Sounds are how we perceive pressure waves in the air. The note F-sharp, more than 2 octaves below the note 'middle C', is a sound wave with an ordinary frequency* f - 61.875 Hertz or cycles/sec Model this note with the sine function, assuming that the amplitude is 1 and the phase shift is 0. g(x) The temperature during the day can be modeled by a sinusoid. Answer the following question given that the low temperature of 30 degrees occurs at 3 AM and the high temperature for the day is 70 degrees. Assuming t is the number of hours since midnight, find an equation for the temperature, T, in terms of t. T(t)

a)

b)

Step-by-step explanation:

Frequency, f = 61.875 Hz

...........(1)

Amplitude, A = 1

Since there is no phase shift,

Substituting the values of A and w into equation (1)

b)

The general equation for a sinusoid

.................(2)

Lot temperature = 30⁰

High temperature = 70⁰

Amplitude,

A = 20⁰

Vertical shift,

D = 50⁰

Since the low temperature of 30⁰ occurs at 3 AM

t = 3, T(t) = 30

Period, ,  

Substituting the values of A, B, C, D into equation (2)

step-by-step explanation:

to find if any function is an inverse of the other, put the first equation in as x in the next one. then simplify and solve. if at the end you get the statement y = x, then it is an inverse. if you get anything else, it is not.