VCE Methods Question Thread!

[@#035;3]

Hey guys quick question, thanks in advance.
Solve for x:
2^2*x+1 -17*2^x + 8=0

[Phy124]

Hey guys quick question, thanks in advance.
Solve for x:
2^2*x+1 -17*2^x + 8=0

[bills]

Can someone please help me with this question:

Sketch the graph of f: R+ U {0} -> R, f(x) = -(root(x)) + x using addition of ordinates.

I understand how to graph each of the two parts separately, however, I am having trouble with the combined function. In particular, I am having trouble finding out the shape of the graph.

Thanks!

[bills]

Another quick question,
Find the implied domain of the following rule:

Thanks

[RKTR]

Another quick question,
Find the implied domain of the following rule:

Thanks

(x-1)/(x+2) = (x+2-3)/(x+2) = 1- 3/(x+2)
for 1-3/(x+2)  x cant be -2
and you cant root a negative number
so implied domain is (-infinity,-2) U [1,infinity)

[bills]

How do I convert into the form of ?

Thanks.

[RKTR]

How do I convert into the form of ?

Thanks.

(2x+3)/(3x-2) = [2/3(3x-2) +13/3] / 3x-2 = 2/3 +13/3(3x-2)

[bills]

(2x+3)/(3x-2) = [2/3(3x-2) +13/3] / 3x-2 = 2/3 +13/3(3x-2)

Where did you get 2/3 and 13/3 from? Also, what is this type of division/converting thing called (I think it has a name)?

[mtse]

You can use algebraic long division.
http://imgur.com/vYXSDKL (sorry the picture's blurry)

[keltingmeith]

Where did you get 2/3 and 13/3 from? Also, what is this type of division/converting thing called (I think it has a name)?

Division by inspection. Here's a nifty video of it - note that they start with a quadratic then move into the linear case, so you might find it easier to start from halfway through and then go backwards/watch it a couple of times to get the hang of what they're saying.

[Sarah P]

I have a question regarding matrices, as I am unable to figure out the equation of this question;

A quartic goes through the points (-5,540), (-4,77), (-1,-56), (1,18) and (3,-364). Find its equation (using matrices).

The answer is y=2x^4 - 7x^3- 56x^2 + 44x + 35

I've already done a question similar to this one, but for some reason I am unable to figure out how to get the above answer despite using the same formula. Can someone please how I get the solution? Any help will be much appreciated 

[@#035;3]

Quick few questions, thanks in advance.
Let a and b be positive real numbers.

(1) Prove that (log_a(b))(log_b(a))=1


(2) Prove that 1/log_a(b) + 1/log_b(a)=log_a(b)+log_b(a)

[mtse]

This requires the change of base rule
log_x(b) = log_a(b) / log_a(x)

(1) Prove that (log_a(b))(log_b(a))=1

Using the change of base rule on log_b(a)
log_a(b) x log_a(a) / log_a(b) = log_a(a) = 1

(2) Prove that 1/log_a(b) + 1/log_b(a)=log_a(b)+log_b(a)

Make LHS one fraction using the common denominator (log_a(b))(log_b(a))
(log_b(a) + log_a(b)) / (log_a(b) x log)_b(a))
From part 1) we know that (log_a(b))(log_b(a)) = 1
therefore (log_b(a) + log_a(b)) / (log_a(b) x log)_b(a)) = (log_b(a) + log_a(b)) / 1 = log_a(b)+log_b(a)

[keltingmeith]

I have a question regarding matrices, as I am unable to figure out the equation of this question;

A quartic goes through the points (-5,540), (-4,77), (-1,-56), (1,18) and (3,-364). Find its equation (using matrices).

The answer is y=2x^4 - 7x^3- 56x^2 + 44x + 35

I've already done a question similar to this one, but for some reason I am unable to figure out how to get the above answer despite using the same formula. Can someone please how I get the solution? Any help will be much appreciated 

I wouldn't worry too hard about this question, as matrices in this sense are no longer in the study design. If you ever had to solve a question like this, you would NOT need to use matrices. I'd suggest using your CAS for this one, too - VCAA would NOT give something like this on a calc-free paper. If your teachers do, they're sadists.

If you want to do it by hand, what you need to do is start with the equation:
y=ax^4+bx^3+cx^2+dx+e

Sub in all five points that they've given you, and then solve the system of five equations using whatever method you prefer (elimination will solve it quickest, though)

[Sarah P]

I wouldn't worry too hard about this question, as matrices in this sense are no longer in the study design. If you ever had to solve a question like this, you would NOT need to use matrices. I'd suggest using your CAS for this one, too - VCAA would NOT give something like this on a calc-free paper. If your teachers do, they're sadists.

If you want to do it by hand, what you need to do is start with the equation:
y=ax^4+bx^3+cx^2+dx+e

Sub in all five points that they've given you, and then solve the system of five equations using whatever method you prefer (elimination will solve it quickest, though)

Thank you so much for this! We're currently doing headstart where we are doing some of the work for yr 12 next year right now and my teacher, sadly, isn't all that flash. She gave us this question but her solutions are without working out, so I have no idea where I went wrong! Now that I know it's not on the study design, I'll try to not stress over it