Question

1) if the castles air conditioner cools the castle when the outside temperature is above 25(degree)C, which inequality or equation correctly represents this situation?

*using f(x)=24 - 5cos(pi/12t)

A. 24 - 5cos(pi/12t) = 0
B. -5cos(pi/12t) - 1 = 0
C. 24 - 5cos(pi/12t) > 0
D. -5cos(pi/12t) - 1 > 0
E. -5cos(pi/12)t - 1 < 0

2) using the answer to question 1, what are the approximate values of the zeros in the given interval [0,24], this is multiple choice.

A. x =~ 4.0
B. x =~ -4.0
C. x =~ 6.8
D. x =~ -6.8
E. x =~ 17.2
F. x =~ -17.2

Please help and thank you!! much appreciated x

Answer 1

1) We think this question is intended to have you use f(t) as a model for the outside temperature, and the answer selection as a statement of when the air-conditioner is running. "This situation" questions are always open to a variety of interpretations.

If our assumptions are correct, the appropriate choice is the one that is equivalent to

... f(t) > 25 . . . . . . . . . . . . . . . outside air temperature is greater than 25

... 24 -5cos(πt/12) > 25 . . . . use the given f(t)

... -5cos(πt/12) - 1 > 0 . . . . . subtract 25; corresponds to selection D

2) A graph shows the solution to be the interval (6.8, 17.2). Selections C and E are appropriate.