Find the Centroid of the Region Bounded by the Given $$y = x ^ { 3 } , x + y = 2 , x = 0$$

question 49

Multiple Choice

Find the centroid of the region bounded by the given curves.
$$y = x ^ { 3 } , x + y = 2 , x = 0$$

• A) \(\frac { 29 } { 75 } , \frac { 93 } { 105 }\)
• B) \(\frac { 28 } { 75 } , \frac { 92 } { 105 }\)
• C) \(\frac { 92 } { 105 } , \frac { 9 } { 75 }\)
• D) \(\frac { 93 } { 75 } , \frac { 29 } { 105 }\)
• E) None of these

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Definitions:

Slope Coefficient

A measure in regression analysis that quantifies the change in the dependent variable for a one-unit change in an independent variable.

Correlation Coefficient

A measure ranging from -1 to 1 that indicates the strength and direction of the relationship between two variables.

Slope

In mathematics, the slope defines the steepness and direction of a line, calculated as the ratio of the vertical change to the horizontal change between two points on the line.

Multiple Correlation

A mathematical method used to evaluate how strong the association is between one dependent variable and multiple independent variables.