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

question 224

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 $\mathrm { y } = \frac { 1 } { 2 } \mathrm { x } ^ { 2 }$ and the line $\mathrm { y } = \frac { 1 } { 2 }$ from $\mathrm { x } = - 1$ to $\mathrm { x } = 1$ . The pool is $10 \mathrm { ft }$ by $20 \mathrm { ft }$ and $8 \mathrm { ft }$ deep.
If the pool is being filled at a rate of $200 \mathrm { ft } ^ { 3 } / \mathrm { hr }$ , what is the force on the drain plate after 4 hours of filling? Round your answer to two decimal places if necessary.

• A) 486.72 lb
• B) 166.4 lb
• C) 76.96 lb
• D) 153.92 lb

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Definitions:

Sympathetic Nervous System

Part of the autonomic nervous system that prepares the body for fast action in situations perceived as stressful or dangerous, often known as the "fight or flight" response.

Stimulates Digestion

The process or action that encourages the digestive system to break down food more effectively, potentially through the release of digestive enzymes or the promotion of gut motility.

Accelerates Heartbeat

Causes an increase in the speed of heart contractions, often as a response to exercise, stress, or excitement.

Endocrine System

A network of glands in the body that secrete hormones into the bloodstream to regulate various bodily functions.