help-10

[kind hawk]

horrible choice of name for the variable btw

if you wanna disprove something, give a counterexample

@tiny temple

[obtuse pebble]

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[drifting sluice]

I do not understand this

[drifting sluice]

at x = a wouldnt x-a be 0?

And why x^k instead of (x - a)^k in Maclaurin series

[obtuse pebble]

@drifting sluice Has your question been resolved?

[tacit scarab]

at x=a x-a becomes 0 and only the f(a) term is left

[drifting sluice]

There also derivatives of f(a) added

I dont get why summation doesn't become just

$\sum_{k=0}^{\infty}\frac{f^{(k)}(0)}{k!}$

[warm shale]

Ñøïr

[tacit scarab]

These series basically approximates the function with polynomials

if you differentiate the series, you'll see that they have same n-th derivative as f(x)

And it happens to ensures the series converges to f(x)

[drifting sluice]

The polynomial is f(x) ?

[tacit scarab]

the Taylor series is a polynomial

[obtuse pebble]

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[fiery aurora]

hey could anyone help how the multiplication in the denominator works? i didnt understand the final answer which came out to be kp/(r^2 + a^2)^3/2

[obtuse pebble]

@fiery aurora Has your question been resolved?

[eternal thistle]

$\sqrt{x} = x^{\frac{1}{2}}$

[warm shale]

tales

[eternal thistle]

$a^{b}\cdot a^{c} = a^{b+c}$

[warm shale]

tales

[fiery aurora]

so is it like it becomes a/r+a, then when it multiples with the r^2+a^2 it becomes r^3+a^3?

which is the same as writing (r^2 + a^2)^3/2

cuz the 2's can be cancelled and it would still be raise to 3?

i think i got it

thank u buddy

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[mellow skiff]

For this one we replace x with 2,-2 and 2/3 ?

How to do it with 2/3?

[ember frost]

sub with 2/3 instead

[mellow skiff]

0.666?

[ember frost]

use 2/3

not its rounded version

[mellow skiff]

But how could i use it in question c

Its already at a/b

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[shell oar]

how would i use this to solve the op

[obtuse pebble]

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[shell oar]

<@&286206848099549185>

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[woven creek]

hello

[woven creek]

what is this equation from

[twin sandal]

this is the hypergeometric distribution

[obtuse pebble]

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[paper sparrow]

Hey, I need to examine if this converges or diverges. I already solved it but I think I did a mistake

[paper sparrow]

I found that this converges by comparing it with another series

but I think I also have to calculate the sum, which i dont think i can

[swift stream]

The easiest way to see if it converges or diverges is noticing $2^{2n}3^{1-n} = 3 \cdot (\frac{4}{3})^{n}$

[warm shale]

smidgin

[paper sparrow]

ohh

i didn't think of aplying the power 2 to the 2

so this diverges, bc |r| > 1

thanks

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[ionic flame]

i have a question

[ionic flame]

They are second degree equations, I don't know if they are correct.

[forest sinew]

i think we can certainly help you but you may also consider using a bot

at least to confirm answers-

[ionic flame]

how

[forest sinew]

,w Solve[ x^2-2x-15==0 ]

[warm shale]

Results provided by WolframAlpha

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Requested by janniku

[forest sinew]

looks like youre off by a half

ah, you maintain the fraction in the last step

youve written for example $$\frac{10}{2} = \frac 52$$

[warm shale]

jan Niku

[ionic flame]

I don't put two then

the number

[forest sinew]

you just simplified incorrectly in the last step

can you see why this is wrong? why 10/2 isnt 5/2?

[ionic flame]

oh

noe

now

[obtuse pebble]

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[oak nova]

Hello

[oak nova]

how did my prof go from the first step to the next

[undone yoke]

Split the second integral

[gilded needle]

you could use partial fractions to split 1/(u^2 - 1) into two terms

[undone yoke]

$\frac{1}{u^2-1} = \frac{1}{u-1} - \frac{1}{u+1}$

[warm shale]

Solomaniac

[oak nova]

why do you subtract them?

[undone yoke]

Think.

[oak nova]

isnt it a difference of squares

so theyre multiplied

[undone yoke]

You'll see it immediately

[tardy epoch]

do the partial fractions yourself to see how solom got it

[timid silo]

you forgot to multiply 1/2

[gilded needle]

and you can always confirm it's correct by carrying out the subtraction and seeing that you get back 1/(u^2-1)

[oak nova]

im so lost ill be honest

[undone yoke]

That's a small thing.

[gilded needle]

maybe a review of partial fractions is in order?

[undone yoke]

Okay. Look at the RHS

[timid silo]

its still wrong tho

[oak nova]

whats an rhs

[undone yoke]

Right Hand Side of an equation

[oak nova]

do u mean smthn like this?

[undone yoke]

Yesss

Split u²-1 = (u-1)(u+1)

[oak nova]

yea so how come in the other question its a subtraction not an addition?

[undone yoke]

Split it in terms of addition. You will automatically get -1 as the coeff.

Also, @oak nova splitting (u²-1)=(u-1)(u+1) is one of the basic mathematical intuitions. Get used to it. Completely.

You'll also encounter this intuition of splitting the terms in Seuqence and Series.

[oak nova]

so would b turn out to become a negative number?

after solving?

[tardy epoch]

yea find a common denominator

just add them and you'll see

[oak nova]

ok 1 sec

[graceful marten]

here its
(u^2 -1) aka (u^2 - 1^2)

so you always split it bc its easier to do when you see something like this

[oak nova]

like this?

[tardy epoch]

oh he's missing a 1/2 here

[undone yoke]

Yeah I didn't write the -1/2 because the uploaded question already had it mentioned in the answer.

[oak nova]

at this point do i sub u back in?

u is tanx btw

[tardy epoch]

No?

[oak nova]

it is

[tardy epoch]

Use int 1/(1+u) du = log(1+u)+C

[oak nova]

whaaat

[tardy epoch]

Are you still working on this problem

[oak nova]

yes

[tardy epoch]

Have you not learned this

[oak nova]

cant i just take the integeral of the fractions and get ln(u-1)

[tardy epoch]

Yes

[oak nova]

and ln(u+1)

[tardy epoch]

So why are you setting u = tan(x)

[oak nova]

because im doing substitution

at the start of the problem i let u=tanx

i just didnt show u thats why i said u = tanx btw

[tardy epoch]

Where is there an x? Or any tan(x)?

[oak nova]

lemme just show u the problem

if u let u=tanx

u get du=sex^2xdx

and get to the point i was at wher eu helped

ohh nvm i got it

ln(x) - ln(x) = ln(x/x)

its a rule i forgor about

okay ty

[obtuse pebble]

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[fleet stag]

how come its positve 2/5 and not negative

[worn yoke]

you subtract the lower bound, so the negatives cancel out

[fleet stag]

omggggg

lol how did i miss that

[fleet stag]

thx

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[earnest lion]

I've been off school for ages really ill and completely missed all of this and sohcahtoa so could anyone help me with this and preferably find the answer? 😭😭

[queen briar]

do you know trigonometric functions?

[earnest lion]

nope😭 sorry

[queen briar]

wha-

sin, cos?

does that ring a bell?

[earnest lion]

I've heard of it but never used it

[queen briar]

do you know the formula for sin(x)

even the slightest idea maybe

[obtuse pebble]

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[earnest lion]

it's okay I did it!

[obtuse pebble]

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[frozen willow]

I was told if

[frozen willow]

How does the left imply the right?

[forest sinew]

this looks so suspiciously like markovs but i cant track it

I guess you need more information about the rv

but to me isnt the left never true?

@frozen willow

so then it may as well imply that dogs never fly on tuesday

[warm shale]

jan Niku

jan Niku

[obtuse pebble]

@frozen willow Has your question been resolved?

[frozen willow]

No. This is just a one-liner proof of Markov's ineq.

[frozen willow]

Correct. It's used in a proof by contradiction

[frozen willow]

I just want to know how the left implies the right

[forest sinew]

i mean F -> X is true for any X

[forest sinew]

idk if thats helpful or not

but if $F$ then $X$ has truth value $\neg F \lor X \equiv T \lor X \equiv T$

[warm shale]

jan Niku

[frozen willow]

The goal here is the prove the inequality

[forest sinew]

markovs?

[frozen willow]

👍

It would be nice to use Markov's to proof itself tho

sksksk

[forest sinew]

hmm

im not sure youve phrased this in a way its equivalent to markovs

wikipedia has a nifty integral proof

[frozen willow]

Sadly, that won't help us understand this proof

[forest sinew]

well the statement you posted is questionable

[frozen willow]

What part of it?

[forest sinew]

i mean does it not end with E > E?

[frozen willow]

Well that is the point

[forest sinew]

i mean then you have a problem

because E > E is false

so if youre doing a contradiction

you want to show the left side is true

right

[frozen willow]

No sadly

[forest sinew]

sorry bad brain day

its not really clear where this statement comes from

[frozen willow]

That's why I'm here 😔

[forest sinew]

its definitely not equivalent to markovs

and idk why not just use the integral proof

[frozen willow]

For verbosity maybe

Here's the whole proof

[forest sinew]

what is the original statement?

should be hopefully right above this?

[frozen willow]

Here is the theorem

[forest sinew]

OH

multiply both sides by cE

i get it

that 1/c c E should be more suggestive

\begin{align*}
P[X\geq c E] &> \frac 1c \
cEP[X\geq c E] &> cE \qty(\frac 1c) > E
\end{align*}

[warm shale]

jan Niku

[frozen willow]

Multiplying both sides by cE will only give us
\begin{align*}
P[X\geq c E] &> \frac 1c \
cEP[X\geq c E] &> cE \qty(\frac 1c)
\end{align*}

won't it?

[warm shale]

Zim

[frozen willow]

Your trailing "> E" is the key to my question 🙏

[forest sinew]

@frozen willow okay, now apply the hypothesis

we assumed the first line, yea?

so apply it to the second

youll get $$cE\frac1c > cE P[X\geq cE] > cE \frac 1c$$

[warm shale]

jan Niku

[frozen willow]

https://tenor.com/view/cristiano-ronaldo-celebrate-oh-yeah-gif-11515686

Thanks jan

.close

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[graceful pendant]

Hello !! A question about permutation. Five applicants for a job are to be interviewed on the same day.
a) In how many ways can the secretary schedule the sequence of interviews?
b) If two of the applicants are friends who requested to be interviewed one after the other, in how many ways can the order of the interviews be done?
c) If one of the applicants has a prior appointment and requested to be the last one to be interviewed, in how many ways can the sequence of interviews be done?

[knotty bronze]

Same question...

[graceful pendant]

<@&286206848099549185>

[obtuse pebble]

@graceful pendant Has your question been resolved?

[obtuse pebble]

@graceful pendant Has your question been resolved?

[summer moth]

Yooo, I gotchu dawg

So, like we went over earlier today, a permutation is when order matters.

So, for part a, you would find the permutation, non-repeating, of 5 options

[graceful pendant]

Yooo, it's youuu

[summer moth]

So, how do you do a permutation non repeating?

[graceful pendant]

10 x 9 x 8 x 7...

Right?

[summer moth]

Precisely

[knotty bronze]

5,040?

[summer moth]

So, if you have 5 sets, and you need to use all five of them, this can be represented by a factorial: "!"

So, this would be 5! Or 5 factorial

[knotty bronze]

Srry to butt in

[graceful pendant]

It's alright dw

[graceful pendant]

This is for a, right?

[summer moth]

Yes

[graceful pendant]

So just 5 x 4 x 3 x 2 x 1?

[summer moth]

Yup

[knotty bronze]

So the final answ is 120?

[summer moth]

Umm, not quite

[knotty bronze]

How so?

[summer moth]

That's correct, yes.

Part a is 120

[knotty bronze]

Okk thank u!!

[summer moth]

So, b and c are very similar

[knotty bronze]

Do we use the same formula for b and c? Or?

[summer moth]

So for part b, we know that 2 are going one after the other, so we can essentially count them as one

[summer moth]

That completely depends on the teachers interpretation of the question

I would assume no, because why ask the same question twice

[knotty bronze]

Good point

Then what would be the formula for b?

[summer moth]

So the order could be abcd or bacd if a and b are friends

That's how I'm interpreting it

[graceful pendant]

Can it also be like, badc?

[summer moth]

Yes, yes it could

[graceful pendant]

Ohhh I see I see

[summer moth]

As long as a and b are next to eachother

[graceful pendant]

Okiee

[summer moth]

So what do you think the formula would be?

[graceful pendant]

n! / (n-r)!

I'm sure

I'm not sure I mean TT

[summer moth]

If we count a and b as one unit, but 2 different options of the sub-unit

Don't look at it as 1 permutation, look it as 2

[graceful pendant]

Sooo, is it like 5! / (5 - 1)!

Oh

[obtuse pebble]

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[summer moth]

.reopen

I think you have to reopen it

[graceful pendant]

.reopen

[obtuse pebble]

✅

[graceful pendant]

There we go

[summer moth]

So, what do you think the first permutation is?

I took a screenshot of that guy, gonna send it to a mod

[brisk matrix]

they took care of it

[graceful pendant]

Thank you kind Sir :))

[graceful pendant]

5!

Not sure again TT

[summer moth]

Close

[graceful pendant]

I don't really get what you mean ;-;

[summer moth]

Very close

If we view a and b as one unit, and there are 5 options, then it would be 4!

[graceful pendant]

Ohhh yeah

I see now

[summer moth]

So originally cdabe was a possibility. But we are going to view a and b together as x, so now it's cdxe

Does that make sense?

[graceful pendant]

Okiee

[summer moth]

So we have the 4! As the first permutation, what do you think the 2nd one is?

The 2nd one is for a and b, to be clear

[graceful pendant]

Sooo

3!

[summer moth]

Just a and b

2 slots, 2 possibilities, non repeating

So, before we had 4 slots and 4 possibilities after we combined a and b, and that was 4!, right?

So what would the permutation for a and b be?

[graceful pendant]

2!

That?

[summer moth]

Yessss

I knew you would get it

So, now that you have 4! And 2!, what do you think you would do with them?

[graceful pendant]

Multiply?

[summer moth]

Yes.

(4x3x2x1)x(2x1)

[graceful pendant]

Hey, thanks for your help bro but I have to go TT

See you !!

Really sorry TT

[summer moth]

Dm me if you need more help

[obtuse pebble]

@graceful pendant Has your question been resolved?

[obtuse pebble]

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[burnt thunder]

is it x^1/2?

,rotate 270

[burnt thunder]

textbook has -

1/2

[pastel wren]

hi again! whats the question?

[burnt thunder]

lol dont get bored of me

okay so

square root c

x

its x^1/2

right?

[pastel wren]

yeah

[burnt thunder]

okay so why did they

its -1/2

[pastel wren]

you did the fraction wrong

[burnt thunder]

at the end

[pastel wren]

i see it already

[burnt thunder]

oops

where…

which fraction

[pastel wren]

you wrote just sqrt(x) not sqrt(x)/x

[burnt thunder]

oh god

[pastel wren]

first to 2nd line

[burnt thunder]

where did fracrion go

help

why did they get rid of ot

it

how

[pastel wren]

they didnt lol

you did

[burnt thunder]

they did too

line 3

x^-1/2

[pastel wren]

thats how they got -1/2

[burnt thunder]

yea i just figured 💀

omg

i acc need to use my brain

[pastel wren]

XD

hope i helped

[burnt thunder]

tyem

ur so smartthanks

.close

[obtuse pebble]

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[tidal vale]

Using the negation of the conclusion, is my solution correct?

[zenith raft]

what's the question?

[tidal vale]

I'm wondering if my steps makes sense and ive correctly understood how to do this (Im sorry I have no idea how its called in english, I would assume its "formal group") using the negation of the conclusion (here the conclusion is =>v C /\ D)

where you have to end with two things who goes against each other, here my (3) and (5) since one is true and the other is false which is a contradiction

The first image is the rules Im allowed to use

Sorry I looked around a bit and I believe its called "proof by contradiction"

Nevermind I found it doesnt work because I tried doing distributivity, but the rule I was actually trying to apply was morgan and that also changes the sign which breaks what ive done

thank you anyway

.close

[obtuse pebble]

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[hollow forum]

Hello

[hollow forum]

I need urgent help with this

[chrome crypt]

Area = l * w

In a square all dimensions are the same

so we can say w = l

Area = l^2

[hollow forum]

Wait I sent the wrong thing it’s the same pic with more progress

Would that be correct

For the a

[chrome crypt]

yep

now for the triangle

split it into two right triangles

then find the area for the individual right angled triangles

add them up

and you have the total area

so in our case (2) (1/2) ((x+20)/2)(2x), we have two of these triangles so multiply by 2. x^2 + 20x would then be the area for the triangle

[hollow forum]

Would I keep it in brackets the (x+20)

[chrome crypt]

looks like you got it. Good job.

[hollow forum]

Yesssss thank u so much

[chrome crypt]

x^2 + 20x or x(x +20)

[hollow forum]

It says algebraic expression so do I just keep it like that

[chrome crypt]

I’d say x^2 + 20x

[hollow forum]

Ah yes I get it

Thank you sooooo much

[chrome crypt]

no worries.

[obtuse pebble]

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[obtuse pebble]

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[grizzled stone]

how to make fraction on ti 84?

[grizzled stone]

like 10 over 5

[teal turret]

search on google

or take a pic of the calc and send here

[grizzled stone]

found it thanks

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[nova obsidian]

i need help with calc1

[ember frost]

!da2a

[obtuse pebble]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[nova obsidian]

please comeback

[unkempt marten]

Sin(given x) + Cos(given x)(x-...)

Same for the other

[obtuse pebble]

@nova obsidian Has your question been resolved?

[obtuse pebble]

@nova obsidian Has your question been resolved?

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[wooden bison]

hey could someone explain why e^(x/2) integrated is 2e^(x/2)?

[hushed totem]

do you know the chain rule

[wooden bison]

yes but that doesn't apply to integration right? you have to use u sub?

[hushed totem]

oh wait my bad i didn’t read integration 💀

[hushed totem]

well do you know u-substitution

[fathom flicker]

let u=x/2

[wooden bison]

all good lol

yeah i know u sub

is that the only way to do it?

[fathom flicker]

it's by far the easiest way to do it

[wooden bison]

ah got it

i'll do that then thank you

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[teal turret]

or u can sub u = e^(x/2)

equally as fast

[obtuse pebble]

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[wispy acorn]

its probability rules and I'm struggling on the 2nd and 3rd question

[wispy acorn]

for the 2nd question I divided 10 by 52

for the third question I divided 17 by 52

[worn yoke]

where did you get 10 and 17 from?

[stone torrent]

Hello I have a question regarding radicals

[worn yoke]

!occupied

[obtuse pebble]

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

[wispy acorn]

10 from the total heart cards avaialbe and 17 from the total cards available lower from 9, including the ace

wait shit

[cedar frost]

there is not only 10 hearts

[wispy acorn]

for the 2nd question

[cedar frost]

nor is there only 17 lower than 9

[wispy acorn]

yeah I had to include the queen of hearts too...

[worn yoke]

you have to include all of the face cards

[wispy acorn]

for both the 2nd and third question?

[cedar frost]

yes

how many hearts are there

[worn yoke]

for the 2nd, you have to include all the heart face cards because those still count as hearts

[wispy acorn]

yeah for the heart cards

it would be 12 in total right?

since including the queen and king of hearts

oh wait

[cedar frost]

there is also the prince

[wispy acorn]

the joker card as well

[cedar frost]

or whatever its called

[worn yoke]

it does say in the question how many are in each suit

[wispy acorn]

or J

[worn yoke]

in english it's called the jack

[cedar frost]

jack yes

if you include the jack how many hearts do you have?

[wispy acorn]

so for the 2nd question, it'd be 13/52

[worn yoke]

yes

[wispy acorn]

and for the 3rd question

I would include all cards ranging from 1 to 8 and the jack, queen, and king card as well right?

not to mention the ace card

[worn yoke]

face cards are usually counted as higher than any of the number cards

[wispy acorn]

ah ok

[cedar frost]

no those are counted above 10

[wispy acorn]

never played cards in my life so lol

so it'd be 33/52

[worn yoke]

33?

[cedar frost]

no

ok wait

go to the image

and circle all the cards that would be counted as lower than 9

[wispy acorn]

well I counted up the ace, hearts, club, and spades cards that are 8 that resulted in 32, and added 1 to count the ace card

[cedar frost]

?

[worn yoke]

aces are the 1 cards on the left, for reference. they're a bit different from the other number cards, because they can be either 1 or higher than kings depending on context

[cedar frost]

yes

and how many cards are there in that circle

[wispy acorn]

32

[cedar frost]

there you go

[wispy acorn]

so I overthinked with the ace part

[cedar frost]

i think you got 33 becuase you were confused with the ace or something

[wispy acorn]

yeah that

[cedar frost]

but just pretend the ace is 1 like the question stated

[worn yoke]

these are the aces

[cedar frost]

then ur good

[wispy acorn]

aight thanks guys

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[obtuse pebble]

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[obtuse pebble]

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[fickle tapir]

halp

[fickle tapir]

#1

[gilded needle]

do you notice anything about the function e^-|x|

like any particular properties it has

[fickle tapir]

I thought I could just guess the antiderivative with -e^-|x|, but based on the crazy answer wolfram is giving me I'm guessing that's not possible

it converges?

I dunno

oh

it's a bell curve

[gilded needle]

not quite, it has a "point" at x=0

what about symmetries

[fickle tapir]

symmetry across y axis

[gilded needle]

yes

aka even function

does that simplify the integral at all?

[fickle tapir]

inegral can be changed from 0 to infinity 2*e^-|x|?

[gilded needle]

yes

and when x is in the interval [0,infinity), can you simplify |x|?

[fickle tapir]

to just x?

[gilded needle]

right

so can you now rewrite the integral using the above simplifications?

[fickle tapir]

ah, answer is 2

thank you sir 🫡

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[timid silo]

There are 5 boys to every 6 girls in a class of 44 pupils. Find the number of boys in the class.

A school helper teached me for 1 and half hours. It went through my brain. My dad who’s Chinese take 1 hour to teach me a simple dimple question, worked to a half degree. sos.

[lone echo]

Focus on the first part. There are 5 boys to every 6 girls. This is the smallest group of people you will be working with.
How many people is in that smallest group?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[graceful marten]

i dunno what to do

[tardy epoch]

,tex .double angle

oh oops

,tex .sum diff trig

[warm shale]

riemann

[tardy epoch]

second one with theta = theta and phi = 2 theta

[graceful marten]

okay?

How do you know

Wait what

[drifting roost]

what's your question specifically?

[graceful marten]

Yes thats what i did

[graceful marten]

Solve this

[graceful marten]

I did this so far

And im stuck

I tried a few things but idk

[drifting roost]

well cos(3x) can be rewritten as cos(2x + x)

yes?

[graceful marten]

yes

[drifting roost]

okay

do you know cos(2x) = 2cos^2 (x - 1?

[graceful marten]

Yes

[drifting roost]

then plug that in

sin(2x) = 2sinx cos (x)

[graceful marten]

2cos^2x -1 (cosx)
2cos^3x - cosx - (2sinxcosx)(sinx)

[drifting roost]

,, 2 \sin^2 (x) \cos (x)

[warm shale]

kanna

[drifting roost]

you can use the pythagorean identity on sin^2(x)

,, \sin^2 (x) + \cos^2 (x) = 1

[warm shale]

kanna

[graceful marten]

1-c^2

[drifting roost]

yes

[graceful marten]

I did that

[drifting roost]

now do the algebra

[graceful marten]

maybe i did something silly mistake

2cos^3x - cosx - (2sinxcosx)(sinx)

2cos^3x - cosx - (2cosx)(1-cos^2x)
2cos^3x - cosx - (2cosx - 2cos^3x)

4cos^3x - 3cosx

unbeleiveable

I dont know i fked up that bad

need more practice

ty

[drifting roost]

sure no worries

[graceful marten]

.close

[obtuse pebble]

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[obtuse pebble]

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[graceful marten]

I started this new chapter just now

[graceful marten]

Why are the numbers 3 and 4 swapped around?

Rcosx
4cosx

Rsinx
3sinx

Shouldnt
Rcosx = 4?
Rsinx = 3

[drifting roost]

look at the red terms and the green terms

match them

R cos(alpha) = 3 then

purple in the left = purple on the right so 4 = R sin(alpha)

[graceful marten]

oh ok

that helped me understand

TY!

scam kanna is here

[zenith raft]

wtf

[graceful marten]

[zenith raft]

i'm the real kanna

[graceful marten]

https://tenor.com/view/maxi-gif-2239479764828891843

.close

[obtuse pebble]

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[drifting roost]

[zenith raft]

[graceful marten]

https://tenor.com/view/cat-cats-cat-meme-meme-meme-cat-gif-14470917232397934693

[drifting roost]

i should ask questions so you can come by my channel

[zenith raft]

maybe i'll ask a question

[graceful marten]

😂

[obtuse pebble]

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[granite bear]

.close

[obtuse pebble]

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[burnt thunder]

hows rhe slope 16

[burnt thunder]

i got 8

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[coarse oriole]

how do i find the x0 on derivative?

[twilit meteor]

!original

[obtuse pebble]

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

@coarse oriole Has your question been resolved?

[obtuse pebble]

@coarse oriole Has your question been resolved?

[coarse oriole]

.close

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[craggy ridge]

.reopen

[late flare]

can someone help

[fleet stag]

How come my anwser different

[late flare]

i got 4ln(x^2+1)

am i correct

bruh

[twilit meteor]

no

[fleet stag]

.clise

.close

[twilit meteor]

differentiate ur ans

[fleet stag]

Oh

Dam

Mb

[obtuse pebble]

@hybrid stirrup Has your question been resolved?

[obtuse pebble]

@hybrid stirrup Has your question been resolved?

[obtuse pebble]

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[timid silo]

how does AUB represent thst

[obtuse pebble]

@timid silo Has your question been resolved?

[vague spindle]

Every point in A or B is in it

That’s the definition of the union operation

[timid silo]

why not {20-x, 8-x}

[vague spindle]

Because it needs to include the intersection

[timid silo]

so

{20-x, x, 8-x}

[vague spindle]

Yes

[timid silo]

so

{20-x, x, 8-x} =23?

[vague spindle]

Well, all of them added up = 23

[timid silo]

true lol

@timid silo i got it

ok good

[timid silo]

.close

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[bronze jewel]

i had an idea to find the function f(x) for x=t where the tangent at any given t will cross the y-axis at y=t so that all tangent lines go through the points (0,t) and (t,f(t)) but i can't for the life of me figure out how to actually find that function.

[obtuse pebble]

@bronze jewel Has your question been resolved?

[livid gate]

bin ingame

wait

[obtuse pebble]

@bronze jewel Has your question been resolved?

[obtuse pebble]

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[bitter spruce]

How do I simplify this further to find out what x is equal to?

[bitter spruce]

I'm not sure how I could get 3tan^2x-1=0 to the point where I find out what just the x value is

[errant lotus]

What in the mathematics is this

💀

[fierce elbow]

I think u went wrong somewhere

Probably

how did u get sin square x = 1

u dont just equate the upper part seperately and stuff

u can solve it atm of this step

[bitter spruce]

Because tan^2x=1/3 and tan=sin/cos

[fierce elbow]

no no no

u dont use that

It dosent work like that

[bitter spruce]

It doesn't?

[fierce elbow]

do u know the values of tan from 0 - 90 degrees

[errant lotus]

My gut feeling says snowflake is right

[fierce elbow]

thats the most imp thing here

[errant lotus]

No wonder i have gut issues

[bitter spruce]

Yeah, if it's on the unit circle I have it memorized

[fierce elbow]

so what is tan 30

[bitter spruce]

2sqrt3/2

[fierce elbow]

thats cos 30

root3/2

[bitter spruce]

Wouldn't it be (1/2)×(rt3/2)?

[fierce elbow]

tan 30 = 1/root3

and u got it here already

so basically x is 30 degrees

u get what im saying?

[bitter spruce]

Oooh right, I got messed up on fractions in my head

[fierce elbow]

when u square root on both sides u get tanx = 1/root3

but tan 30 = 1/root3

thus x = 30 or pi/6

[bitter spruce]

OOOH

I get it now

[fierce elbow]

Noice

[bitter spruce]

That makes so much more sense

Thanks! :)

[fierce elbow]

Np

[bitter spruce]

.close

[obtuse pebble]

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[obtuse pebble]

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[fierce elbow]

Quick question

[fierce elbow]

What is greater log 5 to the base 3 or log 5 to the base 4

also how to identify which one is greater

[night fox]

write it in exponent form

[versed stratus]

what do you think?

Think about what the log function does/ means

[queen briar]

if the base is greater than 1, the greater log is the one with the greater argument

therefore

[obtuse pebble]

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

[queen briar]

bro

[versed stratus]

oops, sorry

[queen briar]

how else am i supposed to answer

[versed stratus]

give a hint

[fierce elbow]

What exactly do u mean

its a representation of a exponential term

[iron edge]

log 5 to the base 3 = log5/log3

[fierce elbow]

yeah

[iron edge]

yeah

So it’s enough

[fierce elbow]

I wrote that but idk how is it enough

I just dont know what is between those 2 steps

[iron edge]

Which steps?

[fierce elbow]

where u seperate them

and then the final answer

[iron edge]

Formula

[fierce elbow]

oh

WAIT OH

YEAH

Got it

.close

[obtuse pebble]

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[fierce elbow]

Thanx btw

[iron edge]

Good for you

[fierce elbow]

ye ye got it

[obtuse pebble]

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[fierce elbow]

how to solve this-

[fierce elbow]

I had this question in my test

Idk have the slightest idea on how to solve it

[iron edge]

100! ?

[fierce elbow]

Yeahh...

[viscid needle]

The exponent of 12, would be the power of 4 and 3

[night fox]

legendre formula

[viscid needle]

Since 4 > 3, then it would be determined by the power of 4

[fierce elbow]

wait wait

If 4 is greater

why will it be determined by 4??

[viscid needle]

4 is greater means that the power of 4 in 100! Is less than the power of 3

[night fox]

we need the maximum amount of 4s to get 12

[viscid needle]

Do you understand this point?

[fierce elbow]

60%

[viscid needle]

Okay

[fierce elbow]

ok ok

got it

makes sense

[night fox]

https://en.m.wikipedia.org/wiki/Legendre's_formula

[fierce elbow]

I thought u were joking when u said legendres formula

[viscid needle]

Okay great, so since the power of 3 is more, and power of 4 * 3 would be determined by the number which had lesser power, which is 4

Thankfully, we have a formula, the above one, for finding it

[fierce elbow]

I can barely understand that formula

[viscid needle]

Okay, so do you know the floor function?

[fierce elbow]

Man I think it was an out of syllabus question

[night fox]

see what midnight says

[fierce elbow]

Nop

I dont know that floor thing

[viscid needle]

$\floor{\frac{a}{b}}$

[warm shale]

Midnight

[fierce elbow]

No idea

[viscid needle]

okay

[fierce elbow]

I thought it was bracket when I was reading that webpage

[viscid needle]

floor(a) is the smallest integer less than or equal to a

[fierce elbow]

square bracket

[viscid needle]

It’s not a regular square bracket, haha

[fierce elbow]

ok yeah

[viscid needle]

So, suppose you had to find the power of 4 in 10!

Wait, let me generalise it

Power of p in n! is:$
\floor{\frac{n}{p}} + \floor{\frac{n}{p^2}} + ……$

[warm shale]

Midnight

[fierce elbow]

can u tell me the steps for it

in some smaller exmaple

[viscid needle]

Suppose you had to find the power of 3 in 7!

$\floor{\frac{7}{3}} + \floor{\frac{7}{9}} + \floor{\frac{7}{27}} +…..$

[warm shale]

Midnight

[fierce elbow]

yeah

7! is

[viscid needle]

Now, since 7 < 9, 7 < 27 and so on, all these would become 0

[fierce elbow]

tends to 0

sorta

decreasing gp

[viscid needle]

Thus, only floor(7/3) = 2 is the answer

Yup

As soon as p^k > n, you stop

[fierce elbow]

ok so it works similar to a gp??

[viscid needle]

Well, yes and no

[fierce elbow]

like the rest ahead wont matter a lot

[viscid needle]

It works like a gp, but you don’t need it

[fierce elbow]

to the original one

[viscid needle]

Exactly

[fierce elbow]

yeah

Hmm

makes sense

[viscid needle]

As soon as you hit p^k > n, the following wont matter

Can you try finding the power of 4 in 100! now?

[fierce elbow]

4

in 100

wasnt it 12

wait yeah

[viscid needle]

I guess you can do 12 too

Yeah

[fierce elbow]

so the sequence would go like

100 / 4^i

where i = 1 to inf

is that right??

[viscid needle]

Wait

It’s only for primes

[fierce elbow]

Oh

[viscid needle]

So we can’t use it on 12 or 4

[fierce elbow]

well 4 isnt

[viscid needle]

We will have to find the powers of 2 and 3

And try to use that

[fierce elbow]

2 would be 50

3 would be what

[viscid needle]

Uh no

[fierce elbow]

100/3??

[viscid needle]

Let me give another example

[fierce elbow]

oh wait p&k>n

I didnt use it

[viscid needle]

Yes

[night fox]

yes

[fierce elbow]

bro the sign

wth

so it would go till 64

as 128 is greater than 100

100/2 + 100 / 4 + 100/8 + 100/16 + 100/32 + 100/64

do I need to calculate that stuff

[viscid needle]

Yes

But remember, take the floor

Not the decimals, the smallest integer less than or equal to them

[fierce elbow]

what was floor again?

oh ok

50 + 25 + 12 + 6 + 3 + 1?

[viscid needle]

👌

[fierce elbow]

97

what should I do with this

we did it for 2

[night fox]

answer!!

[viscid needle]

Now do it for 3

[fierce elbow]

3

Hmm

100/3 + 100/9 + 100/27 + 100/81

so it would be 33 + 11 + 3 + 1

48

wait

yeah

3>2

Is that it??

[viscid needle]

So 100! = 2^97 * 3^48 * something

[fierce elbow]

48 is also the answer to the question

[viscid needle]

We need to form 12 out of this

How would we do that?

[fierce elbow]

didnt u mention before

that 4>3 so we gotta find for 4

while now we going for 3 and 2

so we had to find it for the greater one

[viscid needle]

Because 4 = 2^2

[fierce elbow]

Im not sure if im making sense

[viscid needle]

Try to make the largest 12 you can out of 2^97 * 3^48

[fierce elbow]

u mean the largest power of 12

obtained from that thing?

[viscid needle]

Yup

[fierce elbow]

how-

2^97 seems impossible

3^48 might work out

[viscid needle]

Recall that 12 = 4 * 3 = 2^2 * 3

2^97 = 2^2(48) * 2 = 4^48 * 2

Can you figure out the rest…?

[fierce elbow]

ok u seperated 96+1

I was confused with that

sheesh well thats great

[fierce elbow]

can u tell me one thing

is this thing for me level

I never even heard the name

[viscid needle]

Yes

[fierce elbow]

how can such question come for me at 11th greade

grade

[viscid needle]

The most important thing here is that you learned something new

[fierce elbow]

well yeah that was interesting

[viscid needle]

It can come

The neat thing about it is that it uses a trick, maybe your teachers didn’t do it using it

Did u solve it?

[fierce elbow]

We never had a sum

like that bro

wait I got a call

[obtuse pebble]

@fierce elbow Has your question been resolved?

[fierce elbow]

btw yeah I got it

thanx

[viscid needle]

.close

Wow

[fierce elbow]

oh mb

.close

[obtuse pebble]

Channel closed

Closed by @fierce elbow

Use .reopen if this was a mistake.

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fleet stag]

i dont understnad how they got the frist coloum of graphs

[obtuse pebble]

@fleet stag Has your question been resolved?

[fleet stag]

<@&286206848099549185>

[fleet stag]

how do u get these values

[subtle jetty]

Takes a bus on monday, on tuesday its a 0.4 chance she takes a taxi, leaves 0.6 chance for the bus

[fleet stag]

why cant u do the same logic with .7

then have the other one .3

[subtle jetty]

.7 is when she takes a taxi

[fleet stag]

im confuseddddddd

how do we use this info to work out monday