Question

absolute value equations and inequalities
the v - shaped bottom of a river can be modeled with this absolute value equation, where ( d ) represents the depth of the river bottom and ( s ) represents the horizontal distance from the left shore, in feet.
( d=\frac{1}{5}|s - 250|-50 )
part a
question 1
the harbormaster wants to place buoys where the river bottom is 20 feet below the surface of the water.
complete the absolute value equation to find the horizontal distance from the left shore at which the buoys should be placed.

Explanation:

Step1: Substitute d with 20

We know that \( d = 20 \) (since the river bottom is 20 feet below the surface). Substitute \( d = 20 \) into the equation \( d=\frac{1}{5}|s - 250|-50 \).
\( 20=\frac{1}{5}|s - 250|-50 \)

Step2: Isolate the absolute value term

Add 50 to both sides of the equation to isolate the absolute value part.
\( 20 + 50=\frac{1}{5}|s - 250| \)
\( 70=\frac{1}{5}|s - 250| \)

Step3: Solve for the absolute value

Multiply both sides by 5 to get rid of the fraction.
\( 70\times5 = |s - 250| \)
\( 350=|s - 250| \)

But the question is to complete the absolute value equation when \( d = 20 \), so we just need to substitute \( d = 20 \) into the original equation to get the equation to solve for \( s \). So the equation is \( 20=\frac{1}{5}|s - 250|-50 \)

Answer:

\( 20=\frac{1}{5}|s - 250|-50 \)