Question

The maximum afternoon temperature in a city might be modeled by t= -30cos(x/6) + 60 where t represents the maximum afternoon temperature in month, x, with x = 0 representing January, x = 1 representing February, and so on. Describe how to find the maximum temperature in April and state what this would be. How would you have to change the model if the maximum temperature in April, due to global warming, starts rising?

Answer 1

The maximum temperature in April is 30.0012

Explanation:

Given that the maximum afternoon temperature in a city might be modeled by $t=-30cos(\frac{x}{6} )+60$ where t represents the maximum afternoon temperature in the month x.

We need to determine the maximum temperature in April

The maximum temperature in April can be determined by substituting x = 3 in the model $t=-30cos(\frac{x}{6} )+60$

Thus, we have,

$t=-30cos(\frac{3}{6} )+60$

Simplifying, we get,

$t=-30cos(\frac{1}{2} )+60$

$t=-30(0.99996)+60$

Multiplying the terms, we get,

$t=-29.9988+60$

Adding, we get,

$t=30.0012$

Thus, the maximum afternoon temperature in the month of April is 30.0012