help-0

[marsh rapids]

Since visibly we're listing out a bunch of ways to get the answer

[rigid smelt]

yeah, that works too, lots of way here, since we can be quite flexible here with all the trig identites available

[spring spruce]

im kinda interested by this one. end up getting [sinx*2sqrt(1+cosx)] / U. Im asuming that you can write it as [sin(x) * 2U] / U ?

[distant horizon]

write sinx as 2sin(x/2)cos(x/2)

and 1+cos(x) as 2cos^2(x/2)
simplify and put u=sin(x/2)

[marsh rapids]

That's what I said

But he's interested in the first method

[distant horizon]

whats his first method

putting u = 1+cosx?

[rigid smelt]

eh no, the idea was that the derivative of sqrt(1+cosx) is -sin(x)/(2sqrt(1+cosx)), so this takes care of the sinx on the numerator and the denominator as well

cancelling to only sinx

[marsh rapids]

Which is why it works so well

[rigid smelt]

to which you can rewrite that in terms of cosx and then just sub u in

[marsh rapids]

What did you find not so straightforward with it btw ?

[rigid smelt]

the rewriting sinx to sub u in might not be very straight-foward to those who have not done a lot of substitutions

[distant horizon]

yeah but its the best way

[rigid smelt]

as in, people who just starts out do not see it coming

[distant horizon]

lots of times you need to use half angle formulae in integration

[spring spruce]

Honestly the algebra for it is messing me up. Im trying to manipulate the half angle identities to get 2sin(x/2)cos(x/2) and just not getting it

[rigid smelt]

eh that's not half angle identity

that's double angle

[spring spruce]

well then

[marsh rapids]

sin(x) = sin(2(x/2))

Expand that

[spring spruce]

okay I see now. You can express sin(x) as sin(2(x/2))

[distant horizon]

see we know 2sinxcosx = sin2x

if we sub in 2x = u
u = x/2

or the thing above

@spring spruce did you get it

the integration

[spring spruce]

yeah i got 1/3sqrt(2)

[distant horizon]

cool

[spring spruce]

any tips to recongnize this stuff. Because for me at least. Its been awhile since I've had to use some of these trig identities. and expressing x as (x/2 +x/2) or (2(x/2) and then expanding isnt really intuitive. It might also be the fact I havent slept

[distant horizon]

get some sleep

identification comes with practice

no tips really

you need to see what you can transform it into

[spring spruce]

I think Ill do that after I finish this assignment. Apparently 11 assignments a week plus a lab and a fucking graded review for a exam(idk) is considered reasonable

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[tropic junco]

factor of 956

[grave island]

any idea where to start

[tall topaz]

Start from what number definitely divides 956

[ornate condor]

for one

stuff that end with 0,2,4,6,8 are div by 2

[tropic junco]

HUH

[pine helm]

239 * 2^2

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[candid comet]

let S(n) = n+r for every rational number n
forall n in R. P(n) -> P(S(n))
forall n' in (0, r]. P(n')
Therefore, for all n in R+, P(n).
does this actually mean P holds for all of R+?

[marsh rapids]

By euclidian division yes

Except for 0, which I suppose you don't include in R+ here

Wait no

You said S(n) is defined for rational n

So it doesn't work for irrationals

[pallid scarab]

Oh right

[marsh rapids]

But actually it still does

[candid comet]

it still does what

[pallid scarab]

Actually it's worse

[keen plinth]

what even is r

[ornate condor]

[keen plinth]

seems like P holds for all positive reals

[marsh rapids]

Yes

[candid comet]

i think r is supposed to be <= the upper bound of the range on base cases

[keen plinth]

this is like scuffed induction

[marsh rapids]

You've got (0, r] + rN, which is thus (0, +inf)

[marsh rapids]

No because it's just euclidian division

As I said earlier

[ornate condor]

mean

[keen plinth]

i mean

thats just induction

but on every real number

[ornate condor]

wait can u even do that

[keen plinth]

seems like P holds for all reals im reading it wrong

not just the positive ones

[candid comet]

apparently, but you need to show that P holds for an interval, not just under a well order

does this have a name though?

[lone heart]

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[autumn reef]

i really dont know how to start on this question

[autumn reef]

this one as well

[alpine sable]

Physics but ok

[autumn reef]

no math

well its part of math

mechanics

[alpine sable]

Ok

Well

[autumn reef]

here only for calculus?

[alpine sable]

make fbd

[autumn reef]

whats fbd?

nvm ig

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[modern lark]

hello everyone, how did this happen? what type of rule/formula is this

[rough crown]

its algebra. eg
15=3x
15/3=x

x and y are just numbers

[modern lark]

oh damn i completely forgot ab this

so embarrassing lol

thank you!

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[low current]

hello can u help me soolve this one please

[low current]

lim as x approaches 0 ( (x+tanx)/sinx)

[viral lodge]

note
$\frac{x+tan\left(x\right)}{sin\left(x\right)}=\frac{x}{sin\left(x\right)}+\frac{tan\left(x\right)}{sin\left(x\right)}$

[ocean seal]

Dav1d

[alpine sable]

do you know the limit of x/sin(x)?

[low current]

1?

but for the tanx/sinx?

that is what i find difficult

[viral lodge]

tan = sin/cos

[low current]

yes

so( sin/cos)/sin

[viral lodge]

yes

[low current]

after this one?

will it be 1/cosx?

[viral lodge]

yep

[alpine sable]

and whats cos(0)?

[low current]

1?

[viral lodge]

yep, so 1/cos(x) --> 1/1 as x-->0

[low current]

and sinx/sinx = 1

so its 2?

[viral lodge]

yes

[viral lodge]

sin(x)/x, right?

[low current]

owww \

yeayea

[alpine sable]

,w limit (x+tan(x))/sin(x), x->0

[ocean seal]

Results provided by WolframAlpha

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

Requested by rbit ✨#4860

[low current]

so 2 is the final answer?

AAAAAAAAAAA AMEN

[viral lodge]

yep

did you have this problem on a test or something?

[low current]

YESSS AND THE PAPERS AND NOW BACK

and this number i got wrong answer

[viral lodge]

you didnt get 2?

[low current]

yes

i was wrong at something i multiplied the numbers

not add huhu

anyways thank youu david!!

[viral lodge]

You're welcome

[lone heart]

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[vale pulsar]

Hi
How should I do this?
(1 - cos(a) + cos^2(a)) (1 + cos(a) + cos^2(a)) (sin(a))

[leaden field]

A team leader has 16 tickets with upcoming deadlines. He has nine developers at his disposal. In how many ways can the team leader assign tickets to developers if each developer must get at least one ticket to avoid being out of work? There is no need to discriminate between tickets, only the number of tickets is important.

Hint: First, determine the number of tickets after a team leader distributes one ticket to each developer. Then, apply the formula of combinations with repetition. Use bars to distinguish between developers and stars to denote the remaining number of tickets.

[alpine sable]

this channel is occupied

[leaden field]

how can I find available channel? I read that I shall post in help-0 channel and the only one I found was this.

[limpid spade]

at math help available

[alpine sable]

@leaden field help - 12 is open you can send you question there..

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[vale pulsar]

.close

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[nocturne trout]

the difference in one subtraction is 440 what will be the difference if the decreasing 30 is increased and the output is decreased by 20?
My homework

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[crimson blade]

how would i find lim{x->3} of

[crimson blade]

i know i need to use the squeeze theorem but im not sure how

[abstract fractal]

What's the limit of the left function

[crimson blade]

which one?

oh, i’m not given a limit for that

[abstract fractal]

It's a polynomial

You can find the limit

[crimson blade]

would you just use direct substitution to find that

[tall topaz]

Yes

[crimson blade]

with that i get 2 <= f(x) <= 32

what would i do next?

[tall topaz]

Are you sure it’s 32?

2*9 -33+17

[crimson blade]

is it not -33

as -11*3 is -33

like as in 2*9 - 33 + 17

[abstract fractal]

18 - 33 + 17 is not 32

[crimson blade]

yeah i know i made a mistake i just wanted to clarify if it was -33

[abstract fractal]

Yes

[tall topaz]

Yeah sorry

[crimson blade]

oh right so both sides are 2

so the limit is just 2

[abstract fractal]

Yes

[crimson blade]

cool i think i got it, thanks for the help

.close

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[silk terrace]

since plog(1/(p+n)=-plog(n+p)?

[abstract fractal]

You mean on the ρlog(ρ + μ)?

[tall topaz]

log(1/n) = -log(n)

[silk terrace]

or okay i thought it would be double minus since we are swapping the terms

and thus a plus sign but of course not; as we are taking the sum in the first equation its the same thing

then doing the inverse in the log swaps the sign

[tall topaz]

Yes

[lone heart]

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[dense lily]

what are two numbers that can become the product of 24 and the sum of 14

[storm crystal]

just make 2 equations xy=24 and x+y=14, then substitute y in terms of x in the other equation

like x+(24/x)=14

or x(14-x)=24

[dense lily]

.close

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[nocturne trout]

.reopen

[dense lily]

.close

[peak quiver]

The volume of a certain solution was
reduced by 30% and then diluted by
adding 100ml of water. If the volume
of final solution is 50% more than the
original volume, then, what was the
initial volume of the solution (in ml)?

[peak quiver]

help me with it

got one equation that is initial value 1.375x cause i didn't supposed 100% be actual value

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[lone heart]

Please don't occupy multiple help channels.

[viscid mesa]

how to find a?

[lone heart]

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[viscid mesa]

@lone heart

[neon scarab]

Extend d1 to meet line AB, then find some angles by the parallel lines and proceed 🙂

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[last onyx]

me

[tall topaz]

[last onyx]

so the question is to prove through mathematical induction that Un >= 1/3

And I did this

is this correct?

better pic

[tall topaz]

Yeah seems correct

Maybe explicitly say that u_n+1 >= 1/3

[last onyx]

4/7 isnt greater than 3/4 is it?

it would only make sense if it was

oh i know hold on

this should be it right?

[tall topaz]

Yes this is nice

[last onyx]

Ok thanks

[tall topaz]

[last onyx]

I sleep now

finally

[tall topaz]

Alright good night

[last onyx]

close

.close

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[slender raven]

@mental coyote plz help

[shell urchin]

Omg

[lone heart]

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[shell urchin]

.close

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[alpine sable]

How many subsets of {1,2,3,4,5,6}are of size three which have 1 but not 2?

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[shell urchin]

No idea how to solve

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@shell urchin Has your question been resolved?

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[alpine sable]

what is KL+SK-SA

and why

<@&286206848099549185>

[languid bolt]

Btw don't ping helpers before 15 minutes

[alpine sable]

oh

k

[languid bolt]

where is kl + sk - sa btw

[alpine sable]

it is not said

[compact steppe]

Problem 5 on the first image

[alpine sable]

it's from 5.

[alpine sable]

ye

[alpine sable]

AS maybe

[compact steppe]

Well first try to find the sum of the first two vectors

[alpine sable]

normally i would say KK

and KK-SA= AK

but it is wrong

[compact steppe]

Would it not be SL?

When you put the two together, kl + sk

You can write it like sk + kl

K being the middle end of one and the beginning of the other

[alpine sable]

it's LS?

[compact steppe]

LS yes sorry

[alpine sable]

oh ye

[compact steppe]

I think so

Or waut

SL

Yeah

[alpine sable]

so AS

[compact steppe]

Now you can subtract SA from SL

No

Yeah

[alpine sable]

i meant u get as after subtracting

[compact steppe]

Oh

Yeah

Because it can be written as a sum

And then you should be able to get it from there

SL + AS

AS + SL

Which gives AL

[alpine sable]

AB+BC=AC

[compact steppe]

Yes

[alpine sable]

AB-BC=CB

[compact steppe]

Yes

Errr

[alpine sable]

anyways, time for this

[compact steppe]

Kk

[alpine sable]

shit

imma just close this

.close

[lone heart]

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[lone heart]

Please don't occupy multiple help channels.

[silent parcel]

I think I can do this....

you know pascals triangle?

[fathom forum]

I got 320 but the answer is 326

[fathom forum]

Hmmm. No

[silent parcel]

look it up

tldr, look at the row with the black circle in it

the first entry, there is only 1 way to get there (all along the side), but the second one there are 4 ways to get there (count them)... it follows the pattern found in pascals triangle that I happen to be very familiar with....

so, knowing this we can work out how many "ways" to get to the other circles from each one of those

lets call the row with the black circle row 1, and the row at the very bottom row 2 just to avoid confusion

you cant get to the first entry of row 2 from row 1 entry 2 because it cant reach

so there is only 1 way to get to row 2 entry 1

If we imagine in row 1 that there are mini pascal triangle starting from each entry, you should have some idea of what the value for each bottom row node is

[silent parcel]

So consider, row 1 entry 1 as having a value of 1 and row 1 entry 2 as having a value of 4...

Bottom row
Entry 1: 1 - since it can only be reached by row1 entry 1 once
Entry 2: 7 - since it can be reached from row 1 entry 1 in 3 ways, and via row 1 entry 2 in 1 way (but that must be multiplied by 4 so hense final answer is 7)
Entry 3: 15 (3 ways from entry 1, 3 ways from entry 2)
Entry 4: 17

then just double it cause it'll be same for other 4 last entries
(1+7+15+17) times 2

I make it 80

80*

oof

I only calculated according to the image and not to 10th row, ignore all that :I

[fathom forum]

Yeah no worries. They didn’t; show all I don’t know why :/

How does my answer look?

[silent parcel]

I did just think of another way around the problem though... give me a sec

[fathom forum]

Ok

[silent parcel]

so each row in pascals triangle (usually) adds up to 2^n right where n is the row number (and the first entry row number is 0)?

if they mean that the first entry on that sequence is the "first row" rather than the "zeronth" row like regular pascals triangle then we can simply add two rows to this and calculate:
1 times 2^5
+
4 times 2^5
+
4 times 2^5
+
1 times 2^5

10 times 32

=320

you sure 326? I think you got it right

[fathom forum]

Yeah it says it on the answer sheet

But I think it is wrong too

[silent parcel]

i agree with you, doesnt make sense

each row will add up to 2^n in pascals triangle where the first entry "row" n=0

in this scenario you have 4 pascals triangles with 6 rows total, so n will be 5
Since we know by pascals triangle or binomial theory ( nCk) that each of those traingles will start with a 1 or 4 as described above...

nope, the papers wrong lol. Prove it and complain to your teacher, make sure you tell them though else they might mark you as wrong

[fathom forum]

Yeah, actually there was another question wrong on another paper so…

[silent parcel]

funny story, im not amazing amazing but when I was a kid I made the newspapers for a math discovery to do with the freaking triangle

[fathom forum]

Haha that is a coincidence

[silent parcel]

hense why I recognised the problem lol

good luck

[fathom forum]

Do you know how to do question 24?

@silent parcel

[silent parcel]

my guess is X=59

or 0

[fathom forum]

Answer is 38 but I have no idea

[silent parcel]

technically the answer is infinity but you end up with a complex number

not sure how to do this one at the tope of my head

I'd probably try and play around with it,
Set y= expression and see what you can do

[fathom forum]

Ok thanks

[silent parcel]

also, 38 would lead to a complex number aswell cause of the argument of the second part of the equation

so if your gonna have a complex number, go for x equals infinity

but, since Im gonna guess they dont want that, just use X=59

[fathom forum]

I will ask the photo math and see what happens

Undefined

Lol

[silent parcel]

try X=361

sorry, misread the first time

I think, you need to make both halfs of the expression equal each other

X=420

sqrt(781-420) +sqrt(420-59)
= sqrt(361) + sqrt(361)
= 2 times sqrt(361)
= 2 times 19
= 38

[fathom forum]

Ok but how to know to make x = 420?

[silent parcel]

thats not what the quastion is

its just find the maximum value of the expression

the maximum value is 38 and it occurs when X=420

you know to make it 420 because you're making both parts of the expression equal

so you are left with sqrt(361) + sqrt(361)

[fathom forum]

Oh I see

I would not have known to do that

[silent parcel]

i got dinner now :v

good luck

[fathom forum]

Thanks

[lone heart]

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[earnest oriole]

im not sure how to do this question

[ornate condor]

well

u can expand a part of the rhs

[next pulsar]

Start with the fact that a sum of square numbers is more than or equal to 0

[ornate condor]

n ull get everything on the left

[next pulsar]

That will give you your initial inequality

[ornate condor]

then just have like 1 extra term n u good

[next pulsar]

If you play around a bit with that you’ll get the CS ineq

[earnest oriole]

would expanding be a good idea

for the rhs

[ornate condor]

oh nvm i think what i said is wrong i read it wrong oops

[earnest oriole]

oh all good

[rancid gulch]

¯_(ツ)_/¯

[lone heart]

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[acoustic mirage]

What's the misprint here ?

[ornate condor]

this looks like

geometric sum

[acoustic mirage]

Na its from limits

How are they both equal to the same result?

[ornate condor]

hm ye

actually its not quite like geometric

cuz its not 1+something

[silent parcel]

the first one looks like the second one when n=1

[acoustic mirage]

Yes but this book is just stating the results from the limits so...i beleive that j is a somewhat a typo

[silent parcel]

the first one is right

[acoustic mirage]

Yes but what about the second one ?

[silent parcel]

you shouldn't be dividing by n, you should be multiplying by a^(n-1)

see, i) and j) are equivalent

since we know that i) is correct, that must mean that j) is equivalent, so you can equate both sides (the answers on both sides) and see that they are not equal

[acoustic mirage]

This is just the theory part of the book 💀💀

[silent parcel]

also, when you multiply a^(m-n) by a^(n-1) you end up with a^(m-1)

to be fair, Im not 100% sure

I typed in the expression on wolfram which gave me the left hand side

Im not sure if theres some specific theory where that J) is the case, all I did was go by what I know works; perhaps there is something extra to the limit that makes that happen though

[acoustic mirage]

Ok thanks

.close

[lone heart]

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[echo socket]

Notice that the angle ACB is 90 degrees

[fathom forum]

Yes

Then I am not sure

[echo socket]

Hmm no idea as well

[fathom forum]

Ok

[bronze carbon]

<adc=(360-(75*2))/2

use that in triangle adc all angles added each other is 180 and you can find <dca

and <dca=180-33-105=42 deg

[fathom forum]

Why 75 *2?

[bronze carbon]

its because the agle is in the curcle

its not a central angle

and you have formulas for these types of angle

[ancient meteor]

Sum of opposite angles of a cyclic quadrilateral is 180°

[bronze carbon]

yes you can use this too

[fathom forum]

Got it

Thanks to both of you

[bronze carbon]

welcome

[ancient meteor]

Np

[fathom forum]

How about this?

[bronze carbon]

are you in class having test?

[fathom forum]

Haha no

Preparing

[bronze carbon]

hah nice

its 10^(1/10)

[fathom forum]

Ok

How to know?

[bronze carbon]

1sec

[fathom forum]

Ok thanks

[bronze carbon]

np

[lone heart]

@fathom forum Has your question been resolved?

[lone heart]

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[silent parcel]

use l'hopitals rule

[lone heart]

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[swift sky]

I need help

[north portal]

i need help someone

Whether such functions exist which are differentiable at infinite many points and non-differentiable
at infinite many points. If yes, give any two examples. If no, justify your response.

its a calculus question

[swift sky]

Sorry, this channel is already taken:)

[alpine sable]

@swift sky with

[alpine sable]

Ik which are discontinuous at infinite points

[north portal]

cant there be a function which has both

contineous at infinite and discontineous at infinite

[alpine sable]

It was dirichlet function

[swift sky]

So is this not my channel?

It's alright yall can continue here

I will just go somewhere else.

[north portal]

ill leave

dw

ill get a new one

im sorry

[swift sky]

No its fine

you're already getting help here

[alpine sable]

Nono ask

[swift sky]

30 people (including A, B, C) randomly put themselves in a queue. What is the probability that A always gets ahead of both B and C?

I have some ideas but I am not sure

[alpine sable]

Probability ahh I need to study it

Lemme think

[swift sky]

take your time, no worries

Okay let me explain how far Ive come so far

I divided the problem in different steps

[lone heart]

@swift sky Has your question been resolved?

[lone heart]

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[swift sky]

30 people (including A, B, C) randomly put themselves in a queue. What is the probability that A always gets ahead of both B and C?
I have some ideas but I am not sure

[swift sky]

So far I have tried solving the question this way

by diving it to different steps

I mean if A is in the first place then there is 29! way of placing the rest

If A is in the second place then there is 28! way of placing the rest and then 2! way placing A and the first person before everyone else

If A is in the third place then there is 27! ways of placing the rest and then 3! way placing A and the first 2 ppl

If A is in the forth place then there is 26! ways of placing the rest and then 4! way placing A and the first 3 ppl

And then I should do this until I get to 28, because that last case is the case where B and C are the last.

And then I should add these outcomes and divide it by 30!

I don't know if this is correct but even if it was, there has gotta be a shorter way to solve this question so I need yall help with that.

[prime badge]

there are 6 ways they can be placed relative to each other, it's just 2/6

[swift sky]

What do you mean?

[prime badge]

and like it's 1/3 because there are three of them, it has to be equal chances for each to be first

you asked for short

xd

[marsh rapids]

By symmetry, it can't be anything but 1/3: they are all equally likely to be first

[swift sky]

Yeah I want a short way of doing it but I don't understand what you meant here.

[prime badge]

by symmetry A is first = B is first = C is first

then, there's no way no one is first (or multiple people are)

which means X+X+X = 1, X = 1/3

[swift sky]

I don't know what "symmetry" means in this case, but what about the rest of the 27 people in the queue?

[prime badge]

the other people can't just increase one of ABC chances preferentially

whatever they do, it happens equally to all three

[swift sky]

sorry Im a bit slow so I still don't understand.

[swift sky]

Yeah they all have the same chance of being first but what is the chance that on of them for example A is always before them?

[marsh rapids]

Visualize the list of 30 people. Select A, B, C from them. Compare their order.
That doesn't require knowing anything about the other 27 people. It doesn't even matter A,B,C were. All that matters and what their order is when you extract them

Therefore it's as if there was only A, B and C

[prime badge]

it's 1/3 because they all have the same chance of being first

that's the reason, there's one way to divide one into 3 there are no ooptions here

[finite flax]

I like this question

[prime badge]

also you're adding always which makes it an absurd question, it doesn;t happen always, we're just supposed to say 0, it's not probabilistic

[marsh rapids]

Say you took part in a national contest with your friend. You did great and he thinks he did poorly. You estimate there's a 70% chance you did better than him.
This probability doesn't depend at all on whether you were the only 2 people competing, or if there were 100 or 10000.

[marsh rapids]

So you can just remove other people from the equation, they don't matter

Now say I pick 2 people who participated, at random. I call the first one A and the second one B.
What's the probability A is ranked higher than B ?
The answer is 1/2: there's no reason for my 1st random pick to be better/worse than my 2nd. Rigorously you can say that you were equally likely to have picked B first and A second. So there's no reason your first pick should be a stronger person

That last argument is what we mean when we say there's symmetry in this problem: the roles are interchangeable

This also applies with more people: you chose them at random, there's no reason the order in which you pick them makes a difference

[lone heart]

@swift sky Has your question been resolved?

[swift sky]

I understand what you guys mean now but I feel like the question is more about permutation than just probability too. If I calculate my earlies try, will i get 1/3?

[marsh rapids]

1/3 is the answer yes

[swift sky]

But I mean is my try correct, if you scroll up, you will how i started solving it, and i am wondering if that is right even if it is long

[marsh rapids]

It should work. Probability is, under a uniform distribution, by definition (when there's a finite number of cases), just the ratio of cases in which the property is verified over the number of cases in which it is not.

But here that would be incredibly difficult to compute, especially without a calculator

[swift sky]

I just did calculated it and got 0.0385156546

[marsh rapids]

That's wrong. It's (ways of choosing the people before A) * (permutations of people before A) * (permutations of people after A)

You forgot the 1st one

[marsh rapids]

Which must then be modified to account for the specific positioning of B and C

So it's actually (30-A)P2 * (28-A)C(A-1) * (A-1)! * (28-A)!
With A going from 1 to 30

That hopefully yields 1/3

,w sum for A = 1 to 30 of ((30-A)(29-A) * ((28-A) choose (A-1)) * (A-1)! * (28-A)!)

[ocean seal]

Results provided by WolframAlpha

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

Requested by themateo713#5303

[marsh rapids]

Pain

[swift sky]

Let me try it again, and get back to you

[lone heart]

@swift sky Has your question been resolved?

[lone heart]

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[alpine sable]

<@&286206848099549185>

[stable pecan]

You can only use the helpers tag after 15 minutes have passed

[alpine sable]

oh sry

[tacit arch]

Just l'hopital

[alpine sable]

not allowed

[tacit arch]

Then what is allowed

[alpine sable]

traditional way

[tacit arch]

Which is?

Limit laws?

Taylor series?

[alpine sable]

yes

[tacit arch]

What chapter is this problem from

[alpine sable]

limit and continuity

[tacit arch]

Probably some trig identity then

[alpine sable]

there is one

lim to 0 arctanx/x =1

.close

[lone heart]

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[alpine sable]

wut

45

[last ether]

What am I supposed to with that

[alpine sable]

lmao

u good

[last ether]

Aight then

[alpine sable]

now

[fair dome]

...

[alpine sable]

helpme

[last ether]

.close

[lone heart]

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[alpine sable]

with my limit

😭

@last etherhelp #help-4

[last ether]

Don't people to help you

[alpine sable]

bruh

[lone heart]

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[stiff horizon]

How to solve this please

[stiff horizon]

I need to prove it with calculations

[echo socket]

To prove what?

[stiff horizon]

I know that the equation f(x) = 0 has 1 solution

But i need to prove it

[echo socket]

You can use intermediate value theorem

[gray isle]

ivt to show at least one solution exists
derivative to show its mono so it only has that one

[stiff horizon]

Ok thank you

I am gonna try both ways

[gray isle]

its not both ways

its one way that involves two things

[stiff horizon]

Ok

I did nt learnt that yet

That s why i was confused about it ^^'

[gray isle]

what were the exact instructions

to show that it has a solution or exactly one real solution

[stiff horizon]

It is written in french

Pretty hard to translate tbh

[gray isle]

doesn't hurt to post and some people (not me) can understand french

[stiff horizon]

,rotate

[gray isle]

ahk, multiple choice

asking whether there are
no solutions, exactly one, or many

[stiff horizon]

Yes but I am also on the website of the book

So I went ahead to find the answer of it

And I find it was the b (the equation has 1 solution)

[gray isle]

yes

exactly 1 (real)

[stiff horizon]

But since i did nt learn the method i did nt knew how to do it

But now i am gonna learn it for sure

[gray isle]

so you haven't done any calculus yet?

[stiff horizon]

They were not good

[gray isle]

technically you don't need it if you're familiar with how common functions behave

e^x is an increasing function
sqrt(x) is also an increasing function

[stiff horizon]

True

[gray isle]

hence f(x) is an increasing function

[stiff horizon]

And minus 3 is removing values

[gray isle]

doesn't affect growth rate

[stiff horizon]

I hesitated between the fact that the function has a root or none

[gray isle]

ivt to show at least one solution exists

[stiff horizon]

But without the proper method it was impossible to demonstrate it at 100%

Ty tho

Without you i would probably have spent a lot of time on this

[gray isle]

you can sub 0 which is convenient to use and also gives lowest value of the function
and e^x + sqrt(x) - 3 is clearly positive for an arbitrarily large value of x

[stiff horizon]

How that sub 0 ?

My english is bad sry

[lone heart]

@stiff horizon Has your question been resolved?

[gray isle]

substitute

replace x with (0)

[lone heart]

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[shell pasture]

how to factor this?

[stable pecan]

Where are you stuck?

[keen pasture]

Try to guess one root and solve the quadratic

[shell pasture]

the whole thing, I dont really know how to start factoring this expression

[keen pasture]

There is an easy to find one

[alpine sable]

cubic formula hope that at least one root is rational and use rational root thm

[shell pasture]

I don't really understand how to start the process of factoring this

[keen pasture]

You can either use cubic formula if you know it

Or try to guess a root and then do long division to factor it in a linear term and a quadratic

[gray isle]

hope that at least one root is rational and use rational root thm

[shell pasture]

seems like im good now

.close

[lone heart]

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[trail terrace]

I dont understand this question
3(x + y) = y. If (x, y) is a solution to the equation above and y cannot equal 0, what is the ratio x/y?

[trail terrace]

I know i'm supposed to find what x/y is equal to, but how?

im stuck at 3x = -2y

not sure what to do after that

[manic wind]

make one side x/y

[trail terrace]

how

[manic wind]

move the y over to the LHS

[trail terrace]

and then?

[manic wind]

what do you get?

[trail terrace]

y=-3x/2

[manic wind]

no move the entire thing over

put x and y on the same side

because you want to know x/y

[trail terrace]

can you show me

[manic wind]

ax = by

ax / by = by / by

ax / by = 1

[trail terrace]

i rly dont understand that

[manic wind]

you're dividing both sides by by

where b is just the coefficient

yeah

how did the negative disappear

you gotta use the reciprocal

$$\frac{3x}{-2y} = 1$$

[ocean seal]

Tronsi

[manic wind]

how do you get rid of the -3/2

yes

multiplying by -2/3 and dividing by -3/2 are the same

[lone heart]

@trail terrace Has your question been resolved?

[lone heart]

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[real pasture]

so i have a practice sheet on using trig identities, and i'm a bit confused
this question states that cscx=-sqrt5 and cosx < 0, and i need to find sin2x, cos2x, sin x/2, and tanx/2

[real pasture]

all this in mind, how would i find the adjacent side of the triangle (to find cosine)

wouldn't it be some stupid number

wait i'm being dumb, it would just be sqrt24

.close

[lone heart]

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[wind pawn]

Which of the following 5 relations does not hold in every triangle ABC?

[wind pawn]

<@&286206848099549185>

<@&286206848099549185>

[alpine sable]

are you working with degree or radians?

@wind pawntranslate

[wind pawn]

translate what?

[wind pawn]

prob A+B+C= 180?

[alpine sable]

yes ok so degree

[wind pawn]

yeah

[alpine sable]

try using A+B+C=180 to prove or disprove the options

you get B+C = 180-A for example, then plug it into the first 3 options and see what happens

[wind pawn]

which 3 options

[alpine sable]

well i guess the idea works for all

the first one for example you get
sin(A) = sin(180-A)

and either you already know that from your table of formulas, or you can just get it by using sin(x-y) = sin(x)cos(y)-cos(x)sin(y)

sin(180-A) = sin(180)cos(A) - cos(180)sin(A) = 0*cos(A) - (-1)sin(A) = sin(A)

[wind pawn]

so i gotta prove the 3 options for every single answer?

[alpine sable]

no maybe i formulated that wrong, i meant first three answers

[wind pawn]

so what do i gotta write for the first one

[alpine sable]

that it does hold, so its not the right answer

[wind pawn]

and for the second one

[alpine sable]

do the same again:
cos(A) = cos(B+C)
cos(A) = cos(180-A)
cos(A) = -cos(A)
so it does not hold and its one of the correct answers

[wind pawn]

what

but its C

and its cos2A = cos2(B+C)

[alpine sable]

ohh wait i read that incorrectly my fault

cos(2A) = cos(2(B+C))
cos(2A) = cos(2(180-A))
cos(2A) = cos(360-2A)
cos(2A) = cos(-2A)
cos(2A) = cos(2A)
so it does hold

[wind pawn]

okay third one

[alpine sable]

for C however you get
tan((B+C)/2) = tan((180-A)/2) = tan(90-A/2) = sin(90-A/2)/cos(90-A/2) = cos(A/2)/sin(A/2) = cot(A/2)

and ofc tan ≠ cot

[wind pawn]

can u do the other 2 too?

i dont know the formulas that well

@alpine sable ?

[alpine sable]

just try, for D use
A+C = 180-B

[wind pawn]

no pls can u do it

[alpine sable]

and -A-C = -180+B

[wind pawn]

i cant waste time

pls

[alpine sable]

plug them in, its quick

[wind pawn]

i dont understand anything of this

[alpine sable]

you get cos(-2B) = cos(2B) which is equal

[wind pawn]

can you do the steps

[alpine sable]

do you know how A+C = 180-B?

[wind pawn]

no

[alpine sable]

A+B+C = 180 yes?

[wind pawn]

yes but u dont need to explain it

[alpine sable]

and then cos(A-B+C) plugging it in we get cos(-B+180-B) = cos(180-2B) = -cos(2B)

and cos(B-A-C) plugging it in we get cos(B-180+B) = cos(2B-180) = -cos(2B)

[wind pawn]

and the last one?

[alpine sable]

plug in B+C=180-A you get
sin((B+C)/2) = sin((180-A)/2) = sin(90-A/2) = cos(A/2)

[wind pawn]

tysm!!

can u help me with more questions or no?

they are shorter ones

[alpine sable]

not rly i would open a new channel

[wind pawn]

alr have a good night

.close

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[trim beacon]

HI

2+1

[carmine reef]

3

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@trim beacon Has your question been resolved?

[trim beacon]

no

16x+3=22

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[trim beacon]

.reopen

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✅

[trim beacon]

Round 2310.7 to 1 significant figure

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[analog shadow]

what is (3i)^3/(2i)^4

[alpine sable]

$\frac{(3i)^3}{(2i)^4}$. You know the rule on powers of $i$, just apply them.

[ocean seal]

3317

[analog shadow]

what😭

i dont know how to type the division sign

i didnt mean for it to be a fraction

the i represents an imaginary number

[alpine sable]

$i=\sqrt{-1}\rightarrow i^2=-1$.

[ocean seal]

3317

[alpine sable]

So you're not dividing anything?

[analog shadow]

no

i mean

yes

i am

this is rationalizing the denominator

[alpine sable]

With this in hand, it's quite easy to derive $i^1$, $i^2$, $i^3$, $i^4$,$\cdots$

[ocean seal]

3317

[analog shadow]

yes i know that but like i simplified it and i got 9i^3 divided by 8i^4

what else do i dooo

[alpine sable]

$i^1=1$,$i^2=-1$,$i^3=-i$,$i^4=i^1=4$.

[ocean seal]

3317

[alpine sable]

The pattern keeps going.

[analog shadow]

so what does 9-i divided by 8(1) mean

[alpine sable]

$9-i$ is the complex number $9+0i$ less $0+1i$, I'm sure that's not what you're trying to notate. Notation can deceive if used incorrectly. If you mean nine times negative i, then it'd be $-9i$.

[ocean seal]

3317

[alpine sable]

Literally means $\frac{-9i}{8}$.

[ocean seal]

3317

[alpine sable]

Divide the $-9$ by $8$ and multiply it by $i$. That's your result.

[ocean seal]

3317

[analog shadow]

OH

does it need to be in a fraction

[alpine sable]

Not really, but many people prefer it in that way.

Fractions are pretty much beautified divisions.

[analog shadow]

oh oksy

ty baefy

[alpine sable]

Glad to help.

[analog shadow]

.close

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[stiff surge]

This is the diagram

[stiff surge]

The question

Firstly I don't understand what they mean by "radii"

Is it radius?

or something

[ornate condor]

yea

radii is radius

plural singualr form

english stuff

i think radii is plural

[stiff surge]

Oh yeah

[sonic drum]

yes

[ornate condor]

so oab

u can use iso tri

[stiff surge]

One sec

Okay

@ornate condor Continue

[ornate condor]

just use iso tri

[stiff surge]

full form??

[ornate condor]

isoceles trianglw

[stiff surge]

oh okay

Okay

but then

[ornate condor]

hm?

[stiff surge]

i don't get it

They didn't mention it is a iso triangle

[ornate condor]

its a circle

all its radii has equal length

[stiff surge]

yes

I get that

[ornate condor]

so those 3 hv equal len

then u can use iso tri to find oab

[stiff surge]

Okay

I get it

thanks

[ornate condor]

np

[stiff surge]

Is it 54 degrees?

@ornate condor

no

typo

wait

[ornate condor]

,w 180-72

[ocean seal]

Results provided by WolframAlpha

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

Requested by Circle#0025

[ornate condor]

eh

na

[stiff surge]

54

[ornate condor]

ye

[stiff surge]

@ornate condor

@ornate condor Thanks

[ornate condor]

np

[stiff surge]

It was a typo btw

wait a sec

@ornate condor

[ornate condor]

..

u can

ping me when uve a q

dont spam pinging me

[stiff surge]

ok

.close

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[alpine sable]

Hi, just need some help especially on the second part. Already have an answer for A just unsure if its correct.

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[carmine chasm]

I don’t understand how they achieved the integer -72. Can someone please explain?

[grave island]

from the third line

u have -10y+75+4y=3 right

so we want all pronumerals on one side and all numbers on the other side

so they subtracted 75 from both sides hence -72

[carmine chasm]

Thanks G.

.close

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[proper lichen]

hi im doing parabola's and i need to know how to find the x intercept of y = x^2 + 6x

[gray isle]

what's the first thing you'd generally do when finding x-intercepts

[proper lichen]

make y = 0

but when i do that

you get 0 = x^2 + x

[gray isle]

setting y to 0 doesn't wipe that 6 from existence

[proper lichen]

but dont u have to divide 0 by 6

[gray isle]

no?

[proper lichen]

oh

[gray isle]

you're skipping ahead and doing stuff you're not supposed to

[proper lichen]

alright

then what do i do

[gray isle]

the first step, set y=0 (and doing nothing else) gives you
x^2 + 6x = 0

[proper lichen]

yep

[gray isle]

the left side is easily factorable

[proper lichen]

wait

what would it factorize to

i know its (x+ ?)^2

[gray isle]

no

[proper lichen]

oh

[gray isle]

where are you getting that idea

the first thing you'd usually look for when factoring is whether all your terms have a common factor(s)

identify it/them and factor that out

[proper lichen]

x(x+6)

[gray isle]

yes

[proper lichen]

so what do i do now

[gray isle]

your equation will be
x(x+6) = 0
then apply zero product property/null factor theorem

[proper lichen]

u get x+6 = 0

[gray isle]

that's only part of it

[proper lichen]

x = -6

[gray isle]

that's only part of it

you're missing a solution

[proper lichen]

i honestly dont know what im missing

[gray isle]

when will ab=0

[proper lichen]

when one or the other equals 0

[gray isle]

yes

now compare that to what you did

[proper lichen]

x = 6 or x = -6 ?

[gray isle]

no

you're overthinking

x(x+6) is the product of which two expressions

[proper lichen]

x^2 + 6x

[gray isle]

no

not what i'm asking for

ab = a * b
supposedly when you said

when one or the other equals 0
you meant a=0 or b=0

similarly
x(x+6) = ?

[proper lichen]

0

[gray isle]

x(x+6) = (x+6) * what

[proper lichen]

2

[gray isle]

no

you're overthinking

you're way overthinking this

[proper lichen]

oh

(x+6)

[gray isle]

no

[proper lichen]

x

[gray isle]

yes

x(x+6) is literally just the product of x and (x+6)

[proper lichen]

alright

[gray isle]

and for x(x+6) = 0

when one or the other equals 0

[calm tide]

x intercept = roots of equation

[calm tide]

👍

[proper lichen]

so what do i do now

[calm tide]

how can product of two numbers be zero?

[gray isle]

apply

ab=0
supposedly when you said
when one or the other equals 0
you meant a=0 or b=0

[calm tide]

use common sense to build ur concept

[gray isle]

do the same thing here

[proper lichen]

wait what do i do exactly

[gray isle]

ab=0
supposedly when you said
when one or the other equals 0
you meant a=0 or b=0
right?

[proper lichen]

yeah

[gray isle]

do the exact same thing for x(x+6) = 0

[proper lichen]

so does x = 0

[calm tide]

over here a = x and b = x+6

two roots

x = 0 and x =?

[proper lichen]

6

[gray isle]

overall you'll have
x = 0 OR x+6 = 0