Given `y=wx^(2)` and y is not 0. If the value of x and w are each double, then the value of y is multipled by

Options

A. `1`
B. `2`
C. `4`
D. `8`

Answer

To solve the problem, we start with the given equation:

1. **Start with the original equation**:
\[ y = wx^2 \]

2. **Define the new variables**:
If \( x \) and \( w \) are each doubled, we can define:
- New \( x = 2x \)
- New \( w = 2w \)

3. **Substitute the new values into the equation**:
We want to find the new value of \( y \) (let's call it \( y' \)):
\[ y' = (2w)(2x)^2 \]

4. **Calculate \( (2x)^2 \)**:
\[ (2x)^2 = 4x^2 \]

5. **Substitute back into the equation for \( y' \)**:
Now substituting \( (2x)^2 \) into the equation:
\[ y' = 2w \cdot 4x^2 \]

6. **Simplify the equation**:
\[ y' = 8wx^2 \]

7. **Relate \( y' \) back to \( y \)**:
Since we know from the original equation that \( y = wx^2 \), we can substitute \( wx^2 \) with \( y \):
\[ y' = 8y \]

8. **Conclusion**:
Therefore, when both \( x \) and \( w \) are doubled, the new value of \( y \) becomes:
\[ y' = 8y \]
This means that the value of \( y \) is multiplied by **8**.