help-10

[oblique zodiac]

!rotate

Yep

[stone radish]

so which part are you stuck on?

[oblique zodiac]

Got a 1 in my test💀

Like i only know that there are n+1 terms in a , and i thought d’s ans would be c(n+1,r)-C(n,r)=C(n,r-1) but teacher marked it wrong and b, c and e i dont know how to find the ans/solutions

@stone radish (sorry for pinging) U there?

[stone radish]

oh yeah I forgot this im sorry

[oblique zodiac]

Oh ok no worries

[stone radish]

so you need help with b c and e

[oblique zodiac]

Yh

And kinda need to verify ans of d too

[stone radish]

so what is binomial coefficient?

[oblique zodiac]

I don’t know thats why im here

[stone radish]

oh

its nCr

[oblique zodiac]

Oh ok

[stone radish]

yes

alright

${n\choose r} = \frac{n!}{r!(n-1)!}$

uh

[warm shale]

Wither

[stone radish]

yes

[stone radish]

yeah

[stone radish]

here this would be the binomial coefficient

the general one

[oblique zodiac]

Oh ok

[stone radish]

where 0=<r<n

r goes from 0 to n

[oblique zodiac]

Oh yeah

[stone radish]

general term now

is the

the r-value for the term is one less than the number of the terms (n in this case)

[oblique zodiac]

Is it (r+1) th term??

[stone radish]

no no

oh wait yeah

mb

it is indeed the (r+1)th term

[oblique zodiac]

Yh yh

[stone radish]

$T_{r+1} = {n\choose r} a^{n-r} b^r$

[warm shale]

Wither

[oblique zodiac]

Yep

[stone radish]

so were done with c as well

now the d part

do it using this formula

[stone radish]

this one

[oblique zodiac]

So in d,
Do i replace the a and the x with 1 or ?? (a+x)^n

Im lost

[stone radish]

d or e?

[oblique zodiac]

Oh i was doing e mb

[stone radish]

you've done d correctly in the solution

[oblique zodiac]

Yh my teacher, malai tha bhayena what he did before checking papers

[stone radish]

a = x = 1

[oblique zodiac]

Anyways so in e,
Is it 2^n?

[stone radish]

yeah

and $2^n$ is the general term of a geometric sequence

[warm shale]

Wither

[oblique zodiac]

Alright

Thanks bro

Thanks a lot

[stone radish]

no problem

[oblique zodiac]

How do i close the channel?

[stone radish]

!done

[obtuse pebble]

If you are done with this channel, please mark your problem as solved by typing .close

[oblique zodiac]

.close

[obtuse pebble]

Channel closed

Closed by @oblique zodiac

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.

[merry jetty]

how do i progress in calculus

[merry jetty]

ik basic derivatives and basic integration

are there any books any1 could recommend?

[versed stratus]

A problem Book in mathematical analysis

IA Maron is also good

#book-recommendations might be a better place for such questions

[obtuse pebble]

@merry jetty Has your question been resolved?

Channel closed

Closed by @merry jetty

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.

[half eagle]

I need help :c

[half eagle]

I don't know which one I did was right

b) says "What's a in order for vector x to be vertical on (3 | 1 | 2)

Somehow I used 4 different methods and now am more confused

Im a math noob btw

[cunning burrow]

I think a vector x-bar to be scaled version of vector [3, 1, 2]^T

[obtuse pebble]

@half eagle Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

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.

[lament heart]

I need help with b guys😔

[upbeat lagoon]

you can divide a by 1/a

the two cosines will cancel with each other

leaving sin on both the denominator and enumerator

decompose the fraction

and like this you can find sin in terms of a

and then find cosine in terms of sin

which is already in terms of a

$\frac{a}{\frac{1}{a}} = a^2 = \frac{\frac{1-\sin\theta}{2\cos\theta}}{\frac{2(1+\sin\theta)}{\cos\theta}}$

[warm shale]

mino

[lament heart]

Ohhh ok

Thanks🙏

I’ll try it out

[obtuse pebble]

@lament heart Has your question been resolved?

Channel closed

Closed by @lament heart

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.

[sinful zinc]

i had assumed this was equilateral but it isnt. I thought that two tangent lines should be congruent but im confused. I believe the blue arrow should mean something but i am unaware. btw im studying to do a geometry cbe (exam to skip)

[sinful zinc]

does that rule always apply?

so basically adjacent segments are congruent

ty

.close

[obtuse pebble]

Channel closed

Closed by @sinful zinc

Use .reopen if this was a mistake.

[sinful zinc]

.reopen

[obtuse pebble]

✅

[sinful zinc]

whats the rule for quadrilaterals around a circle

[sinful zinc]

wait does this just apply to every figure?

alr im good now ty

.close

[obtuse pebble]

Channel closed

Closed by @sinful zinc

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.

[lofty field]

in a ucm of a ball tied to a string under the effect of gravity if the velocity at bottom-most point is root 140 m/s how do we find tension in string

[lofty field]

<@&286206848099549185>

[merry peak]

!15m

[obtuse pebble]

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

[alpine verge]

well you can’t really calculate that without the mass of the object

but regardless we can write out newton’s second law

[lofty field]

if mass is 2kg and radius of ucm is 2m then ?

[alpine verge]

alright so write out newton’s second law

what forces are acting on the object

when it’s at the bottom

[lofty field]

tension and mg

[alpine verge]

yep

and they are pointing?

[lofty field]

tension upwards mg downwards

[alpine verge]

yep

and since this is uniform circular motion

we really have the vector sum of these two forces as the centripetal force

[lofty field]

oh t - mg = mv^2/r ?

[alpine verge]

yep

[lofty field]

got it i was equating t - mg = ma my bad

[alpine verge]

ah

it’s all good

[lofty field]

thanks for ur help my friend

[alpine verge]

it isn’t wrong, it’s just that a can be broken down even more

yw!

[lofty field]

.close

[obtuse pebble]

Channel closed

Closed by @lofty field

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.

[solid lodge]

Hey I need help with a combinations question. Please use pascals method but if that’s difficult then your own way would be appreciated.

[tired shell]

pascal's method is when for each point you add the numbers before it, and you sort of build up the whole grid going step 1 step 2 step 3 ...

the direction is going from A to B so start with 1's along everything next to A, then add up the numbers for the points 2 steps away from A, and keep going

it's a little weird visually but as long as you're going down, right, or into the page you're good

[brazen viper]

Shouldn't the corners also be 1?

[tired shell]

oops yea

red is step 1, green is step 2

[solid lodge]

And then total number is the answer?

[tired shell]

yea the number you get at B at the end is the answer

[solid lodge]

But would not there be like more numbers since it’s 3-D?

[tired shell]

there's more branching but there's only a 3d depth of one so it's not so bad

[solid lodge]

So after I get one branch and then the second should I add them for the final answer?

Or should I just multiply the first branch by 2?

[tired shell]

um for each point you add the numbers before it

and only write something in if all the points before them have a number written

[solid lodge]

I got 54 is that right?

I’m not really used to pascals method so is there another way I could do this?

[tired shell]

I believe it's 30

[solid lodge]

Maybe the binomial theorem? But I don’t know if it’ll work with this

[tired shell]

yea it's a harder version of binomial theorem, it'd be the multinomial (5 choose (1,2,2))

[solid lodge]

I’m only in grade 12 I don’t know allat 😭

[tired shell]

the idea is there's 5 steps you make and it's the set {down,down,right,right,in} so you have to count how many rearrangements of that there are

it's like the problem how many words can you rearrange from AABBC

[solid lodge]

I’ve never learned of it before I’m just gonna try the pascals method again and see if I get 30

[tired shell]

5!/2!/2! because you can swap the A's and B's

ok

[solid lodge]

I’m sorry I don’t understand can you just send a pic before with the numbers?

Srry for troubling u

[solid lodge]

HAVE A GREAT DAY!!!

[obtuse pebble]

@solid lodge Has your question been resolved?

[obtuse pebble]

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.

[dark idol]

Is this correct derivative for g?

I don’t see how to simplify

[teal turret]

are u familiar with logarithmic differntiation

@dark idol

itll prolly be so much easier to simplify than that

[dark idol]

But there’s no log

[teal turret]

are u familiar with the concept? when you take the log of both sides, and then differentiate both sides

complexity is greatly reduced by the utilization of logarithmic properties

[dark idol]

Yeah kinda

[dark idol]

It gives me same answer right?

[teal turret]

gives an equivalent answer

yes

[dark idol]

I just watched a video about it again real quick. Why is deriv of lny =1/y dydx?

How get 1/y

[teal turret]

i mean, the derivative of ln(x) = 1/x, derivative of ln(2x) = 2 * 1/(2x)

idrk what ur asking

[dark idol]

Nvm I remembered the equation

So how do I find the deriv of the right?

@teal turret

What rule

[teal turret]

when u take ln of both sides

u have to do the entire side

not the individual numerator and denominator

$0.5\ln \left[{\frac {s^2 + 1}{s^2 + 4}}\right]$

[dark idol]

What about the exponent then

[warm shale]

Stephen

[teal turret]

there we go

thats the right side

now we apply log rules

what do we do @dark idol

[dark idol]

1/2 to the front

?

[dark idol]

@teal turret

[teal turret]

yes

0.5 to the front

then we can separate even more

what else can we do

[dark idol]

Idk

Quotient rule?

[teal turret]

yep, we can do this quotient rule

the log quotient rule

$\ln y = 0.5\ln(s^2 + 1) - 0.5\ln(s^2 + 4)$

use the log quotient rule on this

[dark idol]

1/2 times ln(s^2+1)-ln(s^2+4)

[teal turret]

yep

[warm shale]

Stephen

[teal turret]

now differentiate both sides

[dark idol]

I thought the 1/2 is only supposed to go on one of the equation

[teal turret]

the 0.5 is on the original ln

thus it distributes to every term that the ln turns into

[dark idol]

This?

@teal turret

[teal turret]

yes

keep going

wait

how did u get ln again

there shouldnt be any ln

[dark idol]

Does the 1/2 also disappear?

Like deriv to 0

[teal turret]

no, because it is being multiplied to the term, not added to it

[dark idol]

Ok so it’s just that without on

What after

[teal turret]

show me what u get

on both sides

[teal turret]

yes

remember on the other side u have y' / y

so u have to bring the y over

[dark idol]

1/y dydyx

So I times both sides by y?

[teal turret]

yes

[dark idol]

Ok so dydx=my current equation times The original question?

@teal turret

[teal turret]

yes

[dark idol]

Is that final answer

[teal turret]

see if u can simplify a bit, then u should have the final answer

[dark idol]

Does this only work for sqrt problems?

[teal turret]

works for any

[dark idol]

@teal turret do u know these

The continuous ones

[obtuse pebble]

@dark idol Has your question been resolved?

[obtuse pebble]

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.

[stray timber]

bruh

[daring temple]

lmao

[restive night]

@everyone I love meth!

*math

[obtuse pebble]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[daring temple]

.close

[restive night]

@everyone shut up nerdz

[odd magnet]

dealt with

[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.

[tawdry phoenix]

Hey can somebody recommend me a math calculator which can calculate linear congruence and writes down each step, step by step?

[tawdry phoenix]

i would be fine with somebody teaching me it too tho xd

I am a dum dum so if anybody takes on this challenge be prepared

[brave bramble]

I don't know what "linear congruence" is offhand. Does it relate to anything more common?

[tawdry phoenix]

well when you have something like this 10x≡25(mod35) and the teacher says solve it

i think this is a linear congruence

[marsh birch]

I made a python code for that lmao

So for what values of x is 10x something of the form 35y + 25

[tawdry phoenix]

yea

[marsh birch]

So to do this you can first solve for the inverse

Then just multiply it by 25

[tawdry phoenix]

does that mean for every 10x's you get the value of 25+35y(35y is the remainder)

did i just literally type out the same shit?

[marsh birch]

25 is the remainder

[tawdry phoenix]

oh

[marsh birch]

since 35y = 0 mod 35 for all values of y

[tawdry phoenix]

what is the inverse?

[marsh birch]

(y being in the set of integers and so on)

[marsh birch]

The value of x for which 10x = 1 mod 35

[tawdry phoenix]

i swear to god i am acustic or something

i am seeing what you type

[marsh birch]

You learned euler's theorem yet

[tawdry phoenix]

i don't get it

[marsh birch]

or method I forgot

[tawdry phoenix]

i have not

[marsh birch]

so 10x - 1 is divisible by 35

and 1 is the remainder if you divide 10x by 35

[tawdry phoenix]

i was supposed to but failed calculus 1 last term

[marsh birch]

💀

So

Euler's method? goes like this

35 = 3*10 + 5

Then you get the last two terms and do it again

10 = 2 * 5 + 0

And you keep doing it until the last term is 0

Then you get the second last equation

move the thing to the side and get

5 = 35 - 3*10

[tawdry phoenix]

isn't this the euclidean algorithm?

[marsh birch]

yes

[tawdry phoenix]

if so i do know that one

[marsh birch]

I am bad with names

[tawdry phoenix]

no problem

[brave bramble]

This is really worth pausing on. The inverse here is very important. Make sure to understand what it is, before understanding how to find it

[tawdry phoenix]

im having trouble understanding what an inverse really is

[brave bramble]

I don't believe one exists here though, because 10 and 35 are not coprime

[marsh birch]

Oh wait you're right

The last term should have had a 1 somewhere

So you can do it for 5 and 7 and multiply by 2 later on

[tawdry phoenix]

so first you look out to see if the gcd exist and then do something with it... right?

[marsh birch]

7 = 1*5 + 2

5 = 2*2 + 1

2 = 2*1 + 0

=> 1 = 5 - 2*2

= 5 - 2*(7-5)

= 5 - 2x7 + 2x5 = 3x5 - 2x7

So 1 can be written as 3x5 - 2x7, which is 15-14=1

Here, -2x7 is 0 mod 7 so we can ignore it, giving us the inverse of 5 mod 7, which is 3

Wait I did this wrong again

[tawdry phoenix]

i do know the last answer im taking a test and it will probably be on it honestly i don't see myself wanting to study this but also if there's no solution to do this without studying ill have to study then 😦

im studying computer science and i have to study things like this for no reason xd

[marsh birch]

You could just do it by hand tbh

[tawdry phoenix]

by hand?

[marsh birch]

when x = 1, 10x = 10

which is 10 mod 35

when x = 2, 10x = 20 triple dash 20 mod 35

when x = 3, 10x = 30, 30 is 30 mod 35

x = 4, 10x = 40, 40 is 5 mod 35

x = 5, 10x = 50, 50 is 15 mod 35

x = 6, 10x = 60, 60 is 25 mod 35

bingo

[tawdry phoenix]

what am i missing

[marsh birch]

a mod b is basically the remainder of a divided by b

so 60 / 35 = 1 remainder 25

[tawdry phoenix]

oksay

well i write it down on a paper

maybe that will help

[marsh birch]

Still, there should be an inverse since 10 < 35 right

coprime only matters if we're comparing different modulos

[tawdry phoenix]

what is an inverse? xddd

please could you explain it xd?

[marsh birch]

x for which ax = 1(mod p)

[tawdry phoenix]

like explain it like you would for a 5 year old

[marsh birch]

so

[tawdry phoenix]

or like an 8. grader

[marsh birch]

let's take 4 modulo 5

This just means if you divide a number by five, you get four left over

the inverse means that there's a number which you can multiply the original number by

and get one left over

so idk let's say the inverse is 4 again

[tawdry phoenix]

isn't it the opposite like something divided by 4 has the remainder of 5?

[marsh birch]

four times four is sixteen

[marsh birch]

4 (mod 5)

sixteen divided by five is three remainder one

wait so 10x = 1 (mod 35) I need to solve this

oh wait the other person was right it's unsolvable

[tawdry phoenix]

fr?

[tawdry phoenix]

but why are you calculating 10x = 1 instead of 10x = 25?

like 10x = 25 (mod 35)

[marsh birch]

I can just multiply x by 25 and get the other x

[brave bramble]

If we know an inverse to a number, we can "divide" that number any time we want.

By "divide", I mean "remove by multiplying by the inverse"

[marsh birch]

So yeah euclidian algorithm depends on the two numbers being coprime huh

[brave bramble]

Finding an inverse rocks, and you should definitely know how to do it for some questions. But yeah it won't help us here

[marsh birch]

I was probably thinking about the chinese remainder theorem there

[tawdry phoenix]

ill need to know that as well so that's going to be for another time xd

my friend sent me this

(10,25) = 5 and 5 | 35
so we can divide by 5
2x=5 mod 7

[brave bramble]

Beat me to it lol

With that division in mind, finding an inverse is now relevant

[marsh birch]

Yeah for that you could use euclidian

[tawdry phoenix]

i don't really get how we got here tho

[marsh birch]

gcd(10, 25) you mean?

[tawdry phoenix]

or why it helps to simplify it by 5

[tawdry phoenix]

nah i know how to do gcd but why is it better?

[marsh birch]

Because then the numbers are coprime

Or the gcd between them is 1

which means now you can use the euclidian algorithm to find the inverse

[tawdry phoenix]

you can only use the euclidian algorithm on coprime numbers?

[marsh birch]

Apparently so yea

[tawdry phoenix]

what does that mean? like what does that mess up?

[brave bramble]

To be clear, we would like to find the inverse of 2 in (mod 7)

[marsh birch]

so the greatest common denominator is 1 that means

and you can't divide both of them with another number without getting a fraction somewhere

[brave bramble]

Once we have that, we can remove 2 from an equation by "dividing it away".

[marsh birch]

And then with the euclidian algorithm you can express 1 as a sum of a multiple of a and a multiple of m

where ax is 1 (mod m)

since all multiples of m are 0 (mod m) or they divide cleanly by m without any remainders you can discard it

So you get a number which becomes 1 (mod m) if you multiply it with a

which is the inverse

[obtuse pebble]

@tawdry phoenix Has your question been resolved?

[tawdry phoenix]

you know what

fuck it i'll watch some indian dude solve this you guys can go sleep 😄

[obtuse pebble]

Channel closed

Closed by @tawdry phoenix

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.

[sterile dagger]

my ti84's battery is dead and i also have no clue what to do, this involves newton's law of cooling, i'm taking precalculus

[obtuse pebble]

@sterile dagger Has your question been resolved?

[obtuse pebble]

@sterile dagger Has your question been resolved?

[obtuse pebble]

@sterile dagger Has your question been resolved?

Channel closed

Closed by @sterile dagger

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.

[fringe portal]

Hi, I have a fraction and I'm trying to use partial fractions

[fringe portal]

Is this the correct form?

[gilded needle]

the thing between (z-1/2) and z^2 in the numerator, is that just scratched out?

[obtuse pebble]

@fringe portal Has your question been resolved?

[fringe portal]

Oh that's scratched out

so it's just (z-1/2)z^2

[gilded needle]

ok

notice that if you cross multiply the RHS (ie put it over a common denominator), the degree of the numerator will be at most 2

whereas on the LHS the degree of the numerator is 3

so no, that won't work in general

[fringe portal]

Got it, so I'll have to adjust it so that the cross multiplication gives a numerator of deg 3?

[gilded needle]

you can do polynomial division on the LHS

that will give you a polynomial plus a remainder, where the remainder is the quotient of two polynomials and the numerator has smaller degree than the denominator

[fringe portal]

Ohh okay, can I instead change the numerator of the second term on the RHS to be Bz^2 + Cz + D?

to give deg = 2 for the cross multiplication

3*

[obtuse pebble]

Channel closed

Closed due to timeout

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.

[arctic belfry]

does anyone know how the power series look like this... and would my answer be considered wrong?

[red ice]

This is correct but the answer has it all in one summation, cause it's neater that way

[red ice]

They did a trick which was $\frac{x - 1}{x + 2} = \frac{x + 2 - 3}{x + 2} = 1 - \frac{3/2}{1 - (-x/2)}$

[warm shale]

south

[arctic belfry]

hmm i see. ill try that method out.

[red ice]

Cool

[arctic belfry]

So I got up to here, what would be the next step

[red ice]

Then just use the geometric series formula

On 1/(1 - (-x/2))

[arctic belfry]

what would i do with the 1 and the 3/2

[red ice]

Just leave them as they are

It's fine when the sum gets multiplied by a constant or added to a constant

It's weird when you multiply a sum by something that isn't a constant tho

[red ice]

Yeah and that answer would also work

[arctic belfry]

hmmm... is there a way to simplify further (to the book answer)

[red ice]

So if you take a 3/2 out, you get $-\frac{1}{2} - \frac{3}{2} \sum_{n = 1}^{\infty} \frac{(-1)^n x^n}{2^n}$

And if you subtract the n = 0 in the summation and add the n = 0 term outside the summation

[warm shale]

south

[red ice]

Something's not quite adding up

[arctic belfry]

wait how did it change to -1/2

and n=1 😭

[red ice]

No I'm working from the book's answer

And trying to get to yours

Oh right of course

Then when n = 0, you just have (-1)^0 x^0 / 2^0 = 1

So you subtracted -3/2 * 1 = -3/2

Now you have to add 3/2 back so that you're adding 0 and not changing the expression

-1/2 + 3/2 = 1

That adds up now

[arctic belfry]

hmm could you possibly visually show that... i dont quite understnad

[red ice]

https://www.youtube.com/watch?v=OCGL0w1kjqU

We're changing the index in the summation

So the sum from x = 1 to infinity

Is the same as the sum from x = 0 to infinity minus the sum from x = 0 to x = 0

Or the sum from x = 0 to infinity, minus the number you get when you have x = 0

I mean n instead of x

[obtuse pebble]

@arctic belfry Has your question been resolved?

Channel closed

Closed by @arctic belfry

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.

[grizzled shore]

just a clarification on level curves and lagrange multipliers:

[grizzled shore]

in the 2d case, can i imagine it as like i have some f(x, y) surface, and some g(x, y) - c = 0 curve on the x-y plane

now i take this curve, and lay it on top of my surface

then the min and max on my surface, restricted to this curve, will meet at a tangent point, where 1 curve is the g(x, y) - c = 0 shape, and 1 is the level curve of f(x, y) = c?

sorta like this?

[grizzled shore]

wait we shoildn't have f(x, y) = c

the c just controls what the shape of purple is by controlling which level set of g we consider

[obtuse pebble]

@grizzled shore Has your question been resolved?

[obtuse pebble]

@grizzled shore Has your question been resolved?

[obtuse pebble]

@grizzled shore Has your question been resolved?

[obtuse pebble]

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.

[abstract inlet]

Can someone please help me with the 60th question

[abstract inlet]

I have no Idea how do I solve it

[foggy furnace]

Do you understand how to do it if the right side of the equation's 'log base 6/7)' turned into log base 7? I'm certain there's a way to change the base of the log using some formula.

I just don't know the formula off the top of my head

could be related to change of base theorem but not certain how if so

[obtuse pebble]

@abstract inlet Has your question been resolved?

[abstract inlet]

Nope, its not based on change of base theorem, I have already tried that

[marsh geyser]

You don’t need to solve the equation

You have to understand how the RHS is working

If x>0 then x+7/x>2, so what happen to that log in base 6/7?

The base of the log is between 0 and 1

@abstract inlet

[obtuse pebble]

@abstract inlet Has your question been resolved?

[abstract inlet]

Ohhh, yea understood, thank you

@marsh geyser but won't it be 2root(7) instead of > 2?

[marsh geyser]

Yes, that is the minimum

Just giving u a hint

So then, what happens

[abstract inlet]

And there's one more question I wanted to ask, Can I?

[abstract inlet]

Yea I understood, LHS is > 1 and RHS < 0 so no solution

[marsh geyser]

Good

[abstract inlet]

Can you please help me with 47 too, I have solved it but I am not sure if it's correct

This is what I have done

Here I got a solution for t when it's < 2, and then since log is strictly decreasing, there's only one solution, so I haven't checked for t>2

I did not check for t > 2 as I found it a bit hard and I wasn't able to solve it

@marsh geyser

.close

[obtuse pebble]

Channel closed

Closed by @abstract inlet

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.

[wintry abyss]

Both limits are coming 0

What’s wrong

Pls help, ping me

The answer is pi/2 but I’m getting 0 however I try

[cunning mist]

wow

[wintry abyss]

What happen buddy

[cunning mist]

nothing

just impressed

[wintry abyss]

By what

<@&286206848099549185>

[wraith wing]

I think you have to change the bounds after u sub

[wintry abyss]

That’s what

Both are coming 0

[errant lark]

tan(pi/2) goes to infinity so it's an improper integral.

You need to break it about pi/2.

Write it as sum of two improper integrals.

[wintry abyss]

Ohh what’s that

So I can’t do it without breaking?

+close

.close

[obtuse pebble]

Channel closed

Closed by @wintry abyss

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.

[graceful marten]

Wadda C mean

What could it represent

Cause i used it as k, and then it got me confused, when i had to show k (its more of an understanidng thing for me ykyk)

[timid silo]

Hey I was just wondering if someone could run this through with me and explain the formula

[graceful marten]

cause I used it as K

[timid silo]

Oops

[graceful marten]

nw

[timid silo]

Mb wrong channel

[zenith raft]

:3

[timid silo]

I forgot there’s specific channels here

[zenith raft]

wtf

nice message delete

[graceful marten]

i dont want to be lumped into the same category as u

:3

[zenith raft]

unbelievable

[graceful marten]

increíble

btw, a friend told me the word succulent is a

kinky spanish word

i couldnt figure out what it is :/

wait ur not spanish

wrong person

forget it

back to work

[zenith raft]

[graceful marten]

AAAAAAAAAAAAAAAAA

nvm

ill ask another time

i need to eat

.close

[obtuse pebble]

Channel closed

Closed by @graceful marten

Use .reopen if this was a mistake.

[zenith raft]

sorry for terrible drawing

hard on phone

c is a number

[graceful marten]

wat numba

starting numba of water?

[zenith raft]

just a number

[graceful marten]

oh :<

+C constant bc of integration?

Or just numba

[zenith raft]

no not like that

[graceful marten]

okok

.reopen

[obtuse pebble]

✅

[zenith raft]

there is some constant c for which dV/dt = -cV^(1/3)

you don’t know what it is

[graceful marten]

right yeah

Water out is proportional to cube root (Volume)

which is

• water = -K Cuberoot (volume)

yeah ok ok i got it then

ty

.close

[obtuse pebble]

Channel closed

Closed by @graceful marten

Use .reopen if this was a mistake.

[zenith raft]

[graceful marten]

have a goodddd day

[zenith raft]

i won’t

[graceful marten]

good night?

[zenith raft]

no

[graceful marten]

https://tenor.com/view/goth-girl-goth-girl-green-hair-goth-girl-kiss-its-deitsel-carlo-malis-gif-25978600

.close

.close

.close

run

[graceful marten]

https://media.discordapp.net/attachments/782492147713572878/865482024100691998/4552-sus-dance.gif

[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.

[onyx gyro]

Find $b$ in terms of $a$ if $\lg(a) + \lg(2b) = \lg(2a - b)$.

[warm shale]

☆ Kojo Bailey

[onyx gyro]

really not sure what to do here

The most I've done so far is

$lg(2ab) = lg(2a - b)$

[spare gale]

You know the multiplication proper of log?

[warm shale]

☆ Kojo Bailey

[spare gale]

Yes now after that?

[onyx gyro]

hrm...

what i did was

[spare gale]

think..

[onyx gyro]

$\lg(2a) + \lg(b) = \lg(2a - b)$

[warm shale]

☆ Kojo Bailey

[onyx gyro]

but idk if that's in the right direction

[spare gale]

hint:- you can cancel ln on both sides

[spare gale]

That takes you to question

Or from where you've started

@onyx gyro ?

[onyx gyro]

thinking... but not getting anywhere yet

[onyx gyro]

what do you mean by this?

[spare gale]

Can you cancel log from both sides?

[onyx gyro]

not that i can see

[spare gale]

I mean the base is the same, so that means the argument is also the same right?

Like log a base b = log c base b

Then a = c

[onyx gyro]

don't think so...

[quick ferry]

yo how do i close a channel

[onyx gyro]

that'd be like saying

$\lg(2) = \lg(5)$

[warm shale]

☆ Kojo Bailey

[onyx gyro]

no?

[onyx gyro]

you type .close in that channel

so rn i have

$\log_{10}(2ab) = \log_{10}(2a-b)$

[warm shale]

☆ Kojo Bailey

[onyx gyro]

oh!

[quick ferry]

i typed that but it didnt kick me out the channel

[onyx gyro]

i see what you mean now @spare gale

[onyx gyro]

it takes a few minutes

[quick ferry]

alr, thanks man

[onyx gyro]

alr it seems like

$b = \frac{2a}{2a+1}$

[warm shale]

☆ Kojo Bailey

[onyx gyro]

from

if this looks wrong to anyone, please lmk

otherwise

.close

[obtuse pebble]

Channel closed

Closed by @onyx gyro

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.

[cunning needle]

i couldnt understand this question so i dont really have a way of solving it i hope someone can help me, and thank you

[glossy basalt]

first hint: 5 times 2 = 10

so that you can find some relation between x and y

[cunning needle]

i still dont get it sry

[glossy basalt]

no worries, 2^y=5, try times 2 on both sides

[cunning needle]

2^x=20 ,2^y=10 ?

[glossy basalt]

nah

consider 2^x=10
we multiply 2 on both sides on this equation 2^y=5
we got 2•2^y=2•5

and hence we have
2^(y+1)=10

[cunning needle]

and also 2^(x+1)=20?

then?

[glossy basalt]

nope

[glossy basalt]

we have 2^(y+1)=10=2^x

[cunning needle]

ohh

ok

so x= 2y

[glossy basalt]

nope

x=y+1

[cunning needle]

oh i see

but how we solve for value?

[glossy basalt]

let's say for A
x-y

we will have A=1

[cunning needle]

why?

oh

ok i get it now

nvm complete pls

[glossy basalt]

sorry, no signal just now

A=x-y

since x=y+1

[cunning needle]

its fine

[glossy basalt]

we have A=y+1-y

which is 1

Next, for B, we need to somehow know what's √(x+y)

now
2^y=5

and 5 is between 4 and 8

therefore we know that y is between 2 and 3

and x will be between 3 and 4

can you continue from here?

[cunning needle]

so its √6

and x-y=1

[glossy basalt]

yea, it's around √6

[cunning needle]

ok thank you so much for your help

!close

[glossy basalt]

it's .close

[cunning needle]

.close

[obtuse pebble]

Channel closed

Closed by @cunning needle

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.

[little helm]

Let ABC be an equilateral triangle inscribed in the circle (O) and M be a point of the small arc BC.

[obtuse pebble]

@little helm Has your question been resolved?

[obtuse pebble]

@little helm Has your question been resolved?

[obtuse pebble]

@little helm Has your question been resolved?

Channel closed

Closed by @little helm

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.

[neon orchid]

Hello I need help in study of functions, got lost in doing axis intercept because I don't know how to solve fractional quadratic equations

[neon orchid]

I copied what my professor was doing but got lost as he was doing axis intercept

also don't know how to do limits

[obtuse pebble]

@neon orchid Has your question been resolved?

[neon orchid]

.close

[obtuse pebble]

Channel closed

Closed by @neon orchid

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.

[copper vault]

how would you create a regex for this language?

[copper vault]

its the same as {a,b}* \ {ab}*

[obtuse pebble]

@copper vault Has your question been resolved?

[obtuse pebble]

@copper vault Has your question been resolved?

[obtuse pebble]

@copper vault Has your question been resolved?

[obtuse pebble]

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.

[glass dagger]

Why can the independent sets contain a non-empty set

[glass dagger]

because just from L1, L3 doesn't seem to do much because you only have one set

and L2 concerns subsets, and the only subset of the empty set is the empty set itself

lol sorry I just realized how stupid my question was, the independent sets can certainly only contain the empty set and that forms a valid matroid but it's not a terribly interesting one

.close

[obtuse pebble]

Channel closed

Closed by @glass dagger

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.

[sinful crescent]

Hello, I'm feeling a bit lost with this exercise:

Let $\alpha\in[0,\pi/2]$, $t\in\mathbb{R}$, and let $y^2=tx$ be a parabola. Find all points $P$ in the plane such that there exist exactly two tangent lines to the parabola passing through $P$, and the acute angle formed between these two lines is $\alpha$.

Can anybody help me with this?

[warm shale]

Gkn

[obtuse pebble]

@sinful crescent Has your question been resolved?

[sinful crescent]

.close

[obtuse pebble]

Channel closed

Closed by @sinful crescent

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.

[mint anvil]

Hi community,
For an arbitrary triangle, I know its side length & area
Is there a way to find the cotangent of the angles directly?

[eager niche]

One or all side lengths?

[mint anvil]

All. I actually just figured it out. Thanks for your help!

[obtuse pebble]

@mint anvil Has your question been resolved?

[obtuse pebble]

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.

[real juniper]

I am doing Calc 2, we are doing sequences and series. I am a little confused by what this question is asking. I thought it was just asking the term definitions but I feel like it is specific to this problem listed.

I chose A and B, but I am 40% sure, so not so sure. Could anyone clarify / confirm?

TIA!

[brave bramble]

S doesn't converge, so C,D,E are out

[obtuse pebble]

@real juniper Has your question been resolved?

[real juniper]

That's what I thought, thank you @brave bramble 🙂

I am just not sure if A is true or not.

[brave bramble]

A is true. It's just weird to mention something so general here.

[real juniper]

Ah, thank you for the help, @brave bramble! I agree, that's why it had me puzzled.

.close

[obtuse pebble]

Channel closed

Closed by @real juniper

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.

[opal swallow]

hi

[opal swallow]

i found variance this way

but i can’t get the answer

the rest of the working is the same

[obtuse pebble]

@opal swallow Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

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.

[fierce elbow]

What is an odd function or an even function

[fierce elbow]

We had the question in yesterdays test

but I dont remember it getting taught

[gilded needle]

did you google it?

[stone radish]

if f(-x) = -f(x) then the function is odd
if f(-x) = f(x) then the function is even

[obtuse pebble]

@fierce elbow Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

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.

[exotic palm]

im confused as to how the left side of the equation changes to zero

is it just algebra?

[ember frost]

yes

they brought whole lhs to rhs

[exotic palm]

oh

lmaoo

i didnt think of that

thanks

.close

[obtuse pebble]

Channel closed

Closed by @exotic palm

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.

[quiet rapids]

could anybody assist me i have been stuck for 3 hours

[tawny willow]

.close

[quiet rapids]

no i’m here

<@&286206848099549185> pls¥¥¥

[dire heart]

Helpers needs help too sometimes ☺️

[obtuse pebble]

@quiet rapids Has your question been resolved?

[obtuse pebble]

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.

[graceful marten]

Part C,
I dont understand how its 160....

isnt e ^ 0, 1, so 1x 4840 + 160....

[safe haven]

t is approaching infinity, not 0

-t/4 as t approaches infinity is negative infinity, e^(negative infinity) approaches 0

[graceful marten]

hmm

If the question was, what is its maximum value of V, according to the model

Would it be 4840 + 160 = 5000

[graceful marten]

OHHH I see!!!!!

thank you :3

[green epoch]

im late

[graceful marten]

u r?

WHY u LATE

[low rain]

[graceful marten]

wat?

Its easy no?

5000?

[polar fossil]

yes (assuming t ≥ 0

[graceful marten]

Ok 😄

.close

[obtuse pebble]

Channel closed

Closed by @graceful marten

Use .reopen if this was a mistake.

[graceful marten]

ty ty math fanatics

https://tenor.com/view/squidward-squidward-tentacles-spongebob-look-around-awkward-gif-496727432057798195

[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.

[unborn bobcat]

Hey, I'm trying to create a short probability game with these events.. However my calculations for the theoretical probabilities of all outcomes do not add up to 100%, I'm struggling to find my error, any help would be greatly appreciated.

[unborn bobcat]

(Just to translate the lower portion. HRB/BRW stands for Heads, Red & Black/ Black & Red, Win)

[polar fossil]

RB and BR are different events, you need to count both

[unborn bobcat]

Makes sense, thanks for the quick response

.close

[obtuse pebble]

Channel closed

Closed by @unborn bobcat

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.

[neon orchid]

Need help doing study of functions

[timid silo]

which question exactly?

[neon orchid]

positivity, axis intercept and limits, I copied what my professor was doing but lost track because I couldn't understand

I also don't know how to do fractional quadratic equations

[obtuse pebble]

@neon orchid Has your question been resolved?

[obtuse pebble]

@neon orchid Has your question been resolved?

[neon orchid]

.close

[obtuse pebble]

Channel closed

Closed by @neon orchid

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.

[azure echo]

hi, can anyone explain how these two equations on the left and right side equal each other?

[crude coral]

isnt that sum of geometric series

[azure echo]

yes

[surreal forge]

multiply both sides by 1 - q

[azure echo]

how?

oh wait

how would i multiply the left side?

[surreal forge]

see what happens for (1 - q)(1 + q + q^2 + q^3) or something

[azure echo]

ohhhhh yeah if you multiply it by 1-q it cancels out to the 1-q^n

but im still curious how would i get to that because it isnt explained in the book my lecturers provided

[errant lark]

Multiply Sn with q. See what do you get. What similarities do you see between Sn and qSn?

[azure echo]

it would be the same but instead of 1 we would start with q and it would evolve to q+q^2+q^3+....+q^n

[errant lark]

Yes. So try taking the difference of Sn and qSn.

Then, you should be able to evaluate the value of Sn.

[azure echo]

we would be left with 1-q no?

here is the whole question and i dont know how to translate it

the goal is to evaluate if the geometric progression is "collective or disjointed" (this is the translation google gave me)

im curious how we ended up at 1-q^n/1-q

ok i got it its just a formula

.close

[obtuse pebble]

Channel closed

Closed by @azure echo

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.

[timid silo]

How do I solve (ii)

[modern bison]

Is this correct?

[timid silo]

.close

[obtuse pebble]

Channel closed

Closed by @blazing wave

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.

[echo gazelle]

Can someone please help explain this to me

[echo gazelle]

I dont understand how you solve it

nvm figured it out

.close

[obtuse pebble]

Channel closed

Closed by @echo gazelle

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.

[swift crest]

How do I do this?
Context is AP calc bc fyi

[last pilot]

,rcw

oops

,rccw

[calm quail]

The problem requests "dh/dt" when h=5ft
By chain rule
dh/dt=(dh/dV)(dV/dt)

[swift crest]

But how do you find derivative of volume with respect to time?

[calm quail]

It is already known
「Water flows into the container...」

[swift crest]

lol I’m just dumb

[calm quail]

What you need to compute is dh/dV when h=5ft

[swift crest]

Thanks man

,close

[glass apex]

https://youtu.be/20lhfKoIMoM?si=yCY9YQZ8t-xfkTw1

[swift crest]

.close

[obtuse pebble]

Channel closed

Closed by @swift crest

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.

[timid silo]

The lateral surface of the cone after expansion is a sector of a circle with a radius of 12 cm, the central angle is 225. Calculate the total surface area of the cone.

[timid silo]

what am i doing wrong

okay, i have found my mistake 😆

.close

[obtuse pebble]

Channel closed

Closed by @agile quail

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.

[median dome]

Let $a,b,c$ be three non-zero single digit numbers in A.P. Find the number of 9-digit numbers that can be formed using each of these three digits thrice such that some three consecutive digits in the number form an A.P.

[warm shale]

kheerii

[median dome]

the combinations are $aaa,bbb,ccc,abc$ and $cba$

[warm shale]

kheerii

[median dome]

but idk how to approach this. it seems like most possible words will satisfy this condition

[kind hawk]

might be easier to count the ones which dont satisfy it

maybe. not sure

[median dome]

yeah that's what i was thinking

but how

[obtuse pebble]

@median dome Has your question been resolved?

[tired shell]

this question is extremely painful

[median dome]

really is

[tired shell]

I'm seeing like hour-long solutions online and 5 minute solutions when you forget that aaa is an arithmetic progression

[median dome]

yep pretty accurate

how do i do this accurately?

wait i found a solution on stackexhchange but i didnt quite understand it

https://math.stackexchange.com/questions/4681637/digits-of-a-number-in-arithmetic-progression

[obtuse pebble]

@median dome Has your question been resolved?

[obtuse pebble]

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.

[harsh remnant]

Hello

[harsh remnant]

How do we know that argument = 0?

[brazen gorge]

the number "1+0i" has 0 as its argument

[shy pier]

Do you know what argument means?

[obtuse pebble]

@harsh remnant Has your question been resolved?

[harsh remnant]

Uhhh sort of

Isn't argument = theta and modulus = r?

[harsh remnant]

Is the imaginary part = argument?

[brazen gorge]

no, not at all

i was just pointing to the fact that they are talking about 1 as a complex number

[brazen gorge]

argument is the angle a complex point makes with the real line

and since 1 is a real number, and lies on the real line, the angle between it and the real line is 0

[harsh remnant]

Ohhhh

I see

Great explanation

Thank you

!

.close

[obtuse pebble]

Channel closed

Closed by @harsh remnant

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.

[muted ember]

How can I prove the identity of the tangent of a sum of angles?

[muted ember]

I tried to do this, but I don't know how to continue

[frank monolith]

think of how you can convert cos(a)cos(b) to 1

since sin(a)sin(b) can easily be converted to tan(a)tan(b)

[muted ember]

dividing by cos(a).cos(b)

[frank monolith]

correct.

[muted ember]

dividing by cos(a).cos(b)

[frank monolith]

exactly

so try dividing the denominator by cos(a)cos(b) and to balance it out, divide the numerator by it too.

[obtuse pebble]

@muted ember Has your question been resolved?

[obtuse pebble]

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.

[supple fog]

a plane is parallel to the base of the pyramid, dividing the pyramids H (Vertical) in the ratio of 4:3, counting from the top. Calculate the volume of the truncated pyramid if the volume of the whole pyramid is equal to 686cm^3

[supple fog]

I think i should find the top part of the truncated pyramid which is similar to the whole pyramid and then deduct the top part from whole to get the bottom parts V (Volume)

[untold raven]

right, so what is the volume of the cut off section

[supple fog]

that is what i dont know how to get

im asuming i need to apply some similarity rule but it hasnt come into my mind yet

[untold raven]

right exactly

okay this is actually a quite simple theorem, let me explain

consider two similar triangles with a ratio of 2, how does their area differ

it differs by a multiple of 4, because area is two-dimensional, so we square it