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

Understand the concept of median as a measure of central tendency and its utility over mean in certain datasets.

Appreciate the importance of data archiving for the future utility and secondary analysis in sociological research.

Recognize the significance of publicizing research findings for the sociological community and society at large.

Understand the steps involved in the sociological research cycle, particularly publication as a crucial phase.

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Definitions:

Linear Association

A relationship between two variables where the rate of change in one variable is constant with respect to the other.

Scatterplot

A type of graph in statistics used to display values for two variables for a set of data, showing the relation between them.

Histogram

A graphical representation of the distribution of numerical data, where the data is grouped into ranges and represented as bars.

Daily Sales

The total revenue generated from sales of goods or services in a single business day.