Find the Volume of the Solid Generated by Revolving the Region

question 95

Multiple Choice

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line $y = 2$ $$y = \frac { 1 } { 2 } x ^ { 2 } , y = 2 , x = 0$$

• A) \(\frac { 8 } { 15 } \pi\)
• B) \(\frac { 32 } { 15 } \pi\)
• C) \(\frac { 64 } { 15 } \pi\)
• D) \(\frac { 4 } { 15 } \pi\)
• E) \(\frac { 16 } { 15 } \pi\)

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Definitions:

Regression Assumptions

Conditions that must be met for the regression analysis results to be valid, including linearity, independence, homoscedasticity, and normality of residuals.

F Distribution

A probability distribution that arises in the testing of whether two population variances are equal and in the analysis of variance (ANOVA) for comparing means among more than two groups.

Coefficient of Multiple Determination

A statistic that quantifies the proportion of variance in the dependent variable that is predictable from the independent variables, commonly used in multiple regression analysis.

Regression Equation

An equation derived in regression analysis that represents the expected value of the dependent variable as a function of one or more independent variables.