help-23

[versed wave]

for all values of x in the interval from a to b inclusive, f output will always be strictly smaller than g output

[heavy glade]

okay thank you guys

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[lean nexus]

Stuck on this problem

[lean nexus]

This is what I tried for what it’s worth

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[uneven fossil]

can someone please solve this question, i want to know if i got it right

oh

bruh

[sonic nexus]

for area i got 13500 - 4225pi/2 and perimeter ig ot 330 + 65pi

am i right or wrong

my teacher put 350 +65pi

as the asnwer

and i didnt get that

?

[quick crater]

this is correct

[sonic nexus]

bruh what did i do wrong

i did 150 + 90 + 90 + 65pi

and got 350 + 65pi

not 330 + 65pi

[sonic nexus]

i mean the other way around

[quick crater]

you didnt do anything with the red part

your equation only added the blue parts

[sonic nexus]

bro what

im so confused

OH

ahhh ok

150-150

150-130 = 20

20/2 = 10 on each side

so 330 + 20 + 65pi

350+ pi

ok i got one more though

[quick crater]

correct!

[sonic nexus]

65pi*

this ones only area

i got 42^2pi/6

my teacher got 1470m^2

i got 1764pi/6

what did i do wrong

thanks in advance

i did 60/360 * 42^pi

which is 1/6 * 1764pi

[quick crater]

you calculated this blue part

[sonic nexus]

oh

so i subtract th eblue part from the circle

1764pi - 1764pi/6

?

[quick crater]

ye

[sonic nexus]

ok so is he right

?

im so confused

[quick crater]

yes

[sonic nexus]

how

how did he get 1470m

[quick crater]

this?

[sonic nexus]

yes

[quick crater]

wait meter?

[sonic nexus]

no thats the answer ig ot

[quick crater]

its 1470pi

[sonic nexus]

how is 1764pi - 1764pi/6m = 1470pim

im dumb idk

m = metres

as unit

[quick crater]

1764pi/6=294pi
1764pi-294pi=1470pi

[sonic nexus]

....

thank you

bruh

im so stupid

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[junior axle]

why does this work

[junior axle]

the dxi + dyj

why and how does the dr split into components

i mean i sorta get why and how

but what does it mean really

say graphically

[gentle herald]

A small displacement dr
It's horizontal component is dx and vertical component is dy

[junior axle]

yes but why is it performed in that manner

ive never seen anything actually interact with the dx in an integral

[gentle herald]

Because the force is also variable in x and y direction

U can always break any displacement vector into 3 mutually perpendicular vectors

[junior axle]

ok also why are the vectors distributed that way

like the i and j just drops and the terms in force vector assume the terms respectively for the dr

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[wraith swift]

any other way to find for how many real values of p and q the equation is valid

[digital sparrow]

You can factor it

[wraith swift]

thats what they did

i was wondering of any other way

[digital sparrow]

Not that factor

Like brackets ine

One

[wraith swift]

nah like anything other than factoring?

some kinda inequality or something?

[digital sparrow]

Wait yeah they did lol

[wraith swift]

yea

[digital sparrow]

Lemme think

I got an idea

Divide by q²

so now it's a quad in p/q

And it's D < 0

So no solution other than q=0

[wraith swift]

i mean that is still using quadratics

...

[mortal arrow]

You need to factor

[safe radish]

@wraith swift Has your question been resolved?

[wraith swift]

yeah but

any other way

[digital sparrow]

[wraith swift]

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[raven lance]

Hello, I've been going through the Khan Academy math and I've learned that to find a slope it's (y₂ - y₁)/(x₂ - x₁) but here it seems to be backwards. What is the reason for this? The context is seeing if two lines are parallel. Thank you.

[split ether]

By being backwards you mean they calculated (y1 - y2)/(x1 - x2) rather than (y2 - y1)/(x2 - x1)?

[raven lance]

Yes. I think I'm seeing A as the first set and B as the second set so I'm seeing it as 1-7/8-2 . I must be confused

[split ether]

Take either fraction, multiply the numerator and the denominator by -1 and distribute, you will see that both expressions are equal

[raven lance]

I see. I think I was just hung up on the initial presentation

Thank you for your help

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[thick hamlet]

does anyone have wolfram alpha? i just need help determining why my calculation for a 4x4 determinant is wrong. This is the matrix {{8,2,-1,-4},{3,5,-3,11},{0,0,4,0},{2,2,7,-1}}, and my answer is 8 * 4 * 4 * -300 = -38400. website said the correct answer is -600. Im doing the upper triangular matrix method rather than the long version and i feel like the steps that i took is correct. Please see my resulting matrix after the following operations:
1.) R2 = 2(R2) - 3(R4)
2.) R4 = 4(R4) - R1
3.) R4 = 2(R4) - 3(R2)
4.) R4 = 4(R4) - 139(R3)

[desert juniper]

you're doing operations that modify the determinant

your steps multiply by 2, 4, 2 and 4 respectively

[safe radish]

@thick hamlet Has your question been resolved?

[thick hamlet]

hmmm okay, can i clarify this then?
2) R4 ← 4(R4) - R1 this scales the determinant of by 4 right? whereas;

1. R2 ← 2R2 - 3R4 does not scale determinant? why? arent we scaling r2 by 2 so it still affect the det? im confuzzled

[median vigil]

both of those change the determinant

[thick hamlet]

so i.e. if we manipulat the value of a row by scaling the row "x" and saving that value to row "x", we change the det?

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[terse lichen]

find the equations for the straight lines first

then determine their inequalities

[stoic merlin]

how do i do that

[terse lichen]

find their slopes and intercepts

[stoic merlin]

Could i just have the answer?

[terse lichen]

!noans

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The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[stoic merlin]

Ok how do i find the slopes and exact intercepts?

[terse lichen]

to find the slope, find two points on the line

then use the formula for it

and the intercept is the y-intercept

read it off the graph

then the equation of the line will be y = mx+c

m is the slope and c is the intercept

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[ebon plover]

can someone explain to me the issue with the factorising method i highlighted in red? bcs it works for some old questions i did previously, but now im just confused

[hidden gyro]

in method 3 and 4 if
x=2 (in method 3) then 2(5+3(2))=22 ≠2

The factoring only work when
something1*something2=0
either s1 is 0 or s2 is 0

[ebon plover]

ohh i see, so just to clarify, method 3 and 4 can only be used when it = 0?

[hidden gyro]

yep cuz at least should be
x(5+3x)=2
x(5+3x)-2=0 but that doesn’t help us that much

[ebon plover]

okayyy, tysmm

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[digital sparrow]

It has been like 30 mins

So I'll close the channel

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[lean otter]

Hello, folks. Can u help me to express x via a? P is the centre of face.

[lean otter]

M N are centres of ribs

[lean otter]

With whole solution please 😭

If you need prettier scheme I would like to remake it

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[lean otter]

<@&286206848099549185>

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@lean otter Has your question been resolved?

[covert blaze]

could you please redraw it? I can't determine what i'm looking at

[lean otter]

Sure. Hope it's better now

[clear patio]

hi

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[worn jewel]

!status

[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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[fathom jewel]

I suppose you wanna find a basis respectively for span{u_1, u_2} and span{u_3, u_4, u_5}?

[worn jewel]

yes

[fathom jewel]

What you can do then is check if u_1 and u_2 are linearly independent, the same for u_3, u_4, u_5

[worn jewel]

oh okkk then what should i do

i mean should i find out the indepency between all of these

or just between u_1 and u_2 and between u_3, u_4, u_5

[fathom jewel]

Well that was my first assumption

you wanna find a basis respectively for span{u_1, u_2} and span{u_3, u_4, u_5} or not?

because there is an and

[worn jewel]

ok i see

[fathom jewel]

Ok so I think I changed my mind

I think it really wants you to consider

span{u_1, u_2, u_3, u_4, u_5}

See which of these are linearly independent, those should be a basis for the subspace W

[fathom jewel]

this yes

Since it's five 4-dimensional vectors, you can expect at least one vector to be linearly dependent

[worn jewel]

actually i found out span{u_1, u_2, u_3, u_4, u_5} linearly dependent

yes

what should i do with it

im sorry this question just confused me a lot

[fathom jewel]

can you show what you got

[worn jewel]

u1 u2 and u3 independent

[fathom jewel]

yup

that's it

[worn jewel]

but u4 and u5 dependent

[fathom jewel]

you take these 3 as a basis for W

[worn jewel]

ohh

[fathom jewel]

there are 3 possibilities for a basis for W
u_1 u_2 u_3
u_1 u_2 u_4
u_1 u_2 u_5

[worn jewel]

arent we must to take u_1 u_2 u_3

in this case

?

[fathom jewel]

you can choose this possibility

[worn jewel]

thank you sir for helping me i appreciate for your help 🙂

have a nice day

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[rotund dew]

Im having quite the hard time here

Now don't get me wrong, I see that this is ultra sketchy, but I don't really know why
Now visually, I think I see it? When you start picking point so close to each other, if the function isn't constant then it would eventually be greater than the difference of points square time the constant, but I'm not quite sure how I would do it

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[rotund dew]

@raven vessel

If i'm being honest, my argument is bullshit I just didn't want to have nothing

[tardy mango]

(answered in another server)

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[lean otter]

Can I get help doing these because I don't understand how to input them

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@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185>

[lean otter]

.close

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[lean otter]

.reopen

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✅

[lean otter]

OH

HELP

😀

[minor socket]

algebra aye?
you don't really need to input these anywhere, all the info you need is in the graphs. remember that your domain here will be your possible x values and the range will be your possible y [f(x)] values. for the second row, it's asking along which x values is f(x) increasing, decreasing, or remaining constant. then the last row is just the value of f(x) at the given x. most of those points have been labelled for you, save for f(0) in 29 and 33. since the instructions are cut off, I'm not sure if your teacher wants set or interval notation.
don't forget about your asymptotes!
hopefully that helps if you want to give it a shot and check in if you get stuck lmk :)

also hello, I type too many words sometimes lol

[lean otter]

Wtf are asymptotes tho

Like I know the word

I don't know what it is

[minor socket]

ohh gotcha, so asymptotes are basically a line where the function gets closer and closer to it but never actually reaches that value
let's look at number 33 for example, see how the function gets closer to 0 as x approaches -infinity and positive infinity? (I'm on mobile so formatting is suspect)
it isn't ever actually going to hit zero there, so here you have a horizontal asymptote of f(x)=0
similarly, when x approaches 0 from the left f(x) approaches infinity, and as x approaches 0 from the right f(x) approaches -infinity. the function isn't defined at x=0, so that's a vertical asymptote if that makes sense

and while we're on the subject, since 33 isn't defined at 0, what you'll end up putting for f(0) on that one is DNE (stands for does not exist)
just in case you haven't come across that yet

[cedar owl]

asymptotes asymptotes asymptotes try saying that 3 times fast😃

[minor socket]

lol
oh and the equation for number 33 is -6/x if you want to know. seeing the equation can help some people understand asymptotes a little more you know?

[lean otter]

I can't even say it once right 💀

[lean otter]

I can't even say it once right 💀

[cedar owl]

I can't even say it once right 💀

[cedar owl]

I can't even say it once right 💀

[lean otter]

💀💀

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[noble bane]

help please

[vapid glen]

,rotate

[vapid glen]

what have you tried

or can you explain a bit more why you're saying B

[noble bane]

wait sorry wrong one

thats e

hang on

[vapid glen]

,rotate -90

[noble bane]

I meant to send this

[vapid glen]

,rotate 180

[vapid glen]

!status

[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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[noble bane]

3

[vapid glen]

I see, where you put the derivative it should be 2x+k=3 not 2x+k+x=3

that extra +x shouldn't be in the derivative there

[noble bane]

why is that not a product rule if they are both variables

[vapid glen]

good question

k doesn't depend on x, so when you change x, k stays the same

it's basically a constant with respect to x

[noble bane]

oh ok

is it d?

[vapid glen]

yeah that's what I'm getting, looks good

[noble bane]

thanks

[vapid glen]

you're welcome

[noble bane]

how do I close this?

.close

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[rough ledge]

Yo I'm doing imaginary numbers and i'm stuck on how to simplify a fraction with an imaginary number in the denominator. I understand that i need to multiply both sides by the conjugate but what would happen if i had something like 6 + 5i/-2i?

[median vigil]

,, \frac{6 + 5i}{-2i}

[flat frigate]

cloud

[median vigil]

this?

[rough ledge]

yeah

[median vigil]

well we can still use the conjugate

what would the conjugate of -2i be?

[rough ledge]

i dont really know cuz my teacher only taught me to flip the sign of whatever you're adding or subtracting

[median vigil]

if it helps you can write it as 0 - 2i

[rough ledge]

that does make more sense thanks

.close

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[rough ledge]

/reopen

.reopen

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✅

[rough ledge]

ok so i got it to (6i - 5) / 2 would that just be the simplest form?

[median vigil]

when we have a complex number we often want to separate the real and imaginary parts, which in this case you can do by splitting the fraction

[rough ledge]

and how would I go about doing that

[median vigil]

,, \frac{a+b}c = \frac ac + \frac bc

[flat frigate]

cloud

[rough ledge]

so 3i + 2.5?

[median vigil]

pay attention to the signs

[rough ledge]

true

3i - 2.5

thanks bro

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[brazen parrot]

excuse me how do I do part b?

[bronze gust]

I would guess it’s V=RI

And you already know R and I

[brazen parrot]

its wrong

the answer is 1.64A

[bronze gust]

Rip

Haven’t done electricity in a year

Maybe exclude the resistors on parallel

[brazen parrot]

i dont get what they did

[brazen ravine]

it’s terms you already worked out

multipled together

[brazen parrot]

why

i dont understand

[brazen ravine]

because it asks for voltage

V=IR

[brazen parrot]

27/11R and then the resistance of the parallel part of the circuit?

[brazen ravine]

yes as that’s where the voltmeter is

[brazen parrot]

oh ok

makes sense

would it be. different if the voltmeter was in series instead?

bc voltage is shared?

[brazen ravine]

yes

[brazen parrot]

how so

[brazen ravine]

because the voltage is shared

[brazen parrot]

oh but what would i need to do differently

if theres 2 resistors

do i just divide the voltage i found by 2

[brazen ravine]

you would ratio it between the resistors

[brazen parrot]

ratio?

[brazen ravine]

depending on what their resistances are

[brazen parrot]

oh

like in this question?

[brazen ravine]

if they have the same resistance then yes divide by 2

[brazen parrot]

part B

how would i ratio this

[brazen ravine]

not a ratio situation

[brazen parrot]

20/60 x 6?

[brazen parrot]

how come

[brazen ravine]

it’s not in series

[brazen parrot]

oh

is it not?

[brazen ravine]

series is square

this question is more of understand circuits in general

so do you know what the infinite resistance does

[brazen parrot]

i think

the resistance is infinite so it takes the other pathway

with lower resistance

[brazen ravine]

it means the voltmeter is perfect

[brazen parrot]

oh

[brazen ravine]

as no current can flow through the voltmeter

[brazen parrot]

o

[brazen ravine]

as if you imagine V=IR the R is infinite so the I is zero

[brazen parrot]

im getting a bit confused bc my teacher used a ratio here

[brazen ravine]

oh yeah you can use a ratio there

well no one’s perfect

[brazen parrot]

i dont get the ratios

did they put 60 on top of 80 bc the voltmeter is parallel to the 60ohm resistor

[brazen ravine]

no so

the battery supplies only a certain amount of voltage

all the components has to share that voltage

[brazen parrot]

yea

[brazen ravine]

So it’s V=IR again some components have higher resistances and current is a constant

so if A has a resistance of 5 ohms and B has a resistance of 1 ohm more voltage will go to the 5 ohms because of V=IR

so when you ratio it you divide it by the total reistianxe and multiply it by the resistance of the resistor you want

[brazen parrot]

oh

but isnt the voltmeter being affected by both the 20ohm and 60ohm resistor

[brazen ravine]

a voltmeter measures the difference in voltage between two points

so it’s only measuring the voltage split around that 60 ohms

[brazen parrot]

ohh

ok

i think i get it now :D

thank u

[brazen ravine]

np that was helpful for me too as I forgot most of it

[brazen parrot]

lol r u in uni?

[brazen ravine]

i’m in the british version of college

so the equivalent of specialising in 3 subjects at 17 years old for your country

[brazen parrot]

wat does this mean

[brazen parrot]

oh

wait so uni?

[brazen ravine]

no here university and college is two different things

i’ll go to university in 1 year

[brazen parrot]

waddaflip

so high school?

[brazen ravine]

no college

[brazen parrot]

is that A levels

my physics teacher is british

[brazen ravine]

yes A levels

[brazen parrot]

ohh

i use an a levels textbook

[brazen ravine]

that’s peculiar

[brazen parrot]

yea

wait not textbook its like

practice questions

[brazen ravine]

so I presume it’s not been helping?

[brazen parrot]

no it sucks

[brazen ravine]

i normally just use chagpt

[brazen parrot]

i use this one

[brazen ravine]

Oh I actually have that

[brazen parrot]

it has useful notes on momentum tho

[brazen ravine]

somewhere in my garage

[brazen parrot]

yea it sucks

ive used it like 3 times

.vlose

.close

[safe radish]

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[safe radish]

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[onyx narwhal]

What part do you need help with

[indigo tundra]

Idk how to use a calculator for that

[balmy pewter]

how are you going to use a claculator?

You can do it by finding its derivative rigtht?

[indigo tundra]

Umm it says to do it by using a calculator

,w derivative of ln(x) at x=2

[flat frigate]

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[indigo tundra]

Do u guys think that is right

[balmy pewter]

yeah ofcourse

[indigo tundra]

Omg why does it look like that

In the inage

Inage

Image

[balmy pewter]

liek what?

[indigo tundra]

Delta log over x

[balmy pewter]

its how a discord bot solves it ig

[indigo tundra]

Okii

[safe radish]

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[still charm]

Alex plays a note on his trumpet once every 7 seconds. Bob plays a note on his fiddle once every 5 seconds. Charlie plays a note on his saxophone every 19 seconds. If Bob starts playing 2 seconds after Alex, and Charlie starts playing 1 second after Bob, when will their notes coincide?

[still charm]

is this CRT or something?

<@&286206848099549185> just tell me what the concept here is

[solar hazel]

CRT kinda just says a solution exists. but there are methods to find the solution too

[timber karma]

can i ask, whats CRT?

[idle widget]

Chinese remainder theorem

[timber karma]

oh

[buoyant shadow]

CRT is the theorem that gurantees that this thing has a solution

[timber karma]

thanks

[solar hazel]

if you know a constructive proof for CRT you can use that to find it

[buoyant shadow]

based on 7,5,19 being coprime

x%7 = 0
x%5 = 2
x%19 = 3

i think that's the right direction, like it's not 0,3,16

the simplest way is brute force

[still charm]

ok this is pretty simple then

[buoyant shadow]

you satisfy them from largest to smallest

[still charm]

all i need to do is to do the vector thing my prof taught me

[plucky elk]

There are other proofs besides constructive?

[solar hazel]

[still charm]

so x = 0 (1,0,0) + 2 (0,1,0) + 3 (0,1,1)

oh hey that simplifies nicely

i only really need one set of bezout coefficients

[vapid glen]

there's a gross "closed form" I guess you could call it, 0*(5*19)^6 + 2*(7*19)^4 + 3*(5*7)^18 mod 7*5*19

[buoyant shadow]

so x%7 = 0 but x = 19n+3
3 doesn't work, 22 doesn't, 41, 60, 79, 98
x%5 = 2 but x = 133n + 98
231, 364, 497

[vapid glen]

,w 0*(519)^6 + 2(719)^4 + 3(57)^18 mod 75*19

[flat frigate]

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[vapid glen]

ok we agree nice

[still charm]

ok got it friends. it looked like a hard problem at first but then i figured out that you only need one 'bezouting'

idk if any of you guys know the vector method, it's what my prof uses. basically you set it up as a matrix and then do row operations and such

so like you start with the identity matrix on the lhs and the coefficients on the rhs and then row reduce until you arrive at bezout's identity

i don't know exactly how it works but it does

[solar hazel]

i think that's what i had in mind when i said constructive proof

[safe radish]

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[fair goblet]

Am I doing problem 23 correct?

[pure arch]

yeah look slike it

[fair goblet]

.close

Thanks

[safe radish]

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[fair goblet]

.reopen

[safe radish]

✅

[fair goblet]

Is this how I do problem 27?

[safe radish]

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[sturdy pilot]

Would anyone like to work on the Mathcord logic problems sets with me? #events message #events message

[sturdy pilot]

So far I've attempted 1-3 in the first problem set

[rustic goblet]

👁️

the answer for me is "probably not", but I'll download these anyways to take a look

[dense wadi]

the answer for me is that ion understand what im even looking at

[safe radish]

@sturdy pilot Has your question been resolved?

[safe radish]

@sturdy pilot Has your question been resolved?

[safe radish]

@sturdy pilot Has your question been resolved?

[safe radish]

@sturdy pilot Has your question been resolved?

[safe radish]

@sturdy pilot Has your question been resolved?

[sturdy pilot]

This is what I have for 2.3, any feedback would be appreciated

Ahhhh I need to fix something

[rustic goblet]

you know, Existentialistic

from what I have observed, it's pretty uncommon to get help with logic in the help channels

you of all people should know better than to ask here >.<

[sturdy pilot]

😭

I was hoping this could act as a thread for people working on the problem set

[sturdy pilot]

fixed it

[rustic goblet]

I suspect that everyone working on it wouldn't be in the help channels, for the most part

[sturdy pilot]

F

[rustic goblet]

[sturdy pilot]

maybe I'll link to this in #foundations

[sturdy pilot]

Also I saw you posted a topology question in a help channel earlier

[rustic goblet]

yes but I've actually gotten help with point set here before, and I've seen others get it too

meanwhile, out of the dozen or so logic questions I've ever seen asked in these channels, only 1 or 2 of them ever got answered, and a few days later at that

[sturdy pilot]

[sturdy pilot]

I might close this then

[sturdy pilot]

.close

[safe radish]

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[livid bronze]

How do i do this I don’t know how to find Sas or ssa and triangle congruency

[livid bronze]

For number 9

[manic radish]

What does "AAS" and "ASA" mean?

And, you should notice both triangles share two equal angles, which should tell you all you need to know

[acoustic mulch]

angle angle side, and angle side angle i think

[manic radish]

the side lengths might be very different

For example, here, clearly the sides are of different lengths.

Hint: if I label the two angles a and b, what would the third angle be for each triangle?

[safe radish]

@livid bronze Has your question been resolved?

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[lean otter]

hi sm1 pls help

[limber steeple]

wats the problem

[lean otter]

how is it not right

[limber steeple]

for vertical i know its just where x has a value that the funtion cannot give an answer

here its just when the denominator is zero

cause u cant divide by zero

[lean otter]

oh

so how would i fix it

bc its saying "The graph cannot be drawn. Please correct all mistakes."

[limber steeple]

you need to set the denominator part to zero and see what x value makes the denominator zero

so 4x+4=0

oh idk how to use the program ur using

[lean otter]

ohh okay ty

i get it

[limber steeple]

maybe move the blue points so it makes a vertical line?

for the horizontal asympotote I actually dont know how to solve for that

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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[sullen briar]

I'm relearning some euclidean geometry, eventually to take the CSET in california... I'm trying to understand geometric proofs... I just had a few things I wanted to ask and/or clarify.

1. It seems like everything (can) start with Euclid's 5 postulates and the definitions of stuff (like points and lines and space). So it seems like there's a bit of a "flow chart" in the sense of Theorems needing to be proven in a certain order to prove other theorems down the line. I'm guessing there's certain conventions about what theorems it's acceptable to take for granted when proving certain other theorems, but in general is it safe to assume that all theorems are fair game to use when asked to prove something in geometry?
2. It seems like (I havn't found a counter example yet, but I'm guessing they exist) most if not all of the most popular/useful theorems in geometry are both true for itself and it's converse as well. But it seems like the converse would often need separate proof; the converse would not usually be entailed by a mere proof of the theorem. Is that all fair?
3. Continuing from that, is it convention not to use a theorem's converse when proving it? It seems like you'd have just as much justification (arbitrary) taking a theorem's converse for granted in the theorem's proof as you would taking any other theorem for granted for the proof.

I guess I'll stop here for now. Sorry for the unspecific questions, idk if this is acceptable this is my first time posting here 💖

[sullen briar]

Actually, with regard to #3 I just saw a proof online of corresponding angles theorem which makes use of it's converse (as if best practice might be to prove corresponding angles theorem converse first)

[safe radish]

@sullen briar Has your question been resolved?

[quiet plume]

Others will probably have other answers.

From my point of view at least, 1. is fine. The "process" of mathematics, be it in geometry or any other field of maths, is to distill new truths from known facts (with, at the base of all of it, the axioms). Any theorem you've shown is fair game as this theorem itself is to some extent the result of the axioms.

2. => and <= can be understood as different statements altogether. As in, if you see some proof that P <=> Q, then this is more or less just logical shorthand for P => Q and Q => P. Both of those need a proof to prove the statement "P <=> Q". I think maybe more "simple" theorems in geometry deal with more barebone concepts like angles and lengths that inherently have some sort of symmetry that allows for things to be true "both ways". (This is very rough intuition, there are probably better reasons.)

3. If you're proving P => Q, and it turns out that you've already shown that Q => P independently of P=>Q, then I suppose you could use Q=>P in your proof, but you have to be sure you're not be circular in your argument.
   I don't want to tell you something that isn't true for this, so could just just show me the proof you're talking about for corresponding angles?

[sullen briar]

sure yeah, ill upload a pic

I'm still curious about conventions, in the sense that if I'm asked on a test to "prove corresponding angles theorem", from what I've seen so far, its the wild west in terms of assuming other theorems are true to prove the one being asked.

So both these i kinda paraphrased from online resources

This proof of coresponding angles makes use of it's converse

[quiet plume]

In general, there isn't a unique proof for a statement.
I guess the convention is that more elegant proofs are somewhat better but not truer than other proofs of the same statement.

[sullen briar]

Fair

I imagine that you could acquire a better sense of what theorems are further along the line so to speak

and try to use as few assumptions as possible, but it would be impractical to always derive everything from postulates right

"There isn't a unique proof for a statement" Is that always true? ive never heard that before thats rly interesting

seems for sure true most of the time, but is it always the case?

[quiet plume]

Ok yeah I think that makes sense.
See you can use the converse, notice how the "<=" direction is only used to prove the "=>" direction.

You can't do both though, because then your proofs depend on each other and that's no good.

[sullen briar]

right totally

also I find it interesting that the converse relies on yet another theorem, the externla angle inequality

which I then looked up how to prove and it relies on other stuff lol

[quiet plume]

The reality is that you can always add tautologies (statements that are always true) to a proof without invalidating the proof, so in that specific sense, proofs are never unique. (In other words you could go on "true" tangents in your proof, and while whatever you're saying adds nothing to the proof in terms of getting to the conclusion you want, it's still a different proof.)

[sullen briar]

So from this it just seems like I'd have already have known this "flow chart" so to speak, to know what theorems should and shouldn't be used for any proof

to avoid being circular without realizing

thanks for your help btw, appreciate it

[sullen briar]

gotcha

Is this difficulty im trying to describe somewhat unique to geometry or is this a practical concern in other fields as well?

The idea of practically needing to rely on theorems to prove things, simply due to the length of a proof otherwise

Like, ideally we'd prove things from the axioms

[quiet plume]

It's a concern that arises in any field of maths, since all of them rely on the (more or less) same logic system

[sullen briar]

fs fs

[quiet plume]

I don't think this would generally happen, because it's rare a statement will imply a "greater" statement on its own. So realistically, you would not have proven say the external angle inequality using the corresponding angle theorems, so these "lesser" theorems wouldn't go in circles

If that makes snese

[sullen briar]

no totally, that seems obvious now actually lol

like maybeeee you could get there a slightly different way, but its kinda impossible to go backwards so to speak

i reckon im good for now then, if u wanna close the thread or however that works 😌

[quiet plume]

Yeah ok!
You can just type .close and it'll close it

[sullen briar]

cool, ty again

.close

[safe radish]

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[safe radish]

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[lean otter]

Guys. For a truth table with two input variables and if the input variables are equal then the value of the output variable are true. Otherwise, false.

Is there a logical expression for this? I felt like conjunction is not enough for a logical expression, right?

[lean otter]

Assume the input variables are A and B

[buoyant shadow]

there's a logical expression for any table

idk what you're asking

[lean otter]

i am not saying there is not

i am saying that a conjunction wouldnt be right?

because i cant find the logical expression for it

[buoyant shadow]

there's no shorter way than the obvious way

[lean otter]

idk what you are saying dude

i just want to know what would be the logical expression for the truth table

afaik it is not A&&B

[graceful surge]

hello! do you mean in codeing?

[lean otter]

no?

[buoyant shadow]

(A and B) or (~A and ~B)

[lean otter]

whatever it is. coding or not. as long as it is a logical expression

[lean otter]

aha that makes more sense. idk why that didnt occur to me

okay thanks!

[buoyant shadow]

maybe you can make it shorter tbh

[lean otter]

probably, yeah

but im not adept at logical gates so meh, im happy with that for now lol

[buoyant shadow]

ok

[lean otter]

okay thanks!

.close

[safe radish]

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[safe radish]

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[dense wadi]

what does it mean

v is a vector in R^n

[frozen marlin]

sy

you haven't slept have you

[junior smelt]

v is basically something like (a1, a2, ..., an), it's one of those tuples

[frozen marlin]

sy it's been 72 hours.

[dense wadi]

im going for the 100h streak

[rustic goblet]

SYREX

[frozen marlin]

GO FUCKING SLEEP

[rustic goblet]

WHAT ARE YOU DOING

[dense wadi]

IM JK JK

[frozen marlin]

no you're not

[junior smelt]

I don't believe you

[frozen marlin]

sy i swear we'll put out a serverwide notice to stop helping you until you sleep

[dense wadi]

its just the wording of "v is a vector in R^n"

like

[rustic goblet]

v is an element of R^n, the vector space

that's all

[dense wadi]

cant they just say

v is a vector

[frozen marlin]

i.e.

[rustic goblet]

v could be an element of R^n, not considered a vector space

[dense wadi]

wording had me confused 😔

[rustic goblet]

no

because v could be a vector in a diff vector space

[dense wadi]

ohhh

[rustic goblet]

R^n is a very specific vsp

[flat frigate]

ren

[frozen marlin]

now sy

go to sleep

i'm genuinely worried abt your health rn

[dense wadi]

oh this

[frozen marlin]

yes that

i can barely go a night w/o sleeping. you've gone almost 3.

[dense wadi]

i swear im not doing a 100h awake challenge

[frozen marlin]

sy this isn't funny

i'm not joking when i say that i am concerned for your well-being

[dense wadi]

i joke about it but dw 😭 i slept from like 4am to like 2pm my sleep schedule is messed up but i get enough sleep

[frozen marlin]

what...?

4 am to 2 am?

[dense wadi]

2pm

pm

pm

[frozen marlin]

oh

ok

well

[dense wadi]

guys this is not backing up my claim

💀

[frozen marlin]

frankly this isn't the type of question you'd ask

if you were completely sane

so i don't believe you

[junior smelt]

I wouldn't put it past you to get negative sleep

[dense wadi]

im just new to planes and stuff like

english isnt my main langauge

so im a bit lose by wording sometimes

[frozen marlin]

never seen you do that, but ok

[dense wadi]

have you tried psychoanalysis

[frozen marlin]

yes

i'm actually fairly good at it

informal psychoanalysis ofc

one of my friends didn't talk to me for 3 days because he said it was scary how i could "lay out [his] thought process in front of [him]"

[dense wadi]

youre suffering from your own success

[rustic goblet]

Syrex.

[craggy sedge]

sleep

[rustic goblet]

you need to sleep better

[craggy sedge]

higher that applies to you also

[dense wadi]

guys how can i beat the allegation that im not a vampire and that i do sleep

[frozen marlin]

sy you are definitely sleep deprived rn

you don't usually babble like this

[craggy sedge]

1. you are not an vampire
   2.You do not sleep

[frozen marlin]

or dodge our questions/advice

please, just go to sleep

[dense wadi]

you defo missed some of the chats i had

i say the most random stuff

[frozen marlin]

*sighs*

again

you are attempting to divert our attention

[craggy sedge]

https://tenor.com/view/matrix-neo-keanu-reeves-power-windy-gif-15235043

[frozen marlin]

which is most unlike you

[craggy sedge]

1. that doesn't matter
2. go to sleep

[junior smelt]

Can actually verify this she does

[frozen marlin]

wk

[junior smelt]

But if you really aren't sleeping @dense wadi...

[craggy sedge]

that still does not gives her the permission to stay awake rn

[dense wadi]

all of yall

manually holding your jaws now

[frozen marlin]

i-

what?

[dense wadi]

youre also manually breathing now

[craggy sedge]

all of yall?go to sleep

[frozen marlin]

okay goodbye

.close

[safe radish]

Channel closed

Closed by @frozen marlin

Use .reopen if this was a mistake.

[frozen marlin]

end of discussion

you are sleeping. now.

[safe radish]

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[crystal urchin]

I need help solving this question. I am unable to find the points because there so many different ways to put the same equation and so many different answers.

[safe radish]

@crystal urchin Has your question been resolved?

[limber steeple]

Lagrange multipler method ooo, new term i never heard before

Wat class is this

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[calm iris]

im sooo deaddd its asking to find the interval of length at most 10 grams that contains a break-even point for the sales of cheese, where the break-even point is expressed in kilograms, is in the following interval of length at most 10 grams... it says to use the intermediate value theorem but im LOST and dont know how to do it. pleasee help

[calm iris]

also for the saleof cheese that will result in the lowest profit i dont know

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[lunar roost]

Prove using vectors that the diagonals of a parallelogram bisect each other

[lunar roost]

So far that’s what I got

<@&286206848099549185>

[rocky tartan]

aint AB = DC not CD

[lunar roost]

Oh yeah mb just transcription error

Wait but the vector a is still the same tho right?

[rocky tartan]

it’d be -a

[lunar roost]

Oh ok fixed

[rocky tartan]

since its the opposite way

[lunar roost]

But same magnitude right?

[rocky tartan]

yeah

[lunar roost]

Wait so what if I introduced a vector that bisects AB and DC as well as intersects p?

Would that work

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[lunar roost]

<@&286206848099549185>

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[digital crescent]

i'm doing the june23 calc paper 2 question 22 iterations.

I worked out the iterations and got 22. a) right
x2 was 4.10(..) and x3 was 4.177(..)

22. b) had me confused though
    i did x4 and got 4.23(..) and x5 and got 4.27(..)
    so I put x5 (4.27) > 4.25 and lost a mark on that question
    mark scheme says it has to be 4.25 < value <= 4.39
    why does it have to be like that and why is it 4.39?

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@digital crescent Has your question been resolved?

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@digital crescent Has your question been resolved?

[digital crescent]

<@&286206848099549185>

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@digital crescent Has your question been resolved?

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[steady nest]

How can I solve 2 b) using geometric series?

[last wren]

why are you using geometric series?

[steady nest]

I'm not, I was at a lecture today and the lecturer said it can be easily solved using geometric series. But I solved it like this

Just wanted to understand how I could solve it using geometric series instead, which my lecturer failed to do.

[last wren]

oh I see

he meant this:

actually no, that shouldn't be a geometric series... did he specify which part could be solved using a geometric series?

[steady nest]

bad image. but here's how he solved it

so, 2^3 and 2^4 tells us that we need 3-4 iterations

but I have no clue what he did here

[last wren]

oh I see

[last wren]

does this part make sense to you?

[steady nest]

nope, not really

[last wren]

a geometric series is a series of the form

$\sum_{k=0}^n ax^k$

[flat frigate]

doaby

[last wren]

oops hold on

that's equal to

$\frac{a(x^{n+1} - 1)}{x - 1}$

[flat frigate]

doaby

[last wren]

so if you plug in the numbers, you'll get

$\sum_{j = 0}^{k-1} 2^j = 2^k - 1$

[flat frigate]

doaby

[steady nest]

and how is that applicable for my task? sorry, I'm having a hard time thinking right now hehe

[heavy blade]

Kalle skal slappe af

Good luck Joakim von anka

[steady nest]

Thanks my danish broski!

[heavy blade]

du er velkommen

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[lyric monolith]

i know its in french but question 2/a
prove that for x>=1, f(x)<=1
i feel like its really simple but my brain just cant figure it out

[gleaming hawk]

Hello

@med

[lyric monolith]

hello!!

[gleaming hawk]

Let's make a few observations

Follow me through

[lyric monolith]

alright!

[gleaming hawk]

Is x^2 + 1 > x^2

[lyric monolith]

yes

[gleaming hawk]

So would that imply (x^2 +1)^1/2 > x

[lyric monolith]

yes!!

OH

[gleaming hawk]

I think I don't need to proceed

[lyric monolith]

yeah thank you so much!!

[gleaming hawk]

It's alright mate

Have a good one

[lyric monolith]

you too!

[gleaming hawk]

Pls .close the channel if you don't have anything else to ask

[lyric monolith]

.close

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[rustic whale]

I don't know how to solve this further

[gleaming hawk]

Hello @rustic whale

[rustic whale]

helloo

[gleaming hawk]

Could you kindly explain

What this is

[rustic whale]

log 10 2 = 1/b

[gleaming hawk]

I would recommend that you multiply log_2_ 5*2/2

See where you get from there

[gleaming hawk]

@rustic whale

[rustic whale]

I'm not too sure what to do with this either, sorry 😭

[gleaming hawk]

In the denominator

See if this helps

[rustic whale]

yess it does, tysm!! I was so confused

[gleaming hawk]

And I believe

For the answer

You would have to put log 10 2 as b

Not as 1/b

So either you have noted down the question wrong

Or the answer wrong

Please correct it @rustic whale

[rustic whale]

the question is correct, so the answer should be, but maybe the book has made a mistake

[gleaming hawk]

Answer is wrong then

It's 1/b-1

Not b-1

Anything else i can help you with?

It's alright

[rustic whale]

yep i'm alright, thanks for your help!

.close

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[broken forum]

8.3.1

[broken forum]

could someone just explain what's happening

[elder sentinel]

first question just want s you to find the equation of the curve

[broken forum]

I worked it out; really was just being silly

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[potent path]

do you know how to find the distance between two points?

in this case, the midpoint's x value would be halfway between the sum of the x values of the two points, and its y-value would be halfway between the sum of the y values of the two points.

M_x = (A_x + B_x)/2
M_y = (A_y + B_y)/2

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[wise copper]

i joined this course late as i had to visit family back home and i really dont know where to start

[flat frigate]

bacc (unhelpful)

[fathom jewel]

then I think it should work out applying distributive / De Morgan laws

[wise copper]

okay

thats where i was going down

this is what i have so far where do u think i go next

[fathom jewel]

ok good

now you can also distribute the negation

[flat frigate]

bacc (unhelpful)

[wise copper]

okay

[fathom jewel]

,, (\neg s \land \neg q) \lor (s \land \neg r) \lor ( q \lor r )

[flat frigate]

bacc (unhelpful)

[wise copper]

so thats my next step after what ive got

[fathom jewel]

I would now distribute the 2 left

[wise copper]

okay thats what i was thinking

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[unkempt hawk]

Im having a problem with these 2 probability questions, the 7th question is a continuation of the 6th question. Im guessing the usage of Bayes' theorem could help with the first one if i persume that the whole sample space is worth 1 ( P(S) = 1 ) which would mean that P(S) = P(A) + P(B) + P(C)

The Rule In question

So I would get the P(B)

and then i could do P(D|B) = P(D union B) / P(B)

And since P(D union B) is the same as P(B union D) i would just implement my numbers into the rule

But all of this is still speculation because im not sure if there exists another rule that i should be using

<@&286206848099549185> It has been over 15 min since i've sent my question, can anyone help?

[spice tide]

sorry wait let me check

you can go on from here

[unkempt hawk]

I was guessing that. I tried it and i came up with P(B) = 0.4.

I then took that to the P(D|B) rule and the end total was 0.475 which ive chosen as the third option (C) = 0.47 since its asking from approximation with 2 decimal spaces.

Im now currently facing the problem of the 7th question

[spice tide]

oh i didn’t pay attention wait

[safe radish]

@unkempt hawk Has your question been resolved?

[unkempt hawk]

Any luck ?

[spice tide]

5 mins

sorry my writing is chaotic

but it’s none of the choices

if you’re wondering about the P(D) part, since A, B and C are disjoint and happen to cover the entire sample, P(D) is the sum of D’s intersections with A, B and C

you can visualize it easily on the figure

hope this helped

[unkempt hawk]

Thank you very much 🙏 (sorry for the late reply)

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[harsh sapphire]

Hi, I was wondering how this could be simplifyed using surd and index laws

[harsh sapphire]

The answer is 3t^2

[fathom jewel]

you can split the product

[flat frigate]

bacc (unhelpful)

[harsh sapphire]

ah okay

[fathom jewel]

you can continue from here?

[harsh sapphire]

yeah i think!

[fathom jewel]

ok good

[harsh sapphire]

i dont know how to type it on discord but the first part simplifies to 3

[harsh sapphire]

how is the second part simplified then?

[fathom jewel]

yep

ok let me

[flat frigate]

bacc (unhelpful)

[harsh sapphire]

wouldnt it be t^3/6?

[fathom jewel]

6/3

[harsh sapphire]

ohh yeah you're righ

awesome!!

[flat frigate]

bacc (unhelpful)

[harsh sapphire]

thank you!!

[fathom jewel]

np

[harsh sapphire]

i appreciate it :)

.close

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[polar kettle]

Hi guys

[polar kettle]

Ive tried 4, 5 and 6 for this question

I thought the only thing affecting the order would the the order of the polynomial since e^-8 just means 8 is a root

Can you help me out please

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@polar kettle Has your question been resolved?

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[uneven flax]

hello

[uneven flax]

i need help.

is this sol = 0 ?

how do i make a graph

with this

where would my variable go?

[flat frigate]

bacc (unhelpful)

[fathom jewel]

but this seems like a contradiction

[uneven flax]

exactly, did i mess up my procedure?

it's a simple problem to look at

i just don't think this actually has a solution

[uneven flax]

i just need to make a graph with this (which is the result of the previous one)

[fathom jewel]

this how it would look if you drew it

it being greater than 3 and smaller than 1 doesn't work

like you are having no intersections

[fathom jewel]

between y >= -7/3 and y < -11/3

no intersections

[uneven flax]

yeah, i just have to make a straight, not a graph though

[fathom jewel]

let's have a simple example