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) \(\mathrm { T } \left( \frac { 2 \pi } { 3 } \right) = - \frac { 5 \sqrt { 3 } } { \sqrt { 91 } } \mathbf { i } - \frac { 4 } { \sqrt { 91 } } \mathbf { j }\)

Understand the relationship between the elasticity of demand and supply and the efficiency loss of a tax.

Recognize how the elasticity of demand influences the tax burden on consumers.

Assess viewpoints on the incidence of corporate income tax.

Differentiate between the concepts of efficiency loss of a tax and tax revenue.

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