Find the Speed of a Particle with the Given Position $$\mathbf { r } ( t ) = 4 \sqrt { 2 } t \mathbf { i } + e ^ { 4 t } \mathbf { j } - e ^ { - 4 t } \mathbf { k }$$

question 132

Multiple Choice

Find the speed of a particle with the given position function.
$$\mathbf { r } ( t ) = 4 \sqrt { 2 } t \mathbf { i } + e ^ { 4 t } \mathbf { j } - e ^ { - 4 t } \mathbf { k }$$

• A) \(| v ( t ) | = \sqrt { 4 + 4 e ^ { t } + 4 e ^ { - t } }\)
• B) \(| v ( t ) | = \left( e ^ { 4 t } + e ^ { - 4 t } \right)\)
• C) \(| v ( t ) | = \sqrt { 4 + e ^ { 4 t } + e ^ { - 40 t } }\)
• D) \(| v ( t ) | = 4 \left( e ^ { 4 t } + e ^ { - 4 t } \right)\)
• E) \(| v ( t ) | = 4 \left( e ^ { t } + e ^ { - t } \right)\)

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Definitions:

Predicted Income

An estimate of the amount of money that an individual or entity is expected to earn in the future.

Slope

The measure of the steepness or incline of a line, typically representing the rate of change between two variables in a linear relationship.

Intercept

The point where a line crosses the y-axis in a graph, representing the value of the dependent variable when the independent variable is zero.

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