The Following Table Gives Coordinates of a Particle Moving Through

question 40

Multiple Choice

The following table gives coordinates of a particle moving through space along a smooth curve. $\begin{array}{|c|c|c|c|}\hline \mathbf{t} & x & y & z \\\hline 0.5 & 5.8 & 9.1 & 4.3 \\\hline 1 & 12.6 & 14.9 & 16.8 \\\hline 1.5 & 25.6 & 21.2 & 29.4 \\\hline 2 & 39.2 & 39.5 & 37.9 \\\hline 2.5 & 42.4 & 42.4 & 43 \\\hline\end{array}$

Find the average velocity over the time interval $[ 1,2 ]$ .

• A) \(v = 21.1 \mathbf { i } + 24.6 \mathbf { j } + 26.6 \mathbf { k }\)
• B) \(v = 21.1 \mathbf { i } + 26.6 \mathbf { j } + 21.1 \mathbf { k }\)
• C) \(v = 24.6 \mathbf { i } + 24.6 \mathbf { j } + 21.1 \mathbf { k }\)
• D) \(v = 26.6 \mathbf { i } + 24.6 \mathbf { j } + 21.1 \mathbf { k }\)
• E) \(v = 21.1 \mathbf { i } + 26.6 \mathbf { j } + 26.6 \mathbf { k }\)

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Definitions:

Variable Expenses

Costs that fluctuate with changes in production volume or business activity levels, such as raw materials and direct labor.

Fixed Expenses

Costs that do not change with the level of output or sales in the short term, such as rent, salaries, and insurance.

Break-even Point

The juncture where the sum of all costs matches the total income, leading to neither a profit nor a loss.

Contribution Margin Ratio

A financial ratio that measures the proportion of revenue remaining after variable costs have been deducted, indicating how much contributes to covering fixed costs and generating profit.