4U Maths Question Thread

[chelseam]

What textbook is this? That substitution is a horrible idea; u = sin(x) would be a much better substitution.

Yeah that's what I thought as well! It's from the old version of Fitzpatrick but it's in the same exercise in the new one as well. Thanks Rui

[hanaacdr]

could i get some help on this question too please

[hanaacdr]

could i get some help plz
thanks

[jakesilove]

could i get some help on this question too please

Hey! Check out my brief solution below

[jakesilove]

could i get some help plz
thanks

And here's the answer to your second question

[hinakamishiro]

Hey guys can someone help me with part 3? Thanks!

[RuiAce]

Hey guys can someone help me with part 3? Thanks!

Previous post deleted upon seeing part a)



Again, use graphing software such as Desmos to aid this process. And rememeber the dilation factor in the change of base law, or just directly smack in log₂ if you wish.

[beau77bro]

\begin{align*}&\quad \left[(1-x\cos x)-i(x\sin x)\right][(1-x\cos x)+i(x\sin x)]\\ &= (1-x\cos x)^2+(x\sin x)^2\\ &= 1-2x\cos x + x^2(\cos^2x+\sin^2x)\\ &= 1-2x\cos x + x^2\end{align*}

Cis notation is ew.


I might've made an algebra mistake because I don't quite agree with what they got for b.

woweee. that is some simple but overly complicated algebra. i apologise for the late response but thankyou very much rui. I hope i never get anything like this in a test hahahah. you r a god thankyou

[beau77bro]

4b I feel like I'm Doing something wrong I'm getting 128, the answer is 16?

My working:

[chelseam]

Hi! Do we need to know the condition of the focal chord for conics? Or is that only needed in 3u parametrics? Thank you

[RuiAce]

(Image removed from quote.)

4b I feel like I'm Doing something wrong I'm getting 128, the answer is 16?

My working:
(Image removed from quote.)

Can't quite follow all of your working. I understand the use of 4a = length of latus rectum, but I don't understand how you found the area of the parabolic cross section to use as the volume of your slice.

Hi! Do we need to know the condition of the focal chord for conics? Or is that only needed in 3u parametrics? Thank you

Parabola: The tangents at the end of a focal chord intersect at right angles on the directrix

Ellipse/Hyperbola: The tangents at the end of a focal chord intersect on the directrix.

So simply put, if the chord is a chord of contact from the directrix, it is focal.

[beau77bro]

Can't quite follow all of your working. I understand the use of 4a = length of latus rectum, but I don't understand how you found the area of the parabolic cross section to use as the volume of your slice.

Oh so it's like a rectangle area of ax4a - like length of the directrix x hieght which is a, as it passes through the focus, then you minus the area under the curve so you just have the area of the cross section. then im not sure what to do in terms of working out the volume of the solid correctly, im not even sure the slice is correct. Sorry for unclear working and question, probably ignore my working as it is piss poor, but the help is very much appreciated.

[RuiAce]

Unless I went blind, I just realised you wrote \(4a=\sqrt{36-9y^2}\) and then \(a=\sqrt{36-9y^2}\) without any division by 4?

[chelseam]

So simply put, if the chord is a chord of contact from the directrix, it is focal.

Thanks Rui

[seventeenboi]

HI,
just a conics question:
I can do everything else except q2b(gamma).. helppp!!!
Thanks so much )