Question

Direct Variation PLEASE HELP ME

Answer 1

just to add some to @DeanR's reply above.

`\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}`

`\bf \stackrel{\textit{\underline{d}istance varies with applied \underline{f}orce}}{d=kf}\qquad \textit{we also know that } \begin{cases} f=100\\ d=5 \end{cases} \\\\\\ 5=k100\implies \cfrac{5}{100}=k\implies \cfrac{1}{20}=k~\hspace{8em}\boxed{d=\cfrac{1}{20}f} \\\\\\ \textit{when f = 360, what is \underline{d}?}\qquad d=\cfrac{1}{20}(360)\implies d=18`

Answer 2

Direct variation means when we double the force we double the distance. Here we're increasing the force by a factor of 360/100 so our distance is

`5 \textrm{ cm} * \frac{360 \textrm{ N}}{100 \textrm{ N}} = 18 \textrm{ cm}`

Answer: 18