help-49

[grand pond]

ƒ(why am i here )= I don't know

[twilit field]

so $B=pqB$

[grand pond]

ƒ(why am i here )= I don't know

[twilit field]

so either pq=1

or B=O

or pq=0; B=O

right

[midnight plank]

@twilit field Has your question been resolved?

[runic hamlet]

so what exactly is your question

pq=0 still implies A=B=0

[twilit field]

Just wanted my answer verified

[runic hamlet]

then consider it verified

[twilit field]

Thanks

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[twilit field]

oops

wrong problem

so this is how I did it

$\begin{bmatrix}
1 &-1&-1&3\
2&-1&-3&4\
1&0&-2&1\
\end{bmatrix} \begin{bmatrix}
x_1 \
x_2\
x_3\
x_4\
\end{bmatrix}=b $

and

[grand pond]

ƒ(why am i here )= I don't know

[twilit field]

$\begin{bmatrix}
1 &-1&-1&3\
2&-1&-3&4\
1&0&-2&1\
\end{bmatrix} \begin{bmatrix}
\gamma_1 \
\gamma_2\
\gamma_3\
\gamma 4\
\end{bmatrix}=O{4 \cross 1} $

[grand pond]

ƒ(why am i here )= I don't know

[twilit field]

I then added them to obtain

$\begin{bmatrix}
1 &-1&-1&3\
2&-1&-3&4\
1&0&-2&1\
\end{bmatrix} \begin{bmatrix}
x_1 + \gamma_1\
x_2+ \gamma_2\
x_3+ \gamma_3\
x_4+ \gamma_4\
\end{bmatrix}=b+ O_{4 \cross 1} $

[grand pond]

ƒ(why am i here )= I don't know

[twilit field]

now this is the same as

$\begin{bmatrix}
1 &-1&-1&3\
2&-1&-3&4\
1&0&-2&1\
\end{bmatrix} \begin{bmatrix}
x_1 + \gamma_1\
x_2+ \gamma_2\
x_3+ \gamma_3\
x_4+ \gamma_4\
\end{bmatrix}=b$

[grand pond]

ƒ(why am i here )= I don't know

[twilit field]

So thus proving that the sum of the solution to a specific system + that to the associated system is a soln to this system too

this is what my book did

[runic hamlet]

well the question asked you to actually find the solutions

[twilit field]

I mean I can just say assume $x_i$ to be the solutions, right

If not yeah, I would need guassian elimination

[grand pond]

ƒ(why am i here )= I don't know

[runic hamlet]

sure you could say that but its not what the question meant

you basically just restated the theorem for that particular example

thats trivial

clearly not the point of the question

[twilit field]

hmm, so I solve for both cases( the given and the homogenous case), and then I arrive at my answer

right

[runic hamlet]

well or you do it like the book

which gives the same

[twilit field]

Got it

thanks

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[fierce canyon]

can somebody explain why the triangles are all equal?

[feral sedge]

is this a regular hexagon?

[fierce canyon]

yeah

@feral sedge ?

<@&286206848099549185> ?

[mortal pier]

It would be better to cut hexagon step by step for convenience, so i will go turn up tablet

[fierce canyon]

wdym by turn down the tablet? but yeah ig that could help more

@mortal pier ??

[mortal pier]

I here

[fierce canyon]

how would we start breakiing it down?

[mortal pier]

Firslty by diagonals

We knew that diagonals in polygon cut each other on equal parts

Also, we knew that diameter in hexagon is twice bigger than his side, so:

We would form 6 regular triangles with equal sides

[fierce canyon]

yeah but in this case theres still more right

[mortal pier]

Wdym?

Well, i will continue

Let`s paste in it triangle like in your yeterday's task

His vertices laying on midpoints of hexagon sides

We consider that upper side of triangle (in our case, MN) is parallel and equally distant to both hexagon side and diagonal (AD and BC)

So, MN size is average of BC and AD

[midnight plank]

@fierce canyon Has your question been resolved?

[fierce canyon]

mb

i had to eat dinner

[mortal pier]

Now we will add second similar triangle
Here, upper vertice divide in half (on parts 1 cm long)
If we mark some parallelogram (it surely is, because all sides of inside triangles is parallel to sides of hexagon), we will assure that it has equal sides, so it rhombus

[fierce canyon]

can u explain this a bit?

[mortal pier]

Bon appetit!

[fierce canyon]

lol

[mortal pier]

That polygon ABCD is trapezium
MN in it is midsegment, so it can be found by adding top and bottom sides of trapezium and dividing that sum by 2

[fierce canyon]

why would that be the length of it?

@mortal pier ?

[mortal pier]

Those medians also will cut half of diagonals on equal parts

If we extrapolate all of those theories on each side of that figure, and calculate it, we will get that each side of all small triangles is equal 1

Sorry, it takes so long to explain

[fierce canyon]

nah its alg

[fierce canyon]

can u explain why? i think im a bit confused rn

[mortal pier]

Sorry, was afk
All those steps that i suggested is leading to that point
If you would try to solve some sort of exercise with that hexagon with side 2 cm, guiding by rules from that chat, you surely complete it with all little segments equal 1 cm
So it will be hard to explain it in few words🫠

[midnight plank]

@fierce canyon Has your question been resolved?

[fierce canyon]

<@&286206848099549185> if somebdoy could clarify his explainations it would be greaty appreciated!

[fierce canyon]

<@&286206848099549185> ?

[fierce canyon]

<@&286206848099549185> anybody?

[feral needle]

if its a regular polygon

[gilded dirge]

<@&286206848099549185>
If you may, I seek to ask about Zorn's lemon 🍋.
By the lemon, we know there exists a total order over (0;1), however this order cannot be defined.
If we were to list all binary numbers between 0 and 1 in the list a_∞, the union of all a_n, defined by a_0 = {0.5}, a_1 = {0.5 + 0.25}, a_2 = {0.5 - 0.25}, and in general, a_n+k = {the element in a_n ± 0.25} depending on k.
I feel Zorn's lemma says there does not exist a closed form calculation for the sign given k, or for k, knowing n.
I feel we can have that closed form by using a metric similar to 2-adic absolute value.
I hope my question is clear.

[feral needle]

@fierce canyon
Start with the Hexagon: A regular hexagon is super symmetrical, meaning every side is the same length, and every angle inside it is 120 degrees. If you draw lines from each corner of the hexagon to its center, you'll get 6 equal triangles, each of them an equilateral triangle (where all three sides are the same).

Creating 24 Triangles: To get 24 triangles, you can divide each of those 6 equilateral triangles into 4 smaller triangles. You do this by drawing lines parallel to the sides of the bigger triangles. These lines are drawn in a way that splits each triangle into smaller, equal parts.

Why All the Triangles Are the Same: Since you're dividing up each of the original equilateral triangles in the exact same way, and everything started out equal (thanks to the regular hexagon), all those smaller triangles end up being identical. They have the same side lengths, the same angles, and even the same area.

Conclusion : Each of the 24 triangles formed within the regular hexagon is congruent, meaning they are all equal in terms of side lengths, angles, and area. This equality is a consequence of the regularity of the hexagon and the symmetrical way the triangles are divided.

[gilded dirge]

@fierce canyon correct me if I'm wrong, but I think it's sufficient to see in each equilateral triangle, the triangles within are all congruent, then arguing through rotational symmetry or whatever it's called (60n degree symmetry) that all the triangles within will contain these congruent triangles. Finding the lines pass the same points and are parallel, they are the same lines, so 24 equal triangles

Idk I weirdly feel this makes more sense to me personally, but I'm too neurodivergent to know if my explanation makes sense to others

[fierce canyon]

wait which parallel lines are we talking abt? you can use smt like this the base to ig show it

@feral needle @gilded dirge ?

[fierce canyon]

yo u guys here?

@feral needle do u think u could shoe me the lines u drw

[feral needle]

tbh Im too lazy to draw, just follow the step which I mentioned, ur good to go

[fierce canyon]

Would one of them be like this? @feral needle

One of the parallel lines

[feral needle]

Actually yea

and u gotta draw some more

to get the exact question figure

@fierce canyon nd lemme know if u need some more explanation

if u still didnt get it

[midnight plank]

@fierce canyon Has your question been resolved?

[midnight plank]

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[feral needle]

@fierce canyon u got it?

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[twilit field]

I know this is trivial

just wanted confimation

Ax+Bx=0+0
x(A+B)=0
(A+B)x=0

[worthy wing]

Dont you have to distribute first in the second line?

[twilit field]

I don't follow

[simple field]

there is in issue in your second line in that we cannot guarantee that x can left multiply the matrices

[twilit field]

oh yes

[simple field]

e.g. say A is a 3x2 matrix and x is 1x3

[twilit field]

yeah, that was my concern a. while ago too, forgot that

Well, we know that Ax+Bx=0

[simple field]

yes

[twilit field]

and the final statement also implies Ax=-Bx

[simple field]

i suspect the question is looking for you to move into summation notation

[twilit field]

which follows from this

[simple field]

i cant be sure because i dont know the book, what youve already proven and how etc etc

[twilit field]

what's that

[simple field]

like the explicit form of matrix multiplication in terms of the entries

[twilit field]

Matrix multiplication is the next section

we've just covered vector -matrix multiplication here

[simple field]

its basically the same thing

[twilit field]

I know

[simple field]

but yes then the explicit form for vector-matrix multiplication

[twilit field]

I think this method works well too, no?

[simple field]

well it depends what you have already proven

but its not much of an exercise to say
Ax = 0, Bx = 0
Ax + Bx = 0
(A + B)x = 0

thats not really a proof

[twilit field]

I mean it works

But yeah, I get your point

[simple field]

my point is that it only works if you have already established the truth of the statement Ax + Bx = (A + B)x

i think the point of the exercise is to establish this fact

[twilit field]

We have

yeah

[simple field]

again ^^

i may be wrong

[worthy wing]

I think you are right

I may be wrong too btw

[simple field]

There are two possible cases:
This exercise is meant to test if you learnt how to prove this result
Or
This exercise is testing you can applying it

It's unclear and really up for you to judge physics

[twilit field]

I'm doing this for fun now, so I guess I;ll take the easy path for now. I'll ask my prof when we cover this in class.

thanks!

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[twilit field]

So I'm trying to prove that $\frac{a+b}{2} \geq \sqrt{ab}$

[grand pond]

ƒ(why am I here)= MATHS

[grim vector]

Smells amgm

[twilit field]

I started off with $(a-b)^2 \geq 0$

[grand pond]

ƒ(why am I here)= MATHS

[twilit field]

No AM-GM

[twilit field]

so $(a+b)^2 \geq 4ab$

[grand pond]

ƒ(why am I here)= MATHS

[delicate sage]

You re going correct way no?

[twilit field]

I guess that's it?

[pearl hull]

pro

[dreamy lichen]

Yes, that's correct

[delicate sage]

Another way is to use that Triangle concept

[dreamy lichen]

just divide by 4 and sqrt

[twilit field]

I made a mistake when I did it in my book.

I got $\frac{a+b}{\sqrt{2}} \geq \sqrt{ab}$

[grand pond]

ƒ(why am I here)= MATHS

[delicate sage]

Silly mistake 🥲

[pearl hull]

don't forget this won't work when either or both a,b are negative

[dreamy lichen]

At least it's not wrong lol

[twilit field]

thanks

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[twilit field]

.reopen

[midnight plank]

✅

[twilit field]

Really silly question

But I want to prove that $\frac{a+c}{b+d} \geq \frac{c}{d}$

[grand pond]

ƒ(why am I here)= MATHS

[pearl hull]

[twilit field]

if c/d>a/b

I just reverse engineered the soln

simiplified the inequality

and then got the desired result trivially

how do i avoid doing that

[dreamy lichen]

Now it's the time to apply reverse - reverse engineering

[twilit field]

I know

But that feels like cheating

[dreamy lichen]

But it's correct

nobody must even know that you did the reverse engineering part

and it will be better that way, things like that should be kept out of the proof

[twilit field]

When I'm writing my thesis in 4 years imagine if this is how I get my result

I hypothesise something to be true

then reverse engineer it

[dreamy lichen]

is that a problem?

[twilit field]

In my eyes, yes

[dreamy lichen]

it's not, you arrive at the right proof eventually

[twilit field]

That means I haven't understood the material well enouh

*enough

[hard umbra]

can you give an interpretation of the inequality

[twilit field]

Forgot to mention

all numbers are >0

[dreamy lichen]

(Btw, "simplifying" the wanted conclusion is not uncommon in proofs, it's usually hidden behind the words "it's sufficient to prove that ...")

[olive matrix]

nothing wrong with writing some work then turning it upside down for a proof

[last slate]

uncool tho

[dreamy lichen]

Why?

[hard umbra]

something seems wrong about this inequality

you've got something the wrong way round

[twilit field]

wait, let me check

a/b<c/d

[hard umbra]

yeah thats better

wait you havent changed anything

[twilit field]

that's the same thig

[hard umbra]

thats still wrong

yeah

i cant read

[twilit field]

that's what my book gives

[dreamy lichen]

and here the sign is also correct?

[hard umbra]

are you sure

[twilit field]

oops

should be the other way round

[hard umbra]

,, \f ab \le \f {a + c} {b + d} \le \f cd

[twilit field]

got it

my bad

sorry

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[twilit field]

Thanks everyone!

[midnight plank]

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[twilit field]

this would just be a line segment on [-pi/2,π/2], righty

[twilit field]

As that's arcsin's domain

[sudden yacht]

Yes, but the interval is [-1, 1]

[zealous schooner]

what line segment?

segment of what line?

[twilit field]

yes

[fallen aurora]

y=x if x lies in -1 to 1

[zealous schooner]

!nosols

[midnight plank]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[zealous schooner]

I am not asking you for the answer, I am asking OP for the answer..

[fallen aurora]

okok

[twilit field]

y=x, i knew that

I ask because the last time I asked this , I was told it's a periodic function

[zealous schooner]

that's arcsin(sin x)

[twilit field]

I'm pretty sure that was for this

[twilit field]

that's obvious, right

[zealous schooner]

what?

no, sin(arcsin(x)) is not periodic in the slightest

arcsin(sin(x)) is in fact periodic

[ivory inlet]

yeah

arcsin is not defined for values more than 1 or less than -1

[dreamy lichen]

Nope, i'm 100% sure it wasnt

[ivory inlet]

i meant 1

mb

[dreamy lichen]

that one was arcsin(sin(x)), which indeed is periodic

[zealous schooner]

$f(f^{-1}(x))$ is always just the identity function, on the relevant domain, while $f^{-1}(f(x))$ is periodic with the period equal to the period of $f(x)$

[grand pond]

kheerii

[zealous schooner]

(here I'm talking about f(x) being a trigonometric function specifically)

[twilit field]

oops

yeah

my bad

Sorry for wasting y'all's time( Idk how to pharse it)

[dreamy lichen]

Wdym? You asked another different question

it wasnt wasting time

[twilit field]

thanks

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[twilit field]

This would be an open sentence, right

[zealous schooner]

if we didn't want to utilise our time here we simply would not

[zealous schooner]

what's the context?

.reopen

[midnight plank]

✅

[twilit field]

Here

.close

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[prisma granite]

Can someone explain how to do

🥲

[midnight plank]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[prisma granite]

1

[hybrid crane]

Part a or part b?

[prisma granite]

part a

I tried to do this

on the right top

[visual tiger]

have you tried a change of variables on the integral on the left?

[prisma granite]

ys

wait

let me try on my ipad and send here

[prisma granite]

this

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[prisma granite]

.reopen

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✅

[hybrid crane]

x = a - u

[prisma granite]

So I need to sub x = a - u instead of sub u into the equation?

[hybrid crane]

The bounds should be flipped if the minus is left alone

[hybrid crane]

x = a - u is equivalent to u = a - x so it doesn't really matter

[prisma granite]

ohhh

okie

[hybrid crane]

After you do the u-sub completely

Actually, just send your work so far

[prisma granite]

okkk

May I ask what is the meaning od f(a-x) = f(x)

[prisma granite]

like this?

[hybrid crane]

For example: f(3) = f(a - 3)
but it works for any value of x in the interval [0, a]

[prisma granite]

ahhh I see

thxx

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[twilit field]

let $A$ mean the matrix is invertible, $B$ mean that's $det(A) \neq 0$

[grand pond]

ƒ(why am I here)= MATHS

[twilit field]

$A \iff B$

[grand pond]

ƒ(why am I here)= MATHS

[twilit field]

2. Let $A$ mean that the function has a constant derivative, $B$ mean that it's linear

[grand pond]

ƒ(why am I here)= MATHS

[twilit field]

$A \iff B$

[grand pond]

ƒ(why am I here)= MATHS

[twilit field]

3. Let $X$ mean $x$ is 0; $Y$ mean $y$ is 0

[grand pond]

ƒ(why am I here)= MATHS

[twilit field]

$X \iff Y$

[grand pond]

ƒ(why am I here)= MATHS

[twilit field]

Thanks

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[visual tiger]

uh that's not it

[runic hamlet]

.reopen

[midnight plank]

✅

[runic hamlet]

I am pretty sure you are supposed to write it in one sentence. not one sentence explaining your symbols and then a second sentence using your symbols

[runic hamlet]

terrible choice of symbols btw, A already means the matrix, which is also how you are using it when you are writing det(A)

so for example for the first one you can say: a matrix A is invertible if and only if det(A) \neq 0

[midnight plank]

@twilit field Has your question been resolved?

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[vapid warren]

can anyone explain the basic concept of Taylor Series? I keep watching youtube videos on them but it always feel like they start with the presumption that you already have a basis of knowledge on it and I can't understand much. So i was hoping that I understand the basic concept I could understand the more advanced parts of it in the videos

[runic hamlet]

you know the tangent line of a function at a point, right? its basically the answer to the question "what is the best function of the form f(x)=ax+b which looks like my function near a specific point"

as a next question you could ask yourself, what is the best function of the form f(x)=ax^2+bx+c

[vapid warren]

the way I understood it was that it's a way to estimate the n'th derivative of a function

[runic hamlet]

or f(x)=ax^3+bx^2+cx+d

and if you keep going like that, you basically get the taylor series

[vapid warren]

i see

thanks for the explanation

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[midnight plank]

@timber arrow Has your question been resolved?

[timber arrow]

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[vapid warren]

Can someone tell me the steps for getting the local maximum and minimum for a multivariable function?

so far, from what I understand is that I have to:

1. Do an equation system where I equal the first order partial derivatives to 0

2.Do the Hessian Matrix where I use the second order partial derivatives

and from here i'm lost

[vapid warren]

i know I have to obtain some D1 D2 D3 values but I have no idea what they are or if i have to use the hessian matrix for them

[shadow schooner]

first step is setting the gradient f = 0. that's your first step. next you compute the hessian and check whether it's positive definite (min), negative definite (max) or indefinite (saddle point) when evaluated at your canditate point you found in step 1.

[vapid warren]

i'm sorry, i think I'm just an idiot, but i don't understand the second part. Do i have to do the determinant for the hessian?

i'm catching up on stuff for a failed exam so my head is a mess

[shadow schooner]

to check that it's positive definite my fav way is using Sylvester's criterion.

give me a minute for a drawing

[vapid warren]

so first things first I do this, right?
then comes the hessian matrix, and I'm not sure what to do with it, since in my course it shows that I might have to do it multiple times depending on how many solutions my system has

okay

[shadow schooner]

yeah it's the same as with single variable calculus. you find the critical points (candidate for min max) with gradf(x) = 0 (in single variable calc it's f'(x) = 0) then you check the sign of the second derivative (if the the hessian is positive def negative def or indefinite in multivariable calc) to find the nature of the critical point.

[vapid warren]

i see, thanks for explaining

[shadow schooner]

let me cook some example for the hessian

[vapid warren]

oke

[vapid warren]

thanks!

[shadow schooner]

the hessian can contains x and y. in that case that mean that th concavity of f(x,y) depends on the point of evaluation. it's like f''(x)>0 means concave up

[vapid warren]

i see

i'm gonna have to look a bit more into stuff but this will defo be helpful

.close

[midnight plank]

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[last slate]

Topic: Linear Algebra

[last slate]

Question: How would I get full points on this question? It is quite an easy question, with easy answers. However, I'm sure that my way to tackle this problem would barely give me any points

I know, that for the system to be inconsistent, I would need an entire row to be 0.

So 2α = 0 gives α = 0

But would that be enough of an explanation? Would writing this down get me full points?

And the other answer is α = 1 but now I do not understand how to get that answer

Right now, I have written this down, I created a new system but I honestly am just doing something, it is probably completely wrong

[midnight plank]

@last slate Has your question been resolved?

[last slate]

Anyone?

im still trying but cant figure it out

[last slate]

<@&286206848099549185>

<@&286206848099549185> bro i opened this over an hour ago 💀

[fallen aurora]

I am not good at matrices/determinants thing overall
but how many values of alpha are supposed to be the answer?

[last slate]

2 values

alpha is 1 or alpha is 0

[fallen aurora]

not sure but why -1 isn't supposed to be a value of alpha?

'coz I got 0, 1 and -1

3 answers

[fallen aurora]

so I computed the determinant of A

and for inconsistency, set it equal to 0

but I am not sure how to reject the -1 value

if it is not in the answer key then they probably rejected it someway

[last slate]

i dont know

its my first day of econometrics study

they are already beating me to a plump

[fallen aurora]

I actually don't even remember the exact condition of inconsistent solution😭

[last slate]

[0 0 0 0 | c] with c is not equal to 0

[fallen aurora]

but I remember that if that A thing is invertible then the system will not be consistent

[fallen aurora]

yeah that's one of them

[fallen aurora]

thanks

[fallen aurora]

I used this though

[last slate]

i dont really understand, wdym with invertible?

[fallen aurora]

I mean to solve for that x, you have to pre-multiply by inverse of A on both sides

but if we don't have any inverse then the system will not be consistent

[last slate]

I've never heard or applied that before 😅

[fallen aurora]

that's strange

[last slate]

I only had my first lecture about this today

[fallen aurora]

I mean you've probably learnt it before

[last slate]

(and the last)

[fallen aurora]

the what

[last slate]

I know what inverse is, but just in basic equations

[last slate]

the only lecture where this will be discussed

I didnt have to apply the inverse in linear algebra before

[fallen aurora]

I mean you don't have to calculate it

as far as I remember it inverse{A}=adj{A}/det{A}

if det{A} is zero then

☠️

[last slate]

@fallen aurora

yo

u still here

[fallen aurora]

kinda yeah

[last slate]

i ended here somehow

from this, can i conclude this;

[fallen aurora]

yeah seems alright

[last slate]

is this a correct conlusion? or did i skip steps

[last slate]

imma just keep it like this 😭

tysm for your help brother

.close

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[midnight plank]

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[bright tinsel]

CAN SOMEONE HELP ME W INVERSE TRIGO I JUST NEED TO START IT FROM SCARTCH I MEAH NOT THE BASIC FORMULAS

[midnight plank]

Please don't occupy multiple help channels.

[bright tinsel]

sorry

[rancid hinge]

Send your question

Don't ask to ask

[bright tinsel]

sorry?

[rancid hinge]

It's ok

Dw

[midnight plank]

@bright tinsel Has your question been resolved?

[flat veldt]

Do you have a specific question you need help with?

[bright tinsel]

no i am just dont know from where to start basically i was out of my country in my junior year so didnt attent any math class here i am in my senior year i am screwed

[flat veldt]

[bright tinsel]

nvm

[flat veldt]

I don't think I could teach you inverse trig but I can send some YouTube videos here

[bright tinsel]

SURE PLS

nad derivaties too if you could

and:

[flat veldt]

https://youtu.be/jt7p-mCC0ng?si=ku71xhwKYujn5I9M

https://youtu.be/Z9Pwjgz5NzE?si=yfAdMRwqgA9ph-N3

https://youtu.be/wH3JYo8U2uM?si=8c1PhLwNBqfCiGR5

Here's Going to get flooded with videos

https://youtu.be/xRd5kwufMq0?si=EaqwWKFD1XDBBV61

[midnight plank]

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[forest shoal]

how is the force 2m away from point A?

[midnight plank]

@forest shoal Has your question been resolved?

[main current]

They're replacing the distributed triangular force with a single point force

The position: The geometric centroid of the triangle, which is 2/3rds the way down.
The magnitude: The area under the triangle.

@forest shoal

[forest shoal]

why in mb and ma there is 3 and 1.5 shouldn’t we just multiply the force by the distance

@main current

[main current]

Force = 12(3)
Distance = 1.5

[midnight plank]

@forest shoal Has your question been resolved?

[forest shoal]

why multiplied by 3?

[midnight plank]

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[midnight plank]

Please don't occupy multiple help channels.

[timber arrow]

im a bit confused on how to simplify this into nicer integrals

[midnight plank]

@timber arrow Has your question been resolved?

[wary trail]

0-2 and 4-6 are the same yeah?

c^2 + (a+b)^2 + (2c)(a+b) + 3(a+b+c)=-2

where 0-1 is a, 1-2 is b etc

[timber arrow]

yeah cuz symmetry about x = 3?

i find that by just doing x = 6-x so 2x = 6 => x=3

[timber arrow]

how u get to herE?

[wary trail]

i think it'd be easier if you tell me which bits you don't agree with

[wary trail]

yeah exactly

[wary trail]

(If you're writing out a solution I also suggest you use a separate variable)

[uncut rapids]

u guys know where I could find a study partner at?

[midnight plank]

@timber arrow Has your question been resolved?

[midnight plank]

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[cedar vortex]

@bold tartan

[bold tartan]

Thank you

[cedar vortex]

also im going to TA soon for some physics

[bold tartan]

I dont know know how to do any of it. I have really been trying

[cedar vortex]

so give me feedback if you can

okay let's go through this

[bold tartan]

I know my first answer is right

[cedar vortex]

yeah that looks good

now monthly payment is calculated how @bold tartan

as described in the first paragraph

[bold tartan]

20% of 12k?

[cedar vortex]

well the $12k number will change

[bold tartan]

2400?

[cedar vortex]

as they make payments (and interest is added)

make a more general statement

[bold tartan]

Oh 20% of the amount payment?

[cedar vortex]

20% of the balance + after interest

[bold tartan]

Yeah

[cedar vortex]

sounds good

so mathematically

[bold tartan]

So the payment numbers under 0 will just be 1 and 2

[cedar vortex]

how can we write this

[bold tartan]

Hmm

In the chart

Would the first month finance charge just be 12k?

[cedar vortex]

let's go through the table step by step

so the finance charge

I understand that as the interest right? @bold tartan

so like we would do something like $12000 * 0.0135

because 1.35/100 = 0.0135

[bold tartan]

So not 12000 * 1.35?

[cedar vortex]

well we are working with percent

so we divide by 100

otherwise 100% of 12000 would be 12000 * 100

[bold tartan]

So 162?

[cedar vortex]

and not 12000 * 1

if that makes sense

[bold tartan]

Yeah I remmeber the divide 100 now

[cedar vortex]

yes

payment number - 1; finance charge $162

balance with finance charge would be $12162?

[bold tartan]

Yes

[cedar vortex]

what's 20% of that

[bold tartan]

2432.4?

[cedar vortex]

looks good

that's the payment

so what would be the new balance

[bold tartan]

Would I just add payment and balance w finance charge?

[cedar vortex]

subtract no?

[bold tartan]

Ohhh shoot yes

Mb

9729.6

Looks right?

[cedar vortex]

i think you cooked

ye

[bold tartan]

Alright alright

So then next finance charge

[cedar vortex]

yessirrr

[bold tartan]

0.0135 * 9729.6?

[cedar vortex]

ye

[cedar vortex]

🤷‍♂️

probably

[bold tartan]

But that isnt a $?

[cedar vortex]

yeah

[bold tartan]

It has to be a number that would make sense for money

[cedar vortex]

yeah round no?

@bold tartan did you figure it out??

[midnight plank]

@cedar vortex Has your question been resolved?

[midnight plank]

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[arctic cipher]

im having trouble finding the inverse of this matrix

[arctic cipher]

first i add to the second row -2 times the first getting

1 3
0 3

ph wait

.close

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[twilit field]

If $0<a<b$ .
\
Prove that
\
$a < \sqrt{ab} < \frac{a+b}{2} <b$

[grand pond]

Veni, vidi, perii

[twilit field]

I started off with the fact that $a<b$

[grand pond]

Veni, vidi, perii

[twilit field]

so $a^2<ab$

[grand pond]

Veni, vidi, perii

[twilit field]

or $a<\sqrt{ab}$

[grand pond]

Veni, vidi, perii

[twilit field]

nvm, I'll write it as a single message

$a<b$
\
$a^2<ab$
\
$a < \sqrt{ab}$
\
we also have
\
$ab<b^2$
\
$\sqrt{ab }<b$.
\
so $a < \sqrt{ab}<b$.
\
\
we also have
\
$a+b<2b$
\
$\frac{a+b}{2}<b$
\
similarly
\
$a<\frac{a+b}{2}$
\
\
. We thus have
\
\
$a<\frac{a+b}{2} <b$.
\
We also have
\
\
$(a+b)^2-4ab>0$
so $\frac{a+b}{2} > \sqrt{ab}$.
\
\
which proves that $a< \sqrt{ab} < \frac{a+b}{2} <b$
\
\
QED

[limber salmon]

the first 3 lines are all completely correct

Next 3 lines are also good

now just prove that (a+b)/2

is >a and < b

and your proof should wrap up nicely

[grand pond]

Veni, vidi, perii

[twilit field]

Thanks!

[twilit field]

Does this look right

Like is this enough for spivak ?

[limber salmon]

hmm, im just struggling with the last line.

im just confused on what that thing being greater than 0 has to do with anything

[twilit field]

That's to prove that $\sqrt{ab} < \frac{a+b}{2}$

[grand pond]

Veni, vidi, perii

[twilit field]

I know that $(a-b)^2>0$

[grand pond]

Veni, vidi, perii

[limber salmon]

I would write presume root ab = a+b/2

Square both sides ab = (b^2 + a^2 + 2ab)/4*

Since a>0 and b>0, which we were given at the start, then since ab = ab + ... /4* , and since a and b must be greater than 0, the right side is always greater than the left.

something like that would have been my go to

[limber salmon]

b-a you mean

[twilit field]

Yeah

[limber salmon]

if you're confident on the logic then go with it but i don't follow. i'm a simple man though, it could be correct.

[twilit field]

I know this is right. But is it enough for spivak?

[limber salmon]

I dont know what spivak is

Maybe i can't help

hmm, my proof was wrong anyhow

[twilit field]

A book that's halfway beteern calculus and analysis

[limber salmon]

we then replace abs, we have 2 ab, and b^2 > ab, so we have minimally 4 ab, + a^2, > 4ab

but yah if you dont want to write that all out

then i dont know

that's how i would prove it

oh wait

that is your proof

lol

dude okay, you just didn't write it out

fair, yes that's all correct

[twilit field]

But is it rigourous enoug

hlike how can I assume a<b \implies \sqrt{a} < \sqrt{b}

[limber salmon]

I don't know. If i was confused that our proofs differed until i wrote it out correctly I would say, maybe not. If this is self-study then yes you did a great job and good enough.

Just depends, if you knew all the logic in your head when writing that down, then yes you did what i did but without all the legwork. Its just up to you.

[twilit field]

This is for uni, but I'm sort of studying ahead

like we only do RA in year 2

[limber salmon]

I wouldn't turn in a proof without stating everything i said about presume they are equal etc.

[twilit field]

I've just started year 1

[limber salmon]

Or at least some mention of the form you got to your conclusion from

which should be 2 root ab < a+b

if you want to write it quickly

(and so its obvious to a reader that your statement follows)

[twilit field]

I get that

$a<b \implies \sqrt{a} < \sqrt{b}$

[limber salmon]

actually, to be fair, the line afterwords, is clearly also the form you got it from, so maybe its good enough

[grand pond]

Veni, vidi, perii

[twilit field]

but I have to prove this, no

?

[limber salmon]

since a and b are above 0 i think its obvious, but you could yes.

[twilit field]

How

[limber salmon]

if root r < root y, then r < y

or, now we must prove, squaring is also true?

[twilit field]

wait

ooh

thanks for the hint

$r<y$

[grand pond]

Veni, vidi, perii

[twilit field]

$r<y$\
$r^2<ry$\
$ry<y^2$

[grand pond]

Veni, vidi, perii

[twilit field]

so $r^2<y^2$

!

[grand pond]

Veni, vidi, perii

[limber salmon]

ahhh

that's brilliant, i didn't help at all i'm flattered

well done, yes you could add that in, that's bonus credit i think but its wonderful

[twilit field]

Thanks!

.close

[midnight plank]

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[midnight plank]

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[drifting root]

i need help with part f

i know the perpendicular distance formula, how did i connect that to vectors?

[midnight plank]

@drifting root Has your question been resolved?

[drifting root]

<@&286206848099549185>

[limber salmon]

AP is a vector starting at point A and ending at point P

Point A is on the line of l

Does this help? sorry if im being dumb

@drifting root

I could tell you the distance from P to l, rise over run, but i don't know vector math or what perpendicular distance means.

I assume it wants you to follow that vector in unit lengths of 1 till you get to the point P.

[drifting root]

.close

[midnight plank]

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[drifting root]

Oops sorry thanks for the help

I was being a bit stupid i could just use pythag

[midnight plank]

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[ember sage]

Can someone explain why I put 1 over everything in the equation

[zealous schooner]

You need to consider the amount of work done per hour

if ken takes x hours to do the work then ken does 1/x of the work per hour

Because it's the work that gets added, not the time

[midnight plank]

@ember sage Has your question been resolved?

[midnight plank]

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[wooden knoll]

2x-3y = 7
-4x + 5y = -9

[wooden knoll]

i have to solve this using matrices

so

i solved it

but idk if im right

i got x = -4 and y = -5

[drifting root]

if youre unsure of your answer

the easiest thing to do is to sub it back in your equations

you can do this really easily by using your calc

[wooden knoll]

ohh yeahhh

lemme check rq

[drifting root]

looks alr tho

[wooden knoll]

oohh yeah

got it right

thank you

.close

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[idle phoenix]

whats the least annoying way to find cos55

[fallen aurora]

45+10, ig

[idle phoenix]

nah

10 is annoying

i though of that but finding cos and sin 10 is a pain

[fallen aurora]

wait it is degrees right?

[idle phoenix]

yeah

[fallen aurora]

okok I was scared for a moment

[slender walrus]

how much precision do you want

[idle phoenix]

extremely precise

the exact value

[slender walrus]

can't

[idle phoenix]

should i send the question?

[slender walrus]

yes, ideally you should always post the original question

[idle phoenix]

sorry

my bad

[summer ravine]

cos (90-35)?

[idle phoenix]

the LHS sums up to -1

[last slate]

you dont have to find

cos35

for this

or cos55 whatever

[idle phoenix]

how would i do it then?

[last slate]

using trig identities

[idle phoenix]

i did that on the LHS

and i got -1

the RHS is were im cofused

[last slate]

what did you do

[idle phoenix]

wait

[last slate]

are you sure about -1

[idle phoenix]

sinx+siny= 2sin(x+y/2)cos(x-y/2)

and then that for cos to

[slender walrus]

can you take a pic of your work

[idle phoenix]

sure

itll take 5

,rotate

[idle phoenix]

thats what i did

[last slate]

i suggest converting these sines into cosines

[slender walrus]

290/2 isn't 135+60

[last slate]

using the reduction formulae

[idle phoenix]

damn

silly mistake

sorry

oh

[slender walrus]

=145 = 90 + 55
which would be how 55 is relevant

[idle phoenix]

i see

yeah

my bad

its trivial from here

sorry for bothering

[slender walrus]

didn't double check the rest, that part just stood out.

[idle phoenix]

sorry

.close

[midnight plank]

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[sinful mesa]

HI'

[sinful mesa]

HELLO

HI

[worthy kestrel]

hello there

[sinful mesa]

HI :0

🙂

[worthy kestrel]

🙂

[sinful mesa]

WHAT IS YOUR NAME

[midnight plank]

This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.

[sinful mesa]

MINE IS ABDUR RAHMAAN BIN THASINULLAH BIN SHAJAHAN BIN NOORULAH BIN SHAFI BIN AHMED

MY FULL NAME

[worthy kestrel]

very cool

[worthy kestrel]

go there

[sinful mesa]

THANKS ABOUT YOU

[fallen aurora]

do you have any mathematical question?

[sinful mesa]

YES

[fallen aurora]

then ask that
not off-topic stuff

[sinful mesa]

WHAT IS 27000SQUARE ROOT SO I JOINED THIS SERVER

[dreamy lichen]

,calc sqrt(27000)

[grand pond]

Result:

164.31676725155

[worthy kestrel]

why do u need that

and u can just use a calculator

[sinful mesa]

THANKS

I WANT TO NOW THE METHOD

[idle phoenix]

damn cool it with the caps

[sinful mesa]

okay

i just wanna no the method

[idle phoenix]

go to some #chill

or #discussion

[dreamy lichen]

https://www.youtube.com/watch?v=HBdVVFqTrUU

[worthy kestrel]

whats the question as u were given

[midnight plank]

@sinful mesa Has your question been resolved?

[sinful trout]

what the hell is this channel

[midnight plank]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[sinful trout]

@sinful mesa

[midnight plank]

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[last slate]

"which of the following numbers could be the remainder 26.12"

a) 8
b)16
c) 24
d) 42
e) 55

[last slate]

😭 wth does that mean?

[void glen]

26.12?

[last slate]

yes

i have the 0answer though but the logic doesn't make senes to me

i have the answer as in i solved it

i think?

[void glen]

what's the answer, i could try reverse engineer what the question means

lol

[last slate]

i don't have the answer lmao

if i did then i could prolly rever engineer it too 😭

anyway this is what i did

[junior flower]

what the

[last slate]

26.12 = 26 + 12/100 = 26 + 3/25 and since 3/25 is irreducible

so the remainder has to be a mutliple of 3

💀

is that even sound?

[last slate]

slayyla 💅

[junior flower]

[last slate]

anyway so like what does the question mean

[feral sedge]

is this the wording used

[junior flower]

i have no idea

[last slate]

yes

[junior flower]

hi mqnic :3

[feral sedge]

i would wager the answer's d but i can't prove it

[last slate]

Mqnic_

[feral sedge]

:3 hi layla

!Kiz__

[last slate]

:bending_skull:

[junior flower]

!Kiz__

Mqnic_

[feral sedge]

!Kid__

:bending_skull:

[last slate]

Kid

Kid

wow

[last slate]

why did you choose D?

this is what i did from what i understood

26 + 3/25 and so i can get equivalent fractions of 3/25

so for c) to be right i could just express it as

26 + 24/(25 * 8)

and the "remainder" here is 24?

D also works i guess

[feral sedge]

D is the only option where if you divide it into some whole number and round the result you can get a 0.12

[last slate]

is my "logic" stupid?

[feral sedge]

i have no idea since the question is worded so weirdly

[last slate]

i found something similar online

https://gmatclub.com/forum/if-s-and-t-are-positive-integers-such-that-s-t-64-12-which-135190.html

u think it's related?

[feral sedge]

if the question is asking what this page is asking, then your choice of 24 is correct

hm

[last slate]

what is different about my question relative to the one i linked

or are they both bad questions lol

[feral sedge]

it's a lot less specific

so it's hard to say for certain what it wants you to do

[feral sedge]

this is fine imo

[silk basin]

Thats such a weird question

The remainder one would think is 12

I guess you could try multiplying 26.12 by an integer that gets you a whole number product

[junior flower]

after seeing that, that’s probably what it was supposed to be. but unclear from the original

[feral sedge]

actually 24 and 42 are both divisible by 3 so i have no idea

they're both possible answers assuming that interpretation

[last slate]

yeah that's what i meant

[junior flower]

[last slate]

maybe "numbers" means you can select more than 1

[feral sedge]

yeah just go with that ig

[silk basin]

Yeah

Because the remainder is 3 so

Any multiple of 3 works

Theoretically

Because 26.12 x 175 gets you the whole number of 4,571

And when you long divide 4,571 by 26.12 you get a remainder of 21

Which is a multiple of 3

[last slate]

i guess yeah

[last slate]

is the answer to this the same if s and t are negative integers?

[midnight plank]

@last slate Has your question been resolved?

[midnight plank]

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[midnight plank]

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[pine vine]

how can i get the range of this function?

[fallow scarab]

the range of this function can be found by finding the domain of the inverse function

[pine vine]

thanks

is there a rule to determining whether a function is odd or even

without getting into the f(-x) = -fx things

[fallow scarab]

no. you need to do this

[pine vine]

ok

and

how do i do the odd about things?

[midnight plank]

@pine vine Has your question been resolved?

[midnight plank]

@pine vine Has your question been resolved?

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[formal shore]

In 32^1/5, how could i find a?

[formal shore]

I understand that we have 5sqrt(32) = 32^1/5, but how would we find the answer from that

(not 5*sqrt(32), but the exponent)

[teal hemlock]

Well if you were told that the answer is a integer, there is not much else you can do except try different solutions

[formal shore]

so the only real answer is trial and error?

[teal hemlock]

Or a calculator

[formal shore]

hm alright, awkward as the task asked to solve it without using calculator

[teal hemlock]

That is usually it for roots

[formal shore]

I thought there was some between step we could do

[teal hemlock]

You do not need a claculator

Pick 2 for example

And do 2^5

[formal shore]

not for small numbers no, but i could imagine for big numbers it starts being quite difficult

[teal hemlock]

If it's other roots than 2 than yea

For sqrt u have some basic knowledge of where to look

[midnight plank]

@formal shore Has your question been resolved?

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[timber arrow]

a bit of combinatorics

[delicate sage]

5×4

First of all

[timber arrow]

mhm

[delicate sage]

Of 1,2,3 2 different can be selected in 3c2 or 3 ways

[timber arrow]

yep

[delicate sage]

Of this we will have 4 in one way only 3+1

[timber arrow]

i think we can have repeats of numbers as well so like 2,2 is not allowed

[delicate sage]

Oh sry i didn't see

[timber arrow]

oh nws

[delicate sage]

I got confused with the letter case

[timber arrow]

yeah lmao all gd but yh they cant add up to 4 asw

[delicate sage]

So 3+1 , or 2,2

How many total permutations we have 3×3

[timber arrow]

1,1
1,2
2,1
2,3
3,3
3,2

i think these r all the possible right

for numbers

we have 3! + 3

then we notice

that 3 of these add up to 4

[rustic garden]

it is probably easier and safer to count the complement

[timber arrow]

so we subtract that

[rustic garden]

there are 4*4 different ways to pick 2 numbers

subtract away the number of ways to add up to 4

[delicate sage]

?

[rustic garden]

the digits can be the same

[timber arrow]

i think its just this

[rustic garden]

1,1 is allowed

[delicate sage]

3×3 - 3

[rustic garden]

ohhhh up to 3 whoops

yeah

[timber arrow]

For numbers:
1,1
1,2
2,1
2,3
3,3
3,2
For letters:
5x4?

[delicate sage]

Yeah

[timber arrow]

but the thing is

cant u swap the letters around

so 5 x 4 x2

if i pick A B

B A

[delicate sage]

So it's 4×5×6

[timber arrow]

is a diff number plate

[timber arrow]

nah 4 x 5 x 6

[dreamy lichen]

Then you are double counting

B A was already counted

[timber arrow]

but it says different plates

[rustic garden]

In this case either way you count the digits doesn't make that much of a difference but make sure you keep the complement technique in your back pocket

its super powerful

[timber arrow]

like A B 1 1 is a different number plate to B A 11

so why do i not do 5 x 4 x 2 for the letters

[delicate sage]

We are considering the case

[dreamy lichen]

Yeah, and 5 x 4 already accounts for that

[delicate sage]

In 5×4

[timber arrow]

oh wait does it