help-13

[tropic oxide]

,rccw

[tropic oxide]

okay, alright

[wind maple]

Yeah

[tropic oxide]

so then when it says angle BAC = angle DBC for #9, that's not something you need to prove, that's something you know and can use.

[wind maple]

Ok

can you show how to do this

and vertex coressponding

[tropic oxide]

i'll repost the diagram here

[wind maple]

Ok

[tropic oxide]

you have two triangles here that you care about: triangle ABC and triangle BDC

[wind maple]

Yeah

[tropic oxide]

you in fact have enough information in the diagram to conclude that these triangles are similar.

[wind maple]

Ok

[tropic oxide]

do you see what information i am talking about?

[wind maple]

Yeah isee

what are corresponding veretx

for both traungles

[tropic oxide]

i think you don't see it...

[wind maple]

I do

I made traingle

onmy book

copy*

[tropic oxide]

ok, then tell me: what information lets you conclude the two triangles are similar?

[wind maple]

same angles

[tropic oxide]

that is too vague.

tell us which pairs of angles' equality you are talking about.

[wind maple]

bac and

bda

?

[tropic oxide]

so you are saying angle BAC = angle BDA?

[wind maple]

Yeah

[tropic oxide]

the diagram doesn't indicate that.

how did you get that these two angles are equal?

[wind maple]

it states on q

with the sign

of simmilarity

[tropic oxide]

the question does NOT state that angle BAC = angle BDA.

[wind maple]

What?

[tropic oxide]

look here

the only explicitly-stated equality of angles is angle BAC = angle DBC, not angle BAC = angle BDA.

[wind maple]

Okay

[dull oxide]

Proofs are hard the first time you do them

[wind maple]

Its quiet tricky question...

[dull oxide]

My old geometry teacher used to call your style of proof the "look alike theorem"

[tropic oxide]

it is not any trickier than other questions within the same exercise.

[dull oxide]

The angles look the same, so they must be

[wind maple]

Lets go ahead

with the question

?

[tropic oxide]

yes, let's.

[wind maple]

okay

[tropic oxide]

i was just typing up a thing i wanted to say

[wind maple]

okay

[tropic oxide]

one of the methods of proving two triangles are similar is to identify two pairs of equal angles within your triangle.

[wind maple]

Oh okay thanks

[tropic oxide]

you might see this abbreviated as AA, in line with triangle congruence tests such as SSS, SAS or ASA.

[wind maple]

Yeah

[tropic oxide]

for our problem, we have for triangles ABC and DBC the following info:

• angle BAC = angle DBC (explicitly stated)
• angle DCB = angle BCA (literally the same angle)

[wind maple]

Yeah we have that given

[tropic oxide]

this is enough to establish the triangles as similar, and also clarify which vertices correspond to which.

[wind maple]

Okay which then

[tropic oxide]

vertex A in the big triangle corresponds to B in the small triangle, and C corresponds to C.

because those are the vertices of the known-equal angles.

[wind maple]

Okay let me write that right

[tropic oxide]

so the correct similarity statement is $\triangle ABC \sim \triangle BDC$.

[wraith dagger]

Ann

[wind maple]

how does c correspond with c

[tropic oxide]

• angle DCB = angle BCA (literally the same angle)

[wind maple]

okay what about D? What does

it correspond

with

[tropic oxide]

the two unmatched vertices in both triangles correspond with each other

[wind maple]

OHh

isee

okay

so

nowwhatdo i do furturer

<@&286206848099549185>

Never mind

i solved it

[latent bloom]

[wind maple]

can anyone help me with q11

[latent bloom]

Sure

[wind maple]

Thanks! We have to find the unknown letters in Q11

So,

W, V

[latent bloom]

Okay

Are these triangles similar

?

[wind maple]

Yeha

Yeha

YEah

Yeah*

[latent bloom]

Okay

XY is similar to WY

[wind maple]

Okay

[latent bloom]

Make a ratio between them using XY and WY

[wind maple]

So, 3/4

[latent bloom]

Then use that ratio to get w and v

Ye

[wind maple]

how?

[latent bloom]

What does WY correspond to in the big triangle?

[wind maple]

xy

?

3+v

[latent bloom]

Hmm

Wait wait

[wind maple]

okay

[latent bloom]

WY is similar to XW actually

[wind maple]

oh

[latent bloom]

So like

4/5

[wind maple]

yeah

areu sure

imean

[latent bloom]

Wait

[wind maple]

we aresuppose tofind unkown

[latent bloom]

This triangle is confusing

Okay

XY/XW

Should be it

[wind maple]

yes

[latent bloom]

Because smallest leg of both

[wind maple]

AREU ssure

[latent bloom]

Ye

[wind maple]

though>?

whatare te verext

just tell me the corresponding veretx

it will be good then

[latent bloom]

Okay

X corresponds to itself

[wind maple]

doesnt x=y

?

i think

[latent bloom]

Y corresponds to W

[latent bloom]

Where?

Oh nope

[wind maple]

oh

okay

then

[latent bloom]

The right angle goes with the other right angle

So

XYW corresponds to XWZ

[wind maple]

ok

[latent bloom]

And angle XWY corresponds to Z

[wind maple]

OKaythanku

[latent bloom]

You got the question now?

[wind maple]

Tbh no

[latent bloom]

Hm

Okay

XY corresponds to XW

So

3/5

[wind maple]

yes

then

what doi do

[latent bloom]

3/5 = 4/w

[wind maple]

so

3w=

20

[latent bloom]

Ye

[wind maple]

w=20/3

[latent bloom]

Yeah

[wind maple]

Okay

Thank you somuch

[latent bloom]

The missing side you can get through Pythagoras or through similarity

Because of the right angle triangle

[wind maple]

So

my schooltaught methat

there is another way solving this question

by using porpotionality

dou know of that

[latent bloom]

That's what we used just now

[wind maple]

no

i mean

like

[latent bloom]

[slow sphinx]

Does he mean similarity

[latent bloom]

Yeah she means similarity

Or probably she means something else

[slow sphinx]

Sorry for the misuse of pronoun

[latent bloom]

No worries lol

[slow sphinx]

I think its similarity since it is similar to proportional

[latent bloom]

Yeah

But

[latent bloom]

This

@wind maple

[slow sphinx]

I wish they could explain better with an example

[latent bloom]

Hopefully ocean returns

[slow sphinx]

Yeah..otherwise the problem is straightforward

One triangle is a smaller version of the other

[latent bloom]

Ye

I think Ocean meant that

You can solve this particular one

Through Pythagoras

Because right angle triangle

Also it's a 3-4-5 triangle

[slow sphinx]

So if I use the proportional method $5(bigger)=3(smaller)$ what about $w(bigger) = 4(smaller)$ and $3+v(bigger)= 5(smaller)$

[wraith dagger]

Pyp

[latent bloom]

There are 3 similar triangles here

XWY

XWZ

And

WYZ

All three are similar

[slow sphinx]

I prefer the biggest one and the smallest one

That way you don't worry about anythin

[latent bloom]

Well

You will have to worry about correspondence correctly

[slow sphinx]

Yeah

But if you know that the sides must face opposite angles which are equal

Then it becomes easy

[latent bloom]

Yeah

@wind maple

Where

[slow sphinx]

Let's just hope they return

[latent bloom]

Oh yeah maybe internet died for Ocean

[slow sphinx]

True

Well they'll just ping you when they cone back

[latent bloom]

Maybe

[cedar kiln]

@wind maple Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[vernal yoke]

come on guys... how many triangles in total are there in this goddamn graph

[vernal yoke]

taks was to make it A^3 and then tell how many triangles there are

i see 6 triangles per point

but is there a combined number of all the different points ?

[rustic siren]

so u have 6 3-long roads from each of them

and i think u counted each road from all of its 3 vertices, and also forward and backwards too(?)

so u have to divide it

[vernal yoke]

divide it by what?

[vernal yoke]

there is no forward and backward since it takes 3 roads. To be a closed circle it needs to visit 2 other points and come back to the original point

that's why it's only the numbers on the diagonal that represent each points amount of triangles

[rustic siren]

label the vertices

and u get that the 3-long roads from A are ABCA and can also be ACBA

[vernal yoke]

hmm i am in my car rn, let's just say top left is x1, top right x2, bottom left x3 and bottom right x4

[rustic siren]

but those only represent 1 triangle

and u count them by B too, as BCAB and BACB

[vernal yoke]

ah ok i get what you mean

the other 3 ways are just different ways to draw the same triangle

yeah so we got 3 original triangles per point

now we need to eliminate the ones they share in common

@rustic sirenyou got an idea how to do this?

each 2 points share 2 triangles

so -1 for each 2 points

-8?

so at the end we are left with 4 triangles?

12-8 = 4

[rustic siren]

you count each triangle by each of its vertices

so 3 times

[rustic siren]

and also the directions, as i said here

[vernal yoke]

yeah but in the end there are 4 triangles in that graph with different vertices

[rustic siren]

yes

ofc

6+6+6+6=24

div by 3 as we discussed

[rustic siren]

and also div by 2 because of this

[vernal yoke]

why?

each point has 3 triangles with different points

that's 24:2= 12

ok nevermind

my answer earlier was wrong

hmm

TF i am stuck

[rustic siren]

which part?

the /3 ?

[vernal yoke]

each 2 points share 2 triangles

[rustic siren]

so?

[vernal yoke]

there are 12 connections between points though (wrong)

no 6

6 connections between points

and we can do it :2

since they share

[rustic siren]

so, we have 24 roads

lets look at them

ABCA

its a triangle

[vernal yoke]

yeah i get that part

just need to get how to trim it down

[rustic siren]

find another one which gives us the ABC triangle

[vernal yoke]

i just see reasons to :2, :2

endresult is 6

@rustic sirenhow do you get the :3

that's what i lack the knowledge of

[rustic siren]

u count this 3 long road by A B and C too

so because u counted each of it 3 times more, u div by 3

[cedar kiln]

@vernal yoke Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[stiff merlin]

Hi,please can someone help for solution?

<@&286206848099549185>

I dont have any ideas about this question,if it is possible please write whole solution clearly

[foggy merlin]

Gram Schmidt algorithm

@stiff merlin

[stiff merlin]

Could you write solution please?

[foggy merlin]

no

[tropic oxide]

we don't do that here.

[stiff merlin]

Okay but could you please show some steps?

[foggy merlin]

like I said, look for Gram Schmidt Algorithm

Its everywhere on the internet

@stiff merlin

[cedar kiln]

@stiff merlin Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[austere flame]

Can someone help me with part b of question 5?

[rustic siren]

,rotate

[rustic siren]

u have the altitude

use an area formula which uses it

[austere flame]

It comes out irrational

I might be wrong

[sleek condor]

well its probably irrational yes but why would it be a problem

your altitude also is

[lyric jungle]

Unless you know it's supposed to be a nicer number, it could still be right

[austere flame]

Ok thank you

.close

[cedar kiln]

Channel closed

Closed by @austere flame

Use .reopen if this was a mistake.

[cedar kiln]

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.

[noble palm]

How can I calculate this thing?

[crimson sedge]

Calculate?

Like prove its convergent or find the sum?

[noble palm]

Yeah

[crimson sedge]

... That wasn't a yes or no question

[noble palm]

Sry

Find the sum

[crimson sedge]

Ah pain

[noble palm]

🥲

[crimson sedge]

Hm

[noble palm]

<@&286206848099549185>

[cedar kiln]

@noble palm Has your question been resolved?

[cedar kiln]

@noble palm Has your question been resolved?

[cedar kiln]

@noble palm Has your question been resolved?

[vast beacon]

what?

what is question

cant find it

[noble palm]

.

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[thick pagoda]

Can someone tell me how exactly this step work for induction?

[dire geode]

call a = k+1 and b= k+2 and factor out ab

[thick pagoda]

but what happened with the first k?

[kind patio]

Uh k/3+3/3=k+3/3

[thick pagoda]

aaaaaah

omfg

so simple

.close thaanks ❤️

[cedar kiln]

Channel closed

Closed by @thick pagoda

Use .reopen if this was a mistake.

[cedar kiln]

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.

[cerulean star]

no

there is no value of x that makes either one of these functions undefined

so you just need to find the values of a and b such that LHS = RHS

(when you set them equal)

I mean I guess it would fail to be differentiable if the left tangent at x=1 isn't equal to the right tangent but you can just test I guess
I never had to do that in school though

polynomials are everywhere-defined

remember?

also, just by inspection:
You are not taking even roots of negative numbers;
You are not taking logs of ints less than or equal to 0;
You are not dividing by 0;
etc.

and you know what

you need two equations to solve for two unknowns anyway

so you need to set the position functions (these functions) equal

and also their first derivatives

and I think that will do it

$\text{eq1: } x^2 + 2x - 1 = ax^2 + b \
\text{eq2: } 2x + 2 = 2ax$

(you gotta plug in x=1 tho)

then these are linear equations

😉

$\text{eq1: } 2 = a + b \
\text{eq2: } 4 = 2a$

[modern compass]

+1?

[wraith dagger]

Disorganized

[cerulean star]

ty

[cedar kiln]

Channel closed

Closed by @tight cape

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.

[wraith dagger]

Disorganized

[crimson sedge]

Steal

[crimson sedge]

So I'm kinda unsure how to solve this (possibility(

[dire geode]

show the original problem

[crimson sedge]

It's in Swedish so I'll translate it to my best abilities

A car survey was published, 5% of the cars had problems with the blinkers, 3% had problems with the seatbelts and 1,5% had problems had problems with the steering wheel

What's the chance of car having at least one of the issues?

They want me to use compliment events to solve this

The car problems are also independent

So i did 95/100x97/100x985/1000

1-P(no malfunction)= P(at least a malfunction)

Did i do it correct? It feels wrong

[dire geode]

looks right

[crimson sedge]

Ah okay, thanks for the feedback <3

.close

[cedar kiln]

Channel closed

Closed by @small escarp

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.

[torpid urchin]

could anyone let me know where i went wrong because there is no way this is right

[dire geode]

,w int 0 to pi/2 of sin^5(x) cos^8(x) dx

[wraith dagger]

Results provided by WolframAlpha

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

Requested by riemann#2529

[upper garnet]

Sin^5x is not (sin^2x)^2?

[torpid urchin]

i added that sinx on at the end

[dire geode]

,calc 1/13 - 2/11 + 1/9

[wraith dagger]

Result:

0.0062160062160062

[torpid urchin]

hold up

am i right

[dire geode]

[torpid urchin]

wtf

calculator error

i got like

80

or something

[dire geode]

,calc 8/1287

[wraith dagger]

Result:

0.0062160062160062

[torpid urchin]

interesting

well that answer was right ^

thanks lol

.close

[cedar kiln]

Channel closed

Closed by @torpid urchin

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.

[final raptor]

Can someone solve this?

[cedar kiln]

Please don't occupy multiple help channels.

[upper garnet]

What have u tried

[dire geode]

closed your other channel

[final raptor]

Ive tried 1000/ 8 -25) which is 100 then 100x100 = 10 000 - 150 x 46 + 100 = 7000 = 10 000 -7 000 and then I dont really know what means divided by 1/3

[cerulean star]

what kind of thing is "1/3"

[final raptor]

yeah Im not sure

[cerulean star]

"1/3" is a ....

not a trick question

[final raptor]

yeah xD I dont remember the word in english

[cerulean star]

what is your native language

[final raptor]

Finnish

[cerulean star]

oh, there's Finns in here sometiems

[final raptor]

nice ; )

could you help me solve this problem? do you know how to solve it?

[cerulean star]

yes, everyone is able to LOOK UP the rules for simplifying algebraic expressions

...unless you don't have the vocabulary to describe the problem, I guess

You need to know the "Order of Operations"

You need to know "how to divide by a fraction"

then you should be good

[final raptor]

what means 1/3?

[upper garnet]

???

[cerulean star]

that's the fraction "one-third"

1 divided by 3

it's a number. Fractions are numbers.

[final raptor]

yeah so 0.33?

[cerulean star]

there is a rule (that you can prove) that tells you how you are supposed to divide by fractions

[cerulean star]

you are not supposed to approximate this answer

oh

maybe you are

you got some numbers that don't evenly divide here

[final raptor]

yeah

[cerulean star]

this question is only testing if you know your order of operations

it's testing if you know how to punch expressions into a scientific calculator

this is very, very basic

you just don't have the practice (or the notes?)

so you need to look it up

it is called "Order of Operations" or "PEMDAS"

[final raptor]

Could you say the answer and then I would try to find out why is it that? 🙂

[cerulean star]

no.

[final raptor]

why

[cerulean star]

this is too easy

I would be robbing you

look it up

there will be simpler examples

[final raptor]

wdym look it up

[cerulean star]

GOOGLE

[final raptor]

how to google that?

[cerulean star]

how do you google anything?

I told you what to google

#help-13 message

[final raptor]

order of operations?

k

I still dont know how to find out the answer to that equation tho

I would need to get it pretty quickly

[cerulean star]

you will when you read what Order of Operations is and look at the examples

and you will feel silly for asking

instead of just looking it up and trying first

this class very clearly expects you to know how to do this already

that is a guestbook

you need to solve that just to be counted

[final raptor]

I dont have to alot of time its 1.47 am here, I dont have time to figure out how to solve it

[cerulean star]

you do if you want to pass this class

this is the beginning of your class

or the previous class, maybe?

I'm just guessing what this is for

this is learned in middle school

[final raptor]

yeah Im 17 and I was never good at math, I dont remember

[cerulean star]

that's fine, but you can look it up now

this is how people in math learn math

[final raptor]

my english skills not enough for that

[cerulean star]

they use their tools

including search engines

[final raptor]

are you a teacher?

[cerulean star]

they know how to find the things they need

yes

[final raptor]

do u get paid?

[cerulean star]

yes

[final raptor]

nice

[cerulean star]

translate the page

[final raptor]

no time for that

this is like the last question in this test

so I would need to get it quickly to go to sleep

[cerulean star]

https://www.youtube.com/watch?v=dAgfnK528RA

[final raptor]

I told u I dont have time for that tho 🙂

Im sry

I just wanted to have the answer to this equation

[dire geode]

you're in the wrong place

it's against the rules to give answers

go pay for a tutor

[final raptor]

oh

can u dm me it? no one would know 😉

[cerulean star]

I can't make this horse drink @dire geode

[final raptor]

yeah I done have time right now

im gonna leave soon

[cerulean star]

@final raptor you're a fool man. You are at the bottom of math and there is nowhere to go if you don't know these rules

[dire geode]

[cerulean star]

you're going to be stuck

this is the BOTTOM

[final raptor]

Lol

[cerulean star]

just watch it.

[final raptor]

go do PE

gl in life bro

[cerulean star]

bye

[torpid urchin]

this was fun to read through

could you not have typed it character for character in symbolab and get an answer

[cedar kiln]

@final raptor Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[crimson sedge]

P(7/25, y), y>0 how do I find the exact value of y? P is a point on a unit circle. Also, find the values of the six trigonometric functions for the angle θ with a terminal side that passes through point P. Not sure what they're asking

[crimson sedge]

Oh nvm, duh. x^2+y^2=1

[cedar kiln]

@crimson sedge Has your question been resolved?

Channel closed

Closed by @deep mason

Use .reopen if this was a mistake.

[cedar kiln]

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.

[serene herald]

Hello would this be a correct simplification?

[ancient lodge]

,w 13-1(181-13(13))=1(181(13))

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Civil Service Pigeon#1465

[modern compass]

are you trying to write 1 as a linear combination of 181 and 13?

[serene herald]

nvm i got it

[ancient lodge]

.close

[cedar kiln]

Channel closed

Closed by @ancient lodge

Use .reopen if this was a mistake.

[cedar kiln]

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.

[crimson sedge]

Let $x$ be an irrational number. Show that for some positive integer $j$ not exceeding the positive integer $n$. The absolute value of the difference between $jx$ and the nearest integer to $jx$ is less than $\f1n$

\vspace{3 mm}
So if my understanding is correct; we are considering ${x} = x - \floor{x}$ where $0 \leq {x} <1$ but how should I proceed from here?

[crimson sedge]

Do I apply pigeonhole principle?

[wraith dagger]

♡A(lex)♡

[gilded elm]

the floor may not be the nearest integer actually

[crimson sedge]

Really?

[gilded elm]

like for example

floor 0.6 = 0

but the closer integer is 1

[crimson sedge]

hm

[tropic oxide]

your punctuation contains multiple issues btw

[crimson sedge]

Ah sorry was lackluster haha

did not think it through

[tropic oxide]

anyway

you wish to show that for every irrational number x, some integer multiple of x falls within 1/n of an integer. is that so?

[crimson sedge]

yep

my first thought was the pigeonhole principle

but i am not sure

[tropic oxide]

partition [0,1) into n equally sized "bins" [0, 1/n), [1/n, 2/n), ..., [(n-1)/n, 1)

[crimson sedge]

yes

[tropic oxide]

and place the fractional parts of the numbers x, 2x, ... (n+1)x in these bins

[crimson sedge]

then one pigeonhole must contain at least two of them, i imagine

[tropic oxide]

since x is irrational none of these will be integers themselves

[tropic oxide]

yes exactly

[crimson sedge]

hmmm

so if we say

Some ${ax}$ and ${bx}$ that belong to those pigeonholes with $a > b$, then ${ax} - {bx} < \f1n$

[wraith dagger]

♡A(lex)♡

[crimson sedge]

which is basically what u said, i think

so like

$a-b < n$ too then right?

[wraith dagger]

♡A(lex)♡

[crimson sedge]

oh wait okay i figured it out

thank you ann

.close

[cedar kiln]

Channel closed

Closed by @inner dirge

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.

[crimson sedge]

the first region is region e, i dont understand how should i find which line represents y < 4 - 2x

[crimson sedge]

and for b) i dont understand the last two

[wispy sentinel]

think of the inequality symbol as = for a second

y=-2x+4

[crimson sedge]

i think that was the first step for it

[wispy sentinel]

right

so which like looks like that?

line*

[crimson sedge]

that is how i have found first inequalities

[crimson sedge]

i dont get this

[wispy sentinel]

ok well recall y=mx+b, where b is the y int

[crimson sedge]

like where would be 2x and like 4

i have learnt this y = mx + c, where m is the gradient and c is the y-intercept

[wispy sentinel]

so first look for lines that intercept y axis at +4

[wispy sentinel]

same thing

so c=4 here

[crimson sedge]

i have got confused when it says y = 4 - 2x, like its mx + c, how is 4 as 4x like x with 4

this one

so i became stuck

[wispy sentinel]

rewrite it as $y=-2x+4$ first

[wraith dagger]

nαv

[crimson sedge]

oh

its y = 4 - 2x

[wispy sentinel]

right, so what looks like the m coefficient and what looks like c?

right, but its the same thing: $a-b=(-b)+a$

[crimson sedge]

m will be = -2 and c would be = 4

[wraith dagger]

nαv

[wispy sentinel]

right

so does any line intercept the y axis at 4?

[crimson sedge]

there is one line

[wispy sentinel]

yes

so now you know which line

can you proceed from here?

[crimson sedge]

this one

[wispy sentinel]

yes, the one that has a slope/gradient of -2

[crimson sedge]

so do you focus on y - intercept always

[wispy sentinel]

it's just a nice and simple way to find the line

[crimson sedge]

how do we know that it is -2 as gradient

[wispy sentinel]

in y=mx+c, m is the gradient

and in this equation, -2 preceeds x

so -2=m

[crimson sedge]

one more thing i wanted to ask was that in this line y = 4 - 2x, can we also say like this after considering y = mx + c, that m in this is -2 as that is with x and y-intercept is 4, because that line we see is cutting itself at 4

[wispy sentinel]

yes

[crimson sedge]

so we got to know where how we can find it

thanks very much for making it clear to me, i have understood it and now i can work at last two inequalities

.close

[cedar kiln]

Channel closed

Closed by @zealous thistle

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.

[crimson sedge]

In the triangle ∆ABC, let G be the centroid, and let I be the center of the inscribed circle.
Let α and β be the angles at the vertices A and B, respectively. Suppose that the segment
IG is parallel to AB and that β = 2 tan−1
(1/3). Find α.

[crimson sedge]

<@&286206848099549185>

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[grizzled stone]

hey

[grizzled stone]

why is the answer C?

it’s physics

<@&286206848099549185>

[tropic steppe]

is it ohms law or what?

[dire geode]

#old-network for physics server

[supple moat]

(P/V)^2 is basically= I^2 (current squared)

[glacial pollen]

P = VI; P/V = I; Thus, P - (I)^2R

[grizzled stone]

dk why not able to post there lol

[grizzled stone]

ok wait can u explain why it’s not D?

[grizzled stone]

hey wait can u explain why it’s not D also

[glacial pollen]

Vc indicates the potential difference across the cables

[grizzled stone]

yes

[lethal jackal]

this is so nontrivial to understand lol

what about the fact that voltage and current are not necessarily in phase

[grizzled stone]

wait so why not Vc?

[lethal jackal]

because I is the current that the generator must produce

why would how long the cable is impact how much current the generator has to produce to have a certain output power

[grizzled stone]

“Hi! My idea was as the Power output of generator P minus (P/Vc)^2 then times R which suggest the power from generator - power that loss in cable because Vc stand for the voltage across the cable which make more sense to me if u want to find the power loss in cable?”

this is what my friend said

he chose D

but ans is C

[lethal jackal]

assume for the sake of simplicity that the generator actually makes DC because it's a fat mess with things like phase

or that the load is purely resistive I guess

[grizzled stone]

oh

[lethal jackal]

if the generator is producing 25 kW at 1000 V, how much current does it have to produce for that to even make sense?

[grizzled stone]

hmm ok but where is the error in this?

it seems to make sense to me but it’s not right

[lethal jackal]

the error in it is that it makes absolutely no sense to divide P / Vc

like what is that quantity supposed to mean?

[fair geyser]

the lines have their own R and P and V

the I is not "their own" it's shared with the entire circuit

P/V lets you find the I

[lethal jackal]

P / V is the current that the generator has to produce for it to be producing power P at voltage V

and the same current goes through the transmission lines

but like this question is awful because it specifically mentions an AC generator and the transmission line is never purely resistive, and neither is the load lol

[fair geyser]

(P/V)Vc should also give the answer

does it?

i mean, P − (P/V)Vc

[lethal jackal]

it does

[fair geyser]

yeah, so "local current times local voltage is local power"

i get it

[lethal jackal]

note that Vc = (P/V)R so it's a whatever

[fair geyser]

and the current is the same everywhere

[cedar kiln]

@grizzled stone Has your question been resolved?

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[cedar kiln]

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.

[kindred crown]

how do i express r^2=a^2cos(2θ) into Cartesian form?

[earnest socket]

$\cos(2\theta) = \cos^2(\theta) - \sin^2(\theta)$

[wraith dagger]

tushar

[sullen saffron]

Multiply through by r^2 and use the identity above.

[kindred crown]

can taking values for 2cos^2(θ)-1 as 2(x/r)^2-1 be another solution?

[kindred crown]

the answer comes: (x^2+y^2)=a^2(x^2-y^2)

[earnest socket]

x = rcos(theta)

check your right-hand side

[sullen saffron]

r^4 = a^2(r^2 cos(2θ)) = a^2(r^2cos^2(θ) - r^2 sin^2(θ))

[cedar kiln]

@kindred crown Has your question been resolved?

[kindred crown]

futher simplifying it, comes this answer

[kindred crown]

this

[sullen saffron]

The result should be r^4 = a^2(x^2 - y^2).

Hence (x^2 + y^2)^2 = a^2(x^2 - y^2).

[kindred crown]

cool

[kindred crown]

thanks, that was a typing mistake

[sullen saffron]

Ok. You have it then. 🙂

[kindred crown]

/close

.close

[cedar kiln]

Channel closed

Closed by @kindred crown

Use .reopen if this was a mistake.

[cedar kiln]

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.

[mortal yarrow]

Hello, I have a question if I have a positive integer a and I add an irreducible fraction like p/q where p and q are coprime is the result an irreducible fraction ?

[lethal jackal]

if you add to a to p/q, then you have (aq +p)/q, and (aq + p) must also be coprime to q

wait that sounds like bullshit

lemme think a lil

nah sounds legit

[mortal yarrow]

yes ok i had this also but i wasn't sure thanks

.close

[cedar kiln]

Channel closed

Closed by @mortal yarrow

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.

[deft forum]

hi uh so

[deft forum]

heres the question

uh i'm not sure how can i find vec b

[sacred grail]

shallow

[deft forum]

wait

do i take b= xi+yj+zk?

and then do cross to find x,y,z

?

damn thats really gonna be lengthy

[sacred grail]

lemme read

[deft forum]

i'd need to solve system of eq aswell then

[toxic moat]

[deft forum]

circle

hii

[toxic moat]

[deft forum]

its been a long

[toxic moat]

hi

few hours

[deft forum]

since i hav seen u in help

[sacred grail]

might not be a clean way to do this

you kinda just have to like

brute force it

[deft forum]

sadge

[sacred grail]

i think you can do something like

[toxic moat]

b x (a-b)/||a-b||= (b x a - b x b)/||a-b||
=(-a x b +0)/||a-b||

[deft forum]

wait but then why do we hav dot

[toxic moat]

...

[deft forum]

we just love discord

[toxic moat]

=(-a x b +0)/||a-b||```

[deft forum]

[toxic moat]

wait

crap its doy

dot

oops

wait isit

[deft forum]

[toxic moat]

yaaaa

projection is dot

crap

[deft forum]

projection means dot yea

whats t

[toxic moat]

=(a dot b + b^2)/||a-b||```

[deft forum]

[toxic moat]

bru no what

[sacred grail]

and then solve for t

[deft forum]

uh

[deft forum]

[toxic moat]

i like this more

[deft forum]

where r u pulling this up from

[toxic moat]

deep ass

LOL

[deft forum]

[deft forum]

.e pepewtf

where r u getting this from

[toxic moat]

yaaaaa

[sacred grail]

like

[toxic moat]

i tell u

this is

all of snows explainations

[deft forum]

[toxic moat]

classic

[deft forum]

dumb it down a bit

[toxic moat]

cannot understand the hardships of commoners

[deft forum]

[toxic moat]

no

[deft forum]

bruh

wtf

[toxic moat]

hahhahahaa

[deft forum]

[sacred grail]

[toxic moat]

im so happy

[sacred grail]

like

[toxic moat]

im not being explained to

[sacred grail]

theyre perp

so you just like

[toxic moat]

this is a

fun exp

[sacred grail]

take the perp component

[deft forum]

yes i get it now

[sacred grail]

to a

[toxic moat]

what

:0

[deft forum]

but thats like taking unconventional route

[sacred grail]

[toxic moat]

yaaaa

how did

t even appear

:0

[deft forum]

uh i mean i get ur idea

[toxic moat]

like

[sacred grail]

not sure if theres a cleaner way

[deft forum]

buts its pain

well

[sacred grail]

i think b = xi + yj + zk is also pain

[deft forum]

jee is pain

:sobroll:

[toxic moat]

nono where did that come from

😭

[sacred grail]

wait

[deft forum]

waits

[sacred grail]

you can solve for the angle between them right?

[deft forum]

how do u plan to go on about this

[toxic moat]

errrrrrrrr

lol

[sacred grail]

like

[toxic moat]

oh ya

[sacred grail]

|a x b|

and we know length of a

[deft forum]

b·a - b·b?

[sacred grail]

so

[deft forum]

uhh

[sacred grail]

[deft forum]

[sacred grail]

like

you just calculate the area of the rectangle

t is the width

scaled appropriately

[deft forum]

what rectangle?

axb?

[sacred grail]

the one formed by a and b

[deft forum]

[sacred grail]

needs to be |a x b|

[deft forum]

parallelogram exists

[sacred grail]

yeah but you project

[deft forum]

wdym

[sacred grail]

like

you can remove the a component

because its parallel to a

[deft forum]

uh

what

[sacred grail]

this part will contribute 0

[deft forum]

[sacred grail]

to the area

[deft forum]

oh

icic

[sacred grail]

because its just a shear parallel to the direction of a

[deft forum]

ic

[sacred grail]

[deft forum]

[sacred grail]

still pain

[deft forum]

i'm in constant pain

[sacred grail]

[deft forum]

lets see when i get solutions

if they've made some

[sacred grail]

oh

[deft forum]

nicer

[sacred grail]

it could be +-

[deft forum]

approach

area

[sacred grail]

so you'll have to check handedness

[deft forum]

more pain

[sacred grail]

[deft forum]

i'll just xi+yj+zk

[sacred grail]

[deft forum]

[sacred grail]

if you had wolfram

you could do it in like a minute

[deft forum]

😭

if only i had wolfie

so much of my pain would be gone

anyways

.close

[cedar kiln]

Channel closed

Closed by @deft forum

Use .reopen if this was a mistake.

[deft forum]

wait

.reopen

[cedar kiln]

✅

[deft forum]

uh

i hav another Q

[sacred grail]

[deft forum]

uh in here

how do i find the dist

what i'm thinking of it

[sacred grail]

liens

[deft forum]

find

the normal line

[sacred grail]

yeah

[deft forum]

see where it intersect

[sacred grail]

[deft forum]

find the points

and then find dist

any better way?

[sacred grail]

like

[deft forum]

[sacred grail]

(-6, 7, 1) x (2, 1, 1)?

[deft forum]

[sacred grail]

thats the normal line?

direction

[deft forum]

uh no it'll be plane

[sacred grail]

[deft forum]

[sacred grail]

what

[deft forum]

this

[sacred grail]

no like

its perpendicular to both lines

the vector

[deft forum]

[sacred grail]

then you just project onto it

[deft forum]

yea

project what

[sacred grail]

wait does that work

[deft forum]

uh

[sacred grail]

it does i think

project like

[deft forum]

[sacred grail]

any vector between the two lines

like

(-7, 6, 0) - (7, 2, 6)

oh it should be (-6, 7, 1) x (-2, 1, 1)

[deft forum]

oh uh i see

[sacred grail]

what were you doing

i thought you described the same thing

[deft forum]

so like ((-6, 7, 1) x (-2, 1, 1))·((-7, 6, 0) - (7, 2, 6))?

yea thats what i said

[sacred grail]

yeah but

[deft forum]

[sacred grail]

unit vector

for the x

[deft forum]

oh right

icic

yea

[sacred grail]

[deft forum]

,w sqrt 536

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Shallow.#8817

[deft forum]

,w (-6, 7, 1) cross (-2, 1, 1)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Shallow.#8817

[deft forum]

uh

fuck i cant math

,w sqrt 116

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Shallow.#8817

[deft forum]

[sacred grail]

[cedar kiln]

@deft forum Has your question been resolved?

[toxic moat]

...

brute force is

easier

[cedar kiln]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[frigid frigate]

prove by induction