Determine the Equation of the Graph $\mathrm { s } ( \mathrm { t } ) = - 5 \cos 8 \pi t$

question 141

Multiple Choice

Determine the equation of the graph.
-The position of a weight attached to a spring is $\mathrm { s } ( \mathrm { t } ) = - 5 \cos 8 \pi t$ inches after $\mathrm { t }$ seconds. What is the maximum height that the weight reaches above the equilibrium position and when does it first reach the maximum height? Round values to two decimal places, if necessary.

• A) The maximum height of 5 inches is first reached after \(0.13\) seconds.
• B) The maximum height of 10 inches is first reached after 2 seconds.
• C) The maximum height of 10 inches is first reached after 4 seconds.
• D) The maximum height of 5 inches is first reached after 4 seconds.

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Definitions:

Average Costs

The total costs (fixed and variable) divided by the total output, indicating the cost per unit of output produced.

Decreasing Returns to Scale

A situation in which, when the scale of production is increased, the output increases at a proportionally lower rate.

Minimum Efficient Scale

The smallest level of production a company can achieve while still taking full advantage of economies of scale in terms of costs per unit.

Long-Run Average Cost Curve

A graphical representation showing the lowest average cost of producing any output level when all inputs can be varied.