Question

2. (Topic 3.7) A student wanted to see how well a trigonometric function modeled the time of sunset each day in her city, so she recorded the time sunset occurred on the first day of the month for the first 6 months of the year. The table shows the sunset time S, in hours since 12:00 noon, for each day t since she began her research, where t = 1 is January 1 and t = 32 is February 1. Day t Sunset time S 1 5.633 32 6.1 61 6.55 92 7.95 122 8.317 153 8.683 At this point, she ran a sinusoidal regression with a period of 365 to construct a function $S(t) = a \sin (bt + c) + d$ to try to predict future sunsets. On July 1 of that year, the 182nd day of the year, the sunset occurred at 8:50 p.m., or 8.833 hours after noon. By how many hours does the regression function S overestimate or underestimate the sunset on July 1? (A) S(t) underestimates the sunset time by 1.994 hours. (B) S(t) underestimates the sunset time by 0.557 hour. (C) S(t) overestimates the sunset time by 0.557 hour. (D) S(t) overestimates the sunset time by 1.994 hours.

          2. (Topic 3.7) A student wanted to see how well
a trigonometric function modeled the time of
sunset each day in her city, so she recorded the
time sunset occurred on the first day of the
month for the first 6 months of the year. The
table shows the sunset time S, in hours since
12:00 noon, for each day t since she began her
research, where t = 1 is January 1 and t = 32
is February 1.
Day t Sunset time S
1 5.633
32 6.1
61 6.55
92 7.95
122 8.317
153 8.683
At this point, she ran a sinusoidal regression
with a period of 365 to construct a function
$S(t) = a \sin (bt + c) + d$ to try to predict future
sunsets. On July 1 of that year, the 182nd day
of the year, the sunset occurred at 8:50 p.m.,
or 8.833 hours after noon. By how many hours
does the regression function S overestimate or
underestimate the sunset on July 1?
(A) S(t) underestimates the sunset time by
1.994 hours.
(B) S(t) underestimates the sunset time by
0.557 hour.
(C) S(t) overestimates the sunset time by
0.557 hour.
(D) S(t) overestimates the sunset time by
1.994 hours.

Show more…

2. (Topic 3.7) A student wanted to see how well
a trigonometric function modeled the time of
sunset each day in her city, so she recorded the
time sunset occurred on the first day of the
month for the first 6 months of the year. The
table shows the sunset time S, in hours since
12:00 noon, for each day t since she began her
research, where t = 1 is January 1 and t = 32
is February 1.
Day t Sunset time S
1 5.633
32 6.1
61 6.55
92 7.95
122 8.317
153 8.683
At this point, she ran a sinusoidal regression
with a period of 365 to construct a function
S(t) = a sin (bt + c) + d to try to predict future
sunsets. On July 1 of that year, the 182nd day
of the year, the sunset occurred at 8:50 p.m.,
or 8.833 hours after noon. By how many hours
does the regression function S overestimate or
underestimate the sunset on July 1?
(A) S(t) underestimates the sunset time by
1.994 hours.
(B) S(t) underestimates the sunset time by
0.557 hour.
(C) S(t) overestimates the sunset time by
0.557 hour.
(D) S(t) overestimates the sunset time by
1.994 hours.

Added by Julie J.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

05/22/2022

Step 1

Since we don't have the actual regression function, we will assume that the student has already calculated these values and obtained the function S(t). Show more…

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(Topic 3.7) A student wanted to see how well a trigonometric function modeled the time of sunset each day in her city, so she recorded the time sunset occurred on the first day of the month for the first 6 months of the year. The table shows the sunset time S, in hours since 12:00 noon, for each day t since she began her research, where t=1 is January 1 and t=32 is February 1. able[[Day t,Sunset time S 2. (Topic 3.7 A student wanted to see how well a trigonometric function modeled the time of sunset each day in her city, so she recorded the time sunset occurred on the first day of the month for the first 6 months of the year. The table shows the sunset time S. in hours since 12:00 noon, for cach day t since she began her research, where t= 1 is January 1 and t= 32 is February 1. Day t Sunset time S 1 5.633 32 6.1 61 6.55 92 7.95 122 8.317 153 At this point, she ran a sinusoidal regression with a period of 365 to construct a function St)=asin(bt+ c)+dto tryto predictfuture sunsets. On July 1 of that year, the 182nd day of the year, the sunset occurred at 8:50 p.., or 8.833 hours after noon.By how many hours does the regression function S overestimate or underestimate the sunset on July l? (A) S() underestimates the sunset time by 1.994 hours. (B) S(t) underestimates the sunset time by 0.557 hour. (C) S(t overestimates the sunset time by 0.557 hour. (D S(t) overestimates the sunset time by 1.994 hours.

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Transcript

00:01 Hello students welcome we have a question here and in this question we have some values given into the data table which are month months and time of sunrise and sunset so you can see the data is for zero one two three four five six seven eight nine ten and eleven for eleven and here's some time is given 11 .20 and 10 .09, 8 .37, 6 .47, 5 .47, 5 .47, 5 .201, 3 .24, 3 .04, 3 .05, 4 .34, 6 .09, 7 .3 .05, 4 .34, 6 .09, 7 .35.

01:01 7 .35.

01:01 And 9 .09 this time is for 10 sorry for the extreme of the table and last is 10 .4.

01:15 And the sunset time is 15 .42.

01:20 Next is 17 .13 .13.

01:24 Next is 18 .43.

01:26 After that we have 20 .16 .21.

01:32 23 .27, 23 .57, 22 .3 .34.

01:42 20 .4.

01:43 20 .47.

01:47 19 and 17 .13 .15.

01:54 This data is given into the question.

01:57 We need this data to calculate the first part of the question.

02:00 Into the first part we need to calculate decimal notation decimal notation so let's find out the decimal notation for this given question how do we calculate the decimal notation for this question we need to solve the values for x and y so let's take months and rising time and set.

02:39 So the graph, x y graph we need to plot for this.

02:43 So in 0 the value is 11 .333 and then 1, the rise time will be 13 .15 and 2, then the time is 8 .616.

03:02 17 and i need to string this will be 6 .84 for 4 this is 5 .06 for 5 this will be 3 .4 and for 6 this is equal to 3 .083 we need this much value to plot the graph and etc this is our part k when we need to just get the decimal notation so for this rising time is on half and this will be in an hour.

03:40 So set sunset time is 815 and next is 70 .217.

03:49 Next is 18 .717 and then 20 .26 after that we have 21 .94 and then 23 .4 and then 23 .4...

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