Solve the Problem $\mathrm { V } ( \mathrm { t } ) = 160 \cos ( 120 \pi \mathrm { t } )$

question 183

Multiple Choice

Solve the problem.
-Suppose that a hair dryer operates on a voltage that can be represented by the relation $\mathrm { V } ( \mathrm { t } ) = 160 \cos ( 120 \pi \mathrm { t } )$ and that it draws a current represented by the relation $\mathrm { I } ( \mathrm { t } ) = 8 \cos ( 120$ where $t$ is time measured in seconds. The power consumed by the appliance is $\mathrm { P } = \mathrm { VI }$ . Graph the power in $[ 0,0.04,0.01 ]$ by $[ - 200,2000,200 ]$ and use an identity to write the expression for the power in the form $\mathrm { P } = \mathrm { a } \cos ( \mathrm { k } \pi \mathrm { t } ) + \mathrm { d }$ , where $\mathrm { a }$ , $\mathrm { k }$ , and $\mathrm { d }$ are constants.

• A) \(P = 640 \cos ( 120 \pi t ) + 640\) \([ 0,0.04,0.01 ]\) by \([ - 200,2000,200 ]\)
• B) \(P = 640 \cos ( 240 \pi t ) + 640\) \([ 0,0.04,0.01 ]\) by \([ - 200,2000,200 ]\)
• C) \(\mathrm { P } = 1280 \cos ( 240 \pi \mathrm { t } ) + 1280\) \([ 0,0.04,0.01 ]\) by \([ - 200,2000,200 ]\)
• D) \(\mathrm { P } = - 640 \cos ( 240 \pi \mathrm { t } ) + 640\) \([ 0,0.04,0.01 ]\) by \([ - 200,2000,200 ]\)

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