help-23

[silent roost]

thx

[gaunt garnet]

My pleasure

[silent roost]

im on this problem now btw, solved the other ones

[long copper]

i think student B does it like this :
$$\frac{1 + \tan^2 \theta}{\tan \theta \div \cot \theta}$$
when it should be like this:
$$\left( \frac{1 + \tan^2 \theta}{\tan \theta} \right) \div \cot \theta$$

[flat frigate]

I can't believe you've done this

[gaunt garnet]

First one is correct

[silent roost]

Ok it makes sense now

Took a bit for me to process that

Do they make any other errors?

[long copper]

I don't think so

[silent roost]

this make sense?

I fixed it. That was def wrong lmao but I fixed it in time

[silent roost]

I think this is right?

[spring glacier]

this one is good

[silent roost]

thx

i have another one i think is right

[long copper]

think about if n = 1 then what does f(x) equal

[silent roost]

oh i was thinking about them as separate solutions

they're all one

whoops

it should be the first option then right?

cuz adding or subtracting 2pi is the same angle

[long copper]

yh

[silent roost]

and 16pi/8 is 2pi

[long copper]

i'm pretty sure it's the first one

hopefully im thinking straight

[silent roost]

how do I solve trig equations

and systems

same way as algebra or?

idk how to do this one

i tried im stuck

[spring glacier]

double angle

do you remember it?

[silent roost]

sin^2x + cos^2x

[spring glacier]

almost

[spring glacier]

-cos^2 x*

not +

[silent roost]

oh right

[spring glacier]

but also

[silent roost]

i did right on my paper but i still don't know how to solve it

[spring glacier]

we have more

lemme check something

$\cos{x}$

[flat frigate]

Cycadellic

[spring glacier]

cool

$\cos{2x}=\cos^2{x}-\sin^2{x}=2\cos^2{x}-1=1-2sin^2{x}$

[flat frigate]

Cycadellic

[spring glacier]

thats all of them

i think

the last two come from $\sin^2{x}+\cos^2{x}=1$

[flat frigate]

Cycadellic

[spring glacier]

specifically, the 2cos^2(x)-1 comes in handy in this problem

[silent roost]

ohh makes sense

the only problem is that

none of the choices

[silent roost]

so lost ;-;

[silent roost]

idk

[silent roost]

how could i solve

[silent roost]

this

[spring glacier]

using the formula, we have $\frac{\cos{2x}}{\cos{x}}=\frac{2\cos^2{x}-1}{\cos{x}}$

ugh

[flat frigate]

Cycadellic

[spring glacier]

we love latex

[silent roost]

ofc

[silent roost]

it still doesn't agree with any of the choices .-.

[silent roost]

maybe 2cosx -sec?

[spring glacier]

yeah

thats right

[silent roost]

what else would be equivalent?

[spring glacier]

thats your answer

[silent roost]

yeah there are multiple

[silent roost]

this is why im confused

[spring glacier]

why?

is it saying youre wrong?

if it is then its wrong

$\frac{\cos{2x}}{\cos{x}}=2\cos{x}-\sec{x}$

[flat frigate]

Cycadellic

[spring glacier]

is true

[silent roost]

yeah sort of

there's multiple ways to represent that

[spring glacier]

oh i see

work from your given answers to your problem

yk

tanx=sinx/cosx

applying that, can we get I into the problem?

how about II?

[silent roost]

I just submitted and got it eight

I and III are correct

I just didn't think II would be correct

I didn't verify

I also solved this using a graph

[silent roost]

But I do wanna go over why it works/doesn't

Cuz like I still don't understand them

actually

i have another problem set i have to do asap

@spring glacier

[silent roost]

how would i do this system

oop new person cool

[obtuse plover]

What have u tried for this

[silent roost]

im stuck trying to figure out what to do

ive tried plugging them in but i want to actually solve it instead

[obtuse plover]

Here’s a hint

Get everything in terms of cos

Lmk what u get @silent roost

Tag me

[silent roost]

ok

im working it out rn

[silent roost]

cosx = cos2x

[obtuse plover]

Show ur work

I’m not sure how u got that

[silent roost]

oh i just

used the identity

the double angle

i isolated cosx

i think the answer is the last choice

like im sure

all those answers equal each other for cosx=2cosx

[silent roost]

so im going to move on

for this i have a similar issue idk what cos3x means

i dont have an identity for it so now im lost

[obtuse plover]

Hm

lol maybe try triple angle identities

Kinda nasty but might work out nicely

[mortal sandal]

I mean you can just plug in the answer choices and see which ones work

[obtuse plover]

Ye that’s true but ^

[obtuse plover]

Ye I just tried it, this one works out very nicely

A bit long but yea

[safe radish]

@silent roost Has your question been resolved?

[solid parcel]

https://www.symbolab.com/popular-trigonometry/trigonometry-13149

Check the simplification steps and see if that helps. @silent roost

[silent roost]

oh thx

[silent roost]

all that doesnt make sense to me so im just gonna work out using angle sum and difference identities maybe itll work idk

sry for the super duper long break

[silent roost]

nother long break and i still dont know tbh

[silent roost]

i dont think thats correct

when i put it on desmos i dont get any solutions either idfk

[silent roost]

.close

[safe radish]

Channel closed

Closed by @silent roost

Use .reopen if this was a mistake.

[silent roost]

.reopen

[safe radish]

✅

[silent roost]

woah

.close

[safe radish]

Channel closed

Closed by @silent roost

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[left pier]

Can I ask a programming question here? I'm wondering how many times this line would get executed

I'm thinking it might be n times since it has to check at the end to make sure the condition has been met but i'm not sure.

[dull sequoia]

no

if n = 1

it odesn't run

[light shoal]

that'll execute n-1 times, as long as i is not changed elsewhere in the loop

[dull sequoia]

because 1 is not less than 1

[dull sequoia]

for loops check the condition once before starting

[left pier]

but doesn't the program have to check the condition at least one time even if n = 1

like it has to check to see if n = 1 to know not to go through the loop

[light shoal]

the usual idiom in C++ for iterating n times is for (int i = 0; i < n; i++)

you're starting at i=1 so you do one less

[left pier]

like i know the loop itself excutes n-1 times but im asking how many times that line is checked

[worthy hemlock]

It checks the condition but it won't execute the body

[light shoal]

ahh got it

[left pier]

so is it n then or would it still be n-1

[worthy hemlock]

I believe, the condition is n times while the body is n - 1 times

[light shoal]

technically it would be something like min(1, n) i guess

assuming n could be zero or negative

[left pier]

oh okay

thank you

.close

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• 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!

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[civic sapphire]

who here is good with interior angles with polygons? like indicated angles finding x etc

[civic sapphire]

can anyone do this?

[lean otter]

Use the sum of internal angles formula

[civic sapphire]

do yk how to do it

[twilit spindle]

For any polygon with $n$ sides the total angles of said Polygon is $180(n-2)$ so we know that all the angles in the first shape must sum to to whatever $180\cdot 3$ is

[flat frigate]

XxMrFancyu2xX

[twilit spindle]

Yes I am both too tired and lazy to do 180*3

[lean otter]

It's 540

[civic sapphire]

if u do all 3 except the sum we can work smth out

[civic sapphire]

ye ik

i did the sum already

i just need the x

and the other stuff

except the sum

u understand

[lean otter]

Just add the angles and equate it to 540

[civic sapphire]

can u do it for me bruhh

its not alot

pls

[twilit spindle]

So take a look the angles are $65+x-10+94+x+x-2$ so $65+x-10+94+x+x-2=540$ and solve for $x$

[flat frigate]

XxMrFancyu2xX

[civic sapphire]

.

[lean otter]

Sir/Ma'am, there is an app called Wolfram alpha. Just type your equation into it. It'll solve it for you.

With working

[civic sapphire]

i tried so many google calculators

none works

with the pic

[twilit spindle]

,w 65+x-10+94+x+x-2=540

[flat frigate]

Results provided by WolframAlpha

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

Requested by XxMrFancyu2xX#6050

[civic sapphire]

.

wtf

[lean otter]

Wolfram is no Google calcilator

[civic sapphire]

damn

[lean otter]

Calculator*

[twilit spindle]

WolframAlpha my love ❤️

best thing ever

[civic sapphire]

@twilit spindle can u keep doing that

for all the questions

pls

[twilit spindle]

you can do it yourself my friend!

https://www.wolframalpha.com/

[civic sapphire]

no i cant

pls

pls

i beg

i beg

just this once

wont ask for anything else

[lean otter]

Bruh just type the equation how are you so lazy

[civic sapphire]

from the kindness of ur hearts

please

not even askin for the sum

just the other stuff

beow

below

pls

[lean otter]

What other stuff

[civic sapphire]

the ones below

the sum

[lean otter]

Your q is literally find x

[civic sapphire]

on the pic

[lean otter]

And then substitute x for other ones

[civic sapphire]

the thing is

idk the equation

lol

[lean otter]

I told you how to do it, I'm not gonna be doing it for you

[civic sapphire]

bro

ill give u smth to worth ur time

please

[lean otter]

Add all the angles and equate to 540

[civic sapphire]

bro pls

cmon

ok just the 1st one

ill do the other 2 myself

8 and 9

just 7

[civic sapphire]

can u do this aagain for all of number 7? except the sum @twilit spindle

[twilit spindle]

I did

[civic sapphire]

what

theres more on number 7

[twilit spindle]

that was $x$

[civic sapphire]

look

[flat frigate]

XxMrFancyu2xX

[civic sapphire]

u see the other ones

beside x

m to v

m to x

m to y

[twilit spindle]

well you know $x=131$ by W|A

[flat frigate]

XxMrFancyu2xX

[civic sapphire]

k

[twilit spindle]

so angle x is x-2

so 131-2

which is 129

[civic sapphire]

ok

[twilit spindle]

so if angle y is x-10

then what is its value?

[civic sapphire]

hold up

wait

so

[civic sapphire]

dude ur input in this is confusing

and result

result yeah

how u get 3x

and 147

[twilit spindle]

because we're adding 3 x's

that's a linear equation

[civic sapphire]

ah

alr so

for the y

[twilit spindle]

the solution is x

[civic sapphire]

k

so for the m to the v

but theres no v

on the question

or does v mean smth

[twilit spindle]

V is the angle

[civic sapphire]

k

[twilit spindle]

$x-10º$

[flat frigate]

XxMrFancyu2xX

[twilit spindle]

do you see it in the picture?

[civic sapphire]

ye

[twilit spindle]

aight

so remind me again, what's x

[civic sapphire]

x is uh

10

or

wait for m to v

right

[twilit spindle]

?

[civic sapphire]

bro

[twilit spindle]

ok

[civic sapphire]

idk man

[twilit spindle]

hang on this is uhhh... bad for lack of a better word

$m\angle V=x-10$

[flat frigate]

XxMrFancyu2xX

[twilit spindle]

you agree about that

the measure of angle v

[civic sapphire]

can u like jus use the calculator thingy u did above and do all of this and we get it over and u can go to sleep

this is confusin

g

pls

[twilit spindle]

,w x-10 where x=131

[flat frigate]

Results provided by WolframAlpha

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

Requested by XxMrFancyu2xX#6050

[civic sapphire]

ok so that 121 is for which one

m to v?

[twilit spindle]

ohhhhhh mf that's why

[civic sapphire]

what

[twilit spindle]

$m\angle V$ this don't mean ``m to v" this means measure of angle V

[civic sapphire]

bruh

[flat frigate]

XxMrFancyu2xX

[civic sapphire]

im talking about this one

in number 7

[twilit spindle]

yeaa that is the measure of angle V

[civic sapphire]

ye

so that 121 is that?

question

or

[twilit spindle]

121 degrees

yes

[civic sapphire]

ok

can u do the other 2 below

[twilit spindle]

first can you tell me what $m\angle X$ is?

[flat frigate]

XxMrFancyu2xX

[civic sapphire]

measure of angle x

[twilit spindle]

yes! and on the picture there is an $X$ please tell me the value of the angle corresponding to that point?

[flat frigate]

XxMrFancyu2xX

[twilit spindle]

it should be along the perimeter somewhere

[civic sapphire]

fancy

i dont got enough time

pls

thats why

i gotta go soon

can u like

jus use the wolf thing and we continue this tmr

[twilit spindle]

,w x-2 where x=131

[civic sapphire]

pls

[flat frigate]

Results provided by WolframAlpha

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

Requested by XxMrFancyu2xX#6050

[civic sapphire]

ok

[twilit spindle]

and the other result is just x so 131

[civic sapphire]

wym

[twilit spindle]

$m\angle Y=x=131$

[flat frigate]

XxMrFancyu2xX

[civic sapphire]

k

can u do the last one

measure of angle y

[twilit spindle]

that is

[civic sapphire]

ok uh

thats the same answer as measure of angle x tho

[twilit spindle]

uhhh no it shouldn't be...

[civic sapphire]

yes u said

its 131

for measure of angle x

the top one

in the pic

this

oh mb its not measure of

mb

mb

mb

ok so

[twilit spindle]

\begin{itemize}
\item $x=131$
\item $m\angle V=121$
\item $m\angle X=129$
\item $m\angle Y=131$
\end{itemize}

[flat frigate]

XxMrFancyu2xX

[civic sapphire]

ok

so the measure of y is technically the same as x

[twilit spindle]

YESSS

[civic sapphire]

sick

[twilit spindle]

completely right

ok that's good

[civic sapphire]

can u do this for number 8

pls

running out of time

i wanna finsih this

[twilit spindle]

imma take a guess this is a homework assignment due at midnight

[civic sapphire]

no

lol

bedtime

[twilit spindle]

damn

[civic sapphire]

fr

sucks

[twilit spindle]

So $x$ is $x+32+136+x-6+159+128+x+56+95=180(7-2)$, do you understand how I got that?

[flat frigate]

XxMrFancyu2xX

[twilit spindle]

Just sum the inside bois

[civic sapphire]

ok

[twilit spindle]

to the size minus 2 times 180

ok

no WolframAlpha

[civic sapphire]

ok

[twilit spindle]

,w x+32+136+x-6+159+128+x+56+95=180(7-2)

[flat frigate]

Results provided by WolframAlpha

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

Requested by XxMrFancyu2xX#6050

[civic sapphire]

ok x is 100

[twilit spindle]

so now we have x

[civic sapphire]

alr

for number 8 right

[twilit spindle]

yes

[civic sapphire]

sick

ok next one beside

measure of angle b

[twilit spindle]

what is the value of b?

[civic sapphire]

lemme check

[twilit spindle]

with the x

[civic sapphire]

56

o

right x

with*

[twilit spindle]

x+56?

[civic sapphire]

so is it

100+56

[twilit spindle]

💡

[civic sapphire]

or what u said

[twilit spindle]

100+56 is right

[civic sapphire]

or me

alr

[twilit spindle]

you plugging 100 in for x

[civic sapphire]

yes

awesome

ima need to add u on discord

[twilit spindle]

now rinse and repeat

[civic sapphire]

i like u

[twilit spindle]

😳

😂

[civic sapphire]

lmao

ok uh

measure of angle b

[twilit spindle]

is $x+56=100+56=156$

[flat frigate]

XxMrFancyu2xX

[civic sapphire]

ok so measure of angle b is 156

[twilit spindle]

✅

ok so now whatever your other angle is

idk the image pretty far up

[civic sapphire]

lemme

[twilit spindle]

nice

[civic sapphire]

measure of angle d

[twilit spindle]

is...

[civic sapphire]

ok

wait

lemme try this

ok

so

angle d is 32

right

and x is 100

so my guess is

100+32

?

[twilit spindle]

yes because measure of d is actually x+32

[civic sapphire]

EZ

[twilit spindle]

so your guess would be correct

now $m\angle F$

[civic sapphire]

ima need u to tutor me more on this

[flat frigate]

XxMrFancyu2xX

[civic sapphire]

later

like tmr

ok so measure of angle d is 136

ok measure of angle f

my guess is

oh theres a minus

ok

100-6

?

[twilit spindle]

yesss

less go

[civic sapphire]

ez

[twilit spindle]

ok you're understanding this NICE

[civic sapphire]

so 94 degrees

[civic sapphire]

all bc of u

i never understanded nun

lol

see y i like u

bro fr

[twilit spindle]

all progress is progress my friend

[civic sapphire]

yes

ok so

measure of angle f

is 96

degrees

[twilit spindle]

yesssir

[civic sapphire]

alr

k number 9

[twilit spindle]

send img?

very far up

[civic sapphire]

ok u find x

ill do the measure of angles

myself

teamwork

[twilit spindle]

Ok so if we have time can I logic you through the first step?

[civic sapphire]

i got this dw

[twilit spindle]

So this polygon has 6 sides yes?

[civic sapphire]

yes

[twilit spindle]

ok so the formula $180(n-2)$ tells us the measure of the angles if we know the sides

[flat frigate]

XxMrFancyu2xX

[twilit spindle]

lucky for us, we do!

for if $n=6$ then we have $180(6-2)$

yes?

[flat frigate]

XxMrFancyu2xX

[civic sapphire]

alr

[twilit spindle]

make sense?

[civic sapphire]

ok so

ye ik the formual

formula

already

so its gonna be 4

[twilit spindle]

,calc 180*4

[flat frigate]

Result:

720

[civic sapphire]

so x is 720

[twilit spindle]

ok so 180*4 is 720

no not yet

[civic sapphire]

oh right

[twilit spindle]

the sum of angles is 720

[civic sapphire]

the sum is 720

[twilit spindle]

yess

[civic sapphire]

alr bet

[twilit spindle]

so $(x+40)+122+(x+74)+(x+18)+146+110$ is the sum of angles look at the image as see if that makes sense

[civic sapphire]

ye

got it

[flat frigate]

XxMrFancyu2xX

[twilit spindle]

so now we have two formulae describing the sum of the angles

[civic sapphire]

yes

[twilit spindle]

so what do we do?

[civic sapphire]

divide*

[twilit spindle]

❌

[civic sapphire]

what

[twilit spindle]

we set the them equal to each other because they both are the sum of the angles

right?

[civic sapphire]

right

[twilit spindle]

do you understand that?

[civic sapphire]

y3

yes

can u find x

[twilit spindle]

ok so then we (x+40)+122+(x+74)+(x+18)+146+110=720

[civic sapphire]

ill do the

measure of angles

and tell me if they right

[twilit spindle]

and whatever x is idc we have calculators for that

but it is important you know how to but I can show you tomorrow

[civic sapphire]

yes

[twilit spindle]

,w (x+40)+122+(x+74)+(x+18)+146+110=720

[flat frigate]

Results provided by WolframAlpha

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

Requested by XxMrFancyu2xX#6050

[civic sapphire]

tomorrow is good

[twilit spindle]

aight so $x=70$

[flat frigate]

XxMrFancyu2xX

[twilit spindle]

now plug into the angles and get your measures!

now i gotta go to fucking sleep

imma suffer from paralysis if i stay up any longer

hope I helped man! @civic sapphire also I added u

[civic sapphire]

ok

can we talk in dms

for a little

bit

[twilit spindle]

.close

[safe radish]

Channel closed

Closed by @twilit spindle

Use .reopen if this was a mistake.

[safe radish]

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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.

[summer sphinx]

Can I simplify this implicit equation by factoring x then dividing it both sides? Or that would be illegal?

[plucky elk]

🤔

[light shoal]

well you'd first recognize that x=0 and y = anything is a solution

then you'd consider the case x not equal to 0

in which case you can divide

[summer sphinx]

Oh, thanks! and umm... Is my statement here valid?

[light shoal]

yep that's legit, with the understanding is that either (or both) of the last two equations are true

basically because AB = 0 implies A = 0 or B = 0 or both

[summer sphinx]

ohh that makes sense thank you!

its actually a implicit diff. problem XD

[light shoal]

cool

[summer sphinx]

then do i need to take the deriv. of the two equations?

oh x = 0 is not diff.

[light shoal]

what's the original problem statement

[summer sphinx]

its a straight line

[peak estuary]

for implicit diff problems you don't solve the equation

[light shoal]

ah ok

[summer sphinx]

yea im making my life real difficult.... but u know what, i'll just diff. it as it is

thanks everyone!

.close

[safe radish]

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Closed by @summer sphinx

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[coral wind]

I have no idea where to start please help

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[coral wind]

Need help

[devout shale]

what assignment is this for

[coral wind]

Homework in basic stays

@devout shale can you help?

<@&286206848099549185>

[lavish remnant]

Most people have not taken stats. if they have they probably forgot everything

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[teal cape]

anyone know how to solve this ?

[teal cape]

i dont know where to begin

[plucky pagoda]

what the

that looks like chemistry but mirrored

[hallow egret]

Is this chemistry? @teal cape

[teal cape]

no, what makes you think its chemistry ?

its a factorial math question

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[runic lintel]

help

[runic lintel]

11y=8-3x

find 3 solutions for x and y

<@&286206848099549185>

.close

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[runic lintel]

.reopen

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✅

[runic lintel]

.close

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[runic lintel]

1+1=

?

.close

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[quick niche]

can anyone help me understand why the answer to this is just an empty set?

[quick niche]

this is the working out i was given

[vapid anvil]

What is |X|?

[quick niche]

absolute value of X?

[vapid anvil]

I see

[quick niche]

is the working out i was given correct?

[vapid anvil]

I'm still trying to understand what happened.

[quick niche]

I tried using chatgpt to explain and it gave me this which i think is correct?

[vapid anvil]

This seems correct but i do not understand the absolute value of X part.

[quick niche]

from the working out im assuming it refers to the number of elements in the set

[vapid anvil]

That makes sense

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[silk void]

a) V=R, the set of real numbers is a vector space over the field of rational number Q with the usual addition and multiplication in R b) V=R, the set of real numbers is a vector space over the field of complex number C with the usual addition and multiplication in C

[silk void]

how to check this? i have no idea for proving a) and b)

[final halo]

b is false if that helps you

[silk void]

cause of i?

[hasty wagon]

do you remember how to check if V is a vector space over Field F?

[silk void]

yes I can write 8 properties

[hasty wagon]

hmmm

you can just take a picture if you have the notes

[silk void]

does root2 or i can be counter example?

[hasty wagon]

yea, but for (b) i is not in V , so the i is working is a counter example when you are doing multiplication

[silk void]

then can i prove a) is false through counter example root2+1 doesnt define over Q?

[hasty wagon]

lemme check

note that:
for v,w in V, and f in F you'll just have to check
v+fw is in V

even if √2 is not in Q, it doesn't mean √2 cannot be in V

[silk void]

oh okay

[hasty wagon]

be careful it intentionally didn't use the word (sub-space)

[silk void]

I'm focused on the usual addition

thank you

.close

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[lean otter]

4 employees of Telecom laid a fiber optic cable with a length of 1 962 meters in 11 days during 8-hour working hours.
a) How many workers of the same qualification must the company call from another branch to complete the order for 5 850 meters of cable in 7 days with the same working hours?

[lean otter]

I am using compound Triplet formula for it

<@&286206848099549185>

skuul emoji

can anyone help

[woven canopy]

I would do it like this

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

hmmmm

@woven canopy Can you elaborate?

[woven canopy]

I think my calculations speak for themselves. What part don't you understand

[lean otter]

nvm i was confused in the 1

nvm

thank you

I now understand it

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[quasi bison]

@lean otter if there's something else you want to ask that makes you press "no" on "has your question been resolved" then ask it

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[lean otter]

yo guys i must be dumb but i cant find the pattern

[lean otter]

its not a geometric series

[granite idol]

for b?

[lean otter]

yeah

[peak estuary]

presumably a typo

[obsidian oracle]

Assume the 4th number is 1/32

[lean otter]

das wat am sayin but i might just be trifling

[lean otter]

ait ill do that thanks

.close

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[peak estuary]

otherwise take your favourite OEIS sequence 2,8,16 and continue it

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[bronze talon]

I am working on a math proof in a computer science thesis.

Problem: Let A be a non-empty finite set. Let f:A->A be a bijective map and an involution. Let {x, y} be any pair drawn from A. g is created from f by swapping x and y in the image of f (i.e. g(f^{-1}(x)) := y, g(f^{-1}(y)) := x, \forall z \in A \setminus {x, y}: g(f^{-1}(z)) := z). It is easy to see that g:A->A is a bijective map. It remains to be shown that g is an involution (g=g^{-1}).

I was able to show that g \circ f is an involution. However, I fail to show that g \circ f is commutative or g alone is an involution. Any hints are very much appreciated!

[safe radish]

@bronze talon Has your question been resolved?

[bronze talon]

I know. It's way to much text 🥲

[hasty wagon]

nah, it's just out of my helping league

read twice, no clue

[bronze talon]

I've spend the entire day on this and it just feels like I missed something super basic and obvious

So what I did so far is: As both $f$ and $g$ are bijective, $f^{-1}$ and $g^{-1}$ exist. Thus, $g(f^{-1}(x)) = y = f(f^{-1}(y))=f(g^{-1}(g(f^{-1}(y))))=f(g^{-1}(x))$. Analogues, $g(f^{-1}(y))=x=f(g^{-1}(y))$ and $\forall z\in A\setminus{x,y}:g(f^{-1}(z))=z=f(g^{-1}(z))$. Thus, $(g\circ f^{-1})^{-1}=f\circ g^{-1}=g\circ f^{-1}$, showing that $g\circ f^{-1}$ is an involution.

[flat frigate]

ffraenz

[hasty wagon]

interesting trick, can't you just use that trick to show g is an involution?
$f(g^{-1}(g(f^{-1}(y))))$

[flat frigate]

OldBiscuit

[bronze talon]

I'm not sure how to get from identity $I$ to $g\circ g$ or from $x\in A$ to $g(g(x))$. I tried to use the trick but no matter where I insert the identity I get stuck as I don't have the commutative property on the composition.

[flat frigate]

ffraenz

[bronze talon]

$g\circ g=g\circ f\circ f\circ g=f\circ g^{-1}\circ f\circ g=\dots?=I\ \ g\circ g=g\circ g\circ f^{-1}\circ f=g\circ f\circ g^{-1}\circ f=g\circ f^{-1}\circ g^{-1}\circ f=f\circ g^{-1}\circ g^{-1}\circ f=\dots?=I$

[flat frigate]

ffraenz

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@bronze talon Has your question been resolved?

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@bronze talon Has your question been resolved?

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[neat rover]

i feel like i have hit a huge wall in discrete math and no matter what I read or watch nothing can make it make sense has anyone else had this problem and if so what has helped you?

[neat rover]

its questions like these that I just cant really wrap my head around

[spiral bane]

what kind of proof are you struggling with

[neat rover]

tbh all of them im struggling on

21 is really bad tho

[spiral bane]

so youre just stuck on doing some proofs?

thats like..completely normal

thats the whole difficulty with discrete math

[neat rover]

yeah i just feel like i have hit a wall and no matter what i look at nothing can stick

[spiral bane]

do you know what an induction proof is

i dont but I just googled it and it doesnt look so bad

like for 24

what are you struggling for 24

[neat rover]

yes i do those are the only ones im kinda ok with

[spiral bane]

okay

[neat rover]

its mainly 17-21

[spiral bane]

what is ~

[neat rover]

sorry 17 to 21

like all the ones between an including 17 and 21

it was really easy at first with like prove if n is an even number n^2 is an even number

oh wait

the tilda is not

at least i think

[spiral bane]

no not that lol

the x ~ y

its not approx nor is it negation

[neat rover]

ima be honest i dont really know i have more questions from the practice with the same symbol if that helps

[fallow cairn]

~ is a symbol indicating a binary relation; we can read x ~ y as x is related to y or x relates to y

[spiral bane]

oh then I'm out of my depth here

I'm also taking discrete rn

[neat rover]

i thought it was not

[spiral bane]

it is also not

in prop logic

[neat rover]

like p is true ~p is falce

[spiral bane]

depends on the context

[neat rover]

oh yikes

thats on me

[fallow cairn]

As far as I'm aware this leans into Modern Algebra rather than propositional logic

[neat rover]

that makes sence its just alot for a first year course

like it moved too fast

[fallow cairn]

That's fair

Either way, which of 17-21 are you hoping to tackle first?

[buoyant shadow]

this part is easy enough, has no one helped with it either?

[neat rover]

i will try and start with 17 i can do easy proofs like if 9n-7 is odd n is even

[buoyant shadow]

i mean i've seen it yesterday (for me), like maybe it's actually done by now

[neat rover]

im ok with that stuff

im studying it now and its not to tricky

its mainly proofs i cant do

but relations seem ok

[fallow cairn]

Let's look at number 17; what does it mean when we say a function is one to one? And what does it mean to say that the function is onto?

[neat rover]

when a function is one to one does that mean that like f(g) = g always or somthing

like

1-2

2-3

3-4

im sorry im just really bad at this

like if the domain and co domain only have one value

[fallow cairn]

No, you're fine.

[neat rover]

thats associated with eatchother

[fallow cairn]

I think you've got a right idea, but the phrasing seems a bit off.

When we're doing proofs, we want to be careful to try and use the formal definitions whenever possible, so that we can actually prove things to be true.

Was there a formal definition your professor provided for one-to-one?

[neat rover]

no he did not i we are just suposed to know

i rember doing it in grade 11 i think

[fallow cairn]

Alright

[neat rover]

f(a)=f(b), a=b

is that it

[fallow cairn]

Yep, that's exactly it!

[neat rover]

okk awesome

[fallow cairn]

And we'll also need a definition for onto; do you recall what that is?

[neat rover]

im sorry i dont recall

is it just not one to one

[fallow cairn]

onto cares more about the codomain/range than the domain

When we say a function is onto (or "surjective"), we mean that every element in the codomain is a possible output of the function

Or more formally:

for all b in B, there exists an a in A so that f(a) = b

(if f is a function from A to B)

[neat rover]

okok thank you

does this proof involve pidgenhole?

pigeon

[fallow cairn]

It's actually pretty similar to a proof of the pigeonhole principle, but we have that the sizes are equal, and we already know it's injective/one-to-one

[neat rover]

okok so will we prove using contrapositive?

like is that an option

its the only way i can kinda think to do it

[fallow cairn]

We could do contrapositive, yeah!

[neat rover]

oooh ok awesome

so if f is not onto then f is not one to one or somthing

hm wait

nvrmind

ok i dont really know what to do from here

[fallow cairn]

Well, let's go ahead and do a proof by contrapositive.

If f is not onto, then there exists a b in B where no element in A maps to b

Consider what this means about the size of the image of f

[neat rover]

does that mean that B is bigger then A by one element

wait that makes no sense

sorry

[fallow cairn]

We defined A and B to be so that |A| = |B| = n, so rather than B increasing in size, we say that the size of the image of f is at most n-1

[neat rover]

im sorry i dont understand image

should i google it real quick

the image of a function is the set of all output values it may produce.

[fallow cairn]

yep, exactly

[neat rover]

okok i get what you are saying

[neat rover]

this wasnt me this was google

but i understand now

is the range of f |B| if it is not onto

range of f is < |B|

[fallow cairn]

Yeah, that's something we can determine

A property of one-to-one functions that would help here is the following:

If f: A → B is one-to-one, then |A| = |im(A)|

Unfortunately I don't have a proof of this on-hand

[neat rover]

hmm ok i think i get what you are saying

also i just found a proof of this i think

can you look it over and see if it makes sence

[fallow cairn]

sure

[neat rover]

my teacher just emailed this to me

so ig i have the answer now hahaha thank you for all your help though

[fallow cairn]

That looks like the same method we were going for as well, but with a more direct use of the PHP

But yeah no worries

[neat rover]

thank you i really appreciate your patience haha

.close

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[lean otter]

can someone help me with this?

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@lean otter Has your question been resolved?

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@lean otter Has your question been resolved?

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[frosty granite]

for part b

[frosty granite]

once you change the power to one plus tan squared, and separate it to e times e^tan squared

can you not integrate the e

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@frosty granite Has your question been resolved?

[frosty granite]

nvm

.close

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[stark delta]

.close

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[raven cypress]

3cos²x - 5sinx - 1 = 0
Find the value of sinx

[safe radish]

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

[raven cypress]

1

<@&286206848099549185> please

[buoyant dragon]

there?

[granite idol]

use a trig identity to have only sine in your equation

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@raven cypress Has your question been resolved?

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[hard canopy]

Question 8

I don’t even know how to prove it. All I did was just making an inequality where the discriminant of the quadratic equation is more than or equal to 0…

[maiden grove]

i need help

[hard canopy]

Occupied

[split ether]

Yeah, that's the way

[hard canopy]

And I got k >= 5/9

[split ether]

Although I would also consider the case k = 2/3 as that's when the equation stops being a quadratic one

[split ether]

Could you show your work?

[split ether]

You really rushed with the expansion

Don't you think there should be a k^2 term?

[hard canopy]

oh bruh

wait

[split ether]

Retry

[hard canopy]

k >= 1/3

[split ether]

Did you get 1 - 6k + 9k^2 >= 0?

[hard canopy]

yes

did I expand wrong

[split ether]

No, 1 - 6k + 9k^2 >= 0 is correct

But where is k >= 1/3 coming from?

Ah, did you take sqrt of both sides?

[hard canopy]

yes

[split ether]

(3k - 1)^2 >= 0, so 3k - 1 >= 0?

[hard canopy]

Look

[split ether]

Well, that's not correct actually

A square of a number will always be >= 0

[hard canopy]

I don’t get it?

[split ether]

For example take k = 0

It's not bigger than nor equal to 1/3, but is (3k - 1)^2 >= 0 false?

[hard canopy]

no?

[split ether]

Yeah, it's true nonetheless

So k >= 1/3 is not the solution

What I am saying is that (3k - 1)^2 >= 0 is always true

For all k

Because whether 3k - 1 is positive or negative, its square, (3k - 1)^2, will always be either positive or just 0

[hard canopy]

so do I just stop my working at the (3k-1)^2 step

[split ether]

Yes

That's where the proof ends

[hard canopy]

that’s weird

ok thanks anqyays

anyways*

.close

[safe radish]

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[earnest wagon]

When we say A and B commute with each other, does that mean AB=BA?

[quasi bison]

yes

that's exactly what it means

[earnest wagon]

Ok tysm

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[errant valley]

could someone explain me where does the mean formula come from, please?

[safe radish]

@errant valley Has your question been resolved?

[granite idol]

it's just the definition of expected value for a continuous RV

[errant valley]

yeah but why is it like that?

where does it derive from?

[granite idol]

how is it derived? I'd have to look it up but it's just a definition

[amber socket]

Yeah I know it's a definition but it must have an explanation

I want to understand where it comes from and not just accept it

I have been searching for an answer on the Internet but I can't find anything

[granite idol]

for discrete RV it just comes from the arithmetic mean

the continuous situation is just an extension of discrete, changing the summation to integration

[safe radish]

@errant valley Has your question been resolved?

[safe radish]

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[boreal cypress]

hi, this is a calculus problem. would you say this accurate?

[lean otter]

looks good to me

[bold ferry]

me 2

[lean otter]

i dont see anything wrong

[grim plover]

yeah

[boreal cypress]

ty

.close

[safe radish]

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• Show your work, and if possible, explain where you are stuck.
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[dark shale]

I'm struggling to understand what happens between these two steps. Can someone enlighten me?

[lime dust]

(a-b)/c = a/c - b/c

[granite idol]

they divide each term by x

[lime dust]

by sqrt(x)

[dark shale]

not by sqrt(X), right? because than the right term would be 2sqrt(x)sqrt(x) and denominator should then just be 2x

[lime dust]

the right term is

sqrt(x)(2x-4)/x

multiply by 1

1 = sqrt(x)/sqrt(x)

you get (2x-4)/(x/sqrt(x))

(x/sqrt(x)) = sqrt(x)

so you have (2x-4)/sqrt(x)

[granite idol]

they are dividing both terms by x

[dark shale]

ohhh i see that actually @granite idol

at least for the first term

[granite idol]

$\frac{\sqrt{x}(2x - 4)}{x} = \frac{2x - 4}{\sqrt{x}}$

[flat frigate]

cwatson

[granite idol]

it's the same principle for the second term as well

[lime dust]

i see they are multiplying by sqrt(x)/sqrt(x), but u can see the other way too

dividing i meant

[granite idol]

there is an x in the denominator over both terms, that's how they're simplifying

[lime dust]

but you use the first thing i said

i was talking about the first part

not the whole equation

you did right away

i did maybe unnecesary steps, but because he didn't understand i thought it was needed

[granite idol]

no worries

[dark shale]

cheers

!close

/close

[lime dust]

.

dot

[dark shale]

.close

[safe radish]

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[dark shale]

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