VCE Methods Question Thread!

[Insa]

Ah! Thank you!

[kamil9876]

In general show that the coefficient of in is zero if is odd.

[nooshnoosh95]

hi guys could i get some help with this linear equation stuff

it asks for me to find the number of solutions being either no solutions, infinite number or unique
i know how to find the solutions but without doing this i dont know how to find the number of solutions

if it asks for the number of solutions for these 3 simultaneous equations how do i go about it?
x+4y+3z=10
2x+y-z=-1
3x-y-4z=11
thanks for any help

[Bhootnike]

Is the answer, no solution ??

cause i find it easiest to just put these into a matrix..

1  4    3
2  1   -1
3 -1  -4

then find the determinant, which for this one = 0. so no solution.. ?

[brightsky]

interesting question...
multiply 4 to the bottom two equations:
x+4y+3z=10.....(1)
8x+4y - 4z = -4....(2)
12x-4y-16z=44....(3)
(2) - (1):
7x -7z = -14 ==> x - z = -2...(4)
(2)+(3):
20x - 20z = 40 ==> x - z = 2...(5)
(4) and (5) are parallel.
so there are no solutions for x and z.
hence there are no solutions for y.
So no solutions for these 3 simultaneous eq.

[nooshnoosh95]

thanks guys but for this one the determinant is also 0 but it has infinite solutions :S

x-y+z=6
x-4y+5z=7
x+2y-3z=5

[butene]

x-y+z = 6  ..(1)
x-4y+5z= 7  ..(2)
x+2y-3z= 5 ..(3)
(1)-(3) gives
-3y + 4z = 1 ..(4)
(2) - (3) gives
-6y+8z = 2 ..(5)
2(4) = (5), equations (4) and (5) are the same
therefore infinite solutions for y and z
->infinite solutions for x

[butene]

Is the answer, no solution ??

cause i find it easiest to just put these into a matrix..

1  4    3
2  1   -1
3 -1  -4

then find the determinant, which for this one = 0. so no solution.. ?

if the determinant is 0 there is either an infinite no. solutions OR no solutions so use simultaneous eq's to work it out

[TrueTears]

Is the answer, no solution ??

cause i find it easiest to just put these into a matrix..

1  4    3
2  1   -1
3 -1  -4

then find the determinant, which for this one = 0. so no solution.. ?

just becareful that if the determinant is 0 it does not necessarily mean no solutions, could mean infinite solutions as well

[synchronise3]

This is probabaly a really really easy question, just my brain's not working

Solve for x,    x∈[-π ,π ]

sin x= -1/2


thanks in advance.

[abd123]

This is probabaly a really really easy question, just my brain's not working

Solve for x,    x∈[-π ,π ]

sin x= -1/2


thanks in advance.

Use a sine graph.

so the basic angle for

[nooshnoosh95]

you have to use the general solutions for sine
so
x=2n(pi)+sin-1(-1/2)   or x=(2n+1)(pi)-sin-1(a)
x=2n(pi)-(pi)/6
sub in values for n to find values within your domain
then we know that sin has to be negative so it can either be in the third or forth quadrants
so values for x are
-5(pi)/6 and -(pi)/6
i think...

[Dominatorrr]

Find all values of x:

9*e^x+2*e^-x=9

How would we assign a variable to the equation to obtain a quadratic?

[Phy124]

Find all values of x:

9*e^x+2*e^-x=9

How would we assign a variable to the equation to obtain a quadratic?

Let A =





etc.

I think that was what you were asking and I think that's right, unless I major effed something up

[Bhootnike]

Is the answer, no solution ??

cause i find it easiest to just put these into a matrix..

1  4    3
2  1   -1
3 -1  -4

then find the determinant, which for this one = 0. so no solution.. ?

just becareful that if the determinant is 0 it does not necessarily mean no solutions, could mean infinite solutions as well

is there a way to proceed onwards from there to figure out which one it is using matrices ? 

This is probabaly a really really easy question, just my brain's not working

Solve for x,    x∈[-π ,π ]

sin x= -1/2


thanks in advance.

sin pi/6 = 1/2
so pi/6 is your base angle.
you need to figure out where sin is -1/2, in the given domain of [-pi,pi.]

since you're looking for -1/2, and sine is negative in the 3rd, 4th quadrants. so you'll have 2 solutions.

using the unit circle,
1) pi + (pi/6) = 7pi/6 , which is also the same - 5pi/6
2) 2pi - (pi/6) =11pi/6 , which is also the same as -pi/6