Suppose That $f ( x , y , z ) = g \left( \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } \right)$

question 68

Multiple Choice

Suppose that $f ( x , y , z ) = g \left( \sqrt { x ^ { 2 } + y ^ { 2 } + z ^ { 2 } } \right)$ where g is a function of one variable such that $g ( 5 ) = 8$ . Evaluate $\iint _ { S } f ( x , y , z ) d S$ where S is the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 25$

• A) \(920 \pi\)
• B) \(820 \pi\)
• C) \(800 \pi\)
• D) \(880 \pi\)
• E) None of these

Explain the theory and practice of dual federalism and how it evolved over time.

Differentiate between dual federalism and new federalism.

Identify and articulate the purposes and types of federal grants, including matching grants, grants-in-aid, and categorical grants.

Discuss the concept of "laboratories of democracy" and its significance in the American political system.

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