Find the Unit Tangent Vector $T ( t )$ $\mathbf { r } ( t ) = \langle 2 \sin t , 4 t , 2 \cos t \rangle$

question 42

Multiple Choice

Find the unit tangent vector $T ( t )$ . $\mathbf { r } ( t ) = \langle 2 \sin t , 4 t , 2 \cos t \rangle$

• A) \(\left\langle\frac { \cos t } { 2 \sqrt { 5 } } , \frac { 2 } { \sqrt { 5 } } , - \frac { \sin t } { 2 \sqrt { 5 } } \right\rangle\)
• B) \(\langle3 \cos t , 6 , - 3 \sin t \rangle\)
• C) \(\left\langle\frac { \cos t } { \sqrt { 5 } } , \frac { 2 } { \sqrt { 5 } } , - \frac { \sin t } { \sqrt { 5 } } \right\rangle\)
• D) \(\langle3 \sqrt { 5 } \cos t , 6 , - 3 \sqrt { 5 } \sin t \rangle\)
• E) \(\left\langle- \frac { \cos t } { 2 \sqrt { 5 } } , \frac { 4 } { 2 \sqrt { 5 } } , \frac { 3 \sin t } { 2 \sqrt { 5 } } \right\rangle\)

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Definitions:

Economic Stability

A condition in which an economy experiences steady growth, low inflation, and low unemployment.

Unemployment

The situation where individuals who are capable of working and are actively seeking work remain jobless.

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Inflation is the rate at which the general level of prices for goods and services is rising, eroding purchasing power over time.

Ceteris Paribus

A Latin term used in economics to describe the analysis of a condition under the assumption that all other variables remain unchanged.