help-0

[wet linden]

would equal sqrt -7

which is not a real root

so it cant be that

holy chatgpt

[dim terrace]

whered you get 7

[dim terrace]

i thought we were doing the first one

whoops

okay so

its 4

X=5

[wet linden]

ye

you could also find the domain which would be {7/2, infinity)

[dim terrace]

omg finally

mhm

[wet linden]

so you know it would be answer choice x=5 but

[tidal fox]

The domain of a function is the set of all values ​​of x for which the function is defined. In this case, the function f(x)= (3x+2)/2x-10) is not defined when the denominator is equal to 0. This occurs when x=5. Therefore, the only value of x that is not in the domain of the function is x=5.

Justification:

If you try to calculate f(5), you get the following division:

f(5) = (3(5)+2)/(2(5)-10) = 17/-2
This division is undefined, therefore f(5) is an undefined value.

[wet linden]

bro is the chatgpt king

[dim terrace]

word

[wet linden]

but bascially just remember

the denominator can never equal 0

[tidal fox]

I just told chatgpt to tell me how to justify it, I already knew the result, the evaluations are easier there, here they are more difficult

[dim terrace]

okayokay

[wet linden]

it looks like this graphed

[dim terrace]

good to know

[wet linden]

it apporaches x=-3 but never touches it

[tidal fox]

this

[dim terrace]

so is that it

[tidal fox]

yeah!!!!!!!!!!!!!!!!!!!!!!

i love you ANNA cogratulaions

[dim terrace]

mans is tryna help so bad

thanks fam 🙏

[wet linden]

Well

F(x) is not equal to 5

F(x) is y

[tidal fox]

propus is my f* father

yes

[wet linden]

You said y = 5

[dim terrace]

whoops

[tidal fox]

ok yeah y is 5

[dim terrace]

so x=5

[tidal fox]

yesss

[wet linden]

And you forgot the square root at the bottom but

Ye they should be enough to justify the answer

[dim terrace]

thank you for your service 🫡

[tidal fox]

Anna, if you need help, here I am, be careful with your limits.

[dim terrace]

stfu 💀

[tidal fox]

you´re welcome

[lone heart]

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[bronze rock]

find the limit if it exists

answer is suppose to be 2

i know i’m suppose to factor/simplify something ?

[fierce prairie]

yeah, you can factor the numerator

[tardy stag]

yeah indeterminate form doesn't mean undefined; it means you have more work to do :)

[bronze rock]

yes

correct ?

i love all of you

[tardy stag]

👍

[bronze rock]

question

is it only undetermined in both numerator and denominator are 0?

0/0

if i have let’s say 8/0

limit simply doesn’t exist ?

[tardy stag]

if you have 8/0 it either goes to +inf, -inf, or dne

if your class says infinite limits dne then that's even easier

[bronze rock]

i’m not too sure what my class says but the answer key the limit does not exist

1/8 or just no limit ?

[tardy stag]

look at what you canceled

[bronze rock]

omg

oh

so (t-4)

is 0

thank you

[tardy stag]

ya

so 1/0

indeterminate forms

[bronze rock]

so even after factoring the whole way

and the answer is still over zero

that’s when the limit does not exist

[tardy stag]

when your test evaluation yields n / 0

where n ≠ 0

then yeah it's either ±∞ or DNE

which your curiculum seems to combine (that's unpopular but fine)

[bronze rock]

thank you

[lone heart]

@bronze rock Has your question been resolved?

[sonic haven]

help

how to find pythagoream therom

of iscoelese triangle

[jagged cobalt]

you need to go to your own channel

[lone heart]

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[proud wyvern]

Have no idea how to do this question. Graphically, a horizontal tangent line means slope is 0 right?

[proven leaf]

yes that's what it means graphically but do you know how to calculate such points?

[proud wyvern]

This my work

Forgot the squared part at the end mb

[long axle]

ur right there

[proven leaf]

yep! that's right now you have the slope function so when is the slope 0 then?

[proud wyvern]

When x is 16

The part where I'm confused is how do I get my second y value

It's probably trivial but im genuinely confused

[proven leaf]

simply put x=16 into f(x)

[proud wyvern]

The original function?

[proven leaf]

we have the x-value at which the slope=0

now we need to find the y-value

the way you do that is by plugging it into the function, yes :)

[proud wyvern]

I got 32

[proven leaf]

[proud wyvern]

My question is why plug back in to original function

[proven leaf]

we are interested in the slope of the original function, yes?

[proud wyvern]

Yes

[proven leaf]

if we plugged x=16 back into the derivative we'd just get 0 again

[proven leaf]

simply because that is what we got by setting the derivative=0

[proud wyvern]

I'll try to remember that but atleast I know a horizontal tangent is essentially a horizontal line with no slope

Thank you for the help

.close

[lone heart]

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[prime sonnet]

Hi! For part (b) of the following question, I was wondering if my answer is correct. It is very long and I am not sure how to condense it down or whether I am missing something.

[lone heart]

@prime sonnet Has your question been resolved?

[prime sonnet]

<@&286206848099549185>

[lone heart]

@prime sonnet Has your question been resolved?

[prime sonnet]

its fine i think its right

[lone heart]

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[ripe panther]

Can anyone help me with this exercise?

[median oar]

I hope the exercise is getting sent and loading

[naive valley]

!status

[lone heart]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[naive valley]

have you tried multiplying and dividing by the conjugate of the denominator?

[lone heart]

@ripe panther Has your question been resolved?

[blissful whale]

substitute x² + y² with r²

then send r -> 0

[lone heart]

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[wise warren]

a_n = (3/4)^n

This is a strong decreasing series which converges at 0.
How am i supposed to figure out if some function or series converges at a certain point with analysis alone, without having a program graph it for me, or solving for big n values?

[remote heron]

do you mean converges to 0?

[wise warren]

Yes, if n goes to infinity.

[remote heron]

i think the golden standard is epsilon delta stuff

but this is more proof than figure out

[wise warren]

oh so with tolerance of epsilon

[remote heron]

to me if i wanted to convince myself

id show that the sequence is always decreasing

and that its always positive

and

[wise warren]

ahhh thats clever

[remote heron]

well this doesnt show its 0

because it could be converging to you know some other value but

just staring at this thing its kind of clear the possibilities right

[wise warren]

well epsilon kinda hints to it since its the difference between its limit and a_n when n > some natural number

[remote heron]

either its stuck at some value forever, it goes to 0, or it explodes

[wise warren]

If i have you here already

im kinda dumb

[remote heron]

this is the way youd formally show it, yea

[wise warren]

and im trying to do stuff with analysis alone

how do i even know if a series is decreasing

without pluging in any n values

i tried (3/4)^n+1 - (3/4)^n

[remote heron]

yea this is what id use

[wise warren]

which if negative hints that it decreases

[wise warren]

but how do you simplify that

[remote heron]

try using a ratio instead of a difference

[wise warren]

ah so quotient

will it also be negative if its decreasing?

[remote heron]

you'd want that $\qty| \frac{a_{n+1} }{ a_n } | <1$

[ocean seal]

jan Niku

[remote heron]

for all n

if youre just convincing yourself id just do it for n+1 and n

[wise warren]

right right

ty sir!

[remote heron]

[wise warren]

.close

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[remote heron]

<@&268886789983436800>

[lone heart]

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[north plover]

A is a subset of real numbers. An natural numbers are 0, 1, 2, 3...

1. we say that A is naturally increasing if: for every x that is an element ofA, there exist a y that is an element of A such that x does not equal to y and y-x is an element of natural numbers.
2. we say that A is spottily decreasing if there exist an x that is an element of A such that for every y that is an element of A, x-y is an element of natural numbers.

with the statements above, is it true or false. If A is spottily decreasing, then A is naturally increasing.

[north plover]

Hi, we havent learned how to right proofs yet but this is a hw

[rose sigil]

any thoughts?

[north plover]

I think that it is true but idk how to prove it

[north plover]

Because for example, set A= (0,1,2,3,4,5,...) is increasing and set B=(5,4,3,2,1,0) is decreasing. So both could be increasing or decreasing. I just dont know how to write the proof

[rose sigil]

hmm

you are right but that doesn't important to the problem?

If A is spottily decreasing, then A is naturally increasing

just one A at play

the same set

[north plover]

so the answer is not true?

[rose sigil]

i didn't say that haha but yes that's something to consider

[north plover]

A=(0,1,2,3,4,5,..), then it is increasing. Therefore, there will always be a number bigger than the last one.

And therefore cannot have a number that is bigger than the rest

[rose sigil]

oh that's a little bit different than what it's asking

it sounds like you just disproved: if A is increasing then A is decreasing

[north plover]

yea it was a true or false quesiton

but idk how to write proofs lol

[rose sigil]

ya but it's asking you if
if A is decreasing then A is increasing
is true

[north plover]

I think its false no?

[rose sigil]

yea it is false

do you have an example to show that?

[rose sigil]

for this one writing the proof won't be so hard

all you have to do is present a counterexample

[north plover]

A = (0,1,2,3,4,5, ...)

There will alwasy be a number bigger than the last one

[rose sigil]

yes but...

you want a set that IS decreasing but is not increasing

[north plover]

oh ok then A= (5,4,3,2,1,0) if x=5, then every other number will be smaller. However, there wont be a number thats bigger...

that satisfies ( we say that A is spottily decreasing if there exist an x that is an element of A such that for every y that is an element of A, x-y is an element of natural numbers.)

[rose sigil]

i agree that's decreasing

ok yes and it is not increasing

gr8

so that example totally works but i'll also just add you can use any one element set as a counterexample too

like {0}

[north plover]

can you explain

[rose sigil]

it's decreasing because there is an x in A (only one choice anyway, it's 0) such that if you subtract any element in the set from 0, you get a natural number

[north plover]

but it is also increasing no?

[rose sigil]

how?

[north plover]

because 0-0=0

no nvm

x cannot be y

sorry

forgot that

[rose sigil]

yep that's the important property

[north plover]

would this work?

We haven't learned the steps to write a proof yet

[rose sigil]

hmm

so stating it's spottily decreasing and not naturally increasing is good

but the explanations for those are... idk... symbol soup?

[north plover]

yea that the problem idk how to write proofs :(((

[rose sigil]

haha issok

i would focus on writing some words

like...
A is spottily decreasing because 0 is in A and every y in A has the property that 0 - y is a natural number

since 0 - 0 is a natural number

or something like this might be easier to follow...

let x = 0. then for every y in A, x - y is a natural number since 0 - 0 is a natural number

just explain in words and some symbols along the way why A has the property in the decreasing defn but fails the one in the increasing definition

[north plover]

and let x=0, then for every y in A, x=y which would counter the definition of spottily decreasing

is that ok

[rose sigil]

you mean naturally increasing?

[north plover]

yea mbd

[rose sigil]

then yea sure

there's no y in A with the property that 0 does not equal to y and y-0 is an element of natural (because there's no y in A with 0 does not equal to y)

[north plover]

ok thank you so much for your time. You helped a ton...

[rose sigil]

no problem ^_^

[north plover]

.close

[lone heart]

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[slender fulcrum]

I’m only in 8th grade so VERY young compared to university and stuff but I need help with Scientific notation specifically division and stuff related to that. I’m also in dire need of help because a passing grade is a 75% I have a 17%!

[civic shell]

I need help with one last question on my hw

College algebra

[shy dove]

get your own channel then. This is someone elses'. You can see the available channels under the category "MATH HELP (AVAILABLE)". You may also want to check #❓how-to-get-help

[shy dove]

Do you have any specific example of stuff you need help with? Like a problem you don't understand or something like that. It's hard to help someone with a query this broad

[slender fulcrum]

Oh wait I misunderstood the purpose of this I’m essentially looking for tutoring sorry for misunderstanding I’ll read the rules and stuff closer next time I apologize

Imma go get some paid tutoring now sry for taking up your time

[shy dove]

oh no worries. But yeah, this is more of an "ask a question-get an answer" type server than tutoring :)

[lone heart]

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[quaint meadow]

Hello, I was wondering why this got positive 25pi/4 I ended up getting -25pi/4 I'm trying to see where my mistake occurred during this process because I do not see it,

[mellow shuttle]

can you show your work?

[mellow shuttle]

wait

isn't arcsin of 0 equal to 0

@quaint meadow

[quaint meadow]

o ur right

big oof

thank u

.close

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[night mountain]

Can someone help me with this? I've drawn the free body diagrams but I don't know how exactly to translate some of the masses through the tension.

[night mountain]

For instance, m4 has the applied force on the right of 20N, and then has T_c pulling left, but I'm not sure how to find the force of T_c.

[lone heart]

@night mountain Has your question been resolved?

[night mountain]

.close

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[sand pawn]

Can anyone tell me any shortcut way of doing this?

I know the original and actual way of doing determinant and find the answer

but I am wondering, if this type of math come into a math test, how can I quickly find the value of 'x'?

[vapid shuttle]

I mean you can quickly compute this determinant

[sand pawn]

any more short and clever way to eliminate the options?

[vapid shuttle]

if there is an immediate way that you can see to make two columns/rows dependent by choosing x

that would be a clever way

but I don't see it here

considering the options are 5/2,-31/10, 3/37 the choice of x here is not going to be obvious

[sand pawn]

wdym?

[vapid shuttle]

if say two of the columns were

<1,1,1> and <x,1,1>

an obvious choice of x to make the determinant 0 would be x=1

right

but here the choices of x are clearly not obvious

so the determinant is probably your best bet

[naive valley]

technically none of the answers is correct

there is an x that works, but it's not one of A,B,C

but "D: none" is also false

you can check that x=31/10 works

[rose sigil]

i think we have to take D as meaning none of the before options

[naive valley]

it's not my assignment, i don't have to take it at all 😀

it's stupidly written, and the instructor should be complained to

[rose sigil]

i prefer to take D

[lone heart]

@sand pawn Has your question been resolved?

[vapid shuttle]

how did this happen

[lone heart]

@sand pawn Has your question been resolved?

[sand pawn]

I hate my mind

[rose sigil]

i love my mind

[echo socket]

I guess you could just
[ \begin{vmatrix} 1+x & x & 2 \ 3 & 2 & 1 \ 2 & 5 & 7 \end{vmatrix} = \begin{vmatrix} x-5 & x-4 & 0 \ 3 & 2 & 1 \ -1 & 3 & 6 \end{vmatrix} = ]
[ (x-5)\begin{vmatrix} 2 & 1 \ 3 & 6 \end{vmatrix} - (x-4)\begin{vmatrix} 3 & 1 \ -1 & 6 \end{vmatrix} ]

It's still row reduction but now you just need to calculate two determinants of 2x2 matrices rather than 3

[ocean seal]

A Lonely Bean

[echo socket]

Actually wait

Doesn't the same apply to column operations?

In that case you could just [ \begin{vmatrix} 1 + x & x & 2 \ 3 & 2 & 1 \ 2 & 5 & 7 \end{vmatrix} = \begin{vmatrix} 1 & x & 2 \ 1 & 2 & 1 \ -3 & 5 & 7 \end{vmatrix} = \begin{vmatrix} 0 & x-2 & 1 \ 1 & 2 & 1 \ -3 & 5 & 7 \end{vmatrix} = -(x-2)\begin{vmatrix} 1 & 1 \ -3 & 7 \end{vmatrix} + \begin{vmatrix} 1 & 2 \ -3 & 5 \end{vmatrix} = 0 ]
[ \implies x = 2 + \frac{\begin{vmatrix} 1 & 2 \ -3 & 5 \end{vmatrix}}{\begin{vmatrix} 1 & 1 \ -3 & 7 \end{vmatrix}} ]

@sand pawn

[ocean seal]

A Lonely Bean

[lone heart]

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[lone heart]

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[hallow mesa]

If a,b,c are in AP then prove a^2(b+c) , b^2(a+c) , c^2(a+b) are in AP

[vale wigeon]

!status

[lone heart]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

@hallow mesa Has your question been resolved?

[hallow mesa]

1

[vale wigeon]

do you know what an AP is

[hallow mesa]

yes

[gray isle]

can you try applying the definition here

[vale wigeon]

actually tell the definition to us too

[hallow mesa]

it is a series in which the difference of two consecutive numbers is same

do u want me to use a2-a1 = a3-a2?

[lone heart]

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[lone heart]

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[lethal citrus]

What do you need to do ?

[lethal citrus]

<@&268886789983436800>

[night geyser]

lol

.close

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[night geyser]

imagine expecting to get prompt help at 4 in the fucking morning

and then getting bitter when you dont

the entitlement of children man

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[short pumice]

For each of the following, state whether you expect the distribution to be symmetric, right skewed, or left skewed. Also specify whether the mean or median would best represent a typical observation in the data, and whether the variability of observations would be best represented using the standard deviation or IQR. Explain your reasoning.
(a) Housing prices in a country where 25% of the houses cost below $350,000, 50% of the houses cost below $450,000, 75% of the houses cost below $1,000,000 and there are a meaningful number of houses that cost more than $6,000,000.
The distribution is expected to be:

[short pumice]

I made a box plot looking approximately like this

Would it be representative of the data? - from this box plot I assume distribution is right skewed but the right answer is left skew and I don’t get it

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[worn hearth]

i know this is off topic but i am kind of new on discord and had a frend who wanted to join but didn't find this by searching. Does this site have a link that others can click to find and join

[echo socket]

It looks like you want the invite link

[worn hearth]

yea but i dont know where to find it

[echo socket]

Look at the list of channels to your left

Do you see at the top of it "Mathematics"?

Click on it, you will see some options pop up, one of which is "Invite people"

[worn hearth]

yea

[echo socket]

And just copy the link

[worn hearth]

i did

thanks

and i apologize for asking it on help fourms

[echo socket]

Yeah it would be more appropriate to ask in any of the general channels but it's fine

[worn hearth]

.close

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[devout kite]

could any1 tell me why we have to subtract by 10x instead of just x

[somber eagle]

if you subract by x then theres a 2 in the decimal part instead of just 3s, ie when you subtract them you wont get a whole number

[devout kite]

so its when there is a non repeating digit before the repeating digit

??

[somber eagle]

well 623.3333333... - 6.233333333.... = 617.1

you want the decimal part of both numbers to be identical

[devout kite]

what

[somber eagle]

ie the .33333333333... part

[devout kite]

oh ok

nvm

thanks

so its when there is a non repeating digit before the repeating digit to make whats after the decimal point equal

which is to eliminate whats after the decimal point

am i correct?

[somber eagle]

yeah

thats why they use 100x and 10x, because the parts after the decimal points are equal

therefore they can subtract them and cancel them out

[devout kite]

thanks g

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[twin jolt]

Can someone tell me which axis this equation belongs in

[lone heart]

@twin jolt Has your question been resolved?

[gilded raft]

What do you mean?

[twin jolt]

The quadrant

I’m not sure about the quadrant it’s in

[lone heart]

@twin jolt Has your question been resolved?

[twin jolt]

<@&286206848099549185>

[formal canyon]

Hi

[twin jolt]

hello

[wanton gorge]

Only solution is pi/9

[lone heart]

@twin jolt Has your question been resolved?

[twin jolt]

why is it not -pi/9

[lone heart]

@twin jolt Has your question been resolved?

[lone heart]

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[alpine sable]

How many distinct undirected graphs with 25 vertices and at least one isolated vertex are?

[alpine sable]

2^276 ?

<@&286206848099549185>

[ebon sparrow]

,tex .original

[ocean seal]

Akira 🍉

[ebon sparrow]

wdym by 2^276???

[alpine sable]

The original question is not in english

[ebon sparrow]

oh

[alpine sable]

2^300 is the number of distinct graphs with 25 vertices

[ebon sparrow]

it's Spanish language?

[alpine sable]

No

[ebon sparrow]

what it is then

[ebon sparrow]

I'm not sure what do you mean by this

[alpine sable]

It is a formula

[ebon sparrow]

what formula

[alpine sable]

2^(n(n-1)/2) is the number of distinct graphs with n vertices

[ebon sparrow]

https://math.stackexchange.com/questions/4052384/count-number-of-simple-undirected-graphs-with-exactly-one-vertex-degree-of-n

this might help

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

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[mighty cliff]

The base of a right prism is a rectangle, the diagonals of its side faces are 17 cm and 25 cm, and the height is 15 cm. Find the total surface area. what should the drawing look like?

[lone heart]

@mighty cliff Has your question been resolved?

[mighty cliff]

<@&286206848099549185>

[rapid vector]

I really did not understand the question... They ask you to find what the right prism should look like?

[mighty cliff]

No I'm being asked to find the total surface area, but I don’t quite understand how the drawing should look.

And I don’t understand how to find the sides if the Pythagorean theorem does not work with these numbers.

[rapid vector]

The person who worded the question needs help
So ok I'm thinking of a rectangular prism standing up. Height = 15cm, length = 25cm and width = 17cm

But... "diagonals of its side faces". what does that mean????

[mighty cliff]

i think it's look like this

diagonals of its side faces

[rapid vector]

hm okok

I see

ok

[mighty cliff]

And I'm stuck on the Pythagorean theorem because the root of 544 is not an integer

and if you find the second side for the area formula, then it is also not an integer according to Pythagoras.

[rapid vector]

This is going to be a rough sketch, but something like this right?

hmm

[mighty cliff]

oh my mistake height 9

[rapid vector]

either way I'm still confused on how to approach this 💀

ill try something

[mighty cliff]

I tried to draw it like this

because it is not written which diagonals and I can draw them in any direction

but it didn't give me anything

[rapid vector]

is calculator allowed in this question? do they specify?

[mighty cliff]

More likely no than yes

I think there may be an error in the condition, since I don’t see any other solution except Pythagoras

[rapid vector]

then if we get an answer like sqrt(544), we'll keep it as sqrt(544). I found that when i tried 9^2 + b^2 = 25^2

Calculator says that it can be simplified to 4*sqrt(34), but i guess we have to ignore that

[mighty cliff]

[rapid vector]

did you also try 9^2 + b^2 = 17^2?

[mighty cliff]

yes

there is no root of 208 either

[rapid vector]

did you also get sqrt(208)?

yeah i know, we'll keep it as that

well.. calculator says 4*sqrt(13)...

no way this question is a no-calculator question xd

well now we know the height, base, and length... eugh

Surface Area = \ $2(\sqrt{208} \times \sqrt{544}) + 2(9\times\sqrt{544}) + 2(9\times\sqrt{208})$

Ask your teacher to simplify that without a calculator. I would rant if u were u lmao

[ocean seal]

HqppyFeet

[mighty cliff]

haha

[rapid vector]

what does the answer sheet say? Do you have it?

[mighty cliff]

no answer sheet

[rapid vector]

Welp... too bad for them we found the answer

[mighty cliff]

Perhaps you see some solutions other than Pythagoras?

[rapid vector]

it's just expanded lol

hmm

Well there's trigonometry...

[mighty cliff]

But I don't see a way to solve it like this

[rapid vector]

yeah because we need a calculator to actually find sin^-1(9/25) or sin^-1(9/17), then we use that angle to find the length and width.

hmm

[rapid vector]

But do you understand how this comes about?

[mighty cliff]

yea

[rapid vector]

yeah, out of all methods that I can think of, this seems to be the easiest method to acquire the correct answer (without calculator).

But if this is your homework, you can plug the answer into the calculator and acquire the simplified answer, then write a little note/margin saying "used calculator for simplification" or something. Your teacher will definetly understand.

[mighty cliff]

I'll try to ask the teacher tomorrow, maybe there's a mistake there.

[rapid vector]

that's alright.

[mighty cliff]

And I will definitely share the answer.

)

[rapid vector]

Yeah I think it'll be fine. I personally believe that it's a joke to not be able to use a calculator for questions like these.

But, I'll stop babbling, you did well :)))

[mighty cliff]

.close

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[waxen ridge]

I have no idea what i can use for g that doesnt end up with x^2 also

if i use x^1/2 i get x, but since we also have to get + 3 i get stuc

[echo socket]

If f(x) = x^2 + 2, what's f(g(x)) equal to?

[waxen ridge]

gx is unknown

[echo socket]

In terms of g(x)

[waxen ridge]

(g(x))^2+2?

[echo socket]

Yes, so you can isolate g(x) in (g(x))^2 + 2 = x + 5

You will see two solutions pop up

[waxen ridge]

O yes ill try that

ill do g(x) = u

[echo socket]

Sure

[waxen ridge]

(x+3)^1/2?

[echo socket]

Or minus that

[waxen ridge]

I'll try this answer ye

[echo socket]

Well you are asked to provide just one example so yeah that works

[waxen ridge]

Bruhh why didnt i think fo this

thx

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[hoary goblet]

Not too sure how to go about this.

[slate vortex]

$\frac{4}{x+2}-\frac{1}{x^2-4}=\frac{6}{5x}$

[ocean seal]

Ari

[slate vortex]

$\frac{4(x-2)-1}{x^2-4}=\frac{6}{5x}$

[ocean seal]

Ari

[slate vortex]

because x^2-4 = (x+2)(x-2)

does that help

[hoary goblet]

Why'd you put 6/5x on the other side of the equation?

Same with the 1/x^2-4

[rapid vector]

Hmmm lets take a look at the technique here.
Are you familiar with expanding (a-b)^2?

[hoary goblet]

Into (a-b)(a-b) then doing FOIL?

Or am I thinking of something else

[rapid vector]

mhm, and what do you get when you foil?

[hoary goblet]

What would i be using that for? It doesn't appear that there's any need for it here

[rapid vector]

We're just stepping away from this question to allow you to see what techniques are suited here.

[hoary goblet]

Ahh okay

[rapid vector]

But you have expanded (a-b)^2 before, right?

[hoary goblet]

Well, with (a-b)^2 it would be 2ab + a^2 +b^2

[rapid vector]

Great, you are familiar with this.
Now what happens if you expand this instead? (a+b)(a-b). What do you notice about a and b in its expanded form?

[hoary goblet]

The non-squared values cancel out, so it ends up with only a^2-b^2

I believe

[rapid vector]

aha! So you leave with square values only.

That's where we can get a bit more comfortable ehre

In the form a - b, if both values of a and b are squared numbers, they can be factored into (a+b) * (a-b).

So if we go back to this again,

Ari switched 6/5x and 1/(x^2 - 4) because she noticed that we can get a common denominator here.

Do you see it what you can do to 4/(x+2) to get a common denominator?

[hoary goblet]

Multiply it by x?

Wait no

Maybe that is right. I'm not entirely sure

[rapid vector]

hmmm if you multiply $\frac{4}{x+2}$ by x you get $\frac{4x}{x^{2} + 2x}$ \Try again

[ocean seal]

HqppyFeet

[rapid vector]

Understand what we did earlier.
What do you notice about (a+b)(a-b)?

Or let's look at 1/(x^2 - 4) for a second here... What do you notice about x^2 and the number 4?

[hoary goblet]

Hmm

[rapid vector]

You feel stuck? xD

[hoary goblet]

Very lol

Would I foil x^2 - 4?

[rapid vector]

You mean factor it? You can happily factor this value, and let me know what you see :3

The term "foil" is used to multiply binomials (like (a+b)(a-b))

the term "factor" is used to split a expression (like a x^2 + 4 or a quadratic) into two expressions with no remainder)

[hoary goblet]

Ahh yeah I was thinking incorrectly. I'm not sure how I'd factor it

[rapid vector]

Are you still confused here btw? xD

Let's play around shall we

[hoary goblet]

Sure

Does it have something to do with finding what values multiply to -4 and add to 1?

[rapid vector]

hmm, this would be correct: "finding what values multiply together to get -4"

[hoary goblet]

So it would expand to (x-2)(x+2)

[rapid vector]

YES WOOO

I'm proud that you got that 😄

[hoary goblet]

That's where this came in ohhhhhh

Haha yess!! Thank you:))

I'm getting it, slowly but surely haha

[rapid vector]

yess! ok so lets go back again

We noticed that both values in the denominator are squared numbers: 1/(x^2 - 4). You have x^2 and 4. And you realized that the two expressions that give you this denominator are (x+2)*(x-2)

[hoary goblet]

Correct

[rapid vector]

and you might have already noticed something about the fraction on the left? 4/(x+2)

[hoary goblet]

I feel like something can be canceled out between 4/x+2 and 1/x^2 -4

Since the whole equation is negative, would that make both parts of the factored form of 'x^2 -4' negative?

So would the denominator be (-x-2)(-x+2) or does it not work like that

[rapid vector]

You almost got the idea! But with fractions, they don't really cancel out (not in this format), but instead they can combine if they have the same denominator.

[hoary goblet]

Ohhh

Duh

[rapid vector]

hihihihi, we're getting close.
So we want to have a common denominator, and we know what "ingredients" are needed to produce "x^2 - 4"

(x-2) and (x+2) are the ingredients basically

so- again, we notice that the fraction on the left already has one of the ingredients, (x+2)

So what is the missing ingredient needed to produce "x^2 - 4" (in 4/(x+2))?

[hoary goblet]

We'd need to square the denominator of 4/x+2 ? Or multiply it by a negative version of itself?

[rapid vector]

hmm what do you think? what difference does it make? ; )

[hoary goblet]

If we squared it, it would stay positive, but if we multiplied it by a negative version if itself it would give us (x+2)(x-2)

[rapid vector]

there ya goo!! and we want to have a common denominator so that fractions can be combined

(and just to note, whatever you do in the denominator, you have to do the exact same thing to the numerator. Let me know if you don't understand this part)

[hoary goblet]

Ohh that makes more sense, I knew we'd have to do the same thing to something else but I wasn't exactly sure what. I was thinking we'd have to also multiply the other side of the fraction by -x-2, but it makes sense why we'd just multiply the numerator since it's technically still the same thing, just multiplied by 1

[rapid vector]

Yup!!! Similar to how 32/64 can just be simplified to 1/2 because you divide the numerator and the denominator by 32, and you still get 0.5

[hoary goblet]

Exactly, that makes sense

So would we multiply by 'x-2' or '-x-2'?

It wouldn't be the second right?

[rapid vector]

Mmm what do you think? what difference does it make? xD

[hoary goblet]

There wouldn't be a common denominator if we did the second

I don't think

[rapid vector]

thats right! you're good at this

[hoary goblet]

I just need to stop questioning myself so much haha, that was a dumb question

[rapid vector]

trust your decisions, you're on the right path :3 And nothing's dumb about double-checking, you learn from errors anyway :)))

[hoary goblet]

True true!!

So do we subtract both fractions now that we've found a common denominator?

[rapid vector]

yup!
Do you think the denominator will cancel out or stay the same when you subtract?

[hoary goblet]

I was just wondering that... You mentioned that they'd combine if they have a common denominator, so wouldn't that mean they'll technically cancel out?

[rapid vector]

It's a trick question, the denominator always stays the same when you do addition or subtraction ahhaha

same method used if you do 3/4 pizzas - 1/4 pizzas. If you get 3/4 - 1/4 = 2/0 OH NO U CANT DIVIDE BY ZEROO universe collapses

[hoary goblet]

LOL

[rapid vector]

so you end up with 2/4 pizzas, not 2/0 LOl

[hoary goblet]

That was an amazing example, especially since it explained it perfectly haha

I was just about to ask why you don't subtract the denominators, but that makes a ton of sense now

[rapid vector]

xD concept of fractions in a nutshell. It's a different story when you multiply or divide fractions, but you never actually see something being divided by 0 in early math

but yeah, what do you have in the end? does it look like this?

[hoary goblet]

This is where I’m currently at

I thought I needed to multiply the 4 already

[rapid vector]

aah amazing! you rolled through with it : DD

yeah you eventually had to multiply sooner or later, that's correct :))

And also, it's best if you kept the denominators in its simplified form, i.e x^2 - 4. It's just easier to handle afterwards.

[hoary goblet]

Sweet!! So then I'd combine the denominator into x^2 -4 and that would leave the numerator at 4x-9?

[hoary goblet]

Yeah, that makes a lot of sense

[rapid vector]

yesss!!! look at u gooo!

[hoary goblet]

Haha awesome:))

I've gotta say, you have the energy I wish all of my teachers had growing up. It would have made math so much easier and enjoyable, so I really admire that!

[rapid vector]

< 3 you're making me want to become a math teacher ahhahaha

noo but I understand. I have seen students struggle with having bad teachers lately. It's really sad.

[hoary goblet]

I was going to ask if you were haha, it would make sense!

Yeah... having a good or bad teacher can really make or break a class:/

[rapid vector]

I would recommend watching a guy called "Eddie Woo" on YT. I had good teachers, but this guy on YT was sooo good at explaining concepts, it's makes math 100% easier to understand hahahaj

--well for me at least

[hoary goblet]

So from here, I'm really not sure what to do...

I'll definitely check him out, I've been trying to find some good youtubers to help with math

[rapid vector]

You should be left with this in the end: \ $\frac{4x - 9}{x^{2}-4} = \frac{6}{5x}$

[ocean seal]

HqppyFeet

[rapid vector]

this looks familiar ye?

[hoary goblet]

Yep, that's what I have

Wait what's all?

[rapid vector]

Well it's not the end-end, we still have to find x haha

[hoary goblet]

Ohh okay, I didn't think so lol

[rapid vector]

hmmm, so we don't like fractions, specifically in the position where we are now.

What we want to end up with, is just one flat expression with no fractions

[hoary goblet]

Yeah this feels messy

[rapid vector]

Yeah, have you dealt with something like this before? Where you do [redacted] to remove fractions?

[hoary goblet]

It doesn't sound familiar, but I may recognize it when we actually start doing it

[rapid vector]

Let me expose you with a technique here. \ $\frac{a}{b} = \frac{b}{a}$

[ocean seal]

HqppyFeet

[rapid vector]

If you multiply both sides of the equation by a.

[hoary goblet]

Do we need to multiply by the reciprocal?

I didn't mean to interrupt where you were going with that, I'm sorry

[rapid vector]

aaaa you know this? xD.
Well I would word it differently. We would need to multiply both sides by denominators

So as mentioned, if you multiplied a on both sides, you would end up with \ $\frac{a^{2}}{b} = b$

[ocean seal]

HqppyFeet

[rapid vector]

This is because "a" cancels out on the right side of the equation $\frac{a^{2}}{b} = \frac{ab}{a}$

[ocean seal]

HqppyFeet

[rapid vector]

And you can do the same thing with "b". If you multiply both sides by "b", you end up with \ $\frac{a^{2}b}{b} = \frac{ab^{2}}{b}$

[ocean seal]

HqppyFeet

[rapid vector]

I kinda call this the "butterfly effect", I don't know if other teachers call them by names, but you essentially multiply both sides by one denominator, and then the other denominator. What you notice in the end; the fractions go away because of cancellation, and the values of the denominator goes to the other side of the equation

[hoary goblet]

Wouldn't the left side have no denominator since you're multiplying it by 'b'?

[rapid vector]

so you end up with $a^{2} = b^{2}$

[ocean seal]

HqppyFeet

[hoary goblet]

Ohh that makes sense

[rapid vector]

yess you got it-- i made a little error in the code above... it was supposed to be "ab^2 / a" on the right hand side-- woops

xD

but you got the idea?

[hoary goblet]

Yep!

Does that mean it would be 4x-9(5x) = 6(x^2 -4)

[rapid vector]

techniques gets remembered through practice. So let's test this with what we have here \ $\frac{4x - 9}{x^{2}-4} = \frac{6}{5x}$

[ocean seal]

HqppyFeet

[rapid vector]

you nailed it

before I even introduced it lmAo im proud

[hoary goblet]

I'm not sure how to use the bot haha, I know that would make it look a lot more clean for you

Thank you!

[rapid vector]

hahah you can play around with the bot in your free time. you might find some "TeX math generators" online lol

anyway, yeah, you end up with $5x(4x-9) = 6(x^{2}-4)$ \ from there you can expand and simplify the brackets here

[ocean seal]

HqppyFeet

[hoary goblet]

I may have messed something up, but I'm at 14x^2 -45x+24

[rapid vector]

or "multiply" is the term i was looking for

[hoary goblet]

I'm not sure if it should be on different sides of the equation

[rapid vector]

there! that's what I have too

[hoary goblet]

Oh sweet, that's reassuring haha

Do I simplify from there?

[rapid vector]

ahaha we're on the right path. I stopped here because it looks like we have to factor them, and I'm not so good at that heheh

Have you seen this before btw?

[hoary goblet]

Yep! I take it that's the next step hah

[rapid vector]

yeah I'm going through that step too xd

[hoary goblet]

Okay, I'll run through it real quick

[rapid vector]

these are big numbers, we might have to use a calculator here

[hoary goblet]

When I'm plugging in numbers, do I plug in x as well? Or just the actual number?

Like for "-b" do I plug in just "45" or "45x"

[rapid vector]

just the actual number.
We got to this point with our numbers: ax^2 + bx + c, so we only plug in the values

[hoary goblet]

It's been a while since I've done this haa

[rapid vector]

without the x

[hoary goblet]

Got it

[rapid vector]

these are ugly numbers

[hoary goblet]

Lol very

[rapid vector]

do you have an answer sheet or something?

[hoary goblet]

Yes

[rapid vector]

hmmm what does it say?

it would be funny if we got the wrong answer somehow

[hoary goblet]

45+- sqrt(681)/28

That's what I got too

Phew

[rapid vector]

phew thank god lmao

[hoary goblet]

I wasn't sure if anymore simplifying needed to be done

[hoary goblet]

Right🤣

[rapid vector]

i just used a calculator to simplify that lol

[hoary goblet]

I must not need to, because my teacher just left it at that

Which is fine with me haha

[rapid vector]

but that's good that they left the answer as a fraction

[hoary goblet]

That was quite the trek haha

[rapid vector]

it was indeed a long journey ahhahaha

[hoary goblet]

I can't thank you enough for the help!!

[rapid vector]

but i hope you learned something along the way x)

: D ❤️

[hoary goblet]

I apologize it took so long haha, but I definitely did learn a lot:)

[rapid vector]

And also, don't feel bad if you forget some of this stuff later, memory will build on itself after some time and practice

nono it happens. We need time to grow our understanding with math :3

from the fundamentals to problem solving

[hoary goblet]

True true, I definitely won't retain everything but I'm going to keep practicing them and it'll build overtime

Well, I hope you have an amazing rest of your day:)) Thank you again, SO MUCH!!

[rapid vector]

yess:)) and check out videos on YT, most teachers (like Eddie Woo) are very friendly with math concepts like these

if you find them

[hoary goblet]

Oh I will, I wrote his name down to check out as soon as you mentioned it lol

[rapid vector]

<3<3<3 likewise!! And as always, ask more questions in chat if you have any :3

Wish you well!

[hoary goblet]

.close

[lone heart]

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[dusk umbra]

Hey yall, I'm currently looking over notes on changing coordinate system in the lagrangian in Tong's lecture notes, and I'm a little stuck here. I'm unsure of where q_b is coming from, and I'm also uncertain how they "cancel the dots" in the bottom equation. The parts that confuse me are highlighted.

[dusk umbra]

this is more physics but if anyone can chime in and explain some of this, it would be a great help

[lone heart]

@dusk umbra Has your question been resolved?

[dusk umbra]

additional context from the lectue notes

he seems to be using the substituion from 2.12 in the initial photo, but i am unsure why he decides to use q_b instead of q_a

the last term in the second line is what is confusing me

[lone heart]

@dusk umbra Has your question been resolved?

[lone heart]

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[pale shell]

What is the title of this book?

[jagged cobalt]

you want us to find the title of the book using this page?

[naive valley]

could be pretty much any book on physics/mechanics

[lone heart]

@pale shell Has your question been resolved?

[tacit arch]

Not what help channels are for

.close

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[pale knoll]

hi

[pale knoll]

i need help

[bleak geyser]

!status

[lone heart]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[pale knoll]

1

[bleak geyser]

Do u know what corresponding angles are

,w Corresponding_angles

[pale knoll]

i have no clue

what any of this is bruv

i just need answers

[wary stream]

We are not here to give out answers

[pale knoll]

im not here to get help

[wary stream]

Cool and we aren't here to give out answers

If you're looking for answers, this isn't the server for you

[lone heart]

@pale knoll Has your question been resolved?

[lone heart]

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[thin pivot]

need help

the answers don't say much, they just state the answer

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@thin pivot Has your question been resolved?

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[silent orchid]

I need help

[silent orchid]

@rare spearl

@everyone

Pleaseeee

[wary stream]

This doesn't work here

[lone heart]

Helpers are just people volunteering their time to help you. Be polite and patient.

[silent orchid]

.close

[lone heart]

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[unborn shell]

Cast a die two independent times and let X equal the absolute value of the difference of the two resulting values (the numbers on the up sides). Find the pmf of X. Hint: It is not necessary to find a formula for the pmf.

[unborn shell]

I have set up a table of values for each roll , and the value of their absolute difference, but Idk how this translates into a PMF

[dense meteor]

yo

[unborn shell]

Hi

[dense meteor]

how do i claim a channel

[unborn shell]

no idea dude, Idk if I am even doing this right lol

[tacit arch]

!show

[lone heart]

Show your work, and if possible, explain where you are stuck.

[unborn shell]

how do I upload images?

I can copy text too if better

thank you for the reply I am not familiar w disc

[tacit arch]

Google it?

[dense meteor]

u can copy

and then ctrl v

[unborn shell]

ah this is cool, you can take a screenshot from an imgur and upload it directly via drag and drop

and it doesnt flood my desktop

[unborn shell]

sorry man, but can you help me w this one?

[tacit arch]

Your table is only half complete

You turn it into a pmf by counting all the ways you get an X value

[unborn shell]

why do you say its half complete?

[tacit arch]

E.g. P(X=5) = number of ways getting 5 / total number of distinct rolls

[unborn shell]

have I labeled the induced sample space D correctly?

[tacit arch]

You're missing all the rolls where the second number is greater than the first

[unborn shell]

oh..

damn..

Thanks!

so P(X=5) = 2/36

for example?

[tacit arch]

Yes

[unborn shell]

and the induced sample space would be 0, 1,2 ,3 ,4 ,5 ,6

wait

[tacit arch]

!help

[lone heart]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[tidal lynx]

!help

[lone heart]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[unborn shell]

I have 6 outcomes for X = 0 , 10 outcomes for X = 1 , 8 outcomes for X = 2, 6 outcomes for X = 3, 4 outcomes for X = 4 and 2 for X = 5

ugh nvm rieman, I got it

.close

[lone heart]

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[brisk orbit]

Why do I need the other 3 triangles?

I just did 6tan(20(deg))

[gray isle]

they want you the identify the one that could be used (and use that) to get an approximation

(similar triangles)
as opposed to using tan and a calculator

[lone heart]

@brisk orbit Has your question been resolved?

[lone heart]

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[alpine sable]

hello is this equation
x²+(sin²a+cos²a)x+sin²2a=0
solveable?

[carmine torrent]

Yes

Assuming a is a constant

[heady void]

Yeah

I think you got it right

oh wait

[carmine torrent]

It should be 2a

[heady void]

smth wrong here

[carmine torrent]

In the last

[heady void]

yeah

[carmine torrent]

My bad

[heady void]

besides that I think you're done for this question

[carmine torrent]

Can you solve my question in #help-8

[heady void]

idk how tho sry

you in Calc II?

[carmine torrent]

Nope

[heady void]

oh

[lone heart]

@alpine sable Has your question been resolved?

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[alpine sable]

thanks all

[lone heart]

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[sage ore]

Hey so im particularly stuck from d) onwards.

ill upload my notes

So I'm upto
f''(x) = sin(x)/((1+cosx)^2)

And there's a vertical asymptote at pi. So I'm wondering why when I do a table of signs for second derivative it's always positive

[lunar ravine]

How did you get there?

[sage ore]

Quotient rule

It's in that box but very messy

I'll do it again real quick

First derivative

Thanks lol

Oh wait

Yeah -sin

That fixes it

[lunar ravine]

No it's positive you were right first

If u do it with power rule there's a negative in the power and another negative from deriving the cosx

Now you should check when this is positive and when it's negative

[sage ore]

Oh whoops yeah

Forgot cos differentiates to -sin

Yep

Do you suggest plugging in to the whole equation or separating it in parts?

I've tried both and get the same answers of positive every time

Usually I'd separate it

[lunar ravine]

Yes can you show how you solved it?

[sage ore]

Yep

Just plug it in with a calculator on table of signs

So plugging it in:

[lunar ravine]

Wait you don't have to separate that one the denominator is squared so it's always positive just check the numerator's sign and that's it

[sage ore]

Yep

Sine with anything between 0 and 2pi is positive

Seems like I've missed something

[lunar ravine]

It isn't always positive

It's positive between 0 and pi

[sage ore]

Yeah that's the interval it's based on

There should be change in the middle somewhere

Well at pi there is a vertical asymptote that's what I know

[sage ore]

Huh

Is my calculator wrong? When I plug anything between pi and 2pi it still is a positive number

[lunar ravine]

You sure it's set to radians not degrees?

[sage ore]

Ffs

Thanks

Hahaha

Appreciate it, that woulda stuffed me up for ages

[lunar ravine]

Yea lol no problem

[sage ore]

.close

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[lone heart]

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[alpine sable]

i dont understand why teh solution is the entire square

wouldnt this encompass also for example 2 -2i

[zealous lichen]

yes

Im(2-2i) = -2

[alpine sable]

but isnt 2-2i a complex number? and the equation only allows for imaginary numbers?

[zealous lichen]

.

Im(z) takes a complex number and return its imaginary component

so Im(a+bi)=b

it doesn't mean that z have no real part

[alpine sable]

ah so the a doesnt really matter

[zealous lichen]

yes

[alpine sable]

because we only are looking at b

[zealous lichen]

a.k.a. the y axis

[alpine sable]

ooh

got it thank youu !!

.close

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[lone heart]

@solid fog Has your question been resolved?

[solid fog]

<@&286206848099549185>

[near apex]

You had $\left(u - \frac{9}{5}\right)$. That becomes $\frac{5u - 9}{5}$.

[ocean seal]

Enemagneto

[near apex]

You missed that 5 in denominator.

[solid fog]

no?

i just finished

I got it

thanks tho

.close

[lone heart]

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[sly path]

I want to know the process on how he factored out yx-2y

[prime spindle]

wdym

[vale wigeon]

it's just the distributive law

y * x - y * 2 = y * (x - 2)

[placid zinc]

Take y(x - 2) and distribute it out, to get your line back

[sly path]

Ohhh clearrr

Thank you sm guys

.close

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[sage ore]

Hey when you have a function that has a verticle asymptote and x intercept in the same spot, does the vertical asymptote always win?

[zealous lichen]

?

what do you mean

[sage ore]

im given the function sinx/1+cosx

sinx/(1+cosx)

and i found vertical asymptote at pi

and found x intercepts at 0, pi and 2pi

etc

im working in the interval [0, 2pi]

so now im bout to sketch the graph up

and dont know what to do there, its obviously a tangent function so the asymptote is correct

[zealous lichen]

notice that both $sin(\pi)$ and $1+cos\pi$ equals 0

[ocean seal]

WhereWolf(ping if needed)

[zealous lichen]

that means the function is not defined at 0

[sage ore]

yeah

[zealous lichen]

but that doesn't mean there have to be vertical aymptotes

you take the limit to find out how the function behave

[sage ore]

we arent supposed to do that

wait your saying it isnt defined at 0?

so whats that mean?