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3 years ago

If y varies inversely as x, and y=10 when x=2, find y when x=8

Mathematics

2 answers:

snow_lady [41]3 years ago

5 0

If it varies inversely, then their product is the same. So,
10*2 = y*8
20 = y*8
/8 /8
5/2 = y
y = 2.5

dedylja [7]3 years ago

4 0

$\bf \qquad \qquad \textit{inverse proportional variation}\\\\
\textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby 
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\
\textit{we also know that }
\begin{cases}
y=10\\
x=2
\end{cases}\implies 10=k2\implies \cfrac{10}{2}=k\implies 5=k
\\\\\\
therefore\qquad \boxed{y=\cfrac{5}{x}}
\\\\\\
\textit{when x = 8, what is \underline{y}?}\qquad y=\cfrac{5}{8}$

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$\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}\\\\
-------------------------------\\\\
\textit{we know that }
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\end{cases}\implies 12=k3\implies \cfrac{12}{3}=k\implies 4=k
\\\\\\
thus\qquad \boxed{y=4x}
\\\\\\
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