Solve the Problem $z = 5 x ^ { 2 } + 10 y ^ { 2 }$

question 191

Multiple Choice

Solve the problem.
-Find the average height of the paraboloid $z = 5 x ^ { 2 } + 10 y ^ { 2 }$ above the annular region $9 \leq x ^ { 2 } + y ^ { 2 } \leq 100$ in the $x y$ -plane.

• A) \(\frac { 545 } { 2 }\)
• B) \(\frac { 1635 } { 4 }\)
• C) \(\frac { 2725 } { 4 }\)
• D) 545

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Definitions:

Humerus

The long bone in the upper arm or forelimb, extending from the shoulder to the elbow.

Extensor Carpi Ulnaris

A muscle of the forearm that extends and adducts the wrist.

Pronator Quadrates

A muscle in the forearm that helps to pronate (turn so the palm is facing downwards) the hand.

Medial Border

The side of a structure that is closest to the midline of the body.