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

question 21

Multiple Choice

Find the unit tangent vector for the curve given by $\mathbf { r } ( t ) = \left\langle \frac { 1 } { 7 } t ^ { 7 } , \frac { 1 } { 3 } t ^ { 3 } , t \right\rangle$ .

• A) \(\frac { \left\langle t ^ { 6 } , t ^ { 2 } , 1 \right\rangle } { \sqrt { t ^ { 10 } + t ^ { 4 } } }\)
• B) \(\frac { \left\langle t ^ { 6 } , t ^ { 2 } , 1 \right\rangle } { \sqrt { 6 t ^ { 12 } + 4 t ^ { 4 } + 1 } }\)
• C) \(\frac { \left\langle t ^ { 6 } , t ^ { 2 } , 1 \right\rangle } { \sqrt { t ^ { 12 } + t ^ { 4 } } }\)
• D) \(\frac { \left\langle t ^ { 6 } , t ^ { 2 } , 1 \right\rangle } { \sqrt { t ^ { 12 } + t ^ { 4 } + 1 } }\)
• E) None of these

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Definitions:

Level of Significance

A threshold or cut-off value used in statistical tests to decide whether to reject the null hypothesis, typically denoted by alpha (α).

Protanopia

A type of color blindness characterized by difficulty in distinguishing between red and green colors.

Deuteranopia

A form of colorblindness where individuals have trouble telling green and red colors apart.

Colorblindness

A deficiency in the way one sees color, making it difficult to distinguish certain colors from another.