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Suppose that y is inversely proportional to square root of x. Find the constant of proportionality k if y = 15 when x = 18. k= Using the k from above write the variation equation in terms of x. y = Using the k from above find y given that x = 42. y = If needed, round answer to 3 decimal places. Enter DNE for Does Not Exist, oo for Infinity Question Help: D Video

Suppose that y is inversely proportional to square root of x Find the constant of proportionality k if y 15 when x 18 k Using the k from above write the variati class=

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Answer:

(a)k=63.64

(c)y=9.82

Explanation:

Part A

If y is inversely proportional to the square root of x, we have:

[tex]y=\frac{k}{\sqrt[]{x}},\text{ k=constant of proportionality}[/tex]

If y=15 and x=18:

[tex]\begin{gathered} k=y\times\sqrt[]{x} \\ =15\times\sqrt[]{18} \\ =45\sqrt[]{2} \\ k\approx63.640\text{ (correct to 3 decimal places)} \end{gathered}[/tex]

Part B

The variation equation in terms of x is:

[tex]y=\frac{63.64}{\sqrt[]{x}}[/tex]

Part C

When x=42

[tex]\begin{gathered} y=\frac{63.64}{\sqrt[]{42}} \\ y=9.820\text{ (correct to 3 decimal places)} \end{gathered}[/tex]

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