Question

The temperature on New Year's Day in Buffalo, New York, is given by T(h) = -A-B cos (πh/12), where T is the temperature in degrees Fahrenheit and h is the number of hours from midnight, 0 ≤ h ≤ 24.

a. The initial temperature at midnight was -15° F, and at Noon of New Year's Day it was 5° F. Find A and B.

Answer 1

To find the values of A and B in the equation T(h) = -A - B cos(πh/12), we can use the given information about the initial temperature at midnight and at noon on New Year's Day in Buffalo, New York. By plugging in these values and solving a system of equations, we find that A = 5 and B = 10.

Step-by-step explanation:

To find the values of A and B in the equation T(h) = -A - B cos(πh/12), we can use the given information about the initial temperature at midnight (-15°F) and at noon (5°F) on New Year's Day in Buffalo, New York. Plug in the values for h=0 (midnight) and h=12 (noon) into the equation:

-15 = -A - B cos(0) ...(1)

5 = -A - B cos(π) ...(2)

From equation (1), we get -15 = -A - B. ...(3)

From equation (2), we get 5 = -A + B. ...(4)

Now we have a system of equations (3) and (4) that we can solve to find the values of A and B.

Adding equations (3) and (4) together:

-15 + 5 = -A - B + -A + B

-10 = -2A

Divide both sides by -2:

A = -10/-2

A = 5

Substitute the value of A into equation (3) to solve for B:

-15 = -5 - B

Subtract -5 from both sides:

-15 + 5 = -B

-10 = -B

Divide both sides by -1:

B = -10/-1

B = 10

Therefore, the values of A and B in the equation are A = 5 and B = 10.