help-38

[tough iron]

Which part is confusing you

[bronze eagle]

Everything

[tough iron]

Gotta be more specific

Theres not much to do here

[bronze eagle]

The whole question

I mean

[tough iron]

You have 8x-3y and they told you how much X is and how much Y is

[bronze eagle]

Yea after that what do I do

[tough iron]

After what

[bronze eagle]

You said they told me the y and the x okay and

[tough iron]

Well if i told you you have 8 boxes and i told you in each box there's 6 oranges

How many oranges you got

[bronze eagle]

8*6???

[tough iron]

Yea

And then i came along and brought 3 bags with me

And i filled them with 4 oranges each

How many did i take from you

[bronze eagle]

1

4-3

[tough iron]

Are you sure

I have 3 bags and each has 4 oranges

[bronze eagle]

3*4

[tough iron]

And then how many oranges do you have now

After you counted your own and i took some for myself

[bronze eagle]

16

Hold on I'm confused I need help with the question

[tough iron]

Okay well i cant teach you the multiplication table

This IS the question

[bronze eagle]

I want to show my work then

[tough iron]

Im trying to visualize to you how math works instead of just plopping you the answer

[bronze eagle]

No I just need show work not answers

Okay let's start

You said what

[tough iron]

Lets go left to right

8x

That's 8 times X

Some unknown thing

You have 8 boxes of oranges but you don't know how many are inside

And then I come along and tell you X=6

So now you know there's 8 boxes with 6 oranges each

How many do you have now

[bronze eagle]

How many oranges?

[tough iron]

Yea

[bronze eagle]

6

No no

Wait

8"6

[tough iron]

Which is how much

[bronze eagle]

Uhmmm 48?

[tough iron]

48

So you have 48 oranges

Great

[bronze eagle]

Yea

[tough iron]

Lets move on

Then we have -3y

You are subtracting 3 times some unknown Y

[bronze eagle]

Yes

[tough iron]

I came with my own boxes and i took some oranges and filled 3 boxes and left

And then i told you

Hey my boxes fit 4 oranges

Which means Y=4

So how many did i take

[bronze eagle]

So in each box 4 or 1

[tough iron]

.

[bronze eagle]

4

So

3*4

[tough iron]

Which is

[bronze eagle]

12

[tough iron]

So if you had 48 oranges and i took 12

Now you got?

[bronze eagle]

36

[tough iron]

Thats the solution

[bronze eagle]

Ohhh

But how do I write it

In the box

[tough iron]

What do you think

After doing this chatting exercise here

What did you do

[bronze eagle]

I know but do I say oranges and stuff

[tough iron]

Of course not

What did you do with the numbers

[bronze eagle]

Subtract and multiply

[tough iron]

What did you do with these two numbers

[bronze eagle]

Wait so 8x6 and 4*4

[tough iron]

3*4

[bronze eagle]

Multiply?

[tough iron]

3y

[bronze eagle]

Yea my bad

[tough iron]

You put the values of X and Y in the equation

Instead of 8*x you wrote 8*6

Because x=6

[bronze eagle]

Yea

So I write

[tough iron]

And instead of 3*y you wrote 3*4

Because y=4

[bronze eagle]

86 and 34

So

[tough iron]

You put the values of x and y in the equation

[tough iron]

Yep

[bronze eagle]

Look let me show you rq

Like this

[tough iron]

Sure i guess

I'm not your teacher idk how they grade you

Im just showing you the principle of solving

[bronze eagle]

Oh but you think I will get it wrong

?

[tough iron]

I dont know, write * instead of .

[bronze eagle]

what?

Last one blease okay

Number 3

[tough iron]

You should be able to do this one on your own now

Its just reading comprehension

[bronze eagle]

What

Here in a better picture

[tough iron]

Whats 6x

[bronze eagle]

Wdym

It says 6x-2

[tough iron]

What does 6x mean

If you wrote 6x on a board

How would you explain to a little child

What that means

[bronze eagle]

6 and some random letter but we just put x

[tough iron]

What does "and" mean in your sentence

6 and a number

[bronze eagle]

X

[tough iron]

Is 6x like saying 6 + X

[bronze eagle]

Yea

Like look

6 + x =45

Like this

[tough iron]

Ok but we wrote 6x

Not 6+x

What does 6x mean

[bronze eagle]

I'm just showing

[bronze eagle]

Blank ?

[tough iron]

Just like in the last question

Question 2 has 6x-3y

What does 6x represent

Spoiler because my hair is falling out

It means 6 TIMES X

[bronze eagle]

Bro that's what I was. Saying hey

Bru

[bronze eagle]

Ooooo

Alright so yea

[tough iron]

So 6x is the product of 6 and x

Do you agree

[bronze eagle]

Yes

So is a b c d?

I mean is it

A or D

[tough iron]

Im not gonna solve your question

[bronze eagle]

But you didn't explain bro

[tough iron]

What is the difference between A and D

[bronze eagle]

How am I supposed to know

[bronze eagle]

The other one Is saying it les than 2

[tough iron]

Because we had to have a crash course on what 6x means

[tough iron]

Well in what way are A and D different

They dont mean the same thing

[bronze eagle]

Yes

Soo?

[tough iron]

Sooo im asking you

How do they differ

[bronze eagle]

They are different because the number minus the two

[tough iron]

How would you write A in numbers

Product of 6 and a number less than two

[bronze eagle]

Yes

6 and x

[tough iron]

How would you write it

In numbers

[bronze eagle]

Is least the 2

6x -2

Ooooohhhhh

Oh shi

I see now

Damn I'm good at math

[tough iron]

What do you see

[bronze eagle]

The number

[tough iron]

Which answer would you choose now

[bronze eagle]

A

[tough iron]

Nope

[bronze eagle]

c'mon man

[tough iron]

Do you know what "less than" means

[bronze eagle]

Negative

Right

[tough iron]

If i tell you 2 is less than 3

Does that mean 2-3

[bronze eagle]

No

[tough iron]

Of course it doesnt

So less than doesnt mean '-'

[bronze eagle]

Yea who would say that

[bronze eagle]

Yes

[tough iron]

Have you ever seen this sign

<

[bronze eagle]

Greater smaller

[tough iron]

Or greather than less than

[bronze eagle]

Ye ai learned dem 5 or 6i don't rember long time ago

[bronze eagle]

Yes

Wait so A is saying that the 6 is less then 2

That don't make sense

[tough iron]

It means 6x where x is less than two

Or

6x<2

[bronze eagle]

yea it don't make sense

[tough iron]

Depending on how you read it

It doesn't make sense

That's the point

[bronze eagle]

Yea yea

[tough iron]

Its not the right answer

[bronze eagle]

So we cross 🤞 A

I think it's D

[tough iron]

We cross A

Well lets check

What does D say

A product of 6 and a number minus 2

[bronze eagle]

The product of six and a number minus two

Yea

But we don't say minus

It's a negative

[tough iron]

How will you write The product of 6 and a number

In numbers

[bronze eagle]

Wdym

[tough iron]

Just like i asked you 2 mins ago

Write " The product of 6 and a number "

But not in words

Write it how you would write it in numbers

You did it 3 mins ago

[bronze eagle]

6x -2

[tough iron]

When i asked you the same question

[tough iron]

Thats the product of 6 and a number Minus two

[bronze eagle]

Yes

[tough iron]

Not what i asked you

But whatever

[bronze eagle]

D

Is

[tough iron]

Yes D is the answer, please pay more attention in class

For your own good

[bronze eagle]

6 and a number - 2

[tough iron]

Yes

[bronze eagle]

But I bet on the phone and I also play ball I don't put my mind into school

[bronze eagle]

Ok

So what

[tough iron]

Thats exactly why we had to do these 2 problems for 30 minuts

You gotta pay attention

[bronze eagle]

Yea my bad

[tough iron]

Instead of betting on the phone

[bronze eagle]

Yea

Anyways

[bronze eagle]

Yes

[tough iron]

Yes

[bronze eagle]

Yes

[tough iron]

I hope youll listen to me because youll have a shit ton of problems in older years if you dont know basic arithmetic

[bronze eagle]

Wdym

[tough iron]

If you are struggling so much with these basic ass questions and you aren't listening in class

You'll be one dumbass kid later

[bronze eagle]

I'm in 10th so 2 more years and I go to collage play ball and I might make you don't know I don't knowb

[bronze eagle]

Don't be mean

Ight ight

So I said thai

[bronze eagle]

.

[tough iron]

Saying that for your own good I don't care what you do

Man

I told you 4 times

Yes

6x-2 is that

[bronze eagle]

Alright man don't be mean

We cross D

[tough iron]

Are you also betting while reading this channel

We dont cross D

Did you read the question

[bronze eagle]

Wdym

[bronze eagle]

Yes

It don't make any sense

[tough iron]

They're asking you what 6x-2 is

You figured D means 6x-2

[bronze eagle]

Yes

[tough iron]

Why do you cross it

[bronze eagle]

For D?

[bronze eagle]

Hold on

[tough iron]

Sorry man i give up my batterys drained

[bronze eagle]

Nah c'mon man

[tough iron]

Circle D and good luck

[bronze eagle]

I'm sorry man

So it's D

[tough iron]

Yea

[bronze eagle]

Look man do you want me to give you money or boost your servers

I know you had hard times

[tough iron]

Im good

[bronze eagle]

Look will I be successful in school?

😂

What do you think

[tough iron]

Wish you the best at ball remember to pay attention in class

See ya

[bronze eagle]

Alright

Peace

[tough iron]

You can do it

[bronze eagle]

W

[tough iron]

If you want to!!

[bronze eagle]

Hope so

[bronze eagle]

But bro can't work and do school

At the same time

Can't focus on 2

[trim jolt]

@bronze eagle Has your question been resolved?

[bronze eagle]

Yea

[trim jolt]

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[grave scarab]

Please help find the equation of a circle passing through points (1, -2) & (4, -3) whose center lies on the line 3x+4y=7.

[trim lichen]

!status

[trim jolt]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[grave scarab]

Dunno where to start...

[trim lichen]

you might want to try to find the center.

[grave scarab]

yes. How to.

I'd think u need to find a point on the given line having distance equal from both points.

But i don't know how to do that.

Another method I can think of would be to find the equation of the line created by the points of family of circles passing through those 2 points and find the intersection. But i dunno how to find that eq either...

[round mango]

Are you aware of the mid point formula

[grave scarab]

Yes.

[round mango]

what is stopping you from using it

oh my bad

[grave scarab]

The fact the it's not certain that the center and the 2 points are coleniar.

[round mango]

didnt read the question completely

i thought those were diametric end points

yeah anyway

are you aware of the distance formula

[grave scarab]

Yes.

[round mango]

Great, if you want to find to find a point h,k such that it is equidistant from the two points, equating the distance will give you one relation between h and k, and then using the condition that h,k satisfied 3h+4k+7 will give you another equation. You will have 2 equations and 2 variables and you can solve for them

this obviously is a long and tiring thing imo

but as you mentioned it, family of circles is a better way to solve this

[grave scarab]

What do u think bout let center be (h, k), and them equate the distance from 2 points. Getting an equation of a line. Then get the intersection and that be the center?

[round mango]

that is exactly what i said

[grave scarab]

oh. Sry, couldn't completely understand :p

I'll try and report back.

[round mango]

but anyway as i said that way i dont like since it is a little calculative

Recall that the family of circles passing through the point of intersection of circle S = 0 and line L = 0 is given by S+λL = 0
Now if you think about it youre already given the line L and a circle S

try to formulate something here

[grave scarab]

But we need to find the eq of the circle. And lamda is also unknown.

[round mango]

youre given a condition on the centre

which will help you eliminate lambda

you can easily find out the 'L' in the family's eq right?

and let S just be the circle which has diametric end points as (1,-2) and (4,-3)

[grave scarab]

I think the equation from eating (h, k) will give that line?
I forgot the family of circle part a lil.
L is the line of all the centers or the common cord

[round mango]

L is the common chord yes

in this case the common chord is the line passing through 1,-2 and 4,-3

[grave scarab]

okey.

[trim jolt]

@grave scarab Has your question been resolved?

[grave scarab]

In above 1 I tried the S+λL=0 one but got stuck.

Then tried the other one. And doesn't look right.

[lost wharf]

try algebric parametera

*s

keept x=t and get y with help of line

then use distance formula

[grave scarab]

Didn't get it...

[lost wharf]

what's the answer?

keep centre as (t, 7-3t/4)

[grave scarab]

15(x²+y²)-94x+18y+55=0

[lost wharf]

ok wait

[lost wharf]

got it

@grave scarab

did u get?

[grave scarab]

Nope...

[lost wharf]

ok

I got it

[grave scarab]

Pls tell

[lost wharf]

ok see

keep the centre as (h, k) or anything

then circle cuts the point

put it in equation (x-h)^2+(y-k) ^2= r^2

put values of (x, y) given

then you will get two equations

subtract them

[grave scarab]

But r

[lost wharf]

wait

we will then use the line equation and put h, k

then solve the equation from the upper part

then get h, k

then we can get radius too

then the equation

[grave scarab]

Couldn't understand this part

[lost wharf]

ok so since centre lies on line

h, k will satisfy the line

therefore we put h, k in line

[grave scarab]

Oh

[lost wharf]

I've solved

do u want to see

or u understood

[grave scarab]

Please send. I'mma go solve. Then even if channel closes i can see.

[trim jolt]

@grave scarab Has your question been resolved?

[trim jolt]

@grave scarab Has your question been resolved?

[grave scarab]

Thanks, it was solved.

.close

[trim jolt]

Channel closed

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[trim jolt]

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

Need to differentiate

[stark bison]

!status

[trim jolt]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[wraith hinge]

I know that it is supposed to be solved with chain rule

but i dont really know how to solve it

@stark bison I don't know where to begin basically

[stark bison]

Can you come up with functions f and g such that f(g(c)) = (6 - 2sqrt(c))^2?

(Think about what happens to the variable c before the action of squaring)

[wraith hinge]

before suqaring the power 1/2 will be multiplied i guess and 1 would be subtracted from 1/2

do i have to differentiate inside the bracket first

i have no idea

[stark bison]

Right, so simply pick f(c) = c^2 and g(c) = whatever's in the parenthesis

So that f(g(c)) = the given function

And differentiate using chain rule

What are f'(c) and g'(c) equal to?

[trim jolt]

@wraith hinge Has your question been resolved?

[wraith hinge]

f'(c) is for whole function?

g'(c) for the one inside bracket ig

[stark bison]

Given f(c) is c^2

[wraith hinge]

okay

still like bit clueless

like

it will be 2c

right

and for 6-2^1/2 we have to differentiate

as g'(c)

??

[stark bison]

Where did c go

[wraith hinge]

YES i mean 6-2c^1/2

[stark bison]

Right, what's the derivative of that?

[wraith hinge]

-1/c^1/2

can u tell like the answer i might have got it

f′(g(c))⋅g′(c) have to apply this then right

[stark bison]

Yes

[trim jolt]

@wraith hinge Has your question been resolved?

[trim jolt]

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

i know to expand giving me a^2 + 24a + 144

not sure what to do from there

[timid bay]

you got that for (a+sqrt12)^2?

[fringe abyss]

yes

[leaden wyvern]

a^2+sqrt(24)a+12

[fringe abyss]

oh

[severe stump]

He's also wrong.

[timid bay]

Its not right either

[fringe abyss]

what

[leaden wyvern]

my b

[severe stump]

Write out each term in the distribution

[leaden wyvern]

realized the screwup

[fringe abyss]

wdym

[severe stump]

(a + sqrt12)(a + sqrt12)

Should have 4 terms, two of which you combine since they are like.

[fringe abyss]

oh ok lemme work dat out

a^2 + a sqrt12 + a sqrt12 + 12?

[severe stump]

Yeah, and then you can combine the middle two.

[fringe abyss]

a^2 + 2a sqrt12 +12?

[severe stump]

Yup!

Now they want you to generalize this into the integer parts and the root parts.

a^2 is an integer and 12 in an integer.

[fringe abyss]

ok

so that would be k?

[severe stump]

Right.

And then they have this n sqrt(3) term

[fringe abyss]

so i have to make 2a sqrt12 into n sqrt 3

[severe stump]

Right. What happens when you factor 12?

[fringe abyss]

sqrt12 is 2sqrt3?

[severe stump]

Right.

[fringe abyss]

so n is 4

[severe stump]

So you would get 4a sqrt(3)

[fringe abyss]

cos 2x2

oh

right ye

[severe stump]

But yeah you got the gist.

So what are your expressions?

[fringe abyss]

so n is 4a and k is a^2 + 12?

[heady trail]

For compact two-dimensional surfaces without boundaries, if each loop can be continuously compressed to a point, then the surface is topologically homeomorphic to a 2-sphere (usually just called a sphere). The Poincaré Conjecture, proven by Grigori Perelmán, states that the same is true for three-dimensional spaces.

Someone to solve it

[severe stump]

Brother this channel is occupado already.

But yeah, n is 4a and k is a^2 + 12

It's strange that they asked for expressions instead of equations, they must really hate equal signs.

[fringe abyss]

i guess so

thank u very much tho

[severe stump]

No prob

[fringe abyss]

appreciate it

.close

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[sleek roost]

Hello, I am confused about matrix commutation in one particular task - Determine all the matrix that commute with the following matrix:

[sleek canopy]

wow

it self surely

maybe if you write the coefficient's equation associated with $AB=BA$ where $A$ is your matrix, you'll get some useful conditions

[solid kiln]

everg

[sleek roost]

yeah i already did that, taking matrix b as 2*2 with a, b, c, d as coefficients

[sleek canopy]

what have you gotten ?

[sleek roost]

then i got system of equations with 4 unknowns but it doesnt fit with solution which is:

wait a moment

[sleek roost]

there we go

[low gazelle]

What do u get

[sleek roost]

which is then:

and for final solution i got (a,b,c,d)= (-3b, b, -5/3 b, 0)

honestly i dont know where i messed up

[winged hinge]

This part is right at least

might need to show ur full work :p

[low gazelle]

this is good, what did you get for reduced matrix

You should end up with 2 free variables, so your matrix will be in terms of a and b

[sleek roost]

and there we have problem lol

beacuse i checked now and everything i did in further process was alright

how would u do this from here

[sleek roost]

.

[low gazelle]

I would move all the variables to one side and set up an augmented matrix

since it is a linear system

[sleek roost]

so u would basically solve matrix by using the gauss method right?

[low gazelle]

yeah

[sleek roost]

yeah lemme try so lets see what i will get

i went by usual method by eliminating so myb thats the reason i got something else

it literally came same shit as i got from eliminating method

amazing

[low gazelle]

Send the reduced matrix you are getting

[low gazelle]

Ok well the first issue I see is that you have only 3 rows when you should have had 4

You had 4 equations

[sleek roost]

i removed one row because its repeated

like two same rows

[low gazelle]

I see

Did you use this as your starting matrix?
[0, 5, 3, 0 | 0
-3, -9, 0, 3 | 0
-5, 0, 9, 5 | 0
0, -5, -3 0 | 0]

[sleek roost]

im starting to believe that solution is actually wrong lmao

[sleek roost]

yeah

[low gazelle]

I did the problem myself and got the same thing

well an equivalent thing

[low gazelle]

Probably made some mistake during the process. Do you have the work you did to get to this?

To get what u got*

[sleek roost]

i did it on some paper but trust me my handwriting is awful

anyways i checked on every possible math solver and it keeps giving me same answer that i got by myself

[low gazelle]

What site and maybe send ss of what you entered

I will give you the matrix im getting so you can atleast see what to do from there

[sleek roost]

its on different language so it would be hard to translate

[low gazelle]

[-3, -9, 0, 3 | 0,
0, 5, 3, 0, | 0]

Last 2 rows were all zeros implying that there are 2 free variables

[sleek roost]

interesting

[low gazelle]

You know what to do from here?

[sleek roost]

yeah

we will see what comes

anyways

thanks for the help

[low gazelle]

np

[sleek roost]

have good rest of the day

.close

[trim jolt]

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• Be polite and have a nice day!

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[astral skiff]

hi! i'm new to stats stuff and i wanted to double check to make sure im understanding how to solve chi square test

[astral skiff]

(the data is candies so i just made the expected an equal amount for each color, im not sure if thats correct lol)

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[astral skiff]

<@&286206848099549185>

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[empty brook]

Hi, so this isn't urgent since this isn't a homework or anything, but I was wondering If, let's say, I have an event that has a 1/7500 chance of happening, and I trigger that event x times, what is going to be the % chance that it happens at least once for any value that I decide to attribute to x? What is mathemathical function/equation that represents this problem, if there is one?

[empty brook]

Because it definitely can't simply be x/7500, because it is not magically guaranteed on the 7500th try

[ionic pendant]

looks like a binomial distribution problem

https://www.mathsisfun.com/data/binomial-distribution.html

notice that the binomial distribution models the probability something happens a specific number of times out of all attempts. if you just want to find the probability of happening at least once you can take (1 - probability of happening 0 times)

[austere cedar]

"At least once" has a nice formula, you'd use
1 - (1 - 1/7500)^x

[empty brook]

oh ok

makes sense

[austere cedar]

You can answer more general questions like "what is the probability of exactly twice" with the binomial distribution, which is worth seeing

[empty brook]

ok cool

probabilities are so cool

and fun to play around with

[austere cedar]

Agreed haha

[empty brook]

anyways thanks for the answers, both of you, how do I mark my problem as solved?

[austere cedar]

You can do .close to "return the channel"

[empty brook]

ok thanks

.close

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[cerulean hearth]

what's the trick to solve that?

[wraith hinge]

try dividing by sqrt(x^2+y^2)

*dividing and multiplying

[cerulean hearth]

hum

i don't see how it is easier to calculate this

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[split chasm]

harmonic trig identities to express the sum as a single trig function

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[karmic kernel]

,rotate

[karmic kernel]

Solve for u

(Using ln)

,rotate

[karmic kernel]

I got this far but dont really know what to do next

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[keen void]

$ln(3^x + 3^{x+1}) = 1$

[solid kiln]

Merineth

[keen void]

I need a hint on where to start

Solve x

[atomic socket]

take 3^x out

3^x ( 1 + 3)

so 3^x*4

[keen void]

How? Since I have 3^x+1

[atomic socket]

4 * (3^x)

3^(x+1) = (3^x )* 3

so we will get sometihng like this:

4*(3^x) = e

3^x = e / 4

so x = log_3(e/4)

[keen void]

The answer is 1-ln(4)/ln(3)

But hold on, how do I break out 3^x out of 3^x+1

[atomic socket]

3^(x+1) = 3*3^x

i already say that xd

[keen void]

So the +1 represents a 3?

[atomic socket]

ye u know why?..

if u dont know why we are wasting time here i think

[atomic socket]

we can get the answer in this way as well

[keen void]

Alright, sorry

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[lethal fog]

I am trying to calculate the volume of a cylinder because of an aquarium idea I had.
The units start in imperial units and I need them in metric, because imperial sucks.

(((12^2•Pi)•36)•(2.54^2/1^2))•(1^2/1000^2•9)

I replaced * with •

[lethal fog]

I have no idea how to use volumetric math

[nova spire]

which imperial units are you using and what stands for what in this expression?

[lethal fog]

I am using inches.
12^2 is its radius squared

36 is its height

2.54 was my attempt to convert it to cm

[nova spire]

and both expressed in inches I guess

[lethal fog]

Yes

[nova spire]

ok

r = 12in,
h = 36in

[lethal fog]

Aye

The rest of the equation was my attempt at converting to liter

[nova spire]

so in a first part, if you want the final volume to be in L = dm^3

convert r and h to dm, and you will get your answer

(1dm = 10cm)

also, 1in = 2.54cm

[lethal fog]

Ah, thank you very much, so (((12in(2.54cm/1in)^2)Pi)(36(2.54/1))?

[nova spire]

That will give you the volume in cm^3, so progress!

[lethal fog]

Ah, then multiply that by 1/10?

[nova spire]

be careful about parentheses tho

[nova spire]

Bit more complicated than that

[nova spire]

((12(2.54/1))^2)Pi)(36(2.54/1))
Here is the corrected parentheses

[lethal fog]

I study chemistry, i had to teach myself allcthe math I know, and I never needed cubed, just mL. L

Ah

[nova spire]

ok so

so this is the volume in cm^3. How to convert cm^3 to L = dm^3?

since 1dm = 10cm, 1dm^3 = ...

[lethal fog]

Im having trouble understanding that

Is 1dm 10 cubic cm, as in 10cmx10cmx10cm?

[nova spire]

1dm is not "10 cubic cm"

But you are correct as in 1dm^3 = 10cmx10cmx10cm

[lethal fog]

Ah, so to get my answer in liter, I would have to convert feom inches, to cm, to dm and then do the equation?

[nova spire]

yes that's a bit better

[lethal fog]

(((12in(2.54cm/1in)(1/10))^2)Pi)(36in(2.54cm/1in)(1/10))?

[nova spire]

So r = 12in = 12*2.54 cm = 12*2.54/10 dm

[nova spire]

exactly, that's liters!

[lethal fog]

Wooo, ima need to juice a lemon on my noggin to wrap around that one, Thank you very much, Rafilou

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[stoic flare]

How do I do this i can't even do cos

[ornate kiln]

which one?

[stoic flare]

The main one

[ornate kiln]

you cant do it

with only 2 data given

[stoic flare]

Ok what about this

[ornate kiln]

this is a normal exercise now

not just a thumbnail

[stoic flare]

Ok.

So

[cedar nacelle]

You have 90 degrees at the bottom which means the adjacent angle must also be 90 degrees which means you can apply the SOH CAH TOA rules

[stoic flare]

If 90 is for that triangle would the adjacent line also be 90 or 52 ?

[cedar nacelle]

It would be 90

Remember that a straight line has an angle of 180

Since this line is 90 degrees it means it is perpendicular to the horizontal.

This also means that the adjacent angle will also be 90

[stoic flare]

But then why is the other triangle 52

[cedar nacelle]

52 represents the height in this case

There’s multiple ways to solve it

[stoic flare]

For first I think it's tan 90/x

[cedar nacelle]

For which angle alpha or beta

[stoic flare]

ALPHA

[cedar nacelle]

What are you using tan 90

if you split the triangle into two separate triangles then try to solve for angle

You could also use Pythagorean theorem to since the missing side then use tan

[stoic flare]

Pythagorean with what

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[cedar nacelle]

its a right tringle to you can use it to find the missing side of the triangle

i suggest you focus on one triangle at a time

you can split it up like so

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[calm quartz]

My proof:

If a is congruent to b (mod 5), then a - b = 5k
If x is congruent to y (mod 5), then x - y = 5m
If a + x is congruent to b + y, then:
(a + x) - (b + y)
= (a + x) -b - y (by distribution)
= (a - b) + (x - y)
We know that a - b = 5k
And x - y = 5m,

So, (a - b) + (x - y) = 5k + 5m
5k + 5m = 5(k + m) = 5(n) where n = k + m
The product of 5n will always be divisible by 5.

This concludes the proof.

I'm new to proofs (this is probably my 5th one). This is what I came up with, but I'm not sure if I made any mistakes. It feels like I took some stuff for granted.

[calm quartz]

It's also possible I misread what it was asking. Been doing problem sets for like 4 hours, so my brain is mush.

[merry bluff]

No, seems good

[calm quartz]

Awesome. Thanks a bunch 🙂

[worthy eagle]

!done

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[pallid vine]

how do part a)

[sleek canopy]

just plug in that basis vector and see that they are in the plane

now plane has dimension 2 so the basis would have 2 vectors

notice that the two vector in B are idipendent

[pallid vine]

so like augmented matrix of the basis and eqution?

[sleek canopy]

i haven't understood

[pallid vine]

oh plug in the vector in the basis into x1 x2 x3 u mean?

[sleek canopy]

yes

[pallid vine]

ic ok

[pallid vine]

then what about part b

do i just plug in the vecto for x1 x2 x3 as well

[sleek canopy]

i think is easier than a) ...if you couldn't do b) maybe we have to re study some theories

[pallid vine]

i just odnt understand what hte question says

dyk what i mena

• im on 1 hour of sleep

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[wraith hinge]

how is the 4m in the numerator

would it not be 1

[nimble stone]

what do you mean?

[wraith hinge]

like what did they do to get the 4m in the numerator for the second part

[nimble stone]

$(4m^2)^{-\frac{2}{3}}\cdot 4m=\frac{1}{(4m^2)^{\frac{2}{3}}}\cdot 4m$

they just did that

[wraith hinge]

but it's a 1 in the numerator

instead of the 4m

[nimble stone]

yeah, and they multiplied this by 4m...

[wraith hinge]

oh i see

thanks mate

[solid kiln]

AℤØ

[wraith hinge]

got it ty

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[pliant frost]

Bicyclists Brent and Jane started at noon from points 60 km apart and rode toward each other, meeting at 1:30 PM. Brent's speed was 4 km/h greater than Jane's speed. Find their speeds.

[silent canyon]

!status

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What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

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[atomic geyser]

If $Y\sim\text{Poisson}(1)$, what is $E[(Y+1)^k]$?

[solid kiln]

jsidind810

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Please don't occupy multiple help channels.

[mystic veldt]

!1c

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Please stick to your channel.

[atomic geyser]

Yall so quick to do stuff like this but never help

[mystic veldt]

LMAO true

[atomic geyser]

canu help?

[mystic veldt]

no, i dont mind all these multiple channel occupations, i would have already helped u if i knew how to

also i just saw that u have diff question in your another channel

so according to rules you can hold multiple channels

[atomic geyser]

<@&286206848099549185>

If $Y\sim\text{Poisson}(1)$, what is $E[(Y+1)^k]$?

[solid kiln]

jsidind810

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[cursive arrow]

how do i times these two

[odd onyx]

dot product

not multiplication

[cursive arrow]

so 4s +1 1 + s-4 + 0*2 + s^2 +1`?

[odd onyx]

err

close

(4s+1)(1) -4(s) +0(2) +s^2(1)

[cursive arrow]

that is what i tried to write

[odd onyx]

ah alright then you're right

[cursive arrow]

but that doesnt give me the right answer

i cant see what ive misscalculated

[odd onyx]

f_z

should be v^2 + 3z^2

[cursive arrow]

oh

yes that is why

so s^2 + 9

i got s^2 + 1

thank you

[odd onyx]

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[tame notch]

If zero is in the denominator AND in the numerator, is the solution Zero or is it undefined ?

[cerulean hemlock]

do you mean 0/0? It's undefined

[tame notch]

Yes, I mean that

[maiden hare]

x/0 is undefined, whatever x is

[tame notch]

Ok thx everyone

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[wooden plover]

yea?

[slate barn]

show that this is linear subspace of R^n*n

how?

[wooden plover]

whose subspace is it?

[slate barn]

yo mamas

[rose grotto]

when did jt become a subspace?

[wooden plover]

yeah aight

time for some definition spamming

what does it mean to be a subspace?

you shouldn't be scared by the matrices, it's always the same thing each time no matter what

[slate barn]

so subspace is some non empty set which includes every linear combination of some vectors r and s

if i am right

[wooden plover]

if r and s are in the subspace, then ar+s is in the subspace yea (a is a scalar/number)

I just state it in the more usual manner

or you could just show addition or multiplication seperately

what are you used to when you prove smth is a subspace?

[slate barn]

maybe addition ig

do i have to do both?

[wooden plover]

yeah

you need all linear combinations

if you can't scale it's a bit unfortunate

[slate barn]

hm so to be sure i need to prrove that for some vectors eg r,s from X this exiation holds true?

[wooden plover]

no

you want to prove

1. it's not empty
2. if r and s are vectors in the set, then r+s is in the set
3. if r is in the set, then a*r is in the subset for all numbers a

[slate barn]

hm alright im gonna try to do that and update you later

[wooden plover]

aight

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[slate barn]

so i watched som video to understand it better but they all had easier examples

first point is pretty easy i just multiply everything by zero and i should get 0 shouldnt I? @wooden plover

but on the next step i am not sure what to do exactly

i dont know if even what i wrote is right

in 2 and 3

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[wooden plover]

@slate barn re was playing a game

seems like you're going a bit backwards for 2, but hey we all do that the first time

but yeah the idea is right

you want to show X+Y is in the subset

ie. A(X+Y) + (X+Y)^T B+... = 0

start from the left side

simplify all you can

and get to 0

and same for 3

[slate barn]

np

[slate barn]

yes sorry

[slate barn]

hm but how can i simplify it i dont see anything i could do with it

[wooden plover]

well go backwards from what you did

expand everything

(and don't forget the number 1 rule, you suppose that AX + X^TB + ... = 0, and AY + Y^TB + ... = 0)

never forget your hypotheses

@slate barn

[slate barn]

ahhh alright that seems straight forward

is this it?

[wooden plover]

yeah

[slate barn]

noice

annd for multiplication I take out g so i will get g(AX+XB+...)=0 so g0=0 and thats it?

when g is some scalar

[wooden plover]

yeah

[slate barn]

nice

https://tenor.com/view/cant-thankyou-enough-gif-25170543

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[wraith hinge]

can someone explain why adding p + u gives you the position vector q?

[wraith hinge]

<@&286206848099549185>

[thorny escarp]

Hadoo

Idk if this is understandable but, Adding the vector u to the point p gives the position vector q because it represents the displacement from point p to point q by adding corresponding components of the vectors.

@wraith hinge

[wraith hinge]

I sort of get you, I am going to quickly plot p and u to see what you mean

[nova spire]

p represents point P.
q represents point Q.
u represents the vector that minimizes distance between the line l and P. So u = the vector QP.
Finally, Q = P + QP= p + u

[wraith hinge]

Would it not be p - u?

I get what you mean, visually it is not making sense to me though

[nova spire]

Oops sorry

[nova spire]

Edited

[wraith hinge]

does this visualisation kind of look right?

sorry my brain is so friend I am struggling to understand anything currently

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[wraith hinge]

.close

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[wispy kiln]

for base case we can say F2 = F0 + F1 which is 2 and satsifies the fibonacci sequence
for hypothesis we can use strong induction and say Fn = Fn-1 + Fn-2 is satisfied for all n greater than or equal to 2
For the induction step we can assume the hypothesis but I don't see how to show that F3n+2 is even and F3n+1 and F3n are both odd from it???

[wispy kiln]

🙏

[onyx heart]

try to write $F_{3(n+1)}$, $F_{3(n+1)+1}$ and $F_{3(n+1)+2}$ in terms of $F_{3n}$, $F_{3n+1}$ and $F_{3n+2}$. then you can use the induction hypothesis

[solid kiln]

Robin123

[wispy kiln]

Hello I could write F3n + 2 = F3n+1 + F3n but i still dont see how I can use Fn = Fn-1 + Fn-2 to show they are even and odd? I dont see if there is anything substitute? @onyx heart

[onyx heart]

so you assumed that the statement is true for n. Now you can for example show that $F_{3(n+1)}$ is odd by using $F_{3(n+1)} = F_{3n+2} + F_{3n+1}$.

[solid kiln]

Robin123

[wispy kiln]

how??

[onyx heart]

you know that $F_{3n+2}$ is even and $F_{3n+1}$ is odd by the induction hypothesis. so what does this imply for the sum

[solid kiln]

Robin123

[wispy kiln]

how do you know F3n+2 is even and F3n+1 is odd what?

if its even it has to be divisble by 2 and if its odd it has to equal 2x+1?

[onyx heart]

you assume that this is true in the induction hypothesis. the base case is true since F0 = F1 = 1 and F2=2

[onyx heart]

yes

[wispy kiln]

ok but you dont always add even with odd

for example f3 is odd or 3 and f4 is odd or 5

[onyx heart]

i mean all fibonacci numbers of the form $F{3n+2}$ are even and of the form $F{3n+1}$ and $F_{3n}$ are odd.

[solid kiln]

Robin123

[wispy kiln]

but how did you prove that tho?

I dont get how you went from F0 = F1 = 1 and F2 = 2 to F3n+2 is even and F3n+1 and F3n is odd

[onyx heart]

the base case for the induction to prove the statement is n=0. For n=0, F3n+2 is even and F3n+1 and F3n is odd because F0 = F1 = 1 and F2 = 2. Now you assume that this holds for some n. this is the induction hypothesis. from that you prove that it also holds for n+1

[wispy kiln]

so if i plug in 0 for n in that case it is even and odd but isn't it asking me to prove for all n >= 2 not just for n = 0?

[onyx heart]

in order to prove that statement by induction you first need to prove the statement for a base case (here n = 0). After that you proceed to prove the statement for all n >= 0

[wispy kiln]

ok i see

[onyx heart]

the part with n >= 2 is just the definition of the Fibonacci sequence

[wispy kiln]

what

[onyx heart]

i mean in the first line the fibonacci sequence is defined. after that the statement holds for all n >= 0.

[wispy kiln]

ok so because the fibonacci is always in the sequence of even odd odd even odd odd even ...

by the definition

then every 3n +2 has to be even

and 3n + 1 and 3n is odd

[onyx heart]

no, the definition of the fibonacci sequence is $F_0 = F_1 = 1$ and $F_n = F_{n-1} + F_{n-2}$ for n >0 2. From this definition you can prove that it is always odd odd even odd odd even ...

[wispy kiln]

hmm ok

i think i get it now

[solid kiln]

Robin123

[wispy kiln]

thanks

i will try to prove it

[onyx heart]

no problem

[wispy kiln]

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[lunar parcel]

How to solve something like this? Should the answer be e^{-\frac{1}{x}}-e^{-\frac{1}{2}}+2?

[wispy sparrow]

$e^{-\frac{1}{x}}-e^{-\frac{1}{2}}+2$

[solid kiln]

chlamydia

[tough iron]

depends if x is >2

Its an integral from 0 to 2 of tdt and then an integral from 2 to x of 1/t² e^(-1/t) dt

You split it in two, where the function changes

[lunar parcel]

Yes, I came to this answer this way

but like

But this is the whole exercise and then it asks why it is continuous and is it differentiable. I want to say it is not continuous, because when you look at this answer in desmos it is not

the limit at x=0 not the same as value

[tough iron]

To check if its continuos you should first find what the possible discontinuities are

The value t=2 is a good contender

Because that's where the function splits

Changes shape so to say

So to see if its continuous its smart to see if it approaches the same value from the left and from the right

[lunar parcel]

But if the exercise asks for continuity of F(x) then I need to check the continuity of the f(t)?

[tough iron]

Oh the continuity of F(x)

Well then just check the expression you get when integrating

[tough iron]

This one

If you integrated correctly

And i think you did

Seems continuous to me

Except in one place

[lunar parcel]

Okay, then I don't understand continuity 😄 Like okay, this is what desmos shows. Is it continuous at 0?

no way

[tough iron]

Yeah , you do the same approach

You see if there are any hotspots

1/x in the power

x=0 can be a possible discontinuity

So you check the left and right limit

To see what happens

When it approaches 0+, lim e^(-1/x) is e^(-inf) which is 0

All good

So the left side must also approach 0 if it was continuous

However the limit as it goes to 0- is e^inf which is inf

As seen on the graph

Which means the function is not continuous, it has a discontinuity on 0, seen on the graph

[tough iron]

Thats the first part

[lunar parcel]

Yeah, so this is an error in the question or should I like say it oh this is not continuous actually. Because it doesnt ask whether or not it is, but why it is continuous

[tough iron]

You should say F(x) is not continuous, it has a discontinuity on x=0

The only way it can be continuous

Is if you restrict the domain

It might be that because F(x) is an integral from 0 to x

It only takes in values in that range

And you got a discontinuity from 0- which isn't in there

Im not sure why the textbook says its continuous, thats the only reasoning i can think of

[lunar parcel]

Oh so like the function is only from 0? like (0, x]