graph the absolute value equation that represents the given situation, $d = \\frac{1}{5}|s - 250| - 50$…

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.

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.

Answer

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.