The function y=60+25sin(pi/6)t, where t is in months and t=0 corresponds to April 15, models the average high temperature in degrees Fahrenheit in Centerville.

b.) What is the maximum high temperature and when does this occur?

NOTE: I found the answer online, I just don't understand how to get there. It's July 15, 85 degrees.

Answers

Answer 1

Answer:

The maximum temperature will be of 85 degrees, on July 15.

Step-by-step explanation:

Sine function:

The sine function oscilates between -1 and 1, and it's maximum value is:

[tex]\sin{(\frac{\pi}{2})} = 1[/tex]

y=60+25sin(pi/6)t

The maximum value will occur when [tex]\sin{(\frac{\pi t}{6}}) = 1[/tex], and it will be of 60 + 25 = 85 degrees.

When will it occur?

First we find the value of t for which the value inside the function sine is [tex]\frac{\pi}{2}[/tex]. So

[tex]\frac{\pi t}{6} = \frac{\pi}{2}[/tex]

[tex]\frac{t}{6} = \frac{1}{2}[/tex]

[tex]2t = 6[/tex]

[tex]t = \frac{6}{2} = 3[/tex]

That is the number of months after April 15, which is 3 months. So July 15.


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9514 1404 393

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