help-23

[lean otter]

I got the answer because I am looking at these examples it gives me and I can just substitute the variables they give with the ones in my problem

But I don’t know why it is right and the explanation doesn’t make sense to me

I think I am having trouble relating this to anything that is meaningful to me. They are all variables so I can’t pin them down with any actual numbers and when I try to it doesn’t work. It does clearly state how they relate to each other so I think it probably would work out if I used numbers that satisfy the equations but it’s time consuming and I don’t know if it would actually help me understand anything

It might just be something I have to talk with my teacher about but I’m out of school right now for health reasons so I can’t even do that

And since it’s pretty fundamental parts of algebra it makes it difficult to build onto it when I don’t have that foundation to begin with

wait actually I get it now lol

I just had to read the explanation

I am too dramatic I think I can do this now lol

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[rancid root]

Could someone explain #7 to me

[rancid root]

like how to solvew it

GL2(Zp) is the # of invertible 2x2 matrices in Zp

and so the first row, there are p^2-1 options I believe

but then how would I find the number of options for the 2nd row?

I know that it has to be the number of vectors that aren't linear combination of the first row, making the matrix linearly independent'

but how would I find this number

someone help pls 🙏🏿

<@&286206848099549185>

someone please help 😢

.clse

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[solar cradle]

Hey guys if you have -1/-5 does it become positive 1/5 or stay negative since it didn’t actually divide into it

[lean otter]

This is exactly the same as $\frac{-1\cdot 1}{-1\cdot 5}$, yeah, you can make it positive.

[flat frigate]

3317

[solar cradle]

Even though it didn’t actually divide?

[final halo]

what is "it"?

[solar cradle]

The equation

[final halo]

be more specific

[lean otter]

I think he means it is represented as a fraction instead of 0.2 or something.

Still, algebra knows what it does.

[solar cradle]

-1/-5 can’t divide into itself and when a negative and a negative divide successfully then it becomes a positive

[lean otter]

In Algebra we Trust.

[solar cradle]

But it didn’t

That’s why I’m confused

[lean otter]

What do you mean -1 can't be divided by -5?

[final halo]

-1/-1 = 1

[final halo]

just look at this

[solar cradle]

Yeah but -1 goes into -1

So it’s successful

[lean otter]

You must think of division in other terms.

It's not always to be thought as "how many times this fits in that"?

[solar cradle]

Isn’t that what division is

[lean otter]

Division has many interpretations.

Recursive subtraction, the factor definition, etc.

[solar cradle]

Im just thinking that when something has been divided then the operation has moved forward where as if you try to divide something that isn’t divisible like 1/5 why should the negatives disappear? When the operation did not happen

[lean otter]

There's no "operation", brother.

It's not like there's some mastermind that manually does those calculations for you.

It's just a representation.

1 can be represented as $1$, $\frac{\int_{0}^{\pi}\sin(x)dx}{2}$ or $\sum_{i=1}^{\infty}\frac{1}{2^i}$. It doesn't mean you're actually doing anything of that.

[flat frigate]

3317

[lean otter]

They're just different representations.

I'll explain in a different way.

Can you simplify $\frac{2a}{2}$?

[flat frigate]

3317

[solar cradle]

You can divide the 2s

And it’s just a

[lean otter]

Precisely. If you have a common factor in the numerator and the denominator, removing it doesn't change its value.

Now for any real $n$, isn't $-n$ just $-1\cdot n$?

[flat frigate]

3317

[solar cradle]

Yes

[lean otter]

Mighty fine. Then, you can write your fraction as $\frac{-1\cdot 1}{-1\cdot 5}$, correct?

[flat frigate]

3317

[solar cradle]

I guess so, just seems strange Mayby my brain is faulty

[final halo]

$\frac{\left(\frac{-1}{-1}\right)}{\left(\frac{-5}{-1}\right)}$

[lean otter]

No, there's nothing wrong with your brain.

[final halo]

bit gross but i think this might be the operation youre looking for

[solar cradle]

Oh

[final halo]

wait i missed signs

[lean otter]

Parentheses would help a bit I guess.

[flat frigate]

ΣAC

[solar cradle]

That’s strange but I think I understand a bit

Hmm

Hmm okay I’ll try and remember this , thanks for the explanations

Hopefully it becomes more natural

[lean otter]

Glad to help.

[solar cradle]

Hopefully I’ll become as smart as you guys

[lean otter]

You will!

[solar cradle]

Mayby

🙏

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[jaunty plover]

how do i do 4i ?

[lean otter]

,rotate

[raw pivot]

do you know trig identities?

[jaunty plover]

yes

[stark idol]

sin x = cos(90-x)

[jaunty plover]

so what do i do with that

[stark idol]

cos(60+x)=cos(90-x)
60+x=90-x
x=15

only one value of x in [0,180] range satisfies the equation which is 15

[jaunty plover]

how do i know if there’s more than one value

if there were to be

[stark idol]

there are formulae for that

if sin x = sin y
x=nπ + (-1)^n . y

if cos x = cos y
x=2nπ ± y

where all angles are in radians and n is an integer

[jaunty plover]

hm okay thankyou

what about the next question?

[stark idol]

do the same thing

either convert sin to cos or cos to sin

[jaunty plover]

what’s the cos to sin thing

[stark idol]

cos(90-x)=sin x

sin(90-x)=cos x

[jaunty plover]

so

if i get

45-x=90-x

how@do i solve that

or have i not done that right

[stark idol]

you have

but that means there is no solution to the equation in the 0 to 90 range

use the formula I gave

[jaunty plover]

this?

[stark idol]

yes

don't forget to convert to radians

[jaunty plover]

what is n

[stark idol]

start with 0, find x, n=1, find x, n=2, find x... do this until the value of goes outside the specified range

you can take negative values of n too but it's irrelevant for this question

[jaunty plover]

i don’t think i’m doing it right

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[random cypress]

Which of the given sequences converge? If necessary, determine the limit value. Justify your answers.

need help to start this excerice

<@&286206848099549185>

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@random cypress Has your question been resolved?

[ancient burrow]

this converges, hint: sandwich lemma

[random cypress]

whats that

[random cypress]

.

[ancient burrow]

https://en.wikipedia.org/wiki/Squeeze_theorem

sorry it's called sequeeze theorem in english apparently

@random cypress

[random cypress]

ok thanks

and how can i solve this

@ancient burrow so the awnser must be xy

[ancient burrow]

no

what are your upper and lower bounds?

[random cypress]

upper

n = 1 to + infinity

[ancient burrow]

that's not an upper bound to this sequence

plus keep in mind that your bounds need to converge to the same value

[random cypress]

ok lemme try again

im not sure if i get you to 100%

[ancient burrow]

Start like this: y is strictly bigger than x, so what is an upper bound for x^n+y^n?

[random cypress]

n sqrt y^n?

wait

[ancient burrow]

Close!

If y>x then 2y>= x + y, how can you utilize this?

[random cypress]

sorry im out it is hard for me to understand what you mean im not english

i dont get it fully sorry

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[storm hawk]

heyo

[storm hawk]

I'm doing a math submission and help is allowed, so I'd like some assistance throughout if it's not an issue

[split ether]

Just post the question

[storm hawk]

It's in GeoGebra and there's already a task that's confusing me. I had to make three points in the coordinate system called J, M and F. The first task is "Draw a vector J in a coordinate system so that it starts in the point M"

Does it want me to draw a vector from point M to point J?

[split ether]

Looks like it just needs to start in the point M and J is just the name of that vector (starting in M)

But did you mean that J, M and F are the coordinate names?

[split ether]

Ah

[storm hawk]

Starting in M and ending in origo?

[split ether]

From M to J perhaps

[storm hawk]

Yeah that's what I thought as well

but the task just says that the vector is called J and that it's supposed to start at M

[split ether]

Ah

[storm hawk]

Also the next task is weird as well. "Find all the angles in the triangle JMF"

[split ether]

Maybe you need to move the vector OJ

So that it starts on M

[storm hawk]

wdym

[split ether]

Draw a vector from the origin to J

[storm hawk]

these are the tasks btw

[storm hawk]

But that doesn't start at M?

[split ether]

Yes

Yes

And then draw that vector starting at M

[storm hawk]

So MJ?

[split ether]

No

Draw OJ

Then draw the same thing but in a different place

So that it starts on M

Imagine moving it there

[storm hawk]

oh

how would I do that on geogebra?

[split ether]

Never works with geogebra so idk lol

[storm hawk]

tf the entire submission is supposed to be on geogebra

no use of pen and paper

[split ether]

But you can calculate the coordinates of the end of that vector

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[trim jackal]

how can you go about proving that a parametric equation of the form x(t)=sin(pt)+cos(qt), y(t)=sin(rt)+cos(st) will always be symmetric about the y-axis if p and s are even natural numbers, and q and r are odd natural numbers

[trim jackal]

like what method of proof would be useful? and how would you show that is always the case?

[compact ferry]

write the general equations and you can prove it directly

[plucky elk]

are p=s and q=r ?

if so i'd write
$p = s = 2n$ and $q=r= 2m+1$ for some positive integers $m$, $n$

[flat frigate]

riemann

[plucky elk]

then maybe use some sum angle identities could yield interesting results

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[trim jackal]

oh thats not a bad idea

[trim jackal]

what do you mean by the general equations?

[plucky elk]

x(t)=sin(pt)+cos(qt), y(t)=sin(rt)+sin(st)
didn't you have a cosine somewhere for y?

[trim jackal]

oh yes its supposed to be cosine, I am just really tired

the second term in y is supposed to be cosine

[trim jackal]

here tho, p and s and q and r dont have to be equal, it seems to work if p and s are just any even natural numbers and q and r are any odd natural numbers

[plucky elk]

yea then you just need more integers than just n and m

p = 2n, s = 2m, q = 2a+1, r = 2b+1. already looks awful but hopefully some identities will be useful

another idea is to find the t1, t2 such that when x(t1) = -x(t2), that y(t1) = y(t2)

[trim jackal]

thats what I was thinking of doing

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[mental patrol]

I don’t know how to start this 😢

(This are practice problem)

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[mental patrol]

<@&286206848099549185>

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[mental patrol]

.reopen

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✅

[wheat cave]

this looks like you have to solve it geometrically, make a graph after noting the points

[mental patrol]

So after I plot the points they give me I answer 32 but not sure how they want me to describe relationship? As positive or negative or describe another way?

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[full raft]

yeah basically. so as x increases, what happens to y?

📈 < - in this one, as x increases, y also increases

📉 <- as x increases, y decreases

[mental patrol]

Looks like it decreases

Oh

[full raft]

so yeah you can write that :]

[mental patrol]

Okay. So looking at the graph I had would it be accurate to say that as x increases, y decreases? (I think that’s what it looks like, from the days they give?)

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[bold ferry]

<@&268886789983436800>

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[lean otter]

I have no idea how to solve c). I hope you can help me.

[graceful sorrel]

Ok

[pseudo scroll]

You know the formula for the surface area in terms of height and radius

Equate the derivative to 0

dr/dh

[graceful sorrel]

Ye this guy got this one imma head out

[lean otter]

okay perfect, thank you!

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[lean otter]

we have to make a the subject is it possible to leave your answer as this form

[lean otter]

here it does shows that a is being made the subject

[idle sage]

yesh seems gd

[thin bridge]

ideally you'd adjust the signs a bit to make the expression nicer

[lean otter]

that’s where i couldn’t find my error

[compact ferry]

just multiply by $\frac{-1}{-1}$

[flat frigate]

Gijs

[lean otter]

i think a is being made the subject so i can leave as it is

[compact ferry]

you absolutely can

[lean otter]

maybe i just can then

[compact ferry]

its just that

$\frac{b^2}{b-c}$ looks slightly better lol

[flat frigate]

Gijs

[lean otter]

I didn’t understand how it’s being made actually

[compact ferry]

just multiply by $\frac{-1}{-1}$

[flat frigate]

Gijs

[lean otter]

this last step like how did this turned out

[compact ferry]

$\frac{-b^2}{c-b} \cdot \frac{-1}{-1} = \frac{b^2}{b-c}$

[flat frigate]

Gijs

[lean otter]

i think here i went confused

[compact ferry]

$\frac{-1}{-1} = 1$

[flat frigate]

Gijs

[compact ferry]

so its okay to multiply by that

again though, this is optional

but it will be important to know this concept in the future

[lean otter]

it’s like how did -1 and - 1 came

[compact ferry]

.\

its optional

[lean otter]

alright then

[compact ferry]

its like you can write a third as a fraction as $\frac{-1}{-3}$ but thats weird right

[flat frigate]

Gijs

[lean otter]

as it’s optional i can skip it

[compact ferry]

well yes

but if you look at the answer sheet it will probably say the "nicer" answer

you need to be able to recognise that they are the same thing

[lean otter]

okay thank you

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[hollow nymph]

How do I simply this determinant?

[hollow nymph]

I want to turn it into a Vandermonde type of determinant, or at least simply it so I don't have to calculate so much.

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[hollow nymph]

<@&286206848099549185>

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[lusty widget]

Sup

[lusty widget]

oh damn im green bro

ok anyways

heres my question

the first part of the question

yooo is my buddy here

@lean otter

shit wait shouldnt have pinged

[idle sage]

Hiiiii

you can use similar triangles

[lean otter]

Yeah I'm too dead brained from physics mi can help u lmaoo

[idle sage]

so you can start with $\frac{r}{R} = \frac{\sqrt{h^2 + r^2}}{h-R}$

[flat frigate]

swaggofishballs

[idle sage]

HAHAHAH

[lusty widget]

bruh how tho

[lusty widget]

i geddit man its all g

[idle sage]

let me try drawing it for you

here u go!!

two triangles

the pink and the green one

[lusty widget]

oh bruh

how did i not get that

thx bro

[idle sage]

welcc!!

[lusty widget]

.close

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[waxen hollow]

I can't seem to get the right answer from the textbook

It's number 17

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[waxen hollow]

<@&286206848099549185>

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[lament citrus]

I'm confused on which question you are attempting

[fair oasis]

would the answer be [4/3 -x₃ , -2/3 + x₃, x₃] ?

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[waxen hollow]

17

[waxen hollow]

Yeah

[fair oasis]

oh did u solve it

nice

[waxen hollow]

Actually the problem was that I had to apply all the elementary rows operations to the vector

In order to set the reduced row echelon of the matrix * x = (the projection of b on W)

[fair oasis]

Ah I see

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[mental patrol]

I am having a difficult time with 48. I think that A is correct? I am not sure if it is or how to tell what other statements are true (maybe C I think is true?)

I have never looked at an SPSS output before

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[mental patrol]

<@&286206848099549185>

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@mental patrol Has your question been resolved?

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@mental patrol Has your question been resolved?

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@mental patrol Has your question been resolved?

[grizzled fossil]

Says R is 0.709

[mental patrol]

R squared is a coefficient ?

[safe radish]

@mental patrol Has your question been resolved?

[grizzled fossil]

What?

[safe radish]

@mental patrol Has your question been resolved?

[mental patrol]

I was wondering if you mean the list of answers or what it says in the SPSS output

[grizzled fossil]

if you read the output it says R is 0.709

[mental patrol]

Oh I did not see, in Model 1. I would not Select A then? Since R and R squared are not the same

[grizzled fossil]

R squared is R^2

so yes R and R^2 is not the same

[mental patrol]

Okay, so I would not select it 🤔

[mental patrol]

I think C probably is the only true option?

[grizzled fossil]

yes

[mental patrol]

Okay

[mental patrol]

Tyvm!

.close

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[viscid nacelle]

what is the angle on the red part ?

is it 30 ْ or 60 ْ ?

[kindred cloak]

depends on where the earth is

[safe radish]

@viscid nacelle Has your question been resolved?

[viscid nacelle]

what do u mean ?

[kindred cloak]

you need to give me what status the ball is in

otherwise finding that red angle is pretty much impossible

[wind magnet]

1/ The fomula for potential energy is P = mgh, where P is potential energy, M is mass, G is gravity and H is height
a. Write a fomula for H
b. Find the height an object is raised if the mass is 2Kg and the potential energy is 200J (G = 10m/s)

2/ The function y = 3.5x + 2.8 represents the cost y (in dollars) of a taxi ride of x miles
a. Indentify the independent and dependent variable
b. You have enough money to travel at most 20 miles in the taxi. Find the domain and range of the function

Pls help me for the test next week

[viscid nacelle]

there are no status

[viscid nacelle]

the question gave me those information only

[kindred cloak]

hmm

can you tell me what the dotted line is then?

[viscid nacelle]

its forming a right angle triangle

[kindred cloak]

no like

why is it drawn as 30 degrees

it could be 45 and that would still be a triangle

[viscid nacelle]

no those are from the question

[kindred cloak]

i dont get the context

<@&286206848099549185>

[viscid nacelle]

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[mental patrol]

I am not sure what A wants me to say?

[safe radish]

@mental patrol Has your question been resolved?

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@mental patrol Has your question been resolved?

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@mental patrol Has your question been resolved?

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@mental patrol Has your question been resolved?

[mental patrol]

I think X1 and X2 are the independent variables but I am not sure what A means by interpreting B (or what constant means?)

[mental patrol]

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[tight sentinel]

i think somewhere went wrong on the 4th or 5th one

[peak smelt]

you didn't bracket properly

in 2nd to last line

but u actually follow thru correctly

to be completely honest not sure how you got D = dy/dx

[tight sentinel]

um sorry that was bc i was being lazy and didnt want to write out dy/dx everytime

[peak smelt]

ohhh

everytime there is a dy/dx its a d

ohh so this is differentiation

implicit

i think everything is right? why do u think u made a mistake

[tight sentinel]

$D=\frac{1}{2yx^2+4y^2x+2y^3+2y-1}$

[flat frigate]

minor2ndchar

[tight sentinel]

im not sure but i think this is more correct?

[peak smelt]

to be completely honest that looks right?

oh

wait

[peak smelt]

how did you get the latex version?

[tight sentinel]

uh i typed it out

oh wait thats not what you meant

sorry

[peak smelt]

yea aha

its ok

[peak smelt]

this looks right to me, but u can check it on a website like Wolfram alpha?

[tight sentinel]

i plugged in the third line into mathway

[peak smelt]

its all correct

[peak smelt]

i checked on a differentiation calc

[peak smelt]

thats the same

as what u have

if u expand ur brackets

[tight sentinel]

oh wait its in a different order

[peak smelt]

its equivalent

[tight sentinel]

i didnt notice that

[peak smelt]

yes

ahaha

thats why i was confused earlier

i thought it was the same thing

https://www.derivative-calculator.net/

this website is rly good for checking/doing derivs

i normally double check my answers with this

[tight sentinel]

thx very much

[peak smelt]

no worries

good luck :)

[tight sentinel]

.close

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[lean otter]

Can someone please check what I got wrong

I’ll fix my steps after

[junior smelt]

Looks right to me, but you can convert the (k+1)!(k+2)

And brackets for this to make it clear that it's $(k+1)! [(k+1)^2+1]$ you're working with

[flat frigate]

chartbit

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[orchid patio]

can someone check this work?

i need help with part b

[zinc oasis]

Hey guys, this is a gcse questions I’m about to send but nobody in gcse servers has got it correct

It’s so much harder than it looks

Unless I’m missing something obvious

[lean otter]

make your own channel

[stray socket]

Ah yes, asking for help on a final exam

Idk how you even got a photo of it

[orchid patio]

its from last year dw, my professor gave it to us so we can study for this year's final

it says 2021 up top

[stray socket]

The maximum rate of change is just the gradient

The gradient by its nature will always point in the direction of greatest initial increase

[orchid patio]

mhm, so then the rate of change of it will be the magnitude of the gradient, right?

[stray socket]

Well no, just the gradient

Idk why it says rate of change

Lemme google that they mean by "rate of change"

[orchid patio]

okay

[stray socket]

Well apparently the magnitude of the gradient is the maximum rate of change so

[toxic stratus]

,w e^(xy - y^2){y, x - 2y} at (x,y)=(1,1)

[flat frigate]

Results provided by WolframAlpha

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Requested by 夢雪#2250

[orchid patio]

oh okay, yeah thats what i thought it was

[toxic stratus]

looks okay i guess

gradient gives direction of greatest increase

it's magnitude is the rate of change

it does not make sense to say the gradient is the rate of change as the original function is a scalar quantity

while the gradient is a vector quantity

[stray socket]

Ayo snow you mind helping the guy in #help-28 because I gtg and I fear this man's gonna start mass pinging me

[toxic stratus]

i gtg too

[stray socket]

Poor guy

[toxic stratus]

[wild cape]

it just wants the magnitude of the gradient, not for you to normalize it

[orchid patio]

oh mhm that makes sense

thanks

.close

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[frank mason]

Need help with this please

[frank mason]

No one to help me

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[pastel barn]

i think the first step is to take ln

of both sides, bring the product of x to the front

Not sure where to go from here

[lapis pulsar]

i think the powers of x are for each individual x

either way its just a little trick if u can spot it

the answer is kinda right infront of u

[pastel barn]

I guess i can divide by lnx

[lapis pulsar]

if x^x^x^x^x^... = 2 then you can sub that 2 into the exponents since its infinite

[pastel barn]

Then its ln(2-x)

[lapis pulsar]

the way ur doing it isnt correct since its not x^x * x * x * x...

[pastel barn]

Dont exponents multiply?

[lapis pulsar]

it multiplies if the power is to the whole term

[pastel barn]

Oh yea

[lapis pulsar]

but in this case each x is raised to the x

[pastel barn]

Yup ur right

But can u give me another hint?

[lapis pulsar]

x^x^x^x^x^x... = 2 right

[pastel barn]

Yea as given in the quwstion

[lapis pulsar]

so what can u say x^(x^x^x^x^x^x...) is

[pastel barn]

Root x of 2?

No

2 tp the power x

Right?

[lapis pulsar]

x^2

since x^x^x^x^x^x... = 2

so x^2 = 2

[pastel barn]

So x is root 2

[lapis pulsar]

yeah

[pastel barn]

Makes sense

Ty sm bro

[lapis pulsar]

np

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[south linden]

doing parfrac decomposition and i feel like i messed this up

i have an irreducible quadratic but i dont think i set it like this

[junior smelt]

Why partial fractions? Couldn't you just notice here that the numerator is a multiple of the derivative of the denominator and do it like that?

[south linden]

yeah i just noticed that lol

however running into a similar problem here

[junior smelt]

If you complete the square in the denominator, you should get $(x + 4)^2 + 100$, right? From there, I think change the integral to be of $$\frac{1}{100} \cdot \frac{1}{1 + (\frac{x+4}{10})^2} $$

[stray socket]

So yeah

Complete the square

And then this is where arctangent becomes your best friend

[south linden]

so yeah i have the x+4^2+100

hm

[flat frigate]

chartbit

[stray socket]

Arctangent my beloved

The sole reason why someone had a breakdown in my class

[south linden]

sorry im confused

i have to turn denom into something like x^2+1

so im going to have to take out a 1/100

[stray socket]

Let u = (x+4)/10

[south linden]

oh

ic

is this not the answer?

[stray socket]

Nope

[south linden]

where did i go wrong

[stray socket]

So far you have:
$\frac{1}{100}\int\frac{1}{\left(\frac{x+4}{10}\right)^2 + 1}dx$$

Apply U-Sub:

$$\frac{1}{10}\int \frac{1}{u^2 + 1}du$$

[stray socket]

You didn't apply u-sub correctly

[south linden]

right

[stray socket]

u = (x+4)/10
du = 1/10 dx

Which means 10 du = dx

You cannot forget to write the dx

It's still a part of the integral

[south linden]

ah

so ill have an extra factor of10

[flat frigate]

Umbraleviathan
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[stray socket]

Although somethings feels off

It shouldn't be this easy ...

Yeah no something's wrong

Hold on

Well I'll be damned

It is that easy

[junior smelt]

,w integrate 1/(x^2 + 8x + 116) dx

[flat frigate]

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[south linden]

.close

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[lunar timber]

question

[lunar timber]

does this look good

[junior smelt]

Looks all good to me!

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[shrewd ridge]

How do I solve this

[shrewd ridge]

I don’t think long division will work

[slim oracle]

nope definitely not

because you're x at the denominator has bigger exponents overall

so what would you do

[safe radish]

@shrewd ridge Has your question been resolved?

[shrewd ridge]

Idk? Factorise ?

[slim oracle]

well you can start by putting 4x(x+2) at the top

[shrewd ridge]

Yea I did that

[slim oracle]

and then at the bottom, you can find two numbers that equal to 2 when added together

to create x^4+6x^2-4x^2+9

[shrewd ridge]

The denominator cannot be factorised right ?

[slim oracle]

well it can because then after this, you can say (x^4+6x^2+9)-4x^2

and do a quadratic formula

and that leaves you with (x^2+3)^2

-4x^2

so now you just develop the equation

which gives you a)

I don't know if it was very clear

[shrewd ridge]

Let me try to solve it

[shrewd ridge]

And is a solved it using Photomath

This is way to difficult for an mcq question 💀

Ans*

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[mystic ether]

bro

[mystic ether]

help me sketch this vector

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[mystic ether]

fuck you

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[lean otter]

FOR II

i know its n + 1

but i dont know how to prove it

the cardinaliity of a set is 2 ^ n

meaning if s = {1, 2, 3,4} then there are 16 equivalent classes plus the empty set so 17

but there are only 4 distinct classes

i dont know how to prove this thi

besides me knowing via example

[timber pike]

hello can i ask for help here

[quasi bison]

@timber pike open your own channel. #❓how-to-get-help

@lean otter you are wrong on multiple accounts there

[lean otter]

rip

[quasi bison]

"the cardinality of a set is 2^n" sounds like a misremembered version of something about cardinalities of powersets

[lean otter]

2 to the power of elements in n

[quasi bison]

namely that if |S|=n then the cardinality of P(S), not just any set, is 2^n

[lean otter]

i dont get |s| = n

ohhh

|p(s)| = n

[lean otter]

but is it n + 1

i dont know how to prove that the cardinalty of all the sets are between 0 and n

[quasi bison]

what's "it"?

[lean otter]

equivalence classes based on the relatipn

relatio

relation

[quasi bison]

well, yes, the number of equivalence classes is n+1. each one corresponds to a possible cardinality of a subset of S, which ranges from 0 to n.

[lean otter]

So I have to prove that S always has a cardinality of 0 to n

.close

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[safe radish]

Please don't occupy multiple help channels.

[solemn orbit]

can you elaborate?

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[median blaze]

Hello can somebody help me with Logarithmic Functions

[median blaze]

<@&286206848099549185>

[nova creek]

!15m

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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.

[nova creek]

Everyone's pinging helpers today

[median blaze]

I'm looking for these answers . Can you help me?

[regal girder]

what's the empty log in the first one?

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[little mica]

So I've the following autonomous DE

[sonic widget]

can somebody help me

The length of the smallest side (or leg) of a right triangle is 16. The lengths of the other two sides are consecutive odd integers. Use the Pythagorean theorem to solve for the the larger of the two missing sides (the hypotenuse).

[little mica]

How do I calculate the limit

[sonic widget]

help me

[little mica]

Yo @sonic widget , try another channel. Already have this one

[sonic widget]

Oh

my bad big shaq

[little mica]

Np, can try to solve ur problem whilst I'm waiting for help

[sonic widget]

ight thx bro ping me if u find the answer

[vestal sedge]

#❓how-to-get-help

#help-32

go there

[sonic widget]

Wait waht is the answer

[little mica]

oh sry

[sonic widget]

I don't know what odd integers mean

[little mica]

Coming to u

[sonic widget]

#help-32 @little mica

[wispy sentinel]

[little mica]

Hello

Dont understand how to find the limit, I know the answer, and the theory says something about phase portaits, but cant seem to get the relation between the two

<@&286206848099549185>

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@little mica Has your question been resolved?

[little mica]

<@&286206848099549185>

[little mica]

found the answer online

closing

.close

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[magic scarab]

can yall help me get a formula for the sum of all the equations, up to n terms, by the logic of sequence above

[lean chasm]

you basically have $$\sum_{i = 1}^{n - 1} \sum_{j = 1}^{i} 5j$$

[flat frigate]

i believe in mathemagic

[lean chasm]

do you know sigma notation

[magic scarab]

yes, but im not supposed to use that

basically, i need a one liner to sum up everything given n

[lean chasm]

yes

[lean chasm]

just simplify this now

[iron narwhal]

no offense but math is too tough

[lean chasm]

ok?

$$\begin{align} &= 5\sum_{i = 1}^{n - 1} \sum_{j = 1}^{i} j \ &= 5\sum_{i = 1}^{n - 1} \frac{i^2 + i}{2} \ &= \frac{5}{2} \left(\left(\sum_{i = 1}^{n - 1} i^2\right) + \left(\sum_{i = 1}^{n - 1} i\right)\right) \ &= \frac{5}{2} \left(\frac{n(n-1)(2n - 1)}{6} + \frac{n(n - 1)}{2}\right) \end{align}$$

[flat frigate]

i believe in mathemagic
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[calm musk]

Thanks man

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[lean otter]

hello i need some help with an improper integral

[lean otter]

e^x / (e^x-1) from 1 to infinity

i did u sub and got the integral to be ln(e^x-1) with bounds of 1 to infinity

but that means this diverges right?

[steep dove]

yep

[lean otter]

bruh

i got 8 points off

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[severe pine]

if anyone can help me with this question, thank you.

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[quick geyser]

Need help with this please

[cosmic grove]

$F(x) = \int_1^x \frac{1}{t} e^{\frac{t^2 + 1}{t}} dt$ right ?

ah bot dead

[quick geyser]

let me paste into overleaf give sec

[quick geyser]

yes this is the original integral

[cosmic grove]

ok, you plug 1/x and you do some u-sub, like u = 1/t, so the bound should change

t = 1/x, you have u = x

[quick geyser]

yes, thats up to where I got to, in the U world (assuming i did no mistakes prior)

[cosmic grove]

hmm, t = 1/u, so t^2 = 1/u^2

so (t^2 + 1)/t = ((1/u^2)+1)/(1/u)

= 1/u + u

looks good

[quick geyser]

exactly

I'm not sure how I show that F(1/x)=-F(x) however

[cosmic grove]

1/u + u = (u^2 + 1)/u

[quick geyser]

right, but I'm still in the u world

whereas the original function is in the t world

does this not matter?

[cosmic grove]

the variable of the integrand doesnt matter, I can change u to t without changing the result

like \int f(u) du = \int f(t) dt

[quick geyser]

Okok!

makes sense

this answers the question

thank you for the help!

[cosmic grove]

np

[quick geyser]

.close

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[patent vault]

how do i solve this?

[patent vault]

i heard the first and third are of opposite parity for some reason

[quasi bison]

you heard that but are unable to prove it?

like, it is true, 3k-4 and 5k-3 are of opposite parity. and it is not hard to prove.

[patent vault]

it means one of them is 2

[patent vault]

why tho

[quasi bison]

two integers are of opposite parity if and only if their sum is odd

[patent vault]

right

[unique bison]

Or consider when k is odd or even separately

[quasi bison]

excessive imo

but not fatal

[patent vault]

why?

[patent vault]

also this

[unique bison]

To prove this

[patent vault]

oh

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@patent vault Has your question been resolved?

[patent vault]

(3k-4)+(5k-3)=2n-1

is that what i should do?

7k-7=2n-1

or would it be better to say 1 mod 2

i got that k is even

not sure what else

@quasi bison ?

does it only work for 2?

anyone there, please??

4 works as well too?

oh nvm

got it

.close

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[brazen plover]

not sure if i did this correctly but interval of concavity down is (-infinity,-1> U (-1,0) and interval of concavity up is (0,+infinity) and the inflection point is (0,-1)

[solid shell]

Close

Take a look again at the interval (-infty, -1) and see if it's concave up or donw

[safe radish]

@brazen plover Has your question been resolved?

[brazen plover]

ohhh yeah i made a mistake

its supposed to be positive right?

i forgot that two negatives multiplied make a positive xddd

[solid shell]

Yup it's positive

So that interval will be concave up---otherwise you're good

[brazen plover]

alright thank you!!

.close

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[opaque pasture]

I need help with these

[opaque pasture]

the first one is 1) If y = 2, solve for x
2x + 8y = 20

so 2x + 8(2)= 20?

so the answer is 2

oh

so x = 2?

o

2x=4

yes

so

it is 2?

I SAID THAT

ok

oh

okay

ill try next one

rq

so for each one

I can just do

plug in the number as the variabel

so the second one

the answer would be 5/2?

@lean otter

ahh

so y = 0

for the third one

do I do 5x-2x=3

or 5x-2(2)x=3

WHAT

-2(2x)

?

CONFUSION

😭

ok

so x = 3

ok i think i got it

ill finish it all and see

hiw di U di

how do I do

f(3)=x2-2x-2

no for this

my answer for the other one was y=-3

for this one idk

how to do it

ok

can

u

do

so I can see

no

ok

so the answer is 3?

so the answer is x=3?

😭

how to solve this

i did

the F

is confusing me

😭

idk

idk

my head hurts now

so I can ignore the F?

nope

doesnt make sense

to me

😭

i

i tried

:/

4

😭

9

3

1

i hate this

it doesn't make sense

yes

no

its alg/trig

lol

so

this would be

x=4

x=4=6x+11?

6(4)+11

so answer is 35

OK

ty

let me try next one

x=2 | 2(2)-8

so

-4?

okay

ill try this last one

x=-3 | 3(-3)^2 - 8(-3)+6

?

so 57

YAYYY

BESTTOIEEEE

ok

i have 2 more

cause ist ten problem total

so this is -2

ok

last one yay

mk

so

3(1)^2+13(1)-12

or no 1's?

ok

yes ill do it that way easier for brain

so answer is 4

yay

tysm

oof

one thing

that was for

"solving systems by substitution'

its still right

?

oh yes

duh

the answer

s

yeah

lol

ok

ok