help-27

[proven schooner]

I will mark help-27 to make sure I can com eback to review.

[storm crater]

Okay

I can also explain this transformation formula's idea some more.

Intuitively it should make sense to you.

[zenith hatch]

When finding a limit of a multivariable function aren't there infinite paths that the limit could take?

Doesn't that mean we have to check infinite paths

To make sure they all are equal

And thus prove that the limit exists

But how do we get away with just a few kinds of paths?

Like my textbook solves every limit question in under 3 steps

[polar bolt]

#❓how-to-get-help but yes

[zenith hatch]

What do you mean?

Asking a question isn't rocket science

[feral scarab]

Mate, there’s rules you need to follow for asking questions, do you not understand that?

[devout snow]

@proven schooner Has your question been resolved?

[devout snow]

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[placid rover]

I was curious about the discriminant part. So using the method to solve depressed cubics (pinned in #prealg-and-algebra)

[woven radish]

Shuri2060

[placid rover]

Which indeed gives me that exact discriminant scaled by a constant. But what I was wondering was does it matter I have y^2z =

Why should I not have brought y^2 onto the right hand side at the beginning?

ie. B - y^2 would have been the constant

===
(Asking here cus the other channels r occupied)

Ok now I thought about it... discriminant comes about from setting the equation to zero... something about the roots, so it makes sense to set y^2 = 0 at the start

🤔

So I get 0 =

B^2 - 4A^3/27 is a factor of 27/4 away from what was given... but ig that's good enough

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[misty sky]

Can anyone help this is a qs from differential eqs.

[misty sky]

I cant understand how to proceed

[dim spindle]

you can solve it with the separation of variables method, after you rearrange the equation using the logarithm rules

you'll need the second rule

@misty sky

[misty sky]

Ahh i see i see

Thank you💞💞

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[bronze junco]

round to the nearest tenth it says. am i wrong?

[devout snow]

@bronze junco Has your question been resolved?

[bronze junco]

<@&286206848099549185>

[bronze junco]

<@&286206848099549185>

[narrow plank]

Can you send a larger screenshot? Are you sure there isn't something missing?

(Assuming that they want an angle in the first quadrant)

There are an infinite number of real solutions for x in this case

[devout snow]

@bronze junco Has your question been resolved?

[bronze junco]

I got it

[devout snow]

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[formal haven]

<@&268886789983436800>

[solid trail]

<@&268886789983436800>

[celest dock]

ty.

[solid trail]

bruh

[celest dock]

.close

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[formal haven]

So pointless

[celest dock]

kids will be kids

[tidal plinth]

Can someone help me with my question?

[formal haven]

#❓how-to-get-help (4)

[devout snow]

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[restive river]

Did i do this graph correctly?

[restive river]

.close

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[restive river]

Hello. I need help about this.

[restive river]

Please ping me if you can help me. Thanks!

[formal haven]

Proofs

@restive river The one on the left should use transitive property

[restive river]

I see.

How bout the right one?

[devout snow]

@restive river Has your question been resolved?

[devout snow]

@restive river Has your question been resolved?

[restive river]

<@&286206848099549185>

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[warped pasture]

x^2 + 1/x^2 = 5
x^9 + 1/x^9 = ?

[exotic stump]

what have you tried?

[warped pasture]

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[rich briar]

so in here i have lim x to -1^-

[rich briar]

and im not sure which formula i should use for it

[exotic stump]

well what does that denote

-1^-

[rich briar]

what i think is -1^- is 1/-1 which is eventually = -1

so 2nd ?

[exotic stump]

no, it doesn't represent an inverse

[rich briar]

why

[exotic stump]

because that's not what that notation means

it means "approaching from the negative side"

or the left side, if you prefer

[rich briar]

hold on im not following

which notation

[exotic stump]

$\lim_{x\to \textcolor{red}{-1^-}}f(x)$

[woven radish]

a disappointing son

[exotic stump]

the red

[rich briar]

yes

isnt that gonna give me -1 at the end

[exotic stump]

?

[rich briar]

because the exponent is minus

so 1/-1

[exotic stump]

.

[rich briar]

so what does it represent

[exotic stump]

.

[rich briar]

meaning

[exotic stump]

meaning it approaches -1 though negative numbers

https://www.youtube.com/watch?v=6e4Wtgc43KQ

[rich briar]

im a lil bit confused but -1 is already negative

okay i'll watch this

[exotic stump]

i know it's like 2+ hours, but the first part goes over one sided limits

[rich briar]

ooh

2 hrs

[exotic stump]

the first few minutes should be what you need

[rich briar]

okay but the question i have doesnt have any graphs

[exotic stump]

that was just to get you to understand what a one sided limit was

and what the little plus and minus signs represent

[rich briar]

if they dont match it means DNE

[exotic stump]

if the right side and left side limits aren't equal, the limit does not exist, yeah

[rich briar]

but what they actually mean without the graph

like in an equation

[exotic stump]

same thing, approaching from the negative/positive sides

$\lim_{x\to -1^-}f(x)$ means the limit as x approaches -1 from the left

[woven radish]

a disappointing son

[rich briar]

i still dont understand why from the left side its 2 but from the positive side its 3

IS IT THE ARROW

[rich briar]

yeah i know but why not the opposite ?

what makes 2 specifically " left side " and not right

[exotic stump]

other way around

it's the fact that it's approaching from the left side that makes that limit 2

[rich briar]

so its the arrow indicating that its approaching from the left side ?

[exotic stump]

i drew that arrow indicating it's approaching from the left side

[rich briar]

nono the arrow that is already existing in the graph

with the hollow point

[exotic stump]

no that's indicating that the graph keeps going

[rich briar]

brother... then how am i supposed to tell

[exotic stump]

because i'm assuming you know what left is

[rich briar]

they both lay on the same x axis

[exotic stump]

there is a side to the left of -3

and there is a side to the right of -3

[rich briar]

so he said 2 is approaching from left and 3 approaching from positive

why not the other way around

[exotic stump]

from the left and from the negatives mean the same thing

[rich briar]

my bad

oh okay

i know why now

but how am i gonna use this knowledge to solve my question

[exotic stump]

which one of those equations will use the numbers approaching from the negative/left side of -1

[rich briar]

-1 coming from the negative direction does that mean x is less than -1 to inf

[exotic stump]

yes, the x's less than -1

and which one represents the function for x less than -1

[rich briar]

first

[exotic stump]

right

[rich briar]

so now i just simply plug in x with 1 in the 1st formula

i mean -1

[exotic stump]

yep

[rich briar]

okay what about -1 coming from the positive direction

is it the 2nd formula or the 3rd

[exotic stump]

you want numbers immediately to the right of -1

so which one represents that

[rich briar]

im not sure

they both kinda do

[exotic stump]

one of them doesn't include numbers immediately to the right of -1

one of them does

[rich briar]

so they have to be linked

[exotic stump]

you're just looking for the one that represents the numbers right next to your limit

so for the first one, you wanted the one that represented the numbers immediately to the left

well what's a number immediately to the left of -1? let's take -1.1

-1.1 is less than -1

so we're wanting the one that takes x values less than -1

same concept for this one

you want ones immediately to the right of -1

one of them has those numbers in its range

one does not

[rich briar]

oh so its the 2nd cause its equal or greater than -1

[exotic stump]

yep

[rich briar]

thanks

i'll try to solve it

what about the ones without signs what does it mean in the graph

[rich briar]

can you review before i submit?

@exotic stump hey man i got wrong answer for c

idk why

5(-2)3+3= -2

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[rich briar]

.close

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[viral hawk]

hi

[viral hawk]

how do u find x

if

x is 0 mod 5, 5 mod 6 and 5 mod 7?

i tried

this

6*7 + 5 = 47

47*5 = 235

but then

235/6 is not 5 mod 6

and 235/7 is not 5 mod 7

[restive river]

can you elaborate

[viral hawk]

so

x is divisible by 5

@restive river

[restive river]

yup

[viral hawk]

i tried 6*7 + 5

because x can be 47

47 is 5 mod 6, 5 mod 7

and it is smallest

then i multiplied by 5

because x is divisible by 5

but it doesn't work

[restive river]

47=5[6]
47=5[7]

it's gonna be 5

because x=0[5]

[viral hawk]

wait the question says that x is greater than 7

[restive river]

x=0[5] thus it is a multiple of 5, it can also be written as x=5[6] and x=5[7]

[viral hawk]

yes

but how do u do it

@restive river

[restive river]

im thinking

[viral hawk]

ok

[restive river]

(x-5)=6*a; (x-5)=7*b; (x-0)=5*c

[viral hawk]

hmm ok

oh ok

[restive river]

wait

CRT ?

[viral hawk]

nvm

<@&286206848099549185>

<@&286206848099549185>

ello

@restive river can u solve it?

😦

<@&286206848099549185>

nevermind

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.close

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[outer geyser]

Could I get help for this

[solid trail]

hm

[solid trail]

alright

try rewriting $S_3$ and $S_5$ in terms of $a$ and $d$

then do a system of equations

shouldn't be too hard

[woven radish]

Chromium

[outer geyser]

Am I going in the right direction?

[solid trail]

yea

[outer geyser]

I had online classes for this topic and the wifi was unstable

Ok thanks

How do I do this?

[outer geyser]

How do I do this?

[solid trail]

$\begin{cases}
3a + 3d = 6 \
5a + 10d = 11
\end{cases}$

[woven radish]

Chromium

[solid trail]

shouldn't be too hard

[late estuary]

Solve for one term and substitute into the other equation

[outer geyser]

So I just have to sub a and d into this equation right?

[solid trail]

yea

[outer geyser]

Ok I got the answer

Tysm!!

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[noble cairn]

Can anyone help with number 7 I have no idea

[noble cairn]

Here is worker solution

I don't understan why

Dm me pls I'm going to bed

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[wispy panther]

How do I find the tangent here?

[solid trail]

tangent of this function?

derivatives

[wispy panther]

Yes of this function

[solid trail]

do you know derivatives?

[wispy panther]

Yes

[devout snow]

@wispy panther Has your question been resolved?

[devout snow]

@wispy panther Has your question been resolved?

[wispy panther]

<@&286206848099549185>

[devout snow]

@wispy panther Has your question been resolved?

[wooden wraith]

Your question isn't very clear. What exactly are you trying to do?

[wispy panther]

I’m trying to find the function of the tangent

[marsh linden]

at what point tho

or did you mean the general equation of a tangent? to this line?

at x= x0

you can do that

[restive river]

Yeah ig that is what they want

[marsh linden]

y0 = f(x0)

y-y0 = f’(x0)(x-x0)

so final answer is
y = f’(x0) (x-x0) + f(x0)

[marsh linden]

^^

is that what you wanted ?

you can substitute any value of x for x0 to get a tangent at x =x0

[wispy panther]

I need to find the tangent point that goes through 0,0

[wispy panther]

Hi, if I want to find m for y-y1=m(x-x1) I have to put 0 instead of X in here, however that just makes an error. Any help?

[spare gull]

So, this is the slope the tangent line would have, right?

What would the equation of the tangent be at any given point? Did you find that?

@wispy panther

[wispy panther]

Didn’t find it

[spare gull]

Do you know the general equation of a line when given the slope?

[wispy panther]

Not really

[spare gull]

It's the one Rylo typed out, this one:

This is your equation of the tangent line for the function f(x)=sqrt(-4-x) at any given point x0

But this is not what is asked of you

You are asked to find at which point x_0 the tangent line, namely y = f’(x0) (x-x0) + f(x0) passes through (0, 0)

With me so far?

[wispy panther]

Yes

[spare gull]

Because it passes through (0, 0), we know that x=0, y=0 lie on that line; so you can sub then into the tangent line

And you are left with an equation with one unknown, that is x_0

(x_0, f(x_0)) is the point where the tangent line touches the function f(x)

You can graph it to visualise this better

[wispy panther]

I have this

[spare gull]

Show me f(x)

[wispy panther]

-4-x

[spare gull]

Wait, why do you have 2 lines?

[wispy panther]

h(x)=root of -4-x

[spare gull]

Okay

[wispy panther]

The green line doesn’t seem to be relevant

[spare gull]

Since you chose different notation just to complicate stuff, can you show me the equation you have for the tangent of h(x) ?

[wispy panther]

I am trying to find the equation for h(x)

[spare gull]

You just told me that

[wispy panther]

It’s meant to start with y=

Sorry if I’m not making sense

[spare gull]

Can you please delete what you have and follow the notation that you are given

[woven radish]

Alter

Alter

Alter

[wispy panther]

x=0, y=0

[spare gull]

?

[wispy panther]

I’m just trying to understand 1sec

[spare gull]

Are you unable to substitute x_0 into the derivative and the function itself here?

[wispy panther]

I am unable to do it because it will leave a negative number in the root

In the derivative

[spare gull]

No, you won't

How would that happen?

[wispy panther]

In here

[spare gull]

You have no idea what x_0 is

[woven radish]

Alter

[wispy panther]

I was not taught this, I do know x_1 and y_1

For y-y_1=m(x-x_1)

[spare gull]

It's the same thing

except you don't know y_1 and x_1

Just

;- ;

[woven radish]

Alter

[wispy panther]

Yeah

[spare gull]

Was this hard?

Are you sure you understand where this came from?

[wispy panther]

Yes

I understand

[spare gull]

And what is y?

What does this equation represent

[wispy panther]

The tangent to function

[spare gull]

And what do you know about the tangent to the function f(x)?

In your problem, not in general

[wispy panther]

That the tangent point is 0,0

[spare gull]

Weird way to say that ''The line passes through (0, 0)'' or ''The point (0,0) lies on the line''

[wispy panther]

The line passes through

[spare gull]

So if the line passes through (0, 0) you can substitute x=0 y=0 and get a value for x_0

[wispy panther]

In here, right?

[spare gull]

Yes

That is the line that passes through (0, 0)

[wispy panther]

Same issue I had at the start

Did I do it right

[spare gull]

[wispy panther]

[woven radish]

Alter

Alter

[wispy panther]

So is this the answer

[spare gull]

I believe your question was: "Find the tangent line of $f(x)=\sqrt{-4-x}$ that passes through (0,0)." Right?

[wispy panther]

Can you put it through the bot

[woven radish]

Alter

[wispy panther]

Yes

[spare gull]

Then no

You have some line y expressed in terms of x and x_0

You know the value of y

You know the value of x

You don't know the value of x_0

Find the value of x_0

[wispy panther]

Alright

[spare gull]

This is that y

[wispy panther]

Yeah

We are doing this for 1 hour already I think, maybe I should just talk to my teacher because I think there is a problem with the question

[spare gull]

No, there isn't

There is a problem however when you keep substituting x_0=0 when I keep telling you that you've no idea what x_0 is, you need to find x_0

You know y and x

[wispy panther]

The thing is that we have never used x_0 in class, only y-y_1=m(x-x_1) which is what I’m trying to find rn

[spare gull]

How does the name change anything?

[wispy panther]

I don’t know honestly

[spare gull]

It doesn't

[wispy panther]

Alter I really appreciate your help but I think that I’m just not understanding what I’m supposed to do or what the question wants me to do, it’s fine I will just ask my teacher tommorow

[devout snow]

@wispy panther Has your question been resolved?

[devout snow]

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[proper bloom]

How does 2 root 10 become negative ?

Because I get that it’s adj/hyp so I came to 2root 10/11

[main gull]

The quadrant

Hyp is always positive

[main gull]

And because quad 2 is (-x , +y) that meant adj was negative

[proper bloom]

What would quadrant 4 be ?

Like (blank,blank)

[main gull]

Coordinate plane

It's based on that

[proper bloom]

Ok thanks

.close

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[jaunty badger]

hElp

Been trying to figure this one out for a while

[devout snow]

@jaunty badger Has your question been resolved?

[long kettle]

In order to find the tangent line, we need the slope and a point

How do we find the slope?

[jaunty badger]

We can find the slope by plugging in the point for each function

Sorry for the late response

[long kettle]

I was referring to the derivative

The slope is the derivative

If R(x) = f(x)/g(x), what's R'(x)?

[jaunty badger]

[f'(x)g(x)-g'(x)f(x)]/g(x)^2

[long kettle]

And what's R'(4)?

[jaunty badger]

g'(x) should be -5

[long kettle]

Yep

But we want R'(4)

[jaunty badger]

I don't have my paper to write down with, but from the graph we can find the slope of x=4 for f(x)

[long kettle]

Are you certain about that?

Nvm

I misread your comment

In order to find R'(4), we need f(4), g(4), f'(4), and g'(4). We know g'(4). What about the rest?

[jaunty badger]

We can find f(4) from the graph = -3

f'(4) will be the slope of the tangent at 4

g(4) = -3

I think that's it.

[long kettle]

Are you sure g(4) = -3?

[devout snow]

@jaunty badger Has your question been resolved?

[jaunty badger]

6, my bad

[long kettle]

Yep

So plug those values in for R'(4)

[jaunty badger]

And that's it?

[long kettle]

That'll give you the slope, yes

And you already know the point: g(4) = 6

So you just need to use y-y1 = m(x-x1)

[jaunty badger]

Got it

Thank you!!

[devout snow]

@jaunty badger Has your question been resolved?

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[devout snow]

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[restive river]

How am I supposed to set up this problem?

[restive river]

I know im supposed to use the geometric series formula

but im not sure how to set up the a4 and a7

[solid trail]

suppose the series is $a_n = a \cdot r^n$

you can solve for a and r

[woven radish]

Chromium

[restive river]

n=7 which is the exponent

but how do i solve for a and r?

an equals to both 108 and 2916?

[copper mango]

what is $a_4$ given the general term Chromium wrote out for you?

[woven radish]

Mosh

[restive river]

108 = a * r^4

[copper mango]

and a_7?

[restive river]

2916 = a * r^7

[copper mango]

yes, so you can solve for a and r

[restive river]

2916 + 108 = a * r^4 + a *r^7

is this correct?

[copper mango]

That's correct, not helpful in solving for a or r though

[restive river]

Im not sure what step to take.

Perhaps

2808 = r^3

?

[copper mango]

almost

you get r^3 from 2916/108

not minus

Recall exponent laws

[restive river]

then

27 = r^3

r = 3

108 = a * 3^4

a equals to 4/3

an = 4/3 * 3^n

How do I use this to find the partial sum sn?

[copper mango]

partial sum of geometric series has a known formula

[restive river]

Got it

thank you!

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[untold crow]

Hello?

[untold crow]

May i ask what is the formula of this

I don't know what the formula is

[light oyster]

umm

for the first one

[untold crow]

Never mind!!

[light oyster]

lol

[untold crow]

I GOT IT!

[light oyster]

ok

cool

[untold crow]

Thanks btw

[light oyster]

wc (I did nothing)

[untold crow]

My classmate responded

[light oyster]

ok

[untold crow]

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[pastel glacier]

Ok i just need some misconceptions cleared up about the cauchy integral formula

[pastel glacier]

For this one i know that $|z-i|=1$ is the circle of radius 1 centered around the point $z=i$. so, since $\frac{1}{z^2+1}$ is analytic everywhere in this disk except for the center, that cant be my function $f$ right? so i would make it $f(z)=\frac{1}{(z-3i)(z+i)}$

[woven radish]

united9jackson

[pastel glacier]

if this is right i should be ok, since i had made a mistake with the boundary before. what would i do in the future if every function i try to choose for f has a discontinuity on the boundary itself?

[devout snow]

@pastel glacier Has your question been resolved?

[pastel glacier]

<@&286206848099549185>

[icy depot]

If I understand your question, if that was the case then the integrated function itself would have a discontinuity on the boundary on which you are asked to integrate it, which would mean an ill posed problem @pastel glacier

[pastel glacier]

ah ok

so the reasoning behind what i did here is correct, and if there is a discontinuity on the boundary in the general case i just need to be really careful and cant apply CIF?

[icy depot]

Yes your reasoning sounds good to me.
For the second thing, you won't encounter such a case, because the integral would not be well defined if there is a discontinuity on the boundary

Or do you have a specific example you're referring to?

[pastel glacier]

if its ill defined then thats good to know that i wont encounter such a thing, i didnt have another specific one

thank you mat

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[dark canyon]

one family bought a TV, with its value rising by 12%. What is the initial price of the TV, if after the price increase it pays for a 6-month installment of 336 dollars

[devout snow]

@dark canyon Has your question been resolved?

[dark canyon]

<@&286206848099549185>

[split stream]

what do you understand so far?

can you explain what you've tried?

sdoing that will give your question a better chance of being answered

[restive river]

is the rise per month?

[split stream]

not quite

[dark canyon]

no like in general

[dark canyon]

ok so i have tried 336x6 wich is 2016 and 2016-241.92 which is 1774.08

but i think i am wrong

sorry for the late response'

[split stream]

it can be helpful to give names to unknown variables

you know the total price paid is 2016

can you re-express your problem in form of an equation

[dark canyon]

i dont understand what you mean ?

i am not from a an english speaking country so strange words like that are hard for me to understand

[split stream]

that's ok

[woven radish]

DarQ

[split stream]

can you write 2016 in terms of x?

sry, gtg

you took too long to respond I'm afraid

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[cobalt cloak]

is this

the same as this

[placid narwhal]

Is O18 same as $$\delta x$$

[digital grotto]

is O18 already delta multiplied with x or only one of those variables?

[woven radish]

Pluton

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[full prawn]

I am doing a basic algebra problem in maths where you get certain algebraic expression and get different x-values that you use to solve thet equations

Here, we have a family (with their age), and I have made an expression for their age when:
It's five years later,
Double the age:
Four years ago
ten years ago
and half the age

[full prawn]

I've written the expressions in Excel, and I want to know if there's some way that it solves the expressions for me when I give a certain x-value

[narrow plank]

Switch the rows and the columns, so the ages run up and down:

42
47
18
13
4

And then you can use an equation to tell what Excel should put in a given box relative to another box

[full prawn]

Worked like a champ! Excel is such an awesome tool once you learn how to use it.
Thanks for the help

[narrow plank]

Yeah - np 🙂

Same with Google Sheets 👍

[full prawn]

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[quasi harness]

Can I get help solving this

[patent tartan]

,rotate

[fervent ibex]

8x²+11x-2=0

I couldnt to ( )( )

[exotic stump]

do you know log rules?

[quasi harness]

I got it before but I wasn’t sure if it was correct

[quasi harness]

Yes this is what I got

[exotic stump]

don't do people's work for them

[quasi harness]

.close

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[patent tartan]

lol

[devout snow]

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[fervent ibex]

What do you mean

[fervent ibex]

Isnt helping the thing here?

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[long kettle]

Keyword is help, not do it for them

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[languid mulch]

could anyone help verify my answer? any help will be appreciated.

[devout snow]

@languid mulch Has your question been resolved?

[languid mulch]

<@&286206848099549185>

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@languid mulch Has your question been resolved?

[languid mulch]

<@&286206848099549185>

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@languid mulch Has your question been resolved?

[languid mulch]

<@&286206848099549185>

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[mossy bridge]

Only 39 and 40

[narrow plank]

Mind rewriting those? Somewhat tricky to see

Is lg the natural log (base e)?

[mossy bridge]

base a

And base b

[narrow plank]

log base a of 2 is a?

[mossy bridge]

No

[narrow plank]

And log base b of 3 is b?

[mossy bridge]

It’s just a notanion

U should somehow

Substitute that

In log9(20)

[narrow plank]

What does lg 2 mean?

[mossy bridge]

Log10(2)

[narrow plank]

And it wants you to write the rightmost expression in terms of a and b?

Do you have a screenshot of the original problem?

[mossy bridge]

Yeah

[mossy bridge]

That’s the original

[narrow plank]

Interesting - I guess the problems were handwritten for some reason

[mossy bridge]

Yeah

It’s a homework note

Maybe the teacher couldnt figure out how to place all of that

In word

Or sum

[narrow plank]

Well, I’d start with a change of base in the rightmost expression

To get a base of 10

It might be easier to rewrite the problem on your own and testing things out

[mossy bridge]

Nvm

I’ve already figured it out

Thanks anyways

[narrow plank]

👍

.close if appropriate e

[mossy bridge]

.close

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[thorn sparrow]

I'm having trouble drafting an equation for the graph.

[vast rain]

do you have the graph though?

[thorn sparrow]

Like the Cartesian plane or the actual drawing of the graph?

Wait, forget I said that

No, I don't have the graph.

<@&286206848099549185>

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[thorn sparrow]

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[keen meteor]

how can i convert a matrix to be diagonally dominant? is there a method i can learn? or do i just use trial and error?

[zenith jacinth]

diagonally what ?

[copper mango]

abs value of a_{nn} is larger than anything else in the row

[keen meteor]

like this

but i have to convert it from the systems of equation above

[hidden wind]

Are there any differential equations help channels?

[zenith jacinth]

#odes-and-pdes

[hidden wind]

Thank you!

[zenith jacinth]

well this thing is new for me so I can't really help

[devout snow]

@keen meteor Has your question been resolved?

[haughty torrent]

i'd convert it to RREF and then go from there

i think that's the simplest way actually

[devout snow]

@keen meteor Has your question been resolved?

[devout snow]

@keen meteor Has your question been resolved?

[proper flare]

find the missing number

i don't get it

[winged ice]

(27*2)/6

take the denominator of the first fraction and multiply it by the numerator in the second

devide it by the numerator in the first fraction

[keen meteor]

i need to find the diagonally dominant matrix of this

[keen meteor]

<@&286206848099549185>

[supple knot]

Camil already told you to put it into reduced row echelon form

[keen meteor]

i cant do that since I will use jacobi method

if i do that I will already get the values of xn so I dont need to use jacobi method anymore

[supple knot]

Then what do you need help with?

You're just following the procedure here right?
https://en.m.wikipedia.org/wiki/Jacobi_method

[keen meteor]

yes but before I can use jacobi method it must first be strictly diagonally dominant

which the given matrix was not

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[devout snow]

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[tender kelp]

solving polynomials by factoring

[solid trail]

what have you tried

[tender kelp]

didnt learn in class so idk

well she had a lecture but she did it poorly

40 minute lecture, everyone got lost 5 minutes in

should i add 9x to other side?

[solid trail]

yes

[tender kelp]

done

uh

now wut?

do i factor x out?

x(x^2-10x+9)

[slender mirage]

plug x = 1, 0 and throw out the factors by factor theorem

[tender kelp]

i dont understand sorry

plug 1 and 0 for x?

is that what ur saying?

solved it

just had to search online

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[rustic ivy]

I'm confused on how to write the answer for this one. Do I write it as -2,2 or the (infinity,-2), U (2,infinty) ?

[low plinth]

I need a help

[devout snow]

@rustic ivy Has your question been resolved?

[fleet mauve]

No you can't write $(-∞,-2] U [2,∞)$. Here you will be taking whole interval between -2 and 2, we just have to exclude -2 and 2 , any other value is allowed.
So you gotta write R-{-2,2}

[woven radish]

hoi

[rustic ivy]

I'm struggling to understand. Okay so I can't right it as (-∞,-2] U [2,∞) but then is the answer not written as x≠ -2,2?

type a integer or a fraction so would that just not be it?

or x≠R-{-2,2} going by what you said

[fleet mauve]

Yeah it can be written that way too

[fleet mauve]

No no it isn't x≠ it's x=R-{-2,2}

[devout snow]

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[river thorn]

how do i find the length of ||x-1/2||?

[river thorn]

hm the formatting got weird

let me write it up

how do i calculate the length of x-1/2?

[plucky stone]

what you wrote is weird... Is x a vector? Then you can't subtract 1/2 from it...

[river thorn]

sorry lemme write up the entire thing, its gram schmidt process for a inner product

[plucky stone]

now it makes more sense:)

If you have a scalar product, then $||p||^2=<p,p>$ and $||p||=\sqrt{<p,p>}$

[woven radish]

Alexander42

[river thorn]

ah so its the integral from 0 to 1 of (x-1/2)^2

then sqrt the result?

[plucky stone]

yes

[river thorn]

oooof course it is i had the inner product definition right in my face lmao

thanks

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[median kayak]

hey so I have these Data points and I want to find out at which point the curve that would go through these points has it's elbow so at which point the return on investment starts to get smaller and smaller

I tried using lagrange interpolation to get a polynomial function to approximate the function but it clearly looks like a logarithmic function so I don't know how to approximate that.

[devout snow]

@median kayak Has your question been resolved?

[median kayak]

<@&286206848099549185>

[polar bolt]

Just fit the data to a function?

[median kayak]

yeah exactly

we know that it will probably keep on rising for more hours but we can't keep the pump going that long so we need to find a good cutoff point where the change is minimal

[polar bolt]

?

[median kayak]

yeah

[polar bolt]

What is “yeah” supposed to mean? Do it?

[median kayak]

Yeah I want to fit the data to a function

[polar bolt]

Any software can do it

[median kayak]

I tried lagrange inerpolation and that fits the data but it doesn't fit it correctly

[polar bolt]

Any software can do it, Excel, R, TI…

[median kayak]

Yeah I tried that already but the function I get from the software isn't correct

this is a function I got from software and as you can see it looks correct from -13 to 291 but at higher values it starts to rise waaay too much

[polar bolt]

Because it doesn’t fit log

Its fitting a polynomial

[median kayak]

yeah and thats my problem because I have a x = 0 and y = 0 no software can fit log

[polar bolt]

Yes they can…

Or take exp of your data

Now its linear

[median kayak]

and then?

[polar bolt]

Use any software just as before

Except now even more softwares can do linear

[median kayak]

hmm ok I'll try that. Thank you !

[median kayak]

Ok excel definitely can't do a log fit with x = 0. If I click the log option it just deletes the regression line

[polar bolt]

Yes it can…

[median kayak]

What am I doing wrong?

[polar bolt]

Can’t see what you are doing so how would I know

[median kayak]

I plotted the data as a scatter plot, then added the regression line and tried to fit it as a log instead of linear

[polar bolt]

And what is the problem? It looks fine

[median kayak]

That is a polynomial curve

[polar bolt]

“Polynomisch”

[median kayak]

if I hit the log option the regression line just vanishes with the erorr message "Values can't be negative or 0"

[median kayak]

Yeah it's german sorry

[polar bolt]

Because log(0) isn’t defined?

[median kayak]

Yeah I think thats why

And thats why I said Excel can't fit it when x = 0 and y = 0

[polar bolt]

Because log isn’t defined at 0

That is just a property of log, nothing to do with Excel

[median kayak]

yeah I understand that

[median kayak]

but you said excel can do it

Just wanted to point out that it can't

[polar bolt]

Because you are trying to take log of 0

[median kayak]

That is what I said yeah

[polar bolt]

And hard to understand what you mean with partial sentences

[median kayak]

Sorry for not being clear enough.

But yeah I don't know how to fit a log curve if my data starts from 0

I'll try the exponential thing though

Hmm ok yeah getting the linear function works but I kinda forgot that that doesn't solve my problem of finding the elbow of the curve

[devout snow]

@median kayak Has your question been resolved?

[devout snow]

@median kayak Has your question been resolved?

[median kayak]

.close

[devout snow]

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[blissful elk]

Hallo to everyone here

Was wondering if I could get a little help with this Further Mechanics question.
Part (a) is done and I believe I've got part (b) done as well.
My tension equation looks very much like what v^2 looks like only with m instead of a.
The part I'm stuck on is Part (c) where I get a value that cannot be arcsined to get a value. Wondering if I've gone wrong with my tension equation or the question has incorrect values.
Hope to get a little help soon!

[devout snow]

@blissful elk Has your question been resolved?

[blissful elk]

<@&286206848099549185>
Any of you peeeeeeps able to help me out a little?

[devout snow]

@blissful elk Has your question been resolved?

[blissful elk]

Someone...anyone able to help me with this question?

[analog trellis]

The tension T in the string becomes zero.

[blissful elk]

I understand that much

[analog trellis]

What did you get for part (b)?

[blissful elk]

(mg/2)(5+4sin(theta))

[analog trellis]

I get:

$T = \frac{mg}{2}(5 + 6\sin \theta)$.

[woven radish]

stabulo

[blissful elk]

So I'm a factor of 2 sin out

Am I just missing a 2mgsin somewhere?

[analog trellis]

When theta = 0, we have that the centripetal force is equal to 5mg/2.
When theta = theta, we have the same net force acting toward O but now there's a component of weight too.

[blissful elk]

The weight's going to be in terms of sin, isn't it?
So...in theory I should have started my calc with t - mgsin(theta) = (m(v^2))/r

[analog trellis]

T - mgsin(theta) = mv^2/a where v^2 was found in part (a).

[blissful elk]

Yeah, noice. That makes more sense now that you've shown it like that

[analog trellis]

T = 2mgsin(theta)/2 + mg/2(5+4sin(theta)) = mg/2(5 + 6sin(theta)).

[blissful elk]

Nice, Thanks for pointing that out and thanks for the help!

Makes a lot more sense now, just missed out a key part of the question lel

[analog trellis]

🙂

[blissful elk]

.close

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[restive river]

my question is how to calculate experience needed until level up if:
experience needed to gain 1 level is 5000 BUT:

• every 100 levels:
• 1st level needs 500 experience
  -2nd level needs 1000 experience
  -3rd level needs 2000 experience
  -4th level needs 3500 experience
  -5th level - normally 5000 experience

example:
from level 3 -> 4 you need 3500
from level 45 -> 46 you need 5000
from level 100 -> 101 you need 500
etc
lets say level = 410
and experience = 1988758

[restive river]

answer to that should be about 3700 experience needed

but i need like formula how to calculate

<@&286206848099549185>

[graceful cosmos]

What about level 5 to level 6?

[restive river]

5000

[graceful cosmos]

Oh, okay I must have meant level 6 to level 7

[restive river]

its still 5000

[graceful cosmos]

Okay so it's 5000 all the way up until level 100?

Then back down to the 500,1000,2000,5000 ect

[restive river]

nah every level is 5000 except 1st 2nd 3rd and 4th every 100 levels

so 101 -> 102 is 1000

100 -> 101 is 500

102 -> 103 is 2000

103 -> 104 is 3500

104 -> 105 is 500

105 -> 106 is 5000

and 5k every level up to 200

and again 200 -> 201 is 500

etc

[devout snow]

@restive river Has your question been resolved?

[devout snow]

Channel closed

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[restive river]

.reopen

[devout snow]

✅

[slender mirage]

well, I feel like I can generalize it but are you interested in a game? lmao

[restive river]

i mean it is game

[slender mirage]

here's how to calculate though >_<

choose a starting level

[restive river]

o thats what you mean

lol

[slender mirage]

no I mean

literally

choose a starting level

before we can start the calculation

[restive river]

lowest that is

[slender mirage]

1?

0?

[restive river]

yes 1

[slender mirage]

so you level up to level 2 if you've gained 500 xp at level 1?

[restive river]

wait no

starting level is 0 but you get 500 at start

so its 0

sorry

my bad

[slender mirage]

Aight

so, you start with 0 and to upgrade to level 1, you need 500 xp?

[restive river]

Yeah

to go to 2 level you need 1k

to go to 3 level you need 2k

[slender mirage]

now

choose your final level

till where you wish to calc. total no. of xp needed

[restive river]

There is no final level

[slender mirage]

umm

let's just say for the sake of an example

what level do you wish to calculate the sum till?

[restive river]

3k

[slender mirage]

alright 3k it is

would've been way better if they were random numbers but whatever

So

Let's start

500 for level 1

[restive river]

wait

did i mention

there are inputs?

[slender mirage]

?

Yeah lmao

[restive river]

but two inputs

[slender mirage]

mhmm

[restive river]

overall exp and current level

[slender mirage]

geez, just give me two numbers for initial and final levels

[restive river]

i dont understand what you mean

[slender mirage]

Anyways,

so we started at level 0 [as you suggested we start from level 0]

500 xp for level 1

500 + 1000 for level 2

500 + 1000 + 2000 xp for lvl 3

[slender mirage]

.

500 + 1000 + 2000 + 3500 for lvl 4

500 + 1000 + 2000 + 3500 + 5000(1) for level 5

500 + 1000 + 2000 + 3500 + 5000(2) for level 6

500 + 1000 + 2000 + 3500 + 5000(3) for level 7

.
.
.

500 + 1000 + 2000 + 3500 + 5000(96) for level 100

[restive river]

[slender mirage]

,calc 500 +1000 + 2000 + 3500

[woven radish]

Result:

7000

[slender mirage]

= 7000 + 5000(96) xp for level 100

now,

for level 101, you add 500 to this

so basically, if you count a 100 level upgrade as one cycle, then you've basically begun a new cycle

[restive river]

Yes

[slender mirage]

and since level 0 to 3000 is basically 30 cycles, the total amount of xp you need would be 30 times the amount of xp required for the first cycle

which is 30 times (7000 + 5000(96))

so,

[restive river]

so we remove this from our exp

and we get this?

[slender mirage]

total amount of xp required to upgrade from level $0$ (which you gave me as the initial level) to level $(3000)$ (which you gave me as the final level) is $30 \times (7000 + 5000(96))$

[restive river]

yes

,calc 7000 + 5000 * 96

[woven radish]

Result:

4.87e+5

[restive river]

o

how do i multiply

,calc 7000 + 5000x96

[woven radish]

The following error occured while calculating:
Error: Undefined symbol x96

[restive river]

nvm its right

[devout snow]

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[fast finch]

I have been trying to solve this question for the past 15m and im stuck
When i lower the value of x in negatives x² keeps growing and no need to go to positives since it will make it even bigger (i think)

[devout snow]

@fast finch Has your question been resolved?

[fast finch]

<@&286206848099549185>

||sorry||

[supple knot]

you know $x^2 = - x - 1$ so you can plug that in for $x^{16} = (x^2)^8$

[woven radish]

riemann

[supple knot]

and repeatedly lower your powers

[fast finch]

hmm

Oh

Oh i got it now

Answer is A

Thank you!

[supple knot]

[fast finch]

.close

[devout snow]

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[heady willow]

could you explain this question

<@&286206848099549185>

[restive river]

The y axis gives you your c value

[heady willow]

i do not understand

do you subsitute

[restive river]

Yes

Substitute

The y axis then the x axis

[heady willow]

could u show the full process of working the questioin out

[restive river]

-18=0^2+b*0+c

c=-18

[heady willow]

oh ok

i did that

what would you do next

[restive river]

0=6^2+6b+c

0=36+6b-18

[heady willow]

ok

[restive river]

6b=-18