Reparametrize the Curve with Respect to Arc Length Measured from the Point

question 12

Multiple Choice

Reparametrize the curve with respect to arc length measured from the point where $t = 0$ in the direction of increasing $t$ .
$\mathbf { r } ( t ) = ( 5 + 3 t ) \mathbf { i } + ( 8 + 9 t ) \mathbf { j } - ( 6 t ) \mathbf { k }$

• A) \(\mathbf { r } ( t ( s ) ) = \left( 5 - \frac { 3 } { \sqrt { 126 } } s \right) \mathbf { i } + \left( 8 + \frac { 9 } { \sqrt { 126 } } s \right) \mathbf { j } - \left( \frac { 6 s } { \sqrt { 126 } } \right) \mathbf { k }\)
• \(\mathbf { r } ( t ( s ) ) = \left( 5 + \frac { 3 } { \sqrt { 126 } } s \right) \mathbf { i } + \left( 8 - \frac { 9 } { \sqrt { 126 } } s \right) \mathbf { j } - \left( \frac { 6 s } { \sqrt { 126 } } \right) \mathbf { k }\)
• B)
• \(\mathbf { r } ( t ( s ) ) = \left( 5 + \frac { 3 } { \sqrt { 126 } } s \right) \mathbf { i } + \left( 8 + \frac { 9 } { \sqrt { 126 } } s \right) \mathbf { j } + ( 6 s ) \mathbf { k }\)
• C)
• \(\mathbf { r } ( t ( s ) ) = \left( 5 + \frac { 3 } { \sqrt { 126 } } s \right) \mathbf { i } + \left( 8 + \frac { 9 } { \sqrt { 126 } } s \right) \mathbf { j } - \left( \frac { 6 s } { \sqrt { 126 } } \right) \mathbf { k }\)
• D)
• \(\mathbf { r } ( t ( s ) ) = \left( 5 + \frac { 3 } { \sqrt { 126 } } s \right) \mathbf { i } + \left( 8 + \frac { 9 } { \sqrt { 126 } } s \right) \mathbf { j } - ( 6 s ) \mathbf { k }\)

Comprehend the philosophical concepts and religious practices of Hinduism, Buddhism, and other local beliefs reflected in the art, literature, and architecture.

Identify and describe the significance of key archaeological sites and architectural forms in the historical and cultural context of South and Southeast Asia.

Recognize the role of religious symbolism and iconography in the artistic expressions found in South and Southeast Asian art.

Appreciate the diversity and evolution of artistic styles and genres across different regions and periods in South and Southeast Asia.

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Definitions:

Diminishing Returns

A principle indicating that as more of a variable input is added to a fixed input, the added output from each additional unit of input will eventually decrease.

Resource Labor

The work force considered as an economic resource, emphasizing the skills and abilities workers bring to the economy.

Marginal Output

The additional quantity of output that is produced by using one more unit of a particular input, holding all other inputs constant.

Fixed Resources

Assets and resources owned by a business or economy that cannot be easily changed in the short term, such as buildings and land.