help-17

[gritty sage]

No.

You get the black parts.

You add them together to get the x and y parts of AC.

Then you use the Pythagorean theorem.

[calm swan]

So u find the diganoal, add all the sides

[gritty sage]

The diagonal is what you get at the end.

The purple part.

[calm swan]

So we find all the sides and add them up?

[gritty sage]

You add the x parts together. Separately, you add the y parts together.

[calm swan]

X Parts are the ones on the ground ?

[gritty sage]

Yes.

[gritty sage]

Right. We call that horizontal.

[calm swan]

Why do u add them seperately?

[gritty sage]

It goes left to right, not up to down.

Because the Pythagorean theorem needs the x and y parts separately.

[calm swan]

PHH so After u have added them togeyher u do x^2+y^2

To get the answer

[gritty sage]

Right, then the square root.

[calm swan]

So u find all the sides, and separate your calculations into x and y and use the phyagoren theorem?

[gritty sage]

Yes, that's right.

[calm swan]

Thank you!

[gritty sage]

You're welcome.

[calm swan]

I really appreciate it

[gritty sage]

No problem.

[calm swan]

Wait one more

How do I do question 1

[gritty sage]

Well, let's look at the diagram on 2b.

They draw the angle 145 starting from north and then going towards east.

[calm swan]

Wait not 2b the question 1

[gritty sage]

No, I mean to understand question 1 a bit better, we need to look at 2b.

Do you see how they draw the 140 degree heading starting from north, then towards east?

[calm swan]

Yes

[gritty sage]

You got the angles right, but the diagram should have them drawn like that.

[calm swan]

That’s not even my diagram, it’s my friends

Wait nvm

THAYS hee teachers

[gritty sage]

Oh, OK.

Well, it's not wrong exactly. The information on it is correct.

Let's look at 1b.

[calm swan]

Is it just like question 2, But u have to make the diagram yourself?

[gritty sage]

Yeah, for 1a.

For 1b, we've done something like it already.

It wants to know how far west the boat has travelled.

[calm swan]

Thank you so much for your help

[gritty sage]

No problem.

[calm swan]

Unfortunately I have arrived to school and got to go

See you tysm!

[gritty sage]

OK.

You're welcome.

[calm swan]

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[vocal timber]

If I am adding area of two triangle + rectangle it doesn't give me same answer as when I apply formula of trapezium

[paper harbor]

you should

can we see your working ou

out

[fathom perch]

Its giving the same

Tell us what the formula for the trapezium area is first

Thats probably where ur making a mistake

Since you've not ticked the correct area

[river phoenix]

It is giving the same 36m I guess

[vocal timber]

Now it's giving same

Lol

[river phoenix]

What's the answer by the way

[vocal timber]

there was arithmetic mistake

36.0m

[river phoenix]

Why b is marked

[vocal timber]

this was initially attempted

[river phoenix]

Ohk got it

[vocal timber]

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[wet mango]

this is a really stupid question but what does 2nd mean here

[burnt nova]

?

can you put the full image?

or copy the full question please?

[burnt nova]

put the calc

in deg

[wet mango]

thx ina a little slow

[burnt nova]

@wet mango

the 2nd means that they´re asking you to use arccos(x)

or cos-1(x)

[wet mango]

tysm

[burnt nova]

it doesn´t matter if the calc is in rad or deg

sorry i mixed up heh

[wet mango]

all good I was trying to figure it out for a hour…

[burnt nova]

remember that if they´re asking for the deg you will have to calc the equivalent

that´s all!

[wet mango]

okay tysm have a good night/day

[burnt nova]

.close

write that pls

[wet mango]

.close

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[snow perch]

Don't know how to do question 40 (b) and (c). I also want to know why 6C2 is the answer for (a).

[vocal sleet]

@snow perch Has your question been resolved?

[ripe cedar]

Lets start with a
They use 6C2 because its focusing on the 6 different classes and picking only 2 of those classes
The actual individual people in the committee

So with that being said, part b can be found the same way

To be honest i've forgotten how to solve at most probabilities
I vaguely remember that subtraction could be involved but i'm not 100% on that

[snow perch]

hmm

ill ask my teacher in person 😔

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[desert island]

if i exchange two rows of an identity matrix

[desert island]

can someone explain me why its inverse is itself

intuitively

a matrix like this

[regal bane]

I'll call that matrix P.
The effect of multiplying PA is to swap A's rows. Row 1 and row 2 are swapped

Swapping these rows twice is the same as never having swapped them

[desert island]

yea

[regal bane]

In other words, the effect of P^2 is to do nothing to A. P^2 is an identity matrix.

[desert island]

oh yeah

thats nice

thanks

i see cognitive decline in me

.close

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[regal bane]

Linear alg is abstract and it catches a lot of people off guard. You're fine haha

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[grand verge]

Can someone explain how to find the max and min?

[bitter pilot]

Do you know how sin(t) is usually bounded?

[marsh yacht]

eh

u know how sinus is defined ?

[grand verge]

yeah

between -1 and 1

oh

ok

bruh

thanks

[bitter pilot]

Yep. Now think of the transformations, and how it affected the range.

[grand verge]

like it just shifts 3 up

[bitter pilot]

The scale factor 2 and addition of 3.

[grand verge]

so like 3+2

or 3-2

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[grand verge]

thanks

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[viscid thicket]

Is it correct to say that $\lim_{h \to 0}h^{2\alpha-1}\cos(\frac{1}{h})$ doesn't exist ?

[feral stream]

what is alpha?

natural number?

[viscid thicket]

Real number

Oh wait

[feral stream]

Have you tried writing the taylor expansion?

[twin meteor]

prograce

[viscid thicket]

Look again

[feral stream]

^^?

[fathom perch]

This is 0* (bounded limit)

Which is just 0

[viscid thicket]

No

[viscid thicket]

It depends on alpha I think

[feral stream]

That's the first thing I would try, that should give you a limit to calculate

[viscid thicket]

I think that would complicate it, Executor said cos1/h is oscillating that's what I'm going off of

[fathom perch]

Oh alpha is not N

If it's R then it's complicating things, because h^(2alpha-1) can become infinite

[viscid thicket]

Yes

[fathom perch]

If it was just N then it would become 0

Just try what Vincent said then ig

[viscid thicket]

Damn

[feral stream]

Ye you either get that everything is a mulitple of h plus some constant or you get something like 1/h

[hybrid flicker]

alpha > 1/2 vs alpha <= 1/2

Split cases

[hybrid flicker]

0 × bounded -> 0, oscillating is misleading

[fathom perch]

Bounded oscillating*, sorry

[viscid thicket]

0<alpha<1/2 right

[fathom perch]

You just said alpha is R

[viscid thicket]

Otherwise expression goes to infinity right

[fathom perch]

Why would it stop at 0

Ah so you took 3 cases

[viscid thicket]

Because if it's less than 0 it goes to infinity

[hybrid flicker]

The limit also wouldn't exist

[viscid thicket]

Yes

[hybrid flicker]

You can't say the limit is infinity either

[viscid thicket]

I mean the expression h^2alpha-1

[hybrid flicker]

Well this term goes to infinity in abs value

But the product doesn't

[viscid thicket]

Yea

Idk what happens when u multiply it with cos1/h u said it doesnt exist

How do u explain it doesnt exist

[fathom perch]

cos(1/h) varies between 1 and -1

[viscid thicket]

Oh

Yeah nvm I know

Ty guys

.solved

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[ruby heart]

Im trying to find all isometries f, that satisfy f(0,0,0) = (0,0,0) and f((0,1,0) + span(1,1,1)) is a proper subset of (0,1,0) + span(1,1,1)

[ruby heart]

so far I got that f is linear

and f(0,1,0) = (-2/3, 1/3, -2/3), f(1,0,1) = (-1/3, -4/3, -1/3)

so it remains to find f on a vector like (1,0,0)

I get 3 equations, but one of them has quadratic terms

I mean I can solve it, because it can be reduced to 1 variable quadratic

but I feel this is very inapropriate for lin alg

nvm maybe this is fine?

[vocal sleet]

@ruby heart Has your question been resolved?

[ruby heart]

ok nvm all this above, say f is an affine isometry satisfying

how do I find f?

I got that f(0,1,0) = (0,0,1) or f(0,1,0) = (0,0,-1)

in the first case f'(0,1,-1) = (0,-1,1)

[vocal sleet]

@ruby heart Has your question been resolved?

[ruby heart]

many degrees of freedom here it seems

af means affine

[ruby heart]

nvm I got it!

.close

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[open sage]

Given the system Y' = AY, with A

1. Find the equilibrium points and classify them
2. Draw the phase portrait

where do i go from here

apparently i didnt need to find the general solution?

[vocal sleet]

@open sage Has your question been resolved?

[vocal sleet]

@open sage Has your question been resolved?

[knotty lynx]

Yeah, you didn't. For a homogenous linear system Y' = AY, the only critical point lies at Y = 0 if A has full rank

In this case A clearly has full rank. You can use the eigenvalues to determine the nature of critical point.

For purely imaginary eigenvalues, you get a center - i.e. rings of concentric trajectories.

As for sketching the phase portrait, it's best to just know what they look like. In this case tho, the matrix is pretty telling

y1' = -4y2
y2' = 4y1

Take a point at (y1, y2) in the phase plane, its "velocity" will be (-4y2, 4y1) which is perpendicular to vector from (0,0) to (y1,y2). So, clearly the trajectory containing this point must be circular.

Centers aren't always circular as purely inaginary eigenvalues can occur even if Y' and Y aren't perpendicular

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[open sage]

.reopen

[vocal sleet]

✅

[open sage]

alright, thanks

there’s a lot i need to learn about sketching solutions for these ode matrices

but apparently these are the easiest ones

since they’re just circles spaces out by a “phase” of x

in this case pi/2, no?

[vocal sleet]

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[open sage]

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[silent scaffold]

Hi! Could someone help me with a math problem?

It's about a word problem where I have to use the rectangle method or the diamond (rhombus) method.

Here’s the question:
[you can paste the exercise here or send an image]

I would really appreciate any explanation or step-by-step guidance. Thanks in advance!

[vocal sleet]

@silent scaffold Has your question been resolved?

[outer warren]

Would you be able to post translations?

[vocal sleet]

@silent scaffold Has your question been resolved?

[silent scaffold]

ok, 1:A person wants to share a certain number of candies among his nephews. If he gave each of them 10 candies, he would have 6 left over; and if he gave each of them 11 candies, he would have 6 missing. How many candies does he want to share? 2:In a zoo there are lions and sparrows if there are 20 heads and 62 legs in total, how many lions are there? 3: In a math test, a student answers 50 questions and scores 110 points. If he or she earns 4 points for each correct answer and loses one point for each incorrect answer, how many questions were incorrect? 4: To buy 12 pencils, I'm short 19 soles, but if I buy 8 pencils, I'd have 9 soles left. How much does a pencil cost, and how much money do I have? 5: To win S/. 100 in a raffle with a radio as the prize, 550 tickets were printed. If only 200 tickets were sold, resulting in a loss of S/. 250,
what was the price of the radio?

[acoustic tulip]

which one do you want help in?

[vocal sleet]

@silent scaffold Has your question been resolved?

[vocal sleet]

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[celest silo]

4 mknths before the exam and I'm still having to re-learn stuff I'm so cooked, I need help with number 9 here

[meager shoal]

what have u noticed

abt the sequence

any pattern u recognize?

[celest silo]

Nope

I truly cannot see the pattern

It feels simple but my brain just can't catch on

[meager shoal]

ok

[paper depot]

what if the minus signs were gone

what if it was just 1, 4, 9, 16, ...

that look more familiar?

[celest silo]

Oh

Wait hold on

Ok yeah I can figure them out with them being all positives

[meager shoal]

what is the inductive formula

if they are all positive

[celest silo]

Idk man I can't put the formula down, I just have a vague understanding

[paper depot]

tf is an "inductive formula"

[meager shoal]

i might have mixed up the terminology

[celest silo]

I think it's something like x+ (difference+1)

[meager shoal]

but it should be something a_n = f(n)

[celest silo]

What is the underscore for

[meager shoal]

[ a_n = f(n)]

[twin meteor]

k

[celest silo]

And I don't know the f

[meager shoal]

can u find

a function that takes in the index

[celest silo]

Ok I'm just gonna take a blind shot at figuring it out with the negatives just ince

[meager shoal]

and outputs each term

[paper depot]

explicit formula?

[meager shoal]

oh ye

[celest silo]

Man I haven't done sequences in so long I forgot these terms man

Or math in general

Oh wait it's starting to come back

Still don't know what Index is though

[meager shoal]

the first term is a_1, second term is a_2, third term is a_3, etc.

[celest silo]

That's called index?

We always just said n, damn I don't know a lotta terminologies

But when we put down the negatives I can't find the n

[meager shoal]

lets ignore the negative

assume that the sequence is all 1,4,9,...

first

cuz its simpler

and lets work from there

[celest silo]

Yeah we did that

[meager shoal]

so whats a_n if all terms are positive

[celest silo]

It's (previous difference+2)

I think

Okay yknow what

I'll come back to this later I gotta move along

How do I close this chat

[meager shoal]

[ a_n = n^2]

[celest silo]

.close

[twin meteor]

k

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[celest silo]

Thanks for helping though

[vocal sleet]

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[meager shoal]

it was supposed to be this. i found it

[meager shoal]

.close

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[paper depot]

easier to just say explicit, no?

[meager shoal]

fair

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[tulip anvil]

Guys I need help plz

anyone able to help me?

plz?

[tulip anvil]

how 2 know which parts are the five point sum?

plz anyone 🙁

i rly need help

i gtg son 2

[knotty briar]

For the first one

[tulip anvil]

ye?

[knotty briar]

We need to find min, max, median q1 and q3

[tulip anvil]

and how 2 do that?

[knotty briar]

Try to find min and max first

They are the easiest

[tulip anvil]

16

25

median is

19

[knotty briar]

Correct

[tulip anvil]

now what

[knotty briar]

For the first quartile, we need to find the middle of this :
16, 16, 18, 18, 18, 19

[tulip anvil]

wait

[knotty briar]

Wait

I just realized the median is not 19

[tulip anvil]

howd o uknow that that is the first qaurtile?

how?

[knotty briar]

It should be the 8th number

[tulip anvil]

o yea

[knotty briar]

Mb for not noticing that earlier

Well, what is the median then?

[tulip anvil]

alg

21

[knotty briar]

Yes

The first quartile is the median of all data points less than the median

The third quartile is the median of all data points greater than the median

[tulip anvil]

q2?

[knotty briar]

Can you try to find q1 and q3 now?

[tulip anvil]

18

[knotty briar]

Q2 is the mean

[tulip anvil]

and

23

[knotty briar]

Yes

Nice work

Then can you do the next part?

[tulip anvil]

idk how 2 though

[knotty briar]

You don't know how to draw the plot?

[tulip anvil]

no

i meaen like i do

but i aint bothered rn

its 11 pm for me rn

i do know that each segment of the box plot is 25%

and

[knotty briar]

Ah ic

Well, if you do not have any more questions you should close this channel

[tulip anvil]

k

wait

ik this aint relevant

to the topic

but u have so much potential

dont waste it on being lgbtq

or trans

gl man

the real life aint that fair

cya

gl

and gud day

.close

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[knotty briar]

Bro what

[tulip anvil]

ur they/them

[knotty briar]

Yes but

[tulip anvil]

jst pick between m or f

[paper depot]

<@&268886789983436800> transphobia

[tulip anvil]

im not racis

I SWEAR IM NOT

I SWEAR

[knotty briar]

Sorry bro

[paper depot]

you're being TRANSPHOBIC.

[tulip anvil]

mb

[knotty briar]

You were a bit disrespectful

[paper depot]

that's a different thing than racism.

[tulip anvil]

wait

[paper depot]

not a bit, very

extremely

[tribal elk]

Handled, thanks

[knotty briar]

Oof

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[wanton kiln]

Given a pyramid S.ABCD with a trapezodial base ABCD, where AD || BC and AD = 2BC. Let M be a point on edge SC such that SM = 1/3 SD.
Find the intersection point E of SC and the plane (ABM) and determine SE/SC.

Let me define some stuff here
Let F be the intersection point of AB and DC. Hence, the intersection line of plane (SAB) and (SCD) is SF. Connecting F to M create a line that intersect with SC, which is E.

So far, I've tried Menelaus theorem to calculate SE/SC, but failed due to the unknown ratio FE/EM. I can't think of any ways to solve this problem, can anyone help me?

[wanton kiln]

I've tried to brute-force this problem, that SE/SC = 1/2, but I cannot reverse it 😢

[vocal sleet]

@wanton kiln Has your question been resolved?

[gleaming sluice]

I might have an idea

When you draw the face SDF, you can see that CD = CF. Then draw a line parallel to FM starting at C and intersecting SD, label the intersection T. The triangle CDT should be similar to FDM.

That should allow a relation in between DT and DM, then by applying Thales inside SCT, you should be able to find the ratio SE/SC = 1/2

[wanton kiln]

Woah! Let me try it and will let you know

YO

THANK YOU SO MUCH!

you are so talented, I've learnt a lot from you

again, thank you a lot!

[gleaming sluice]

np

[wanton kiln]

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[fathom venture]

bro

how

[faint pumice]

multiply it out

[grim lotus]

calculus

[fathom venture]

,rotate

[fathom venture]

this is what i have so far

[grim lotus]

then square both sides

[fathom venture]

no idea where to even start

[fathom venture]

you're like.. allowed to do that?

[faint pumice]

yeah

algebraic manipulation

also

[fathom venture]

so far when we were solving inequalities in class we could only work on one side of the inequality to make it look like the other side

[faint pumice]

x > x^1/2

[grim lotus]

depends

[faint pumice]

so 1/x < 1/(x^1/2)

[grim lotus]

if both sides are non-negative

[fathom venture]

well ye its for x >= 1

[grim lotus]

induction won't work cuz u need to prove for all real x not just natural

[fathom venture]

uh the question is induction

so

[grim lotus]

wdym

[fathom venture]

wym induction wont work

[grim lotus]

ok maybe it does work

but if it does then u only show it's true for x natural

[fathom venture]

its fine

[grim lotus]

so u haven't proved for x=1.5 for eg

[fathom venture]

this is the full question, its from a past paper

the entire q is on induction

doesnt matter just gotta use induction

[faint pumice]

honestly i'd just multiply it out to get the full denominator

[grim lotus]

bro

[fathom venture]

ya

[fathom venture]

ill try

[grim lotus]

notice how part a and c which use induction say n is an integer but part b says that x is real

[lone linden]

are you sure that part b says to use induction

I think you're supposed to prove b for all real x__>__1

and use that as a lemma for c

[fathom venture]

ye we dont do any other methods of proof in our syllabus

[lone linden]

I don't think they'd explicitly teach you how to do algebra

[fathom venture]

im like

[fathom venture]

confused on this mostly

[grim lotus]

that doesn't matter u can manipulate both sides

as long as ur logical

[fathom venture]

coz

1. is using the assumption a MUST
2. can you work both sides or do you stay focused on one side

[lone linden]

@grim lotus anyway mb for jumping in, I'll leave ygs alone

[grim lotus]

nah u good

[grim lotus]

u can go on actually

[fathom venture]

hmmmm ok

[grim lotus]

i'm here temporarily

[fathom venture]

Ok this just made me more confused

[lone linden]

Ngl you could always work backwards

Then either invoke reversibility

Or just write the proof in the reverse of your scratch

Fraction = square root of fraction

[fathom venture]

I dunno how to do that………..

[lone linden]

Square both sides and reduce to polynomial

But that’s just my two cents

[fathom venture]

Oo wait

[lone linden]

You don’t know how to write a series of steps backwards?

[fathom venture]

Holddd in

On

Trying something

I figured it out

Just turn assumption into polynomial

Do the same for step 3

Compare w assumption

Done

[fathom venture]

Thanks for helping me figure this out

.close

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[ornate hemlock]

Im genuinely losing my shit. Someone explain this to me please i.e. what I'm doing wrong and how to do the partial fractions

[flat whale]

this part is mostly right

you can simplify and just get rid of the +1 because you should know how to integrate that

[ornate hemlock]

Idk I'm on the a level chapter on integration doing substitution but I need partial fractions. It's an improper fraction so I'm confused as to how to do it - I forgot

[flat whale]

from there just find a common denominator and use cover up method

[ornate hemlock]

Err yeah I'm confused still

[flat whale]

which part

[flat whale]

here?

[ornate hemlock]

Is that correct there? And what do I do afterwards

[flat whale]

$\frac{-4}{(u+2)(u-2)} = \frac{A}{u+2} + \frac{B}{u-2}$

[twin meteor]

riemann

[flat whale]

^ that's what i mean by "get rid of the +1"

[ornate hemlock]

Where de 1 go lol

How

[flat whale]

you can just set it aside

$\frac{-4}{(u+2)(u-2)} + 1 = \frac{A}{u+2} + \frac{B}{u-2} + 1$

[twin meteor]

riemann

[flat whale]

partial fractions is only for the actual fraction

when there's no variable in the denominator, you don't need partial fractions

$\int 1 du = u + C$

[twin meteor]

riemann

[ornate hemlock]

I don't understand why or how I'm supposed to know why or how to like add the constant like the 1

How do I do this bro

[flat whale]

because $\int [f(u) + g(u)]du = \int f(u)du + \int g(u)]du$

[twin meteor]

riemann

[flat whale]

so when you integrate the sum, you can just integrate each term individually

[flat whale]

so instead of doing partial fractions on the whole left side, you can use the integral of sum = sum of integrals property to simplify

[ornate hemlock]

Yeah but why is there a + 1 after the partial frCtion

How do you know to do that

[flat whale]

just explained it here

[ornate hemlock]

That didn't explain this though

[flat whale]

then i don't know what you mean by "that"

[ornate hemlock]

I think you fail to comprehend the fact you are a postgrad and I am self studying the a level curriculum

I'm asking why this is only partly right, and where to go from here if the clarification helps

[flat whale]

you're just being vague so i have to guess what you're confused by

[ornate hemlock]

Ah sorry

Yeah that's what I'm confused by I suppose

The partial fractions

[flat whale]

still vague

[flat whale]

apply this to your integrand with g (u)= 1

[ornate hemlock]

Well the 1. You said I am partially right. I am asking why I am partially right.

[flat whale]

i've been explaining it the whole time

[ornate hemlock]

How and where

I'm just asking about the partial fractions

You know what mate nevermind I'll just do it on my own

Here a tip - you're a post grad, I'm self studying a level maths - my mathematical maturity is leagues below yours. Bit too early for sum of integrals is the integral of the sum and whatnot, that is not what I was asking for

.close

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[flat whale]

integrals properties should be taught before integrating rational functions. it's your order of studying that's wrong

[ornate hemlock]

It's the a level curriculum 😭😭 I did say already

[flat whale]

that's meaningless

[ornate hemlock]

I don't make the curriculum. Yes I've seen the calc sequence and see why they teach calculus much better. However I am studying a level maths

[flat whale]

then you didn't pay attention when the sum property was taught

[ornate hemlock]

Err

It hasn't been taught yet.

Because I am reading the book and it hasn't been taught yet...