Question

The average high temperature during the hottest month in Beijing, China, is 72°F. The average high temperature during the coldest month in Beijing is 18°F. The function 1 =27 cos( π/6(m-6)) +45, where m represents the number of months after January, models the temperature throughout the year in Beijing. During which monke in the year would the temperature reach 55°F?

- August
- September
- November
- December

(it'll be SEPTEMBER, i just couldn't find the answer for it anywhere else, so here ya gooo.)
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Answer 1

Answer: September

Explanation:

Edge

Answer 2

- September

Explanation:

The temperature in Beijing, in m months after January, is given by the following equation:

`T(m) = 27\cos{(((\pi)/(6))(m-6))} + 45`

In which m is the number of months after January.

During which month in the year would the temperature reach 55°F?

We have to find m for which: T(m) = 55. So

`T(m) = 27\cos{(((\pi)/(6))(m-6))} + 45`

`55 = 27\cos{(((\pi)/(6))(m-6))} + 45`

`27\cos{(((\pi)/(6))(m-6))} = 10`

`\cos{(((\pi)/(6))(m-6))} = (10)/(27)`

Now, we apply the inverse cosine, on both sides of the equation, to find the value of m.

`\cos^(-1){\cos{((\pi)/(6))(m-6)}} = \cos^(-1){(10)/(27)}`

Now, with the help of a calculator, in radians:

`(\pi)/(6)(m-6) = 1.19`

`\pi m - 6\pi = 6*1.19`

`\pi m = 6*1.19 + 6 \pi`

`m = (6*1.19 + 6 \pi)/(\pi)`

`m = 8.27`

8.27 months after January, since 8.27 + 1 = 9.28, it happens during the month of September.