VCE Specialist 3/4 Question Thread!

[#1procrastinator]

Also, more of an basic geometry question but I guess it came up in vectors - are two lines that are collinear also considered to be parallel?

[rife168]

Also, more of an basic geometry question but I guess it came up in vectors - are two lines that are collinear also considered to be parallel?

Two lines that are collinear would be the same line, so I would say yes, unless there is some technicality that states a line isn't parallel to itself...
Two vectors that are collinear would be parallel but not neccessarily the same vector, remember vectors are free to move in space.

[TrueTears]

Express (1-i)^3 in cartesian form. isn't that already in cartesian form? if not, what is that form called?  the solution just expanded and simplified it

well the formal definition is given on wiki http://en.wikipedia.org/wiki/Complex_number#Definition

and so (1-i)^3 isn't in the correct form, you need to expand it

[Special At Specialist]

There are two ways to expand (1 - i)^3. Using a purely algebraic approach:
Using the formula (a - b)^3 = a^3 - 3(a^2)b + 3ab^2 - b^3
(1 - i)^3 = (1)^3 - 3(1^2)i + 3(1)(i^2) - (i)^3
= 1 - 3i - 3 + i
= -2 - 2i

Using the polar form approach:
(1 - i)^3
= (sqrt(2)*cis(-pi/4))^3
= 2*sqrt(2)*cis(-3pi/4)
= 2*sqrt(2)*(-1/sqrt(2) - 1/sqrt(2) i)
= -2 - 2i

[#1procrastinator]

^ Thanks guys

[#1procrastinator]

What's the difference between a parameter and a variable?

[Special At Specialist]

A parameter is like an added variable that is not part of the cartesian equation. For example:
x = cos(t) and y = sin(t)
The independent variable is x, the dependent variable is y and the parameter is t.

[TrueTears]

I think the best way to define a "parameter" in general, is to just check the wiki entry on it, or simply use the definition provided in your text (which should apply thereon-forth), there is too many possible definitions of a parameter

[#1procrastinator]

^ I'm too dumb to fully understand the wiki article

This, I get
...a parameter is a quantity that serves to relate functions and variables using a common variable when such a relationship would be difficult to explicate with an equation.

This loses me
[/i]Mathematical functions have one or more arguments that are designated in the definition by variables, while their definition can also contain parameters. The variables are mentioned in the list of arguments that the function takes, but the parameters are not. When parameters are present, the definition actually defines a whole family of functions, one for every valid set of values of the parameters. [/i]

[soccerboi]

Simple question but i forgot the reason behind it: How do you determine the domain of something like y= sin^-1(x/2)?
it's [-2,2] but why? why not [-0.5,0.5]? Can someone explain the logic behind it? Thanks

[pi]

The way I would do it is that the x-cords of the endpoints would be:

x/2 = -1 and x/2 = 1   ie. whatever is inside the arcsin is either 1 or -1
Hence, x = -2 and x = 2

Hence domain = [-2, 2]

Alternatively, you could see from the equation that the simple y=arcsin(x) has been dilated and work the domain from there

[soccerboi]

I having trouble with this:
A is the point (-1,2) and B is (-5,1). Find P such that AP=2PB using a vector method.

[Jenny_2108]

I having trouble with this:
A is the point (-1,2) and B is (-5,1). Find P such that AP=2PB using a vector method.

Let OP (x,y) (I dont know how to write vector on computer man just see whatsoever I wrote later as vectors)
AP = OP-OA = (x+1, y-2)
PB = OB-OP = (-5-x, 1-y)
Given: AP=2PB => x+1= 2(-5-x) and y-2=2(1-y) => DIY to solve x,y

[soccerboi]

Thanks

Can someone evaluate x root 1-x² from 0 to 1.

I keep getting -1/3, but it should be 1/3.
Aslo can someone show me how to type the antidiff sign and other maths symbols using latex?

[b^3]

Let

Changing the terminals then and if then (this may be why your answer is -ve, if you forgot this step)
The reason we change the terminals is because we are no longer integrating with respect to x, we are now integrating with respect to u.



As for the integral

Code: [Select]

[tex]\int[/tex]
For the square root

Code: [Select]

[tex]\sqrt{}[/tex]