Question

given that s varies directly with t, and that s = 4.56 meters when t = 3 seconds, find s when t is 4.2 seconds

Answer 1

`\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}\\\\ -------------------------------`


`\bf \textit{\underline{s} varies directly with \underline{t}}\qquad s=kt \\\\\\ \textit{we also know that } \begin{cases} s=4.56\\ t=3 \end{cases}\implies 4.56=k3\implies \cfrac{4.56}{3}=k \\\\\\ 1.52=k\qquad therefore\qquad \boxed{s=1.52t} \\\\\\ \textit{when t = 4.2, what is \underline{s}?}\qquad s=1.52(4.2)`