Questions: Evaluate ( frac5 xy^2 ) for each of the following combinations: - ( x=-2, y=-4 ) - ( x=-0, y=-4 ) - ( x=-4, y=0 )

$Evaluate ( frac5 xy^2 ) for each of the following combinations: - ( x=-2, y=-4 ) - ( x=-0, y=-4 ) - ( x=-4, y=0 )$

Transcript text: Evaluate $\frac{5 x}{y^{2}}$ for each of the following combinations: \[ \begin{array}{l} x=-2, y=-4 \\ x=-0, y=-4 \\ x=-4, y=0 \end{array} \]

Solution

Solution Steps

To evaluate the expression $\frac{5x}{y^2}$ for each given combination of $x$ and $y$, substitute the values of $x$ and $y$ into the expression and compute the result. Be cautious of division by zero, which occurs when $y = 0$.

Step 1: Evaluate for $ x = -2, y = -4 $

Substituting $ x = -2 $ and $ y = -4 $ into the expression $ \frac{5x}{y^2} $: \[ \frac{5(-2)}{(-4)^2} = \frac{-10}{16} = -\frac{5}{8} \]

Step 2: Evaluate for $ x = 0, y = -4 $

Substituting $ x = 0 $ and $ y = -4 $ into the expression: \[ \frac{5(0)}{(-4)^2} = \frac{0}{16} = 0 \]

Step 3: Evaluate for $ x = -4, y = 0 $

Substituting $ x = -4 $ and $ y = 0 $ into the expression: \[ \frac{5(-4)}{0^2} \] This results in division by zero, which is undefined.