Find the Curvature of the Curve $\mathbf { r } ( t ) = 3 \sin 4 t \mathbf { i } + 3 \cos 4 t \mathbf { j } + 3 t \mathbf { k }$

question 86

Multiple Choice

Find the curvature of the curve $\mathbf { r } ( t ) = 3 \sin 4 t \mathbf { i } + 3 \cos 4 t \mathbf { j } + 3 t \mathbf { k }$ .

• A) \(\frac { 4 } { 3 }\)
• B) \(\frac { 3 } { 4 }\)
• C) \(\frac { 51 } { 16 }\)
• D) \(\frac { 16 } { 51 }\)

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Definitions:

Surplus

An excess of something, such as goods, services, or resources, beyond what is needed or used.

Balance of Trade

The difference in value between a country's imports and exports over a certain period.

Exports

Goods or services produced in one country and sold to buyers in another, contributing to a country's economy and trade balance.

Deficit

An economic condition where expenditures exceed revenue.