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Nastasia [14]
3 years ago
5

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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Answer:

Yes, the given parallelogram is a rectangle.

Step-by-step explanation:

The vertices of parallelogram are J(-5,0), K(1,4), L(3,1) and M(-3,-3).

The slope formula is

m=\frac{y_2-y_1}{x_2-x_1}

JK=\frac{4-0}{1-(-5)}=\frac{4}{6}=\frac{2}{3}

KL=\frac{1-4}{3-1}=\frac{-3}{2}

LM=\frac{-3-1}{-3-3}=\frac{-4}{-6}=\frac{2}{3}

JM=\frac{-3-0}{-3-(-5)}=\frac{-3}{2}

The slopes of opposites sides are same it means they are parallel to each other.

The product of slopes of two consecutive sides is

\frac{2}{3}\times \frac{-3}{2}=-1

Since the product of slopes of two consecutive sides is -1, therefore the consecutive sides are perpendicular to each other.

Yes, the given parallelogram is a rectangle.

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Y varies directly as x when x= 3 and y =12 find y when x =12
andrew-mc [135]
\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 }
\begin{cases}
x=3\\
y=12
\end{cases}\implies 12=k3\implies \cfrac{12}{3}=k\implies 4=k
\\\\\\
thus\qquad \boxed{y=4x}
\\\\\\
\textit{when x = 12, what is \underline{y}?}\qquad \qquad y=4(12)
3 0
3 years ago
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