Question

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

Answer 1

(a)k=63.64

(c)y=9.82

Step-by-step explanation:

Part A

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

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

If y=15 and x=18:

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

Part B

The variation equation in terms of x is:

`y=\frac{63.64}{\sqrt[]{x}}`

Part C

When x=42

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