VCE Methods Question Thread!

[b^3]

Check my last post again, should be able to see non latex sol now.

[e^1]

Check my last post again, should be able to see non latex sol now.

what do you know, latex is back on speed : )
Or press the space key at some place in the code : P :

[b^3]

Or press the space key at some place in the code : P :

It worked the first time I did it a week or so ago.... and then we realised that the updated latex needed the spaces, I tried that and it still didn't work -.-....

[zvezda]

cheers b^3.
another one which i think is seriously bizarre; dont know why im wrong:
A cylinder is inscribed in a sphere with a radius of length 6cm. For the cylcinder:
a) Define a function V which gives the volume of the cylinder as a function of the height (height of the cylinder in case specification is required cos i cant paste the image on here)

[Will T]

Use pythag for r squared + h on 2 squared = 6 squared.
Stefan >.<

[zvezda]

Use pythag for r squared + h on 2 squared = 6 squared.
Stefan >.<

omg... i read the 6cm as being the radius of the cylinder.

[zvezda]

chapter 1 review in the essentials text (extended response q8d), i dont see how foh exists?
 (according to the textbook it exists)

[Will T]

Deal with each separately. But as for the overall function, the range of h(x) is a subset of the domain of f(x), so it does exist. Just be careful with the domain of each of the functions in the overall foh hybrid.

[zvezda]

Deal with each separately. But as for the overall function, the range of h(x) is a subset of the domain of f(x), so it does exist. Just be careful with the domain of each of the functions in the overall foh hybrid.

cheers treb

[zvezda]

in fact, how would you find the domains?

[Will T]

For x^2 - 4, the domain is neg infinity to 2, exclusive, and so the range of h(x) = 2x has to be at most that. So, what domain corresponds to a range of neg infinity to 2, exclusive, for 2x?

You just solve y = 2x, 2 = 2x, x = 1. So x has to be less than 1 (i.e. from neg infinity to 1 exclusive).
Because as you know with composite functions, ran h(x) has to be a subset of dom f(x) and the dom of the new foh(x) function will be the dom of h(x).

Same deal with the other one. What range corresponds to a domain of [2,inf) for 2x? obviously 2x has to be greater than or equal to 2, so x has to be greater than or equal to one, and so the dom of the second part of the hybrid function is from 1 to positive infinity inclusive.
(Sorry no LaTeX I'm on my iPad + lazy).

[zvezda]

all right cheers will.
Anyone know how to find the inverse of a 3x3 matrix. Is that even in the VCE methods course ?

[KevinooBz]

all right cheers will.
Anyone know how to find the inverse of a 3x3 matrix. Is that even in the VCE methods course ?

Use your CAS. Takes too much time to do it by hand. If you want you can google how to by hand but it is unnecessary in methods.

[Will T]

You can augment the matrix and perform elementary row operations to get an identity matrix on one side and the inverse on the other. Or you can do it the long way (Google Khan academy or MIT linear algebra lectures if you want to see this, it's the same as for an n by n matrix.

Easiest way is Computer Algebra System (CAS). And no it's not required by hand for the course, it says that on one of the pages.

Edit: sorry was thinking of determinants for the first bit.

[b^3]

all right cheers will.
Anyone know how to find the inverse of a 3x3 matrix. Is that even in the VCE methods course ?

For those who are interested in knowing how to do it by hand there is this thread Re: BORED already? Want to learn a bit of maths? :P

But as the others have said, I must stress that this isn't on the course, when you need to do it do it on the calc (for now anyways )