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 surface)

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

Step2: Solve for the absolute value term

First, 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 \( |x|=a \) (where \( a\geq0 \)) has solutions \( x = a \) or \( x=-a \). So we have 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 are at \( s = 100 \) and \( s = 400 \), so we mark the points (100, -20) and (400, -20) on the graph.