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

question 64

Short Answer

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

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Definitions:

Debt-to-Equity Ratio

A financial ratio used to measure the relative proportion of shareholders' equity and debt used to finance a company's assets.

Times Interest Earned

A metric indicating a firm's capability to cover its debt payments, by contrasting its earnings before interest and taxes with its interest costs.

Interest Expense

The cost incurred by an entity for borrowed funds, representing the interest payments made on any borrowed capital.

Tax Rate

is the percentage at which an individual or corporation is taxed by the government.