$\text { Find } \mathbf { r } ( t ) \cdot \mathbf { u } ( t ) \text { given the functions below. }$

question 28

Multiple Choice

$\text { Find } \mathbf { r } ( t ) \cdot \mathbf { u } ( t ) \text { given the functions below. }$ $\mathbf { r } ( t ) = 3 t \mathbf { i } + \frac { t } { 5 } \mathbf { j } + 2 t ^ { 2 } \mathbf { k } , \mathbf { u } ( t ) = 6 t \mathbf { i } + 6 \mathbf { j } - 5 t \mathbf { k }$

• A) \(18 t ^ { 2 } + \frac { 6 } { 5 } - 10 t ^ { 3 }\)
• B) \(- 18 t ^ { 2 } + \frac { 6 } { 5 } t + 10 t ^ { 3 }\)
• C) \(18 t ^ { 2 } + \frac { 6 } { 5 } t + 10 t ^ { 3 }\)
• D) \(18 t + \frac { 6 } { 5 } t - 10 t ^ { 2 }\)
• E) \(18 t ^ { 2 } + \frac { 6 } { 5 } t - 10 t ^ { 3 }\)

---

Definitions:

High-Income Earners

Individuals or households that have an income significantly above the average or median level.

Low-Income Earners

Individuals or households that earn less than the median income level, often qualifying them for certain government assistance programs.

Proportional Tax

A tax system where the tax rate remains constant regardless of the taxpayer's income level, meaning everyone pays the same percentage of their income.

Tax Schedules

Detailed tables or charts provided by tax authorities that dictate the tax rates applicable to different levels of taxable income or types of taxpayers.