Solve the Problem $y = 4 ( \cos 2 \pi x \cos b t + \sin 2 \pi x \sin b t )$

question 30

Multiple Choice

Solve the problem.
-A vibrating wire has a vertical displacement given by $y = 4 ( \cos 2 \pi x \cos b t + \sin 2 \pi x \sin b t )$ . Assume $b$ and $t$ are constants. Write $y$ as a cosine function of $x$ .

• A) \(y = 4 \cos ( 2 \pi x - b t )\)
• B) \(y = 4 \cos ( 2 \pi x + b t )\)
• C) \(y = 8 \cos ( 2 \pi x + b t )\)
• D) \(y = \cos ( 2 \pi x - b t )\)

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Definitions:

Marginal Cost

The price associated with the creation of one more unit of a product or service.

Average Total Cost

The per-unit cost of production, calculated by dividing the total cost of production by the quantity of output produced.

Economic Profit

The difference between the total revenue generated by a business and the total costs, including both explicit and implicit costs.

Short-run Marginal Cost Curve

A curve that shows the change in total cost associated with producing one more unit of output in the short term.