3U Maths Question Thread

[RuiAce]

Oh, didn't learn that rule.
Similarity for ∫sin(x)=-1/a cos(ax) right?

sin(ax) that is.

These are on the reference sheet. You should refer back to them.

[anotherworld2b]

i see now thank you

I was wondering for arithmetic and geometric progression what is the difference betweem recursive, general form? I am not sure why i struggle with Arithmetic and Geometric Progression. Would anyone know reources that could help me?

Looks like you approached it correctly. We know that a food drop can feed 24 hikers for 6 days. We want the days to INCREASE from 6 to 10. This works by multiplying the days by 10/6. We expect the hikers to DECREASE, by the same ratio, as this is what the question stipulates. So, I'm going to DIVIDE 24 by 10/6. This gives me 14.4 hikers. Now, 15 hikers would be too much, so the answer is (I think) anywhere between 6 and 14 hikers

[RuiAce]

i see now thank you

I was wondering for arithmetic and geometric progression what is the difference betweem recursive, general form? I am not sure why i struggle with Arithmetic and Geometric Progression. Would anyone know reources that could help me?

Never heard of these before. Might wanna check your textbook.

One way of tackling it is to explicitly find T₂ and T₃, then check that \( \frac{T_3}{T_2}=\frac{T_2}{T_1}\). Although to me just by inspection that's going to form a GP... because it rearranges into \(T_{n+1}=\frac12T_n\) which is beyond obviously a GP


(@2U and 3U students: Glossary term wise this is not in the course. Everything else is doable)

[legorgo18]

Hey guys need some help with part b,c of this simple harmonic motion q

A particle moves according to x=3-2cos^2 (2t), in units of cm and seconds

a) Express equation in form x = 20 - Acos omega t
I did- cos^2 (2t) = 1/2 (1+ cos4t) x= 3- (1+cos4t) = 2- cos 4t

b) Find the centre of motion, the amplitude, the range of motion and the period.
Im not quite sure how to mathematically show the range of the motion, but for the rest I did- C=2, A=1, T = 2pi/omega = 2pi/4 = pi/2

and c) what is the maximum speed of the particle and when does it first occur?
I tried subbing in t= pi/2 in to the equation but the answer says  4(cm/s) and pi/8 I graphed it and it doesnt even go to 4 so wtf

[RuiAce]

Hey guys need some help with part b,c of this simple harmonic motion q

A particle moves according to x=3-2cos^2 (2t), in units of cm and seconds

a) Express equation in form x = 20 - Acos omega t
I did- cos^2 (2t) = 1/2 (1+ cos4t) x= 3- (1+cos4t) = 2- cos 4t

b) Find the centre of motion, the amplitude, the range of motion and the period.
Im not quite sure how to mathematically show the range of the motion, but for the rest I did- C=2, A=1, T = 2pi/omega = 2pi/4 = pi/2

and c) what is the maximum speed of the particle and when does it first occur?
I tried subbing in t= pi/2 in to the equation but the answer says  4(cm/s) and pi/8 I graphed it and it doesnt even go to 4 so wtf

[legorgo18]

omg thanks didnt see that the equation was in x not v

[Rathin]

Whats the difference between:
1. Region under the curve y=sinx and y=cosx and the x-axis
and just
2. Region under the curve y=sinx and y=cosx

[RuiAce]

Whats the difference between:
1. Region under the curve y=sinx and y=cosx and the x-axis
and just
2. Region under the curve y=sinx and y=cosx

Those are too arbitrary. There's like an infinite number of those because of how the sine and cosine curves repeat.

Please provide the full question.

[Rathin]

Those are too arbitrary. There's like an infinite number of those because of how the sine and cosine curves repeat.

Please provide the full question.

between 0 and pi/4 sorry

[RuiAce]

[Rathin]

The original question wanted to find the area between y=sinx, y=cosx and x axis from x=0 to x=pi/4

but I was curious what does it mean when it is only between y=sinx, y=cosx..graphically

[RuiAce]

The original question wanted to find the area between y=sinx, y=cosx and x axis from x=0 to x=pi/4

but I was curious what does it mean when it is only between y=sinx, y=cosx..graphically

Tbh, the original question doesn't even make sense.

After graphing them, clearly NO area is bound between all three curves (the two trig curves and the x-axis) simultaneously. There must be a typo somewhere.


If it were just the region between y=sin(x) and y=cos(x) that's pretty clear. Look closely at the diagram. There is only one "curved-triangle-like" region bounded by y=sin(x), y=cos(x), and x=0. (x=pi/4 just gives it an endpoint so you don't keep going). So if it said just between y=sin(x) and y=cos(x), from 0 to pi/4, it's just that curved-triangle.

[Rathin]

I READ THE QUESTION WRONG.
Its between y=sinx, y=cosx and Y-AXIS

sorry about this mistake


Mod edit: Hi everyone, just letting you know that I (Rui) have resolved this with Rathin through external means.

[michaelalt]

Binomial Theorem Question:
The coefficients of x^4 and x^5 in the expansion of (3-x)^n are equal in magnitude but opposite in sign. Find the value of n.
Thanks!

[RuiAce]

Binomial Theorem Question:
The coefficients of x^4 and x^5 in the expansion of (3-x)^n are equal in magnitude but opposite in sign. Find the value of n.
Thanks!