wildareal's questions thread

[wildareal]

Here's another Vectors one. Thanks.

[evaever]

a) OG=OB+BC+CG=OB+BC+BA=b+(c-b)+(a-b)=a-b+c

b) CD=BG=BC+CG=BC+BA=(c-b)+(a-b)=a-2b+c

OR from a), OG=OB+BG=a-b+c, so CD=BG=a-2b+c

[wildareal]

I know Circle Geometry is not an integral part of Spec, but how would you do this? Thanks.

[wildareal]

How do you go about simplifying ellipses in the form 25x^2+16y^2=400. Thanks.

[kamil9876]

Firstly look at the small triangle (the one where "a" is inside it). It has angles and and some unknown . We see that:



hence

Now look at that triangle that contains that "c". It has angles , ,

Hence we have:



Should be simple from here on.

[kamil9876]

The only way that it is not a question is that it is missing a question mark?

By "simplify" I assume you mean get into the standard form.

Divide both sides by :

[cohen]

Wouldnt it be (x^2/25) + (y^2/16) = 1, instead of your answer kamil? :S

[taiga]

merged on request

OT.

I assume Kamil's form is one step away from what you are looking for, so if the rest of the working is correct, then



should be the answer you are looking for

That is the general form (look in the book for the defining characteristics) you are probably looking for when you ask for "simplify"

[kamil9876]

oh yeah wtf how did I not simplify 20/4 to 5 and 20/5 to 4  

Still I prefer rather than as it readily shows that it is a unit circle dilated by a factor of horizontally and vertically (hence giving the axis intercepts).

[taiga]

oh yeah wtf how did I not simplify 20/4 to 5 and 20/5 to 4 

Still I prefer rather than as it readily shows that it is a unit circle dilated by a factor of horizontally and vertically (hence giving the axis intercepts).

Yeah I think that's the convention if I remember correctly, my bad

Though it is very rare, if you are required to write out the equation of an ellipse it is probably best to convert stuff like 5^2 to 25, just in case markers are petty.

[pi]

I know Circle Geometry is not an integral part of Spec, but how would you do this? Thanks.

Its not circle geo, but the answer is attached (I needed to annotate the diagram, that's why I used MS word)

[luken93]

Firstly look at the small triangle (the one where "a" is inside it). It has angles and and some unknown . We see that:



hence

Now look at that triangle that contains that "c". It has angles , ,

Hence we have:



Should be simple from here on.

Is this how we should attempt any of these questions, work out what you know and work from there as opposed to learning some of the rules stated in the essentials book?

[kamil9876]

Out of curiosity, what rules would you use here?

I think that's how mathematics should be learnt in general and not just mathematics, many areas of life require you to "work out what you know, and work from there" as it is too complicated to learn a specific recipe for everything you may come across.

[luken93]

Out of curiosity, what rules would you use here?

I think that's how mathematics should be learnt in general and not just mathematics, many areas of life require you to "work out what you know, and work from there" as it is too complicated to learn a specific recipe for everything you may come across.

dw, essentials just had some rules for certain angles that occur if shapes are put inside/outside circles...

The "work out what you know" was probably a bit generic for what I actually meant, I meant it more specifically to the case of these sort of questions.

[Mint]

First we use difference of perfect squares to factorise
Sin^4(x) - cos^4(x)
= [sin^2(x) - cos^2(x)][sin^2(x) + cos^2(x)]

Then use the identity : cos^2(x) + sin^2(x) = 1
so [sin^2(x) - cos^2(x)][1]
= sin^2(x) - cos^2(x)

Hope that's right :p