Solve the Problem $y = \frac { 1 } { 2 } x ^ { 2 }$

question 111

Multiple Choice

Solve the problem.
-A rectangular swimming pool has a parabolic drain plate at the bottom of the pool. The drain plate is shaped like the region between $y = \frac { 1 } { 2 } x ^ { 2 }$ and the line $y = \frac { 1 } { 2 }$ from $x = - 1$ to $x = 1$ . The pool is $10 \mathrm { ft }$ by $20 \mathrm { ft }$ and $8 \mathrm { ft }$ deep. If the drain plate is designed to withstand a fluid force of $200 \mathrm { lb }$ , how high can the pool be filled without exceeding this limitation?

• A) 5 ft 1 in.
• B) 5 ft 6 in.
• C) 5 ft 9 in.
• D) 4 ft 11 in.

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Definitions:

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The amount of oxygen carried by the blood, usually measured to assess lung and heart efficiency and overall health.

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A condition characterized by the narrowing of the aortic valve opening, restricting blood flow from the left ventricle to the aorta.

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A valve in the human heart between the left ventricle and the aorta that prevents blood from flowing back into the ventricle.

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The activation of the vagus nerve, which can reduce heart rate, stimulate digestive activities, and influence various metabolic pathways and immune responses.