VCE Methods Question Thread!

[knightrider]

Have a read through the chapter of integration in your textbook. For the first one you'd want to divide it through first though.

I have but still cant understand

[Reus]

For two lines to be parallel, they need to have the same gradient. So the answer will be any linear line such that it's gradient is , in other words .

Thank you!!

[LiquidPaperz]

what is the graident at the point of inflection?

the one here: http://www.mathsrevision.net/advanced-level-maths-revision/pure-maths/calculus/uses-differentiation would be 0
and here: http://wwwf.imperial.ac.uk/metric/metric_public/differentiation/applications/points_of_inflexion.html would be a negative?

edit: a p.o.i signals a change in direction however in the second link wheres the change?

[Zealous]

what is the graident at the point of inflection?

the one here: http://www.mathsrevision.net/advanced-level-maths-revision/pure-maths/calculus/uses-differentiation would be 0
and here: http://wwwf.imperial.ac.uk/metric/metric_public/differentiation/applications/points_of_inflexion.html would be a negative?

The gradient of a stationary point of inflection is 0 - because it is a stationary point where the slope is zero.

The gradient of a point of inflection can be positive, negative, whatever. A point of inflection is a point where the double derivative changes sign, which may not occur when the derivative equals 0.

In methods you'll mainly look at stationary points of inflection, you do more double derivative work in specialist.

http://mathworld.wolfram.com/InflectionPoint.html

[psyxwar]

I have but still cant understand

there isn't that much to understand, you're really just rote learning integration rules.

[knightrider]

How would you do this question.

Find the maximum deflection. (Be careful.)

[lzxnl]

How would you do this question.

Find the maximum deflection. (Be careful.)

Well...I don't see a stationary point there, so the max deflection is at x = 2
So integrate this expression to get y = -0.02(x+1)^3 +  0.06x + 0.02
Where the extra 0.02 term is added so that when x = 0, y = 0.
Now sub in x = 2. That would be your maximum deflection

[knightrider]

Well...I don't see a stationary point there, so the max deflection is at x = 2
So integrate this expression to get y = -0.02(x+1)^3 +  0.06x + 0.02
Where the extra 0.02 term is added so that when x = 0, y = 0.
Now sub in x = 2. That would be your maximum deflection

Thanks but i don't understand why did you use  x=2

[silverpixeli]

Thanks but i don't understand why did you use  x=2

2m long board
x is the distance in metres from the fixed end
max deflection is as far away from the fixed end as you can get

max deflection is at x=2 (m)

[LiquidPaperz]

if the det of a matrix equals 0 what does this mean? that solutions do not exist (undefined?) however the inverse exists? this stuff i havent learnt so if someone could clarify the meanings of this that would be awesome.

Also, if the inverse exists what does this mean?

[Orb]

if the det of a matrix equals 0 what does this mean? that solutions do not exist (undefined?) however the inverse exists? this stuff i havent learnt so if someone could clarify the meanings of this that would be awesome.

Also, if the inverse exists what does this mean?

If the det of a matrix equals 0 then the inverse cannot exist.

[psyxwar]

if the det of a matrix equals 0 what does this mean? that solutions do not exist (undefined?) however the inverse exists? this stuff i havent learnt so if someone could clarify the meanings of this that would be awesome.

Also, if the inverse exists what does this mean?

A matrix having a determinant of zero means it is a singular matrix; that is it has no inverse.

Furthermore, it means that the system of equations defined by the matrix is linearly dependent. If you don't do spesh, that simply means that (in 2 dimensions) parallel lines are being defined. This is useful to know when you have to find the number of solutions given by a system of equations, because if the determinant is zero you know there are no unique solutions (either there are no solutions, in the case of parallel lines that do not overlap, or they have infinite solutions where the two lines are the same)

For example, the system of equations ax+by=e and cx+dy=f is defined by the following matrix:



If the determinant is equal to zero, this means that ad-bc=0. This means that ad=bc, which means that the two lines are parallel (as it implies a/b = c/d, ie. the ratio of the coefficients of x and y terms is identical).

[LiquidPaperz]

how would you do this manually, ie use the proportions such as 0.2 * 300 etc.

i got D however answer is C

[silverpixeli]

how would you do this manually, ie use the proportions such as 0.2 * 300 etc.

i got D however answer is C

I get D too,

looks like, for the 300 in labour, 0.6 stay, 0.2 go to liberal and 0.2 go to other so that's 0.4*300=120 changers here
as for the people in liberal, 0.8 stay, 0.1 change to labour and 0.1 go other so that's another 200*0.2 = 40 changers
finally, of the 100 people in other, 0.1 go labour and 0.3 go liberal and 0.6 stay, i.e. 0.4*100 =40 changers

120 + 40 + 40 = 200 --> D

is there a worked solution?

[keltingmeith]

I get D too,

looks like, for the 300 in labour, 0.6 stay, 0.2 go to liberal and 0.2 go to other so that's 0.4*300=120 changers here
as for the people in liberal, 0.8 stay, 0.1 change to labour and 0.1 go other so that's another 200*0.2 = 40 changers
finally, of the 100 people in other, 0.1 go labour and 0.3 go liberal and 0.6 stay, i.e. 0.4*100 =40 changers

120 + 40 + 40 = 200 --> D

is there a worked solution?

Notice they haven't actually given us an initial state matrix or what the matrix they've given us means - you've just assumed that it goes Labour-->Liberal-->Other.

In fact, if you do 0.4*200+0.2*300+0.4*100, you'll get 180. Personally, I don't think we have enough information, and that what they've given is meaningless data. This question is not solvable with any method that I know.