If y varies inversely as x and y=−97 when x=28, find y if x=36. (Round off your answer to the nearest hundredth.)

Question

03-11-2022
Mathematics

contestada

If y varies inversely as x and y=−97 when x=28, find y if x=36. (Round off your answer to the nearest hundredth.)

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TanisU19514 TanisU19514 · Answer 1 · 2022-11-03T13:26:00+01:00

For this problem, we were informed that two variables "x" and "y" vary inversely to each other. We were also informed about one data point on the relation between the two (28, -97). From this information, we need to determine the value of "y" when "x" is equal to 36.

We can write the expression between two variables that vary inversely according to a constant, K, as shown below:

[tex]\begin{gathered} y\cdot x=k \\ y=\frac{k}{x} \end{gathered}[/tex]

We can find the value of k by applying the known datapoint.

[tex]\begin{gathered} -97=\frac{k}{28} \\ k=-97\cdot28 \\ k=2716 \end{gathered}[/tex]

The full expression is:

[tex]y=\frac{2716}{x}[/tex]

Now we can apply the value of "x" to calculate the desired "y".

[tex]y=\frac{2716}{36}=75.44[/tex]

The value of "y" is 75.44, when "x" is 36