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

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
Transcript text: " $y$ is directly proportional to $x$ and inversely proportional to the square of $w$ " Give the equation. $y=\frac{k x}{\sqrt{w}}$ $y=\frac{x}{k w^{2}}$ $y=\frac{k x}{w^{2}}$ None of the above
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Solution

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Solution Steps

Step 1: Understand the Relationship

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.

Step 2: Substitute Given Values

We are given:

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

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

Step 3: Simplify the Expression

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

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

Step 4: Calculate the Result

Perform the division: \[ y = 7.5 \]

Final Answer

\(\boxed{y = \frac{kx}{w^2}}\)

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