3U Maths Question Thread

[bluecookie]

Could you please provide working out for the first parts? If you've already worked through them, I don't really want to repeat, but I'll need the solutions to attack the final part.

[bluecookie]

Could you please provide working out for the first parts? If you've already worked through them, I don't really want to repeat, but I'll need the solutions to attack the final part.

[bluecookie]

Could you please provide working out for the first parts? If you've already worked through them, I don't really want to repeat, but I'll need the solutions to attack the final part.

Sorry for the multiple posts. I had to post them separately because it exceeded the maximum size.

[jakesilove]

Sorry for the multiple posts. I had to post them separately because it exceeded the maximum size.

First, let's find the gradient of PQ. That's going to be



By difference of two squares and cancelling common terms. What does this tell us? p+q is a constant value. Not sure how this helps us yet; let's find out.

We want the locus of N, which has co-ordinates



Hmm, actually, looks like you basically solved it! We want to show that it is a normal to the parabola. So, let's find the derivative.



by rearranging the original equation. At the point x=2km



Therefore, the negative reciprocal (normal) will be -a/km, which is the gradient you found in your working! Does that make sense? A bit of a weird, all over the place question. I'm in a rush so I hope this answer makes sense; if someone else wants to elaborate, feel free to!

[bluecookie]

It does, thanks :3

[bluecookie]

What's the proof for:

Any three non-collinear points lie on a unique circle, whose centre is the point of concurrency of the perpendicular bisectors of the intervals joining the points.


What's the proof for angle at centre is twice angle at circumference for this particular case: https://theoremoftheweek.files.wordpress.com/2010/07/angle_at_centre_is_twice_angle_at_circumference_2.png

Mod edit: Posts merged. At times like this, please resort to the modify function at the top right corner of a post.

[RuiAce]

What's the proof for:

Any three non-collinear points lie on a unique circle, whose centre is the point of concurrency of the perpendicular bisectors of the intervals joining the points.

Normally, you take that for granted, however if you want I can give you a non-rigorous explanation.

It's the same thing as with a parabola. There exists one and only one parabola through any set of three points.
For the circle, the explanation is as follows.







_____________________


_____________________

What's the proof for angle at centre is twice angle at circumference for this particular case: https://theoremoftheweek.files.wordpress.com/2010/07/angle_at_centre_is_twice_angle_at_circumference_2.png

Mod edit: Posts merged. At times like this, please resort to the modify function at the top right corner of a post.

Hint: Just use the theorem "angles standing on the same arc are equal" with the standard case. (Aka angles in the same segment are equal)

[bluecookie]

Normally, you take that for granted, however if you want I can give you a non-rigorous explanation.

It's the same thing as with a parabola. There exists one and only one parabola through any set of three points.
For the circle, the explanation is as follows.







_____________________


_____________________

Hint: Just use the theorem "angles standing on the same arc are equal" with the standard case. (Aka angles in the same segment are equal)

Thanks! Aha why didn't I think of that!

[anotherworld2b]

Hi i was wondering if could get help with the first 2 questions. I am not sure how to approach the question. 

[RuiAce]

Hi i was wondering if could get help with the first 2 questions. I am not sure how to approach the question. 

First one: Let u=2^x and you get a quadratic.
Second one: Let u=3^x instead. And rewrite 3^2 as 9

[Rathin]

When finding an area by integration do we need to write the value as for example 55 or 55 unit^2?

[jamonwindeyer]

When finding an area by integration do we need to write the value as for example 55 or 55 unit^2?

If specifically finding an area, definitely with the \(\text{u}^2\)! definite integrals, by default, you just write the number. As soon as you associate that integral with an area, you slap the units on the end

[RuiAce]

When finding an area by integration do we need to write the value as for example 55 or 55 unit^2?

Eeeeeexcept I was beaten by Jamon for using LaTex

[jamonwindeyer]

Eeeeeexcept I was beaten by Jamon for using LaTex

Ahhh, beating Rui to a Math question. Great to be back

[anotherworld2b]

Thank you for your help

First one: Let u=2^x and you get a quadratic.
Second one: Let u=3^x instead. And rewrite 3^2 as 9