Question

a water park manager reviews plans for a water slide. the expression 30 - \frac{5}{8}x^2 represents the elevation of a person on the water slide, where 0 ≤ x ≤ 6. what does -\frac{5}{8} represent?\
\bigcirc the total number of seconds the person is on the water slide\
\bigcirc the height of the water slide at the start of the water slide, when x = 0\
\bigcirc the number of feet of elevation lost by the person from the initial height of 30 feet after x seconds on the water slide\
\bigcirc the number of feet of elevation gained by the person from the initial height of 30 feet after x seconds on the water slide

Explanation:

To determine what \(\frac{5}{8}x\) represents, we analyze the context of the water slide elevation formula \(30 - \frac{5}{8}x\) (where \(x\) is time in seconds). The total elevation starts at 30 feet (initial height) and decreases over time. The term \(\frac{5}{8}x\) should represent the elevation lost as time \(x\) passes, since it's subtracted from the initial 30 feet. Let's check the options:

• "the total number of seconds the person is on the water slide": This would be \(x\), not \(\frac{5}{8}x\), so incorrect.
• "the height of the water slide at the start of the water slide, when \(x = 0\)": At \(x = 0\), \(\frac{5}{8}(0)=0\), and the start height is 30, so this is 30, not \(\frac{5}{8}x\), incorrect.
• "the number of feet of elevation lost by the person from the initial height of 30 feet after \(x\) seconds on the water slide": Since elevation decreases (lost) over time, and \(\frac{5}{8}x\) is the amount subtracted from 30, this matches.
• "the number of feet of elevation gained by the person from the initial height of 30 feet after \(x\) seconds on the water slide": The formula has subtraction, so it's loss, not gain, incorrect.

Answer:

the number of feet of elevation lost by the person from the initial height of 30 feet after \( x \) seconds on the water slide