Find the Unit Tangent Vector for the Curve Given By \mathbf

question 39

Multiple Choice

Find the unit tangent vector for the curve given by $\mathbf { r } ( t ) = \left\langle \frac { 1 } { 5 } t ^ { 5 } , \frac { 1 } { 3 } t ^ { 3 } , t \right\rangle$ .

• A) \(\frac { \left\langle t ^ { 4 } , t ^ { 2 } , 1 \right\} } { \sqrt { t ^ { 10 } + t ^ { 4 } } }\)
• B) \(\frac { \left\langle t ^ { 4 } , t ^ { 2 } , 1 \right) } { \sqrt { 4 t ^ { 8 } + 4 t ^ { 4 } + 1 } }\)
• C)
• \(\frac { \left\langle t ^ { 4 } , t ^ { 2 } , 1 \right) } { \sqrt { t ^ { 8 } + t ^ { 4 } + 1 } }\)
• D)
• \(\frac { \left\langle t ^ { 4 } , t ^ { 2 } , 1 \right\rangle } { \sqrt { t ^ { 8 } + t ^ { 4 } } }\)
• E) None of these

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Definitions:

Receptor Molecules

Specialized proteins located on or within cells that bind to specific substances, triggering cellular responses.

Chemically Altered

A term describing a substance whose chemical composition has been changed through a reaction or process.

CAMP

Cyclic adenosine monophosphate; a second messenger important in many biological processes.

Protein Kinase

Class of enzymes that phosphorylates other proteins. Many of these kinases are responsive to other chemical signals (e.g., cAMP, cGMP, insulin, epidermal growth factor, calcium, and calmodulin).