Question

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

Answer 1

Hope this helps.

Explanation:

Answer 2

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

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 = ((T_(max) - T_(min)))/(2)\\\\`

`= ((3 - 18))/(2)\\\\= - (15)/(2)\\\\ = -7.5`

`B = (2 \pi)/(24)\\\\`

`= (\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 (\pi)/(12)( t - 4 )+ 10.5`