Question

Which equation represents an inverse variation with a constant of 56? A: y/x = 56 B: 1/4y = 14x C: 7/y = 8/x D: xy/2 = 28

Answer 1

`\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{xy}{2}=28\implies \stackrel{\textit{cross-multiplying}}{xy=56}\implies y=\cfrac{\stackrel{\stackrel{k}{\downarrow }}{56}}{x}`

Answer 2

The equation that represents an inverse variation with a constant of 56 is:

Option: D

D.
`(xy)/(2)=28`

Explanation:

Inverse Variation--

It is a relationship between two variables such that it is given in the form that:

If x and y are two variables then they are said to be in inverse variation if there exist a constant k such that:

`y=(k)/(x)`

i.e.

`xy=k`

Here the constant of variation is 56

i.e. k=56

Hence, we have:

`xy=56\\\\i.e.\\\\xy=28* 2\\\\i.e.\\\\(xy)/(2)=28`

Hence, option: D is the correct answer.