Question

graph the absolute value equation that represents the given situation, $d = \frac{1}{5}|s - 250| - 50$. then mark the points that represent the horizontal distance from the left shore where the river bottom is 20 feet below the surface.

Explanation:

Step1: Set \( d = -20 \) (since 20 feet below the surface)

We know the equation is \( d=\frac{1}{5}|s - 250|-50 \). Substitute \( d=-20 \) into the equation:
\( -20=\frac{1}{5}|s - 250|-50 \)

Step2: Solve for the absolute value expression

Add 50 to both sides of the equation:
\( -20 + 50=\frac{1}{5}|s - 250| \)
\( 30=\frac{1}{5}|s - 250| \)

Step3: Eliminate the fraction

Multiply both sides by 5:
\( 30\times5 = |s - 250| \)
\( 150=|s - 250| \)

Step4: Solve the absolute value equation

The absolute value equation \( |s - 250| = 150 \) gives two cases:
Case 1: \( s - 250=150 \)
Add 250 to both sides: \( s=150 + 250=400 \)
Case 2: \( s - 250=-150 \)
Add 250 to both sides: \( s=-150 + 250 = 100 \)

Answer:

The points representing the horizontal distance \( s \) are \( s = 100 \) and \( s = 400 \). So we mark the points \( (100, -20) \) and \( (400, -20) \) on the graph (but since we are asked for the horizontal distance \( s \), the values are 100 and 400).