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

question 92

Multiple Choice

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

• A) \(\frac { \left\langle t ^ { 4 } , t ^ { 2 } , 1 \right) } { \sqrt { t ^ { 10 } + t ^ { 4 } } }\)
• B) \(\frac { \left( t ^ { 4 } , t ^ { 2 } , 1 \right) } { \sqrt { 4 t ^ { 8 } + 4 t ^ { 4 } + 1 } }\)
• 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:

Crossover Point

The point at which two different options have equal costs or benefits, influencing a change in decision.

Fixed Costs

Costs that do not vary with the volume of production, such as rent, salaries, and insurance.

Variable Costs

Expenses that vary directly with the amount of production or operational activity within a company.

Mass Customization

The production approach that allows for the creation of personalized products or services to meet individual customer needs, while still achieving economies of scale.