Answer :
To find the highest average temperature in Phoenix for the given situation, we need to analyze the function that models the temperature:
[tex]\[ f(x) = 26 \cos (0.0055 \pi x) + 89 \][/tex]
Here's how we determine the highest temperature:
1. Understanding the Function:
- The function is composed of a cosine term, [tex]\(26 \cos (0.0055 \pi x)\)[/tex], and a constant term, [tex]\(+89\)[/tex].
2. Properties of the Cosine Function:
- The cosine function, [tex]\(\cos(\theta)\)[/tex], varies between -1 and 1 for any real number [tex]\(\theta\)[/tex].
- Therefore, the term [tex]\(26 \cos(0.0055 \pi x)\)[/tex] will vary from [tex]\(-26\)[/tex] to [tex]\(26\)[/tex].
3. Finding the Maximum Value:
- The highest value of the cosine function is 1.
- When [tex]\(\cos(0.0055 \pi x) = 1\)[/tex], the term [tex]\(26 \cos(0.0055 \pi x)\)[/tex] reaches its maximum value of [tex]\(26\)[/tex].
4. Calculating the Highest Temperature:
- Substitute the maximum value of the cosine term into the function:
[tex]\[ 26 \times 1 + 89 = 26 + 89 = 115 \][/tex]
- Therefore, the highest average temperature is [tex]\(115^\circ F\)[/tex].
So, the highest average temperature in Phoenix that year would be approximately [tex]\(115^\circ F\)[/tex].
[tex]\[ f(x) = 26 \cos (0.0055 \pi x) + 89 \][/tex]
Here's how we determine the highest temperature:
1. Understanding the Function:
- The function is composed of a cosine term, [tex]\(26 \cos (0.0055 \pi x)\)[/tex], and a constant term, [tex]\(+89\)[/tex].
2. Properties of the Cosine Function:
- The cosine function, [tex]\(\cos(\theta)\)[/tex], varies between -1 and 1 for any real number [tex]\(\theta\)[/tex].
- Therefore, the term [tex]\(26 \cos(0.0055 \pi x)\)[/tex] will vary from [tex]\(-26\)[/tex] to [tex]\(26\)[/tex].
3. Finding the Maximum Value:
- The highest value of the cosine function is 1.
- When [tex]\(\cos(0.0055 \pi x) = 1\)[/tex], the term [tex]\(26 \cos(0.0055 \pi x)\)[/tex] reaches its maximum value of [tex]\(26\)[/tex].
4. Calculating the Highest Temperature:
- Substitute the maximum value of the cosine term into the function:
[tex]\[ 26 \times 1 + 89 = 26 + 89 = 115 \][/tex]
- Therefore, the highest average temperature is [tex]\(115^\circ F\)[/tex].
So, the highest average temperature in Phoenix that year would be approximately [tex]\(115^\circ F\)[/tex].