$$\text { Find the required quantity given the wire that lies along the curve } r \text { and has density } \delta .$$

question 97

Multiple Choice

$$\text { Find the required quantity given the wire that lies along the curve } r \text { and has density } \delta .$$
-Moment of inertia $I _ { x }$ about the $x$ -axis, where $\mathbf { r } ( t ) = \frac { 10 } { 3 } \sqrt { 2 } t 3 / 2 \mathbf { i } + ( 5 t \cos t ) j + ( 5 t \sin t ) \mathbf { k } , 0 \leq t \leq 1$ ; $\delta ( x , y , z ) = \frac { 9 } { y ^ { 2 } + z ^ { 2 } }$

• A) \(\mathrm { I } _ { \mathrm { X } } = 45\)
• B) \(\mathrm { I } _ { \mathrm { X } } = 0\)
• C) \(I _ { X } = 90\)
• D) \(\mathrm { I } _ { \mathrm { x } } = \frac { 135 } { 2 }\)

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Definitions:

Antietam Victory

Marks the victory of Union forces during the Battle of Antietam in the Civil War, which represents one of the bloodiest single-day battles in American history.

Robert E. Lee's Army

The principal military force of the Confederate States of America under the command of General Robert E. Lee during the American Civil War.

Confederates

Individuals or entities aligned with or supportive of the Confederate States of America, a group of southern states that seceded from the United States leading to the American Civil War from 1861 to 1865.