The pair of points is on the graph of an inverse variation. Find the missing value. (1.6, 6) and (8, y) 0.03 30 1.2 0.83

Question

The pair of points is on the graph of an inverse variation. Find the missing value. (1.6, 6) and (8, y) 0.03 30 1.2 0.83

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    0
    2021-09-08T23:39:52+00:00

    Answer: 1.2

    Step-by-step explanation:

    The formula for inverse variation  is given by :-

    x_1y_1=x_2y_2

    The given points : (1.6, 6) and (8, y)

    It means at x = 1.6 , y=6 .

    To find the value of y at x=8 , we substitute x_1=1.6,\ y_1=6\, \text{ and}\ x_2=8,\ y_2=y in the above formula , we get

    1.6\times6=8y\\\\\Rightarrow\ y=\dfrac{1.6\times6}{8}\\\\\Rightarrow\ y=1.2

    Thus, the missing value = 1.2

    0
    2021-09-08T23:40:30+00:00

    one may note that (1.6 , 6)  is just another way to say x = 1.6 when y = 6.

    and that (8 , y) is another way to say x = 8 and y is who knows.

    \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}\\\\ -------------------------------

    \bf \textit{we know that } \begin{cases} x=1.6\\ y=6 \end{cases}\implies 6=\cfrac{k}{1.6}\implies 6(1.6)=k\implies 9.6=k \\\\\\ \qquad therefore\qquad \boxed{y=\cfrac{9.6}{x}} \\\\\\ \textit{when x = 8, what is \underline{y}?}\qquad y=\cfrac{9.6}{8}

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