help-13

[idle thicket]

is there a calculator for these type of expressions?:
14n + 6p – 8n = 18p either for p or n

[tropic oxide]

there's wolfram alpha but this equation is not particularly hard to simplify manually

[cedar kiln]

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[flint plinth]

any thoughts on which is correct?

[gleaming sequoia]

Alright, so for this one, I know we cant tell anything about whether it diverges because were only given that it converges somewhere

so Im assuming it has to do something with, if the bigger function converges, the smaller one does

So either D or C

[flint plinth]

does the given info tell you anything about the radius of convergence?

[gleaming sequoia]

no

oh shoot

[flint plinth]

close.

[gleaming sequoia]

We are given

|x-3| < 1

[flint plinth]

well if the series converges at x=5, then the radius of convergence must be at least how much?

[gleaming sequoia]

how can it converge at 5

if 5 - 3 > 1?

Ik its given in the problem, but i think im confusing myself with something here

[flint plinth]

what does 1 have to do with this?

[gleaming sequoia]

geometric test

[flint plinth]

a power series can have a radius of convergence greater than 1

as long as the coefficients are small enough

[gleaming sequoia]

I thought whatever is inside of here needs to be less than 1

absolutely

in order to converge

[flint plinth]

that would be true if the a_n's were all 1

[gleaming sequoia]

Oh i see now

yeah i forgot about the an

[flint plinth]

in general the radius can be larger than 1 (or smaller than 1, for that matter) depending on the a_n values

[gleaming sequoia]

yea

[flint plinth]

you don't know the a_n values but you don't need to know them to answer this

[gleaming sequoia]

so how would we calculate the Radius with the given info?

[flint plinth]

you can't find the exact radius, but you know it's at least ____ given that it converges for x=5

(fill in the blank)

[gleaming sequoia]

2?

[flint plinth]

yes!

so that's already enough to rule out several answers

[gleaming sequoia]

I just subtracted from 3 but im not sure why that gives us what the radius of converge is at least

[flint plinth]

it's because the series is centered at x=3, and the distance from x=3 to x=5 is 2

[gleaming sequoia]

Oh gotcha

[flint plinth]

so if you draw an open interval from 1 to 5 , which is centered at 3 and has radius 2 on either side, you know that the series converges for any x inside that interval

(the endpoints aren't guaranteed)

[gleaming sequoia]

yea so it can be bigger than 2

[flint plinth]

yep it could be bigger

but it can't be smaller, because then it wouldn't converge at x=5

[gleaming sequoia]

Wait so then that would rule out C and E

leaving us with D

that was a good refresher, thx for the help

[flint plinth]

yep D is correct

[cedar kiln]

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[ivory flare]

question 23 helppl

[ivory flare]

pls

[livid hound]

what have you tried

[ivory flare]

i havent tried anything idk where to tart

[livid hound]

look up converting degrees to radians

[ivory flare]

i got 32pi/180

[livid hound]

yes, then use a calc to get the decimal approximation

[ivory flare]

ok ty

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[floral oyster]

A bag contains ninety-nine balls numbered from 1 to 99. How many balls must be randomly selected without replacement to guarantee that:
At least two balls will leave the same remainder when divided by 3

[floral oyster]

i knwo this is related to combinatorics and the pigeon hole principle but i have no idea how to apple those ideas to this question.

[flint plinth]

well how many possible remainders are there?

[floral oyster]

hmm

idk

[flint plinth]

i bet you do know

if i divide a number by 3, can the remainder be 5?

[crimson sedge]

Is maybe a valid answer lol

[cedar kiln]

@floral oyster Has your question been resolved?

[floral oyster]

yes

by remainder it means if i divide 20 by 3 remainder is 2

right

then in that case

it will be 1, 2

[finite lion]

what aboue 18?

about*

18/3

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[floral oyster]

it means by remainder if i divide a non multiple for exampke 17 i get remainder 2

28 ig et remainder 2

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[night sonnet]

Yo i need help i dont know how do i find the measure angle of P, my teacher did not teach this to us. I think i need to use sohcahtoa but idk what to do next

[tribal granite]

40

[night sonnet]

How?

[tribal granite]

sorry i meant 40

angle A and angle B are perpendiculars

AOBP is a quadilateral

angle sum theory which is 360 degree here

[night sonnet]

So how u do the math

[tribal granite]

have you been taught the angle sum theory?

[night sonnet]

No not yet

[tribal granite]

then you should probably wait for your teacher to teach you or watch videos on yt on the topic

[finite lion]

do you know that, the tangent and radius form a 90 degree angle?

[night sonnet]

Yea if it connects to the same external point i think

[finite lion]

and do you know the sum of angles in a quadrilateral?

[night sonnet]

I read about it and all the angles sum up to 180

[finite lion]

are you sure?

[night sonnet]

Idk

[finite lion]

seacrh up sum of angles in quadrialteral

[night sonnet]

Its 360

[tribal granite]

good

[night sonnet]

No matter how long it is in the visual its always 360?

[tribal granite]

yesss

angles do not matter on the size

[night sonnet]

Hmmm

So how you get 70? What formula u use

[finite lion]

the formula is the 4 angles in a quadrilateral = 360

[night sonnet]

Okay

[finite lion]

more of a theorem if you ask me

so, now

you know the angle at the cirlce center is 140 since the problem ggave it

[night sonnet]

Okay

[finite lion]

and you know the 2 angles are 90 degrees (tangent)

and, you know the sum of the 4 angles is 260

[tribal granite]

40*****

[finite lion]

360*

can you find the last angle>

?

[night sonnet]

Im gonna take a bit of time

[tribal granite]

it A+B+140+P=360

A=B=90

[night sonnet]

Nope cant find it, but i understand that all the angles are all 90 and sums up to 360

[finite lion]

so now youve got

140 + 90 + 90 + the angle you want = 360

[night sonnet]

Okay

OHHH OKAY

I JUST REALIZED IT

SO IN MY CASE 140+90+90=320

Then do i just 360-320

I get 40

?

I minus it to 360 because thats the sum of the 4 angles

But then i was only given 3

.close

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[merry beacon]

hi

[merry beacon]

how do i solve this?

integration btw

[agile portal]

first

x-1+1/(x-1)^3

[merry beacon]

why did it become x-1+1

[agile portal]

it's the same

then

it'll become

(1/(x-1)^2)+1/(x-1)^3

you get it?

then you integrate normally

[merry beacon]

ok am gonna write it down cause i cant really understand it through discord 😅

[agile portal]

wait i'll use the bot

[obsidian coral]

So you can u sub

[agile portal]

$\frac{x}{\left(x-1\right)^{3}}=\frac{x+1-1}{\left(x-1\right)^{3}}$

[wraith dagger]

RulzerFly.

[merry beacon]

ik how to u sub but if i do that i get dx=du

[obsidian coral]

$\frac{x}{(x-1)^3} = \frac{(x - 1 )+ 1}{(x-1)^3}$

[agile portal]

then you simplifiy

[wraith dagger]

dldh06

[agile portal]

no need for that

it's simple

[merry beacon]

ohhh

i see

yeah i got it

ty!

[agile portal]

np now send me the results

[merry beacon]

aight

am sorry

forget what i said

i dont got it

nvm i got it

@agile portal

u sub made things easier

am thankful to whoever invented this method

.close

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[modest blade]

Hi, I am struggling on this probability question, I do not really know how to approach the problem:

show that when P(z) is any p.g.f. with finite first moment P'(1), the function (1-P'(z))/P'(1)(1-z) is also a p.g.f. (probability generating function)
I have tried many analytical approaches but I think there may be a clever trick I am missing. Thanks!

[finite lion]

(whats a pgf?)

[cedar kiln]

@modest blade Has your question been resolved?

[modest blade]

probability generating function

G_X(t) = E[t^X]

where X is a random variable

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[cedar kiln]

@modest blade Has your question been resolved?

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[mighty drift]

You need to show the union is countable

and it's not just the union of G1 to Gn

Whatever n is

that is not arbitrary, that is finite

R is the union of all the {x} for x in R. That is an arbitrary union of countable sets

Define arbitrary

You proved it in the finite case

You definitely didn't

Show X is a countable union of countable sets

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[white wadi]

So I have point P which is (-2,3) and point Q which is (1,-4)

and PQ→ = (3,-7)

but i dont understand how i get (3,-7)

how do i get the distance between these two points?

not distance but

coordinate

how do i get (3,-7)?

[iron jackal]

The direction vector between 2 points (A and B): AB -> = B-A

You take the point you are starting from and minus it from the destination

[white wadi]

oh so

if im starting from p

aka PQ

I do

AHHH

(1--2,-4-3)

(3,-7)

oh my god ive been struggling with this thank you so much

[iron jackal]

👍 np

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[grim fulcrum]

Can someone solve this please

[inland ocean]

n letters?

[grim fulcrum]

Yeah

Like a word of 4 letters can be "good"

Or 3 letters can be "you"

Please help, this has been eating my head

[fair geyser]

it just means you can change half the word

2^(n/2)

round up probably

[grim fulcrum]

Yeah, symmetric word

[grim fulcrum]

Sorry what?

[fair geyser]

for n/2 you have to round it

and you round up

2^(3/2) = 4

[grim fulcrum]

Is that the answer?

[grim fulcrum]

This one

[fair geyser]

oh no palindromes my bad

[grim fulcrum]

Not even palindromes ig, see my example above in the image

It has 5 pairs of palindrome words

But according to you it should be 2^(4/2)=4

Do you see that?

[fair geyser]

what

[grim fulcrum]

Look in the upper part of this

[fair geyser]

no okay i get it

[grim fulcrum]

Actually I have a solution but don't know how it works

[fair geyser]

yeah

so every word "appears twice", but all palindromes appear once

if you add palindromes again, now every word appears twice, and you can divide cleanly

[grim fulcrum]

What

How does every word appear twice

[fair geyser]

well you can see it in your picture

[grim fulcrum]

It's just a pair of palindromes

Not every word is appearing twice

[fair geyser]

the pairs are not palindromes

the non paired words are

every word, except the ones you couldn't find a pair for, appears twice

the words without a pair, is what people call palindromes

because ZEZZ is the same word as ZZEZ, i can claim it appears twice

[grim fulcrum]

Let's bee clear, I've matched the words which are a reverse of each other

[fair geyser]

yeah

[grim fulcrum]

And those words are palindromes

[fair geyser]

no

[grim fulcrum]

How

[fair geyser]

how is ZZZE a palindrome, it's not

a word is either a palindrome or not, it's not a pair relation

[grim fulcrum]

Ah I see, I've written the description wrong

[fair geyser]

ZZZZ is a palindrome, and those are the words you didn't pair

[grim fulcrum]

It's should be a word by reversing the letters

Remove this palindromey thingy

It's just reverse

Words

[fair geyser]

but that's how it works, though

it still works by counting palindromes

[grim fulcrum]

But palindromes are no way related to this

It works but I'm asking how

[fair geyser]

i;m answering, palindromes are the key, that's how it works

[opaque bane]

Palindrome is a special subset of symmetric words.
Starting at a palindrome, you can then modify individual characters, of which you have 25 choices on the left for any of the 25 choices on the right, without making it a palindrome.

[fair geyser]

wrong

[grim fulcrum]

Isn't symmetry itself saying it's same from both sides and hence a palindrome

[fair geyser]

yeah

[grim fulcrum]

But @fair geyser i still didn't get what you answered 😔

[fair geyser]

i don't know what's missing, because your picture makes it clear, i used it as a reference

[grim fulcrum]

How does palindromes come into this

[fair geyser]

you want to count one word from each pair, plus unpaired words correct?

[opaque bane]

I thought you guys are talking about symmetry in terms of formation, like not x - x - not x. But you're right, symmetric words are palindromes

[grim fulcrum]

Yeah

[opaque bane]

(Don't worry about me

[fair geyser]

unpaired words are palindromes

you can look at them and see that

it makes sense because you wouldn;t have two identical words, so no palindrome can have a pair

[grim fulcrum]

Wow

[fair geyser]

so if you count plaindromes, and add them to total count

you get exactly 2 of each thing you care about

[grim fulcrum]

And 2^(n/2) is the number of palindromes

[fair geyser]

yes,you can only change the first half if it has to stay a palindrome, there's one choice for rthe rest of the word

[grim fulcrum]

Yeah

[fair geyser]

thank you for the problem

[grim fulcrum]

Learned something?

[fair geyser]

no but it was fun anyway

[grim fulcrum]

😂 for me too, i can't sleep without an answer

.close

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[crimson quarry]

these are the same or not?

[crimson quarry]

idk if i factorised it wrong or the maths website doesn't recognise it

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[crimson quarry]

.close

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[gray marten]

can someone help with probability hw

[granite eagle]

[surreal tangle]

Hmm

I need some body to teach me integration pls

[still frost]

oh my god

[granite eagle]

💀

[still frost]

bro how many times does it need to be said

[surreal tangle]

Are you the same person

[empty peak]

just watch khan academy videos about integration

[surreal tangle]

How

[still frost]

Learn it yourself, and stop asking here for help in integration. This isn’t even your channel

[granite eagle]

bro just go to khan acad no one's gonna teach you

[still frost]

send your question

[surreal tangle]

Wait

[still frost]

<@&268886789983436800> do something abt this person, constantly asking for someone to teach them the entirety of integration despite be told to stop by many people

[granite eagle]

6 no?

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@gray marten Has your question been resolved?

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[languid void]

How do you solve d^2x/dt^2 = Ax

[strange summit]

Could you put in in latex ?

Also what's A

[languid void]

Constant

[crimson sedge]

[\frac{d^2x}{dt^2}=Ax]

[wraith dagger]

Jester

[languid void]

Yeah

I’m in physics and they seem to just jump from this to x=xMAXcos(wt) where w=sqrt(1/A)

With no explanation

Like simple pendulum equation

Or mass on a block

[crimson sedge]

its cuz they prolly derive the equation in previous semester or earlier

[languid void]

I’m in high school and it’s an AP class, I don’t think we are gonna solve the differential equation

[strange summit]

Honestly I don't even understand the notation here, perhaps you are missing some context ?

[languid void]

Well let’s say we have a pendulum going back and forth

If we use Newton’s second law F=ma

Or actually give me a moment

[crimson sedge]

if you want to solve in general a 2nd ODE's https://www.youtube.com/watch?v=uI2xt8nTOlQ

and if you have further questions #odes-and-pdes

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[meager river]

Help as soon as you can please

[sleek condor]

,rccw

[meager river]

I can get s clearer imsge

[sleek condor]

its ok

[meager river]

Alr

[sleek condor]

but when you rotate a shape it doesnt change the angle or distances right?

[meager river]

It shouldn't

[sleek condor]

it doesnt

right

so the angle after rotation is just the same as before rotation

so you just need to calculate that

whats BAC

[meager river]

Like the points?

so the degrees would be 60 degrees

as it’s an equilateral triangle

[sleek condor]

ok

yeah

unless the problem has been poorly worded thats the answer

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[crimson sedge]

This looks really scetchy. Can anyone give me a better understanding? that he just replaced dz with dx+idy

[frail root]

could you show a full screenshot of all the related content

I feel like there isn't enough information for me to help. Though I might just be inexperienced since I'm only in hs Calculus

[crimson sedge]

is a link okay too?

https://youtu.be/qTDDFMAt7j4

[frail root]

Sorry I think this is beyond my understanding

[crimson sedge]

dw

i dont get most of it either

[dire geode]

That's just the definition of dz

https://youtu.be/Iv4n33Pwpcc

[crimson sedge]

thanks!!

.close

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[cedar kiln]

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[dull oxide]

@sharp kestrel why delete

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[sharp kestrel]

im in #help-26

[cedar kiln]

Please don't occupy multiple help channels.

[sharp kestrel]

.close

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[sleek condor]

there doesnt seem to be a constraint on W?

ok so put yourself in the case where WK goest through the center

since it doesnt change the arc

or even just ignore W altogether no?

just use incribed angle theorem

ok W is here for that and probably W can be defined

as the symmterical point to K

yeah do that

just use inscribed angle: WCK =2*WVK

C= center

and then since you can chose W to be the symmetrical

WVK = 2* XVK

and WCK = 2*XCK

ok nice

180 - 2*36

yes

[cedar kiln]

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[undone star]

A locker has 8 buttons. Each button could have any random letter between A to H and letters can be repeated. What is the maximum number of combinations that exists if the order matters

[undone star]

im struggling a bit with combinatorics and permutation so sry if this seems blantantly obv

its just 8 objects being selected into 8 ways

right

8P8

that was also what i had answered

but the answer was 512

i dont particularly understand why it would be 512

yeah?

as in formula?

im using permutation

none of the above

just on paper

or am i misunderstanding

its just homework on paper

[sleek condor]

wdym the order matters?

[undone star]

in the original quote of the question it states that "how many different codes are possible if the letters could be repeated and their order is important"

[sleek condor]

is it alphabetical order stuff or just the regular ABCD =/= DACB

[undone star]

i think what is meant here is that 123 and 213 are different

etc.

or that

abc =/= cba

if the order did not matter

then abc would be the same as cba

[sleek condor]

i dont get it then because the answer should be 8^8

[undone star]

yeah thats what i also had filled out

that will have to be the next day

im not too pressed on it

alright, seeya

thanks for the help

[sleek condor]

maybe its just 3 buttons

lol

[undone star]

yeah that would make sense

idk

maybe the question left something out or the answer is wrong

thx for the help. i will just ask my teacher about this tmr

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[honest panther]

what am I doing wrong

[bold vine]

each lateral area has a height of 3

[hollow dust]

Every day at school, Jo climbs a flight of 6 stairs. Jo can climb using 1, 2
or 3 steps or a combination of any of them. How many ways can Jo climb
the flight of 6 stairs?

[bold vine]

#❓how-to-get-help

[hollow dust]

ok

[honest panther]

ok so I have the 4 faces and they all have a height of 3 but I only have 2 other numbers?

like this?

[bold vine]

Correct!

[honest panther]

awesome thank you

[bold vine]

Keep in mind 2 faces will be identical, and the other 2 will also be identical to each other

[honest panther]

ok I was confusing the rectangle with the triangle

thank you so much

[bold vine]

np np

Note: There is no triangle

[honest panther]

I have another if that's fine

[bold vine]

Sure

[honest panther]

the correct answer is 18771.2

[bold vine]

Aight

Lateral surface area = 8 times (one rectangle), right?

Remaining: 2 octagons

[honest panther]

yeah

so multiply 28 times 50? and multiply that by number of faces?

[bold vine]

For the LSA, yes

[honest panther]

ok and then I just get the area of the two front faces

[proud karma]

one front face= ((1/2)(33.8)14)*16

[honest panther]

wait what?

[bold vine]

1 octagon = 8 triangles = 16 "half triangles"

[proud karma]

yes

for each half area is 33.8 *14 times 1/2

[honest panther]

ok so just get the area for 1 add them up and * by 2

[bold vine]

ye

[honest panther]

ok thanks

you saved me fr

[bold vine]

🫡 ❤️

[honest panther]

.close

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[azure vault]

can someone explain how constructions even work or the rules of it (Geometry) , I dont understand what i should be learning

[azure vault]

all the videos i've watched arent very helpful

[crimson sedge]

it's just properly drawing shapes to scale

like if it gives you angles and side lengths and curve radius and stuff just drawing it

[buoyant latch]

Try this game called Euclidea

[azure vault]

Okay

[azure vault]

are there any good videos explaining it

[buoyant latch]

(It’s like an actual game but geometry based)

[azure vault]

all the rules and stuf

[buoyant latch]

(It gives you increasingly more challenging things to recreate)

[crimson sedge]

i mean do you know how to use a protractor

[azure vault]

yeah

[crimson sedge]

then ur chillin lol

[azure vault]

what the hell

[crimson sedge]

1

i think

[azure vault]

it looks about right but im so confused

how am i supposed to find which are the right constructions

this is false right

what am i looking at

[cedar kiln]

@azure vault Has your question been resolved?

[cedar kiln]

@azure vault Has your question been resolved?

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[meager barn]

i dont know if this is right because i tried checking my answer on a math app and it had a different answer so i dont know what i did wrong

[fair mortar]

what is vertex ?

$y=(x+8)^2$

[wraith dagger]

bettim

[meager barn]

its the line in the middle of a parabola

on a graph

[fair mortar]

oh okay

[obsidian coral]

Because you didn't do (-8)^2

You just did -8

[meager barn]

ohhhh

okay let me retry it

[meager barn]

so the answer is -128?

[obsidian coral]

No

[rain drift]

you forgot to square 🙂

[obsidian coral]

$(-8)^2 \neq -8^2$

[wraith dagger]

dldh06

[obsidian coral]

You need parentheses around the -8

[meager barn]

so the one being multiplied by 16 is to the power of 2?

[obsidian coral]

What?

[meager barn]

next to 16

(-8)

[obsidian coral]

This is your expression

When you plugged in -8, you need parentheses around the -8 when you do the x^2

Because as mentioned $(-8)^2 \neq -8^2$

[wraith dagger]

dldh06

[meager barn]

so i put parentheses on the first -8 here ?

[obsidian coral]

You should ideally put them whenever you have a negative sign

[meager barn]

so the equation when plugging in x would be (-8)^2+16(-8)+64?

[obsidian coral]

Yes

[meager barn]

ohh okay i see

so the vertex is (-8,0)

[obsidian coral]

Yes

,w plot x^2 +16x+64

[wraith dagger]

Results provided by WolframAlpha

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

Requested by dldh06#2659

[obsidian coral]

See

Plotting helps

[meager barn]

okay thank you

[obsidian coral]

Don't forget to .close

[meager barn]

.close

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[last basin]

i dont know where to really start with this one

i could do all the other questions except this

[dusk finch]

multiply them as normal fractions, $\frac{a}{b}\cdot\frac{c}{d}=\frac{ac}{bd}$. Then expand the product in denominator and simplify. This will lead to form $a+c\sqrt{b}$ in denominator so just multiply the fraction by $\frac{a-c\sqrt{b}}{a-c\sqrt{b}}$ aka the conjugate. then simplify

[wraith dagger]

MathIsAlwaysRight

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[rain vine]

I don't understand the problem and how to do it. I don't even know what the question is asking to find?

[tropic oxide]

the sides of a triangle are 4x+10, 2x+40 and 3x+18. the triangle is known to be isosceles but it is not known which pair of sides is supposed to be equal.

find the value of x and the perimeter of the triangle in all three cases, and report the largest perimeter.

[rain vine]

yeah I did it for no reason already they are 15,8,22

[tropic oxide]

did "it"?

[rain vine]

i suppose x=22 will give largest perimeter?

why we are finding the value of x that give largest perimeter?

[tropic oxide]

...

finding the largest possible perimeter is your goal, is it not?

[rain vine]

like what's the question is about, I don't understand I can solve it if i can understand the question

[tropic oxide]

the sides of a triangle are 4x+10, 2x+40 and 3x+18. the triangle is known to be isosceles but it is not known which pair of sides is supposed to be equal.

[rain vine]

what's mean by the "largest perimeter"

I think i understood the question

.close

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[shy pebble]

I don't know how to find question a.

[long swan]

sure.

we know that the average for 30 students is 12.8

what was the sum of all their scores?

[shy pebble]

12.8 times 30?

[long swan]

yea

which is?

[shy pebble]

384

[long swan]

yep

now it says the average for 31 students was 13

what was the sum of their scores?

[cedar kiln]

@shy pebble Has your question been resolved?

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[livid tundra]

I have struggle with multplying the numerator can someone tell me how to do it

[livid tundra]

i just mutliply -2 . 2?

because I remember her saying you should ^2

[copper plinth]

What's the doubt?

[livid tundra]

how did we get -4

or -2 x 2

[copper plinth]

(a+b)(a-b)=a²-b²

[livid tundra]

so -2^2?

[copper plinth]

If -(2)^2 means -4

[livid tundra]

no

[copper plinth]

Sry, i didn't understand your question

[livid tundra]

you said it's a^2-b^2

well b^2 = 4

[copper plinth]

Yep

[livid tundra]

so it's her mistake?

[copper plinth]

So 2^2=4

[livid tundra]

she put -4

[copper plinth]

There's no mistake?

[copper plinth]

It's in the formula a²-b² not +b²

[copper plinth]

Here can you tell me what is "a" and what is "b"?

[cedar kiln]

@livid tundra Has your question been resolved?

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[tawny flare]

If Q1 = 44.5 and Q3 = 79.75. Q2 value could be:

A- Between 44.5 - 79.75 inclusively
B- Between 44.5 - 79.75 exclusively

[upper abyss]

I suppose inclusive

[tawny flare]

I thought Q2 can't be equal to Q3 or Q1. Can they?

oh

I didn't mention that the question is about Quartiles

[upper abyss]

If your data set is:
44.5, 79.75

Then Q2 is the same as Q3

[tawny flare]

The question was if Q1 = 44.5 and Q3 = 79.75. The value of Q2 can be:

(44.5, 79.75)
[44.5, 79.75)

So In the range does it include 44.5 and 79.75 or no

With this information, the only thing we can say about median (m)
is that it satisfy: 54.52≤m≤78.86. Found it

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[oblique sky]

i mean f(-1) is obviously 4

but f prime (-1) is a bit weird

i used f(x+h)-f(x)/h

and still got a wrong answer

[uneven crater]

Could you tell me, what does a derivative of a curve indicate

[oblique sky]

the slope

the rate of change

wait i think i can just

y+1=m(x-4)

and then substitute

wihth 2,1

2=m(-2)

[uneven crater]

great you got the answer

[oblique sky]

rise over run

therefore

3/-3=-1

so

2=-1(-2)

so

ok

umm

back to the equatio

(f(x+h)-f(x))/h

[uneven crater]

f'(-1) implies the slope of the curve at x= -1

don't overthink it

you just had to find the slope of the tangent

[oblique sky]

oh...

ok then

y+1=m(x-4)

3=m(-2)

so i need that m value

3/-2

this?

-3/2

wait no

[oblique sky]

wait i got it

already

what am i doing

huh

loool

[uneven crater]

ok, don't worry,
f(-1) = 4 pretty obvious

Then we know when we take a derivative of a function we, get the slope of the function
this new "derived function" is given by f'(x), when we put in values of f(-1), this indicates the slope of the tangent to f(x) at x=-1
Now as given, we know that the tangent passes through (2,1) and intersects the curve at one point which is (-1,4).
Using the slope formula we can find the slope the line passing through (2,1) and (-1,4)
which then happens to be f'(-1)

[cedar kiln]

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Show your work, and if possible, explain where you are stuck.

@crimson sedge Has your question been resolved?

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[median rover]

I need help solving this

[finite lion]

sine = opposite / hypotenuse
cosine = adjacent / hypotenuse
tangent = opposite / adjacent

[robust pagoda]

Just remember, SOH CAH TOA.

[finite lion]

absolute banger catchphrase

[robust pagoda]

OMG TEACHER SAYS SUCK A TOE LOLOLOL

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[tulip pecan]

What do I do with this do I just apply the Summation formula cus I'm going nowhere with that

[vagrant elbow]

I mean if you want an answer just sub in an AP; maybe 1, 2, 3

That makes n = 3

[uneven crater]

Multipy by sqrt(a_r+1) - sqrt(a_r) in the general term

[wraith dagger]

Try_hard

[uneven crater]

New to latex 💀

[wraith dagger]

Try_hard

[cedar kiln]

@tulip pecan Has your question been resolved?

[tulip pecan]

shit I'm so sorry I didn't see this message

[tulip pecan]

I could do that yeah

and I just substitue a1, a2, a3.... with 1, 2, 3 ad nauseam?

I'm not really acquainted with the sigma symbol what does this expression do

[uneven crater]

It denotes the summation eg.

we write the general term, the lower thing set the counter and the upper thing shows till what value do we keep on increasing the value

[tulip pecan]

makes sense ye

[tulip pecan]

So s=1, r=n?

[uneven crater]

give me a minute, I will change the latex thing to make more sense

[tulip pecan]

summon thee ye bot

[uneven crater]

$(\sqrt{a_1} + \sqrt{a_n})\sum_{r=1}^{n-1}{\frac{(\sqrt{a_{r+1}} - \sqrt{a_r})}{(\sqrt{a_{r+1}} + \sqrt{a_r})(\sqrt{a_{r+1}} -\sqrt{a_r})}}$

[wraith dagger]

Try_hard

[uneven crater]

Now, if you don't understand anything you can ask,
the question given was based on Telescopic Sum

[cedar kiln]

@tulip pecan Has your question been resolved?

[tulip pecan]

alrighty then thanks for your time

is it fine if I continue this in DMs though since I'll be outside for a while so I won't be able to solve the question right now but later

[uneven crater]

No, issues

[tulip pecan]

Understandable

[cedar kiln]

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[tulip pecan]

.close

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[fringe canyon]

hi

[fringe canyon]

just need help in this one tan6tan42tan66*tan78

all of them are multiplied

can someone actually do it without trig identities

thanks

[cedar kiln]

@fringe canyon Has your question been resolved?

[vague rapids]

Pretty much you need trig identities

[fringe canyon]

alr can you solve it pls

i guess we are using tana *tan60 -a * tan 60+a

= 3a

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[bold mauve]

For my homework I saw that my teacher did this question different than me. I was wondering if my solution is valid. I attached a picture of their work

[bold mauve]

I used the fact that I know the power series expansion for ln(1+x)

instead of recognizing that ln(1+x) is the derivative of 1/(1+x)

is my final form a "power series representation" ?

[clear berry]

only the odd terms should survive in the end

as the even terms will get cancelled

[bold mauve]

yeah that seems obvious once you say it, I did not recognize it though

[clear berry]

I mean it's almost there

[bold mauve]

My solution is still slightly different than theirs after taking that into consideration

it is missing a factor of 2

$\sum_{n=0}^{\infty}\frac{x^{2n+1}}{2n+1}$

[wraith dagger]

donut

[clear berry]

oh, found it

see whenever n is odd, n-1 is even and so they'll combine to give a 2; where as whenever it is even it would combine to cancel each other

[fringe canyon]

um

it got closed

can i reopen now?

[bold mauve]

i am in it

[clear berry]

nope, get a new channel

[fringe canyon]

ty

[bold mauve]

huh?

[clear berry]

i mean (-1)^{n-1} will give 1 when n is odd and -1 when n is even

do you see that

[bold mauve]

yes

[clear berry]

then $(-1)^{(n-1)} + 1$ is 2 when n is odd and 0 when n is even

[wraith dagger]

numbpy

[bold mauve]

hmm makes sense

thank you very much. i didnt think my form and their form were anyway close to being eachother but some obvious "telescoping" changes that

[clear berry]

sure

[bold mauve]

[clear berry]

it's also generally helpful to expand the series and check few terms

[bold mauve]

.close

[cedar kiln]

Channel closed

Closed by @bold mauve

Use .reopen if this was a mistake.

[fringe canyon]

.reopen

[cedar kiln]

✅

[fringe canyon]

can someone solve tan6.tan42.tan66.tan78

[vagrant elbow]

Hmm

$\tan x \cdot \tan (60^{\circ} + x) \cdot \tan (60^{\circ} - x)$

[wraith dagger]

NEONPerseus

[vagrant elbow]

Do you know what this simplifies to?

[fringe canyon]

yep

i guessed that

3x

right?

[vagrant elbow]

Yes

So multiply and divide by tan 54°

[fringe canyon]

how are you taking it tho

6 and 66

[vagrant elbow]

Taking what?

[fringe canyon]

like the grouping

[vagrant elbow]

x = 6° here

We have 6° and 60° + 6°

We need 60° - 6°

Also I think it would be for the better if you opened your own channel

[fringe canyon]

sorry shall it be tan 18?

[vagrant elbow]

Should what be tan 18°

[fringe canyon]

the multiplication

tan6 * tan54 * tan66 = tan18

we're supposed to find this out

[vagrant elbow]

Yes so multiply and divide by tan 54°

[fringe canyon]

yea

got it

ty

[vagrant elbow]

Alright

Close the channel if you're done

[fringe canyon]

ok so it should be 1

right?

just to verify

.close

[cedar kiln]

Channel closed

Closed by @fringe canyon

Use .reopen if this was a mistake.

Available help channel!

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[static parrot]

Im not too sure about the point at 30.8s

How would I solve for it?

[clear berry]

you the fact that the graph is periodic

notice that the graph repeats after every 4 seconds

[static parrot]

yes

[clear berry]

then take 30.8 modulo 4

[static parrot]

so would I be pinpointing the distance at 7.7s

[clear berry]

huh? how'd get 7.7 sec?

[static parrot]

oh multiply

[clear berry]

mb

[static parrot]

wait misunderstanding

[clear berry]

modulo mean finding the remainder

[static parrot]

oohhh

[clear berry]

technically it wouldn't be called finding the modulo cause the number is not an integer

but it's close enough

basically keep removing 4 till you get something less than 4

[static parrot]

I see

tysm

[clear berry]

and then the answer would be the value at the point

[static parrot]

tyty

[cedar kiln]

@static parrot Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

[vivid shoal]

help

[vivid shoal]

Calculate the general equation of the circunference that across the point (3,-2) and the center is (0,2)

[runic garnet]

Do you want the circumference of the circle or the equation of the circle?

@vivid shoal

[vivid shoal]

the equation

[runic garnet]

Ok what have u tried

[vivid shoal]

i tried with the general equation

but i get incorrect answers

[runic garnet]

Show me ur work

[vivid shoal]

its an exam review :v

[livid hound]

how does that affect whether you can show work

[vivid shoal]

oh ok xd

exam is closed alreadi

[livid hound]

still not showing your work

[vivid shoal]

i copied all the questions i dint understand

[livid hound]

still not showing your work

[vivid shoal]

:v

[livid hound]

is there any reason you can't show what you did

[vivid shoal]

OHHH

ok

[vivid shoal]

well i dont have camera

[livid hound]

write the work out on paint

[vivid shoal]

but i think u was talking about the question

ok

[livid hound]

question and work are clearly different words

and we've already seen the question

[vivid shoal]

im from spanish countri

[runic garnet]

cual

[vivid shoal]

so i dont understand totalli english :v

[runic garnet]

Colombia?

[vivid shoal]

Si

[runic garnet]

a ok

Asi no tienes cámara

Usa la aplicación “paint” en windows

[crimson sedge]

find the radius by calculating dist between 0,2 and 3,-2

then use the equation x-x1^2 + y-y1^2=r^2

where x1, and y1 are cordinate of centers

[vivid shoal]

Ok

[crimson sedge]

stephen can u translate

for me

[vivid shoal]

i understand

[crimson sedge]

oh cool

[runic garnet]

Sabes cómo hacerlo con lo q scop te dio?

[vivid shoal]

usando la formula general para sacar el radio

luego usar la equiacion x-x1^2 + y-y1^2=r^2

[livid hound]

missing ()

[crimson sedge]

dio is give?

[runic garnet]

gave

[crimson sedge]

my linguistic skills finally coing into play

lol

[livid hound]

${\red{(}x-x_1\red{)}}^2 + {\red{(}y-y_1\red{)}}^2 = r^2$

[wraith dagger]

ℝamonov

[runic garnet]

Sip necesitas calcular la distancia entre el centro del círculo al punto (3,-2)

Para el radio

[crimson sedge]

yh as it will be the radius

[vivid shoal]

ok

[runic garnet]

Sabes la fórmula ?

[vivid shoal]

la de a - ab+ b?

[runic garnet]

para la distancia entre dos puntos

[vivid shoal]

no xd

no es la que esta arriba?

[runic garnet]

No

[vivid shoal]

cual es?

[vivid shoal]

ok

[runic garnet]

Es la equacion para círculo

[runic garnet]

Es la equacion para distancia entre 2 puntos

[vivid shoal]

pero lo que busco es la equacion del crculo

no de la distancia

[crimson sedge]

I am picking some apsnsh lol by reading this

[vivid shoal]

apsnsh?

[crimson sedge]

spanish

[vivid shoal]

XDDDD

[runic garnet]

Sip, pero para calcular el radio, necesitamos calcular la distance del centro al (3,-2)

[vivid shoal]

ok

[runic garnet]

Y necesitamos el radio pa la equacion de círculo

[crimson sedge]

where center is at 0,2

[runic garnet]

Tas bien? La puedes calcular? @vivid shoal

[vivid shoal]

eos hago

(-2-2)=-4?

[crimson sedge]

si

[vivid shoal]

el radio es 5

[crimson sedge]

si

radius is 5

[vivid shoal]

C:

finalmente entiendo algo de este jodido tema :v

[runic garnet]

jaja

Te mejorarás con practica

[vivid shoal]

ok

[runic garnet]

Así tienes el radio

[vivid shoal]

ahora toca la general no?

[runic garnet]

Así ahora usa la fórmula

[runic garnet]

Aquí

[crimson sedge]

If u want to learn cordinate geometry you can purchse cengage publlication

of cordinate geometry

[vivid shoal]

tratare

remplazo solo los valores de h k?

o remplazo tambien x i?

[crimson sedge]

x1 is x cordinate of center

y1 is y cordinate of center

[runic garnet]

Aquí?

Reemplazas x_1, y_1 y r

[vivid shoal]

ok

son h k xd

[runic garnet]

Sip

[vivid shoal]

como pongo el simbolo de elevado?

[runic garnet]

Elevado?

[vivid shoal]

osea potencia

2 a la 2 por ejemplo :v

o 2 elevado a la 2

[runic garnet]

2 a la 2 es 4

2 * 2

[vivid shoal]

si io se xd

[crimson sedge]

my face whn

[vivid shoal]

no ese es el simbolo de multiplicacion :v

io hablo de que es como la v pero hacia arriba