Question

if x and y vary inversely and x=-12 when y=3/2 what is y when x=2 ?

Answer 1

Step-by-step explanation:

12-6 -- 6

6+2-- 8 answer

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Answer 2

Concept

When one quantity's value rises relative to another's decline or vice versa, it is said that the two are inversely proportionate. It implies that the two quantities exhibit opposing behaviors in essence.

Given

Inversely varying x and y, with $x=-12$ for $y=\frac{3}{2}$.

Find

We have to find the value of $y$ for the given relation between $x$ and $y$ when $x=2$.

Solution

x and y both varies inversely which means x and y are inversely proportionate, i.e.

$x$∝ $\frac{1}{y}$

This can be written as-

$x=k\frac{1}{y}$    ....(1)

where, $k$ is any constant.

Now, substituting $x=-12$ and $y=\frac{3}{2}$ in equation(1), we get

$-12=k\times\frac{1}{\frac{3}{2} }$

$-12=k\times\frac{2}{{3} }$

$k=\frac{ -12\times3}{2}\\k=-18$

Substituting this value in equation (1), we get the following relation-

$x=\frac{ -18}{y}$ ....(2)

Now, substituting $x=2$ in equation(2), we get

$2=\frac{-18}{y} \\y=\frac{-18}{2} \\y=-9$

Hence, $-9$ is the required value of $y$.

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