Verify That the Equation Is an Identity $\mathrm { P }$

question 162

Multiple Choice

Verify that the equation is an identity.
-In a particular situation, the pressure, $\mathrm { P }$ , exerted on a person's eardrum at a distance of 6 feet fron the source is given by the function: $\mathrm { P } ( \mathrm { t } ) = \frac { \mathrm { a } } { 6 } \cos ( 2 \mathrm { n } \pi - \mathrm { ct } )$ , where $\mathrm { n }$ is a positive integer. Use the difference identity for cosine to simplify $\mathrm { P }$ in this situation.

• A) \(P ( t ) = \frac { a } { 6 } \cos ( c t ) - \frac { a } { 6 } \sin ( c t )\)
• B) \(P ( t ) = \frac { a } { 6 } \cos ( c t )\)
• C) \(\mathrm { P } ( \mathrm { t } ) = \cos ( \mathrm { ct } )\)
• D) \(\mathrm { P } ( \mathrm { t } ) = \frac { 6 } { 7 } \cos ( \mathrm { ct } + 6 )\)

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Definitions:

Annuity Due

A type of annuity in which payments are made at the beginning of each period, rather than at the end.

Present Value

The current worth of a future sum of money or stream of cash flows, given a particular rate of discount.

Sinking Fund

A fund established by a government or corporation for the purpose of reducing debt by repurchasing bonds or shares.

Maturity

The date on which a debt instrument (such as a bond) is due to be repaid in full.