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matrenka [14]
3 years ago
11

In the month of June, the temperature in Johannesburg, South Africa, varies over the day in a periodic way that can be modeled a

pproximately by a trigonometric function. The lowest temperature is usually around 3^\circ C3 ∘ C3, degrees, C, and the highest temperature is around 18^\circ C18 ∘ C18, degrees, C. The temperature is typically halfway between the daily high and daily low at both 10\text{ a.M.}10 a.M.10, start text, space, a, point, m, point, end text and 10\text{ p.M.}10 p.M.10, start text, space, p, point, m, point, end text, and the highest temperatures are in the afternoon.
Mathematics
1 answer:
Art [367]3 years ago
6 0

Answer:

The answer is "\bold{T = - 7.5 \cos \frac{\pi}{12}( t - 4 )+ 10.5}"

Step-by-step explanation:

Given value:

Temp-maximum=18^{\circ}  

Temp. minimum = 3^{\circ}

It is halfway between 10 am and 10 pm to 4 am.  

The sinus and cosine roles could be used throughout the year to predict fluctuations in climate models. Its type of formula that can be used to model such information is:  

T = A \cos B(t-C) + D, where parameters are A, B , C, D, T is the ° C temperature and t is the time (1-24)

A = amplitude = \frac{(T_{max} - T_{min})}{2}\\\\

                       = \frac{(3 - 18)}{2}\\\\= - \frac{15}{2}\\\\ = -7.5

B = \frac{2 \pi}{24}\\\\

   = \frac{\pi}{12}

C = \text{ units translated to the right}= 4

D = y_{min} + amplitude = units \ translated \ up\\\\

D = 7.5 + 3 = 10.5

Its trigonometric function equation that model temperature T hours after midnight in Johannesburg t.

T = - 7.5 \cos \frac{\pi}{12}( t - 4 )+ 10.5

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