Find the Unit Tangent Vector to the Curve Given Below $\mathbf { r } ( 2 ) = 5 \cos t \mathbf { i } + 4 \sin t \mathbf { j } , t = \frac { 2 \pi } { 3 }$

question 4

Multiple Choice

Find the unit tangent vector to the curve given below at the specified point. $\mathbf { r } ( 2 ) = 5 \cos t \mathbf { i } + 4 \sin t \mathbf { j } , t = \frac { 2 \pi } { 3 }$

• A) \(\mathrm { T } \left( \frac { 2 \pi } { 3 } \right) = \frac { 5 \sqrt { 3 } } { \sqrt { 91 } } \mathbf { i } - \frac { 4 } { \sqrt { 91 } } \mathbf { j }\)
• B) \(\mathrm { T } \left( \frac { 2 \pi } { 3 } \right) = \frac { 5 \sqrt { 3 } } { \sqrt { 91 } } \mathbf { i } + \frac { 4 } { \sqrt { 91 } } \mathbf { j }\)
• C) \(\mathbf { T } \left( \frac { 2 \pi } { 3 } \right) = - \frac { 4 \sqrt { 3 } } { \sqrt { 91 } } \mathbf { i } - \frac { 5 } { \sqrt { 91 } } \mathbf { j }\)
• D) \(\mathrm { T } \left( \frac { 2 \pi } { 3 } \right) = - \frac { 5 \sqrt { 3 } } { \sqrt { 91 } } \mathbf { i } + \frac { 4 } { \sqrt { 91 } } \mathbf { j }\)
• E) \(\mathrm { T } \left( \frac { 2 \pi } { 3 } \right) = - \frac { 5 \sqrt { 3 } } { \sqrt { 91 } } \mathbf { i } - \frac { 4 } { \sqrt { 91 } } \mathbf { j }\)

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A financial metric that measures how many times a company collects its average accounts receivable in a period, indicating the efficiency of extending credit and collecting debts.

Average Accounts Receivable

The average amount of money owed to a company by its customers for goods or services provided on credit over a specified period.

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A measure of how quickly a company sells and replaces its stock of goods within a given period.

Cost of Goods Sold

The total cost of materials and labor directly involved in producing goods or services sold during a period.