Question

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the...

Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 100 degrees occurs at 4 PM and the average temperature for the day is 80 degrees. Find the temperature, to the nearest degree, at 7 AM.

Homework Answers

Answer #1

Max is 100, average is 80.

so the variation of this sine function is 20 degrees in either direction from the mean=80.

So fitting this data onto the interval [pi/2, 3*pi/2]. max heat of the day at 4 pm where sine is 1

sunrise at 7 am where temperature begins to rise where sine is -1.

The sinusoidal wave can be represented by the equation:y=A∗sin[ω(x−α)]+Cy=A∗sin[ω(x−α)]+C
where, A is the amplitude; ω=2π/period, ω=2π/period; α=α= phase shift on the Y-axis; and C = midline.

Given C=80, A=20, period =24, a=10, x=7

y=20∗sin[2π/24(7−10)]+80

On solving,the temperature, to the nearest degree, at 7 AM is 79.72

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the...
Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 57 degrees occurs at 3 PM and the average temperature for the day is 50 degrees. Find the temperature, to the nearest degree, at 7 AM.    degrees
Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the...
Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 72 degrees occurs at 5 PM and the average temperature for the day is 65 degrees. Find the temperature, to the nearest degree, at 6 AM.
Q.1 Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know...
Q.1 Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the high temperature of 83 degrees occurs at 6 PM and the average temperature for the day is 65 degrees. Find the temperature, to the nearest degree, at 10 AM. (Answer: degrees) Q.2 Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 60 and 90 degrees during the day and the average daily temperature...
Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the...
Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature varies between 58 and 72 degrees during the day and the average daily temperature first occurs at 8 AM. How many hours after midnight, to two decimal places, does the temperature first reach 60 degrees?
Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the...
Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 80 degrees and the low temperature of 50 degrees occurs at 4 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t. D(t)=
Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the...
Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature for the day is 102 degrees and the low temperature of 68 degrees occurs at 3 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t. D(t)D(t) =
part a.) Outside temperature over the course of a day can be modeled as a sinusoidal...
part a.) Outside temperature over the course of a day can be modeled as a sinusoidal function. If the low temperature for the day is 42°F and the high temperature is 86°F, calculate the amplitude of the model function. part b.) Outside temperature over the course of a day can be modeled as a sinusoidal function. If the low temperature for the day is 42°F and the high temperature is 86°F, what is the midline of the model function?
In a certain city the temperature (in °F) t hours after 9 AM was modeled by...
In a certain city the temperature (in °F) t hours after 9 AM was modeled by the function T(t) = 40 + 11 sin πt 12 . Find the average temperature Tave during the period from 9 AM to 9 PM. (Round your answer to the nearest whole number.).
1.Find a possible formula for the trigonometric function whose values are in the following table. x...
1.Find a possible formula for the trigonometric function whose values are in the following table. x 0 2 4 6 8 10 12 y -2 -5 -2 1 -2 -5 -2 y= 2. A population of rabbits oscillates 21 above and below an average of 103 during the year, hitting the lowest value in January (t = 0). Find an equation for the population, P, in terms of the months since January, t. P(t) = What if the lowest value...
Suppose you had daily temperature data indicating the "high" point of each day for 2015. If...
Suppose you had daily temperature data indicating the "high" point of each day for 2015. If you want to show how the high differs over time, what are some of the plot types that will allow you do this? What are some benefits to binning the data into one of 52 weeks and plotting the average high for each week? Would it make sense to do something similar for the four quarters in the year? Why or why not?