Find the Speed of a Particle with the Given Position $$\mathrm { r } ( t ) = t \mathbf { i } + 5 t ^ { 2 } \mathbf { j } + 3 t ^ { 6 } \mathbf { k }$$

question 84

Multiple Choice

Find the speed of a particle with the given position function.
$$\mathrm { r } ( t ) = t \mathbf { i } + 5 t ^ { 2 } \mathbf { j } + 3 t ^ { 6 } \mathbf { k }$$

• A) \(| v ( t ) | = \sqrt { 1 + 100 t ^ { 2 } + 100 t ^ { 10 } }\)
• B) \(| \mathrm { v } ( t ) | = \sqrt { 1 + 100 t + 324 t ^ { 9 } }\)
• C) \(| \mathrm { v } ( t ) | = 1 + 100 t ^ { 2 } + 324 t ^ { 10 }\)
• D) \(| v ( t ) | = \sqrt { 1 + 100 t ^ { 2 } + 324 t ^ { 10 } }\)
• E) \(| \mathrm { v } ( t ) | = \sqrt { 1 + 100 t + t ^ { 9 } }\)

---

Definitions:

Mixed Cost

A cost that contains both variable and fixed cost elements.

High-low Method

A technique in managerial accounting used to estimate the variable and fixed cost components of a cost formula, analyzing the highest and lowest levels of activity.

Scattergraph

A graphical method used in statistics to display the values of two variables for a set of data, helping to identify the relationship between them.

Independent Variable

A variable that acts as a causal factor; activity is the independent variable, as represented by the letter X, in the equation Y = a + bX.