help-0

[fallen sentinel]

?

[past sundial]

Like I know it’s infinatly small, but idk about large

[ember lava]

this is a test

[fallen sentinel]

It's over long ago

I just want a different approach to solve it

[ember lava]

idk about that

@sullen karma

[fallen sentinel]

I have solved it .. want my solution!? .. then try another way to solve this

[ember lava]

what should i do

[ember lava]

what should i do

[past sundial]

If it is long overdo, ask for them to send full screenshot with proof that it’s long overdo

Simple 😄

[ember lava]

ohk

@fallen sentinel send an ss of entire screen

[past sundial]

If they don’t have proof, u may administrate punishment

[fallen sentinel]

😐 you want the source !?

[past sundial]

But if they are telling truth, that shouldn’t be a problem

[ember lava]

hmm

[past sundial]

I mean a not cropped screenshot

I THINK that might count as valid proof, they got from another source, so I think that’s fine

[ember lava]

ok ig

[past sundial]

Cause it doesn’t seem they cropped it themselves

[fallen sentinel]

So it's a question from a grp .. of my friends

And so I ended up with this q.

I'm Indian.. grp is for IIT jee people

[ember lava]

even im an indian

u preparing for jee?

[fallen sentinel]

Yes

[ember lava]

which grade are you in

[vagrant kayak]

me

too

[fallen sentinel]

12th .. 2022 my first attempt

[ember lava]

me too

[fallen sentinel]

Nice

[ember lava]

hmm

[vagrant kayak]

i am in 8th

studying for jee

concepts

HELP ME

pls

[ember lava]

..

[vagrant kayak]

solve pls

i hate maths in jee

[ember lava]

..

[crystal tapir]

is this yr 12?

[ember lava]

do u want soln of all questions?

[vagrant kayak]

yes

[ember lava]

ok

[vagrant kayak]

be quick pls

[fallen sentinel]

Highschool

[ember lava]

but i shouldnt tell u the answer

[vagrant kayak]

why?

[ember lava]

i'll help you get the idea

[crystal tapir]

ah ok

[vagrant kayak]

its not my test

[ember lava]

you should also try solving it

[crystal tapir]

good teacher fr

[ember lava]

so i'll just guide you

[vagrant kayak]

ok!

[ember lava]

ok

so

for the 15th one

so lets ignore the lines for now

so how many points of intersection will be there for circles?

2 are concentric

@vagrant kayak

[vagrant kayak]

i-

idk

[ember lava]

concentric will not have any point of intersectiion right?

[vagrant kayak]

yes

[ember lava]

ok

[vagrant kayak]

Omg exam in 10 mins

[ember lava]

so now take another circle and draw it such that it will intersect both the concentric circles

[vagrant kayak]

pls tell the answers

[ember lava]

i

i cant solve all in 10 mins lol

[vagrant kayak]

solve how much u can

pls

[ember lava]

but

if i just tell you the answer

whats the point

you anyways wont get it

huh

[vagrant kayak]

atleast they will come in exam

i mean'

[ember lava]

how can you be sure theyll come in exam

only these questions

sus

[vagrant kayak]

teacher said

[past sundial]

I guess summarize and lead miracle to answer, but don’t tell the answer

[ember lava]

hmm but each question will take quite some time explaining

xD

idk what to do lol

[vagrant kayak]

ok tell me

how to find the even divisors of n

[past sundial]

Use time to explain now, don’t talk, explain, if time is short, best to explain then to talk

[ember lava]

k

[ember lava]

.

[past sundial]

Explain as in lead, but not give direct answer

[ember lava]

bruh

u shud be helper

[past sundial]

I don’t know what u are talking about so I can’t really help lol

I’m just taking notes on infinity and pondering about infinity lol

[ember lava]

@vagrant kayak draw circles and make them intersect the concentric circles. now draw lines that intersect the circles

do something like that

[vagrant kayak]

ok

[ember lava]

p&c sucks

lol

[fallen sentinel]

Lol I have given up on PnC

[ember lava]

i see

[ember lava]

lool

p&c comes in jee

study it

lol

[fallen sentinel]

These questions are still bit easier... but I literally haven't solved any PnC problem in months ..

[ember lava]

...

practice them

try solving them

im sure you can do it

[vagrant kayak]

i am gonna get bad marks in maths

for sure

:((((

[ember lava]

;-;

[vagrant kayak]

;9

😭

[frail anvil]

Why man, STUDY HARD.

Is anybody is of Class 9 or below?

[noble crypt]

just ask your question if you have one

[rich basin]

I was wondering what is wrong with my query

,w solve ( 4 choose 3) * (3 choose 1) * (2 choose 1) + (4 choose 2) * (3 choose 2) * (2 choose 1) + (4 choose 2) * (3 choose 1) * (2 choose 2) + (4 choose 1) * (3 choose 2) * (2 choose 2) + (4 choose 1) * (3 choose 3) * (2 choose 1)

[ocean seal]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by Travelling Salesman#4998

[rich basin]

,w solve (4 choose 1) * (3 choose 3) * (2 choose 1)

[ocean seal]

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[rich basin]

(4 choose 1) * (3 choose 2) * (2 choose 2) + (4 choose 1) * (3 choose 3) * (2 choose 1)

,w solve (4 choose 1) * (3 choose 2) * (2 choose 2) + (4 choose 1) * (3 choose 3) * (2 choose 1)

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by Travelling Salesman#4998

[rich basin]

,w solve (4 choose 2) * (3 choose 1) * (2 choose 2) + (4 choose 1) * (3 choose 2) * (2 choose 2) + (4 choose 1) * (3 choose 3) * (2 choose 1)

[ocean seal]

Results provided by WolframAlpha

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[vivid breach]

So, to solve the following a very convinient sol. has been given here : https://www.youtube.com/watch?v=ePIKlri8FYg

Instead of such calculations and me being in 8th grade I just verified that; lets assume 10 before the infinity radical then;
10x10 = 100 and sqrt.100 = 10 continuing this process the last ans comes as 10*10 = 100 hence, i replied for the following as x = 100 though the ans, was correct can we appreciate this as a solu. for such similar questions, also maybe this wont work with nums. in series such as the 2nd example from the vid. mentioned above,
where a series of nums. (3, 5) were used

[distant violet]

Geyo

[ornate grove]

Inh2o to mmscf formula

?

[thorn kindle]

10sqrtx=x

100x = x^2
x=0
x=100

,w 10sqrt(10sqrt(x))=x

[ocean seal]

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[thorn kindle]

100 checks out

[rugged tide]

https://cdn.discordapp.com/attachments/760130942785421312/861522280122155018/unknown.png

[thorn kindle]

Are we to assume Z+

Wait no nvm thats not possible

Assume a=b=c

3x=3x^2=1

No i dont think that works nvm

,w expand (a+b+c)^2

[ocean seal]

Results provided by WolframAlpha

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Requested by AMD#4434

[thorn kindle]

2(ab+ac+bc)=0

[fallen sentinel]

Divide by abc you have your ans

[thorn kindle]

Oh damn thats it

[teal epoch]

Are we giving the answer now

[thorn kindle]

Fun problem

[vagrant kayak]

just finished my exam

GUESS WHAT

[thorn kindle]

Gg

[vagrant kayak]

almost every question is p&C

EEEEEEEE

IT WAS THE ONLY TOPIC I DIDNT STUDY'

UGHH

[teal epoch]

ded

[thorn kindle]

Its ok bro shit happens dont let it get you down

P&C?

[vagrant kayak]

p&C

[teal epoch]

permutations and combinations i think

[thorn kindle]

Lmao i hate that

[vagrant kayak]

ME 2

[vagrant kayak]

welp

[thorn kindle]

Its the only basic math topic i was never taught in school

[vagrant kayak]

when did they teach u that topic

[thorn kindle]

I was never taught it

[teal epoch]

p&c are taught starting at 8th Grade nowdays i think

[thorn kindle]

But its kind of intuitive and you can brute force it if all else fails

[vagrant kayak]

bruh

they taught me basics of pnc in 7th grade

now i am in 9th

still dont even understand the basics -_-.

[ivory otter]

can i use this channel?

guess i can

So

if i get tan 270

what do i do in this case

since its undefined

[ionic jewel]

,w tan(270 degrees)

[ocean seal]

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Requested by 兔子#6562

[ionic jewel]

you say undefined

[ivory otter]

but

ok wait check this

show that: $\tan(v - 270) = - \frac{1}{\tan v}$

how do i add space

[ionic jewel]

don't put the words in the dollar signs

and also it's \tan

[ocean seal]

MEOWBRO 父

[ivory otter]

if i would want to prove this

ill get undefined values

or nooo

waait

i get it

[ionic jewel]

the other side is undefined at the same points

so it's fine

[ivory otter]

ye

[ionic jewel]

[ivory otter]

no idea how im supposed to solve this

[ionic jewel]

what's the tan(a+b) formula?

I'm willing to bet you just use that

[ivory otter]

i did

i used the tan(a-b)

formula

[ionic jewel]

and what did you get

[ivory otter]

lemme get my phone and take a pic

instead

no energy to use latex

lol

[alpine sable]

I found the maximum possible no. of student using circle venn diagram.

how to find the minimum no. of student

[ionic jewel]

max I assume you got 85?
for minimum I get 60, but I'm not completely sure that's right

and sorry meowbro, idk how to finish your problem

[hasty hedge]

Sin 270 = -1

[ivory otter]

no problem!

<@&286206848099549185>

[alpine sable]

solved using the venn diagram, found i drew it wrong

min. 48

[teal epoch]

same I got 48.
I don't know if there's anything lower than that

[strong furnace]

tan(v-pi)=tan(v) , tan(pi/2-v)=cot(v) , cot(x)=1/tan(x) , this is what you need

[alpine sable]

thanks

[ivory otter]

Not supposed to use any reciprocal identities

Like cot and sec

[thorn kindle]

Sin(v-270)/cos(v-270)

cos/-sin

Use unit circle

[ivory otter]

Interesting

[ionic jewel]

wait how do you get 48

10 in all 3, then the best you can do is have everyone else in two clubs

oh

i see

i can't do mental math this late

[ornate grove]

Can I convert inh2o to mmscfd

[vale wigeon]

mmscfd?

[rocky cape]

x = log3(6561)

The 3 is small and is on the bottom of the log

Does anyone know how to do this?

I can't find it anywhere, they are always slightly different.

Here's the screenshot.

How do I solve these two ?

[teal epoch]

I don't know much about logarithms yet but it's easy to see that $3^8=6561$ if you haven't found yet

[ocean seal]

Callaway

[rocky cape]

Where did the X go

hm

other way around

its ddown arrow

if that even exists

like the small number is on the bottom

oh i got that too

idk what to do from there tho

can i put x in the power????????

damnn

im doing it wrong then

i used the solver on graphics calculateor

thats for X right

rule 5

wait no

ya but idk how to do in the calculator

but thats the power of be

B*

I dont understand 💀

[teal epoch]

wait are you new to logarithms

[rocky cape]

Nah

i literally did them like 9 weeks ago

i just forgot bruh 💀

i got an exam on wednesday

algebra + probabibility

it'll be fine tho

[alpine sable]

thanks mate for all the rules

[calm rock]

can anyone here help me understand/clarify the concept of the principle argument in complex numbers? im more comfortable with DM's if it helps but im fine talking about it here.

its less of a question and more of a clarification on a topic if thats allowed. i do not understand the principal argument or how it works. all i know is that it helps somehow with dealing with the multiple angles that arise from computing the angle of a complex number.

[alpine sable]

I know if dot product of two vector is 0, then it means both are perpendicular to each other

but how to make it lie in the plane P ? or verify if it lies in the plane P

[lethal stump]

a vector will lie on the plane P if it satisfies the equation for the plane P

i.e. the v = lambda(6,6,9) + mu(7,8,10)

soz i can't latex

umm

actually let me just see if i can do this q first

do you have answers @alpine sable

[alpine sable]

we get (1, 2, 1)

and scale it to unit vector by dividing by v/|v| i.e. root 6

well it lies in plane P, but how can i verify that and what if it does not lie?

[lethal stump]

well the way i verified it was by subbing it into the plane eqn

but i'm more curious as to how you got ur vector in the first place

because i had to dot product the plane and vector and find a lambda and mu value, which is already enough confirmation that it's on the plane

[alpine sable]

dot product should be 0

[lethal stump]

yea i got the right answer

(1/sqrt(6))(1,2,1)

but i doubt that you would need to confirm it given that you've already dotted the plane and the vector

unless ur teacher is super pedantic or smth

in that case you can sub ur vector back into the plane eqn and confirm that it satisfies all three simultaneous eqns

after you equate the x, y and z components

[alpine sable]

How can I justify part (a)?

For part (b), I think the acceleration is forward, since his cheeks are going back, so wind is hitting against them

[lethal stump]

yah you gots it

[alpine sable]

But how do I justify part (a)/

[lethal stump]

for part a i think you gotta assume that he's experiencing an unbalanced force

and objects that are moving at constant velocities do not experience any net force

like if ur in a car and the car is moving at 60kph without speeding up or slowing down, you don't feel like it's movingi

i.e. ur not experiencing any force

but then when the car speeds up or slows down you jerk back

i.e. ur experiencing a force

because ur acelerating

*accelerating

[alpine sable]

Yeah but we haven't been introduced to forces yet

[lethal stump]

wait so ur telling me that you learned acceleration before u learned forces?

[meager vault]

Well, the velocity is. Acceleration Depends if he's slowing down (braking or accelerating)

[lethal stump]

damn what is ur science faculty smoking

no offense

but srsly wut

[alpine sable]

Yeah, he is accelerating because his cheeks are backward.

So the acceleration is forward.

It wouldn't matter that the velocity is forward I think.

[slate kayak]

I learned acceleration before forces too.

[blazing crater]

whats 1 + 1?

[alpine sable]

A person standing on the edge of a cliff at some height above the ground throws one ball straight up with initial speed v0 and then throws another ball straight down with the same ini- tial speed. Which ball, if either, has the larger speed when it hits the ground? Neglect air resistance.

How do I build equations for this?

y = y0 + v0y * t - 9.8/2 t^2 is the position of the ball at time t, where y0 is the height of the cliff

So the velocity is y'(0) - 9.8t

I have no idea how to account for making it fall straight down or thrown up first, though

<@&286206848099549185>

[vale wigeon]

let $y_0$ be the starting height of both balls and let $v_0$ be the magnitude of the balls' initial velocities (the same for both balls as stated by the problem)

[ocean seal]

Ann

[vale wigeon]

then the equations of motion for our balls are:

$y_1(t) = y_0 + v_0t - \frac12 gt^2 \ \ y_2(t) = y_0 - v_0t - \frac12 gt^2$

[dull onyx]

would i ask for help here or is this being used

[ocean seal]

Ann

[dull onyx]

kay nvm

[vale wigeon]

@dull onyx this channel is being used. ask in one that's free.

[dull onyx]

sorry!

[alpine sable]

How do I know this is true?

[vale wigeon]

one's going straight up, the other's going straight down...

they are subject to the same gravitational acceleration and start at the same height

all that differs is the direction of their initial velocity

do you have any objections to this?

[alpine sable]

No that makes sense

So we would be comparing |v_0 - gt| and |-v_0 - gt|

But when its position equal to 0

At some time t

[vale wigeon]

we would be comparing their velocities at the time of their landings

these are different

for the two balls

[alpine sable]

Oh

[vale wigeon]

but also i suppose we could cheat a little

[alpine sable]

Yes that is right

[vale wigeon]

and avoid the laborious computations

[alpine sable]

How?

[vale wigeon]

i'm making a picture, hold on

[alpine sable]

doing it this way (with minimizing the LP) is an overkill. At the moment I am very busy, maybe I can post al solution the next 24 hours

[vale wigeon]

the red and black parabolas are the position-time graphs for our two balls

the solid parts of them, in any case

[ember lava]

but the guy is throwing the ball straight up

[vale wigeon]

the horizontal axis is time.

[alpine sable]

It's up to scaling

[ember lava]

i have another way of solving it

nvm

you go on

[vale wigeon]

do you agree that for any parabola, the slopes of the two tangent lines at the x-intercepts are equal in magnitude (and opposite in sign)?

if your only objection is that you don't see how it relates to the problem, hold that thought. i'll get to it in a moment.

[alpine sable]

Yes of course, a parabola is a reflection of its other branch across a line going through its vertex

[vale wigeon]

okay great

well now here

the black parabola is a reflection of the red about the y-axis

[alpine sable]

Yes

[vale wigeon]

yeah so there you have it

[alpine sable]

[vale wigeon]

the slopes of the tangent lines at all four horizontal intercepts visible in the picture are the same (in magnitude)

[alpine sable]

Why would it be a reflection of the other parabola about the y-axis axis?

[vale wigeon]

.........

you should have asked this when i said it

but ok

$y_2(t) = y_1(-t)$

[ocean seal]

Ann

[vale wigeon]

if we ignore the restriction of t ≥ 0 for a moment

[alpine sable]

Makes sense, thanks

[spring harbor]

Does this mean that both balls have same speed when they hit the ground?

[vale wigeon]

that's the conclusion i've been leading up to.

[spring harbor]

But I thought the one you threw up would have higher speed since the potential energy would be larger than the potential energy of the other ball

mgh=mv^2 /2

[vale wigeon]

nah

they start out with the same total energy

kinetic plus potential

[spring harbor]

Oh I see

Hmm yeah then I can see them having same speed

thanks

[alpine sable]

But what about reasoning it like this: The ball thrown directly up has more time to accelerate while coming downwards, since it'll be higher up?

[spring harbor]

yeah but the ball that's thrown down starts with a speed and keeps accelerating, while the other one decreases in speed and once v=0 it starts accelerating

or something at least from what I just understood

[vale wigeon]

but it also starts with velocity going the wrong way

it has more time to accelerate, but that time will be spent getting its velocity to zero and then pointing downward

[alpine sable]

Thanks

That doesn't bother me now

[vale wigeon]

in fact, once the upward ball falls back to the same height it was thrown from, it behaves identically to the downward ball, only delayed in time

[spring harbor]

actually we can try this out, let's say we're at h=5 and the start v0 = 5m/s and both balls have m=2kg
We get for ball that's going down: 5.10.2 + 2.5^2/2 = 2.v^2 /2
<=> v ~ 11.18 m/s

For the second ball: mgh=mv^2 /2 + mgh
2.10.h = 2. 5^2 /2 + 2.10.5 or h = 6.25
so we get mgh = mv^2 /2 or 2.10.6,25 = 2.v^2/2 or 11.18m/s as well

damn that's sick

Physics

[fathom jungle]

The rules said not to allow 12 or younger than 12

I'm turning 13 in 6 days so... am I allowed?

[vale sapphire]

unfortunately them's the rules

[fathom jungle]

ok Ill wait then

[alpine sable]

I feel like such a grandma when I read that people on here are like 12 or 13.

[storm stirrup]

Ive been looking over this one question, as self study but I'm not able to figure out how regions in the venn diagram are being wrote as values of x

[sleek elbow]

wtf dude

[storm stirrup]

???

[fading citrus]

thanks

[sleek elbow]

🤔

[limpid spade]

lol

[sleek elbow]

thanks dGhost

[fading citrus]

All good :)

[sleek elbow]

btw am I allowed to ping mods if stuff like this happens? @fading citrus

[fading citrus]

Of course

Either that or modmail is okay

[sleek elbow]

okay ty

[storm stirrup]

If someone could answer my question, I would appreciate it

[lament wyvern]

x is the number who take all 3 languages.
we know that 25 take F and G. This covers 2 possible regions; (F, G) and (F, G, S).

so (F, G) + (F, G, S) = 25.

(F, G, S) is x, so (F, G) + x = 25.
(F, G) = 25 - x.

[storm stirrup]

Ohhh, thanks

[teal epoch]

Hmm, it seems it's too late for me to explain this for someone has already explained it, oh well

[storm stirrup]

😆

Thx for trying anyways

[alpine sable]

A second ball is dropped down an elevator shaft 1 s after the first ball is dropped. (a) What happens to the distance be- tween the balls as time goes on?

For ball 1 the distance from ground is y'(0)t - gt^2/2

For ball 2 it is y'(0)(t + 1) - g(t + 1)^2/2

Subtracting, we get -y'(0) + gt - g/2

So as t -> infinity, the distance -> infinity, right?

[alpine sable]

If x is a

prime number, then LCM of x2,x4,and x6 is. Please explain it throughly

[thorn vortex]

$\text{You did an error in the equation}
\text{first ball has:}
y_1 = at^2 + y_0
\text{second ball has:}
y_2 = a(t-1)^2 + y_0
\text{so the distance between the two balls is:}
y1-y2 = at^2 - a(t-1)^2
= a(2t +1)
\text{so what you should say at the end is that the distance between the two balls is gradually increasing (as t is a positive variable) }
\text{also note that a = g}$

[ocean seal]

Pealover

[thorn vortex]

@alpine sable

Sorry for the bad output

[alpine sable]

Please answer this I have to complete my homework

[past thicket]

Is it x multiplied with 2 or x to the power 2

[alpine sable]

you could note for the next time to just write $'s inside math code, and leaving the text outside, saves some time, as well as if you want to create a different line to use double \.

[alpine sable]

X to the power 2

[past thicket]

So x square is common and multuply everything else

That is left

[alpine sable]

So the answer is x7

[past thicket]

X8

[alpine sable]

How?

I took LCM of them and the answer is x7

[past thicket]

U take x2 common so in first term there nothing left and in 2nd term x2 and 3rd x4 so when u multiply x2 x2 x4 = x8

Term them into fraction

[past thicket]

x6 /x2 = x4

x2 *x4 = x6

Powers add when multiplied

[alpine sable]

Ok my silly mistake

[glass lichen]

what are you stuck on?

[alpine sable]

Now I am getting this answer

[glass lichen]

stem is the start of the number

1st stem is 1

the leaves are just the ones digits

first line of the plot is 1 0

yeah, cause there's only 1 10..

[glass lichen]

since x is prime, you just need to consider the LCM of the powers themselves

[alpine sable]

Is answer x6?

[glass lichen]

you dont have any data that starts with 2, so clearly not

[glass lichen]

write it properly, x^6.. but no

LCM(2,4,6) isnt 6

[alpine sable]

What does part (a) mean? I don't understand the English.

[alpine sable]

If I consider x=2 that x^6 is the correct answer

[glass lichen]

actually yes it's x^6

[alpine sable]

But why does this logic fails

[glass lichen]

because you can make it smaller

the quick LCM is just multiply them all together

but you then check if it can be reduced via prime factorization

[alpine sable]

Ok

[glass lichen]

ex the LCM of (2,4,6) is 12 because 2=2, 4=2^2, 6=2*3, so the LCM has to be 2^2*3

[alpine sable]

Ok thanks for your help

[glass lichen]

well what are the stem of them?

yes

[dire pilot]

would i stll make the - and -8q postive here?

I still*

[glass lichen]

yes, -1*-1=1

[dire pilot]

even if it is in parenthesis

[glass lichen]

it's still -1*-1...

[dire pilot]

ok thanks m8

[glass lichen]

$-1\cdot -1\cdot 8q$

[ocean seal]

Mosh

[dire pilot]

so this right?

[glass lichen]

no

since when was -4+8=-4

[dire pilot]

oh

im dumb

thanks

[glass lichen]

looks like it

[dire pilot]

can someone help me with ths

this

nevermind

[alpine sable]

33k-15 is the answer

[glass lichen]

that's not helping

[alpine sable]

8k +25k - 15
33k -15

[dire pilot]

I already figured it out

thanks tho

[stiff moth]

how would i go about proving this trig identity

so far i have gotten til:

[warped phoenix]

Can someone help me on how to solve this?

[stiff moth]

= RS

[muted crown]

How do I find x here
X^5 +2x - 7 = 0

[shell widget]

Either completing the square, factorization, quadratic formula

@stiff moth sec^2(x) = 1 + tan^2 (x) and cosec^2 (x) = 1 + cot^2 (x)

Use these identities

[stiff moth]

im confused how would that work

[shell widget]

Start from LHS and write sec^2 (x) as 1 + tan^2 (x)

But for cot^2 (x), rearrange the identity cosec^2 (x) = 1 + cot^2 (x)

Plug in whatever u get for cot^2 (x) too

@warped phoenix What you basically have is $(81 x^6 y^7 )^{\frac{1}{3}}$ And recall that $(abc)^n = a^n b^n c^n$

[ocean seal]

Sup?

[alpine sable]

Hey

Are they equal?

[final viper]

what function satisfies f(x+y) = f(x) + f(y)

[alpine sable]

I am not talking about the results, ofc

just the syntax

[shell widget]

yes

[queen wigeon]

yes, but usually its written like it is on the right side. however, rational functions with one in the numerator are written as, for example, $\int \frac{dx}{x}$

[ocean seal]

mchen10

[alpine sable]

Aight! Thank you both!

[alpine sable]

A school offers three subjects: Mathematics, Art and Science. At least 80% of students study both Mathematics and Art. At least 80% of students study both Mathematics and Science. Prove that at least 80% of students who study both Art and Science, also study Mathematics.

Students can study any combination of Art, Math and Science. Draw a Venn diagram and you see that the set of students can be split into 8 different groups. Now we introduce the following variables: none is the number of students that do not attend a course. a is the number of students that only attend art, but no other course. am is the number of students that attend art and mathematics but not science. ams is the number of students that attend arts, mathematics and science. m, s, ms, as are defined in a similar way.
From the Venn diagram we see, the number of all students is none+a+m+s+am+as+ms+ams. The number of art and science students that is attending the math course is ams, the number of art and science student that is not studiing math is as. The number of students that study at least math and science is ms+ams, the number of students that is studing math and arts is am+ams. So your problem can be stated in the following way:
Given the nonengartive integer numbers none, a,m,s,am,as,ms,ams.
if
am+ams\<= (80/100)*(none+a+m+s+am+as+ms+ams)
and
ms+ams >= (80/100)*(none+a+m+s+am+as+ms+ams),
then
ams >= (80/100)*(as+ams).
ProofWe have
none+a+m+s\>=0
and so
am+ams >= (80/100)*(am+as+ms+ams)
and
ms+ams >= (80/100)*(am+as+ms+ams).
These inequalities can be transformed to
-4am+ ms+ams >= 4as
ma-4ms+ams >= 4as
If we add these two equations and divide them by 2 we get (1/2)*(am+ms)+ams >= 4as. But -(1/2)* (am+ms)>= 0 and so
ams>= 4as. Adding 4ams and dividing by 5 gives
ams >= (80/100)*(as+ams).

[warped phoenix]

Hey guys

what is domain and range?

I am learning to graph radical functions and its asking me what the domain and range is

how do i find it

from what i can tell its what x and y can be on a graph?

[velvet forum]

domain is x value

range is y

[warped phoenix]

so how do i find it

that could be any point on the graph

x and y

@velvet forum

[velvet forum]

for domain

visual a straight horizontal line across anypoint of the graph

if the horizontal line only touch the graph once then it's domain function

called horizontal line test

vertical line test for range

for example a parabola have 2 roots or points that a horizontal line would touch

therefore it's not a domain function

but is a range

basically any x value that doesn't repeat is a domain

and of course y is range

at least that's what i can remember after a year out of school

makes sense?

[warped phoenix]

kinda

what does it mean when they say the domain is all real numbers

@velvet forum

[night token]

who can help me with some statistics is something complicated

[glass lichen]

it means any real number can be plugged into the function

[warped phoenix]

@glass lichen how would i figure that out?

[glass lichen]

you'd look at the function

[warped phoenix]

that its all real numbers

oh

so if its a domain function

[warped phoenix]

then its all real numbers?

[glass lichen]

no

domain of a function will be a subset of the real numbers

[alpine sable]

@warped phoenix The domain of a function is the set of all x-values of a function, which gives the range. (Or, the set of y-values of a function from a given set of x-values.)

For example, let's take y = 2x + 3. This function has a domain and range all consisting of real numbers. When graphed, you can visually see this is true.

Let's take y = x^2 + 2x + 5. Just by looking at it, you can use any real number as an x-value. But, the output is not infinite. When graphed, you can see it has a minimum* value. of 4 when x = -1. Thus, the domain is (-∞, ∞), but the range is [4, ∞).

There are some functions that have restrictions with their domain. For example, y = sqrt(x). We know that the square root of a negative number creates imaginary or complex numbers, so anything x-value below 0 will give an imaginary output. Thus, the domain is [0, ∞). The range is also affected by this, and thus, the range is also [0, ∞). You can see this visually by graphing it.

So, in short, the domain is the set of x-values of a function/relation, and the range is the set of y-values of a function/relation.

[warped phoenix]

Wdym by "the output is not infinite"?

[glass lichen]

the range isnt R

[warped phoenix]

so y is not guaranteed to a real number? @glass lichen

[ionic jewel]

i didn't read the question but I imagine he means the y is a real number, but not every real number is a possibility

read: a subset of reals

[glass lichen]

It is since functions map from R to R, it just means that maybe some real values wont be reached (the function isnt surjective is the proper phrasing)

[warped phoenix]

im...still confused

[glass lichen]

ok, are you gonna ask a meaningful question or just state you're confused?

[warped phoenix]

wow

[neat mesa]

Hi, I am just starting geometry and I’m struggling to understand it and didn’t do so well on my last test. Any tips for understanding it and studying effectively???

[sleek elbow]

main thing is probably practice

[neat mesa]

may I ask what kind of practice? Such as online worksheets or using the textbooks? But ty for your help!!

[sleek elbow]

first comes understanding tho

[sleek elbow]

I imagine worksheets probably

[neat mesa]

Alright thank you so much!

[sleek elbow]

also if you have trouble understanding stuff, feel free to ask here @neat mesa

[arctic wren]

So, how i can manipulate this limit to get the answer and dont fall on 0/0 ?

[hazy dome]

You have to rationalize

Actually

Use L’Hôpital’s

Yea that’s easier

[arctic wren]

@hazy dome i don't know L'Hopital's

[hazy dome]

Do you know what a derivative is?

[arctic wren]

It's before the book demonstrates L'Hopital's

[arctic wren]

Yes

[hazy dome]

Basically take the derivative of the top and bottom and reevaluate the limit

[arctic wren]

But i just saw y'=( f(h+x) - f(x) )/ h

[velvet forum]

@warped phoenix

[arctic wren]

This is because i can found the derivate throughout the limits and vice versa?

[neat mesa]

In this chat right? Also again thank u for your help!!

[hazy dome]

No. Basically L’Hôpital’s rule states that should a fractional limit yield an indeterminate form via direct substitution, that the limit of the derivative of the numerator divided by the derivative of the limit of the denominator will yield the same result

[arctic wren]

Ok

Thankss

[glass lichen]

or.. just dont resort to L'H

[hazy dome]

Don’t mind the sec stuff on the top. Just look at the limit stuff as a point of reference

[hazy dome]

How else would you go about it?

[glass lichen]

rationalize

[hazy dome]

How? It seems very difficult and cumbersome to do

[glass lichen]

like any other rationalization.. just need to know difference of cubes and squares

[hazy dome]

But it’s the difference of cube roots and square roots

[glass lichen]

$\frac{\sqrt[3]{x}-1}{\sqrt{x}-1}\cdot\frac{\sqrt{x}+1}{\sqrt{x}+1}\cdot\frac{\sqrt[3]{x^2}+\sqrt[3]{x}+1}{\sqrt[3]{x^2}+\sqrt[3]{x}+1}=\frac{\sqrt{x}+1}{\sqrt[3]{x^2}+\sqrt[3]{x}+1}$

[hazy dome]

Oh wow

[sleek elbow]

yup

[ocean seal]

Mosh

[arctic wren]

The second one is the difference of cubes?

[hazy dome]

The numerator is

At least it can be manipulated to be one

[glass lichen]

yeah the fraction w/ 3 terms is the congujate for difference of cubes

$(a-b)(a^2+ab+b^2)=a^3-b^3 \ a=\sqrt[3]{x} \ b=1$

[arctic wren]

I cant remeber that

[hazy dome]

Thanks for reteaching me that

[ocean seal]

Mosh

[arctic wren]

[hazy dome]

I prefer L’Hôpital’s in this case tho because it’s easier

[glass lichen]

eh

if you dont know L'H you cant use it, plus this is more elegant imo

[arctic wren]

Yes

Thanks

[still jasper]

why is sin of 2x 's period 2pi divided by 2 instead of 2pi multiplied by 2? Graphically it's obvious but wanted to know if there was a formula or something to reach this result

[arctic wren]

Period= 2π/k , i think

Sin(kx)

[still jasper]

oh I see

I was doing the rule of 3

but they were Inversely proportional

[alpine sable]

|15 - 51| - |150 - 510| - q = 100

$|15 - 51| - |150 - 510| - q = 100

[gilded nova]

hello

I have to clear the variable x from the function

so that i'm left with something like x=...y...

[tawny condor]

what do u mean

isolate x?

thats..

uh

what

[dull onyx]

r u trying to find the solutions or something

[gilded nova]

So for example if I have something like y=x+2

I need x=y-2

[tawny condor]

ohno he wants to isolate x

[dull onyx]

?!

oh

[tawny condor]

FROM THIS

[gilded nova]

sorry english isn't my main language

[tawny condor]

LEMME GRAB MY CUBIC FORMULA REAL QUICK

@gilded novar u trying to find the inverse maybe

[gilded nova]

not the inverse

[tawny condor]

welp

-x^3 + 3x^2 + x - (y + 3) = 0

[gilded nova]

I'm trying to solve a solid of revolution exercise

I'm given that function

And it rotates around x=0

[tawny condor]

wth

[gilded nova]

in the (0,1) interval

[dull onyx]

i have no clue what ur trynna do

sorry!

[gilded nova]

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

[tawny condor]

here u go

replace a with y

and u got ur x

[gilded nova]

omfg

I guess i'm skipping it

[alpine sable]

Hey guys, having a bit of trouble with this problem:

Find the equation of the tanget line to y = x^3 - 3x at x = 2.
Watching a video on it and I don't understand this one step.

Wouldn't it be (2 + h)^3 - 3(2 + h)? where did they get the end part from?

[tawny condor]

why are you using limits?

Are you allowed to differentiate normally?

if not,

then

the (2 + h)^3 - 3(2 + h) is like x^3 - 3x but u put in 2+h instead of x

thats f(2+h)

then they subtract f(2), which is 2^3 - 3 * 2

[alpine sable]

oh so its for the entire thing! got it, thanks

[alpine sable]

just following a tutorial currently

@alpine sable by definition, $f'(x_0) = lim_{h \to 0} \frac{f(x_0+h )-f(x_0)}{h}$

[ocean seal]

magnos

[alpine sable]

thanks guys, much appreciated

thats where the 2nd part comes from

[tawny condor]

np

[alpine sable]

[harsh acorn]

Simplify the expression, leaving your answer in its factorised form. 2(2x – y)² – 6x(2x – y)

can someone tell me how I can work this out?

[arctic wren]

Whats is the derivative of this function? The answer on my book is (e^x)(3x²+x-5) but my result is (e^x)(3x²+11x+5)

[glass lichen]

$f'(x)=e^x(6x+5)+(3x^2+5x)e^x$

[ocean seal]

Mosh

[glass lichen]

your answer is correct.

[arctic wren]

Thanks

[keen surge]

how do i solve this?
105 = 25m + 9c + 16s

[sleek elbow]

what do you want to solve for?

[keen surge]

ok, so in order to solve for all 3, i need to solve 3 times?

[sleek elbow]

Im not sure you can

[keen surge]

?

[sleek elbow]

like

wait

are m and s units

or variables

[keen surge]

just variables

could be x,y,z or a,b,c doesnt matter

[sleek elbow]

I dont think you can solve an equation with 3 variables 🤔

not sure tho

[keen surge]

mm, lemme give a word problem, this was my attempt in coming up with an equation to solve

[sleek elbow]

we have a case of https://xyproblem.info

[keen surge]

was hoping it would help, but if not nw ill bounce

[sleek elbow]

add the original qquestion, might help

[noble sinew]

What? 3380000 is what? And where does 105000000 come from? (It isn’t 3380000 * 5 * 6)

And right below you say they make another amount

[keen surge]

yes, thats where the 105 comes from

[noble sinew]

They aren’t equal

,calc 338000065

[ocean seal]

Result:

1.014e+8

[noble sinew]

Notice that isn’t your number

[keen surge]

wdym

[noble sinew]

.

[noble sinew]

And why do you say a new amount just below?

[keen surge]

platinum is being converted into the other number

[noble sinew]

Instead post original question wording instead of this

[noble sinew]

What?

[keen surge]

lets call the other number N

25N = 80 platinum

[noble sinew]

.

[keen surge]

ah nw, i think since i wrote out the word problem myself i can probably solve now

thanks for the help!

idk how to close the channel if thats a thing here

[noble sinew]

The other thing still applies

[keen surge]

?

[noble sinew]

,w 338000065

[ocean seal]

Results provided by WolframAlpha

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

Requested by ScapeProf#9427

[noble sinew]

Notice that isn’t 105,000,000

[keen surge]

o right, 😕 mb

this isnt in a book or anything, its a real world problem

but ye, ill just calc for the hour

instead of trying to calc for the whole thing at once

thanks 😄

mm, i lie, my math isnt good enough

18,200,000 = 25m + 9c = 16s

finding the lcd and solving for m [3600 is the lcd for 25, 9 and 16, and multiplying by 144 got me the next line], m, c and s being arbitrary

2,620,800,000 = 3600m + 153c + 2304s

[past minnow]

Piper Nakamura Mawji

[glass lichen]

if you're not going to ask a question, dont type in the help channels. #❓how-to-get-help

[past minnow]

Did you get the job

[glass lichen]

again, only use the help channels if you have a math/math-related question

[past minnow]

Did you?

[glass lichen]

#❓how-to-get-help , this is a help channel.

If you are not going to follow the rules of the server, then stop typing.

[past minnow]

My guy did you or did you not

Who’s dick are you trying to suck

[glass lichen]

Again, this is a help channel either use it properly or leave

[quaint trout]

<@&268886789983436800>

Only has 5 messages, obvious troll is obvious

[glass lichen]

Yeah

[past minnow]

NOOOOO PLEASE DONT BAN ME!

😡

[glass lichen]

And can confirm they should be banned in ModMail / dms

[past minnow]

OH GOD NO

I AM GOING TO BE BANNED FROM THE MATHEMATICS DISCORD SERVER?!

WHAT WILL I DO

MY WORLD IS ENDING

[quaint trout]

Hopefully look at yourself and the mirror and reflect on what your life is

[past minnow]

MY LIFE IS NOTHING WITHOUT THE MATHEMATICS DISCORD SERVER

PLEASE DONT BAN ME!

I WANT TO ROLEPLAY ON MINECRAFT WITH MOSH

[candid torrent]

hi

why'd you guys ban them

they seems like a cool guy

👍

[glass lichen]

Not of your concern.

[candid torrent]

...

it was sarcasm I know why they got banned and I don't really care

[glass lichen]

k

[rocky cape]

Can someone help me with a ii) ?

[mossy lion]

we cant do it for you

do you mean you need help doing it or are you just looking for a calculator

[candid torrent]

yeah...

it's so strange

fanks

ok you

[mossy lion]

lmfao wtf. just read the conversation

[candid torrent]

don't need to criticize them that much

it's just weird that's all

[warped phoenix]

Can someone help me out with derivatives

wtf

[candid torrent]

sure

send

[mossy lion]

alright is this a hw question?

[warped phoenix]

We can move to a different channel

[mossy lion]

alright do you have your notes on polynomial long division? the textbook can help too

[candid torrent]

sure whcih one

[warped phoenix]

1 is free i think

[mossy lion]

thats very courteous of you. thanks

[warped phoenix]

ofc! ❤️

[glass lichen]

<@&268886789983436800> same person as Gombo

[tall wing]

how do we know this is gombo again?

i mean i guess

"don't ban me again"

is obvious

but

[glass lichen]

they're saying the exact same stuff

[tall wing]

oh

alright mosh

banned

[violet hemlock]

Ty

[random talon]

How would you prove the following limit? $lim_{m,n\rightarrow\infty}\frac{(-1)^n}{(-2)^m}=0$

[ocean seal]

econguy

[glacial hedge]

set x = m= n;

because they both approach infinity

or wait

u mean like formal proof?

[random talon]

Formal proof. Epsilon style proof

[glacial hedge]

😦

[glass lichen]

F

[glacial hedge]

uno seconda

[glass lichen]

that's an F

[glacial hedge]

yo thats lame who would make u do that

for

epsilon > 0 and delta >0

$ 0 < \sqrt {(x-a)^2+(y-b)^2} < delta$

uh

$0 < \sqrt {(x-a)^2+(y-b)^2} < delta$

[ocean seal]

Elonmosqito96

[glass lichen]

\delta

[slow monolith]

have a question

can yall help?

i need a run diwn on how to solve this and simplify

[mossy lion]

?

[glacial hedge]

then:
$|(-1)^n/(-2)^m-0|<\epsilon$

[ocean seal]

Elonmosqito96

[slow monolith]

run down

[sterile escarp]

Please help me

[glacial hedge]

dafuq people stop spamming

[slow monolith]

pls i just need help man

[mossy lion]

jesus this is a mess

#❓how-to-get-help

2. Before asking a question, make sure that the channel you are using is not currently in use. An occupied channel would generally have an ongoing discussion or a trailing unanswered question. Likewise, when you are done using a channel, make this clear so that it's open for others to use.

afaik @zinc oar was here first but idk if they actually want to go through their problem or not

[solar tapir]

Is this channel available?

[slow monolith]

can somone help me in channel one

[mossy lion]

no. there are like 3 people trying to ask questions at the same time lmao

[glacial hedge]

sorta being used rn

[solar tapir]

Sorry, will go to another

[random talon]

Okay, so why this then?

[glacial hedge]

yikes man

im not very fluent with epsioln delta proofs in multi var case

😩

[random talon]

Haha neither am I. It’s kinda crazy. Otherwise any other kind of approach, I guess I can work with that

I used Matlab to kinda check if this was true, but that’s it

[glacial hedge]

were u not paying attention.....

this channel is sorta being used...

he asked way before u

[glacial hedge]

yeah man... u cant really use the like formal way because u cant plug in a and b in $ 0 < \sqrt {(x-a)^2 +(y-b)^2} < \delta$ because they are inf

$0 < \sqrt {(x-a)^2 +(y-b)^2} < \delta$

[ocean seal]

Elonmosqito96

[mossy lion]

yeah that looks great

[glacial hedge]

no thats wrong

it doesnt satisfy remainder theorem

[mossy lion]

actually it looks like aral was first

[random talon]

Thanks man, at least I don't feel dumb for not knowing how to do it @glacial hedge . Good to hear a second opinion

[glacial hedge]

oh wait nvm

hehe

[mossy lion]

ye that was the result

[glacial hedge]

my bad

xD

[mossy lion]

youre good

[glacial hedge]

i thought that was what he was dividing

[jagged pendant]

what should i use for latex code inside of html for ease?

[glacial hedge]

um

[jagged pendant]

is there not a good browser extension or something?

[glacial hedge]

probably mathjax

[jagged pendant]

seems a lot of junk software out there

[glacial hedge]

mathjax is pretty well trusted and pretty good too

[jagged pendant]

i forgot i had that already lol

[glacial hedge]

not sure what that means but ok xD

[strong citrus]

Twenty bored students take turns walking down a hall that con-
tains a row of closed lockers, numbered 1 to 20. The first student opens all the
lockers; the second student closes all the lockers numbered 2, 4, 6, 8, 10, 12, 14,
16, 18, 20; the third student operates on the lockers numbered 3, 6, 9, 12, 15, 18:
if a locker was closed, he opens it, and if a locker was open, he closes it; and so
on. For the ith student, he works on the lockers numbered by multiples of i: if a
locker was closed, he opens it, and if a locker was open, he closes it. What is the
number of the lockers that remain open after all the students finish their walks?

[glacial hedge]

draw a picture

[slow monolith]

(x*x^(-2)y^((5)/(3)))^(2)

need help with this

[alpine sable]

why is it as h approaches 0 again?

[glass lichen]

h is the distance b/w the 2 points you base the secant off

[glass lichen]

so to get the tangent you make the points get closer and closer

[alpine sable]

right right, its the run in rise/run i believe? so as it approaches 0.. it means, yeah, they get closer and closer (the points)

[glass lichen]

yes, h is the run

[alpine sable]

the slope of the tangent right?

[glass lichen]

yes

[glacial hedge]

WaIt

I just had a flash of brilliance

the abs in the proof

removes the -'s

so

(-1)^n

doesn't affect the thing

so its really

1/2^m

which can be proven using single var stuff

[random talon]

Well, but holding m=1 and allowing n to vary we would have something (1/2 -1/2 1/2 -1/2...) so it diverges

But my apologies, what I want to prove is $\lim_{m,n\to\infty}\frac{(-2)^n}{(-3)^m}=0$

[ocean seal]

econguy

[alpine sable]

@glass lichen what does it mean when youre given a function and not 2 points? youre still trying to find the slope of the tangent line (the tangent line in this case is f(x) = 1/x right?), just without the 2 points?

[glass lichen]

You have 2 points

(x,f(x)) and (x+h,f(x+h))

those are always the 2 points, which you can get by reading first principles

[alpine sable]

oh, it all clicked now. thanks

[full wasp]

are all countably infinite sets numerically equivalent??

[mossy lion]

i think the idea is that you can find a 1:1 correspondence but someone can correct me

[tired hamlet]

How would I start this one?

[marble comet]

P = principal amount

(20,000)

e I believe refers to Euler's natural number

r = rate which we have to find

A = 43,957.90

t = 15 years

[tired hamlet]

I got 43957.90=20000(2.718)^r(15) I’d that right

*is

[marble comet]

yeah

are u allowed to use a calculator?

[tired hamlet]

Yeah

[marble comet]

aight then rearrange the equation in terms of r

[tired hamlet]

How would I do that?

[marble comet]

here lemme try doing it

@tired hamlet have u done logarithms yet?

[tired hamlet]

Yeah

[marble comet]

great

so once u divide A/P

u get around 2.198 = e^(15r)

now take the log base e of each side

on the right side, according to the inverse property of logarithms u get 15r

and on the left side u get log base e of 2.198

so log _ e (2.198) = 15r

on a calculator, u input (log 2.198)/(log e)

u get .787547 so on

divide that by 15

and u get .0525 around

so 5.25 percent is the answer

[tired hamlet]

Thx so much

[marble comet]

np

: )

on a calc it's ez, but without it it's hard

[acoustic bay]

Can someone who knows R help me find the correlation values for my data set?

I have over 90 columns, I want to test the correlation between all of these variables against one other variable which is already contained in the 90.

This is what I have so far

for(col in 1:ncol(longitudinalbl)){
myCortest = cor.test((longitudinalbl)[col], IDE.BL$SSI_worst, na.action=TRUE, method = "sp")
myCortest$estimate
}

[ocean seal]

kevinFDG

[alpine sable]

Can someone give me a good math problem? (Of any topic)

[acoustic bay]

Can you try the problem I just posted above

<@&286206848099549185>

[sullen karma]

?

What msg

[acoustic bay]

the one above, i was asking about how I can find the correlation values in R for my dataset. i posted the code I have so far above

[rich basin]

I was wondering why is my answer not correct

$\frac{2}{2^{8}-2}$

[ocean seal]

Travelling Salesman

[acoustic bay]

@rich basin you have to ask in a channel where someone hasnt asked a question, I just posted above.

[rich basin]

This is what I have right now

sorrry

[acoustic bay]

Your good, I dont think anyones gonna answer mine anyway so you can have it actually.

[rich basin]

Thanks

[tough hedge]

where can i post my question?

[rich basin]

You can post on question 1

[tough hedge]

okay thanks!

[rich basin]

<@&286206848099549185>

[indigo storm]

What's the answer?

[hasty narwhal]

yup. take the lcm and add, and use a^2-b^2=(a+b)(a-b)

[rich basin]

Sorry, but I already post a question

Too much noise covering up my original question

[hasty narwhal]

I'm sorry. I didn't realise

[rich basin]

Please delete

,w solve (8 choose 4) / (2^8-2)

[ocean seal]

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[rich basin]

,w solve 81/127

[ocean seal]

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[rich basin]

,w solve (8 choose 4) / ((2^8)/2-2)

[ocean seal]

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[coral pagoda]

Why the -2?

[rich basin]

,w solve ((10 permutate 6) + (10 permutate 5) + (10 permutate4) + (10 permutate 3) + (10 permutate 2) + (10 permutate 1))/ (15 permutate 6)

[rich basin]

@coral pagoda So this is all the combination minus the combination when one person hold all of it

[ocean seal]

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