Musical notes are classified by frequency. The note middle C has a frequency of 262 hertz. The note C above middle C has a frequency of 524 hertz. The note C below middle C has a frequency of 131 hertz. 1) Write an equation of the sine function that represents middle C if its amplitude is 0.2.

2)Write an equation of the sine function that represents C above middle C if its amplitude is one half that of middle C.

3)Write an equation of the sine function that represents C below middle C if its amplitude is twice that of middle C.

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  1)  f(t) = 0.2·sin(524π·t)

  2)  f(t) = 0.1·sin(1048π·t)

  3)  f(t) = 0.4·sin(262π·t)

Step-by-step explanation:

The general form of the desired equation is ...

  f(t) = A·sin(2πf·t)

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1) f = 262; A = 0.2

  f(t) = 0.2·sin(524π·t)

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2) f = 524; A = 0.1

  f(t) = 0.1·sin(1048π·t)

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3) f = 131; A = 0.4

  f(t) = 0.4·sin(262π·t)

$‭75,604.6‬0

Explanation:

The lump sum that would make the employee indifferent between the two option is the one that is equal to the present value of the part payments.

Given a constant payment of $26,000 per year this will be the present value of an annuity.

Present Value of the Annuity = 26,000 * Present Value interest factor of an annuity, 3 years, 8%

= 26,000 * 2.5771

= 67,004.6‬0

Total present Value = 8,600 + 67,004.6‬0

= $‭75,604.6‬0

If the lump sum offered was $‭75,604.6‬0, employee would be indifferent.