The Math Thread!
- Thread starter Argetlam
- Start date
I need to find the coefficents for the quadratic equation (meaning a, b, and c) to a graph with the folowing points (35,161), (7,21), and (105,133). Unless someone knows off the top of their head what the quadratic equation for the Xcelerator rollar coaster in knotts berry farm is.Zyflair said:
So we have the standard quadratic form as:
And we have three points to find a, b, and c. If we plug in x and y as the points we get the following:
Simplifying that mess leaves us with:
And all we're left with is a simple systems of equations (of three variables). If you need help for that as well, let me know.
Code:
y = ax^2 + bx + c
Code:
(35,161): 161 = a(35)^2 + b(35) + c
(7,21): 21 = a(7)^2 + b(7) + c
(105,133): 133 = a(105)^2 + b(105) + cSimplifying that mess leaves us with:
Code:
161 = 1225a + 35b + c
21 = 49a + 7b + c
133 = 11025a + 105b + cAnd all we're left with is a simple systems of equations (of three variables). If you need help for that as well, let me know.
Ya I got that already, but from there I can't find an answer.Zyflair said:
Okay so you want help for the system of equations then, lol.
Subtract the first equation from the second and you get:
Subtract the first from the third and you get:
Take the two equations together and add:
Divide both sides by -2744 and:
Plug that in for a and start all over again for b and c. I hope you know the rest, but if not, I'll post that as well.
Code:
161 = 1225a + 35b + c
21 = 49a + 7b + c
133 = 11025a + 105b + cSubtract the first equation from the second and you get:
Code:
140 = 1176a + 28bSubtract the first from the third and you get:
Code:
30 = -9800a - 70b, or
3 = -980a - 7b (divided both sides by 10), and finally:
12 = -3920a - 28b (multiplied both sides by 4)Take the two equations together and add:
Code:
140 = 1176a + 28b
12 = -3920a - 28b
--------------------------
152 = -2744aDivide both sides by -2744 and:
Code:
a = -152/2744 = -19/343Plug that in for a and start all over again for b and c. I hope you know the rest, but if not, I'll post that as well.
Thanks for the help I should be able to get the rest from there.Zyflair said:
There is a reason I am in Alegebera 2 , but sometimes this stuff just doesn't make sense Thanks again .I'm in top set maths class at the moment "D, But I don't like my maths teacher because hes really intimidating :L
I love the creation of this thread.
I kinda need a wee bit of help with some mathamatical smart-stuff
Is there a rule for how numbers with negative exponents work?
Ex: 11 to the -5th power or 11 to the -6th power
And then what would happen in a situation when the co-efficient is negative and the exponent is negative/positive?
Ex: -11 to the 5th power/-11 to the 6th power or +11 to the -5th power and +11 to the negative 6th power
And lastly, variables for exponents? What would be done in this case
You are asked to combine the terms here
6x to the second power + 6x to the B power
And the last situation being
Simplifiy
6x to the second power + 6x to the B power
Thanks, if you could answer each example for me, that'd be appreciated. BTW, the powers of 5 and 6 are just because I need an example for an odd and even exponent. Thanks again!
I kinda need a wee bit of help with some mathamatical smart-stuff
Is there a rule for how numbers with negative exponents work?
Ex: 11 to the -5th power or 11 to the -6th power
And then what would happen in a situation when the co-efficient is negative and the exponent is negative/positive?
Ex: -11 to the 5th power/-11 to the 6th power or +11 to the -5th power and +11 to the negative 6th power
And lastly, variables for exponents? What would be done in this case
You are asked to combine the terms here
6x to the second power + 6x to the B power
And the last situation being
Simplifiy
6x to the second power + 6x to the B power
Thanks, if you could answer each example for me, that'd be appreciated. BTW, the powers of 5 and 6 are just because I need an example for an odd and even exponent. Thanks again!
WHERE HAS THIS THREAD BEEN ALL MY LIFE
DV, Negative Exponents multiply said number by 0.1, as opposed to 10 (or divide the number by 10 for negative exponents if you like that better). So 11 ^-5 would be a decimal answer. I'm too lazy to get out my calculator to solve it though.
Technically, -11 ^5 is an illegal operation. However, putting parenthasis around the number make it work. ex. (-11) ^5. Then it just becomes like any other exponent problem, so its just like solving positive 11 ^5.
On your last one about the exponents being variables, I'm not so sure on. I haven't done those in a while.
DV, Negative Exponents multiply said number by 0.1, as opposed to 10 (or divide the number by 10 for negative exponents if you like that better). So 11 ^-5 would be a decimal answer. I'm too lazy to get out my calculator to solve it though.
Technically, -11 ^5 is an illegal operation. However, putting parenthasis around the number make it work. ex. (-11) ^5. Then it just becomes like any other exponent problem, so its just like solving positive 11 ^5.
On your last one about the exponents being variables, I'm not so sure on. I haven't done those in a while.
@Hatman
FRom the extent of my knowledge, I've been taught that negative exponents work as so
5 to the second power = 25
5 to the first power=5
5 to the 0 power=1
5 to the -1 power= -5
5 to the -2 power= -25
But I may be wrong, which is why I'm posting here.
BTW, hatman, what about having a negative coefficent and a negative exponent or positive co-efficient and a negative exponent?
FRom the extent of my knowledge, I've been taught that negative exponents work as so
5 to the second power = 25
5 to the first power=5
5 to the 0 power=1
5 to the -1 power= -5
5 to the -2 power= -25
But I may be wrong, which is why I'm posting here.
BTW, hatman, what about having a negative coefficent and a negative exponent or positive co-efficient and a negative exponent?
Yes there is. When a negative number is an exponent, the number will get smaller. Basically it becomes 1 / the base number times the exponent, ignoring the negative sign.
Ex. 2[sup]2[/sup] = 1 / 4.
When the coefficient is negative and the exponent is even, the resulting number will be positive because a negative multiplied by a negative gets you a positive. When the coefficient is negative and the exponent is odd, the resulting number will be a negative number because a positive times a negative nets a negative.
Ex. -6[sup]4[/sup] = -6 * -6 * -6 * -6 = 1296
Ex. -5[sup]3[/sup] = -5 * -5 * -5 = -125
You need to combine coefficients that have the same exponent. You can't combine terms that have different exponents. This is like how for quadratic equations you can't combine the x[sup]2[/sup] with x.