help-27

[quaint citrus]

What

[tawny summit]

huh

im i dumb

[quaint citrus]

Bro u gotta brush up on ur fundamentals

[tawny summit]

bro i need help in maths

want to be my buddy

[quaint citrus]

Right, but ur problems stem deeper than just these types of equations

[tawny summit]

this is all just a joke

i know the answer

haha

the answer for 3+-7

is

uh

-4

[quaint citrus]

Google calculator isn’t conducive to ur learning

[tawny summit]

nah i didnt use it

[quaint citrus]

I suggest u use khanacademy to brush up on adding integers

[tawny summit]

are u set 1 maths

[quaint citrus]

Positives and negatives

[quaint citrus]

What is that

Are u British or smth

[tawny summit]

school sets?

yes

[quaint citrus]

Ok I’m American

We don’t do that here

[tawny summit]

are u top math student

[quaint citrus]

I’m in college if that’s what ur asking

[tawny summit]

WHAT

ayO

your my guyy

can u be my helper forever

[quaint citrus]

Lol nah bruh I’m busy

[tawny summit]

nah bro

your up at 1:32 in the morning

[quaint citrus]

It’s 8:30 here lol

I’m on New York time

[tawny summit]

aH

okay

[quaint citrus]

What grade u in bruh

[tawny summit]

uh

do u know britain

grades

[quaint citrus]

Oh u call it years

Year 1-12 right

[tawny summit]

yes

year 1-11

[quaint citrus]

Which are u in

[tawny summit]

9

[quaint citrus]

I see

[tawny summit]

your my upperclassman

my guyy

come on

Dab me up

[quaint citrus]

There are people here that graduated like 20 years ago

[tawny summit]

im trying to sound like a roadman

YO

[quaint citrus]

What

[tawny summit]

THISE GUYS ARE PROBABLY SMART

THISE

THOSE

[quaint citrus]

Dab me up…. interesting

[tawny summit]

like high five me

or fist bump me

Its slang

[quaint citrus]

Nah what

We say dap

[tawny summit]

AYO

[quaint citrus]

Not dab

[tawny summit]

WHAT U THINKING

bro said dap

[quaint citrus]

?

[tawny summit]

BRO SAID DAP

wHaT

ay man

im pro at english and science

its just that im shit in maths

my parents hate me for it

[quaint citrus]

Nah u just gotta put the work in

[tawny summit]

so i need help in maths badly

parents are abusive

strict

[quaint citrus]

Put the work in

[tawny summit]

my goal in life is still strangely to make them proud

to do that i need maths

ur my guy

come on

daily we have to

[quaint citrus]

Lol I have school too

And work

And a life

[tawny summit]

ah

[quaint citrus]

Homez this not gonna work

[tawny summit]

gimme a old dude

[quaint citrus]

LOL

[tawny summit]

those guys are SMART

[quaint citrus]

Yea fr

Some ppl here have phd’s in math

[tawny summit]

sheeesh

I NEED THEM

do u know any old dude

yO MAN

I STILL NEED HELP

[quaint citrus]

I suggest u review ur basics then come back

[tawny summit]

how long u willing to wait

ive gone over a few

SIMPLE

HEY DUDE

.close

[devout snow]

Channel closed

Closed by @tawny summit

Use .reopen if this was a mistake.

[tawny summit]

HA

[devout snow]

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.

[tender wind]

I need help with this

[supple knot]

try uhhh t = 1/x ?

[tender wind]

its indeterminate form

wait what

[supple knot]

then t goes to 0 from the right

[tender wind]

where did u find t

[supple knot]

substitution is a common way to do limits

[tender wind]

what i did is this

[tender wind]

wait can i do chain rule

Im not sure what to do with the 2/x

[supple knot]

you can do it that way of course. sure is tedious though

[tender wind]

wait is that what u meant with 1/x

i can put the 2 aside

1/x

[sand dove]

I don’t think there is a necessity for l'hôpital

[tender wind]

2d / dx (1/x)

well it gives 0/0

[sand dove]

I suggest, as riemann suggested, a nice substitution

Maybe u = 2/x

[steel sage]

$=\frac{1}{10}(\frac{e^{t}-e^{0}}{t})$

[tender wind]

so i derive u which gives 1?

[woven radish]

Cogwheels of the mind

[steel sage]

Where t=1/5x

[sand dove]

Nonono

[steel sage]

t->0, so a derivative appears

[sand dove]

You don’t have to always "derive" when calculating a limit

[tender wind]

well when its a hopital

yes

[sand dove]

Are you just dropping the solution like that ? 😂

[sand dove]

Here it's not a hôpital you gotta use

[steel sage]

Wait let me edit it

[tender wind]

whats the substitution method

Well i know what it is

But i never done it in limits

[sand dove]

I suggested u = 2/x

[tender wind]

well yea but what goes after that

[sand dove]

Two things for substitution methods :

• If x-> infinity, u -> ?
• Express the function inside the limit ONLY in terms of u

[tender wind]

u tends to inf

[sand dove]

if u = 2/x ???

[tender wind]

oh no

[sand dove]

Yes

[tender wind]

wait

ah it was 0

[sand dove]

Now second step, write $\frac{e^{\frac{1}{5x}}-1}{\frac{2}{x}}$ in terms of u only

[woven radish]

rafilou2003

[sand dove]

(Make all the x disappear)

[tender wind]

like so?

wait no

wait no

[sand dove]

This was closer

But not quite

You succesfully replaced the denominator, 2/x, by u

But now, if u = 2/x, then 1/(5x) = ?

[tender wind]

0

[sand dove]

?

[tender wind]

Hmmm im not sure

[sand dove]

We're not taking the limit here

Not yet

Ok, let's try to reverse engineer this

[tender wind]

well isnt it u again

[sand dove]

Clearly it's not, 2/x is not the same as 1/(5x)

[tender wind]

u*5x

[sand dove]

But we're getting closer

[sand dove]

Not * 5x, * something else

So 1/(5x) = Constant × 2/x

Find the constant

[tender wind]

1/10

[sand dove]

Yes !

So 1/(5x) = 1/10 • u

Or u/10

[tender wind]

oh yes

[sand dove]

So now can we finish this ?

[tender wind]

so u tends to 0 right

[sand dove]

Yes, but what is this in terms of u only ?

[sand dove]

👍

And now take the limit of this as u->0

[tender wind]

well the answer comes back to 0/0

indeterminate form

[sand dove]

Yes but now that you wanted to hôpital so badly

[tender wind]

ahh

now i derive it

[sand dove]

Verdict?

[tender wind]

1/10

is the other way longer

if u decide not to sub

[sand dove]

If you try to brute force l'hôpital, you will be stuck in an endless loop of 0/0

So yeah the other way is a tad longer 😂

[tender wind]

😂 if my teacher gives me a problem where i see it will be long

i will use the sub method

i never learnt that

should I differentiate this normally or sub method as well

[sand dove]

Sub won't help here, however

Power series will

[tender wind]

when do u learn power series tho

what year

[sand dove]

Oh you haven't done power series yet mb

Well then it's l'hôpital twice

[tender wind]

💀

hahaha alr

[sand dove]

For doing l'hôpital the first time, the best expression of tan'(x) to use is 1+ tan²(x)

For l'hôpital the second time around, the best expression of tan'(x) to use is 1/cos²(x)

[tender wind]

well the derivative of the numerator is tan²(x)

[sand dove]

Yes

[tender wind]

,r

.r

,rot

[tender wind]

like this

.rotate

,rotate

[tender wind]

.close

[devout snow]

Channel closed

Closed by @tender wind

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.

[wooden axle]

2^80 mod 100

[wooden axle]

How to solve this one?

2=2mod100
2^2=4 m 100
2^3=8 m 100
2^4=16m100
2^5 =32m100
2^6=64m100

[random temple]

ok write 80 in binary

and then decompose 2^80 into products of 2^(2^n)

which you can find with repeated squaring

[wooden axle]

2^(2^2) ×5

[sand dove]

This is not what he meant

Write 80 in base 2

So here 80 = 64 + 16 = 2^6 + 2^4

Then 2^80 = 2^(2^6 + 2^4) = 2^(2^6) × 2^(2^4)

From here hopefully you see how to finish ;)

[wooden axle]

How to find 2^(2^6) now?

I guess we should do this again?

Like we did for 80

@sand dove

This is going to big number again

Like we will need to multiply

[sand dove]

I think it's pretty straight forward

Knowing that 2^(2^(n+1)) = [2^(2^n)]², you can reason by induction

[steel sage]

By CRT, Z/100Z isomorphic to Z/4Z product Z/25Z. 2 in Z/25Z has order 20 because 2^10=-1 mod 25, so what you are looking for is the inverse image of (0,1)

(Use (-6)4+(1)25=1, 25 mapped to (1,0),-24 mapped to (0,1))

[devout snow]

@wooden axle Has your question been resolved?

[steel sage]

? I already told you, you don’t know -24=? mod 100 ?

[devout snow]

@wooden axle Has your question been resolved?

[wooden axle]

I know this 76

I haven't read isomorphic yet

[steel sage]

I used it only because 100 is big

4,25 small

[wooden axle]

But it seems fast and easy

[steel sage]

It is

[wooden axle]

I'll learn it soon

Does it work for all?

[steel sage]

For all?

What do you mean

Question like this?

[wooden axle]

Like all the numbers

Yes

[steel sage]

Sure. It always works

When your number can be factored

(Not being a power of a prime)

[devout snow]

@wooden axle Has your question been resolved?

[wooden axle]

What if it being a power of prime@steel sage

[wooden axle]

.close

[devout snow]

Channel closed

Closed by @wooden axle

Use .reopen if this was a mistake.

[wooden axle]

Any direct method by value putting?

[devout snow]

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>.
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• 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.

[wooden axle]

Any direct method by value putting?

[hybrid snow]

I mean or

[wooden axle]

Yes. I did and solved

[hybrid snow]

You can logic your way through

[wooden axle]

I am looking for a direct method

[hybrid snow]

You know tan^2(x/2) >= 0

[wooden axle]

I know you are talking about sin2x

[hybrid snow]

So you can eliminate A and C

[wooden axle]

Yes right

[hybrid snow]

If you square csc(x) - sin(x), you'll get csc^2(x) + sin^2(x) - 2

And you know csc^2(x) and sin^2(x) are also nonnegative

[wooden axle]

Hmm yes

D directly

So here only@hybrid snow d has (-2) so it is option

. close

.close

[devout snow]

Channel closed

Closed by @wooden axle

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.

[slender sleet]

Someone help

[slender sleet]

Please

[rocky iris]

Which one

[slender sleet]

32

[rocky iris]

!status

[devout snow]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[slender sleet]

2

So for the abc triangle

[rocky iris]

Can you give me a clearer pic?

[slender sleet]

I got all the angles but idk what to do next

Ok

[rocky iris]

Thx

[normal vale]

i want to recommend investing in a folder to not crumple your homework 👍

[slender sleet]

That was from me raging

[normal vale]

diagram isn’t entirely clear still

[rocky iris]

What can you get when ABC~ECD?

In terms of angles

[slender sleet]

I dont know how 8 is similar to 9

[normal vale]

look at the top left of your paper here

right sorry

[slender sleet]

Yeah that stands for m?

[normal vale]

nono

[slender sleet]

8

[normal vale]

‘Congruent and Similar Triangles’

define congruent to me please

[slender sleet]

Both triangles are the same length and all have the same angles

But right now its saying that their similar

[normal vale]

not same length, but angles, yes

[slender sleet]

For similar 2 or more of the angles have to be the same

I dont know which ones

[normal vale]

adjust the triangles so they’re the same orientation

[slender sleet]

Ok

[normal vale]

now just put the angles from the original onto this triangle

straight away we find m, which is?

[slender sleet]

So m is 46?

[normal vale]

yes

now we need n

[slender sleet]

The lengths wouldn’t be similar

Since its only similar not congruent

[normal vale]

that is correct

[slender sleet]

Nine minus six

[normal vale]

here wait

[slender sleet]

I think

Ok

[normal vale]

i’ve gotta get dinner sorry

[slender sleet]

Oh

[normal vale]

here

@rocky iris can you finish this off?

if no one comes, do @ Helpers

without the space

[slender sleet]

Ok

[normal vale]

or

close and reopen

sorry mate

[slender sleet]

K

It’s ok

<@&286206848099549185>

<@&286206848099549185>

.close

[devout snow]

Channel closed

Closed by @slender sleet

Use .reopen if this was a mistake.

[slender sleet]

.reopen

[devout snow]

✅

[slender sleet]

<@&286206848099549185>

<@&286206848099549185>

[pseudo basin]

pinging helpers twice back to back is a great way to make them not want to help you

[slender sleet]

Sorry

<@&286206848099549185>

[empty flame]

you said sorry and then pinged helpers again

[wooden zodiac]

Lol

[slender sleet]

Ik that but I’ve been waiting for over an hour

Can anyone help

[empty flame]

you have been waiting for 18 mins from here i saw people opening a channel for 4 days or so

[slender sleet]

Ive been opening diffrent channels

Cuz no one saw

Ive been opening diffrent channels

A4 paper helped me on one of them

….

And he had to go

[dry oxide]

nones gonna help you now, no one would be willing to, helpers are also just like any other normal person who helps people like because they just like to, you should have patience

[slender sleet]

Well according to the rules it says that you can ping a helper after 15 minutes

I went to three difrrent channels already

Without pinging

[empty flame]

yea the duration between these pings was some seconds

[slender sleet]

… after the 15 minute mark

It dosent say how much times

[empty flame]

between the above 2 and this is 3 mins

[slender sleet]

It dosent say the amount of times

Why did you come here in the first place then?

[empty flame]

between this and the 2 below 11 mins not 15

before this someone was helping

[slender sleet]

If you aren’t gonna help then leave since im just look for help..

And you just looking to roast me

Whats the point in that

[empty flame]

i am just clarifying if you want to stand on details and check them then i will talk to you with these small details

[slender sleet]

I waited 15 min it never said the amount of times i can ping Ive opened other channels for help to..

I’m just looking for help not looking for a smash bros fight..

.close

[devout snow]

Channel closed

Closed by @slender sleet

Use .reopen if this was a mistake.

[empty flame]

ik what you are feeling because you didnt get help directly but this happens with me alot

so now type .reopen

fast before channel closes @slender sleet

[slender sleet]

Why

.reopen

[devout snow]

✅

[empty flame]

i am not trying to roast i am clarifying things

now ill check the question

[slender sleet]

Ok

33

[empty flame]

ok what have you tried

[slender sleet]

Ive made them all 90 degrees

So far

But idk how to find the single angles

[empty flame]

which angles

[slender sleet]

Add

AED

[empty flame]

first question asks for congruence so you can try sides if you are having trouble with angles

[slender sleet]

But there’s no clue on the sides

[empty flame]

no there is enough given

first what is the nature of triangles DAE and ABF

[slender sleet]

We are trying to prove that they are congurent

[empty flame]

yes ik that

what is the nature of each of these triangles

[slender sleet]

Both have a 90 degree angle in them

[empty flame]

so what is their nature

right , isosceles ,equilateral ,right isosceles,...etc

[slender sleet]

Isosceles

I think

[empty flame]

what is an isosceles triangle

[slender sleet]

A triangle with two angles that are the same

[empty flame]

also 2 equal sides right

[slender sleet]

Yeah

Since its a square its sides should be equal right?

[empty flame]

ok now are there equal angles in triamgle AED

[empty flame]

yes but are the sides of the triangle the same as the sides of the square

[slender sleet]

No

Oof

[empty flame]

ok the sides arent equal it is not isosceles not right isosceles and not equilateral

[slender sleet]

Scalene

[empty flame]

it has a right angle so its nature is

[empty flame]

it is scalene but a special type of scalene triangles

a triangle with a right angle what is this triangle called

[slender sleet]

Right angled triangle?

[empty flame]

ok so it is a right triangle

how do you prove that 2 triangles are congruent

[slender sleet]

If they have the exact same angles and length

If its a 90 degree triangle then its other sides should be 45 degrees i think

[empty flame]

thats the defintion of congruence of triangles but proving that 2 triangles are congruent needs less than that

[empty flame]

no thats not true also how can sides be measured by degrees

[slender sleet]

The other angles should be 45

[empty flame]

no

[slender sleet]

I cant see what we can use to prove the triangle is congurent

[empty flame]

to prove that 2 triangles are congruent its sufficient to prove one of the following :
1.to prove that all sides of one triangles are equal to the sides of the other triangle

2. to prove that 2 sides and the angle between them are equal to those of the other triangle

3. to prove that 2 angles and the common side between them are equal to those of the other triangle

these work for any triangle

[slender sleet]

The only thing i have right know is two triangles with 90 degrees and i don’t know how i can say their congurent

[empty flame]

for right triangles (triangles with angle 90 deg) you can use something else which is to prove that the hypotenuse (longest side of the right triangle) and another side are equal to that of the other triangle

you have enough information to prove this

[slender sleet]

Technically both angles have 90 degrees and a long side

From the same square so couldn’t i just say that

[empty flame]

so you have 2 right triangles

whats the hypotenuse in triangle DAE

[slender sleet]

A to D

[empty flame]

and whats the hypotenuse in triangle ABF

[slender sleet]

B to F

[empty flame]

wrong

also you can just say AD

but it is wrong

[empty flame]

wrong

do you know what a hypotenuse is ?

[slender sleet]

The long side angle of a triangle

[empty flame]

its the longest side of the right triangle

so now whats the hypotenuse in triangle DAE

[slender sleet]

Ed

ED

[empty flame]

ok and whats the hypotenuse in triangle ABF

[slender sleet]

AF

[empty flame]

ok given AF=DE

so hypotenuse of 2 triangles are equal

now we need 2 equal sides and we are done

can you figure them out

[slender sleet]

How would we know how to make them equal

.close

[devout snow]

Channel closed

Closed by @slender sleet

Use .reopen if this was a mistake.

[empty flame]

why .close

[slender sleet]

.reopen

[devout snow]

✅

[slender sleet]

I thought you went offline

[empty flame]

wdym by how we make them equal

[empty flame]

bro be patient if you do this you wont get anything

[slender sleet]

Sorry

[empty flame]

np i am talking for your own good i wont be harmed if you just .close but you will not get what you want like that

now lets continue

[slender sleet]

Ok

[empty flame]

we are not making them equal

we are given that they are equal

now for the other 2 sides

look for sides that you know something about

so do we know anything about AE and BF

[slender sleet]

They have a 90 degree angle

[empty flame]

no

AE and BF are sides

ohhh i understand what you mean

you are right

but let me state my question in a clearer way

[slender sleet]

Ok

[empty flame]

do we know anything about AE and BF that can enable us to know whether they are equal or no

[slender sleet]

As far as i can see no

[empty flame]

ok what about AB and AD

[slender sleet]

Both have the sides of a square

Which leads them to having the exact same length

[empty flame]

exactly

so to summarize what we got

the two triangles are right they have equal hypotenuse and another equal side

[empty flame]

we proved this so we proved that the triangles are congruent

[slender sleet]

So i can say both triangles are congurent since they have a equal hypothenuse and have a equal side basically?

[empty flame]

and because they are right triangles

[slender sleet]

Thanks

[empty flame]

if they werent right then we need to prove using one of the 1.,2.,3. ways

[slender sleet]

Thanks a lot for the help

.close

[devout snow]

Channel closed

Closed by @slender sleet

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.

[fast garden]

?

[spiral gazelle]

why is that

why not 3x^2?

omg

im dumb

[fast garden]

it is 3x^2

[spiral gazelle]

dont even say it

[fast garden]

but it put it together

[spiral gazelle]

yeah

[fast garden]

loool happens to the best of us

[spiral gazelle]

ahahaha

thx

.close

[devout snow]

Channel closed

Closed by @spiral gazelle

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.

[limber lily]

sin(y) = sin(arccos(x))

how does this help me

xd

[sonic smelt]

That doesn't really help, would be better if you could express side opposite to angle y in terms of x

You may use Pythagorean theorem to do that

[limber lily]

ok i will try

sin(arccos(x)) is suppose to evaluate to something righ

[pseudo basin]

thinking in the wrong direction here

[sonic smelt]

Yeah it will evaluate to the answer that you get using the method I mentioned

Alternatively, since you've noticed that cos(y) = x, you could use the Pythagorean identity (keep in mind that the angle y is acute)

But Pythagorean identity and Pythagorean theorem are pretty much equivalent

Any progress?

[limber lily]

arccosx = y

x^2 + (siny)^2 = 1

based on pythag

[sonic smelt]

Yes

Now isolate siny

[limber lily]

sqrt(1-x^2)

LFG

thanks for help

[sonic smelt]

Yup

[limber lily]

i should have realized this faster

10/10

where do i give review

xd

.close

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[spiral gazelle]

3. calculate g(1)
4. deduce the sign of g(x) on the interval 0; +infinity

[spiral gazelle]

how should i deduce the sign of g(x) from knowing g(1)=0 ?

[odd palm]

What did you get for g'(x)?

[spiral gazelle]

1. was calculate g'(x) and his sign

here is everything

[odd palm]

Okay so you got that g'(x) > 0 when x>0 right?

[spiral gazelle]

ye

[odd palm]

What does that mean the graph will look like when x>0?

[spiral gazelle]

positive

[odd palm]

Yes

The g'(x) > 0 means the graph will be going upwards

But the interval is 0 to infinity

So what is g(0)?

[spiral gazelle]

0

wait

i think i got it

so g(x) is positive between 1 and + infinity

and g(x) is negative between -infinity and 1

thats right ? @odd palm

[odd palm]

Idk about between -infinity and 1

But the question only asks about 0 to infinity

[spiral gazelle]

negative between 0 and 1

positive between 1 and +infinity

[spiral gazelle]

ye?.

[odd palm]

Yep :)

[spiral gazelle]

alright thx

😄

but why does it say "THE sign" @odd palm

deduce the sign

[odd palm]

Idk, that is just not correct

We can plug in a very small number like 0.001 and see it's negative

[spiral gazelle]

alright thx

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[wooden axle]

2^80 =x mod 25

[wooden axle]

How to solve this one?

[sonic smelt]

Tried Euler's theorem?

[wooden axle]

I am confused x is in between

I have solved questions with euler when x left side

[wooden axle]

Best idea wait a minute

2^24 = 1 mod 25

2^24^3 = 1 mod 25

[steel sage]

No, 20

2^20=1 mod 25

(p-1)p^(r-1)

[wooden axle]

,w 2^20 value

[woven radish]

Results provided by WolframAlpha

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Requested by arjunn5589

[wooden axle]

It's not divisible by 25

Ohh wait

[sonic smelt]

And 2^80 is just (2^20)^4

[wooden axle]

Yes correct

[steel sage]

Yeah inverse image of (0,1) in Z/4Z times Z/25Z

[wooden axle]

How do we connect these equations
2^80 = 1 mod 25
2^80 = 0 mod 4

[sonic smelt]

What

Where did 0 come from

[wooden axle]

Edited

[steel sage]

Z/100Z->Z/4Z times Z/25Z

Mapping a to (a,a)

[sonic smelt]

That's it, you don't need the other equation

[steel sage]

(-6)4+(1)25=1

[wooden axle]

2^80 =76 mod 100

No? I want to learn how you get 76 without isomorphic

[steel sage]

So inverse images of (1,0),(0,1) are 25,-24 respectively

[sonic smelt]

Ah

[steel sage]

If you don’t want to use CRT, there is no point factoring 100 into 4 times 25

[sonic smelt]

You can do this then

[steel sage]

You can calculate 2^k mod 100 manually, just little bit longer

[sonic smelt]

2^80 = (2^8)^10 = 256^10 = (-44)^10 = 44^10 mod 100

Yeah and so on

[steel sage]

Oh wait, not longer much at all

You don’t need CRT here indeed

Φ(100)=φ(4)φ(25)=2 times 20=40

[sonic smelt]

Yeah but you can't use Euler's theorem

[wooden axle]

No restrictions

[steel sage]

Yeah forgot gcd (2,100) isn’t 1

So little longer

[wooden axle]

What next?

[steel sage]

That was a dead end

[wooden axle]

Ohh i see

[steel sage]

So it went back to either CRT, or calculating manually

[wooden axle]

(56)^10 is long process

[steel sage]

Bean gave you 2^8^10, I wanted to say 2^10^8, but anyway, neither is long

[wooden axle]

But got the answer from it too

[wooden axle]

Let me try

[steel sage]

I noticed a pattern

[wooden axle]

(24)^8

[steel sage]

Calculating a^k mod n

You seems always calculating a^k, then mod n

Which is not necessary

[wooden axle]

I guess i learnt only one thing yet

So i do all the time

[steel sage]

You can do it step by step

For example, bean told you 2^8^10=44^10 mod 100 right, take that as an example

44^2=1936=36 mod 100

Then 44^3=(36)(44)=1584=84 mod 100
44^4=(84)(44)=-4 mod 100
…

You don’t have to calculate a^k itself then mod n

[wooden axle]

I got a pattern by your method

Which is 24^8

And i remember 24^2

So it is easy to calculate

[steel sage]

Okay

[wooden axle]

(76)^4

(-24)^2

[steel sage]

Yeah and 76^2=76

mod 100

Anyway, it’s always easy to calculate as long as you have your phone nearby

[devout snow]

@wooden axle Has your question been resolved?

[devout snow]

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[visual maple]

this is a domain yeah?

[restive river]

sorry didn't realised you had already posted a question here 😅

[visual maple]

allg

[restive river]

yeah thats domain btw

[visual maple]

mmm alr

im supposed to define what a domain is

lemme do that rq and lmk if its right

[wooden veldt]

You want to describe a domain in relation to functions

I.e. what does the domain of a function mean

[visual maple]

The domain of a function is the permissible values that can be plugged into our function.

is that right

[wooden veldt]

Yeah that sounds good

[visual maple]

would domain be like the x-axis only like

uh

idk how to really say it

but do you know what i mean

cause like isnt domain for x axis

and range for y axis?

[wooden veldt]

Yes, domain are the x values that are allowed to be put in the function

[visual maple]

The domain of a function is the permissible values that can be plugged into our function in the x-axis.

does this make sense?

[wooden veldt]

I would just leave out the x axis part really

[strange arch]

you'd rather consider it the x-values for which the function is defined

[wooden veldt]

What you said here is perfectly fine and more general

[visual maple]

wouldn't it be important though?

[wooden veldt]

Depends on the context really, the inputs to a function don't have to be called x in general

[eager lodge]

and there might be more inputs

[visual maple]

nah cause its asking me to justify why a domain was used

[strange arch]

Definition-wise no, your graphical understanding of it would limit it to a single variable and the functions graph

[visual maple]

so first im defining what a domain is

and then i would explain why

[wooden veldt]

Do you have a picture of the original question

Are you looking at arccos

[visual maple]

nope thats a cos graph

unless thye're the same even when arccos

[strange arch]

nop

[wooden veldt]

Right but "why a domain is used" is a bit vague without context

[visual maple]

nah, made up my own question but it isnt really that math related, its more about defining terms and then applying it to graphs

[visual maple]

yeah i see what you mean, i know what to do for that bit though anyway

so just to clarify, should I exclude or include the bit regarding the x axis in my definition?

The domain of a function is the permissible values that can be plugged into our function in the x-axis.

[wooden veldt]

If you're strictly only considering functions that are functions of x then that's fine

[strange arch]

Your definition would be the set of numbers for the inputs for which the function is defined, you can then interpret this as the allowed x-values on the axis for 1D functions and x as the parameter

[visual maple]

yeah cause all my functions are equal to y

im using sinusoid functions

so it would be y = ....

yeah

y or f(x), same thing right?

[strange arch]

no, but regard it as a yes

[wooden veldt]

The technical no is that the equation y = f(x) is giving you a graph that represents the function f(x), there is a slight and subtle difference but not much to worry about

[visual maple]

alright thanks guys

have a good one

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[unreal vector]

does anyone know how to count perpendicular length?

[red turret]

count?

[unreal vector]

find*

[red turret]

of?

[unreal vector]

of a point to two points

[red turret]

huh?

[brazen star]

give example.

[unreal vector]

A (1,4), B (4,7), C(7,3)

find the length of the perpendicular line from C to AB

[red turret]

first write the equation of line passing through AB

[unreal vector]

do we need the straight line equation for this?

oh

y = 4/3x + 5/3

wrong?

wat

uh the gradient = 4/3 right?

[red turret]

of AB? no

[unreal vector]

dem

formula of gradient is

y2 - y1/x2 - x1 right?

oh

[red turret]

yes

[unreal vector]

3/4

[red turret]

no

[winter patrol]

how are you getting 3/4 from that?

[unreal vector]

oh

3/3

it's really late here, very sleepy men

oh wait it's supposed to be A (1,3)

dem

after we have the straight line equation wat we do?

[winter patrol]

there' s the long way and then there's a short way

[unreal vector]

teach me both men

tomorrow i have exam

😔

[winter patrol]

the short way would be to:
apply the preestablished formula for perpendicular distance from a point to a line

[unreal vector]

wat

[woven radish]

Dyssrupt

[unreal vector]

wat is ah?

oh hk

[red turret]

yeah

[unreal vector]

so hk is which coordinate?

i haven't learned abt that

[winter patrol]

the point you're using

[unreal vector]

ab ?

[winter patrol]

no

AB is your line

[unreal vector]

c

[red turret]

yes

[unreal vector]

oooo

[winter patrol]

caiptal C

[unreal vector]

oh yea

C*

then what is the a and b?

[winter patrol]

they're defined in the pic

[red turret]

I think its better to show an example ramonov

[unreal vector]

wait reaaly?

[winter patrol]

$\red{a},\blue{b}$ refer the the coefficients of $x,y$ of your line when represented in the form:
$$\red{a}x + \blue{b}y + c=0$$

[woven radish]

ℝam()n()v

[winter patrol]

if you forget that and/or not allowed to apply that, you could go the long way and do:
determine slope of a line perp to AB
find equation of a line with that slope passing through C
find intersection point between that line and AB
apply distance formula for that point and C

[unreal vector]

😭

so basically ax is x ???

wat

[winter patrol]

depends

lets go back

[unreal vector]

okok

[winter patrol]

what's the equation line line AB

[unreal vector]

y = 4/3x + 5/3

[winter patrol]

no

[unreal vector]

i corrected the question*

[winter patrol]

we already said that was wrong

[unreal vector]

it's supposed to be (1,3) and (4,7)

[winter patrol]

can you repost the whole question with what the values are supposed to be

[unreal vector]

A (1,3) B (4,7) C (7,3)
find the length of the perpendicular line from C to AB

[winter patrol]

can you rearrange that equation to general form?

ax + by + c = 0

[unreal vector]

oh yea

qait

wait

4/3x + 5/3 - y = 0

?

[winter patrol]

to make stuff less tedious, ideally you'd want integer coefficients/constants
keeping stuff in order may also help avoid messing up variables

[unreal vector]

hmmm

[winter patrol]

so do something like multiply both sides of the equation by 3

[unreal vector]

okay

[winter patrol]

and write the y term as the middle term

[unreal vector]

4x - 3y + 5 = 0

like this?

[winter patrol]

yes

[unreal vector]

oh yes

then we can insert it to

[unreal vector]

this?

[winter patrol]

yes

[unreal vector]

okay wait

[winter patrol]

first, identify the values of a,b,c

[unreal vector]

wait let me send it again

a = 4
b = - 3
c = 5

[winter patrol]

not quite

yes

[unreal vector]

okay

so i just count now?

[winter patrol]

wdym count

[unreal vector]

h and k are the points of C right?

[winter patrol]

yes

[unreal vector]

like insert the abc into the formula

[winter patrol]

capital C

"count" is a horrid word to describe that action

[unreal vector]

sorry, english isn't my main language

😭

[winter patrol]

you're looking for a word like substitute

[unreal vector]

so h is x and k is y right?

aight noted

substitute the abc to the numbers

[winter patrol]

yeh, sub in everything

[unreal vector]

28 - 9 + 5/5

so 21?

hmm how did my teacher found 4.8 units

[winter patrol]

because you screwed up the order of operations

[unreal vector]

wait really?

[winter patrol]

not sure how you even got 21 with that screw up either

[unreal vector]

wait let me count again

[winter patrol]

the whole numerator is being divided by the denomintor

not just the last term or whatever you feel like

[unreal vector]

OH

so

24

4.8

WAT

the formula works??

ajshsiwj

[winter patrol]

ofc the formula works

[unreal vector]

u made perpendicular fun man

[winter patrol]

formulas are made to work

[unreal vector]

thanks, i should get some rest for tomorrow

[unreal vector]

yeaa

again appreciate it man 😭

.close

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[acoustic spruce]

would there be a written solution to this aside from just finding one-sided limits?

our professor didn't tackle limits of exponential functions

[devout snow]

@acoustic spruce Has your question been resolved?

[pastel pasture]

This isn't even indeterminant

What's the problem

[acoustic spruce]

wouldn't substituting x for 0 result in 1/0?

according to the module given to us, the limit of a constant over 0 would be equal to infinity

[pastel pasture]

Did you examine the left and right hand limits

[acoustic spruce]

yeah

[pastel pasture]

So you would know that the LHL is negative infinity right?

Only the RHL is infinity

[acoustic spruce]

the LHL shows up as undefined when calculating it

would that mean as equal to negative infinity then?

[acoustic spruce]

i meant that all values starting from -0.01, -0.001 and so on approaching from the left side shows up as undefined in the calculator

sorry my bad, i looked at the graph again and found the negative infinity limit

my original problem was if i still have to show a solution to getting the answer, if there is any, aside from just writing the one-sided limits

as far as i know logarithms can be used on the numerator function but still the denominator ends up as 0 as i don't see a way to remove the x from the denominator completely even with that

i guess i'll settle for just writing the one-sided limits, thank you vm though

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[finite stream]

how do I start this?

[restive river]

First out the line in slope intercept form

Getting y = k - x

Simplify the terms in your quadratic equation

[grand torrent]

the gradient of the tangent is -1, and the gradient of the graph will be its deravative
if you equate these, you will get the x-coordinates of the points were they can meet

then you find the y-coordinates using the graph function

then you subsitute them into the equation of the tangent to find the two values of k

[finite stream]

no?

[finite stream]

what is gradient of tangent

[grand torrent]

-1

y= -x + k

m=-1

[finite stream]

slope?

oh

[grand torrent]

yes

[finite stream]

so y=-x+k is tangent line equation

[grand torrent]

yes

the tangent will meet the graph when the gradient of both functions are equal

[finite stream]

so the slope of the other equation is also -1?

[grand torrent]

no no

you have to derive it

what is the deravative of y=2x^3 -9x^2 -x +1

[finite stream]

6x^2-18x-1

[grand torrent]

correct

[finite stream]

and that is equal to -1?

[grand torrent]

yes

to find the points where they can meet

[finite stream]

so I set the equations to each other

[grand torrent]

-1 = 6x^2-18x-1

m=m

[finite stream]

x=0,3

[grand torrent]

yes good

now find the y- coordinates

[finite stream]

using original equation of y?

[grand torrent]

yes

[finite stream]

okok

(0,1) and (3,-29)

[grand torrent]

correct

now use y= -x + k to find the two possible values of k

[finite stream]

wait ok my brain lag but what are the chords represent

coords

[grand torrent]

the two points where the tangent can meet with the graph

they are the two points where the gradient of the graph is equal to -1

to be a tangent it has to have the same gradient as the graph

capiche?

[devout snow]

@finite stream Has your question been resolved?

[finite stream]

ohhh ok

k=1,-26?

[grand torrent]

correct

well done

[finite stream]

o ok

thank u

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[vale mesa]

what's the difference between disjoint and pairwise disjoint sets?

[wooden wraith]

A and B are disjoint if they have no elements in common

If you have more than two sets, the collection of them is called pairwise disjoint if any pair of sets in the collection is disjoint

for example the sets X, Y, and Z are pairwise disjoint if

X and Y are disjoint

Y and Z are disjoint

and Z and X are disjoint

[vale mesa]

what about if only X and Y are disjoint?

and Y and Z and Z and X aren't disjoint

is that still pairwise disjoint?

[wooden wraith]

then X,Y,Z are not pairwise disjoint

pairwise means every pair is disjoint

[vale mesa]

I see thank you

[wooden wraith]

no problem 👍

[vale mesa]

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[uneven patio]

I need help as how to start on this problem.
1/x+1/x+4=1/3

[restive river]

Get rid of the fractions to get a nicer equality you can work with would be my suggestion

[uneven patio]

Im not exactly sure how I would do that

would it be multiplying the denominators?

[devout snow]

@uneven patio Has your question been resolved?

[devout snow]

@uneven patio Has your question been resolved?

[uneven patio]

.close

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[green verge]

i need help on 32

[green verge]

nvm

.close