Question

If y varies directly as x, and y is 400 when x is r and y is r when x is 4, what is the numeric constant of variation in this relation?

Answer 1

EDGE 2020

Explanation:

A) 10

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Answer 2

`\bf \begin{array}{cccccclllll} \textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\ \textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\ y&=&{{ k}}&\cdot&x \\ && y={{ k }}x \end{array}\\\\ -----------------------------\\\\`


`\bf \textit{now, we also know }\qquad \begin{cases} y=400\\ x=r\\ ---\\ y=r\\ x=4 \end{cases}\implies \begin{cases} 400=kr\\ r=k4\\ ----------\\ now\\ 400=kr\implies (400)/(k)=\boxed{r}\\\\ thus\\\\ r=k4\implies \boxed{(400)/(k)}=4k \end{cases} \\\\\\ 400=4k^2\implies \cfrac{400}{4}=k^2\implies 100=k^2\implies √(100)=k \\\\\\ 10=k\impliedby \textit{constant of variation}`