Ok I'm in a Trig class but we're reviewing some Algebra at the moment and I got a worksheet with this problem that I need to solve before Tuesday. I will supply the question and all my information. If you want to contact me on AIM my s/n is emximer.
"A group of students dropped a rubber ball and measured the height in inches of the ball for each of its successive bounces. The results are shown in the table."
Bounce 1= 47 inches
Bounce 3= 26 inches
Bounce 4= 21 inches
a. Find a model for the data
b. What was the height of the ball before it was dropped?
c. What was the height of the ball on the 2nd bounce?
Basically I just need to know the model then I can find the rest.
OK there it is, the way I was told to go about it ( I forget the proper name for this formula/method EDIT: Quadtradic function?). Basically take the data and put it into a formula like such:
1. a+b+c=47
2. 9a+3b+c=26
3. 16a+4b+c=21
(To get these I did ax^2+bx+c=h where x= the bounce and h= the height)
And then I subtracted 3 from 2 to get 7a+b=-5
Then I subtracted 2 from 1 to get 8a+2b=-21
Then I multiplied 7a+b=-5 by 2 to get 14a+2b=-5, allowing me to subtract that from 8a+2b=-21 so I could isolate the variable 'a'. Then once getting a I subtracted it back into one of the above formulas to find the value of b, then subtracted both a and b into an earlier formula to find c. However everytime I did this I found my end model would only work for the first bounce or the first 2 bounces. I think I may be using the wrong formula or method here. Anyways heres the solutions I've found so far that fit some of the data but doesn't satisfy all of it.
f(x)= (11/2)x^2-32.5x+74 (Satisfys bounce 1 and 3, but not 4)
f(x)=(11/6)x^2+(107/6) + 82/3 (Satisfys bounce 1 only)
It would seem to me that the B value would have to be negative, but I dont know if this method will work for this problem because when the X gets larger it will gain height, which shouldn't happen in this problem.
Thank you for reading/helping, if you want more information or want me to clarify something please post here or contact me on aim (mentioned above) or email me.
"A group of students dropped a rubber ball and measured the height in inches of the ball for each of its successive bounces. The results are shown in the table."
Bounce 1= 47 inches
Bounce 3= 26 inches
Bounce 4= 21 inches
a. Find a model for the data
b. What was the height of the ball before it was dropped?
c. What was the height of the ball on the 2nd bounce?
Basically I just need to know the model then I can find the rest.
OK there it is, the way I was told to go about it ( I forget the proper name for this formula/method EDIT: Quadtradic function?). Basically take the data and put it into a formula like such:
1. a+b+c=47
2. 9a+3b+c=26
3. 16a+4b+c=21
(To get these I did ax^2+bx+c=h where x= the bounce and h= the height)
And then I subtracted 3 from 2 to get 7a+b=-5
Then I subtracted 2 from 1 to get 8a+2b=-21
Then I multiplied 7a+b=-5 by 2 to get 14a+2b=-5, allowing me to subtract that from 8a+2b=-21 so I could isolate the variable 'a'. Then once getting a I subtracted it back into one of the above formulas to find the value of b, then subtracted both a and b into an earlier formula to find c. However everytime I did this I found my end model would only work for the first bounce or the first 2 bounces. I think I may be using the wrong formula or method here. Anyways heres the solutions I've found so far that fit some of the data but doesn't satisfy all of it.
f(x)= (11/2)x^2-32.5x+74 (Satisfys bounce 1 and 3, but not 4)
f(x)=(11/6)x^2+(107/6) + 82/3 (Satisfys bounce 1 only)
It would seem to me that the B value would have to be negative, but I dont know if this method will work for this problem because when the X gets larger it will gain height, which shouldn't happen in this problem.
Thank you for reading/helping, if you want more information or want me to clarify something please post here or contact me on aim (mentioned above) or email me.
.