VCE Methods Question Thread!

[#1procrastinator]

For x^9 > 9, why is it ±x > 3 not x > ±3

assuming x^2>9

+ or - x >3

case 1: x>3

case 2: -x>3 => x<-3

Why +/- x and not +/- 3?

[TrueTears]

For x^9 > 9, why is it ±x > 3 not x > ±3

assuming x^2>9

+ or - x >3

case 1: x>3

case 2: -x>3 => x<-3

Why +/- x and not +/- 3?

because x^2-9>0 => (x-3)(x+3)>0

1. x-3>0 and x+3>0 => x>3 and x>-3 => x>3

2. x-3<0 and x+3<0 => x<3 and x<-3 => x<-3 => -x>3

so + or - x >3

[#1procrastinator]

Oh yes, forgot difference of two squares...so in general, you'd root the side with the variable? hypothetically if have something you can't factor

[#1procrastinator]

How do you derive the combination formula? I'm having a hard time trying to understand intuitively why it works

[nisha]

Having a hugely hard time in doing Absolute values, and drawing them. I understand the basics, and all the transformations, but when it comes to multiple dilations/reflections and translations with a mod sign. I get stumped.

[#1procrastinator]

^ haha, I hate absolute values also

[TrueTears]

Oh yes, forgot difference of two squares...so in general, you'd root the side with the variable? hypothetically if have something you can't factor

i wouldn't remember it like that, there's no set way of solving inequalities, sometimes you just play around, sometimes you need a bit of wishful thinking, but in this case, factorisation was needed.

How do you derive the combination formula? I'm having a hard time trying to understand intuitively why it works

see attachments, taken from Art and Craft of problem solving, combinatorics chapter.

[TrueTears]

Having a hugely hard time in doing Absolute values, and drawing them. I understand the basics, and all the transformations, but when it comes to multiple dilations/reflections and translations with a mod sign. I get stumped.

a general tip is always expand out the modulus as a hybrid and go from there, ie, just apply the transformations onto the hybrid equations as you would on any other function, unless you are given it in the form of y = |f(x)| or y = f(|x|) in which case you can sketch straight away.

[breadkay]

Hey,

I am stuck on this question...

Write in the form of

Any help would be greatly appreciated

[TrueTears]

there's a few ways, you can either long divide it, or just do this:

2(x+1/2)/[5(x+3/5)] = (2/5)[x+1/2]/[x+3/5] = (2/5)[x+3/5-3/5+1/2]/[x+3/5] = (2/5)[1+((-3/5)+(1/2))/(x+3/5)] = (2/5)+ [(2/5)*((-3/5)+(1/2))]/(x+3/5)

in other words a = (2/5)*((-3/5)+(1/2)), b = 3/5 and c = 2/5

[breadkay]

there's a few ways, you can either long divide it, or just do this:

2(x+1/2)/[5(x+3/5)] = (2/5)[x+1/2]/[x+3/5] = (2/5)[x+3/5-3/5+1/2]/[x+3/5] = (2/5)[1+((-3/5)+(1/2))/(x+3/5)] = (2/5)+ [(2/5)*((-3/5)+(1/2))]/(x+3/5)

in other words a = (2/5)*((-3/5)+(1/2)), b = 3/5 and c = 2/5

Ah, you are a legend! I was doing this originally and thought it couldn't be right, haha

[brightsky]

long divide as you would do for any polynomial (but this time you'll have fractions in your quotient). should get 2/5 - (1/5)/(5x+3) = -(1/25)/(x+3/5) + 2/5, where a = -(1/25), b = 3/5, c = 2/5

[monkeywantsabanana]

Does anyone know how to draw a vertical line on the TI-nspire?

[Phy124]

Does anyone know how to draw a vertical line on the TI-nspire?

Note sure if this will work, but found this by googing.

I've been creating vertical lines on Graph and Geometry pages by using
parametric functions.  For example, setting x1(t) = 3 and y1(t) = t
will graph the vertical line x = 3.  In my work, I set x1(t) = p
where p is a parameter controlled by a slider.  In that way, the user
can move the vertical line left or right as necessary.

[b^3]

Does anyone know how to draw a vertical line on the TI-nspire?

Note sure if this will work, but found this by googing.

I've been creating vertical lines on Graph and Geometry pages by using
parametric functions.  For example, setting x1(t) = 3 and y1(t) = t
will graph the vertical line x = 3.  In my work, I set x1(t) = p
where p is a parameter controlled by a slider.  In that way, the user
can move the vertical line left or right as necessary.

That will work, although if you know the equation of the asymptote that last part with the p isn't necessary. You may end up with a vertical line that doesn't cover the whole screen, if so change the to say or something that will cover the y-values (will depend on the scale you are using).
This next part isn't necessary and I wouldn't waste time on it in exams or sacs, but if you want to make it dotted then [Menu] [1:Actions] [4:Attributes] then hover over the line, click and select the second drop down box and change the style of the line to whichever dotted line you want.
Also on that note, if you want a break at sometime and just want to play around with the calc, you can make a rollercoaster , drawing a sin(x) wave, then drawing a small box with two points on that line. Then using the attributes menu and animation speed dropdown, you can see it so that the box will move and follow the curve, like a cart riding a rollercoaster (ok this last bit is just wasting time, I got bored in one of my further classes one day and was playing around and figured it out ).