A Particle Is Moving Along the Curve Described by the Parametric

question 1

Essay

A particle is moving along the curve described by the parametric equations $x = 5 t , y = 2 t ^ { 3 } , z = \frac { 3 } { 5 } t ^ { 5 }$ . Determine the velocity and acceleration vectors as well as the speed of the particle when t = 3.

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Definitions:

Common Bile Duct

A tube that carries bile from the liver and gallbladder into the duodenum, the first part of the small intestine.

Gallbladder

A small organ located beneath the liver that stores and concentrates bile, aiding in the digestion of fats.

Pancreas

An organ in the body that produces insulin and enzymes important for digestion.

Oral Cavity

The mouth's internal space, including the lips, gums, teeth, tongue, palate, and the opening to the throat, integral for speech, breathing, and the initial stages of digestion.