VCE Methods Question Thread!

[paulsterio]

Use difference of squares



and

Factorised:

Possible to simplify further maybe, but that's enough to be considered factorised.

[Insa]

Thanks man! 

[Genericname2365]

Sorry about this mess; I'm not sure how to code in matrices. Hopefully it's understandable. Fair enough if it isn't.

I have a worked example I'm trying to follow that I don't understand:
For the Matrix A= [3 2] find: X if AX = the second matrix posted below (5, 6, 7 2)
                            [1 6]


*first step skipped*

Therefore IX = X =  1/16 [6 -2] [5 6] = 1/16 [16 32] (I understand the next step)
                                       [-1 3] [7 2]             [16  0]
             
                                        ^ That is the inverse of A x A
How does this multiplication of the inverse of A and A lead to the last matrix that I've typed?  Any help appreciated

[Phy124]

Using:

[Genericname2365]

Using:

(Image removed from quote.)

Cheers.  I evidently confused the addition step.

[Bhootnike]

For f (x) = 4 − x and g(x) = |x|, find f ◦ g and g ◦ f and sketch the graphs of each of these functions.


so i know fogx = 4-|x| , but im having trouble sketching this , can someone please help me on how to do this.
the graph is meant to look like:

https://www.desmos.com/calculator/dnxzglwomq

[TrueTears]

For f (x) = 4 − x and g(x) = |x|, find f ◦ g and g ◦ f and sketch the graphs of each of these functions.


so i know fogx = 4-|x| , but im having trouble sketching this , can someone please help me on how to do this.
the graph is meant to look like:

https://www.desmos.com/calculator/4dm5z6eiq1

First sketch y=|x| (the v shaped graph)

then apply the transformation, the - just means reflection in the x axis, then 4 up

[Bhootnike]

For f (x) = 4 − x and g(x) = |x|, find f ◦ g and g ◦ f and sketch the graphs of each of these functions.


so i know fogx = 4-|x| , but im having trouble sketching this , can someone please help me on how to do this.
the graph is meant to look like:

https://www.desmos.com/calculator/4dm5z6eiq1

First sketch y=|x| (the v shaped graph)

then apply the transformation, the - just means reflection in the x axis, then 4 up

o god, im a nuff nuff.
 

thx tt

[ashoni]

The height of a firework is modelled by the equation h(t) = -at^2 +5t where h(t) is the height of the firework and a>0.
a) Factorise the function and thus determine when, in terms of a, it would land on the ground (ie h(t)=0) if the firework was to follow this path completely.
b) Making the equation equal to d, solve for t in terms of a and d.
c) Using the discriminant from part (b) what value must a take in terms of d for this height to be reached only once?

sorry about the really long question guys.. just needed help with this one

[Bhootnike]

The height of a firework is modelled by the equation h(t) = -at^2 +5t where h(t) is the height of the firework and a>0.
a) Factorise the function and thus determine when, in terms of a, it would land on the ground (ie h(t)=0) if the firework was to follow this path completely.
b) Making the equation equal to d, solve for t in terms of a and d.
c) Using the discriminant from part (b) what value must a take in terms of d for this height to be reached only once?

sorry about the really long question guys.. just needed help with this one

for a),  i think you can complete the square.
so by taking out -a out as a factor, youre left with
complete the square using standard procedures,
and i believe you are left with
thus when t = 0, it would be on ground
now solve for t in the bracket
so,
finding LCD, and simplifying you get

b)

therefore,
from here i'd use quadractic formula ,
which'd give something like
o and i think for the  , you can simplify that down to 

c)

so
thus



i have a feeling i have made a mess of this, but i tried haha

[ashoni]

ohhokay thanks for the help Bhootnike!

[Bhootnike]

ohhokay thanks for the help Bhootnike!

was that the answer haha ?

[Kanon]

Oh this one has been killing me all day, I absolutely hate using the Binomial Theorem.

The first six rows of pascal's triangle are shown below.
(insert Pascals Triangle here)
When is expanded into a polynomial in decreasing powers of x, from left to right, the fifth term is

I think I might have missed the relationship between the Binomial Theorem and Pascal's Triangle.
Would I look at the 5th row and add all the numbers and that is the co-eff of it?

It's a multiple choice from VCAA 2000 if anyone's curious.
also, have a pascal swirl.

[Deceitful Wings]

Consider the function f: (-infinity, -1] -> f(x) = (x-1)/ (x^2 + x + 2)
Find the rule for the inverse function f^-1

[aznxD]

Oh this one has been killing me all day, I absolutely hate using the Binomial Theorem.

The first six rows of pascal's triangle are shown below.
(insert Pascals Triangle here)
When is expanded into a polynomial in decreasing powers of x, from left to right, the fifth term is

I think I might have missed the relationship between the Binomial Theorem and Pascal's Triangle.
Would I look at the 5th row and add all the numbers and that is the co-eff of it?

It's a multiple choice from VCAA 2000 if anyone's curious.
also, have a pascal swirl.

Calling the first row of Pascal's triangle row 0, look at the 7 row of Pascal's for the coefficinets of the binomial expansion of .
So
Basically for the coefficients of the binomial expansion of  , look at the nth row of Pascal's triangle assuming the first row (1) is row 0.