Given `w=-2,x=3,y=0 & Z=-1/2,` Find the value of `w^2 sqrt((Z^2+y^2))`.

Options

A. `+_2`
B. -2
C. 2
D. 4

Answer

To find the value of the expression \( w^2 \sqrt{(Z^2 + y^2)} \) given the values \( w = -2 \), \( x = 3 \), \( y = 0 \), and \( Z = -\frac{1}{2} \), we can follow these steps:

### Step 1: Calculate \( w^2 \)
Given \( w = -2 \):
\[ w^2 = (-2)^2 = 4 \]

### Step 2: Calculate \( Z^2 \)
Given \( Z = -\frac{1}{2} \):
\[ Z^2 = \left(-\frac{1}{2}\right)^2 = \frac{1}{4} \]

### Step 3: Calculate \( y^2 \)
Given \( y = 0 \):
\[ y^2 = 0^2 = 0 \]

### Step 4: Sum \( Z^2 + y^2 \)
Now we can sum \( Z^2 \) and \( y^2 \):
\[ Z^2 + y^2 = \frac{1}{4} + 0 = \frac{1}{4} \]

### Step 5: Calculate \( \sqrt{(Z^2 + y^2)} \)
Now we find the square root:
\[ \sqrt{(Z^2 + y^2)} = \sqrt{\frac{1}{4}} = \frac{1}{2} \]

### Step 6: Multiply \( w^2 \) and \( \sqrt{(Z^2 + y^2)} \)
Finally, we multiply \( w^2 \) by \( \sqrt{(Z^2 + y^2)} \):
\[ w^2 \sqrt{(Z^2 + y^2)} = 4 \cdot \frac{1}{2} = 2 \]

### Final Answer
The value of the expression \( w^2 \sqrt{(Z^2 + y^2)} \) is \( 2 \).

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