Import favoritesMVNU Students Ho...AALEKS - Jameson C...Trigonome tric GraphsWord problem involving a sine or cosine function: Problem type 2JamesonEspañolThe average monthly temperature changes from month to month. Suppose that, for a given city, we can model the average temperature in a month with the following function.f(t)=60−27sin(6πt)In this equation, f(t) is the average temperature in a month in degrees Fahrenheit, and t is the month of the year (January =1, February=2, … ).Find the following. If necessary, round to the nearest hundredth.Time for one full cycle of f□ monthsNumber of cycles of f per month: □Minimum average temperature in a month: □□० FahrenheitExplanationCheck(C) 2024 McGraw Hill LLC. All Rights Reserved.Terms of UsePrivacy CenterAccessibilityType here to searcht0(1))2:21 PM4/22/2024
Q. Import favoritesMVNU Students Ho...AALEKS - Jameson C...Trigonome tric GraphsWord problem involving a sine or cosine function: Problem type 2JamesonEspañolThe average monthly temperature changes from month to month. Suppose that, for a given city, we can model the average temperature in a month with the following function.f(t)=60−27sin(6πt)In this equation, f(t) is the average temperature in a month in degrees Fahrenheit, and t is the month of the year (January =1, February=2, … ).Find the following. If necessary, round to the nearest hundredth.Time for one full cycle of f□ monthsNumber of cycles of f per month: □Minimum average temperature in a month: □□० FahrenheitExplanationCheck(C) 2024 McGraw Hill LLC. All Rights Reserved.Terms of UsePrivacy CenterAccessibilityType here to searcht0(1))2:21 PM4/22/2024
Calculate period: To find the time for one full cycle, we need to determine the period of the sine function. The period of a sine function sin(Bt) is (2π)/B. Here, B is (π/6).
Determine cycles per year: Calculate the period: (2π)/(π/6)=2π×(6/π)=12.
Find minimum temperature: The time for one full cycle of f is 12 months.
Find minimum temperature: The time for one full cycle of f is 12 months.To find the number of cycles of f per year, we divide 12 months by the period of the function. Since the period is 12 months, there is 1 cycle per year.
Find minimum temperature: The time for one full cycle of f is 12 months.To find the number of cycles of f per year, we divide 12 months by the period of the function. Since the period is 12 months, there is 1 cycle per year.For the minimum average temperature, we look at the sine function. The minimum value of sin(6πt) is −1. So, we plug −1 into the function for sin(6πt).
Find minimum temperature: The time for one full cycle of f is 12 months.To find the number of cycles of f per year, we divide 12 months by the period of the function. Since the period is 12 months, there is 1 cycle per year.For the minimum average temperature, we look at the sine function. The minimum value of sin(6πt) is −1. So, we plug −1 into the function for sin(6πt).Calculate the minimum temperature: 120.
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