Solve the Problem $V ( x ) = 5 x ^ { 2 }$

question 36

Multiple Choice

Solve the problem.
-The volume of a rectangular box with square base and a height of 5 feet is $V ( x ) = 5 x ^ { 2 }$ , where $x$ is the length of a side of the base. Find the instantaneous rate of change of volume with respect to $x$ when $x = 3$ feet.

• A) \(45 \mathrm { ft } ^ { 3 } / \mathrm { ft }\)
• B) \(30 \mathrm { ft } ^ { 3 } / \mathrm { ft }\)
• C) \(6 \mathrm { ft } ^ { 3 } / \mathrm { ft }\)
• D) \(15 \mathrm { ft } ^ { 3 } / \mathrm { ft }\)

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Definitions:

P-Value

A measure of the strength of evidence against the null hypothesis provided by a statistical test, representing the probability of observing the test results under the assumption that the null hypothesis is true.

Explanatory Variables

Factors in a statistical model employed to account for changes in the outcome variable.

Multicollinearity

A statistical phenomenon in which two or more predictor variables in a multiple regression model are highly correlated, potentially distorting the results of the model.

Variables

Elements, characteristics, or features that can assume different values in a study or experiment, influencing the outcomes being measured.