Question

The mean average temperature for Washington, DC is 53.8 degrees. The monthly average temperature ranges up to 32.5 degrees above and below this value. If t=0, represents March and the phase shift is -8. Write a model for the average monthly temperature in September. According to the model, what is the average temperature in September.

Answer 1

A collection of quarters and nickels is worth $14.80.
There are 88 coins in all.

how many of each coin are there?

quarters??
nickels??

Answer 2

you can use
y = A*cos[2Pi/Period*(t - p.s.)] + v.s.
or
y = A*sin[2Pi/Period*(t - p.s.)] + v.s.

Answer 3

does the problem say to use sine or cosine ?

Answer 4

I think we want to use cosine , since the phase shift -8 makes sense with cosine (using the fact that January is the coldest month in the northern hemisphere).

y = 32.5 cos [ 2Pi/12 (t - (-8) ] + 53.8

simplified this gives

y = 32.5 cos ( pi/6 ( t + 8) ) + 53.8

now can you answer the question.

Answer 5

also be careful about what month september is

Answer 6

I agree, cosine is the function to use....
However...I thought the model could be:
y=32.5cos ( Pi/6t+8 ) +53.8... this differs from your model within the quantity...cos (Pi/6t+Pi/6(8) )....
What do you think ??

If t=0, represents March.... then September would be t=6 ????

Answer 7

@Austin122131
Let x and y be the number of nickels and quarters respectively.
{.05 x + .25 y = 14.80, x + y = 88}
{x = 36., y = 52.}