Solve the Problem B) C) D)

question 22

Multiple Choice

Solve the problem.
-Let D be the smaller cap cut from a solid ball of radius 9 units by a plane 3 units from the center of the sphere. Set up the triple integral for the volume of D in spherical coordinates.

• A) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \tan ^ { - 1 } ( \sqrt { 72 } / 3 ) } \int _ { \sec \varphi } ^ { 9 } \varrho ^ { 2 } \sin \varphi \mathrm { d } \varphi \mathrm { d } \varphi \mathrm { d } \theta\)
• B) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \tan ^ { - 1 } ( \sqrt { 72 } / 9 ) } \int _ { 3 \sec \varphi } ^ { 9 } \varrho ^ { 2 } \sin \varphi \mathrm { de } \mathrm { d } \varphi \mathrm { d } \theta\)
• C) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \tan ^ { - 1 } ( \sqrt { 72 } / 9 ) } \int _ { \sec \varphi } ^ { 9 } \varrho ^ { 2 } \sin \varphi \mathrm { de } d \varphi d \theta\)
• D) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \tan ^ { - 1 } ( \sqrt { 72 } / 3 ) } \int _ { 3 \sec \varphi } ^ { 9 } \varrho ^ { 2 } \sin \varphi \mathrm { d } \operatorname { d } \varphi \mathrm { d } \theta\)

Recognize the entrepreneurial role in economic profit generation and the functions they typically do not undertake.

Understand the concept and importance of profit in entrepreneurship.

Grasp the distinction between economic and accounting profits.

Recognize the structure of income distribution in capitalist economies, including the shares for labor and capitalists.

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Definitions:

Evaluate

To compute the value of a particular expression.

Irrational

A type of number that cannot be expressed as a simple fraction, including numbers like \(\pi\) and \(\sqrt{2}\).

Rational

Pertaining to a number or expression that can be expressed as the quotient or ratio of two integers.

Square Root

The number that produces a specified quantity when multiplied by itself (e.g., the square root of 9 is 3).