brightsky's Maths Thread

[xZero]

and





since |RA|=|RB|, |b|=|a|, since |AQ|=|QC|, |c|=|a|=|b|

[b^3]

You need to use information form b part of the question.
You know that OR and AB are perpendicular,
so OR.AB=0
(a+b).(b-a)=0
(a.a-b.b)=0
(|a|²-|b|²)=0
|a|²-|b|²=0
i.e. |a|²=|b|²

Now you also know that OQ and AC are perpendicular, so
OQ.AC=0

(a+c).(c-a)=0
(c.c-a.a)=0
(|c|²-|a|²)=0
|c|²-|a|²=0
i.e. |c|²=|a|²

Now |a|²=|b|² and also |c|²=|a|²
So |a|²=|b|²=|c|²
|a|=|b|=|c| as required.

EDIT: beaten.

[brightsky]

when trying to prove that a shape is a rectangle, is it sufficient just to prove that its diagonals are equal in magnitude?

[dc302]

Technically yes, but I'm not sure what kind of 'expectations' VCAA has for those types of questions.

[brightsky]

just a question on notation, is it wrong to write (-2,1) U (3,6)? i remember dr he saying something about how it's wrong to mix up set and interval notation...

[pi]

Nah, that's okay.

You could also write it as {x E R | -2<x<1 or 3<x<6}


edit: removed some incorrect info

[dc302]

Yeah, considering that an interval is just a set of real numbers, they shouldn't be too harsh, if at all, on you if you mix them up.

[brightsky]

what symbols/letters do people usually use in the exam to represent resultant force, normal force and friction? and is it necessary to introduce these symbols formally in your working out?

[Planck's constant]

what symbols/letters do people usually use in the exam to represent resultant force, normal force and friction? and is it necessary to introduce these symbols formally in your working out?

For both spesh and physics I got into the habit of using

Fnet ('net' subscript), N and Fr ('r' subscript) respectively

As for formal introductions, even though I am a great believer in starting a solution with the necessary 'Lets', in this instance a neat and well annotated diagram will do the job.

ie

Draw a little 'compass' clearly showing the positive x and y directions
Draw your real forces with solid arrows and force resolutes with dashed arrows and make sure that there is consistency between your symbol for the resolute and your 'compass' eg Wx points in the x-direction, Wy points in the y-direction

[brightsky]

ahh okay i shall use that then. i've heard of people using 'sigma' F for resultant force, and F for friction, which i find kind of dodgy in the sense that 'sigma' F means the sum of all F (frictions). however, there's no doubting that it is more convenient to write than F_net.

anyone know what vcaa uses in exams? //anal

[dc302]

I've seen VCAA use plain F for friction, not sure about resultant force. I wouldn't use sigma F though if F is friction, for the reason you stated.

[brightsky]

Why is the standard deviation more useful than the variance? I have here 'because every piece of data counts' but I forgot why that's the case.

Any help appreciated.

[stonecold]

Why is the standard deviation more useful than the variance? I have here 'because every piece of data counts' but I forgot why that's the case.

Any help appreciated.

I don't know if what you are asking for...but standard deviation is in the same units is the variable you are discussing.

For example, say the mean height is 170cm with s.d. 10cm, straight away you know that around 95% of people are between 150 and 190cm.

It is harder to draw conclusions using the variance because it is in units squared when the mean is just in units.

Sorry if it isn't what you were after.

[brightsky]

solve x^(p/q) = a for x. how many cases do i need to consider?

[kamil9876]

I assume p and q are integers? I think it depends on what planet you are living on, different people define differently. Are you defining it over the non-negative reals only? or can take any non-negative complex value? etc. etc.