Post by: stonecold on November 04, 2010, 04:06:14 pm
Or only linear denominators?
Post by: superflya on November 04, 2010, 04:07:41 pm
Post by: stonecold on November 04, 2010, 04:09:02 pm
Post by: superflya on November 04, 2010, 04:10:43 pm
Post by: stonecold on November 04, 2010, 04:12:42 pm
sec^2(x) is simple and easy, but this stuff shouldn't even come up should it?
Post by: superflya on November 04, 2010, 04:16:52 pm
Post by: Blakhitman on November 04, 2010, 04:22:21 pm
Post by: stonecold on November 04, 2010, 04:23:29 pm
odds of finding the area under a log by finding the inverse and then finding the area under this for the appropriate domain?
and yeah, antidiff of sec^2(x) is easy...
Post by: stonecold on November 04, 2010, 04:31:35 pm
say they want the general solution for the assymptotes on a tan graph, you just find the equation of one. then add that to the period multiplied by n, where n is an element of z, and done...
yeah?
Post by: Souljette_93 on November 04, 2010, 04:35:15 pm
have decided to rename this thread haha.
say they want the general solution for the assymptotes on a tan graph, you just find the equation of one. then add that to the period multiplied by n, where n is an element of z, and done...
yeah?
An asymptote? Wouldn't that be on tan^-1(0)?
Otherwise, yeah, just as n-pi
Post by: stonecold on November 04, 2010, 04:47:57 pm
have decided to rename this thread haha.
say they want the general solution for the assymptotes on a tan graph, you just find the equation of one. then add that to the period multiplied by n, where n is an element of z, and done...
yeah?
An asymptote? Wouldn't that be on tan^-1(0)?
Otherwise, yeah, just as n-pi
lol, i don't get it. what i mean like is the general solution of asymptotes for say tax(x) is
pi x n + (pi/2) where n is an element of z...
Post by: Souljette_93 on November 04, 2010, 04:51:12 pm
have decided to rename this thread haha.
say they want the general solution for the assymptotes on a tan graph, you just find the equation of one. then add that to the period multiplied by n, where n is an element of z, and done...
yeah?
An asymptote? Wouldn't that be on tan^-1(0)?
Otherwise, yeah, just as n-pi
lol, i don't get it. what i mean like is the general solution of asymptotes for say tax(x) is
pi x n + (pi/2) where n is an element of z...
Sorry i made a mistake before. But yeah that's what i meant. I believe it's correct.
Post by: costa94 on November 04, 2010, 04:52:24 pm
Post by: kenhung123 on November 04, 2010, 04:54:11 pm
Post by: Souljette_93 on November 04, 2010, 04:55:34 pm
We need need to rationalise denominators and put answers over a common denominator?
When doing general solutions? I don't think so, i never do.
Post by: stonecold on November 04, 2010, 04:57:51 pm
I know numerical answers must be in simplest form...
Post by: stonecold on November 04, 2010, 05:00:28 pm
Post by: lovingit on November 04, 2010, 05:06:56 pm
Post by: stonecold on November 04, 2010, 05:08:37 pm
What does it mean if the determinate of a matrix is negative
that unique solutions exist, same as if it is positive.
it is when it = 0, the matrix is singular, meaning that either none or infinite solutions exist.
Post by: lachymm on November 04, 2010, 05:11:33 pm
Post by: stonecold on November 04, 2010, 05:12:53 pm
I havent learnt how to do them by matrice's is it still ok to just know the other way ?
unless it says using matrices...
Post by: Souljette_93 on November 04, 2010, 05:14:21 pm
I havent learnt how to do them by matrice's is it still ok to just know the other way ?
me too..it's easier the other way. And you can do it another way, so long you get the answer.
Stonecold: can you explain how to do it by matrix?
Post by: stonecold on November 04, 2010, 05:19:37 pm
say you have 2x + my = 4 and 5x + 9y = 10, then you set it up as matrices, and solve the determinant to equal 0.
| 2 m |
| | = 0
| 5 9 |
2(9) - 5m = 0
5m =18
m=18/5
then you gotta sub you m values back in to see whether it gives infinite solutions or no solutions...
Post by: lachymm on November 04, 2010, 05:20:07 pm
Post by: kenhung123 on November 04, 2010, 05:20:40 pm
Umm not specifically like for a question I had 2 fractions as my answer, 1 with a root denominator. The solutions put everything under 1 denominator and rationalised it. Is that advised/required?We need need to rationalise denominators and put answers over a common denominator?
When doing general solutions? I don't think so, i never do.
Post by: stonecold on November 04, 2010, 05:22:15 pm
Umm not specifically like for a question I had 2 fractions as my answer, 1 with a root denominator. The solutions put everything under 1 denominator and rationalised it. Is that advised/required?We need need to rationalise denominators and put answers over a common denominator?
When doing general solutions? I don't think so, i never do.
yeah, try not to have square roots on the bottom...
Post by: lachymm on November 04, 2010, 05:24:14 pm
| | = 0
| 5 9 |
but how do you know what values of m correspond to a unique, no or infinite solutions?
Post by: stonecold on November 04, 2010, 05:26:55 pm
| 2 m |
| | = 0
| 5 9 |
but how do you know what values of m correspond to a unique, no or infinite solutions?
Sub them back into your equation(s)
If you get two identical equations, then there are infinite solutions. And note x+y=1 and 2x+2y=2 are identical etc.
If you get two different equations, which will have the same gradient but a different y-intercept, then there are no solutions, as they are parallel lines which will never intersect.
Post by: kenhung123 on November 04, 2010, 05:30:47 pm
ThanksUmm not specifically like for a question I had 2 fractions as my answer, 1 with a root denominator. The solutions put everything under 1 denominator and rationalised it. Is that advised/required?We need need to rationalise denominators and put answers over a common denominator?
When doing general solutions? I don't think so, i never do.
yeah, try not to have square roots on the bottom...
Post by: Blakhitman on November 04, 2010, 05:45:44 pm
To get the inverse of a (2x2) matrix:
Notice the determinant in the denominator? well if it doesn't equal zero then
Post by: schnappy on November 04, 2010, 06:04:21 pm
Post by: Elnino_Gerrard on November 04, 2010, 06:05:58 pm
I've managed to get a fair idea of this binomial expansion stuff... but if I'm asked to find the coefficient of the 'x^11' term, how do i know which term this is in the expansion? TSFX appear to magically now.
its pretty easy.
What i do is write the powers of all the terms---like the first is is 14,0 (o for the 3/x bit) The next one 12,1 and 12-1 is 11 so thaats it
Post by: Whatlol on November 04, 2010, 06:48:34 pm
So:
for infinite solutions, find when the discriminant = 0?
for unique, find when the discriminant (does not)= 0?
What about no solutions :S?
for no unique solutions find when DETERMENANT = 0 .
this covers the case of both infinite and no solutions.
when you have no solutions, the two equations are parallel and will never intersect. i.e same gradient different y intercept.
for infinite, they both the same.
Post by: akira88 on November 04, 2010, 06:49:10 pm
So:No solutions would also be when the determinant is 0. Then you have to make sure the lines aren't the same.
for infinite solutions, find when the discriminant = 0?
for unique, find when the discriminant (does not)= 0?
What about no solutions :S?
Post by: stonecold on November 04, 2010, 06:50:10 pm
So:
for infinite solutions, find when the discriminant = 0?
for unique, find when the discriminant (does not)= 0?
What about no solutions :S?
Nah, it is:
Determinant = 0 can mean either infinite or no solutions. You have to sub back into the equations to check.
Determinant not equal to 0, means there are unique solutions, and you can proceed to solve as normal. :D
Post by: andy456 on November 04, 2010, 06:56:07 pm
So what would you do after you've found out there are unique solutionsSo:
for infinite solutions, find when the discriminant = 0?
for unique, find when the discriminant (does not)= 0?
What about no solutions :S?
Nah, it is:
Determinant = 0 can mean either infinite or no solutions. You have to sub back into the equations to check.
Determinant not equal to 0, means there are unique solutions, and you can proceed to solve as normal. :D
Post by: stonecold on November 04, 2010, 06:58:49 pm
So what would you do after you've found out there are unique solutionsSo:
for infinite solutions, find when the discriminant = 0?
for unique, find when the discriminant (does not)= 0?
What about no solutions :S?
Nah, it is:
Determinant = 0 can mean either infinite or no solutions. You have to sub back into the equations to check.
Determinant not equal to 0, means there are unique solutions, and you can proceed to solve as normal. :D
Depends what the question wants. Usually it will ask for the values which a unique solution exists or doesn't exist.
When you get given an equaution, you generally assume that it has solutions though...
Post by: lovingit on November 04, 2010, 07:59:16 pm
Post by: 3Xamz on November 04, 2010, 08:02:54 pm
So:
for infinite solutions, find when the discriminant = 0?
for unique, find when the discriminant (does not)= 0?
What about no solutions :S?
Nah, it is:
Determinant = 0 can mean either infinite or no solutions. You have to sub back into the equations to check.
Determinant not equal to 0, means there are unique solutions, and you can proceed to solve as normal. :D
So, if you sub back in and the variables cancel out and you end up with something like 2=2, does that mean no solutions? :)