Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 75 degrees and the low temperature of 35 degrees occurs at 4 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

D(t) = 20°*cos((pi/4)*t) + 55°

Step-by-step explanation:

using that t = 0 is midnight, we know.

We know:

Max temp = 75°

Min temp = 35° (occurs at t = 4 hours)

Now we can model this as:

D(t) = A*cos(c*t) + B

Where A, c and B are constants.

we have a minimum at t = 4 hours, a minimum means that cos(c*t) = -1

then we have that:

D(4) = A*cos(c*4) + B = A*(-1) + B = 35°

here we also have that cos(c*4) = -1

this means that c*4 = pi

c = pi/4

We also have that the maximum temperature is 75°, the maximum temperature is when cos(c*t) = 1

D(t0) = A*(1) + B = 75°

with this we can find the values of A and B.

-A + B = 35°

A + B = 75°

We isolate B in the first equation and then replace it in the second equation.

B = 35° + A

A + B = 75°

A + 35° + A = 75°

2A = 40°

A = 40°/2 = 20°

B = 35° + 20° = 55°.

Our equation is:

D(t) = 20°*cos((pi/4)*t) + 55°

20

step-by-step explanation:

first, we define the variables:

x: number of years after 1950

f (x): amount of vinyl sold.

then, with the variables defined, we have:

68594 vinyl records were sold in 1958 > f (8) = 68594

91299 vinyl records were sold in 1961 > f (11) = 91299

38720 vinyl records were sold in 1952 > f (2) = 38720

161743 vinyl records were sold in 1967 > f (17) = 161743

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step-by-step explanation: