help-39

[vital crescent]

nw

[pearl pond]

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[rustic tendon]

So again I think this has to do with extending bases

[jolly parrot]

dyxn

[rustic tendon]

I don't know how to argue that the dimension of U_1 + U_2 is m + k + l though

I was thinking again of writing linear combinations but the intersection is not necessarily 0 this time, so won't it be possible for some elements to repeat?

[toxic lichen]

#bots

oh whoops

other person already deleted

move along

[rustic tendon]

I think I figured it out nvm

.close

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[nimble barn]

i don't know how to word it but, it's basically an extension, let's say you assume that the dim(U1 intersection U2) is defined by k then you will extend the basis for both U1 and U2 since k is defined by a basis of (v1 up to vk) then you will have that in both U1 and U2, you add the part of u1 up to um and w1 up to wn (respectively) so U1=k+m and U2=k+n then you continue your job, (forming the basis for the addition) check linear independence which leads you to spannig and calculate the dimension, it should give the same formula take my word with a grain of salt

[midnight haven]

Which chapter is this

[pearl pond]

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[nimble barn]

alright i went to look for the exact proof, this is the book Linear Algebra Done Right - Sheldon Axler Chatper 2, section C page 47-48 you will find the same problem written in blue

[midnight haven]

Thank you

When is this taught in ur area?

[nimble barn]

i think i have studied this in my first year of University, but it wasn't really up to these details "before 7 years or so" and no it's not related to my field👀

[midnight haven]

Oh i see
I am in my first year aswell but I haven't been taught these yet

Yeah it's not related to our field aswell

[nimble barn]

Good luck with your studies and take care

[midnight haven]

Thank you brother

[pearl pond]

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[pearl pond]

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[supple roost]

The number of ways in which ( (m + n) ) different things can be divided into two groups such
that one of them contains ( m ) things and other has ( n ) things, is
$$
\frac{(m + n)!}{m! , n!}
$$

[jolly parrot]

Abdul sharma

[supple roost]

Can anyone explain it in simple words?

[vestal tapir]

like you have 18 different tasks and 2 people

no that's wrong

like one person says he won;t do more than 5 tasks, and another says he can't do more than 13

so you don't have a choice how many tasks to assign

it would need to be 5 and 13

you only get to choose which tasks to give

then this is like counting permutations of AAAAABBBBBBBBBBBBB

any order would count one way to assign the tasks

i guess i can't

[vital crescent]

well think of it like this: you want to separate 8 people, ABCDEFGH into two groups: one with 5, and one with 3. What is one way to do it? well, you tell them to form a random line, and the first 5 people goes to the first group, and the rest goes into the second group.

how many ways are there to form a line? 8! should be the answer. So should there be 8! ways to group these people into one group of 5 and 1 group of 3? Certainly not, notice that if the peoples lined up as ABCED FGH, it would yield the same grouping as ABCDE FGH. similarly EDCBA HGF also gives you the same grouping. We double counted each grouping 5! * 3! times. So the true answer should be 8!/(5!*3!)

this is a somewhat vague explanation.

[vital crescent]

This is also a good way to view it, one can view 1 2 3 4 5 as A's and 6 7 8 9 10 .... 18 as B's. Note instead of permuting A's and B's, we can permute 1,2,3,...., 18. This gives 18! ways to permute things. But note that each permuation of A's and B's really corresponds to 5!*13! ways of permuting 1 through 18. So 18!/(5!*13!) should give us the right answer.

[pearl pond]

@supple roost Has your question been resolved?

[vital crescent]

or another way: Suppose a person has to do 5 task on day 1 and 13 task on day two. How many ways are there to pick the tasks for day 1 and day 2?

well there are 18 ways to pick the first task in day 1, 17 for the second task... which should give us 18*17*16*15*14 ways of picking tasks. But wait, picking task A then task B then task C then task D then task E is no different from picking task E then task D then task C then task B then task A. So we have counted each way of picking 5 tasks for day 1 a total 5! times.

Thus the number of ways to split your tasks into two days is 18*17*16*15*14/5!, which is the same as 18!/(5!*13!)

@supple roost are these explanations clear?

[supple roost]

Yeah I am taking my time

Reading

Can we do it by bars and stars?@vital crescent

[vital crescent]

doesn't "stars and bars" somewhat relies on the claim in your original post?

separating n+m objects into n stars and m bars.

[supple roost]

I didn't understand your sentence

I am not fluent in English

[supple roost]

Yes

[vital crescent]

it is the same as what I did in the previous examples

its just just switch "group of people" to "group of objects", it is pretty much the same thing

[supple roost]

Thank you very much

I understood now

[vital crescent]

I meant doesnt the bars and stars method rely on the fact that there are (m+n)!/m!n! ways to separate things into two groups

[supple roost]

8! Means they all are sitting

But we removed some common

[vital crescent]

they are are sitting?

8! = ways to arrange 8 people.
5!*3!=common (equivalent ways of grouping)

[supple roost]

Actually no

We are only choosing

[pearl pond]

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[pearl pond]

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[midnight haven]

can someone help me with this

[west sapphire]

is it written in invisible ink?

[brittle tinsel]

the answer is 1/e

[midnight haven]

thank you

[orchid heath]

!original

[pearl pond]

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.

@midnight haven Has your question been resolved?

[pearl pond]

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[knotty geyser]

can someone explain why the base is 1/2 and why it's 1/5700 not 5700 in the exponent?

[wet osprey]

Well

Half life talks about how much time it takes for half of the carbon-14s to decay away

Let’s say the half-life is 1 year

Then you’d expect (1/2)^(t)

For how much carbon-14 is left after t years

As, every year that passes you multiply by 1/2 to again half the number of carbon-14 atoms

Now if we want to only halve every 2 years, we would want to do (1/2)^(t/2) so that every 2 years we multiply by 1/2

[knotty geyser]

ohh ok thanks

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[pearl pond]

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[hasty hamlet]

Hi

Please help solve

[meager frost]

Simple interest = PRT/100
Amount = P+Interest

Use these two formulas to get your answer. Set amount =2P

[magic olive]

Ain’t it just 50 or am I tripping?

[meager frost]

Yes, it's 50 years 😅
That's a lot of time.

[magic olive]

Fr💀

[hasty hamlet]

Like this?

[pearl pond]

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[cursive wraith]

!status

[pearl pond]

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

[stoic imp]

what does GL even mean bro

Lie Group

[cursive wraith]

invertible here

[stoic imp]

wdym?

[cursive wraith]

A in GL(n,R) means A is an invertible matrix

[stoic imp]

why is that

never seen that notation before

[cursive wraith]

GL means linear group

as you know square n*n matrices represent linear maps from R^n to itself

to make it a group with the composition operation (equivalently matrix multiplication)

we have to only consider invertible mappings

which correspond to invertible matrices

Don't worry too much about the "why" if you haven't seen groups too much

and in the meantime, just know that A in GL(n,R) means A is an invertible n*n matrix

[stoic imp]

prof expects us to understand group things when we have only seen basic linear algebra

[cursive wraith]

again, you don't have to understand what a group is

[cursive wraith]

just remember what the notation means

[stoic imp]

ok gotcha

now what

[cursive wraith]

well, try the questions on your own if you haven't had the time yet

the first right/wrong statement is "if A^2 + 2A = I_n, then A is invertible"

[pearl pond]

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[stoic imp]

can I get help with 3

.close

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[stoic imp]

if A in GL(n,R) then A is invertible and then, it represents an isomorphism right? A is bioactive linear map and thus, Ax = b has unique solution

[cursive wraith]

yes if A is bijective then Ax = b has for unique solution x = A^-1 b

[stoic imp]

A(A-2I) = I

AB = I

B = A-2I

[stoic imp]

A-2I is the inverse of A, thus A in GL(n,R)

[stoic imp]

yeah, since A is an isomorphism j think it's guaranteed one input one output solution for Ax=b is unique only solution for that is x = A^-1b as you said

for 2. we can just rref wrt the basis and find the rank and check the dimension of the subspace

AB = I ==> B = A^-1

[stoic imp]

A.A^-1 = I

==> A in GL(n,R)

B = A^-1

AB = I

A.A^-1 = I

[pearl pond]

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[magic knot]

How did the n^2 and 6 switch sides? It doesn't seem to be cross multiplication x-x

[sturdy bane]

.rotate

[drowsy adder]

1/(ab) = 1/(ba)

[smoky mountain]

,rccw

[toxic lichen]

it isnt, its just shuffling factors around in the denominator

the product of fractions is essentially thought of as one big fraction and factors are shuffled freely between the numerators and (separately) between the denominators

[magic knot]

Oooh yeah that makes sense. I got thrown off since the tops weren't really affected. Thank you :D

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[tropic zephyr]

Ignore my pfp

This is a troll account

But

Please help with the question

<@&286206848099549185>

[spare lark]

!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.

[tropic zephyr]

sorryy

<@&286206848099549185>

damn

<@&286206848099549185>

🙃

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@tropic zephyr Has your question been resolved?

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[lethal ruin]

Here, why mustn't it be an ADDITION sign (+)?

[bitter lodge]

They factored out -2

So $\frac{+2}{-2} = -1$

[jolly parrot]

King Leo [Ping For Help]

[lethal ruin]

Yes but wouldn't that become $-2(-x-1)$?

[jolly parrot]

Elliot Pixel

[bitter lodge]

No, because $\frac{-2x}{-2} = x$

[jolly parrot]

King Leo [Ping For Help]

[lethal ruin]

So if it was only factored by 2, it would become $-2(-x+1)$?

[jolly parrot]

Elliot Pixel

[lethal ruin]

@bitter lodge

[bitter lodge]

I added ✅

[lethal ruin]

Oh I thought that was by the bot

[bitter lodge]

Lol

But ya youre correct

[lethal ruin]

ok thanks this factoring is so confusing lol

[lethal ruin]

because I need to find out the common (x+?) factor

is there a trick for always getting the right one or is it just trial and error?

like here I got -x-2x

[bitter lodge]

Gtg

[lethal ruin]

Cya

thanks

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✅

[jolly parrot]

Elliot Pixel

[rough forge]

<@&268886789983436800>

[plush bramble]

<@&268886789983436800>

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[pearl pond]

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[plush bramble]

!15m

[pearl pond]

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

[torn thicket]

B

you should find a relative maxima

so look where the graph has point, where all points in its vicinity are lower than that point

[pearl pond]

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[lyric mauve]

i'm doing ex 3.7 using the thm 3.3 in P2, i got stuck when verifying (2) in the case where U is the set containing 0' and V is the set containing 0''. U intersect V is (0, min(b,c)) but in the definition, the basis element (a,b) is for 0<a<b, not for a=0 which is what i got. how to show U intersect V in \B in this case

[pearl pond]

@lyric mauve Has your question been resolved?

[lyric mauve]

<@&286206848099549185>

[marble sigil]

you're right, though (0, min(b,c)) is the intersection and you only need a W that's a subset of it

[lyric mauve]

ohh got you

i know how to do the rest of it

thank you！

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[west dagger]

Plz check it as where am wrong

[pearl pond]

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[fiery maple]

Need help on this problem

[fiery maple]

Hello

Pls someone help

I just need this question and one more

[fiery maple]

Half an answer for the next one

I haven’t tried anything

I’m confused

Help

Hello

Bru

[fair creek]

okay so

firstly please just rotate the picture by 90 degrees 😭

[fiery maple]

,rccw

[fiery maple]

bruh

[fair creek]

secondly, you have to do a bit of construction

[fiery maple]

,rccw

[fiery maple]

OH

,rccw

[fiery maple]

there

[fair creek]

finally

assume a line parallel to YB going through A and intersecting OE at M and BR at N

[fiery maple]

K…

I don’t need a whole explanation I know how to do I just need help setting up the equation

[fair creek]

triangles AME and ANR would then be similar

[fair creek]

yes, i'm getting to that

[fiery maple]

I

K*

[fair creek]

since the triangles are similar, the ratios of the sides is constant

there, you got your equation

[fiery maple]

No

bro what

[fair creek]

how are you having an issue with this?

y+16=24

you get the value of y

y/4=24/(4+x)

you get value of x

[pearl pond]

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[lapis lynx]

what is the question asking? like is it asking if the car bumper will collide with the object?

[bitter lodge]

I'd assume the car's bumpers can handle hitting an object at 10mph

So you need to calculate how fast the car is still travelling 100yd later

[lapis lynx]

alr thanks

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[wet latch]

how to find area enclosed by secx y = x so that my answer does not include any trig terms

[wet latch]

im stuck on how to integrate sec(x) so that it doesnt have trig terms in it

[toxic lichen]

the antiderivative of 1/cos(x) does have trig terms in it

so if you have this strange requirement imposed on you by authority, you're kinda cooked

[raven girder]

I'm pretty sure you're asked to calculate the numerical answer and that is way you're asked without any trig functions but not in the primitive which is trig in nature but in the final numerical solution on (-π/4, π/4).

why

[wet latch]

ok

but which method would i even use

[leaden tulip]

If you really dislike trigonometry a lot, I suggest Weierstrass Substitution.

They turn Trig Functions to Algebraic expresstions.

But...

You have y=x here.

[worn bear]

this is just the area under secx minus 2*(area under y=x from 0 to pi/4)

[leaden tulip]

Here.

Substitute the boundaries yourself.

[worn bear]

basically moving the triangle around

[wet latch]

how to get ln|secx+tanx|-x^2/2

[toxic lichen]

!nosols

[pearl pond]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[leaden tulip]

Nah she can't

She can't have that as answer.

[worn bear]

this integral is simpler and is equal to what u want

[leaden tulip]

See @toxic lichen

[worn bear]

do u see where the 2 integrals come from? @wet latch

[wet latch]

i dont know where the -2 came from

[worn bear]

oki 1 sec

[leaden tulip]

If there's rule to help someone, I might as well as step aside.

[worn bear]

so the red region is the first integral, and the blue is the chunk ur cutting off from the red

the right blue stuff is cutting the red

[wet latch]

alr

[worn bear]

and the blue stuff on the left just has 'negative area'

both triangles have the same shape so ur subtracting twice of that

[wet latch]

ok

[worn bear]

not really sure what u mean by u dont want any trig in the math

since ur dealing with definite integrals, ur just gon get a number at the end anyhow

[wet latch]

how to integrate sec x though

[worn bear]

oh i have no idea how to do that on hand, u just gotta look up what it is

like, have u ever done the integral of cosine before from scratch? or do u just know it from memory

but if u r curious, just search up "integral of sec proof"

[wet latch]

cosine is easy though no because its the deriviative of sin is cos

[worn bear]

yeah but how do u know that

[wet latch]

have deriviative of sin memorized

[worn bear]

exactly

do the same for secant

[wet latch]

was never forced to memorize integral of sec in class though

[worn bear]

https://www.youtube.com/watch?v=85amlAB1vQo

this one is better

[pearl pond]

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[neon comet]

hi, i don't understand how to solve part a graphically. could someone be able to drop me a hint?

[toxic lichen]

graph y = |x-2| and y = x/2 on the same set of axes

note where their intersections happen

and see on what interval the graph of |x-2| is below that of x/2

@neon comet does this make sense to you?

[neon comet]

hmm yes

but since it's an inequality

how would i express my answer after finding the pts of intersections

[toxic lichen]

see on what interval the graph of |x-2| is below that of x/2

it's gonna be an interval of x-values. that interval will be your answer

if you're still unsure, follow my instructions re: graphing both functions and show me your result

[neon comet]

don't mind my algebraic working out, i already know it's wrong

so is it just 4/3 <x<4

[toxic lichen]

indeed it is

[neon comet]

alr i think i just overthought it, thanks

.close

[pearl pond]

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[pearl pond]

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[neon comet]

How would you solve part b graphically

[neon comet]

this is what desmos shows

[midnight haven]

put y = 7

in desmos

[neon comet]

alr

but no what im saying is how can you figure out the shape if you add two absolute values of |x-4| and |x+2|

[toxic lichen]

you can do it algebraically and see that the function is constant between -2 and 4 and has slope ±2 outside of that

[pearl pond]

@neon comet Has your question been resolved?

[pearl pond]

@neon comet Has your question been resolved?

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[sweet shoal]

anybody knows how to do this one ?

[next halo]

1

[pearl pond]

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[sweet shoal]

thanks

[pearl pond]

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[craggy portal]

#help-39

how to solve

[craggy portal]

what should i do now

[fierce totem]

$x^2\le 5 \text{ and } x^2\ge 3$

[jolly parrot]

TargetVN

[fierce totem]

Solve each of them separately then take the intersection of both sets of solution

[craggy portal]

then

[verbal whale]

Then you have the solution 😅

[craggy portal]

can u explain how to solve the square term

[open rivet]

sqrt

[fierce totem]

im aware that you dont know how to solve this kind of stuff, so here's one detailed hint:

$x^2\le 5 \longrightarrow x^{2}-(\sqrt{5})^2\le 0$

[jolly parrot]

TargetVN

[toxic lichen]

better to put two mathmode formulas

[fierce totem]

note, it's just a detailed hint to get over with inequality. over time you can pretty much skip that step

[toxic lichen]

$x^2\leq 5$ and $x^2\geq 3$

[jolly parrot]

ann.in.a.teacup

[toxic lichen]

rather than \text

\text should be used sparingly

[fierce totem]

ik, but im lazy to type 2 equations yes, blame my laziness :/

[fierce totem]

uh oh

ok nevermind, we go for a different route instead

$A^{2}\le B\to \sqrt{A^2}\le \sqrt{B}\to \left| A \right|\le \sqrt{B}$

[jolly parrot]

TargetVN

[fierce totem]

since you dont even know how to solve A*B < 0, ig this might be easier to do

[craggy portal]

what language is this

[fierce totem]

take the square roots of both sides of the inequality

then use: $\sqrt{A^2}=\left| A \right|$

[jolly parrot]

TargetVN

[craggy portal]

can u show the detailed procedure iam stuck on this for about 15 mint

[fierce totem]

that is the detailed procedure

since both sides are positive, you are free to square root both sides

[fierce totem]

add a brace there

this indicates that both happen at the same time

[craggy portal]

hooo

[fierce totem]

if A>0, then sqrt(A^2) is just A

if A=0, it's just 0

the case when A<0 is where people get wrong the most

[craggy portal]

-A

[fierce totem]

ye

so, a way to combine all the cases together is |A|, since |A| is also defined the same way

[craggy portal]

thankz u helped me alot

[fierce totem]

a small note just in case you missed:

$\left| A \right|\ge \sqrt{B}\longrightarrow A\ge \sqrt{B} \textbf{ or }A\le -\sqrt{B}$

[jolly parrot]

TargetVN

[fierce totem]

< then it's and
> then it's or

[craggy portal]

ooh

is there any free resource in internrt earn all this

[fierce totem]

i mean you can just search on google

[craggy portal]

any playlist or something

[fierce totem]

honestly, i have no idea since i never needed them

but you can guess what knowledge do you need
for example, here we just discussed "absolute value inequality"

[craggy portal]

is redoing a math problem good or bad

[fierce totem]

that's good

but don't repeat it too much, what you should redo is problems that are similar to the one you encountered

[craggy portal]

hoo

thanks

see u soon

with another problem

[fierce totem]

k

[craggy portal]

.close

[pearl pond]

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[craggy portal]

how to solve inequalities having GIF

[rustic tendon]

Just think about it lol

[-1, 2) in this case

[craggy portal]

how GIF works

[rustic tendon]

do you know what the function does?

[craggy portal]

1.9=1,0.2=0,-1.9=-1 isnt it

[rustic tendon]

yeah

[trim crest]

has anyone ever used laughing gas i'm doing a research about it

[rustic tendon]

what an odd question for a math server

[plush sundial]

nah

-1.9 is -2

[trim crest]

hahaha okey

[rustic tendon]

yeah mb

it always rounds down

[open rivet]

!occupied

[pearl pond]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[trim crest]

does anyone know where I can get an answer to that question

[craggy portal]

google it

[trim crest]

noo

i need people to fill in my survey

[craggy portal]

how to solve problem like this

[plush sundial]

u dont do it like that

[craggy portal]

i dont knwchatgpt give me this when i ask for a problem

[plush sundial]

basically GIF gives u an integral value

[craggy portal]

yeah

[plush sundial]

so u check for values of the integers and in bw the integers

in this case u see for -1,0,1

so u break it into 3 parts

i assume u hv to find the range

or domain>?

[craggy portal]

yeah

everthing

i just need to know how to solve problem having linear equalties and GIF

[plush sundial]

u break it into 3 parts

[craggy portal]

hm

[plush sundial]

u check for values from [-1,0) , [0,1) and {1}

u basically get 3 values

for range

-1,0,1

[craggy portal]

ooh

[plush sundial]

or the better way to do this wud be to use graph

[craggy portal]

graphical method

how to plot this in graph

[plush sundial]

now can u tell me the domain of x?

[craggy portal]

R

[plush sundial]

no

[craggy portal]

pling

[plush sundial]

keep x as 10

its greter than 1

ineq not satisfied

[craggy portal]

sry i dont understanding anything thing can u teach me from basic

[plush sundial]

hm

[craggy portal]

iam just a high schooler

[plush sundial]

even im a high schooler

what did u not understand

[craggy portal]

i dont feel anything while looking into the ineqlautiy

complete blank

[plush sundial]

do uk the basic stuff for GIF?

domain of [x] is R

for this question its not R

[craggy portal]

why

[plush sundial]

cuz if u put x as 10 suppose

-1<=10<=1 makes no sense

it tells that 1 is greater than 10

[craggy portal]

what is wrong with me

[plush sundial]

bro thats for general

im telling for the question u asked me

[craggy portal]

i thinked that this was a question

imao

[plush sundial]

huh

[craggy portal]

can u give a example of inequalty having GIF

[plush sundial]

this is the question i suppose

[craggy portal]

[-1,2)

[plush sundial]

ye thats the domain

[craggy portal]

range[-1,1]

[plush sundial]

na

range {-1}{0}{1}

[craggy portal]

i shit i wrong

can u give a example

[plush sundial]

u want a question?

[craggy portal]

yeah

[plush sundial]

uk jee?

[craggy portal]

Joint entrance exam

[plush sundial]

u giving it?

[craggy portal]

no

how do u know that

[plush sundial]

cuz im giving it

[craggy portal]

indian

[plush sundial]

ye

[craggy portal]

iam writing keam

keam is lite version of jee

but have more questions

[plush sundial]

hmm

if u want questions and stuff, i suggest u to go and srch them up on yt

[craggy portal]

can u makeup a easy question

[plush sundial]

ok gimmi a min

its ez

[craggy portal]

https://tenor.com/view/npc-npc-processing-processing-npc-processing-npc-thinking-gif-18378041742925308956

[plush sundial]

or leave that

[craggy portal]

is it integer

[plush sundial]

the answer is none/ not possible

[craggy portal]

wasted my entire brain ram

[plush sundial]

for this ques how wud u approach?

[craggy portal]

press the skip button

[plush sundial]

bruh

ig i shud do the same with this channel

[rustic tendon]

For this you can utilize the fact that $x\floor{x} \leq x^2$

[jolly parrot]

dyxn

[craggy portal]

imao

[rustic tendon]

So x can at max be 4 anyways

[plush sundial]

ye, but expl this wud be a bit difficult so i skipped it

[rustic tendon]

hmm okay

[craggy portal]

talk btwn math gods

[fierce totem]

$\text{Just}\left\lfloor x \right\rfloor=\frac{15}{x} \text{ then brute force}$

[jolly parrot]

TargetVN

[craggy portal]

https://tenor.com/view/amicat1-math-do-the-math-computing-gif-9934140128705343939

[plush sundial]

do u wanna know how to do the 2nd ques?

[craggy portal]

what is brute force

yeah

[plush sundial]

facorize it

and tell me what comes

[craggy portal]

(/x/-3)(/x/-2)

[plush sundial]

right now that =0

so 2 cases

[x]-3=0
or
[x]-2=0

so [x]=3

x=?

[craggy portal]

wait one min'

1 ans

[plush sundial]

?

[craggy portal]

option

[plush sundial]

no

[craggy portal]

https://tenor.com/view/ogli-gif-17468683305861986751

is this correct

[plush sundial]

from where is > symbol coming?

it shud be=

[plush sundial]

alr, if u want it like that

[plush sundial]

the answer is still wrong 😭

its (3,inf)

[plush sundial]

.

for the original one, its option 4

[craggy portal]

rethinking my life

is this correct

[plush sundial]

ye

[plush sundial]

2 is exclueded

lmao

accent

[craggy portal]

south india

[plush sundial]

ye lol

blr

[craggy portal]

what is blrrrr

why 2 is exculded

does puting 2 makes the equation zero

[plush sundial]

nvm

4 is exclueded

nvm

its correct

im blind

[craggy portal]

https://tenor.com/view/happy-tears-gif-13449471066643700197

[plush sundial]

man i was in a bit of hurry mb

[craggy portal]

kerala

[plush sundial]

im karnataka]

[craggy portal]

https://tenor.com/view/oh-yea-gif-24745435

thnkz now i understand how to solve GIF if comes in quadratic equation form

.close

[pearl pond]

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[neon quest]

A circle is inscribed in the right-angled triangle KLM (see the diagram). ∠LKO + ∠KOM = 155°. Calculate the measures of the acute angles of the triangle.

[neon quest]

i asked earlier but didnt manage to solve it

[open rivet]

write x=KOM

then try writing as many other angles in terms of x

[neon quest]

KOM=LOM=x?

sorry i dont really get what you mean by "in terms on M"

LKO=OKM

[open rivet]

mb

i meant in terms of X

like, if x=KOM, then OML=x

and then LMK=2x

etc etc

[neon quest]

wait, if we look at triangle KOM, KOM=x, OKM = 155-x, KMO= 25-2x?

or is it bs

[open rivet]

the 155 you cant use here yet

KOM isnt 155

LKO+KOM=155

[neon quest]

but LKO=OKM

and LKO is 155-x

because LKO + X = 155

[open rivet]

so you have LKO=OKM

OKM+KOM+OMK=180 and OKM+KOM=155, thus OMK=25

make sense?

[neon quest]

yes

[open rivet]

now from here it should be simple

[neon quest]

mhmm so i will try to solve now and we will check answers

ok?

[open rivet]

yes

gl

[neon quest]

bro

i got LKM=65

[open rivet]

that doesnt seem right

what did you get for KML?

[neon quest]

yea, its 50, doesnt add up to 180

[open rivet]

180=KML+MLK+LKM

KML=50

MLK=90

[neon quest]

omg

[open rivet]

then what is LKM

🙂

[neon quest]

bro i tried to calculate through x

[open rivet]

we found x already

its 25

[neon quest]

see what 8 lessons does to people

thanks a lot

sorry that it took so long

.close

[pearl pond]

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[viscid mural]

Hey im not sure where i went wrong with this problem.

[midnight haven]

,rotate

[midnight haven]

what's the question?

can you post a screenshot of the original question?

[viscid mural]

Yes sorry

[severe quarry]

Did you misplace your 90° angle?

[midnight haven]

yup that does seem to be the case

notice how it says angle D is pi/2 aka 90 degrees

whilst your figure clearly shows that angle E is 90 degrees thereby leading to incorrect answers

[viscid mural]

Ok I’ll redo that thank u

[pearl pond]

@viscid mural Has your question been resolved?

[pearl pond]

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[brisk condor]

Hi 👋
May someone please explain to me how to answer Q1 b)

[brisk condor]

I tried adding the 5 and 8 to get 13, then I did 13 sin 60° = 11.258...

[open rivet]

you need to do 8+cos(60)*5

for the x

the 8N vector in x and y: x=8, y=0

[severe adder]

You can only add like that if the direction of vectors is same

[open rivet]

the 5N vector in x and y: x=5 * cos(60), y=5 * sin(60)

[severe adder]

To do that, you have to divide the vector into it's components

[open rivet]

and then you add the x and y components

[severe adder]

Like bonk showed here

[brisk condor]

To work out the magnitude?

The correct answer is 11.4 N (3 s.f.) for the magnitude, but I dont know how to work out the question to find that answer

[pearl pond]

@brisk condor Has your question been resolved?

[pearl pond]

@brisk condor Has your question been resolved?

[pearl pond]

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[thick copper]

Number 4

How do we start

Can we solve it as if its a triangle and get the area?

[pearl pond]

@thick copper Has your question been resolved?

[pearl pond]

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[prisma escarp]

I watched a video on elliptic coordinates but from where does this come from?

[prisma escarp]

https://www.youtube.com/watch?v=R8IUWml71II

this is the video and he just starts off with x = ccosh mu cos v and y = csinh mu cos v

[pearl pond]

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[grizzled viper]

I am doing some worldbuilding for a writing project and I need to work out the size of an alien planet. This planet is comprised of floors and only floors, no natural planet structure, each floor of it spans the entire planet, basically making it a giant Russian nesting doll, a sphere inside of a sphere^100

I want gravity to be equivilant, which is where I need help. I want this planet to be as large as possible, with 3ft thick layers between the airspaces (which for an average lets just say 30ft).
I need to work out how big this planet can be with an equivalent volume to earth, and I have no idea how to model this volumetric formula
(Alien planet for all intents and purposes is perfectly sphereical, alternating solid layers 3ft thick and space layers of 30ft thick, and assuming similar composition to earth to ignore desnity)

[bitter lodge]

“how big this planet can be with an equivalent volume to earth”

?

[grizzled viper]

Yes, I need help figuring out how large this planet can be with the given specifications.
equivalent volume to earth (only counting the solid layers)
3ft solid layers
30ft spaces in between (not worried abt structural integrity)
As large as possible

[bitter lodge]

shouldnt the planet be just as large as earth?

[warm copper]

You are asking how many layers?

[grizzled viper]

The 30ft spaces in between aren't counting towards the volume, the volume preservation is to keep gravity similar

[grizzled viper]

How many layers and how large is the final layer, yes

[pearl pond]

@grizzled viper Has your question been resolved?

[warm copper]

Ah

$E_V=\sum_{r=1}^{n}{\frac{4}{3}\pi (3r+30\left\lfloor \frac{r}{2} \right\rfloor)^3(-1)^{r-1}}$

[jolly parrot]

AkitoLite

[warm copper]

I think it should look something like this...?

where E_v is the volume

Then solve for n

n must be odd

[grizzled viper]

because of the alternation yeah, i think i was originally heading in the wrong direction with my own try

This looks perfect, thank you

[pearl pond]

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[warm copper]

Ouch that's wrong

[warm copper]

$E_V=\sum_{r=1}^{n}{\frac{4}{3}\pi (3 \left\lfloor \frac{r+1}{2} \right\rfloor +30\left\lfloor \frac{r}{2} \right\rfloor)^3(-1)^{r-1}}$

[jolly parrot]

AkitoLite

[warm copper]

I forgot to alternate +3 and +30, and instead just did +3,+33,+3,+33

.closed

.close

[pearl pond]

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[small needle]

im trying to solve

[small needle]

if a solution exists it would be in the form

[plush bramble]

X is an integer

[small needle]

yes i know

sorry I should rephrease what I was trying to do

im trying to figure out if the equation has solutions modulo 1009

[plush bramble]

https://www.youtube.com/watch?v=ped6r2UFk78j

[small needle]

so if y^2 = 45 is a quadratic residue mod 1009 thhen sqrt 45 is the integer solution

wait nvm im tripping i guess

[plucky python]

so if 45 is a QR mod 1009 then we're done

note that 45 is a QR <=> 5 is a QR

then you can quadratic reciprocity it, 1009 is prime

[small needle]

wait so im confused am I wrong to use the sqrt(45) notation here, I just thought it represented some integer y modulo 45 such that y^2 = 45

not that sqrt(45) is a non integer value mod 1009

[plucky python]

yh it normally does since we work in F_1009 or a suitable extension if necessary

i think Riemann just meant that (1+sqrt(45))/2 \in R is not literally a solution

[small needle]

oh then i just exaplained it poorly i guess

cause I've already showed sqrt(45) is a qr mod 1009 in my own work

my issue was trying to find y, but instead I pivoted to just focusing on the parity of y since if y is odd X = (1+y)/2 will always be a possible solution no?

[plucky python]

hmm unfortunately i personally don't know how to explicitly find sqrt(45) mod 1009

wolframalpha tells me it's 277 tho

[small needle]

yea me neither thats why I didnt bother

but I thought finding the parity of sqrt(42) would've been more doable

[plucky python]

wait sorry i'm confused by what ur doing now

[plucky python]

you've shown that the soln will be 1+-sqrt(45)/2

and then you've shown sqrt(45) exists

so ur done

[small needle]

yea but if sqrt(45) is even then 1+-sqrt(45)/2 is not an integer right?

[plucky python]

what's 1/2 mod 1009?

[small needle]

1/2?...

wwait

[cursive wraith]

1/2 exists in Z_1009

[plucky python]

please always remember that notations like 1+-sqrt(45)/2 are always just because integers modulo 1009 is a field

we are not 'embedding' F_1009 into R, there isn't really a sensible notion of "embedding F_1009 in R"

it's just shorthand because the number 505 + 1009Z in Z/1009Z behaves like 1/2 in R

[small needle]

oh okay.... hmm maybe trying to solve it this way is not the way my course is expecting me to then

or at least trying to use the notation

[pearl pond]

@small needle Has your question been resolved?

[pearl pond]

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[mighty timber]

I don't know how to integrate the absolute value of x 😭

[vagrant trout]

You have two integrals

One is $\int{xdx}$ and the other is $\int{-xdx}$

[jolly parrot]

alex <3

[vagrant trout]

Since |x| = x for x>=0 and -x for x<0

in other words

the answer would be represented as $\frac{x^2}{2} \times sgn(x) + c$

[jolly parrot]

alex <3

[vagrant trout]

But in this case

[mighty timber]

I'm so confused

[vagrant trout]

Since |x| is an even function (f(x) = f(-x)), and since the integral is in the form of $\int_{-a}^{a} f(x) dx$, you can represent the integral as $2 \times $\int_0^a f(x)dx$

[jolly parrot]

alex <3
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[vagrant trout]

In this case, $\int_{-12}^{12} 12 - |x| dx$, you can represent the integral as $2 \times $\int_0^{12} 12 - x dx$

[jolly parrot]

alex <3
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[vagrant trout]

https://youtu.be/S5zFfQODQOo?si=5bK9UBUxts7J-XEF

or you can use this video for explanation:

[pearl pond]

@mighty timber Has your question been resolved?

[pearl pond]

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[wary bolt]

Hello, I've completed the square and gotten (x+3)^2 - 17

im just really unsure of how to do this part

[summer imp]

Well that’s right so far

Now you set this equal to 0 and solve for x+3 first

[wary bolt]

oh

im stupid

lol

Well if we solve for x

we get one of them as -3

and we set -17 = 0

as thats the other thing?

Or am I wrong

Hmm

[summer imp]

Well usually you would do like
$(x+3)^2 = 17$

[jolly parrot]

Azyrashacorki

[wary bolt]

I had gpt explain it, and their way of completing the square is completly diff from mine

Yes that makes sense, adding over

They just didn't do that in our notes/videos

lol

We're currently doing partial fraction and they only really wanted the u^2 + a^2 format

thank you, for pointing in right direction

.close

[pearl pond]

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[pearl pond]

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[lusty frost]

can someone tell me in one simple sentence what the sqrt(15) means?

[lusty frost]

my learning uni site is down

and i dont have my script downloaded

[ocean hornet]

it is the magnitude of the vector x

or the length

[lusty frost]

isnt the length just |x| ?

[ocean hornet]

yeah

the double bars is another notation for the same thing

[lusty frost]

okay thank you!

[pearl pond]

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[tawny pewter]

how can you yell

[rough stream]

Geometric series can be written in the form Σ aⁿ for some constant a

[midnight haven]

n can be negative also

[rough stream]

We can both be right!

It may take some algebraic work to get these into the correct form

[bitter lodge]

a can also be 1/a

[midnight haven]

yes i was hinting at that

[tawny pewter]

why is the last one a geo series but the first idnt

oh wait

is it bc the ()

so is geo series where it has to be n on top and bottom terms

[bitter lodge]

@tawny pewter why do you think the first series isnt geometric

[pearl pond]

@tawny pewter Has your question been resolved?

[pearl pond]

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[teal drift]

I’m confused as a mf ngl

[pearl pond]

@teal drift Has your question been resolved?

[teal drift]

No

[thin heath]

is the question 3/124 + 9/24?

[teal drift]

No it’s 12y not 124

[thin heath]

r u solving for y or just combining the fractions

[teal drift]

I am combining them

And then simplify it

[thin heath]

ok so first u want to get a common denominator

[teal drift]

Yeah

[thin heath]

both 12y and 24 go into 24y

yeah?

[teal drift]

Wait what

How did u do that

[thin heath]

so to find a common denominator you wanna find the LCM (least common multiple) for both the denominators

for example, if you had 1/2 and 1/3, the least common multiple between the two would be 6

[teal drift]

I think I’m slow

[thin heath]

you can get a common denominator by multiplying the denominators of each fraction

[teal drift]

ok

So then what is my denominator

[thin heath]

so for the example 2*3 = 6

you can apply the same logic to your question, i just did extra steps

so multiply 12y * 24

[teal drift]

Ok

I got 288

[thin heath]

288y, cuz you are also multiplying the y

[teal drift]

Ok

[thin heath]

so now in order to put the numerators in the same fraction you have to also multiply them by the other denominator (that kinda sounds confusing lemme do an example)

if you have 2/3 + 1/2, first we found the common denominator to be 6

but we have to manipulate the numerator as well, so we multiply the 2 in (2/3) by the 2 in the denominator of 1/2

2/3 --> 4/6

its technically the same fraction, just manipulated

does that like kinda make sense?

[teal drift]

Wait so

My teacher

Can I tell u how she taught me

[thin heath]

yep

[teal drift]

And then u tell me if it’s right

Ok

So like if the equation for the bottom was 2(x-3) and the other one was (x-3) she would just multiply a 2 into whatever side is missing the 2 on top and bottom of the fraction

Is that what u mean

[thin heath]

yes

[teal drift]

Ok

[thin heath]

so for your question you would multiple the 3 by 24 for the first fraction

[teal drift]

Yup

So 72

[thin heath]

yep

and then do the same for the other fraction numerator

[teal drift]

What did I even multiply the denominator by

Do u just multiply them together

[thin heath]

yes

[teal drift]

So would I do 12 times 9

12y

Times 9

[pearl pond]

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[thin heath]

yeah

[teal drift]

Bro wtf

.reopen

[pearl pond]

✅

[teal drift]

Ok

[wet spruce]

r u solving for y

[teal drift]

So I got

No

So now I got 108

[wet spruce]

whats the question

[teal drift]

108y

3/12y + 9/24

[thin heath]

u got it?

[teal drift]

I got 108y

[thin heath]

right so now you add that to the other numerator we found

since u can combine fractions due to the common denominator

and put that all over the common denominator

[teal drift]

Ok

So now my g fraction is 108y + 72/288y

[thin heath]

yes, see if you can try and pull out some common factors from the top and bottom to simplify it

like you could pull a two from the numerator and denominator to make it simpler

[teal drift]

Ok

I almost did the problem before

But I did a error on the denominator

Ok so I got

3y+2/8y

[thin heath]

that should be right (:

[teal drift]

ok

I hate math so much bru

.close

[pearl pond]

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[thin heath]

lmao

[teal drift]

Thanks btw

[bitter lodge]

That About Me is peak

[thin heath]

tuff about me

[versed mica]

,av whatsup123

[jolly parrot]

whatsup123's Avatar

Click here to view the image.

[versed mica]

nice

[thin heath]

its my dog lol

[versed mica]

golden?

[thin heath]

yep

[versed mica]

nice

i have one as well

[thin heath]

the best dog frfr

[teal drift]

.reopen

[pearl pond]

✅

[teal drift]

I can’t factor the top one and I don’t know what to do next

I think it’s miswritten

<@&286206848099549185>

Is this even doable bru

[broken fossil]

what is blud doing is it 6 ?

[broken fossil]

.

[teal drift]

Wdym

Yeah it’s 6

Oh wait

No

It’s 4

I don’t think the top is factorabke is it

Idk how to solve it

Bro went to go steel bananas

[pearl pond]

@teal drift Has your question been resolved?

[teal drift]

.close

[pearl pond]

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