Find the Curvature K of the Curve Given Below $$\mathbf { r } ( t ) = t \mathbf { i } + 2 t ^ { 2 } \mathbf { j } + 2 t \mathbf { k }$$

question 6

Multiple Choice

Find the curvature K of the curve given below. $$\mathbf { r } ( t ) = t \mathbf { i } + 2 t ^ { 2 } \mathbf { j } + 2 t \mathbf { k }$$

• A)\(\frac { 5 } { \sqrt { \left( 5 + 16 t ^ { 2 } \right) ^ { 3 } } }\)
• B)\(\frac { 4 \sqrt { 5 } } { \left( 5 + 4 t ^ { 2 } \right) ^ { 3 / 2 } }\)
• C)\(\frac { 2 } { \sqrt { \left( 5 + 16 t ^ { 2 } \right) ^ { 3 } } }\)
• D) \(\frac { 4 } { \sqrt { \left( 5 + 16 t ^ { 2 } \right) ^ { 3 } } }\)
• E) \(\sqrt [ 4 ] { \frac { 5 } { \left( 5 + 16 t ^ { 2 } \right) ^ { 3 } } }\)

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Definitions:

Reagents

Chemical substances or compounds added to a system to bring about a chemical reaction or to see if a reaction occurs.

Transformation

A general term for any process or reaction that changes the chemical structure, physical properties, or molecular composition of a substance.

Organic Product

A compound containing carbon atoms that has been produced through chemical reactions involving organic molecules.

β-Ocimene

An isomer of ocimene, which is a monoterpene showing a double bond at the beta position, found in various plant oils and used in fragrances.