help-39

[winter agate]

I know the formula for when its ln( 1+ x) but idk what to do now that its ln(1/2 + x) can someone help me understand what to do?

pls ping me if you know how

[calm wing]

do you know the general process of finding maclaurin expansions?

[winter agate]

you can differentiate and sub in 0 to find the coefficient of the first second third terms ext

I did that and got some really ugly numbers

IDK if this is right or not but it definitely looks wrong

@calm wing

[calm wing]

it does look wrong, but let me check

[winter agate]

ok thanks

[calm wing]

$f(x) = ln\left(\frac{1}{2}+\cos(x)\right)$
$f(0) = ln\left(\frac{1}{2}+\cos(0)\right) = ln(1.5)$ - first term

$f'(x) = \frac{-2\sin(x)}{2\cos(x)+1}$ (chain rule)
$f'(0) = \frac{-2\sin(x)}{2\cos(x)+1} = 0$ - term is 0, move on

$f''(x) = -\frac{\left(2(\cos(x)+2\cos^{2}(x)+2\sin^{2}(x))\right)}{(1+2\cos(x))^{2}}$ (idk an easier way)
$f''(0) = -\frac{2}{3}$

hence, $f(x) \approx ln(1.5) - \frac{1}{3}x^2$

[jolly parrot]

artemetra

[pearl pond]

@winter agate Has your question been resolved?

[pearl pond]

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[raw summit]

how are either of these wrong

i even plugged it into symbolab

got the same answer

[pearl pond]

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[pearl pond]

Please don't occupy multiple help channels.

[violet sparrow]

How do u do part b

[hollow cobalt]

Aren't you given the solution?

[violet sparrow]

that is the asnwers

.close

[pearl pond]

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[elder agate]

$x$ is a positive real number such that:
$x - 2\sqrt{\frac{3}{x}} = 5$
What is the value of $x - \sqrt{3x}$?

[jolly parrot]

gkeocog

[tawdry vessel]

Have you tried rewriting the middle term?

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

[jolly parrot]

Alice

[elder agate]

Yes and We get $x^2 - 2\sqrt{3x} = 5x$

[jolly parrot]

gkeocog

[tawdry vessel]

I'm sorry

<@&286206848099549185>

[pearl pond]

@elder agate Has your question been resolved?

[elder agate]

<@&286206848099549185>

[pearl pond]

@elder agate Has your question been resolved?

[golden orbit]

,w x-2sqrt(3/x) = 5

[jolly parrot]

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[golden orbit]

You can sub that in to the equation you have

,w ((7+√33)/2) - √(3((7+√33)/2))

[jolly parrot]

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[golden orbit]

Hence 2.

@elder agate

[pearl pond]

@elder agate Has your question been resolved?

[elder agate]

Thank you for trying to help, but I'm looking for a method that doesn't involve that much computing, I mean where u get the whole expression equals something not computing both terms independently

[pearl pond]

@elder agate Has your question been resolved?

[pearl pond]

@elder agate Has your question been resolved?

[golden orbit]

,w x-√(3x) =(x²-7√(3x))/5, x≠0

@elder agate

I don't think it's possible to put in terms of the original equation

[jolly parrot]

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[golden orbit]

<@&286206848099549185>

How does this make sense?

[pearl pond]

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[tulip fox]

not sure how to do this, i was thinking of making any element "k" be in the set A which makes it be in the other sets B and C but i rly dont know

[toxic lichen]

are you allowed to use the fact that S ⊆ T ⊆ U implies S ⊆ U?

[tulip fox]

that does look familiar

and if i use that it would be A subset C and i can use C subset A

which means A = C ?

and then C subset A subset B

which is equal to C subset B

and then using B subset C

C = B ?

[void grail]

I am trying to visualise this

[pearl pond]

@tulip fox Has your question been resolved?

[pearl pond]

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[sage patrol]

can someone help me with this?

[atomic ferry]

U can use cosine rule

[sour pivot]

tan 12= BC/AB (ig, not sure)

[woeful fern]

I don’t think so,

[sour pivot]

oh yeah right

i din read question properly

sry my bad

[woeful fern]

No you’re 👍

[sour pivot]

use cosine rule

[sage patrol]

i don't have a c tho

[atomic ferry]

But u have a angle

U have b c and angle

[woeful fern]

Another way you can do it is that you can find the height of c by doing sine of 12 = x/ 786

Then use py theorem to find the length of b to the base of c. Add that and AB together and then use the py. Theorem again to find AC. I did that because I forgot the law of cosine lol

Sorry if that sounds confusing

[sage patrol]

should i just use py theorem to find c then do cosin law?

[woeful fern]

U mean angle C? You can do that too. There are multiple ways to do this

You can’t find length of c to the bottom at the moment because we don’t have the length of b to the base

[sage patrol]

my question is how do you get angle c and b

[woeful fern]

Angle b is 180-12 since a line is 180 degrees
C is 180-90-12 since a right triangle has 1 90 degree angle that is perpendicular to the ground

[sage patrol]

alr thanks

.close

[pearl pond]

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[woeful fern]

Np

[pearl pond]

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[frosty vale]

last question help

[frosty vale]

ping me if ur gonna help

[copper ridge]

diagram?

[frosty vale]

um ok

[copper ridge]

nice diagram

[frosty vale]

yea

do u want me to send everything in picture

[copper ridge]

everything??

[frosty vale]

here

last question i need help

[copper ridge]

Is Ans : 3c2 x 7c1 ?

[frosty vale]

yup

[copper ridge]

OK So See it is mentined we have to just select the passanger not to arrange so we just gonna use nCr

[frosty vale]

yup

[copper ridge]

So We have 3 Couples and 5 Unmarried Ones
According To Question we Require 2 couples and 1 person which may or may not be marries

[frosty vale]

yes

[copper ridge]

SoTell me for Selecting 2 couples from amount of total 3 couples will be?

[frosty vale]

3c2

😄

[copper ridge]

yeaa

[frosty vale]

ok makes sense

[copper ridge]

Next we need 1 person that may be or may not be marries

[frosty vale]

yea

[copper ridge]

So we had total 3 marries + 5 unmarries thats = 11 Member

[frosty vale]

yes

[copper ridge]

From which we alredy picked 2 couples thats 4 member

we remain with 11-4 = 7

now we need 1 member from total of 7 member

[frosty vale]

yes

[copper ridge]

so what it will be?

[frosty vale]

7c1

ok got it

[copper ridge]

There u go

3c2 * 7c1

[frosty vale]

Thanks 😄

[frosty vale]

mhm

[copper ridge]

In case u are confused where to use * or +

let me know

[frosty vale]

ok

[frosty vale]

u mean 3c2 multiply 7c1

[copper ridge]

Ya

[frosty vale]

right?

ok cool

thanks

.close

[pearl pond]

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[broken burrow]

When solving absolute value inequalities, I'm having a confusion where when having the equation |3-2t|>4. In the picture, in the number line why can we also say that 3-2t<4 and 3-2t>-4, originally |3-2t| can has to less than 4 so why does it have to be bigger than -4 as well?

[jolly parrot]

Modus

[buoyant panther]

generally it's enoguh to remember that we just rotate inequality sign about 90 degrees clockwise

and it tells if it's OR / AND

[broken burrow]

I dont really get it, I have no idea what the \wedge sign means either

[buoyant panther]

you know what union/intersection of sets is?

[broken burrow]

yeah

[buoyant panther]

union = v (or)
intersection = ∧ (and)

[broken burrow]

Jeez I've never seen it, I always saw this ∩

[buoyant panther]

like these signs are revelant for intervals

e.g. x ∈ ...

not necessarily sets like A, B or something

[broken burrow]

I dont get you, I'm sorry

when having absolute value of something it can be either positive or negative, that's clear, but when it has to be smaller than 4, why does it have to be also bigger than -4?

[buoyant panther]

"when having absolute value of something it can be either positive or negative" - absolute value is always non-negative, it can't be negative

[broken burrow]

Yeah I meant that that = |-x| = x and |x| = |x|

[buoyant panther]

because look at this simple example, e.g. if |x| < 4 notice that if x = -3, we have |-3| < 4 ---> 3 < 4 ---> true

and if x was -5 for instance, then we would have |-5| < 4 ---> 5 < 4 ---> false

this is why in this case

-4 < x < 4

[broken burrow]

I still dont get it, if |x| < 4 that means that x has to be smaller than 4, why would by extension it would also mean that it has to be bigger than -4.

[buoyant panther]

and generally geometrical interpretation of the abs explains it clearly

[buoyant panther]

"x has to be smaller than 4" - inequality says: absolute value of x has to be less than 4, not x !!

[broken burrow]

I mean yeah, but that still doesnt explain it

[buoyant panther]

okay, maybe try with equality

|x| = 4

what x can be in this scenario?

only x = 4?

[broken burrow]

no x=-4

[buoyant panther]

yeah, x = -4 or x = 4, same logic can be used with inequalities

[broken burrow]

I mean x can be -4 as well

yeah then. x<4 and x<-4

that still doesnt prove it

[buoyant panther]

noo, x > -4 why is that?

because |x| = -x for x < 0

[broken burrow]

What?

[buoyant panther]

that's definition of absolute value

[broken burrow]

Yeah I mean if something is smaller than 0 then it is negative

But that still doesnt explain it to me 😄

[buoyant panther]

mhmm, one more chance haha

other strategy

when dealing with |x| < 4 we can firstly assume x is positive, then we can say:
|x| = x
right?

[broken burrow]

yeah

[buoyant panther]

so now we're going to solve x < 4 (because |x| = x), for x >= 0

right?

[broken burrow]

yeah

that's clear

[buoyant panther]

and this is just x < 4, but x is positive right, so the solution is 0 <= x < 4

do you agree?

[broken burrow]

yeah I do

[buoyant panther]

Now let's see what if x is negative, so when x < 0

then by def. of modulus we have |x| = -x

is it true?

[broken burrow]

yeah

[buoyant panther]

we're going to solve -x < 4 for x < 0

[broken burrow]

yeah

[buoyant panther]

we multiply it by (-1) both sides (so we have to reverse sign)

and it becomes x > -4

but x is negative right, so solution is -4 < x < 0

right?

[broken burrow]

yeah

[buoyant panther]

and finally

we should take both solutions

because we considered different cases

reminder:

1. 0 <= x < 4
2. -4 < x < 0

And it gives:

-4 < x < 4

[broken burrow]

wow

now it makes sense

[buoyant panther]

try to deny it

[broken burrow]

wdym?

[buoyant panther]

nvm, I'm just happy you've understood the stuff

[broken burrow]

thanks very much

I appreciate your help

and your patience 😄

[buoyant panther]

That's fine! If we can't explain something in a little words then it means we don't really get it

[broken burrow]

exactly

you damn right

[pearl pond]

@broken burrow Has your question been resolved?

[pearl pond]

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[pearl pond]

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[mossy perch]

Given a pyramid A-BCD, AB=CD=AC=BD=a. AD=BC=b, if A, B, C, D are all located on the surface of the same sphere with a radius of 2, determine the range of a+b.
I would like to know the plan of action needed to solve this problem. I don't really know where to begin as I can't yet of any ways to relate the sides to the sphere with radius 2. Also, what would range even mean in this context? The possible values for the sum a+b?

[mossy perch]

<@&286206848099549185>

I originally thought of using analytic geometry but this is way too messy and probably will not get me anywhere

[pearl pond]

@mossy perch Has your question been resolved?

[mossy perch]

any pointers would be appreciated, rather than a solution. I'm just trying to figure out some steps I could take

[pearl pond]

@mossy perch Has your question been resolved?

[pearl pond]

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[peak pilot]

I want this channel

[peak pilot]

I'm telling you this shi is hard

No human on earth likes proofing

[pearl pond]

@peak pilot Has your question been resolved?

[pearl pond]

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[misty hamlet]

HELP PLS!!

<@&286206848099549185>

HELP ME!!!!!!!!

[twin oar]

what is t supposed to be?

[misty hamlet]

huh

[twin oar]

in PMT formula

[misty hamlet]

where did u get t from

isnt pmt just

payment

[twin oar]

its a formula

[misty hamlet]

yeah

for a payment

[twin oar]

and you plug in P r n and t

[misty hamlet]

u say to plug it in but

clearly it doesnt work

[twin oar]

?

im asking you what does P =

and r

and n

[misty hamlet]

p is 61000

minus

13000

since down payment

r is the rate

7.77% interest rate

and time

4 years loan

like u ask me this

like i dont know

are u making a fool out of me

i am asking because i dont know the answer

[twin oar]

im asking you because i dont know what those variables are

whats n?

[misty hamlet]

number of times interest is compounded per year

[twin oar]

so 1 i assume?

[misty hamlet]

where did u get 1 from?

[twin oar]

interest only happens 1 annually? or is it assumed its monthly interest?

[misty hamlet]

yeah

its annuaklly

ur probably right

[twin oar]

so if its anually then interest would only compound once per year

do you know if its meant to be compounded monhtly?

[misty hamlet]

sir im not sure

i've been stressing for the past 30 minutes

its too hard

i think

im gonna go crazy

[twin oar]

it feels like the question is worded poorly

it doesnt say how often the interest is compounded

unless it means its just 7.77% interest at the end of the 4 years

[misty hamlet]

i think so

do u happen to knlw

the answer

i am dying

[twin oar]

i feel like if u were to ask GPT it would be able to give you a decent answer

and you can post it here to make sure its right, i havent really worked with stuff like this since first semester of gr 12

[misty hamlet]

😭

what am i gonna do

[twin oar]

eventually someone here will respond that knows fully what to do

until then ill try my best to figure it out

[misty hamlet]

thank you

pls

help me

[twin oar]

also its better for you the farther down it goes

dont close the channel, the ones at the bottom get more attention

[misty hamlet]

okay

😭

[twin oar]

@misty hamlet what happens when u put the wrong answer?

[misty hamlet]

i get one more try

maybe 2 morew

it depends

[twin oar]

i really wanna assume it means monthly interest

but i cant know for sure, anything else doesn't really make much sense to me

[misty hamlet]

i think

it is monthly

yeah

[twin oar]

okay well we might as well get the information we know out of the way

oh wait apparantly r should be in a decimal (divided by 100)

this is for part A ^

you get a 5000 discount if you choose A

so your present value you because 61k-5k-13k

wait

[misty hamlet]

interesting

[twin oar]

and then for incentive B dont you have this?

nvm i get something undefined

[misty hamlet]

oh

[twin oar]

do you have any notes on calculating PMT for free financing?

[misty hamlet]

no

my professor is

like

he doesnt teach us

only paperwork

[twin oar]

alright

well it seems like for part A at least

[twin oar]

this is monthly interest

[cinder flower]

where is @last summit when you need him

[twin oar]

do you understand this?

i watched like 10 vids so far

[cinder flower]

idk bruh i didn't even read anything here

[twin oar]

also sorry for bothering you in dms

[cinder flower]

i honestly don't even remember you dming me i'm sorry

[misty hamlet]

it is too hard

please

save me

[twin oar]

prob went to message requests

whats the command to repost original image

[cinder flower]

yes it would have and then i must have pressed ignore and forgotten you

[twin oar]

fair

, help

[jolly parrot]

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

[misty hamlet]

:C

[twin oar]

im almost done i just dk how to do with part B

if u want to see what i did for part A you can watch this he explains it p well https://www.youtube.com/watch?v=-5cw1xc8pTw

[misty hamlet]

oh my

ok

okok

ty for helping me :)

[misty hamlet]

are u still working?

[twin oar]

i kind of found something

[misty hamlet]

omg

[twin oar]

but idk if it';ll work and u shouldnt waste ur try on it

you cant have an interest rate of 0

[misty hamlet]

yeah

true

[twin oar]

in calc we learn something abt limits, so if u just plug numbers in closer and closer to 0 u'll get pretty much what the answer would be if u were to plug in 0

[misty hamlet]

i see

[twin oar]

so thats the best answer so far for payment B but ima keep looking

also desmos kinda doesn't know what to do with rlly small numbers and just think theyre 0

so when i make it smaller it just doesnt work

[misty hamlet]

wait

what did u get for

The difference in monthly payments between the two offers is ____

[twin oar]

i kept playing around and i got like 500 for B

[twin oar]

so just subtract this from B

so 1045.11-500

500 works

[misty hamlet]

so

545.11

[twin oar]

it seems so? but i dont want you to mess up ur last try lol

[misty hamlet]

lol

[twin oar]

ugh i think i figured it out just now too

can you retry?

[misty hamlet]

im not sure

do u at least know this one

its B right?

[twin oar]

i think so because you pay more with A

if u can retry, i learnt how to do it for p much any problem so i can give u the answer

the way we did A was right

but for B you just divide by however many years, because there is no interest

[twin oar]

im curious why this method didnt work tbh

desmos might of broke

[misty hamlet]

yeah

wait so

OPTION A

or

OPTION B

cuz i meant option B

[twin oar]

incentive B is the better deal i think because you end up paying more monthly

[misty hamlet]

o

yeah yeah

i agree

it says i got it right

for that one

[twin oar]

can u re-do?

do you understand how i did A ?

[misty hamlet]

yeah i do

but

its a little complicated

thank you for helping me anyway

i can't redo

but

you've helped me enough

and i am really thankful

[twin oar]

still wish i figured it out sooner

[misty hamlet]

its ok

thank you

:)

i mean it

.closew

.close

[pearl pond]

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[plush bramble]

Sure

How old are you little dude

<@&268886789983436800>

[pearl pond]

Channel closed

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[fiery glade]

.close

[fiery glade]

I was trolling im 18

[pearl pond]

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[unreal maple]

Hey was wondering if anyone could help find the inverse of the function

All I know is that you switch the x and y values

But that’s where I’m lost

If you could also check if I found the vertex form right, that would be nice

[manic wadi]

Inverse of y=-2/25x^2+4?

[unreal maple]

Yea

[manic wadi]

Solve for x first then interchange x and y

[unreal maple]

What

[manic wadi]

y=-2/25x^2+4, find x in terms of y from this equation

[unreal maple]

I’m confused sorry

[teal wren]

Replace the x in the equation with y and replace the y in the equation with x, then you solve for y.

[unreal maple]

Yea but I don’t know how to solve that

I see some videos of people square rooting and stuff

[teal wren]

Damn well im on phone so I can't really write it down sorry lol

[unreal maple]

You’re good

[manic wadi]

y=-2/25x^2+4
4-y=2/25x^2
25/2(4-y)=x^2
x=sqrt(25/2(4-y))
x=5/sqrt2*sqrt(4-y)

Replace y with x and you have the inverse function

, w inverse of - 2/25x^2+4

[jolly parrot]

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[manic wadi]

Perfect

[unreal maple]

Wait so to get rid of squared you need to square root it?

Oh wait got it thanks

.close

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[kindred solar]

I’ve been stuck on 10-12 because I still don’t understand how to do increasing/decreasing

[regal herald]

whens the gradient positive, and whens it negative

ie increasing and decreasing respectively

[kindred solar]

Um, maybe I’m slow but is the increasing for 10 (infinite, 0)?

[regal herald]

if you mean (-infinity,0) then yeah

but theres a second interval its increasing on too

[kindred solar]

Is it (-infinite, 0) U (2, infinite)

?

[regal herald]

seems valid to me

[kindred solar]

@regal herald do my answers look right?

[regal herald]

its a bit hard to read from that angle

[regal herald]

,rccw

[regal herald]

i cant really see the graphs that well but they seem okay yeah

[kindred solar]

Okie dokie!

Thank you 😁

.close

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[pearl pond]

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[dark ingot]

Can I interchange sigma and integration?

[dark ingot]

This is the question

I applied king rule and got
I = integration-pi to pi of sigma_r=0 to 999 cosrx

Can I interchange sigma and integration then?

[scarlet nimbus]

This is almost a fourier series

[dark ingot]

I haven't studied that

[scarlet nimbus]

Hm, what is a king rule?

[dark ingot]

Integration of f(x) from a to b is same as Integration of f(a+b-x) from a to b

[scarlet nimbus]

Btw, with a finite sum you can always exchange integral and sum

[dark ingot]

Thanks

.close

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[pearl pond]

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[dark ingot]

{x} = fractional part of x

{x}= x- floor(x)

[toxic lichen]

how tf are you expected to do this in 30 seconds

it's like... $\sum_{k=-3^{11}}^{3^{11} - 1} \int_{k^{1/11}}^{(k+1)^{1/11}} x^8 (x^{11} - k) \dd{x}$ i guess?

[jolly parrot]

Ann

[toxic lichen]

nasty as fuck

[tropic saddle]

why cant {x} be symmetric. that would be nice here

[dark ingot]

Is frac(x)+frac(-x)=1?

[toxic lichen]

think so yes

[dark ingot]

Then it is solvable in 30 seconds lol

[pearl pond]

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[bleak pecan]

Hello! I'm right now preparing for my mid-term in Real Analysis/Intro to Functional Analysis.
Given a metric space $(X,d)$:

1. If $S \subset X$ and $S$ is compact, prove that $S$ is complete.
2. Does the converse hold?

For 2. I am pretty sure it doesn't hold and the counterexample I picked was $(\mathbb{R},|\cdot|)$ as my metric space, and $S=\mathbb{R} \subset \mathbb{R}$, which is complete (completeness of real numbers) but it isn't compact.
I'm still thinking about number 1. so I need a bit of help with that.

[jolly parrot]

Darksaurous

[plush bramble]

what definition of compact do you use

topological or sequential

[pearl pond]

@bleak pecan Has your question been resolved?

[bleak pecan]

Sequential

[plush bramble]

you can try to do the usual eps/2 proof

|x_n - x_m| < |x_n - x_n_k| + |x_n_k - x_m|

[bleak pecan]

That's the usual way to prove that every Convergent Sequence is also a Cauchy Sequence, correct?

[bleak pecan]

But In this context we're using subsequences?
Let me recall the sequential compactness definition, every sequence has a convergent subsequence.
So in particular, let (x_{n}) be a Cauchy Sequence of said Compact Set, since every sequence has a convergent subsequence
then this Cauchy Sequence MUST have a convergent subsequence.

Ah I see

[plush bramble]

should be less than or equal to here, but you get the idea

[bleak pecan]

Yeah, and we use that convergent subsequence to prove that the Cauchy Sequence converges, said convergent subsequence is guaranteed to exist due to the compactness, therefore every compact set is a complete set since for any Cauchy Sequence in said set we'll get convergence.

Thank you, triangular inequality is the real deal

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[midnight haven]

Trying to understand sequence notation here and I see why he put "for n >= 2 here:

[midnight haven]

but why not something similar here:

Bottom right, it doesn't say something like "for k >= 1"

Any particular reason why please?

[bleak pecan]

Probably a mistake/forgot about it, but you're right, it should say "for k >=2", since you are defining the sequence recursively, which means you need to know the first term a_1 (k=1), and then every "subsequent" (k>=2) term will be defined as a result of operating the previous term.

Because clearly if you "evaluate" in k=1 you get a_1=a_0+3, and a_0 is not a "thing" so it would be absurd to consider that, but if you "evaluate" in k=2 then you get a_2 = a_1 +3 , and since you know a_1=1 then you get a_2= 1 + 3 = 4.

[midnight haven]

Ah okay, this makes sense.

Thank you so much for explaining!

[bleak pecan]

No prob! Sequences are cool, good luck with your studies!

[midnight haven]

Appreciate it, see you.

.close

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[ornate lotus]

Can someone describe how to solve this example?

[ornate lotus]

I don't know what I should do next

[scarlet nimbus]

You made a mistake somewhere that I can't spot but that last line is just wrong

The cubic factorizes to (x+1)(x-1)^2

[ornate lotus]

May be I'm stupid, but I am misunderstanding

<@&286206848099549185>

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[drifting spire]

Heyy

[drifting spire]

Is anyone avail?

[rigid mist]

just post your question

[pearl pond]

@drifting spire Has your question been resolved?

[drifting spire]

The width of rectangle card is 2cm less than its length the area is 35cm^2. Find the length and width

My answer was :
In this problem let l be the length and l-2 be the width

lxW=A
lx(l-2)=35
l^2 - 2l - 35 =0
(1+5)(1-7)
1+5=0
l=-5 (but since there is no negative measurement , this is not the solution)
Therefore
l-7=0
l=7
l-2=5

Width=5cm
Length=7cm

But I'm hesitating if it's right or wrong BC we're gonna do a presentation tomorow and my group members aren't helping me as I'm a transferee so please correct me (⁠ ⁠･ั⁠﹏⁠･ั⁠)

[rigid mist]

its right!

but whos a transferee

[drifting spire]

Meee

😭😭

[rigid mist]

what is a transferee

[drifting spire]

A new student

hshshshshs

[rigid mist]

oh

[drifting spire]

Also I have one question left and I've been tryin to figure it out 😭😭

[rigid mist]

you can post it here

[drifting spire]

Okay okay hold on

The difference of two numbers is 5 and their product is 925. Find their sum

THIS IS WHAT IM STRUGGLING TO UNDERSTSND ಥ⁠‿⁠ಥ

[rigid mist]

,w solve x-y=5 and xy=925

[jolly parrot]

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[drifting spire]

AHHH TAHNK YOUU

😭😭

Waitt but could you please explain how you got the formula? I'll add that to my knowledge so if I ever get asked I know what to say BC I reviewed HSSHS (⁠´⁠ ⁠.⁠ ⁠.̫⁠ ⁠.⁠ ⁠`⁠)

[rigid mist]

let two numbers be x and y and x>y
according to given conditions-
x-y=5
xy=925
and you have 2 equations and 2 unknown, solve it by substitution method

[drifting spire]

Oo substitution method?

[drifting spire]

Waitt how did the equation get

5 sqrt/149 + 1 ^ y
2

I'm a bit confused BC I'm a slow learner I'm sorryyy!! I wanna learn tho ಥ⁠_⁠ಥ

[rigid mist]

give me a min

,w y^2+5y-925=0

[jolly parrot]

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[rigid mist]

are you sure this is a correct question?

im pretty sure they wouldnt give you a question like this where values are this bad

[drifting spire]

Yeah

😭😭

I'm pretty sure it's 924 but the teachers said 925

[rigid mist]

,w y^2+5y-924=0

[jolly parrot]

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[rigid mist]

it should be 924😭😭

[drifting spire]

EXACTLY

[rigid mist]

can you confirm the value from your teacher

[drifting spire]

Yess I confirmed earlier but the teacher said 925

That's why I'm so confused TT

[rigid mist]

cant you just say that idk how to solve this💀

[drifting spire]

That's automatically zero grade for our group TT

[rigid mist]

what are your group members even doing

[drifting spire]

Sleeping..

But I was telling them to make a gc to discuss but no one sid

It's currently 2:10 am and I'm trying to finish 3 problems.on my own

Nd also BC I'm gonna be presenting 3 problems tomorrow

TT but I think I could only present 2

[rigid mist]

,w \frac{5\sqrt{149}}{2}-\frac{5}{2}+5

[jolly parrot]

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[rigid mist]

calc are allowed right?

[drifting spire]

Yessss

Sometimes TT

[rigid mist]

,w \frac{5\sqrt{149}}{2}-\frac{5}{2}

[jolly parrot]

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[rigid mist]

this decimal expansion upto 2 decimal places for the value of 'x'

[rigid mist]

and this one upto 2 decimal expansion for the value of 'y'

you can show this then

x=33.01
y=28.01

[drifting spire]

AHH ALL OF THESE R BIG HELP THANK YOU SO MUCH TT

[rigid mist]

TT?

[drifting spire]

Crying emojii

[rigid mist]

oh

[drifting spire]

Emoticon

[rigid mist]

okay

[drifting spire]

AHAHSAH

[rigid mist]

np

gl

[drifting spire]

THANK TOU SO SO SO SO SO MUCHH

ACKK TY FOR BEING CLEAR AT EXPLAINING

😭😭🤍

[pearl pond]

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[twin vessel]

I don't understand the part last part why the solution is 0.119, how can I put it into the calculator? I have fx-570

[twin vessel]

the math is about standard normal approximation to binomial

nvm

solved

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[fading hare]

how do we solve this?

[fading hare]

I am solving the partial derivatives with respect to r and s and then idk what im supposed to do

[feral sedge]

Find a linear equation with the same partial derivatives

z = ax+by+c

[fading hare]

Liks this?

[fading hare]

is this the right way? i feel like im missing something

[feral sedge]

That doesn't go through the point (2,1,-13)

[fading hare]

.close

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[rustic owl]

how to check convergence of this series?

[rustic owl]

i do in fact see that it should converge, because limit n->inf ln(1+1/n)/(1/n) = 1, but i have no idea how to show this

[plush bramble]

what test did you use there

[pearl pond]

@rustic owl Has your question been resolved?

[rustic owl]

I'm not entirely sure how it is called in English

if limit of an/bn exist, then they both converge or both divergent

but i'm sure i cannot use it here because i am basically dividing by zero

[plush bramble]

what's your b_n ?

if it's (1/n), then you should know sum 1/n diverges

[rustic owl]

1/n - 1/n

soo yeah, i do know i cannot do it this way

any ideas how to do this differently? 🤔

[pearl pond]

@rustic owl Has your question been resolved?

[rustic owl]

<@&286206848099549185> 🥺

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[kind mural]

Why is there an isomorphism between R^2 X R^3 and R^5?

[kind mural]

Course : Linear algebra

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[ivory harness]

how do i make a help channel

[drifting oasis]

this is what i’m working with <@&286206848099549185> however i’m not really fully understanding of it all and where to go with it

[pearl pond]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

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[drifting oasis]

<@&286206848099549185>

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[midnight haven]

b is tricky..

[midnight haven]

I get $1230=t^3+8t^2+40t$

[jolly parrot]

RecRio

[midnight haven]

I tried going the synthetic division way but I wasn't able to since no factors I could add gave me 0

[solid ivy]

can u use a graphing calculator

[midnight haven]

I don't have access to one

[solid ivy]

But you can use one

?

[midnight haven]

no

[solid ivy]

oh

[midnight haven]

not on the test anyways

[solid ivy]

w/e imma pull up wolfram alpha anyways ot check if we're not just chasing something hopeless first

,w t^3 + 8t^2 + 40t - 1230

[jolly parrot]

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[opal moss]

trying to solve that by hand is pure lunacy

all you need is an estimate

[solid ivy]

Yeaaaah we were never gonna get that root

Maybe the practice problems do assume you can use a calculator

[midnight haven]

maybe my work is wrong

[opal moss]

quickly checking by hand t=7 leads to a number smaller than 1230 and t=8 is way bigger so good enough

no, seems right

[solid ivy]

Actually yeah cus you divide by 0.92

[midnight haven]

so finding roots won't lead me anywhere

[solid ivy]

And so that should make 1500 bigger

,w 1500/.92

[jolly parrot]

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[solid ivy]

That's ugly

[midnight haven]

I just used the .5 rounding rule 😂

[solid ivy]

OK still should be 1630

,w 0.92*1500

Oops not 1630 I get u now

I didn't see the constant term at the end

Yeah ur work is right

[midnight haven]

okay, so it would have to be through actual math

and not roots

[opal moss]

you either give an estimate or say that you can find the real root of that polynomial and leave the actual root finding work to someone else

probably the latter

[midnight haven]

hmm

I guess this question is an exception

not sure why my teacher would recommend I do this

My teacher hates me 😂

[pearl pond]

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[sweet junco]

Is there like a theorem for this

[pearl pond]

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@sweet junco Has your question been resolved?

[pearl pond]

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[dawn gazelle]

how did they get 90 degrees when rho/z is undefined? when would it be 270 degrees?

[mental hinge]

remember that tan is opposite over adjacent

meaning the x coordinate of the point is 0

and the y coordinate is 6.325

so the angle would be 90 deg

270 would be if it was -6.325 on the numerator

[pearl pond]

@dawn gazelle Has your question been resolved?

[dawn gazelle]

yes thank you!

[pearl pond]

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[odd marsh]

i dont understand how to solve this

[midnight tartan]

this is a compositions of functions

to find f dot g

plug in the function for g(x) into f(x)

[pearl pond]

@odd marsh Has your question been resolved?

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[wild fable]

I’m pretty sure I did something wrong but don’t know

[pearl pond]

@wild fable Has your question been resolved?

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[tribal heath]

I need help with part B. I already found the derivative.

[west sapphire]

what did you find the derivative to be

[tribal heath]

2x

[west sapphire]

ok, just plug in x=-3

[tribal heath]

so answer is -8?

ohh

[west sapphire]

-3 times 2 has never been -8

[tribal heath]

-6

im sorry lol

[west sapphire]

yes

[tribal heath]

thanks

haha

.close

[pearl pond]

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[last summit]

bungo spotted

[west sapphire]

austin!

[last summit]

Bungo!

[west sapphire]

what's -3 times 2

[last summit]

-6

[west sapphire]

wd

[last summit]

it depends

[west sapphire]

you must be a mathematician

[last summit]

I am

apparently I accidently proved Bezout's lemma earlier today

atleast that is what Garlic said

when I was trying to do the gcd(n, n+1) thing

lol

[west sapphire]

i had to look that up, i forgot what it is

just the ax + by thing

for gcd

[last summit]

yes

[plush bramble]

Is it party time

[west sapphire]

it is now!

[last summit]

no actually

I have no questions

perhaps soon

[west sapphire]

ah bummer

[plush bramble]

Get in here @cinder flower

[west sapphire]

ask your prof for some new ones

[last summit]

well I mean I have a question

if we really want one

[cinder flower]

hi

[west sapphire]

sure

[last summit]

but this channel is claimed by not me

oh well

.reopen

[pearl pond]

✅

[last summit]

I will take over

[west sapphire]

tjay won't mind

[cinder flower]

@last summit

[plush bramble]

Austjay

[cinder flower]

where am i getting in

[last summit]

it seems obvious to me that for any 2 points in R2 there is a line connecting them, so like if it was required that a line go through 7 points this is like a linear algebra thing

[west sapphire]

damn these visualization questions haha

[last summit]

null space 5D

right

[cinder flower]

draw some pictures

[last summit]

somehow someway this is a 2x7 matrix with 5D nullsapce

is that not true

given 2 points in R2 there is a unique line that touches them both (unless you think lines are directional)
if this line must also go through a 3rd point, that 3rd point must be colinear.
If there is a 4th point not on the line, then you know it gets connected to one of the points on the line, and then again we have to add a colinear 5th point to this new line
but here is the deal now, these 4th and 5th points can have lines made with the 1st and 2nd points that were not colinear with them
and then those lines must both have another point, say point 6 and 7 on them, but then those two points you know, have a line in between them, and it must contain another point, but it doesn't so we are screwed

this is what my beautfiul drawing tells m

[west sapphire]

but is your beautiful drawing handling all possible cases

how do you know?

[last summit]

well I mean like no not if the 3rd point is on our original line

and the thing is I don't know

Layla is the one who wanted a picture

and I guess my professor too

[cinder flower]

yes pls, send picture

[west sapphire]

how do you know those new lines involving the 4th and 5th points don't intersect with two of the points you already accounted for

[cinder flower]

@rustic gate

send picture as well

[last summit]

there are too many points going on for me to understand this question

[west sapphire]

maybe choose one point as an anchor

draw a line through it

and then let that line rotate

it has to hit all the other points at some angles

each time it hits one, it has to hit at least two

see if you can find a contradiction by assuming they aren't all collinear

[last summit]

well then there has to be more than 7 points

[west sapphire]

why?

[last summit]

well

in words

our first line

like just p1 and p2 for now

we have 2 distinct points in R2

the line connecting them

is unique

and must contain p3

Now, like we assume that p4 and the other points are not also on this line

otherwise, we are done

so for contradiction suppose p4 is not on this line containing p1, p2 and p3

also for now we will call that line ^ L1

Okay, so then there is a line connecting any two points in R2.
So we get L2 connecting p4 and p1,
L3 connecting p4 and p3 and,
L4 connecting p4 and p2.

also, two lines in R2, so long as they are not the same line, intersect only once (if at all)

and since our L2 and L3 and L4 are all going to points on L1, they only intersect L1 once each

at those points which are already contained on L2 and L3 and L4

so these L2, L3, L4 have only 2 points on them each, from our p1,p2,p3, and p4

so L2 L3 and L4 must each have one more point on them

but the second we add these 3 new points, we get like new lines that must be formed, and new points that must be placed on those lines, and it keeps going

[tribal heath]

wait guys im tryna asl a qiestopm

[last summit]

and that is the only part I can;t formulate

[west sapphire]

so 7 accounted for now

[tribal heath]

its not letting me becaus this one is occupied

[west sapphire]

but now is the tricky part

[last summit]

omg lol sorry, I'll go open a new one

[tribal heath]

your fine haha

[last summit]

didn't realize you were actually still around XD

[west sapphire]

can you draw a new line through exactly two of those 7 points

[tribal heath]

[last summit]

Bungo, lets move to a new one!

[west sapphire]

ok!

[last summit]

.close

[pearl pond]

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[rain pagoda]

How do I find the roots of a polynomial equation given one imaginary root?

[toxic lichen]

show the polynomial?

[rain pagoda]

x^4 -5x^2 -10x -6=0
one of the roots is -1+i

[toxic lichen]

well

this is a polynomial with real coefficients

what do you know about the complex roots of such polynomials

[rain pagoda]

theres a conjugate right

so theres another root thats -1-i

[toxic lichen]

yes

right, so from the roots -1+i and -1-i you can write down a real quadratic that is a factor of your thing

and factor it out by any means you know

[rain pagoda]

so
x^4 -5x^2 -10x -6
(x+1+i)(x+1-i)

[toxic lichen]

simplify (x+1+i)(x+1-i) first

[rain pagoda]

(x+1)^2 +1?

x^4 -5x^2 -10x -6
x^2+2x+2

alr i got x^2-2x-3 so ima just factor that

so the roots are -1 and 3?

[toxic lichen]

seems correct

[rain pagoda]

other roots*

[toxic lichen]

yes

[rain pagoda]

tysm

.close

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[pearl pond]

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[midnight haven]

the two contrasts [
\omega_1 = \sum_{i=1}^k b_i \mu_i \tss{and} \omega_2 = \sum_{i=1}^k c_i \mu_i
]
are said to be orthogonal if $\sum\limits_{i=1}^k \ff{b_i c_i}{n_i} = 0$ or when the $n_i$ are all equal to $n$ if [
\sum_{i=1}^k b_i c_i = 0
]

[midnight haven]

i'm looking to prove this definition if possible, but I'm unsure on how that's meant to be done?

.close

[pearl pond]

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[pearl pond]

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[lucid wharf]

help

[lucid wharf]

this all i got so far

[primal blade]

sec^t=tan^t+1

Use this one the bottom

[lucid wharf]

oh

do i break the sec and tan down to sin and cos

[dim tangle]

rearrange tan^2 + 1 = sec^2 to get sec^2 - 1 on one side.

that'll give you the identity

then you can break into sin and cos and go from there

[lucid wharf]

so subtract 1 from each side?

how do i do that

or do i just move stuff

[dim tangle]

pythag identity is tan^2 + 1 = sec^2

[lucid wharf]

so just rewrite?

[dim tangle]

the original expression has sec^2 - 1, so we need to find something equivalent to sec^2 - 1, we take the pythag identity and rearrange to get tan^2 = sec^2 - 1

so we know sec^2 - 1 must be the same as tan^2

so we can now write as sec^2/tan^2

break into sin and cos and go from there

[lucid wharf]

?

[pearl pond]

@lucid wharf Has your question been resolved?

[pearl pond]

@lucid wharf Has your question been resolved?

[plush grove]

the sec^2(t) -1 on the bottom can be rewritten as tan^2(t) due to the Pythagorean identity, so that gives you

let me draw it

do you follow?

The top would just be 1/cos^2(t) because csc^2 can be rewritten as 1/cos^2

and the bottom is rewritten as sin^2(t) /cos^2(t) because sec^2-1=tan^2

afterward, you multiply bottom and top by the denominator of the top fraction like so:

@lucid wharf

[lucid wharf]

ohh

ok

yeah that made sense

[plush grove]

so what did you get as your final answer

@lucid wharf

[lucid wharf]

its 1/sin^2(t)

?

[plush grove]

yes and what does that translate into

[lucid wharf]

csc

[plush grove]

since its a sin^2(t) it would be csc^2(t) but yes, correct

[lucid wharf]

ty

[pearl pond]

@lucid wharf Has your question been resolved?

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[wintry leaf]

i got a question

[wintry leaf]

i need help with my math test - dilations and scale factors

[fleet sky]

like with a current test you're taking?

[wintry leaf]

yes

well

forget the test i need personal help with my delta math

[fleet sky]

sorry my dude it's against the rules to help on a test in this server

[wintry leaf]

no not the test anymore

i need help on my delta math

[fleet sky]

if this is a non-test question than feel free to post the problem and where you're stuck and if someone knows how to do it they'll jump in

[wintry leaf]

ok

[pearl pond]

@wintry leaf Has your question been resolved?

[pearl pond]

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[pearl pond]

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[high geyser]

I need help with part C