help-27

[smoky gyro]

Bum chicken

If you get a decimal in these ap sequences stuff u probably fucked up somewhere lol

[inner ibex]

ik.

can u help me

[smoky gyro]

In a few min

[daring stag]

It is 30th term not 13th term

[inner ibex]

omd.

..

[daring stag]

Read the question properly

It's written thiertieth not thirteenth

@inner ibex

[inner ibex]

pls stop being mean to me

😭

[inner ibex]

u always say this and then u dip

frick u

[daring stag]

Have you got it?

[left flower]

bro its number 30th not number 13th

i fell the same mistake lol

[daring stag]

I told him already

Why everyone uses wolfram alpha

[left flower]

because in wolframalpha i can also brute force, solve my algebralol

[daring stag]

It degrades your creativity

[left flower]

bruhh?

[left flower]

it helps

[left flower]

it is actually a programming languange

[daring stag]

Well you should solve by yourself rather than taking help of some other applications

[left flower]

maybe we got Out of Topic just continue in discoussion

[smoky gyro]

What is the point in helping when someone has already helped u lol

[inner ibex]

bc ui are big

[left flower]

bro WolframAlpha is supposed to help me to think quicker i know the steps already

[left flower]

stop fighting

[smoky gyro]

What does that mean

[left flower]

btw the question has the 30th number = 85

[daring stag]

But in competitive exams wolfram alpha will not come in help

[left flower]

nah u can do some really good bruteforces for some question :
ex
(x+2y)^2+2x+5y+9=(y+z)^2

this question is from AOPS

,w (x+2y)^2+2x+5y+9=(y+z)^2

[woven radish]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by .ivmcs

[left flower]

you can find (x,y,z) easy

[inner ibex]

am i doing this right

no 😭😭😭😭😭😭😭😭

[left flower]

wait what question

th new one?

[inner ibex]

this one

[daring stag]

No

[inner ibex]

baaakaaaa ~~~

how then

[daring stag]

It should be a + 11d

[inner ibex]

wuett did. I do weong

omg

[daring stag]

Not a + 19d

[left flower]

yes

[inner ibex]

can u plz stop being mean to me 😔😔

[left flower]

what is the meaning of being mean

??

[daring stag]

Truth seems to be bitter

[left flower]

we did nothing bruv

[inner ibex]

ur being mean to me

[daring stag]

We should learn from our mistakes

[inner ibex]

😭😭😭😭😭😭😭😭

[left flower]

what do you expecting

[inner ibex]

can u plz buy me this

[left flower]

gimme you address

[daring stag]

@left flower is this man insane?

[left flower]

idk

[left flower]

he's weird + insane

idk he's trolling around

[inner ibex]

wtf

after i told yous to stop being rude

have u no manners

ok bai some math time

[left flower]

in what world u ask strangers to buy you something

[left flower]

if you're done do .close

[inner ibex]

well

sometimes some ppl feel generous

[left flower]

do .close

[inner ibex]

why didnt u say please 😭😭

[left flower]

just do that command if you don't wanna get any math help

[inner ibex]

.close

[devout snow]

Channel closed

Closed by @inner ibex

Use .reopen if this was a mistake.

[daring stag]

@left flower

Can we do with wolfram alpha

?

[left flower]

bro u're expecting to do every math problem with wolframalpha

[daring stag]

I am not telling that

[left flower]

btw that question can't but i know the answer

[daring stag]

But everytime we should solve by hand instead of using this program

[daring stag]

What's the answer?

[left flower]

if i am not mistake all odd number

[daring stag]

I also know

It was easy

[daring stag]

We can use lemma

[left flower]

the program was meant to ease our problem not to entirely solve it

[daring stag]

But it should be used only when you are master in algebra or something

[left flower]

yeah for this problem i know the steps already

so why not?

[daring stag]

I have one problem in a question

Can you solve it?

[left flower]

ur asking me to solve it?

[daring stag]

Ya?

[devout snow]

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

I have a question

[mild sorrel]

nO i NEED HELP with a question.

the question is not mad eby me.

Ok wait.

!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/

[boreal helm]

Yo

[mild sorrel]

hey

So, If DABC is a square

EDF = 45 deg

And DC = 1 cm = DA = AB = BC

Find the perimeter of EFB

@astral elk

omg I pinged helpers it's not even passed 15 minutes. It's illegal and I will now be banned ! 😦

or did I? I pinged Helper not Helper_s_ if you see closely.

please ping me if you help me.

<@&286206848099549185>

[mild sorrel]

.

[open vale]

@mild sorrel

[mild sorrel]

Yeah

Right time nice.

[open vale]

is there any other condition without angle EDF is 45

[mild sorrel]

Only that a square and 1 cm its side with EFD = 45 given.

[open vale]

if then insufficient condition

[mild sorrel]

Wiat let me give you the exact question.

[open vale]

question is angle of EFB?

[mild sorrel]

Wdym?

No.

5 sec.

In the figure, ABCD is a square of 1 cm and ang PAQ = 45 deg. The perimeterof the triangle PQC is:

ang EDF = ang PAQ

lemme tell you that the answer isn't 1+root2.

[open vale]

let me give you a hint

what if you rotate triangle DAE 90deg on the center of D

so that DA and DC equals

make sense?

[mild sorrel]

I didn't get this.

wdym center of D?

D is just a point.

[open vale]

make sense?

[mild sorrel]

yeah

[open vale]

if then EF = FA

[mild sorrel]

how?

[open vale]

that's because EDF = 45

so FDA = 45

clear?

[mild sorrel]

nope

oh

get it

[open vale]

so the answer is...

[open vale]

there?

[mild sorrel]

nope

[restive river]

Um hello I need help sorry I just joined idk how it works

Here question 6 mind helping please it’s urgent

[open vale]

let me explain

[mild sorrel]

yeah sure take your time.

[open vale]

B

[open vale]

answer is B

[restive river]

Tysm

[mild sorrel]

<@&286206848099549185>

[daring stag]

Yo

[boreal helm]

Yo

[mild sorrel]

Help please

[buoyant holly]

@restive river if you need help on how to actually solve problems like that lmk

[mild sorrel]

<@&286206848099549185>

[spark nymph]

alright so

[mild sorrel]

Yes.

[spark nymph]

You don't know anything else?

[spark nymph]

One way I am thinking of solving it is to use the similar triangle theory

[mild sorrel]

no.

[spark nymph]

You have tried?

[mild sorrel]

to you.

!status

[devout snow]

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

[spark nymph]

I have tried solving it but I have got no idea, sorry. Try using similar triangle theory

[mild sorrel]

got the answer thanks.

.close

[devout snow]

Channel closed

Closed by @mild sorrel

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[devout snow]

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[late flax]

Hi

I just want a hint

[devout snow]

@late flax Has your question been resolved?

[late flax]

<@&286206848099549185>

[spark nymph]

still need help? @late flax

[late flax]

Yup

I tried rewriting it in every possible way that i know of

[late flax]

Any ideas?

[spark nymph]

Second I have had something similar.

Did you try Taylor series?

[late flax]

What is that 😅

I just know very very basic stuff

It is supposed to be solved with them tho

[spark nymph]

I think yea

I could be wrong but I think you could solve it using it

[late flax]

Using what? The taylor series?

[spark nymph]

wait

Got no ideas sorry

[late flax]

Its alr

Thanks anyways

[spark nymph]

Maybe attempt to use permutations

[late flax]

Ok thanks ❤️

.close

[devout snow]

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[devout snow]

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[last sequoia]

28°20'20.4"S 48°42'07.2"W

[fleet moth]

?

[last sequoia]

im stuckings

helpings

[fleet moth]

What does that mean

[last sequoia]

28°20'20.4"S 48°42'07.2"W

[fleet moth]

What's the problem...

[last sequoia]

ugh

ur stped

[fleet moth]

U are the one asking ?

[topaz beacon]

,w 28°20'20.4"S 48°42'07.2"W

[woven radish]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by garlicbredfries

[topaz beacon]

tada

what are looking for?

[fleet moth]

That's what I'm asking lol

[topaz beacon]

bruh

[fleet moth]

??

U didn't give a question

U gave coordinates

[topaz beacon]

if theres something at that location, just look it up yourself

[fleet moth]

Yea lol

[topaz beacon]

if you type that in maps, itll give it to you

[fleet moth]

Ikr

[last sequoia]

u guys are severe mean

[fleet moth]

😭

[topaz beacon]

yknow ive seen you around and i thought you were better than this

<@&268886789983436800> trolling

[last sequoia]

ok ok stop

it's 3am and idk

HAHAHA

[topaz beacon]

!redir

[devout snow]

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

[fleet moth]

<@&268886789983436800> trolling

[dire forge]

If you don't have a question, don't use help channels

.close

[devout snow]

Channel closed

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[devout snow]

Available help channel!

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Remember:
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[dark bough]

.open

help

[dark bough]

someone help me do this chat gpt cant do it correctly

simplifying

[severe crystal]

u have to write both terms to have the same power of z

for the first term, notice that sqrt(10z^5) = sqrt(10)sqrt(z^5)

and sqrt(z^5) = z^(5/2)

for the second term we have sqrt(40)z^2*sqrt(z)

and sqrt(z) is z^(1/2)

can u take it from there

[dark bough]

so u have to seperate the variable and the coefficient into different square roots

[severe crystal]

yea the idea is you want the same power of z on both terms and then you can just subtract the numbers in front

so we have z^(5/2) in the first term

[dark bough]

and then z^1/2

[severe crystal]

try to make a z^(5/2) out of the second term

the 2nd term we have z^2*z^(1/2)

can you combine those

[dark bough]

that multiplies to just z right

[severe crystal]

it should be z^(2+1/2)

[dark bough]

oh

z^5/2

[severe crystal]

yup

so then you can just subtract the two terms directly

any idea how to do sqrt(10)-sqrt(40)?

[dark bough]

make the inside of the radical the same number

hol up

[severe crystal]

yep

[dark bough]

2 root 10

and root 10

so 3 root 10

[severe crystal]

its sqrt(10)-2sqrt(10)

[dark bough]

oh yeah i gotta write this down

so negative sqrt(10)

[severe crystal]

yes

[dark bough]

in the answer key it says the answer is -z^2 sqrt(10z)

[severe crystal]

yes same thing

bc the z^2*sqrt(z) becomes z^(5/2)

theyre the same answer

[dark bough]

do u know how to do it with multiple variables as well

[severe crystal]

yes

same idea

write any square root as exponent of 1/2

and then use properties of exponents

[dark bough]

so do u add 7 and 6 to 1/2

[severe crystal]

no

u cant combine any x’s with y’s

u have to leave them separate

try to combine all the y’s together, the x’s together, and all the #’s together

notice u can write the sqrt(150x^7y^6) as sqrt(150)sqrt(x^7)sqrt(y^6)

[dark bough]

i made sq root of 150 into 5sqrt(6) and then sq root of x^7 into x^2sqrt(x^3) and sq root of y^6 into y^2sqrt(y^2)

wait i did it wrong

[severe crystal]

you’re close

5sqrt(6) is correct

remember we said sqrt is the same thing as ^1/2

so sqrt(x^7) = (x^7)^(1/2)

[dark bough]

i got the answer 40x^3y^5sqrt(6x)

[severe crystal]

suuuper close

double check the y factor

everything else looks good

[dark bough]

its all multiplied by 8y^2 so 8y^2(y^3) gets y^5 on the inside right

[severe crystal]

oh nvm youre correct

my mistake

nice job

[dark bough]

oh

thanks for the help

[severe crystal]

np

[dark bough]

.close

[devout snow]

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[devout snow]

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[spring oak]

How to solve this one?

[devout snow]

@spring oak Has your question been resolved?

[safe jasper]

check if P is orthonormal

if it is, then P^T = P^-1

then P^T (Q^2005) P = P^T (PAP^T)^2005 P, and (PAP^T)^2005 would become PA^2005P^T so this could already just simplify X to A^2005

and A looks simple enough to compute powers of

[devout snow]

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[devout snow]

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[elder osprey]

I just want to understand step by step of how to solve this, I’m just confused atm

[wicked turtle]

try doing some row manipulations to make the 2nd and 3rd entries of column 1 equal to zero

(without changing the determinant)

[elder osprey]

R1 —> R1 - R3

R2 —> R2 - R3

Would this work?

[devout snow]

@elder osprey Has your question been resolved?

[elder osprey]

.close

[devout snow]

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[vague estuary]

Need help

[vague estuary]

How should I do this

That’s the original equation

<@&286206848099549185>

[covert root]

Use the unit circle definitions of the trig function

[vague estuary]

What do you mean?

[covert root]

The trig functions are defined using the unit circle

[vague estuary]

Yeah but what specifically should I look for

[covert root]

So you need to know the definition to perform the calculation

[vague estuary]

Ok what should I do next?

[covert root]

The answer comes directly after applying the definition.

I would rather not get into details of the unit circle definition of the trig function as it is quite visual. I think you should refer to YouTube. Also make sure you understand radians

[vague estuary]

I’m getting stuck on the sin2(pi) part

Negative pi

What does the 2 outside of the angle mean

[covert root]

using the unit circle definition you will find sin(2pi) = 0.

The 2 should not be outside the brackets

[vague estuary]

Ok

[covert root]

!done

[devout snow]

If you are done with this channel, please mark your problem as solved by typing .close

[vague estuary]

.close

[devout snow]

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[devout snow]

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[restive river]

If A is a non-empty set bounded from below in R, show that the set -A={-a/ae A} is bounded from above and sup(-A) = - infA.

[restive river]

Sorry if that doesn't make any sense

I used Google translate

😅

[radiant anvil]

what does {-a/ae A} mean?

{-a|a in A}?

[restive river]

Yes

@radiant anvil

<@&286206848099549185>

..

.close

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[willow wadi]

For the question below (referring back to the sine function general form being y = Asin(Bx - C) + D) wouldn't the phase be 3, as it represents C in this instance?

Also, if possible, PLEASE verify the other values below because i'm unsure 🙏
Amplitude: (5)
Period: (π)
Centre/Midline: (1)

[willow wadi]

apologies i should've included the image with the original question

[devout snow]

@willow wadi Has your question been resolved?

[willow wadi]

i got my question resolved mb

[devout snow]

@willow wadi Has your question been resolved?

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[quick anchor]

to prove the implication from right to left can we add complementary of A union in both sides so we get the expression in the left ?

[devout snow]

@quick anchor Has your question been resolved?

[devout snow]

@quick anchor Has your question been resolved?

[devout snow]

@quick anchor Has your question been resolved?

[quick anchor]

Not yet

[devout snow]

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[timber maple]

Hey, if the new triangle could be formed by dotted line, why the T angle doesn’t fit with 162 angle, as the table? TKX

[devout snow]

@timber maple Has your question been resolved?

[sudden yarrow]

you copied some angle wrong

W + U + (some other) should give you 180

but 123 + 85 is already greater than 180

unless you have somehow created negative angles

[devout snow]

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[viral lynx]

I dont see what I did wrong

(-3x-4)/(x+1)^2

A(x+1) + B

Ax + A + B

A = -3

A + B = -4

B = -1

A/(x+1) + B/(x+1)^2

-3/(x+1) - 1/(x+1)^2

Ah

I see

.close

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[long prairie]

idk how to solve this

[long prairie]

im doing x^(2)=36+16-2*6*4*cos10

but i get x = 2.17 which idk if its right

and from there idek how to get y

[devout snow]

@long prairie Has your question been resolved?

[north roost]

Ok

U know x right?

So, also cosine law

6^2 = 4^2 + x^2 - 2(4)(x)cos(y)

Do arccos, and you’re good

@long prairie

[long prairie]

so y is

151.4?

[north roost]

According to my calculator, not quite

But I’m using wolfram alpha lol

[devout snow]

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[mental rover]

Hey
Can I simplify $2 \times \frac{1}{x}$ to $2\frac{1}{x}$?
I guess no because in $2\frac{1}{x}$, between the 2 and $\frac{1}{x}$ it's like adding them, right?

[woven radish]

𝓣𝓪𝓼𝓴

[dense jay]

its not really a simplification by any means, but sure

[olive snow]

You can write 2/x

Too

[dense jay]

i dont believe in mixed fractions, they do not exist in mine eyes

[trail eagle]

Mixed numbers are used seldom, since the multiplication sign is mostly omitted.

[mental rover]

Ok

[mental rover]

So you say because it is confusing since we don't write the multiplication sign on mixed numbers? Just to make sure I understand what you say

[distant plume]

can you guys please help me too?

[trail eagle]

Yeah. Conventionally, symbols strung together are multiplied.
Mixed numbers are not used enough to warrant changing that, so instead we just avoid using them to prevent ambiguity.

As your example exhibits, how would you differentiate between someone who means $2 \cross \frac{1}{x}$ or $2\frac{1}{x}$ if both use the same notation?

[woven radish]

Azyrashacorki

[mental rover]

Ok thanks!

.close

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[white topaz]

i keep getting 0 and error depending on the way I solve this what am i doing wrong

[radiant hare]

How did you solve it

[white topaz]

bcz when i put it in calculators it gives error but when i hand solve it i did [tanx]from 0 to pi

and that became tan(pi)-tan(0)=0

[radiant hare]

Look at tangent graph

,w Plot tan(x) from 0 to pi

[white topaz]

at 0 its 0

[radiant hare]

Or rather look at sec2(x)

,w Plot sec^2(x) from 0 to pi

[woven radish]

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[white topaz]

wait since the area under this doesn't work

would it be none of the above?

[radiant hare]

Yeah

[white topaz]

ohh ok ty

.close

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[tardy stag]

A recycling company in Colorado collects three types of recyclable materials: paper, plastic, and glass. The company has a limited capacity to process each type of material and wants to maximize the total amount of material it can recycle while minimizing the transportation and processing costs. Data:

The company can process a maximum of 100 tons of paper per day.
The company can process a maximum of 80 tons of plastic per day.
The company can process a maximum of 60 tons of glass per day.
The cost to transport and process one ton of paper is 20USD.
The cost to transport and process one ton of plastic is 30USD.
The cost to transport and process one ton of glass is 40USD.

[tardy stag]

It's about linear programming btw

[devout snow]

@tardy stag Has your question been resolved?

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[native aspen]

<@&286206848099549185>

[dire forge]

Please don't ping Helpers before 15 minutes have passed

[native aspen]

my bad

can you help me

[devout snow]

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[tardy stag]

A recycling company in Colorado collects three types of recyclable materials: paper, plastic, and glass. The company has a limited capacity to process each type of material and wants to maximize the total amount of material it can recycle while minimizing the transportation and processing costs. Data:

The company can process a maximum of 100 tons of paper per day.
The company can process a maximum of 80 tons of plastic per day.
The company can process a maximum of 60 tons of glass per day.
The cost to transport and process one ton of paper is 20USD.
The cost to transport and process one ton of plastic is 30USD.
The cost to transport and process one ton of glass is 40USD.

[tardy stag]

can you help me with this one

i tried to solve it but i got 3 variables and no restrictions

it's about linear programming

can anyone check it?

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[tardy stag]

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@tardy stag Has your question been resolved?

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[gentle heron]

this function is non periodic right?

[crisp zealot]

Assuming it keeps the same patterns, yes

[gentle heron]

as long as it keeps increasing like that?

[crisp zealot]

Although you can never tell from looking at a finite interval

[gentle heron]

if it stops right there

is non periodic?

[crisp zealot]

Periodic on what?

[gentle heron]

it only asks if it is non-periodic

[crisp zealot]

I would go with yes

[gentle heron]

Okok

[crisp zealot]

It is non-periodic

[gentle heron]

I also had trouble with two others

[gentle heron]

thanks

Im not sure how to do this one

could you explain it please?

[crisp zealot]

Periodic means does the pattern repeat

[gentle heron]

yeah

[crisp zealot]

Does it?

[gentle heron]

Yes

[crisp zealot]

I think then you know how this works

[gentle heron]

so is it just the same as the question before?

worded differently

[crisp zealot]

Oh sorry I didn't see the question at the top of the pic

[gentle heron]

Ohhh ok

how would it work then?

[crisp zealot]

It is asking what how long is the section that repeats

[gentle heron]

50s?

[crisp zealot]

If we cut the x-axis in blocks in which the image looks identical

How wide is each block

[gentle heron]

OHHHHH

10s?

[crisp zealot]

Yes!

[gentle heron]

I remember that know

that makes sense

so the answer would be, the period of the function is 10s?

[crisp zealot]

A function is periodic with period T if f(x)=f(x+T) for all points in the domain

[gentle heron]

okok that makes sense

so then is this one like the height of it?

or is it different?

[crisp zealot]

It is either the height or half the height

Depending on how you define it

[gentle heron]

what do you mean?

for the amplitude?

[crisp zealot]

Some people call "peak to peak amplitude," amplitude

Though it is less common

[gentle heron]

peak to peak would be the whole thing right?

[crisp zealot]

Normally people use half the peak to peak

When talking about amplitude

[gentle heron]

do you know which one it is asking for tho?

[crisp zealot]

Ask your source for the problem

[crisp zealot]

Default to this though imo

[gentle heron]

Like the teacher?

[gentle heron]

what would it be in that case then?

[crisp zealot]

Or notes/textbook

[gentle heron]

if it is half

or the common one

that way I can already know in case it is half

[crisp zealot]

Purple is what we usually call amplitude

Green is peak to peak

[gentle heron]

so from 0 to 2?

that is half

[crisp zealot]

No

[gentle heron]

how does it work then?

[crisp zealot]

Look at the graph

[gentle heron]

.5 to 2?

[crisp zealot]

0 is distinctly not in the middle of the green

[crisp zealot]

Right, the difference of those 2

[gentle heron]

ohhhhh

I see it now

[gentle heron]

what do you mean the difference?

[crisp zealot]

Amplitude is one number

[gentle heron]

yeah

so 1.5?

[crisp zealot]

Yes

[gentle heron]

so answer would be, amplitude of the periodic function is 1.5

no units?

is a graph so I would guess not lol

[crisp zealot]

Units is whatever the units of y-axis are

[gentle heron]

it doesn't say any so ill just leave it blank

so peak to peak would be 2?

[crisp zealot]

No

[gentle heron]

why not?

isnt it the diff between 0 and 2

oh wait nvm

I got confused

is at one

so diff between 1 and 2

1 then?

[crisp zealot]

Go back to the picture I drew

[gentle heron]

yeah

does the -1 influence it?

[crisp zealot]

Of course

[gentle heron]

oh mb

im slow

3?

I thought about the negative one only after I said it was 1 😭

HOL ON

IM STUPID

If half is 1.5 then ofc peak to peak is 3 😭

im way too slow sometimes

esp for math

I got one last one

I just want to double check it

would the value of f(15) be 8?

[crisp zealot]

This function takes values between 3 and -3

No idea how you got 8

[gentle heron]

yeah math aint my forte

what's the right way to do it?

0.7764?

g(x)=3sin(x) right?

and that then you go from that?

<@&286206848099549185> sorry im using it but I just need help with the question. I waited a couple minutes before pinging.

[boreal helm]

Yooooo

Me here

[gentle heron]

helloo

[boreal helm]

What u want

Yo

[gentle heron]

I was struggling with the question in the pic

[gentle heron]

this one

[boreal helm]

This

[gentle heron]

yes

ik is not 8

[boreal helm]

Function is even

[gentle heron]

then I said ths stuff

[boreal helm]

Tell me how it is even

[gentle heron]

goes from -3 to 3?

[boreal helm]

Do you know even function

[rugged crater]

hi

[gentle heron]

cant say for sure I do

sorry

[boreal helm]

Listen

if for x and -x function spits same value it is even

Like here function has same value at 2,-2

[gentle heron]

so like I said 3 and -3?

[olive snow]

1 and -1 ?

[boreal helm]

Wait I saw it

Now

It's not even

Only f(2)=f(-2)

A even function spits the same value for x and -x for every value of x

@gentle heron

[gentle heron]

mmmm

[rugged crater]

-5,0

doesn’t it just keep repeating so you find the values of that and then multiply by 3

[olive snow]

A cool proprety with the graph is that it does an axis-symetry when even function

[rugged crater]

right ?

[olive snow]

With y axis

[gentle heron]

hold on

[rugged crater]

wait

[gentle heron]

im confused tho

[boreal helm]

Pattern is getting copied

[rugged crater]

sorry nvm

[boreal helm]

Understand the pattern and draw the further graph

[gentle heron]

is what I said about g(x)=3sin(x) right?

[boreal helm]

Wait let me see

[gentle heron]

or no

[rugged crater]

wouldn’t it just be -3 then

[boreal helm]

How you got g(x)=3sinx

Do u know graph of 3sinx

[rugged crater]

that compresses it

[boreal helm]

Graph of 3sinx is smooth

[gentle heron]

no

[rugged crater]

ohhh

[boreal helm]

It is not like this

[gentle heron]

makes sense

[boreal helm]

Send picture here again

[gentle heron]

there

[rugged crater]

i think f(15) would just be -3

or is your question different

[gentle heron]

how do you know tho?

yeah I just want to determine f(15)

[rugged crater]

bc every interval of 5 starting at -5 is -3

it’s a pattern

then yea i’m pretty sure it’s -3

[boreal helm]

!nosolns

Bro u told him soln

We have to help him

[gentle heron]

oh

[boreal helm]

U told him directly the answer

[rugged crater]

my bad i didn’t know

[gentle heron]

thanks tho

[rugged crater]

i did not know i couldn’t do it

i can explain it tho

[boreal helm]

Did u understand @gentle heron

[gentle heron]

yeah I would appreciate it

no thats why I asked

[boreal helm]

Okok explain him

[gentle heron]

if I only put in the answer without understanding then im screwed for the test lol

[boreal helm]

Yes

[rugged crater]

okay so the function is a periodic function

where the graph basically repeats itself

examples are like sin cos and tan

[gentle heron]

yes

that makes sense

[rugged crater]

there’s an interval within the function where it just keeps repeating

[boreal helm]

And the length after which it repeats itself is called it's period

[gentle heron]

Yesss

im understanding it

[boreal helm]

Now see the graph and tell what maybe it's period

[rugged crater]

the graph you were given within the question is one of them and it repeats from -5 to 0

[boreal helm]

Wait bro let him aaah

[gentle heron]

MMMMMM

YESSS

[rugged crater]

sorry

[gentle heron]

Good tho

[rugged crater]

alright ima shut up

[gentle heron]

I was going to say that

[boreal helm]

Okok good

Oolig explained well

[gentle heron]

bc it goes from -5 on the x axis to 0 right?

[rugged crater]

thank youuu and i’m sorry i didn’t know before hand

[gentle heron]

and keeps going

[rugged crater]

yes yes

[boreal helm]

Yes

He got it

[gentle heron]

yay

[rugged crater]

and that makes it easier for us to get answer

[gentle heron]

hahaah

[rugged crater]

good job !!!

[gentle heron]

thanks a lot

I really appreciate it

[rugged crater]

i’m sure you’re going to do well on ur test

[boreal helm]

Now tell what is f(5)

[gentle heron]

like genuinely

-3 then?

[boreal helm]

Yea keep grinding test will become a cake walk for you

Yea u got it

[gentle heron]

good

thanks a lot @boreal helm and @rugged crater

[rugged crater]

good jobbb !!

[boreal helm]

Good all the best

[gentle heron]

you guys explained it very good :))

it wsa very clear

[boreal helm]

.close

[rugged crater]

no problem and you picked it up pretty quick

[gentle heron]

thank youuu

[boreal helm]

Yea he understood quick

[gentle heron]

im glad I did

again thanks to you two

[boreal helm]

Np welcome

[gentle heron]

ill close the channel now

[boreal helm]

yea ok

[gentle heron]

hopefully I do well on the test then

imma study this tmrw morning

gnnn

.close

[boreal helm]

Gn

[devout snow]

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[finite briar]

yo, anyone know how to find A_0?

from https://en.wikipedia.org/wiki/Recurrence_relation#Solving

[finite briar]

I think I can convert the product to a sum

and then do some sum stuff

[uncut crow]

is it not just a_0/f_0

[finite briar]

the -1 causes a problem

'n-1'

[uncut crow]

oh

[iron sun]

arent they defined to be 1 (likewise 0 for sums) if the product is empty (resp. if the sum is empty)

e.g. if we have an upper bound which is less than the lower bound

[finite briar]

Idk i think yeah

[iron sun]

usually thats by definition, so that they make sense

[finite briar]

https://math.stackexchange.com/questions/35080/upper-limit-of-summation-index-lower-than-lower-limit suggests the same thing

[iron sun]

i guess if i instead ask this, does it make sense for A_0 = a_0 ?

[finite briar]

not really imo

but the definition suggests this only

[iron sun]

im out of ideas, hopefully someone else might chime in and help unless u find something more about this specific type of recursion

[finite briar]

hmm

i'll see

thanks

.close

[devout snow]

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[limber nimbus]

I'm trying to find F'(x), which is apparently 2x * sqrt(3x^2 +1), but I'm not sure what I did wrong.

[sand dove]

chain rule

for starters you didn't take into account the derivative of 3(x^2-1)+4, then f(x) is wrong from the start I believe (the factor should be 2/9)

and finally, you're not required to find f(x) if you want F'(x)

you just need to write the chain rule of derivation formula

[devout snow]

@limber nimbus Has your question been resolved?

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[urban harbor]

for a) for this problem in Axler, i've managed to show that if the set spans V' then gamma is injective, but i'm at a bit of a loss of how to do the proof for the other way

[urban harbor]

V' is dual space by the way, i think some books write it V*

<@&286206848099549185>

[devout snow]

@urban harbor Has your question been resolved?

[magic thicket]

@wanton temple

[timber pebble]

i dont have a solution but this is a fun problem

[magic thicket]

if it doesn't span V', find a nontrivial element of Ker(gamma)
equivalently, ||the intersection of their kernels is not {0} but something larger||
||consider the associated set of vectors in V. Use the fact it is not spanning||

[urban harbor]

hmm

i was kinda trying to do something like that and failing

may have found a different approach

[magic thicket]

does Axler cover Riesz's theorem or is that later?

[urban harbor]

apparently later

[magic thicket]

right
annoying

[magic thicket]

that kinda does rely on it

so what do you know about V'?

[urban harbor]

my only thought with that approach to find something in the ker gamma is
assume gamma is injective and there's some linear functional psi not in the span of the phis: there's some nonzero vector v for which psi(v) =/= 0 and i have a feeling gamma(v) = 0 but not sure how to show that

[magic thicket]

yeah that's what I do, but I'm not sure if you can

[urban harbor]

i think i found another method, lemme see if i can think it out here

ill just call gamma G for simplicity
so if G is injective then the dual map G': F^m' -> V' is surjective, so for every phi in V' there's some f in F^m' so that G'(f) = phi

[wanton temple]

....

oh hell no

[arctic field]

?

[arctic field]

[magic thicket]

didn't you solve it?
Is it still not done?

[arctic field]

i tortured kia with this problem the other day

[urban harbor]

it is torturing me too

the other direction was like really simple and this one i find really hard for some reason

[wanton temple]

no it's just

after spending 4h on it

I do not want to look at it

[urban harbor]

lol

so G'(f) = f(G) right?

which is f(phi1, ...phi_m) = phi still

so that's kind of phi as a linear combination of the set almost?

f : F^m -> F

[magic thicket]

f in (F^m)' so F^m -> F

[urban harbor]

so wait can we use this to write phi as a linear combination, i thought i had it in my brain a minute ago but maybe my brain is just fried now 😄

[magic thicket]

f(ai) = sum fi ai
phi = sum fi phi_i

[urban harbor]

ok

i hope b) is easier

lol

[wanton temple]

honestly, imo, it was equally pain

[urban harbor]

btw how do you write the dual space of F^m, latex seems to give some double super script error if i try using $mathbb{F}^m'$

$\mathbb{F}^m'$

[woven radish]

∫oosh (lemonsaurus appreciator)

$\mathbb{F}^m'$
```Compilation error:```! Double superscript.
<recently read> ^
                 
l.80 $\mathbb{F}^m'
                   $
I treat `x^1^2' essentially like `x^1{}^2'.

Preview: Tightpage -1310720 -1310720 1310720 1310720
[1{/usr/local/texlive/2023/texmf-var/fonts/map/pdftex/updmap/pdftex.map}{/usr/l
ocal/texlive/2023/texmf-dist/fonts/enc/dvips/lm/lm-mathit.enc}{/usr/local/texli
ve/2023/texmf-dist/fonts/enc/dvips/lm/lm-mathsy.enc}] (./218476117101772801.aux```

[urban harbor]

seems to render but it isnt happy about double superscript 🤷‍♂️ what's the proper way to do it?

[arctic field]

,, \mathbb F^{m\prime}

[wanton temple]

crap

nearly got sniped

[urban harbor]

ty

[devout snow]

@urban harbor Has your question been resolved?

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[devout snow]

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[cursive skiff]

Can someone please help with 16 and 19

[olive snow]

Apply formula of the slope

[devout snow]

@cursive skiff Has your question been resolved?

[cursive skiff]

How

[olive snow]

Y2-Y1 / X2-X1

[devout snow]

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[cursive skiff]

Then what

[olive snow]

What do you get ?

[cursive skiff]

2/-7

[olive snow]

Should be 2/7

[cursive skiff]

It’s -3 - 4

[olive snow]

And on top ?

[cursive skiff]

5-7

[olive snow]

So -2/-7

[tranquil flower]

-x/-x = 1

[cursive skiff]

Yea that’s what I meant

Okay

[olive snow]

So 2/7 after simplify minus sign

[cursive skiff]

So I’m just supposed to take the minus sign away?

How do I know when to do that

[olive snow]

Like this

[cursive skiff]

Okay

Now what

[olive snow]

When its on top and bot

Anyway you have y = 2/7 * x + p

Choose 1 point

[cursive skiff]

X + p ??

[tranquil flower]

p or b same thing

just a variable

for constant

[cursive skiff]

Okay

Wdym choose one point

[tranquil flower]

they gave you cooridnates

right?

[olive snow]

Among the two in the exercice

[tranquil flower]

(x,y)

is a point

[cursive skiff]

Okay (-3, 5)

[tranquil flower]

so sub those values into your equation that you got : y = 2/7 * x + p

[olive snow]

And solve for p

[tranquil flower]

@olive snow sorry for interrupting

was bored waiting for help on my question

[olive snow]

Nah dont, pair work is great

[cursive skiff]

So like would it’s be y = 2/7 * -3 + 5

[olive snow]

No y is 5

[tranquil flower]

not quite

[cursive skiff]

Then what’s X and p

[tranquil flower]

p is the value we're trying to find

(x,y) remember this notation?

[cursive skiff]

Yes

[olive snow]

(x,y) ==> (-3,5)

Just replace carefully

[cursive skiff]

So I have 5 = 2/7 * -3 + ___

[tranquil flower]

yes

now isolate for ___

[cursive skiff]

So how do I find the blank

[tranquil flower]

do you remember how to isolate for a variable?

[olive snow]

Send all you know to the left

[cursive skiff]

What

[olive snow]

Like solving an equation

[cursive skiff]

I’m confused

[tranquil flower]

let me write it out so you can see

[cursive skiff]

Ok

[tranquil flower]

here

so how would you move the values over?

[olive snow]

That flashbang me xd

[tranquil flower]

mb xd

i have to buy the pro version of the app im using on my ipad to be able to change paper colour

broke student life

[tranquil flower]

@cursive skiff

[olive snow]

No crack version ?

[cursive skiff]

I’m not sure

[tranquil flower]

nahh can find it xd

[tranquil flower]

alright ill explain it

when moving terms from one side to the other you have to basically take that term and perform the opposite of what the term is

so if we have 10 + x = 1

to move the 10 over to the other side

we have to?

[cursive skiff]

-10?

[tranquil flower]

yes

and we have to do that to both sides

so we'll get?

[cursive skiff]

So am I plussing 5 then for this one

I mean taking away

[tranquil flower]

well

we want to have b by its self on the right side

[cursive skiff]

+3?

[tranquil flower]

remember that its not 2/7-3 but 2/7 * (-3)

[cursive skiff]

Okay

[tranquil flower]

because we have the form y = mx + b

[cursive skiff]

Okay

So what do I do

[tranquil flower]

to make it easier lets simplify 2/7 * (-3)

what does this give you?

[cursive skiff]

Not sure

[tranquil flower]

do you remember how to multiply fractions>

[cursive skiff]

Nope

I’m in summer break mode still don’t remember a lot😂

[tranquil flower]

ok so if you have 2/7 *3, you have to make the 3 whole's as a fraction of 1/7 th

[cursive skiff]

No idea

[tranquil flower]

so 1 whole is what?

[cursive skiff]

1?

[tranquil flower]

in terms of 1/7

[cursive skiff]

Wdym

[tranquil flower]

say 1/2 is half right?

whats 1 whole

[cursive skiff]

2/2

[tranquil flower]

yes

whats one whole of 1/7

[cursive skiff]

So it’d be 7/7

[tranquil flower]

yes

now we need 3 wholes

that would be?

[cursive skiff]

21?

[tranquil flower]

nice!

now back to the question

2/7 * 3

so we want 3 as a fraction of 1/7

[cursive skiff]

So 21?

[tranquil flower]

not quite 21

but you're close

[cursive skiff]

Idk what I’m trying to do

[tranquil flower]

it would be 21/7

[cursive skiff]

Why

[tranquil flower]

because 7/7 = 1, 14/7 = 2

right?

[cursive skiff]

Yea

[tranquil flower]

so 21/7 = 3

[cursive skiff]

I don’t understand where we got that from tho

[tranquil flower]

here

2/7 *(-3)

[cursive skiff]

Don’t understand how that turns into 21/7

[tranquil flower]

when dealing with fractions

we want to have a common denominator right?

[cursive skiff]

Yes

[tranquil flower]

so 2/7 x 3