Given $\mathbf { r } ( t ) = 7 t ^ { 2 } \mathbf { i } + 4 t ^ { 3 } \mathbf { j }$

question 13

Essay

Given $\mathbf { r } ( t ) = 7 t ^ { 2 } \mathbf { i } + 4 t ^ { 3 } \mathbf { j }$ .
a. Find $\mathbf { r } ( - 1 )$ and $\mathbf { r } ^ { \prime } ( - 1 )$ .
b. Sketch the curve defined by $\mathbf { r }$ and the vectors $\mathbf { r } ( - 1 )$ and $\mathbf { r } ^ { t } ( - 1 )$ on the same set of axes.

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Definitions:

Standardized

A process of making something conform to a standard in order to ensure consistency and comparability.

Scoring

The process of assigning a value to responses or performances in assessments or competitions.

Correlation

A statistical measure that describes the extent to which two variables change together, but does not necessarily imply causation.

Cause-And-Effect

The principle that an action or event will produce a certain response or effect in the form of another event.