Question

the function p(t)p(t)p, left parenthesis, t, right parenthesis models the average high temperature, in degrees celsius, of paityn's town on the t^\text{th}t th t, start superscript, start text, t, h, end text, end superscript day of the year. the function v(t)v(t)v, left parenthesis, t, right parenthesis models the average high temperature of vince's town on the t^\text{th}t th t, start superscript, start text, t, h, end text, end superscript day of the year.

Answer 1

The solution set for the last equation represents the set of all days when the towns have the same average high temperature.

• The hotness of matter or radiation is expressed by the physical quantity known as temperature. The average air temperature for a specific time period, often a day, a month, or a year, as measured by a thermometer that has been properly exposed.
• P(t) is the average high temperature, in degrees Celsius, of Paityn's town on t days.

       $\begin{aligned} P(t)&=22.5+7.5\cos\left(\dfrac{2\pi (t-28)}{365}\right)\\\\ \end{aligned}$

• V(t) is the average high temperature, in degrees Celsius, of Vince's town on t days.

        $\\ V(t)&=30.5+1.5\cos\left(\dfrac{2\pi (t-90)}{365}\right)$

• So, P(t) = V(t) represents the set of all the days when both towns have the same average high temperature.

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