Question 1189907
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.


<a href = "https://www.youtube.com/watch?v=b75PEalga4c" target = "_blank">https://www.youtube.com/watch?v=b75PEalga4c</a>


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


<img src = "http://theo.x10hosting.com/2022/012301.jpg" >


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.


<a href = "https://www.desmos.com/calculator" target = "_blank">https://www.desmos.com/calculator</a>


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.


<img src = "http://theo.x10hosting.com/2022/012302.jpg" >


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


theo