help-10

[tepid solstice]

one sec hmm

this term wont consider all orders right

basically u have chosen E,E,A,N

from the scrabble box

u havent considered

the order u pick right

this is same as nCr for extra info

[modern palm]

I thought if we did order doesnt matter, we would just multiply this result times 4 * 3 * 2*1

but then that wouldnt make much sense i guess

number would be too big

[tepid solstice]

if order does matter u wud multiply with 4* 3* 2*1 that is correct if the letters were ABCD

im trying to emphasize that they have given A B but 2 Es

u cannot consider both of those Es as distint right

[modern palm]

Hence why i was trying to do something with 5C2 earlier

[tepid solstice]

ur logic is correct upto the choosing but for permutating heres the method ill try to be as clear as possible

[modern palm]

but i didnt really know what i was doing

[tepid solstice]

mhm that is correct only

keep it ike that

but u just have to multiple smtg extra

to account for the permutations

lemme explain

wait

bruh

im tryna type 4 underscores doesnt seem to work

[modern palm]

yes discord problems

u can do here

with the lowercase ~

[tepid solstice]

• _ _ _ _ -

~ _ _ _ _ ~

[modern palm]

3 of `

[tepid solstice]

ah ok

_ _ _ _

now assume we have 4 spaces to fill

[modern palm]

ok

[tepid solstice]

with 2Es one A one N

the method is

first fill in the distinct letters

if we want to place 2 distinct things in 4 places

would u agree number of ways wud be 4P2

because it is indirectly permutations right

[modern palm]

Yes

[tepid solstice]

yes

so now we have filled the A and N

now all that is left are the two Es right

now the Es can just fill in the rest two empty spots

and u have a word

right?

[modern palm]

Yes

[tepid solstice]

for filling the two Es there are no permutations

because they re the same letters

and they re just filling the empty space left

so wud u agree if i say the number of words we can form is 4P2?

[modern palm]

Yes but in this situation we are starting with 2 E tiles, and 1 A tile, and 1 N tile

right?

Given we have those tiles, what you are saying follows

[tepid solstice]

yep

we have to arrange them in all orders

to account for all cases

of an ordered sample

[modern palm]

Ok what's next

[tepid solstice]

yep so now we found number of words with 2Eone A and N

now we have to go back

to get these letters at all

we have to find number of ways we can pick

2Es one A and one N

im assuming u understand how to get this right

[modern palm]

is it going to be what i had basically in the numerator

[tepid solstice]

u had it written right in the first image

[modern palm]

yeah the 5C2 * 4C1 * 3C1

[tepid solstice]

5C2 *4C1 * 3C1

mhm

yeah so basicall

we need to pick AND order them right

so just multiply this with the result we got above

[tepid solstice]

^^

[modern palm]

So 5C2 * 4C1 * 3C1 * 4P2 ?

[tepid solstice]

yep

if i didnt do any calc mistake

hmmm

just wait one second

there is smtg abt this which makes option (a) hard

we have number of favourable events

we need to find total events and divide them right

[modern palm]

yes i had total events as 14P9, but i think its supposed to be 14P4? right?

[tepid solstice]

yeah 14P4

hmm

i think we cant do just 14P4

one second

okay it is 14P4

no doubt

[modern palm]

Ok revised version, do these numbers seem right?

[tepid solstice]

hmmm sounds good

[modern palm]

Ok thank you

Very helpful

🙏

.close

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[upper shuttle]

show that there exists a g in Z(G)\{e} such that g^p=1, where G is nilpotent and p is prime.

[upper shuttle]

is this true, how would i go about this

[timid silo]

pokedance

[upper shuttle]

the original question was showing that a group being nilpotent implies all sylow subgroups are normal. the first step done was this

qylo!

[obtuse pebble]

@upper shuttle Has your question been resolved?

[candid yarrow]

p can be any prime?

[gilded needle]

there must be more hypotheses
does p even divide |G|?

!original

[obtuse pebble]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[upper shuttle]

https://youtu.be/TFl_dw6_pbI?si=YBoADlCKk7qxiR-a&t=584

wanted to go from 2 to 3

[obtuse pebble]

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[karmic rapids]

Before you is a board containing an m x n grid and a collection of outwardly blank tiles. There is one tile for every empty space on the grid, and whenever a tile is placed, the letter "C", "A", or "T" mysteriously reveals itself. Beside the grid, beams of light tally the numbers of each letter remaining. Below the grid, an inscription reads: "Tile the board without spelling 'CAT' and you shall be rewarded with a harem of catgirls. Beware, however, if at any point the word 'CAT' is spelled horizontally, vertically, or diagonally, the catgirls will maul you to death. Many adventurers have perished here before you; Continue at your own peril."

What are your chances of survival if you continue?

[karmic rapids]

.close

[obtuse pebble]

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[karmic rapids]

.reopen

[obtuse pebble]

✅

[karmic rapids]

(updating channel name)

[obtuse pebble]

@karmic rapids Has your question been resolved?

[obtuse pebble]

@karmic rapids Has your question been resolved?

[obtuse pebble]

@karmic rapids Has your question been resolved?

[obtuse pebble]

@karmic rapids Has your question been resolved?

[obtuse pebble]

@karmic rapids Has your question been resolved?

[obtuse pebble]

@karmic rapids Has your question been resolved?

[sour sun]

is this a troll

[hearty terrace]

lmao

[sour sun]

@karmic rapids don't use the help channels to troll please

[hearty terrace]

i applaud the persistence

[sour sun]

.close

[obtuse pebble]

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[karmic rapids]

it's not a troll

?????

[polar fossil]

https://www.youtube.com/watch?v=6jovMx_c1SU

[obtuse pebble]

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[mild zenith]

hiiii can anyone help me with limit stuff

[hearty terrace]

send question

[mild zenith]

ok well heres the thing

So i did this quiz

and i click check my answeres and I got some points off but it dosent tell me whats actually wrong

so im going through problem by problem

i have a good feeling of what might be wrong but

like ok hold on

is anything wrong here?

[hearty terrace]

this isnt a graded thing for school right

E and F are wrong though

[mild zenith]

no not really its a practice test for an upcoming exam its based on completion

but I wanna get them all right

oh are they

lemme check those

[hexed river]

what's wrong with E?

[mild zenith]

oh is E positive infinity ?

[molten spear]

it's approaching from positive side, same logic as d so yes

[hexed river]

oh yeah it is

[mild zenith]

ahhh right ok that makes more sense

lemme check F

[hexed river]

(i thought infinity was DNE 🪦 )

[mild zenith]

oh ok so that means there is also an asymptote at x=1

right?

[hexed river]

x?

hmm

[mild zenith]

is this correct now

[hexed river]

why x = 1?

[hearty terrace]

not x=1

ur missing an x=

[hexed river]

there is another x, but not @ 1

[mild zenith]

what the flip

hold on

[hexed river]

(x = blah is a vertical line)

sry if obvious

[mild zenith]

no i still dont get it

what am i not seeing

theres one at 0 i know that

but if X-->2 from the right is infinity does that not mean there is an asymptote there

oh

im stupid

[hearty terrace]

x=2

lol

[mild zenith]

yes i read the graph wrong

kill me

is this right?

ok wonderful

i have more questions tho is that ok

[hexed river]

sure

[hearty terrace]

yuh

[mild zenith]

anything wrong here??

[hexed river]

15 is perfect

a couple more you can check for 16

[mild zenith]

ah shit ok lemme re do 16

[hexed river]

sure

(if it helps, the plot just looks like y = 1/x, but then shifted over to the left by 3)

,w plot y = 1/x

[warm shale]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by ginger4557

[mild zenith]

how about now???|

yes the graph helped

[hearty terrace]

looks good to me i think?

[hexed river]

@mild zenith @hearty terrace yeah same

[mild zenith]

ok great

one last one

how do these look?

[hearty terrace]

[hexed river]

[mild zenith]

ok awesome thank you guys

.close

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[fathom kindle]

ok so this question is super easy bc

i just did f(1) and plugged x as 1 and found that p = 2

but i dont understand what the answer key shows

so can someone actually explain the answer key??

so i get that u do long division

but how do u know that p is 2

[fathom kindle]

also can i always do this?? will it always work?? bc why didnt the answer key do it as well...

[ivory depot]

Basically u follow the rules of long division with algebra

[dim yacht]

Multiply the quadratic and c-1 again is how I would get p after long division but idk what the answer is doing

x-1*

[ivory depot]

You know that all the terms have to cancel in order to be a factor

Using that info u can derive p using long div

[fathom kindle]

but the way i did it would it always work for like x-k cases

[ivory depot]

Yes

It's actually better

[fathom kindle]

what if it would be x^2-k

then i need to do the long division right

[ivory depot]

Then use dif of squares

Or just find the roots

[orchid wind]

You could always do synthetic division as well lol

Probs easier

[fathom kindle]

ya that too

[orchid wind]

If you have factor that is linear

[ivory depot]

Only works with 1 as leading coefficient though

[orchid wind]

Why would you ever do long divison

[ivory depot]

In general or for these problems?

Bc in general it's very useful

[orchid wind]

For these problems

[fathom kindle]

also i wanted to ask

when i write the division statement

do i need to factor the quotient

or is the quotient always not factorable..

bc i was looking at some of the questions i did and the quotients arent factorable

[dusty bronze]

the "p+1-3" step is a bit confusing cause they're essentially skipping a step, note how in the second step, they multiply (x-1) by (3x) , and subtract ( (p+1)x^2 - x) by (3x^2 - x), but they put the result as (0 + 2x - 2)

[fathom kindle]

yaa i sawwww i was confused where the 3 came from

its rlly weird

[dusty bronze]

that is because, if (x-1) is known to evenly divide the original polynomial, the x^2 term must disappear at this step! in other words, the (p+1 -3)x^2 term they should have at the end must zero out. in other other words, the coefficient on that x^2 must be 0

so that is where they got the (p+1-3 = 0) equation from! if you know the p-1 has to evenly divide the polynomial, then you know that there has to be a zero on that step, which gives you that equation, because (p+1-3) is the coefficient on x^2 !

[fathom kindle]

wow

[dusty bronze]

yeah def not intuitive!

[dusty bronze]

as for this part, in this question it does not seem you would need to factor the quotient, no

[fathom kindle]

but what about in general?

[dusty bronze]

in general, you only need to factor to find the roots of a polynomial, so if you are just asked for the quotient then you would not have to! if they wanted you to fully factor the original polynomial, for example, then you would, or if they wanted the other roots

so yeah the quotient is just looking for a polynomial, factored or not!

[fathom kindle]

I see, thank you so much!!!

[dusty bronze]

no worries! good luck!

[fathom kindle]

.close

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[noble shell]

hello! im currently stuck with measures of variation for my intro to stats, specifically this part of the formula, i am unsure of how my study plan got to the point of 30.5. these were my answers, as i am also following along on paper. thank you!

[dusty bronze]

so you got the same for all the numbers you plugged in, but when you used the calculator you got a different answer?

[noble shell]

ah well i believe i may be calculating the actual formula wrong? like the wrong order i guess? i get the same answers shown in the problem that plug in correctly, but actually trying to solve for s gives me a waaaaaay greater answer than the correct one shown in the example

[dusty bronze]

i see! well, it should just be an issue with the calculator's interpretation of what you're putting in, then

i'll take some pics rq!

[noble shell]

thank you, ill attach my work as well

i censored the language i wrote lol it helps me keep calm if i get frustrated

[dusty bronze]

first i'd do the top part of the fraction, which gives me this

then the bottom, 11(11-1) is 110

so in the end, i just need to do sqrt( 102176 / 110 )

[noble shell]

is it okay if u please explain how you got to this point as well?

[dim yacht]

is this a strxwberrymilk reference

🙂

[noble shell]

idk who that is.... im sorry /.\ lol but i do like strawberry milk and cigarettes, def has some bangers

good for studying and relaxing to

[dusty bronze]

sure, i just took this last part and broke it down, i started with the numbers on top here! i entered them onto the calculator as theyre written here, and i got 102176

[noble shell]

ahhhh okay! i see! i was overcomplicating it. thank you!

[dusty bronze]

no worries! good luck!

[noble shell]

i continued the formula but got 928.87,,,,

am i still missing a step to get to 30.5?

[dusty bronze]

did you take the square root of that? i have a feeling that could be it!

[noble shell]

oh god is square root just division

no...

math is my absolute worst subject so sometimes i am starting off of the absolute first step

i dont understand how i got 930 before the 30.5 if the problem got 30.5 first????

i didnt even get the full 930.3 i got 928.87 :( its really frustrating

ill just settle for a second and retry a similar problem, now that i got the order of the first half corrected. thank you again!

.close

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[obtuse pebble]

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[last cave]

isnt it opt c is also correct

[worn yoke]

it says "only"

[obtuse pebble]

@last cave Has your question been resolved?

[last cave]

so

how opt c is incorrect

[worn yoke]

but if n = 1 + 3k is correct, then the integers given by n = 1 + 6k are not the only solutions

[obtuse pebble]

@last cave Has your question been resolved?

[last cave]

okk

this "only" is really a great trap

[obtuse pebble]

@last cave Has your question been resolved?

[obtuse pebble]

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[lyric cave]

Hi, I'm stuck on this past exam paper question and I've just got no idea what the question is asking me. What does it mean estimate?

[tepid mountain]

What is meant by estimate is that to assume that the 2 arcs are lines and use the trapezoid area formula to calculate the cross section area

[lyric cave]

oh

so how do i do that

[tepid mountain]

You know the formula of trapezoid area right?

[lyric cave]

no

wait let me google it

[lyric cave]

Oh, so i just sub the values into that twice?

wait so what is a and b and h?

[tepid mountain]

They are written on the image

A and b are the bases of the trapezoid and H is the height of the trapezoid

[lyric cave]

so is 1.9 and 1.7 the a and b

and then 8 is the height?

[tepid mountain]

Do you see that big shape as a trapezoid

You know that trapezoid have 4 sides right

[lyric cave]

yes

[tepid mountain]

Then is that big shape a trapezoid?

Divide it into 2 trapezoids

[lyric cave]

it has 5 sides so no

ohh

so for the first trapezoid it's 1/2 x (1.9+2.7) x 4

and then for the second its 1.2 x (2.7+1.7) x 4

[tepid mountain]

Yes

[lyric cave]

and then i add those two together and it will give me the answer

[tepid mountain]

1/2 *

Not 1.2

[lyric cave]

1/2 sorry

ok one sec lemme do it and then check the answers

[tepid mountain]

Yeah estimation of the area

[lyric cave]

ok its right

and then for part b do i just times 18 by 0.8 to find the volume?

[tepid mountain]

Why 18

[lyric cave]

18 is the answer from part a

[tepid mountain]

Oh yeah

[lyric cave]

so 18 x 0.8 is 14.4

[tepid mountain]

But you still need to do something else

[lyric cave]

do i then leave the answer as 14 since its 2 significant figures

[tepid mountain]

This way you got the volume 14.4 m³

You haven't got the weight

Read the question carefully

[lyric cave]

oh

so then i times 14.4 by 3.52

because that's how many tonnes it is

[tepid mountain]

Yeah because its density is 3.52 ton/m³

[lyric cave]

ok so the answer to that is 50.688

but I leave the answer as 51, right?

[tepid mountain]

Yeah

[lyric cave]

ok one other thing

if i screw up the part in part a and i forget the formula on an exam

and then I use that answer to do part b, will I still get some marks?

[tepid mountain]

That depends on your tracher

Or instructor

[lyric cave]

alright well thanks so much for your help, I really appreciate it

[tepid mountain]

If you forgot the formula then you can calculate the area of trapezoid by dividing it to a rectangle and 1 or 2 right angle triangles

[lyric cave]

ohhhh

[tepid mountain]

But that would cost you a bit more time

And I don't see that the formula is that hard

Do you know where that formula came from though

[lyric cave]

Yeah I know but on my last exam i really screwed up a simple formula and lost so much marks so I'm worried that might happen on this exam

I don't know

[tepid mountain]

You know why that's the formula like the logical sense behind it

[lyric cave]

is it because the formula is made from like a combination of (bh) for a rectangle and (1/2bh) for a triangle and then it's like combined together?

[tepid mountain]

I mean you can say that but there is a better explanation for it

Do you know what that part
(1/2)(B1+B2) Give

[lyric cave]

so for trapezoid one it would be 1/2 x (1.9 + 1.7)

which is

[tepid mountain]

When adding 2 quantities together then divide them by 2
What is the result indicates

[lyric cave]

1.8

[tepid mountain]

I am not talking about the question I am talking in general on the formula

[lyric cave]

oh

[tepid mountain]

It would give you the average

[lyric cave]

oh yeah I learnt that awhile ago

[tepid mountain]

And also in the same time the median

[lyric cave]

so it gives u the mean and median of the trapezoid?

[tepid mountain]

So now I want you to imagine

Because it is the median it lies exactly at the middle of the trapezoid

Which divides the height into 2 equal parts
And also divide each leg by half

As seen in the picture

[lyric cave]

ohhh

[tepid mountain]

Form that picture you can see that the left 2 right triangles are congruent right?
Because they got a right angle and two equal sides

The same goes to the right ones

[lyric cave]

yes

so if I can remember that it's the top + the bottom timsed by the height then I should be good on an exam right?

[tepid mountain]

Because they are congruent I can cut them off from the bottom and attach them to the triangles on the above to make them form 2 rectangles by themselves on the corners
That would make the whole shape look like a rectangle which has the formula L*W

Here L is just the median of the 2 bases as we saw earlier
And W is just the height of the trapezoid

Did you understand where the formula came from?
@lyric cave

[lyric cave]

Ok yeah I can sort of understand that

so if you took the bottom half of the trapezoid and placed it upside down on the top then it would make a rectangle

and then it's that times the height of it which is bassicly the same thing as a rectangle???

[tepid mountain]

Not the whole bottom half
Only the triangles on the bottom half

[lyric cave]

ohh

OHHHHHH

thats actually so easy to remember ok

so if I do that on a similar exam question, I'll ace it and get top marks

cooo

[tepid mountain]

Yeah

Anything else?

[lyric cave]

Thanks so much man I really appreciate it that's helped so much

no there's nothing else thank you though

[tepid mountain]

You are welcome

[obtuse pebble]

If you are done with this channel, please mark your problem as solved by typing .close

[lyric cave]

.close

[obtuse pebble]

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[obtuse pebble]

Please don't occupy multiple help channels.

[vapid tiger]

i need help with this question

I just need someone to confirm my work

i placed the vectors in echelon form and reduced it getting c4 as a free variable which a identified as k

the reduced echelon form i got it

[ (1 0 0 1) , (0 1 0 (4-i/2)), (0 0 1 (2+i/2))]

this all is equal to [(x, 3x + (yi-3z)/2, x + (yi-z)/2)]

can you check if i did it right

this should solve part a

the span would then be to write this as a linear combination

This should solve part b

since we have a free variable in our Span X it is not linearly independant

in order to do that we remove that vector

we are then left with

after that we find a subset of X B which is a Basis of C3

what i did is the linearly independant set of values of X i named it as B

being linearly independent is one condition of being a basis another is to span C3

we know that X is a subset of C3

and Span X spans C3

we then found a linearly independant set of vectors from Span X and named it B

so B should also span X

then this implies that B spans C3

so it is a basis

so this solves d

now last part e

i generalised the basis using xyz

and got a unique solution

which also proves that B is a basis of C3

and satisfies e

can anyone confirm my findings

then i can sleep in peace

<@&286206848099549185>

dang

left on seen again

<@&286206848099549185>

<@&286206848099549185>

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[runic arrow]

why does this step just become x element A

of means or

en means and

[obtuse pebble]

@runic arrow Has your question been resolved?

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@runic arrow Has your question been resolved?

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[safe coyote]

hey i dont understand the logic of module

[safe coyote]

if module of x+2 is greater than 0 then how do i get rid of module?

how in generally i get rid of it?

ohhh

nevermind i got it

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[gloomy pelican]

I need help with this inequality

[gloomy pelican]

I tried multiplying by a1a2a3 and it looks like I could use the rearrangement inequality, but sadly a1^2,a2^2,a3^2 neednt be in increasing order unlike a1,a2,a3, so that fails

[obtuse pebble]

@gloomy pelican Has your question been resolved?

[gloomy pelican]

<@&286206848099549185>

[worn coyote]

I can't offer a super useful hint, but I'd start using symmetries in some way

For example if f(x1, x2) = x1 + x2 + 1 / (x1 x2), then
LHS = f(a1/a2, a2/a3)
RHS = f(a2/a1, a3/a2)
Or, after denoting t1 = a1/a2 <= 1, t2 = a2/a3 <= 1, we want to prove
f(t1, t2) >= f(1/t1, 1/t2) for all t1, t2 from (0, 1]

[gloomy pelican]

alright ty ill try that

[gloomy pelican]

actually this was a very useful hint

this simplifies to (t1-1)(t2-1)(t1t2-1)<=0

thanks a lot @worn coyote

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[open mountain]

I wanted to find the limits of integration

x varies between 1 and 2

[digital kite]

Hi

[open mountain]

Hi

While y varies between -1/x above

[digital kite]

Yes

[open mountain]

And under?

[digital kite]

-x

y=-x

[open mountain]

Ah ok, thanks !

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[sinful falcon]

This is an optimization problem, can I ask why do you need to find the first derivative in order to find x?

[teal junco]

You're finding the minimum of a function and when the derivative is equal to zero is where the turning points are

Here the derivative is zero at the maximum and minimum

[red ice]

actually you have a quadratic, and it's concave up because the leading coefficient is 1 = positive

so the minimum occurs at the vertex

which is at x = -b/(2a) = -40/(2 * 1) = -20

no need for calculus

[teal junco]

based

[red ice]

but if you had any other function which wasn't a quadratic

then yes you need the derivative = 0 to find the maxima and minima

[sinful falcon]

Ah that makes sense

Thanks

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[obtuse pebble]

Please don't occupy multiple help channels.

[obtuse pebble]

Please stick to your channel.

[tardy epoch]

You have a channel open already

[stray sable]

how do i delete

[tardy epoch]

Do .close

[stray sable]

.close

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[vernal yacht]

if im doing Gauss Jordan Elimination and
i have a 3 x 4 matrix, does the 4th column have a fixed answer?
or do i say "element of real numbers gg goodluck"

i get crazzzyyyy numbers in my 4th column because i thought they didnt matter

but a calculator gives me x1= -2/3, x2= 26/3,x3= -1/3, i thought i wasnt even supposed to be getting values here

[obtuse pebble]

@vernal yacht Has your question been resolved?

[vernal yacht]

<@&286206848099549185>

has noone done matrixes before 😔 its a theory question i dont need da result

[obtuse pebble]

@vernal yacht Has your question been resolved?

[light quarry]

In gauss jordan elimination the 4th coloumn are some real numbers and as to why the calculator is giving you different answers maybe some step got messed up

[vernal yacht]

so mine is fine aslong as the way i got there is good?

[light quarry]

Yeah

[vernal yacht]

thanks

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[long kettle]

I need help

[nova raptor]

Multiply by 12

[long kettle]

Thanks

[long kettle]

Now what

[nova raptor]

for the total you add up all the results

[long kettle]

Ohhh

[long kettle]

Multiply by 12 bcs of 12 months a year right

[nova raptor]

right

[long kettle]

Thanks that helped me alot I was halfway in when I realized I made a mistake

[nova raptor]

Question:
Now that the Merkles know their yearly expenses, they need to plan for their savings. They would like to save $45.50 a month. How much will they have saved by the end of the year?
Monthly savings = $45.50
Yearly savings = $45.50 × 12 = $546.00

Mr. Merkle would like to cut one of his bills in half. He currently pays $75.40 for cable. If he cancels everything except for basic service, his bill will be reduced to half of what he currently pays. How much would he pay for basic service?
Current cable bill = $75.40
Reduced cable bill (half) = $75.40 ÷ 2 = $37.70

What would be his yearly bill for basic service?
Monthly basic cable service = $37.70
Yearly basic cable service = $37.70 × 12 = $452.40

checking....

[nova raptor]

don't worry, but keep on learning...
best wishes!!!!

[obtuse pebble]

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[long kettle]

Yes

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[bright bobcat]

am I done or is there more to do?

[dusk widget]

your work is a little hard to follow

[bright bobcat]

I can rewrite it or I can explain what I did

[dusk widget]

you can explain

I'll be okay I think

I can tell you factored the numerator, and then cancelled the (x - 2)s

but then idk what you did afterwards

[bright bobcat]

for starters this is the problem I'm working on

[dusk widget]

sure

[bright bobcat]

i found what you add to get -9 and multiply to get 14 and factored to end up with (x-7) and (x-2)

[dusk widget]

fwiw, the first thing I would do is change this into multiplication 😵‍💫

[dusk widget]

sure

[bright bobcat]

you can turn it into multiplication?

[dusk widget]

,, \frac{4x - 8}{x^2 - x} \cdot \frac{x^2 - 9x + 14}{3x^2}

[warm shale]

higher!

[bright bobcat]

that's something you can just do?

[tranquil geyser]

Flip

[dusk widget]

,, \frac{a}{b} \divisionsymbol \frac{c}{d} \implies \frac{a}{b} \cdot \frac{d}{c}

ah

I don't remember the command

[tranquil geyser]

Oh

[dusk widget]

@bright bobcat this is smth you can do in general

a/b divided by c/d is equal to a/b times d/c

because division by a number x is just multiplication by 1/x

[brave magnet]

Y

[dusk widget]

so dividing by c/d means multiplying by 1/(c/d) = d/c

[dusk widget]

this channel is occupied rn

you can open your own

[brave magnet]

How

[bright bobcat]

(available)

[brave magnet]

Yay

[dusk widget]

go to the available ones

[brave magnet]

Thanks bye

[bright bobcat]

np

[warm shale]

higher!

[dusk widget]

there we go

[bright bobcat]

so I put the 3x^2 over the x^2 -9 + 14

[dusk widget]

,, \frac{4x - 8}{x^2 - x} \divisionsymbol \frac{x^2 - 9x + 14}{3x^2} = \frac{4x - 8}{x^2 - x} \cdot \frac{3x^2}{x^2 - 9x + 14}

wait

I messed up

[tranquil geyser]

Flip

The right 🙂

[warm shale]

higher!

[dusk widget]

there we go

[bright bobcat]

right

[dusk widget]

now you can factor everything and cancel

[thick moon]

bru can someone after this help me pls

[bright bobcat]

do I do anything with the 3x^2 or do I leave it as it is

[dusk widget]

you have to leave it

it's already a monomial

[bright bobcat]

okay

[dusk widget]

so now factor everything out, cancel, and then multiply it all together et voila

[brave magnet]

No one helped me there

[dusk widget]

please be patient

[bright bobcat]

oh I'm supposed to multiply

[dusk widget]

indeed

[bright bobcat]

I'm not sure I'm done with my previous problem

[brave magnet]

There was no one

[dusk widget]

you can focus on this one for now

[bright bobcat]

is there any rule about crashing other peoples help channel 😕

[dusk widget]

you opened the channel 3 min ago

be patient!

[bright bobcat]

i feel like people are being very rude

[dusk widget]

it's frowned upon, but no rule iirc

[bright bobcat]

okay

alright time to do this math!

thanks again

[dusk widget]

lmk what you get

[bright bobcat]

@dusk widget how exactly do I multiply these?

[dusk widget]

just stick the numerators together and the denominators together

but!

you didn't finish simplifying yet!

[bright bobcat]

hmmmm

[dusk widget]

,, \frac{4}{x(x-1)} \cdot \frac{3x^2}{x - 7} = \frac{4 \cdot 3x^2}{x(x -1) \cdot (x-7)}

[warm shale]

higher!

[dusk widget]

this is what I mean

[dusk widget]

now you can see the x^2 in the numerator and an x in the denom

so time to cancel!

@unreal musk

[bright bobcat]

i didn't know you can cancel that way

so it would make it just 3x then?

[dusk widget]

it would

[bright bobcat]

okay

[dusk widget]

,, \frac{3x^2}{x} = 3x

[warm shale]

higher!

[dusk widget]

ah, I've got to go now

@unreal musk do you mind making sure Cassie gets this through to completion?

[bright bobcat]

thank you (:::

[dusk widget]

I think she's basically done though

just need to multiply the numbers together

[dusk widget]

and by the numbers I mean the 4 and the 3

okie I go

https://tenor.com/view/peach-bye-byebye-goodbye-peachandgoma-gif-8591038124537837527

[bright bobcat]

12x / x^2+7

bye bye

[unreal musk]

Careful with the denominator

[bright bobcat]

okay 12x/(x-1)(x-7)

and then it's done

[bright bobcat]

is this right :3

[unreal musk]

Yep, that’s all good

[bright bobcat]

thank you chartbit

[unreal musk]

Awwww I barely did anything but why thank you

[bright bobcat]

.close

[obtuse pebble]

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[dusk widget]

@bright bobcat yippee!

well done

[obtuse pebble]

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[vital moat]

Can someone help with number 2?

[sacred rapids]

I can try

is anthony a boy or a girl?

[vital moat]

Boy

Do you know if I would use permutations or combinations

[sacred rapids]

I don't know what that is but I thought it was probabilities

[vital moat]

Yea it’s probability

This is the permutations and combinations unit

I know for 2b I’d use combinations since order matters

If you don’t know it’s okay you don’t have to help :)

[sacred rapids]

what class is this

[vital moat]

Data management

MDM4U if you’re in Ontario

[sacred rapids]

I´m in germany hahah

[vital moat]

Oh haha!

I think that since there are 3/5 girls that would be the probability that the first one to show up is a girl

Since there are 4 people total left to arrive and 2 other girls need to arrive the prob that the second one to arrive is also a girl would be 2/4

And we would multiply these two probabilities to get the total so it would be 3/5 * 2/4

[sacred rapids]

I guess so

[vital moat]

which would be 6/20 or 3/10

Thanks for trying Brot! :D

[sacred rapids]

it's a pleasure

[vital moat]

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[open spoke]

any tips on doing this in python?

[pseudo swift]

it's not really a python question it's a math question

compute the partial derivative $\pdv{f(x_i,y_i,a,b)}{a}$ by hand

[warm shale]

aPlatypus

[pseudo swift]

they tell you what f is

after that scratchwork the function is easy to implement

[open spoke]

Oh I see

Is the -a * x_i a dot product or a multiplication btw?

[pseudo swift]

x_i and y_i are scalars here

[open spoke]

And in that case I think the derivative is 2(y_i - ax_i - b)(-x_i)

But it's confusing since they are vectors

part of vectors*

[pseudo swift]

so what

I take an element out of my vector, it's just a scalar

[open spoke]

Oh so its just normal differentiation

[pseudo swift]

yes

you're just doing something on linear regression right ?

[open spoke]

Yeah

[pseudo swift]

that's what your question looks like

[open spoke]

It's like an AI course

[pseudo swift]

yea

[open spoke]

Whatd you think about my answer

[pseudo swift]

doing that damn gradient descent

[open spoke]

Kinda rusty

[open spoke]

True that

Wait not yet I will code it first

[open spoke]

Basically copy it like this?

def dL_da(x_vals,y_vals,a,b):
    return (1 / len(x_vals)) * np.sum(2 * (y_vals - a * x_vals - b) * (-x_vals))

[pseudo swift]

yeah

@open spoke

[obtuse pebble]

@open spoke Has your question been resolved?

[obtuse pebble]

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[bright bobcat]

what do I do at this point

[zenith raft]

what’s the question?

[bright bobcat]

i see the x+1 cancels

it's factoring rational expressions

[unreal musk]

(do you want it as a single fraction?)

[bright bobcat]

wait. . huh?

did I make a mistake?

[unreal musk]

What do you mean by "cancels" here?

[olive zodiac]

subtract x+1 with x+1

[olive zodiac]

do common factor thing on denominator

[olive zodiac]

u need it as one term?

[unreal musk]

Also ?

[bright bobcat]

I believe so. . I'm not exactly sure because I've never done this before

[olive zodiac]

if you have 1/2 -2/3 how do you subtract that

do u know how to do that

[bright bobcat]

do I multiply the numerator by the denominator of each fraction

[olive zodiac]

yes

make sure you distribute the - sign for second fraction to all

[bright bobcat]

how does that work

[olive zodiac]

like on top it should be something like 2((x+3)(x+1)-((x+5)(x+1)

so everyone gets a term

[bright bobcat]

oh

[olive zodiac]

divide it by (x+5)(x+1)(x+3)(x+1)

since you got common denominator to subtract them

[bright bobcat]

I'm just a bit confused

[olive zodiac]

think of it like this when u subtract 1/2-2/3

you would do 3-4 for the top part

but does 1/2 -2/3= 3-4

u need to get the common denominator

[bright bobcat]

so I need to find the LCM on both sides

and then multiply the top and bottom by it

[olive zodiac]

yes

[bright bobcat]

so its 5 on the left and 3 on the right

[olive zodiac]

for 1/2 - 2/3?

common lcm is 6 so u wanna get 6 on bottom

so u would do times 3 on left side both on top and bottom and times 2 on 2/3 bottm and top

[bright bobcat]

I don't understand how it's 1/2 or 2/3

[olive zodiac]

oh i was just comparing it to a problem to see how you would do your problem

so you understand the lcm and do it the exact samy way for your problem above

[bright bobcat]

i didn't know that I was so confused

so going back to my problem

[frigid burrow]

Just take LCM

[bright bobcat]

I think the LCM is 5 on the left side and 3 on the right side

[frigid burrow]

Multiply and divide the first term by x+3
And the second by x+5

Then the denominator will be the same for both fractions

[bright bobcat]

oh the x is included

okay

[olive zodiac]

when you subtract fractions the bottom ahve to be the same on both sides

multiply 5(x+5)(x+1)-3(x+3)(x+1) doesnt change anything

one side has x+5 other side has x+3

u wanna multiply right side by x+5 and left side by x+3

[bright bobcat]

then I'm guessing I distribute the 2 and the 1 ?

or. . .

[olive zodiac]

yes

[olive zodiac]

you dont have to write it as 2 separate things as both denominators are teh same on both sides now

[bright bobcat]

im not sure what you mean

so now the denominators are cancelled out

[olive zodiac]

so you see how your denominators are both (x^2+15)(x^2+5)

you can wrrite it as one thing now

[bright bobcat]

yes

[olive zodiac]

2(x+3)-(x+5)/(x^2+15)(x^2+5)

thats why we did common denominator to combine the fractions without messing up its values

[olive zodiac]

divide it all by (x^2+15)(x^2+5)

[bright bobcat]

it would be helpful if I saw how that looked

[olive zodiac]

yea i got u give me a sec

[bright bobcat]

okay

[olive zodiac]

https://cdn.discordapp.com/attachments/734396425722658818/1292301516144902205/IMG_6333.jpg?ex=67033d13&is=6701eb93&hm=acfa9831fbbcc74384cd61dd4732006e23c38da9f2dffd7253ea6cf1e920d4e4&

[bright bobcat]

that is some handwriting heh

thanks you

[olive zodiac]

np

[bright bobcat]

.close

[obtuse pebble]

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[fervent void]

Im trying to find the radius of a cylindrical object where I have been given four points detected by a perfect LiDAR system. The system has a FoV of 57°. I realise there is a lot of decimal places...don't worry about them. There seems to be something in my process that I have gotten incorrect and i'm not sure what.

[fervent void]

Perhaps my assumption to add a value x to length d in order to make a right angle triangle to touch the other points on the circles circumference was incorrect?

<@&286206848099549185>

[obtuse pebble]

@fervent void Has your question been resolved?

[fervent void]

I think it might be the 90° assumption for line d. As that would change the distances for the other sides attacted to the 1.78125° angle

Yeah I think I may have gone wrong when I added the "Let d be a horizontal line" as that would change the length of the other sides. If i did that the length x would actually need to be on the hypotenuse side.

[obtuse pebble]

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@fervent void Has your question been resolved?

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[neon gazelle]

how do you connect glass panes in minecraft?

[neon gazelle]

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[winter citrus]

is it possible for a function to not be an odd or even function but still have point/line symmetry?

[timid silo]

Yes. For example, y = (x - 1)^2 is neither odd nor even, but is symmetrical about x = 1.

[worn yoke]

a function is even if it's symmetric about the y-axis and odd if it's symmetric about the origin. but a function can be symmetric about other lines or points

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[coarse charm]

solve

.help

[obtuse pebble]

Commands:

• clopen: .close, .reopen
• consensus: .poll
• factoids: .tag
• help: .help
• version: .version

Type .help <command name> for more info on a command.

[coarse charm]

.reopen

.close

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[coarse charm]

.reopen

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✅

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[vernal yacht]

.close

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[plucky rivet]

@celest grail

!status

[obtuse pebble]

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

[celest grail]

This true?

[plucky rivet]

It is, do you not know FOIL?

[celest grail]

FOIL?

[celest grail]

I dont know

[celest grail]

And its?

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[dark orchid]

bro what? erm how do i still find my real zeros?

[dark orchid]

nvm, already got em.

its just the non-reals

that i need help with

<@&286206848099549185>

https://tenor.com/view/sleep-sleeping-zzz-sleep-gif-23126162

[obtuse pebble]

@dark orchid Has your question been resolved?

[dark orchid]

https://tenor.com/view/gohine-hohino-no-hohineee-gohineee-gif-17792172174678204487

<@&286206848099549185>

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.close

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[heady turtle]

I really don't udnerstand why they impose this condition

[hexed river]

probably so that $y'_p$ only depends on $y'_1$ and $y'_2$

[warm shale]

Ginger

[hexed river]

it seems like the reason will be more clear later in the text

[hexed river]

(this is equivalent to the case where $u_1$ and $u_2$ are constants instead of functions)

[warm shale]

Ginger

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[waxen cliff]

Why’d i get different answers?

[crude coral]

isnt that 3/4 supposed to be 1?

[waxen cliff]

ah fk mb

Ok i see it now

Thank you

.close

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[compact wing]

can anyone help

[compact wing]

Karina operates a sari-sari store. her fixed monthly coat for electricity an rent is ₱7,000. Each item in her store has a variable cost of ₱18 and is sold for ₱35. If she sells 400 items in a month, what is her total revenue, total cost and profit?

[obtuse pebble]

@compact wing Has your question been resolved?

[primal roost]

what is the cost of 1 item and how would you find the whole cost of 400 items?

and then what is the profit made by 1 item and how would you find the profit made by 400 items?

[compact wing]

uhh

idk

thats why Im asking help

could you explain it to me

pls

[obtuse pebble]

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[brave cargo]

.close

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[brave cargo]

C)

[brave cargo]

I subsituted u= ln(x+2)

I think my dx is somewhat wrong

[timid silo]

Rewrite it as 1/2 * ln(X + 2) / (X + 2) first

[brave cargo]

No substitution?

[timid silo]

u = X + 2 after that should work out

[brave cargo]

Hmm

U sure not ln(x+2)?

What Will my dx/du be ?

The answer says substitute ln(x+2)

[worthy birch]

yea

2x+4 = 2(x+2)

[brave cargo]

The nominator ln(x+2)

[worthy birch]

you took u = ln(x+2)?

[brave cargo]

Yes

[worthy birch]

du = 1/(x+2) dx

[brave cargo]

Yes

[worthy birch]

just apply it

[brave cargo]

What is dx?

[worthy birch]

take constant out

[brave cargo]

Like tjat?

That?

[worthy birch]

just integral of u

[brave cargo]

?

What Will my Dx be !!

[worthy birch]

huh

dx?

[worthy birch]

du = 1/(x+2) dx

[brave cargo]

I have dx

[worthy birch]

you took u = ln(x+2)

[brave cargo]

Yes

[worthy birch]

now you have to change the variable

from dx to du

[brave cargo]

I have my u = ln(x+2)

The derivative of u = 1/(x+2)

Which is du / dx

Now i need my dx

Or have i been thpught substitution wrong?

[worthy birch]

I don't understand what you mean

[brave cargo]

😢

[worthy birch]

but

I will start again

[brave cargo]

Here

[worthy birch]

ok

so you solve for du

[brave cargo]

What is du ???