystyle \sf{x \propto \: \frac{1}{ {y}^{3} } }$

$\displaystyle \sf{ \implies \: x = \: \frac{k}{ {y}^{3} } } \: \: - - - - (1)$

Now x = 81 when y = 2

$\displaystyle \sf{ \: 81 = \: \frac{k}{ {(2)}^{3} } } \: \:$

$\displaystyle \sf{ \implies \:k = 81 \times 8 }$

$\displaystyle \sf{ \implies \:k = 648 }$

From Equation 1 we get

$\displaystyle \sf{ \implies \: x = \: \frac{648}{ {y}^{3} } } \: \: - - - - (2)$

Now when x = 3 we get

$\displaystyle \sf{ \implies \: 3 = \: \frac{648}{ {y}^{3} } } \: \:$

$\displaystyle \sf{ \implies \: {y}^{3} = \: 216} \: \:$

$\displaystyle \sf{ \implies \: y = 6} \: \:$

Hence the required value y = 6

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