Question

supose that x and y vary inversely, and x=8 when y=10. Write the function that models the inverse variation

Answer 1

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Answer 2

so given that y(8) = 10
then if you take the inverse \[8 = y^{-1}(10)\]so if you let f be the inverse of y(x), then \[f(10)=8\]

Answer 3

Translation : "y varies inversly with x" means
\[y=\frac{k}{x}.\]
Now use what you know: when x = 8 then y = 10. Plug these numbers in so you can solve for k.
\[10 = \frac{k}{8}.\]
To solve for k, multiply both sides of the equation by 8,
\[80 = k.\]
Thus you have the desired function,
\[y = \frac{80}{x}.\]

Answer 4

Thank you so much