Question

when y varies directly as the square root of x, the variation equation is y=kx^2
I) y=50 and x=10 find k
ii) calculate y when x=30​

Answer 1

$\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill$

$\stackrel{ \begin{array}{llll} \textit{\tiny "y" varies directly}\\ \textit{\tiny as the square of "x"} \end{array}}{y = kx^2}\qquad \qquad \textit{we also know that} \begin{cases} y=50\\ x=10 \end{cases}\implies 50=k(10)^2 \\\\\\ \cfrac{50}{10^2}=k\implies \cfrac{1}{2}=k~\hfill \boxed{y=\cfrac{1}{2}x^2} \\\\\\ \textit{when x = 30, what is "y"?}\qquad y = \cfrac{1}{2}(30)^2\implies y = 450$