help-27

[honest trout]

I am grateful for the help

[wheat pawn]

dont forget the parenthesis on the first line, (x-5)(x-5)

[honest trout]

thx

[wheat pawn]

also, try not to use the "x" as multiplication sign. use $\cdot$ instead to avoid ambiguity

[woven radish]

LordFelix

[honest trout]

will do

[wheat pawn]

on this one, your... last? 2nd to last (this one is difficult to see)? you're dividing:

$\frac{y^3}{y^5}=\frac{1}{y^2}$

[woven radish]

LordFelix

[wheat pawn]

whereas you put y^3 instead on the denominator result

[devout snow]

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[robust bobcat]

Can someone help me with these two problems

[robust bobcat]

NVM I understand the first but still don't get the second

[devout snow]

@robust bobcat Has your question been resolved?

[cyan surge]

(number of females)(females in medium hostility)
/(Total students)

Find female students provided they belong to medium hlt score

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[restive river]

help

[restive river]

i forgot what to do for b

[faint gorge]

I think you can use Horner's method

[restive river]

what is that

for the first part

snce u know 5-i and 5+i

u make the quadratic

etc

so

i got z^2-10z+26

now what

[faint gorge]

Oh if you decomposed it already

continue

solve that quadratic as usual

[restive river]

ok

wakt

waht

what would that do

[faint gorge]

you are solving f(z) = 0

[restive river]

yh

[faint gorge]

you managed to find the quadratic factor

f(z) = (z-(5-i))(z-(5+i))(z^2-10z+26) = 0

[restive river]

wait

why did we do that

[faint gorge]

how else are you gonna solve a quartic equation?

[restive river]

like

long division

[faint gorge]

,w expand (z-(5-i))(z-(5+i))(z^2-10z+26)

[woven radish]

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[faint gorge]

ok they don't math with the original

[restive river]

ohhhhhhh

thats it?

nit that doesnt make sense

cos then

we just doing

the quadratic twice

cos

expanding this gives us the first quadratic

[faint gorge]

i see now what you did

and why you are confused

i misunderstood you

yea you would do long division

to find the other quadratic factor

[restive river]

but how tho

cos we have

2 unknowns

[faint gorge]

just treat them as constants

[restive river]

give me a min

bro

i cant do

[woven radish]

𝔸dωn𝓲²s

[faint gorge]

Make sure the remainder gets 0

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[vale turret]

can some one please help with this

$

Find all the integer pairs (m, n) such that:
[
m^3 + n^3 + 99mn = 33^3
]

\textbf{Solution:}

Starting with the given equation:
[
m^3 + n^3 + 99mn = 33^3
]

Rewriting:
[
m^3 + n^3 = 33^3 - 99mn
]

Using the sum of cubes factorization:
[
m^3 + n^3 = (m+n)(m^2 - mn + n^2)
]

Substituting, we have:
[
(m+n)(m^2 + n^2 - mn) = 33^3 - 99mn
]

Simplifying further:
[
(m+n)(m^2 + n^2 - mn) = 99(363 - mn)
]

Assuming (m+n = 99), we use the identity (m^2 + n^2 = (m+n)^2 - 2mn). Then:
[
m^2 + n^2 = 99^2 - 2mn = 9801 - 2mn
]

Plugging this back, we get:
[
99(9801 - 2mn - mn) = 99(363 - mn)
]

From here, we attempt to solve for (m) and (n). Testing (m+n = 99) and (m^2 + n^2 = 363), we find:
[
mn = 4719
]

The quadratic equation for (m) and (n) becomes:
[
x^2 - 99x + 4719 = 0
]

$
However, solving this equation does not yield integer solutions, suggesting an error in the assumptions or steps. It is unclear where the mistake lies.

[stray spade]

m + n is not necessarily 99

[swift oasis]

why did you consider m+n = 99 ?

[vale turret]

isn't the left side factored matches the right side ?

[vale turret]

isn't the left side factored matches the right side ?

[stray spade]

just because 4 * 3 = 12 * 1 you cant say 4 = 12

[vale turret]

All clear now thanks

.close

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[indigo jewel]

Hello, I’ve been trying to understand these types of questions for a few days now, no luck, I think where I tend to get stuck is when I get to all the fractions and negative signs and such, messes with my brain lol, but I’m also not fully clear on the elimination and substituting methods

[indigo jewel]

This is also a no calculator course

This is the work I’ve done, although not much help because I realized afterwards it isn’t correct

[devout snow]

@indigo jewel Has your question been resolved?

[indigo jewel]

<@&286206848099549185>

[night wraith]

This is system of equations, correct?

[indigo jewel]

Yeah

the exact title of this specific one as it shows on my homework is Manipulating Expressions/Equations

But the title of the whole thing is systems of linear equations yes

[fast cliff]

the sign - of -4 disappeared

[indigo jewel]

Wow ur right idk why I did that lol

But regardless would I have even been able to achieve the right answer with the way I was going in that problem

[lone sage]

awm can u like rotate it

[indigo jewel]

Wym?

Oh yeah my bad

[fast cliff]

Sure, if you didn't change de sign

[night wraith]

So can you just tell me what strategy you're taking

Step by step

[indigo jewel]

I guess where I tend to get confused is when the negatives are either on one number in a fraction or the whole fraction, for example, -1 over 2 versus just a -1/-2, if there’s one negative sign on one number, can I put that negative in front of the whole fraction?

[indigo jewel]

Yeah sure

So my goal was to get y by itself so I can find the value of y

Then plug that into the other equation to find x

Like said before I changed the sign for no reason when I shouldn’t of but I tend to struggle with getting that first y value

[fast cliff]

Now I noticed that you're right in that step your put the sign of -4 before the term, so I didn't notice that

[indigo jewel]

Oh so it is a positive 4?

[fast cliff]

Yeah you put the sign before the term

But, the wrong step that I didn't understand is why you change the sign of 20x

It should be -20x

[indigo jewel]

Ur right I see that now idk why I didn’t do that I think I was just super stressed solving this earlier and made silly mistakes

[fast cliff]

You should multiply the -5x by 4(demoninator) not -4

[indigo jewel]

I thought when multiplying fractions thought since it was multiplied by -3, the 4 turns into -4 bc it’s multiplied by -1

[fast cliff]

I see

The real problem

Why +18x is still +18x after you multiply by -

[indigo jewel]

I see, give me one moment I’m gonna redo that part so I can get the real equation

One quick question

If I’m multiplying a -3 times that 2-6x over -4, does that -4 stay negative ?

Is the denominator of 1 also technically negative since the 3 is negative

[fast cliff]

If youre multiplying that

Remember multiply the numerator with numerator, denominator with denominator

In this case -3 is equal to -3/1 or 3/-1

But not -3/-1

[indigo jewel]

I see

So then this is the equation ?

[fast cliff]

should be this

Or something like this changing sign in both side

[indigo jewel]

I see, and then I can combine like terms making that 38x - 6 over -4 but then that’s where I get stuck how do I isolate that x

[fast cliff]

Then

You can multiplying -4 in both side

So you don't have to warry about fraction

[indigo jewel]

I forgot about that rule that makes perfect sense

[fast cliff]

Yeah sometimes you may forgive that

So then, you can get the value of x

[indigo jewel]

Yes I see it now I think I can solve it from here now, thank you for clearing that up truly

Questions like this were beating me up for days lol

[fast cliff]

So good luck, and more practice you do for it better you can manage it

[indigo jewel]

Yep, thank you for your help

[devout snow]

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[shy hound]

I'm lost! I need help I'm unsure how to get this anwser

[lusty sapphire]

The y intercept of the graph of a function is the point where the graph intersects the y axis (the vertical axis). Note that the x=0 at the y axis. So the y intercept of the graph of h is just the value h(0)

[shy hound]

Thanks!

[swift oasis]

is the answer 3?

[swift oasis]

Oh sorry I misread it.

[shy hound]

To be quite honest, I am still confused 😅

[swift oasis]

so we are going to find the h(0) and we already have f(0) and g(0). h(x) = g(x) * f(x).
do you think we can proceed from here?

[shy hound]

Yes?

[swift oasis]

can you tell me what happens when we plug x=0 ?

[shy hound]

No I can't I don't know how to do this problem I was absent on Friday when my instructor told us how to do these.

[devout snow]

@shy hound Has your question been resolved?

[swift oasis]

okay so can you see that the h(x) function is the product of f(x) and g(x) function?

in these types of problems where we have a function like h(x) expressed in terms of two different functions like f(x) and g(x) whose y-intercepts are known, and we need to find the y-intercept of h(x), then simply put x = 0 or any other point whose value is needed.

then we will get, h(0) = f(0) * g(0), can you please tell us what we can do after this?

[devout snow]

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[glossy dune]

Hello, I don’t know how to solve 3), I’m kinda confused with homothethy vectors and modules, I have a test tomorrow and I don’t understand

[devout snow]

@glossy dune Has your question been resolved?

[glossy dune]

<@&286206848099549185>

[glossy dune]

,help

[woven radish]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[glossy dune]

Please I need help I don’t understand haha

[glossy dune]

Hi I don’t understand please help

😔😔

Hii can someone help me

Please

[devout snow]

@glossy dune Has your question been resolved?

[glossy dune]

Hi I need I help please with the question

[glossy dune]

Hi pls help I wanna close this

[spark juniper]

@glossy dune

what is homothetic

[glossy dune]

When you obtain a figure in base of another figure increasing or decreasing his scale all coming from the center of homothecy

[frosty gyro]

stretching a figure about a point

like this

Q is a homothety of P about S (I think that's how it's called)

[frosty gyro]

so for 1. find the distance between the point and P, then multiply by the ratio to get the new distance

the image will be on the line connecting the two points

[glossy dune]

Ohhh I see I see, but I don’t understand the vector thing from the 3) part

[frosty gyro]

I haven't done vectors but

I think the x value should be 3(x coordinate of u) - 2(x coordinate of v)

same with y value

[glossy dune]

Umm I’m gonna try that!

Ty

.close

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[mental cloak]

how do i evaluate this using riemman sums?

[mental cloak]

i calculated ∆x and 𝑥*
​

im just not sure how to manipulate it

[livid thorn]

can you list out the expression you've come to?

[mental cloak]

im not necessarily sure how to type it but i can explain my steps?

after i found 𝑥* i used the formula for a riemman sum like sigma f(x)∆x

i plugged in x*

and im just unsure how to manipulate from there

i know i can separate the sum

like for 1 + sq(1-x^2)

but idk how to manipulate sq(1-x^2) in order to evaluate the limit?

like as n --> inf

[livid thorn]

what expression do you get when you sub in x* to sqrt(1-x^2)?

[mental cloak]

sqrt(1-(-1/sqrt(2) + k((sqrt(2)+2)/(2sqrt(2))/n)^2)

i might've forgotten a bracket

sorry

[livid thorn]

ok what is k here?

I will try and type out what you wrote and you can correct anything thats not right

[mental cloak]

k is just the counter no?

we don’t use i

[livid thorn]

ok gotcha so k is what you are summing over?

[mental cloak]

yeah

[livid thorn]

$\sqrt{1 + \frac{1}{\sqrt{2}} - k((\sqrt{2}+2)/(2\sqrt{2}))/n)^2}$

ok let me tidy this up a bit lol

[mental cloak]

yeah it looks right to me tho

[livid thorn]

sorry its a bit cutoff is the upper limit of the integral 1/2?

[mental cloak]

yup

[livid thorn]

ok how does this look?

[woven radish]

VortexNerd

[livid thorn]

lets narrow in on the definition of x*. How did you go about deriving that

[mental cloak]

lower bound so -1/(sqrt(2)) + k*delta x

and my delta x is just (b-a)/n

[livid thorn]

so delta x when you plug in the limits is?

[mental cloak]

0

[livid thorn]

sorry the limits of integration

so the bottom and top number

b and a

[mental cloak]

oh

(1/2+1/(sqrt(2))/n

[livid thorn]

Great so that part looks correct to me

[mental cloak]

i’m just not really sure how to find the riemann sum when given a definite integral that’s a square root function

[livid thorn]

so $x^* = -1\sqrt{2} + \Delta x$ right?

[woven radish]

VortexNerd

[mental cloak]

i think the firm term is a fraction

[livid thorn]

I guess I'm trying to follow your steps so I can try and help out wiht the limit

[mental cloak]

got it

[mental cloak]

And delta x is multiplied by k

but maybe you use i

[livid thorn]

right yeah dropped that accidentally. I used i in the past but lets stick with k. So rewriting we have:

$x^*_i = -\frac{1}{\sqrt{2}} + k\Delta x$

[woven radish]

VortexNerd

[mental cloak]

yess

[livid thorn]

I think a small mistake potentially is that the 1/sqrt{2] should be inside thing being squared

since you should get $\sqrt{1 - (x_i^*)^2}$

[woven radish]

VortexNerd

[livid thorn]

which would be $\sqrt{1 - (-\frac{1}{\sqrt{2}} + k\Delta x)^2}$

[woven radish]

VortexNerd

[mental cloak]

oh right oops

[livid thorn]

and youre going to multiply $f(x^*_i)$ which is that whole big thing by $\Delta x$ on the outside

[woven radish]

VortexNerd

[mental cloak]

yes i understand that part

there’s also that +1 though

but i can split the sum right

so it just becomes n

[livid thorn]

yeah you should be able just focus on the square root term

since the 1 term is really simple

[mental cloak]

do you know how to approach the square root 😞

i havé no idea

[livid thorn]

messing with it a bit

this is pretty gnarly, maybe someone with better alebraic chops can help out in the evaluation 😦 What is the statement of the entire problem?

do they expect you to set up the limit or fully evaluate it?

even the solution to the integral isn't pretty

[devout snow]

@mental cloak Has your question been resolved?

[devout snow]

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[buoyant escarp]

How did he get that 3! in the numerator? (the 3 with the red circle)

[buoyant escarp]

trying to figure out how to solve this problem

would this be right?

looks like it is.

.close

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[manic ridge]

ive been stuck on this question

for the past 7 hours

this is the answer i got

[inland sapphire]

and how did you get to that answer

[manic ridge]

first i found the eigenvalues of the matrix

which are(-9+3sqrt(17))/2

and (-9-3sqrt(17))/2

[inland sapphire]

yea I think that's wrong

[manic ridge]

hmm

maybe

coz the answer is like

ridiculously long

[acoustic leaf]

could you show your working on the eigenvalues?

[acoustic leaf]

,rccw

[manic ridge]

oops sorry

[inland sapphire]

um

[manic ridge]

its probably extremely wrong

im really tired

[inland sapphire]

yea it is bro

so to find the eigenvalues what is the characteristic equation determined by

[manic ridge]

det(Mat(A) - Lambda(Identity Mat))

[acoustic leaf]

you wrote your matrix down wrong, it should be +12 in the bottom right

[manic ridge]

oh

fuck off

one sec

lemme redo it, and ill get back to u in a jiffy

ah

i see now

its 6 and 9

wow

ok ty

thats why

W mans right there

.close

[devout snow]

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[manic ridge]

ty guys!

[inland sapphire]

still so many more steps to do after that but I assume you got it 😭

[manic ridge]

nah this is easy peasy

[inland sapphire]

are you fine with the eigenvectors

[manic ridge]

yeah

[inland sapphire]

and diagonalising

[manic ridge]

i got the eigenvectors last time

yep

[inland sapphire]

aight sweet

[manic ridge]

ill keep this open for another 15 minutes

just in case

[devout snow]

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[manic ridge]

BRUH

[inland sapphire]

lmaoo

[manic ridge]

ok how is that wrong

[inland sapphire]

u legit wrote the answer

just in a different form

than what they wanted

[supple knot]

what's the question

[manic ridge]

wdym?

[supple knot]

and show all your work

[inland sapphire]

am I seeing things or did you enter the correct answer just in a different form

[manic ridge]

i swear it is the correct answer no?

[inland sapphire]

it is

it just didnt accept what u put

how can u not see that...

[supple knot]

show

your

work

[manic ridge]

hold up bro

jeez

[inland sapphire]

he did, scroll up. He reopened the channel

I helped him before

[manic ridge]

idk what i did wrong here

[inland sapphire]

listen

These are the same thing bro

you are correct

[manic ridge]

fuck webwork

[supple knot]

,w {{-1,-1/2},{1,1}}^-1

[woven radish]

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Requested by rie.mann

[supple knot]

your P inverse is incorrect

[cinder nova]

that's just the latexified view of what they entered
not the actual correct answer

[manic ridge]

how is it wrong?

[supple knot]

oh i can't read

[inland sapphire]

yea but on paper he got it right

its just an input error in the website

[supple knot]

M is not equal to P D Pinv

,w {{-1,-1/2},{1,1}}{{9,0},{0,6}} {{-2,-1},{2,2}}

[woven radish]

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Requested by rie.mann

[manic ridge]

,w {{-1,-1/2},{1,1}}{{9^n,0},{0,6^n}} {{-2,-1},{2,2}}

[woven radish]

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Requested by kyoshimtl

[acoustic leaf]

your eigenvectors must be in the same order as your eigenvalues

[devout snow]

@manic ridge Has your question been resolved?

[manic ridge]

but they are?

[acoustic leaf]

which eigenvector corresponds to which eigenvalue?

[manic ridge]

(-1, 1) corresponds to 9

(-1/2 , 1) corresponds to 6

[acoustic leaf]

try multiplying those by your matrix and verify that

[manic ridge]

multiplying the eigenvalues?

or the eigenvectors

[acoustic leaf]

multiply the eigenvectors by your matrix

[manic ridge]

seems correct

[acoustic leaf]

what i mean is, multiply your eigenvectors by your original matrix M, and verify that they are actually scaling by the correct eigenvalue

[manic ridge]

seems wrong

[acoustic leaf]

from that, we can see that the first column must have eigenvalue 6 and the second column must have eigenvalue 9

[manic ridge]

so do i flip the columns or P, P^-1 and D?

[acoustic leaf]

well we can see that the columns of P and D are mismatched, so you'll have to swap one of the two

[manic ridge]

only one?

ok

ill redo this tmr

ty guys!

.close

[devout snow]

Channel closed

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[manic ridge]

@acoustic leaf @inland sapphire @cinder nova @supple knot

YEAHHH

.close

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[wanton flint]

I am in class 9. Can iget all help here?

[terse solar]

!da2a

[devout snow]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

@wanton flint Has your question been resolved?

[strange nimbus]

Yes. Scroll up in #❓how-to-get-help to see how.

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[hexed willow]

I need help solving this problem.

[hexed willow]

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[hexed willow]

what is the process for finding the angle between vectors u and v?

[mortal tinsel]

dot product

[hexed willow]

the dot product is 9 but what do I do with that info?

[mortal tinsel]

$a \cdot b = |a| |b| cos(\theta)$ or something

[woven radish]

Bean Man

[hexed willow]

wait so how would I find a and b?

[mortal tinsel]

?

$$u \cdot v = ||u|| ||v|| cos(\theta)$$

$$cos(\theta) = \frac{u \cdot v}{|u||v|}$$

[hexed willow]

im confused on where to go next

[woven radish]

Bean Man

[mortal tinsel]

Do you know the magnitude of a vector?

[hexed willow]

magnitude is the length

[mortal tinsel]

Alright so what the length of u and whats the length of v

[hexed willow]

$$|u|=9$$

$$|v|=\sqrt{65}$$

[woven radish]

KXLI

[mortal tinsel]

Alright now can you solve for theta?

[hexed willow]

going through it rn

$$\text{So: }\cos{\theta}=\frac{\sqrt{65}}{65}$$

[woven radish]

KXLI

[mortal tinsel]

alright

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[plucky kernel]

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[restive river]

lol

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[restive river]

I am not sure how to continue for solving part a.

[restive river]

I deduced that given we are attempting to prove that it ABCD is a parallelogram

[woven radish]

forMaths

[restive river]

which I was able to prove as I have found out that

[woven radish]

forMaths

[restive river]

Which in this case, they are clearly parallel

[woven radish]

forMaths

[restive river]

Which is clearly not the case as they are not parallel. In fact, they are perpendicular.

Any idea where I could have went wrong?

[frozen aurora]

show your work

wait

[frozen aurora]

BD and AC are diagonals

not the sides

you should consider BC and AD instead

[restive river]

Take a look at this. This is essentially the diagram I am basing my work on:

Wait hold on

Wrong one. Give me a moment

[frozen aurora]

yeah BD and AC are diagonals

[restive river]

Give me a quick moment

[restive river]

Okay so look here

I know this is not the conventional way to label the sides of a parallelogram but that's how I did it

[frozen aurora]

this parallelogram isn't ABCD then

it would be ABDC

the order matters in the name

adjacent letters denote connected vertices

[restive river]

Aha, so that is how to interpret it

[frozen aurora]

so AB is a side, BC is a side, CD is a side and BA is a side

[frozen aurora]

yep

[restive river]

Okay. I understand now. Thanks!!

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[prime marten]

https://www.youtube.com/channel/UCZNVO9Fr09YqhH8fzgf78lQ subscribe pls i beg

[proud perch]

is there a math problem you needed help with

[eager nova]

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[dusky apex]

Can anyone solve this and also explain so I understand please

[inner grove]

Can’t help too much rn but check these out: https://www.mathsisfun.com/algebra/trig-cosine-law.html

note that the first one is just a trig definition

soh cah toa

(it’s opposite/adjacent, so tangent)

that for first, cosine law for second, sine law (https://www.mathsisfun.com/algebra/trig-sine-law.html) for 3rd

should work

[devout snow]

@dusky apex Has your question been resolved?

[winter patrol]

don't need cos or sine law, that's overkill for these

soh cah toa is enough for all of them since you have right triangles

first set up an equation that relates your angle and sides from that

[dusky apex]

So uhm could you explain how, I wasn't paying attention and I kinda regret it now sorry

[winter patrol]

start by looking up sohcahtoa

you should get some nice images from google

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[dusky apex]

Thanks ok

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[honest trout]

can somebody help me on the way with this?

[devout snow]

Please don't occupy multiple help channels.

[solar goblet]

what have you tried?

[stable cloak]

It's a parallelogram

Opposite angles are equal

[honest trout]

I know ooposite angles are same

[stable cloak]

Adjacent angles are supplementary

[honest trout]

and all int. angles are 360

[stable cloak]

Use this

[honest trout]

and adjacent are 180

[stable cloak]

Yes

Use those properties

[honest trout]

how can us use x form angle E if i have only one equation for that?

[stable cloak]

first of all the angle is given outside the shape

You'll have to use linear pair first

Then just add the adjacent angles to 180 and solve for x

Then solve for y

J will be equal to E

[honest trout]

what do you mean with this?

[stable cloak]

you can't directly use x+10 +2x -60 =180

[stable cloak]

I have to go now but this is basically all you have to do

[honest trout]

alright, thx

[honest trout]

Can you help because I am getting stuck on this

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[misty zinc]

Yall please help me

Light enters glass from air at an angle of 25 degrees, and refracts at an angle of 16 degrees. Calculate the index of refraction for the glass. Draw a well labelled diagram for the situation above. Must include the following labels: ∠i, ∠R, principle axis, normal, incident ray, refracted ray, mediums

[thin basin]

bro this is a maths server
not physics one

[restive river]

Use Snell's law

In this case, n1 = 1 because you're coming in from air.

[misty zinc]

Ok

And how do I do that

K never mind

[restive river]

The problem is asking you to solve for n2

[misty zinc]

Never mind I got it

Thank u

How do I close this

[devout snow]

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[misty zinc]

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[chilly totem]

Hey, a little confused where to start with some proofs. If someone could talk me through the approach / logic of this one that would be much appreciated.

[devout snow]

@chilly totem Has your question been resolved?

[chilly totem]

<@&286206848099549185>

[valid silo]

so

the LHS is

ceiling of (ceil(x)+m)/n and the RHS is xeil(x+m/n)

assuming that they have different values

clearly the LHS is bigger

let us take x to be between 0 and 1 (not equal to 1)

this works because we can just add the integer part of x to m

so if x is 0, both of them are the same

so x>0

and so ceil(x) = 1

no if ceil of (m+1/n) is gretaer than ceil(m+x/n)

it is also greather than

ceil(m/n)

so that means

m is a multiple of n

but if x>0

ceil(m+x/n) is also greater thab ceil(m/n)

so ceil(m+x/n) = ceil(m+ceil(x)/n)

[chilly totem]

Appreciate the help, can't say I fully understand the process though

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[serene horizon]

hello, how do i prova that if f:R ->R and and g:R->R are both continuous, then min(f,g) is continuous too? Using the definition.

If we take a an element of R; and we use the definition; exists E such that: if |x-a| < n then |f(x) - f(a)| < E and |g(x) - g(a)| < E. (n = min(n1, n2) in the continuity definition of f and g)

Then we assume f(a) <= g(a) first. Now i'm stuck

[serene horizon]

here min(f(a), g(a)) would be f(a)

i don't know how to get min(f(x), g(x)) tho

i need to assume f(x) <= g(x) too first?

[lone ravine]

min(f,g) = (f + g - |f-g|)/2

[serene horizon]

how do i put that in the definition?

[lone ravine]

Do you know that the sum and composition of continuous functions is continuous?

[serene horizon]

yes

[lone ravine]

Now since f,g and absolute value are continuous this means that f,g is the sum/composition of continuous functions and itself continuous

[serene horizon]

yes but i want to use the definition

with epsilon

[lone ravine]

I would try to make wlog two cases first:

• f(a) > g(a)
• f(a) = g(a)

Can you tell me why the first case is easy?

[serene horizon]

if f(a) > g(a); i can only know that min(f(a), g(a)) = g(a)?? but i dont know how to get the conclusion that min(f,g) would be continuous

[lone ravine]

By intermediate value theorem we know that there is a neighborhood (a-d,a+d) such that min(f,g)(x) = g(x) in (a-d,a+d)

[serene horizon]

sooooo, |x - a| < n means that x in (a - n, a + n) so that would be the neighborhood then since x is in that neighborhood, the min would be g(x) too

[lone ravine]

Yes

[serene horizon]

ok, so the min is continuous because the min is g; for the second case; i don't know what the min is

[serene horizon]

wait, here i dont really get it. Clearly d cannot be anything right? i cannot just say that the neighborhood is (a-n, a+n)?

[lone ravine]

If you choose small enough (n < d) you can.

[serene horizon]

but here isnt n a fixed value?

uhh yes actually i understand

thank youuuu

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[opaque abyss]

help

[opaque abyss]

someone send working please i cannot do it

here what i did

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[upbeat stone]

I am trying to understand this for hours, can anyone help me?

[upbeat stone]

How to go from the first to the second?

[devout snow]

@upbeat stone Has your question been resolved?

[devout snow]

@upbeat stone Has your question been resolved?

[upbeat stone]

<@&286206848099549185>

[supple knot]

did you try binomial theorem

[upbeat stone]

Binomial theorem was used to get there

So idk why i should use it again

If you want i can send the entire problem, but it does not have much to do with what i am asking

[upbeat stone]

I also did not understand why -1 + sqrt (2) and -1 -sqrt(2) being roots of that polynomial mod 5 leads to that recurrence relation

[supple knot]

showing all context is always important

[upbeat stone]

Yeah sorry

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[devout snow]

@upbeat stone Has your question been resolved?

[devout snow]

@upbeat stone Has your question been resolved?

[fiery marten]

It's a theorem. Given a recurrence like
$$c_k a_n + \dots + c_0 a_{n-k} = 0$$
One can solve this equation:
$$c_k x^k + \dots + c_0 = 0.$$
Let $x_1, \dots, x_m$ be the roots with multiplicities $r_1, \dots, r_m$ respectively. Then
$$a_n = P_1(n)x_1^n + \dots + P_m(n)x_m^n,$$
where $P_j$ are polynomials of degree $r_j$.

[woven radish]

EQUENOS

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[real monolith]

guys i am having problem because how can p,q,r and s be in a same plane

[devout snow]

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[valid silo]

lambda?

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[silk rampart]

wondering if i did this problem correctly?

[fossil locust]

yep, that's correct

[silk rampart]

thanks

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[acoustic ocean]

Hello

[acoustic ocean]

How can I use this

.close

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[foggy fable]

hey can someone explain this

[foggy fable]

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[formal sierra]

so like

[formal sierra]

i slept through the class and was awoken by this assignment

we were tasked to pick 2 problems to solve

i would appreciate it if someone helped me solve this step by step ^^

[safe knoll]

first find ur 'new' x and y
x = X cos theta - Y sin theta
y= X sin theta + Y cos theta

and then u can substitute them into the given equation and simplify

(i would choose the question with theta = 45 degree , cuz cos(45) = sin(45) but u can choose question 20 for a change in question)

@formal sierra

[formal sierra]

hi

hmm

thank you!!

i cant seem to find any videos with this topic

do you have any recommendations?

[safe knoll]

search something like
rotation of conic sections

probably gonna find a few

also ping me if u reply :d

@formal sierra if ur done then `

!done

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[restive river]

Please help me find the limit of d)

[final drift]

do you know calculus?

[olive snow]

key is probably conjugate, have you tried this ?

[final drift]

oh yes this does work

[restive river]

think i got it confused

thought it was something else

thanks!

[final drift]

multiplying with the conjugate should work

[fervent hornet]

yaku in C++ arc?

[thin basin]

PUT THE SYNTAX DOWN

THIS IS FOR MY C++ ARC

[fervent hornet]

segfault core dumped

[olive snow]

day and night actually xd

[fervent hornet]

my condolences

hope you can survive this

[olive snow]

im loosing hp but im fine

[fervent hornet]

also shouldn't it be cout<<"YakuBros"<<endl;

[olive snow]

i'm a variable

but if i was a str yes

[fervent hornet]

ah makes sense

[olive snow]

nobody can change me except going with an &

[fervent hornet]

[devout snow]

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[woeful meadow]

On the left side box how did they use -5 to get -29/2 and 145/2

[supple knot]

Maybe -5 * R1 gets added to R2

[devout snow]

@woeful meadow Has your question been resolved?

[woeful meadow]

-5 + 8 isn’t -29/2

…

[supple knot]

Where does -5 + 8 come from

[woeful meadow]

-5 plus the 8 in the 2,2 position

Cuz 5-5 makes it zero and I assume it does that for the rest

[supple knot]

5 * R1 added to R2
means 5 times the entries in row 1 gets added to the entries in row 2

https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/matrices-elimination/v/matrices-reduced-row-echelon-form-3

please watch that example

[woeful meadow]

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[cerulean ruin]

Show that if p is prime and p >= 7, then there are always two quadratic residues of p that differ by 2.

i feel like this is kind of tricky maybe

[final drift]

same idea as the one where they were consecutive

[cerulean ruin]

hmm

juust pick different numbers?

[final drift]

yeah

they need to be 2 away from a square

for example, 2, 3 and 6 should work this time

[cerulean ruin]

ohhh i was thinking 6 11 and 66

but i 8 > p so maybe not

hmm

[final drift]

also, technically for the last one 0 was considered a quadratic residue

[cerulean ruin]

ah

[final drift]

so technically 0 and 1 always work

[cerulean ruin]

ye that makes sense

[final drift]

but i think they forgot about that

[cerulean ruin]

ah

[final drift]

whoever wrote the problem

[cerulean ruin]

💀

so hm 2 3 6

either 2 or 3 or 6

if 2

0, 2 (trivially)

if 3

1, 3 (trivially)

if 6

4, 6 as 4 = 2^2

ok! that makes sense actually

[devout snow]

@cerulean ruin Has your question been resolved?

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Use .reopen if this was a mistake.

[devout snow]

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• Show your work, and if possible, explain where you are stuck.
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[versed wyvern]

@iron sun Did I do it right?

[olive snow]

Seems fine

Actually you didn't need the second part

[versed wyvern]

Are my logical implications or whatever theyre called correct?

[versed wyvern]

I was just taught about existential quantification

[olive snow]

Where ?

Ah

Existential

[versed wyvern]

Yes, I mean those statements I did

[iron sun]

When you write a statement like that, you are simply asking, does such a number exist and you fulfilled it in the first part

[versed wyvern]

"there exists" seems pretty confusing to me

[iron sun]

Yeah so don’t use symbols when you don’t need to

[olive snow]

Id have add something like, " we want to show that : " and after start what you said

[void void]

there exists means there is atleast 1 situation where something is ... so if you have 1 that works, then it works

[versed wyvern]

Isn't it more of "for the following equation, x is a natural number:"

[versed wyvern]

Oh nice

[olive snow]

Its not what it told

[iron sun]

This is why you should avoid using symbols without understanding them, just write with words

[olive snow]

But yeah you don't need it

[versed wyvern]

It's too verbose?

[iron sun]

When you’re solving an equation you want to check all solutions, so this is inherently the wrong statement to write

You want all such natural numbers in your original problem

[iron sun]

It’s just simply misleading for your own sake

[versed wyvern]

What do you mean by "all such"?

[olive snow]

If you was really ask to show that there exist a x natural such that your equation true, you won't need the x_2 part which is not what asked here i bet

So if there was some others solution true

Youd be doomed

[iron sun]

In your original problem, you wanted to find all natural numbers that satisfy the equation

[versed wyvern]

Yes but what if x2 was also a natural number?

[versed wyvern]

Yes.

[olive snow]

Thats why don't say there exist

[iron sun]

Then simply use natural language

You don’t need symbols for this

You’d be confusing yourself and possibly others

[versed wyvern]

When is there exists used then?

[iron sun]

It is a way of quantifying a predicate, a statement with free variables.

You don’t need that for now.

[olive snow]

Definition or abstract proof

[versed wyvern]

So it's basically never used in equations?

[olive snow]

Never seen

[void void]

sometimes they could ask you show that there exists an x intercept.

Or sometimes you could say : The sum of 2 consecutive integers is even,

You could disprove it by showing THERE EXISTS a possibility , in which you show, of how this statement is not true

[versed wyvern]

We just learned about ∴ and ∈ so I thought this was relevant

[versed wyvern]

Oh so it's basically only used for proof then

[olive snow]

Yes

[void void]

yeah kinda

[olive snow]

,w show me formula of limit definition with epsilon

[woven radish]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
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Requested by yakubros

[olive snow]

Anyway

[iron sun]

When you’re solving an equation you usually don’t know beforehand the solution. When you use quantifiers you’re usually making a statement about the equation, but it does not give you the solutions, only if it’s true or not

[versed wyvern]

So what's the difference between universal and existential?

[iron sun]

There are verbose ways of expressing what you’re looking after, but it would not at all be a more effective way of showing your work in a high school setting; which I presume this is in.

[iron sun]

Why does that matter?

Or are you simply curious?

[versed wyvern]

curious

[olive snow]

They opposite some kind

[versed wyvern]

Yes that's correct haha

[iron sun]

An universal quantifier is a stronger condition than existence in some sense.

It says in essence, that your statement has to hold for all elements you’re suggesting

It’s a way of quantifying all elements at the same time for the predicate

If I write the predicate x = 1

Then its truth may depend on x

It is for example certainly not the case that x = 1 is true for all natural numbers x

But it is true that there exists a natural number x so that x = 1

This does not however say what x it has to be

[versed wyvern]

Sorry if I'm getting this wrong but in essence, existential is more for specifying an equation, while universal implies that something is that way for all numbers within the domain range?

[iron sun]

It doesn’t have to be about equations, think of any kind of predicate.

So like P(x): x is bigger than 5

So if our universe for x is natural numbers

Then is the statement

“There exists an x such that P(x)”

True?

Now in order to show this statement is true

We need to find atleast one natural number x so that, x is bigger than 5.

Can you find one?

[versed wyvern]

6 😂

[iron sun]

Yes!

Now, you’ve shown the statement is true. But simply knowing whether it’s true or not says nothing about the actual value for x for someone else, unless they in our case follow your proof and use x = 6.

Quantifiers in this instance is simply a tool to logically express the statement we had above

So we’d use the existence quantifier in this instance

Now what if you’re wondering if

“x is bigger than 5 for all values of x”

is true?

Then you’d express this logically using the universal quantifier

And you’d get a statement that is either true or false

[versed wyvern]

Ohh I think I get it

A bit at least 😂

We're gonna go through this in the extracurriculum in 2 years

[iron sun]

Don’t worry, good on ya for asking such questions this early!

Fun that you’re interested!

[versed wyvern]

This wasn't really too verbose, though?

Just basic expressions

[versed wyvern]

Yeah I've always been

[iron sun]

Quantifiers are very important and it took me a while to fully appreciate them

[iron sun]

Personally I would avoid writing stuff like this as it may potentially confuse you or others! But yes in this instance that looks fine

[versed wyvern]

Yeah because we've been introduced to only ∴ and ∈ so I think it's fitting

[iron sun]

Ah I see, interesting

[versed wyvern]

Only a very brief introduction to number types, though (natural, complex, irrational etc)

[iron sun]

I see, well in that case go for it!

[versed wyvern]

I will! My semester exams are in 2 weeks

[iron sun]

I wish you luck on them in that case!

[void void]

what do you study?

[versed wyvern]

I'm actually still wondering about this, though 😅.. Why is the equation (1-1/x)=4/9 and not 1/x=4/9?

[versed wyvern]

I translated the page but you get it

[void void]

what program is that

[versed wyvern]

It's a Swedish app called NOKflex

[void void]

wait so are you in uni or school?

[iron sun]

Oh you’re Swedish!

[versed wyvern]

Yes

[iron sun]

Samma :)

[versed wyvern]

Year 1 in "gymnasium" as we call it

[versed wyvern]

nice

[versed wyvern]

Vet du?

[iron sun]

Oj är detta bara första året, du kommer klara matten fint!

[versed wyvern]

Matte 1c

[void void]

ahh thats cool, in doing cegep (french province of canada) which is basically the same thing

[versed wyvern]

Nice

[iron sun]

Hm, ska se, så vi har att bara ett svar är rätt för de två frågorna, och både frågorna har lika många svars alternativ, korrekt?

[versed wyvern]

Ja.

[void void]

Massive tip ill give you is as aslan said becareful with these quantifiers and Idk if your persuing CS or same range but understanding is crucial, especially in a subject like Discrete maths

[versed wyvern]

CS?

[iron sun]

Okej så antag att du har x st svars alternativ. Vad är sannolikheten att hon väljer rätt för första frågan?

[void void]

Computer Science

[versed wyvern]

1/x

Kanske?

[iron sun]

Hm okej, ser nu vad som bekymrar dig. Ska se om jag tolkar frågan rätt

[versed wyvern]

Alltså min mattelärare sa att det är 1-1/x i stället men vet inte varför

[iron sun]

Okej nyckeln är här att dem ger dig givet vad sannolikheten är för henne att gissa fel på bägge frågorna

[versed wyvern]

Vänta

Jag ritade ner

[iron sun]

Så vad är snarare sannolikheten att hon gissar fel på en av frågorna?

[versed wyvern]

Stämde det att sannolikheten att hon har rätt är 1/x?

[iron sun]

Ja!

Men vi har bara givet vad sannolikhet är att hon gissar fel på bägge

[versed wyvern]

Hm men varför är just den inte 1-1/x?

[iron sun]

Så vi vill gärna ta vara på denna information

[versed wyvern]

Varför inte 1-1/x att hon har rätt?

[iron sun]

Om x = 3

Stämmer det då?

[versed wyvern]

Alltså svaret är 3, ja

[iron sun]

Alltså om x = 3, stämmer det att 1-1/x är sannolikheten att hon får rätt?

[versed wyvern]

Nej

[iron sun]

(Nu struntar vi i förutsättningen som ficks men bara mer allmänt)

[iron sun]

Precis!

Så 1/x är som du sa först precis rätt sannolikheten att hon får rätt

Men tyvärr är detta inte användbart

Vi vet nu i förhand att sannolikheten är 4/9 att hon inte gissar rätt för bägge

[versed wyvern]

Alltså jag vet att P(rätt) + P(fel) = 1

[versed wyvern]

Ja

[iron sun]

Precis

Så vad är P(fel)?

[versed wyvern]

Måste vara 1-1/x då

[iron sun]

Precis!

[versed wyvern]

Tror jag fattar nu

[iron sun]

Nu är vi även intresserad när hon gissar på nästa fråga, detta görs ju oberoende av den första frågan

Så vi har att P(fel)*P(fel) är sannolikheten att hon gissar fel på bägge frågor

[versed wyvern]

Exakt

[iron sun]

Men vad var detta lika med?

[versed wyvern]

(1-1/x)^2

[iron sun]

Precis!

Och vad hade vi givet?

[versed wyvern]

Vad menar du

[iron sun]

I frågan fick vi en viktig bit av information

[versed wyvern]

Att P(fel)*P(fel)=4/9 eller?

[iron sun]

Japp!

[versed wyvern]

Tack så mycket, jag förstår nu.

[iron sun]

Vad är bilden?

[iron sun]

Uh vad menar dem med ”färg” tro?

[versed wyvern]

Hjärter fem säkert

[iron sun]

Dvs. alla är röda?

Aha

Okej, hur många hjärters finns det i en kortlek?

[versed wyvern]

13?

[iron sun]

Mhm, eftersom 4*13 = 52 om jag inte räknar fel

Okej, men nu har du ju redan 3 st hjärter, korrekt?

[versed wyvern]

Just det.

Alltså tar man bort tre hjärter? 52-3=49

Är jag på rätt spår?

[iron sun]

Precis men även från antalet hjärter. Men kom ihåg att du även har 2 st ointressanta kort innan du byter kort, så du borde ta bort ytterliga 2 kort från totala

[versed wyvern]

Just det.. 47

[iron sun]

Så, säg att vi först byter en av korten

Precis innan detta görs

Då finns som sagt 47 kort i kortleken, varav 10 är hjärter

[versed wyvern]

Ja

Tar man 10/47?

[iron sun]

Precis!

Om du nu har lyckats

[versed wyvern]

Och sedan upphöjt till två?

[iron sun]

Nej!

Om du har nu lyckats då finns ju bara 9 hjärter i kortleken!

[versed wyvern]

Just det

10/47+9/47?

[iron sun]

Gånger!

[versed wyvern]

Just det.

[iron sun]

Hoppas jag inte har missat något, brukar vara ur usel på sannolikheter

[versed wyvern]

Men det stämde inte, alltså 4.1% var inte svaret

Men det var 4.2%?? Konstigt?

[iron sun]

Hm

[versed wyvern]

De kanske gjorde ett fel?

[iron sun]

Om någon har gjort fel så är det med störst sannolikhet jag

[versed wyvern]

Alltså det är bara en decimal ifrån

[iron sun]

Tittar igenom nu ifall jag har missat något

[versed wyvern]

JAHA

Det är ju så klart 9/46

Eftersom ett kort eliminerades

[iron sun]

Men det märkliga är ju att vi ersätter ett ointressant kort tillbaka, då behålls ju totala antalet kort?

Eller kastar vi dessa iväg?

[versed wyvern]

Oklart alltså

[iron sun]

Men det verkar ge rätt svar åtminstone

[versed wyvern]

De var bara otydliga antar jag

Ja

Nästa är: Hur stor är chansen att du får stege (3, 4, 5, 6 och 7)?

[iron sun]

Som sagt, jag är inte den bästa på dessa

[versed wyvern]

Jag ska försöka skriva lösningen här

[iron sun]

Tipsar stort ifall du vill få rätt svar att öppna en kanal på nytt och fråga på engelska :)

[versed wyvern]

52-(5 kort i handen) = 47 kort
(1/47)(1/46)(1/45)(1/44)(1/43)

[versed wyvern]

Du var 0.1 procent ifrån 😅

[versed wyvern]

Nu blev det lite fel...

Jag tänker för snabbt.

[iron sun]

Har också nämligen plugg att göra som jag prokastinerar med haha

[iron sun]

Ta din tid!

[versed wyvern]

haha ja

[versed wyvern]

Matte skadar inte

[iron sun]

Trevligt att få träffa en svensk; men måste tyvärr plugga jag med, hoppas du hittar någon som kan hjälpa!

[versed wyvern]

Jaha, okej, inga problem!

Jag ska sova nu ändå

[iron sun]

Låter bra det

Sömn är bäst!

[versed wyvern]

Godnatt!

Och tack

.close

[devout snow]

Channel closed

Closed by @versed wyvern

Use .reopen if this was a mistake.

[versed wyvern]

@iron sun Vill bara säga att jag förstår uppgiften nu!

[iron sun]

.reopen

[devout snow]

✅

[versed wyvern]

Bara ville säga snabbt

[iron sun]

Jasså hurdå om man får fråga?

[versed wyvern]

Eller nej, det var typ rätt. Alltså jag trodde det var 4/47*4/46, eftersom vi redan har 3 av korten för stege (3, 4, 7). Då återstår 2 kort. Och eftersom det finns fyra valörer/färger gjorde jag så. Men facit säger att det är 8/47*4/46. Varför 8 i stället för 4?