Question

write as a power function:
y varies directly with the square root
of x and y is 10 when x is 25.

y = ?√

Explanation:

Step1: Recall direct variation formula

For direct variation, if \( y \) varies directly with \( \sqrt{x} \), the formula is \( y = k\sqrt{x} \), where \( k \) is the constant of variation.

Step2: Substitute known values

We know \( y = 10 \) when \( x = 25 \). Substitute these into the formula: \( 10 = k\sqrt{25} \).

Step3: Solve for \( k \)

Since \( \sqrt{25}=5 \), the equation becomes \( 10 = k\times5 \). Divide both sides by 5: \( k=\frac{10}{5}=2 \).

Step4: Write the power function

Substitute \( k = 2 \) back into \( y = k\sqrt{x} \), we get \( y = 2\sqrt{x} \).

Answer:

\( y = 2\sqrt{x} \) (So the first box is 2 and the second box is \( x \))