$D _ { t } [ 2 \mathbf { r } ( t ) - 5 \mathbf { u } ( t ) ] \text { given the following }$

question 8

Multiple Choice

$D _ { t } [ 2 \mathbf { r } ( t ) - 5 \mathbf { u } ( t ) ] \text { given the following }$ Use the properties of the derivative to find vector-valued functions. $$\begin{array} { l } \mathbf { r } ( t ) = 2 t \mathbf { i } + 6 t ^ { 3 } \mathbf { j } + 2 t ^ { 2 } \mathbf { k } \\\mathbf { u } ( t ) = 2 \mathbf { i } + 4 t ^ { 2 } \mathbf { j } + 3 t ^ { 3 } \mathbf { k }\end{array}$$

• A) \(4 \mathbf { i } + \left( 36 t ^ { 3 } - 40 t \right) \mathbf { j } + \left( 8 t - 45 t ^ { 2 } \right) \mathbf { k }\)
• B) \(4 \mathbf { i } + \left( 36 t ^ { 2 } - 40 t \right) \mathbf { j } + \left( 8 t ^ { 2 } - 45 t \right) \mathbf { k }\)
• C) \(4 t \mathbf { i } + \left( 36 t ^ { 2 } + 40 t \right) \mathbf { j } - \left( 8 t + 45 t ^ { 2 } \right) \mathbf { k }\)
• D) \(4 \mathbf { i } + \left( 36 t ^ { 2 } + 40 t \right) \mathbf { j } + \left( 8 t + 45 t ^ { 2 } \right) \mathbf { k }\)
• E) \(4 \mathbf { i } + \left( 36 t ^ { 2 } - 40 t \right) \mathbf { j } + \left( 8 t - 45 t ^ { 2 } \right) \mathbf { k }\)

Understand the fundamental questions of economics regarding what, how, and for whom goods and services are produced.

Comprehend the concept of consumer sovereignty and its effect on the production of goods and services.

Identify the factors influencing the selection of production techniques and the implications for economic efficiency.

Understand the principles and development of Scientific Management and its origins.

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Definitions:

Minimum Wage

Legislation requiring that workers be paid at least the stated minimum hourly rate of pay.

Tax Rates

The percentage at which an individual or corporation is taxed on their income or profits.

Economic Recession

A significant decline in economic activity spread across the economy, lasting more than a few months, typically visible in GDP, real income, employment, industrial production, and wholesale-retail sales.

Keynesian View

An economic theory proposing that government intervention, through monetary and fiscal policy, can mitigate the adverse effects of recessions and depressions.