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

Step-by-step explanation:

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

$T(m) = 27\cos{((\frac{\pi}{6})(m-6))} + 45$

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

$T(m) = 27\cos{((\frac{\pi}{6})(m-6))} + 45$

$55 = 27\cos{((\frac{\pi}{6})(m-6))} + 45$

$27\cos{((\frac{\pi}{6})(m-6))} = 10$

$\cos{((\frac{\pi}{6})(m-6))} = \frac{10}{27}$

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

$\cos^{-1}{\cos{(\frac{\pi}{6})(m-6)}} = \cos^{-1}{\frac{10}{27}}$

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

$\frac{\pi}{6}(m-6) = 1.19$

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

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

$m = \frac{6*1.19 + 6 \pi}{\pi}$

$m = 8.27$

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