Questions: y is directly proportional to x and inversely proportional to the square of w. Give the equation. y = kx / sqrt(w) y = x / kw^2 y = kx / w^2 None of the above

Solution Steps

The problem states that \( y \) is directly proportional to \( x \) and inversely proportional to the square of \( w \). This can be expressed mathematically as: \[ y = \frac{kx}{w^2} \] where \( k \) is the constant of proportionality.

We are given:

• \( x = 10 \)
• \( w = 2 \)
• \( k = 3 \)

Substitute these values into the equation: \[ y = \frac{3 \times 10}{2^2} \]

Calculate the denominator: \[ 2^2 = 4 \]

Substitute back into the equation: \[ y = \frac{30}{4} \]

Perform the division: \[ y = 7.5 \]

Final Answer