SOLUTION: Hi, can someone please help me out with this question? https://drive.google.com/file/d/1xs44rvhwHo0ttZc7btuhRwRhorbWTUuG/view?usp=sharing

Question 1189907: Hi, can someone please help me out with this question?
https://drive.google.com/file/d/1xs44rvhwHo0ttZc7btuhRwRhorbWTUuG/view?usp=sharing
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52799)   (Show Source): You can put this solution on YOUR website!
.

If I be a student and if this assignment be given to me,
I would go to the Internet and would request there

        " online calculator for sinusoidal regression "

in GOOGLE search engine.

It would give some links and I would look into them.

Doing this way, I would select one, for example, this one

https://drive.google.com/file/d/1xs44rvhwHo0ttZc7btuhRwRhorbWTUuG/view

and quickly complete the assignment on my own.

I think, it would be consistent with the contemporary educational methodology
and conceptions on how to perform such job/exercises in twenties of XXI century.

Pocket (graphing) calculators also provide such service.

For instructions and to get necessary skills, see this video-lecture on YouTube

https://www.youtube.com/watch?v=wbsXheT9KqA

Or see and listen another video-lecture

https://www.youtube.com/watch?v=ivPZ0tJZkGE

Happy learning and calculating ( ! )

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
not sure if they wanted you to do this manually.
if so, let me know and i'll work on a manually derived solution configuration.

the easiest way i can see is to use the desmos.com calculator.

here's a video on how to do that.

https://www.youtube.com/watch?v=b75PEalga4c

i followed the directions on the video and this is what i got.

the little hourglass on the left allows you to zoom in on the graph automatically.

othrwise, use her instructions to set the x and y limits.

the equation is entered from the keyhboard using the tilde rather than the equal sign.

here's the link to the desmos.com calculator.

https://www.desmos.com/calculator

your regression eqution of y = a * (b * (x - c)) + d becomes:

y = 13.8091 * sin(.509283 * (x - 4.11135)) + 13.4074.

to find the value for next march, just add 12 to 3 to get x = 15 and solve the equation for x = 15.

the equation becomes y = 13.8091 * sin(.509283 * (15 - 4.11135)) + 13.4074.

you should get y = 4.1187.

to find the month when the average tmperature first reaches 17 degrees centigrade, solve the equation for y = 17.

the equation becomes 17 = 13.8091 * sin(.509283 * (x - 4.11135)) + 13.4074.
subtract 13.4074 from both sides of the equation to get:
17 - 13.4074 = 13.8091 * sin(.509283 * (x - 4.11135))
simpliy to get:
3.5926 = 13.8091 * sin(.509283 * (x - 4.11135))
divide both sides of the equation by 13.8091 to get:
3.5926 / 13.8091 = sin(.509283 * (x - 4.11135))
simplify to get:
.2601617774 = sin(.509283 * (x - 4.11135))
find the arcsin of .260167774 to get:
arcsin(.260167774) = .263189746
solve for .509283 * (x - 4.11135)) = .263189746 as follows:
divide both sides of the equation by .509283 to get:
x - 4.11135 = .5167848642.
add 4.11135 to both sides of the equation to get:
x = 4.628134864.
that should be some time in april.

there's an easier way to do this using the desmos.com graph.
set x = 15 to find next march.
set y = 17 to find where the graph goes above 17 deegrees.

it will look like this.

check out the video.
it's pretty good.
let me know if you get hung up trying to do it yourself.

theo

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