help-10

[vapid tiger]

oh

0 ?

[chrome compass]

right it's +0z. so it doesn't matter what z is, that's why you need the second variable

[vapid tiger]

[(i+4)j -2i, j, 0]

[chrome compass]

nono, it's [f(j), j, k]

for whatever f is. haven't worked it yet

the point is z can be anything and it still solves the equation

[vapid tiger]

yup

z is arbitrary

S1 = ( -3i + (i-1)k , i - 1 + k, k) S2 = (-2i + (i+4)j, j, k)

[chrome compass]

okay S2 looks good

[vapid tiger]

hopefully these are correct

nice

some good news

[chrome compass]

guh y for S1 is gross

[vapid tiger]

is it wrong ?

or does it just give you the ick

[chrome compass]

just icky

yeah i think it's right

[vapid tiger]

phew

ok

next step

[chrome compass]

intersection is the easy part. at least for these ones; you chose good variables

[vapid tiger]

so ig it would be the element are the same

[chrome compass]

right

[vapid tiger]

so k

[chrome compass]

(if we were being careful we really should have used a third variable l for S2. but then we'd get k=l from the z-coordinate, so it's fine)

[vapid tiger]

ig i made z = k for both

but since they are separate equations ig it would make sense

[chrome compass]

right x2

looking at the y-coordinate gives us j in terms of k

[vapid tiger]

so S1 intersect S2 = {k}

[chrome compass]

bruh

S1 intersect S2 is a subset in C3

[vapid tiger]

oh

my bad

[chrome compass]

y'all good

[vapid tiger]

do i need to make a matrix ?

3x1

[chrome compass]

eh

oic

[vapid tiger]

1x3

[chrome compass]

yes, i guess, but you already did that

But yeah, if $( -3i + (i-1)k , i - 1 + k, k) = (-2i + (i+4)j, j, k)$ then $j=i-1+k$ from the y-coordinate, and now we have to check if the x-coordinates match.

[warm shale]

ENStucky

[vapid tiger]

what

so we made both y's equal

[chrome compass]

right

if two vectors are equal then all of their entries are equal

[vapid tiger]

because they are subsets of C

hmm

so now i check x1 = x2

[chrome compass]

right

[vapid tiger]

ok

but k=z and j=y

does that do anything ?

[chrome compass]

so we already used the y-coordinate, right?

that's how we got j=i-1+k

[vapid tiger]

oh substitute that in ok

[chrome compass]

right

and the z-coordinate, well we didn't use it because of that "third variable" thing I talked about above. here it just tells us k=k

so the only information left is in the x

[vapid tiger]

so i got -3i + ki - k = i -5 +ki +4k

[chrome compass]

love that

keep going

[vapid tiger]

so -5k -4i +5 =0

k = -5+4i/-5

k = 1 -4i/5

[chrome compass]

arright

so. now you gotta back-substitute

i'm gonna trust you on that

[vapid tiger]

hell nah

[chrome compass]

but let's think for a second about what we got here

[vapid tiger]

into x

both ?

[chrome compass]

...no

[vapid tiger]

j /

[chrome compass]

you just showed that k is not a variable in S1 intersect S2, but has a specific value

and j is written in terms of k, so that's also not a variable

conclusion: there's no variables here. so only one point in the intersection

[chrome compass]

...wait i'm stupid. yes, actually >.<

and y

[vapid tiger]

noooooooooo

[chrome compass]

gotta find that point

[vapid tiger]

so then i get a single solution ?

[chrome compass]

right

[vapid tiger]

gg

[chrome compass]

gg indeed!

[vapid tiger]

is k correct doh

[chrome compass]

yes

[vapid tiger]

nice

[chrome compass]

i'm gonna go to bed

but you got it from here mate

[vapid tiger]

wait just check my sol

so S1 = (-2i +3/5, i/5, 1-4i/5)

S1 = (-1/5 -6i/5, i/5, 1-4i/5) S2 = (24/5-21i/5, i/5, 1-4i/5)

[obtuse pebble]

@vapid tiger Has your question been resolved?

[vapid tiger]

can someone verify this

<@&286206848099549185>

[still swift]

hi

[vapid tiger]

yo

if you scroll up you can see the context

[noble sail]

How you know you a helper?

[vapid tiger]

?

so am i good ?

hello ?

<@&286206848099549185>

anyone ?

[obtuse pebble]

@vapid tiger Has your question been resolved?

[obtuse pebble]

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[sullen prawn]

Can someone please draw the free body forces diagram FOR THE SYSTEM for this question?

I understand there has to be a tension force upwards in the string but then i don’t know which force will balance the horizontal component of the tension?

[obtuse pebble]

@sullen prawn Has your question been resolved?

[obtuse pebble]

@sullen prawn Has your question been resolved?

[obtuse pebble]

@sullen prawn Has your question been resolved?

[frigid burrow]

What chapter is this from

If it's NLM then I can help

If it's rotation then I can't

@sullen prawn

[sullen prawn]

Yes it is

[frigid burrow]

Okk

[sullen prawn]

Nah this aint rotational motion

I just need the freebody forces diagram

Actually i figured out that the reaction force must be at A

[frigid burrow]

If we take it to be our system both rods

[sullen prawn]

Wait lemme just show u and u tell me if its right

[frigid burrow]

Then you will have mg

Hinge force from A

Only 2 i think

@sullen prawn

[sullen prawn]

Like this?

[frigid burrow]

Yes

You should break the hinge force in horizontal vertical or radial tangential

[sullen prawn]

Im talking moments abt A so no need?

[frigid burrow]

Oh yes

But you will need it for forces

Are you prepping for JEE? @sullen prawn

[sullen prawn]

No

I mean i will give jee and i’ll prep for it but only in the last 2 months, im not prepping for it seriously

This is for further mechanics in further maths a-level

@frigid burrow some other dude gave this

Said no reaction force at A

[frigid burrow]

There should be

As "A is attached to a smooth fixed pivot"

So there would be some force exerted by the pivot

A special case might be that it is zero

But we should always assume it

[frigid burrow]

Oh can you tell me more?

[sullen prawn]

Further maths is an A-level subject offered by cambridge assessment international education, further mechanics is one of 4 components offered(other beings further pure 1, further pure 2 and further stats) for further maths

[frigid burrow]

Ohh

[frigid burrow]

That's super cool

So you are planning to go abroad for uni?

[obtuse pebble]

@sullen prawn Has your question been resolved?

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[sullen prawn]

Hope is that

[obtuse pebble]

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[frigid burrow]

Nice

I donnu bro

Use @ helpers

Lol

[sullen prawn]

Im getting a complex number

[tardy epoch]

<@&268886789983436800>

Lotta trolls this hour

[north cradle]

why would you block me...

[modern cosmos]

[high lily]

@split sailDon't troll.

[obtuse musk]

.close

[obtuse pebble]

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[timid silo]

Is there any systemized way of multiplying 2 digit by 2 digit numbers in your head?

[timid silo]

Like a way that can work everytime?

Aslong as it's 2 by 2 digits

[tough reef]

Few ways, you can memorise a times table or just memorise a method to multiply numbers

[rare flicker]

You just need a good brain. Try like.

[tough reef]

Do you know how to multiply numbers without a calculator?

[rare flicker]

Odd number and even number.

[timid silo]

Well ofc

I just need to find a more of an efficient way to do it

[worn yoke]

if you can multiply a 1 digit number by a 2 digit number, then you can multiply by the 1s place, then multiply by the 10s place and multiply by 10, then add together

[timid silo]

Wait you mean like 1s places then the 10s and multiply both results by 10 and theb add together?

Then*

It's just easier to do it in my head most of the time I just need more speed+slightly more accuracy

I'm like at a 75% accuracy but I need more speed

[wary badger]

what is this for?

[timid silo]

For my own personal development

In math

The more u can do in ur head in an exam the easier

[tough reef]

You can break numbers down into simpler ones. Multiplying 27 and 25 is also 3 by 9 by 5 by 5

[worn yoke]

e.g 24 * 32 = (4 * 32) + (2 * 32) * 10

[tough reef]

Multiply in the order that you can do the quickest

[timid silo]

So you would only multiply by 10 the 2•32? Following that notation ofc

[timid silo]

I'll try both

[worn yoke]

yes, because 2 is in the 10s place it's really 20*32

[timid silo]

Does this work for every single one?

[wary badger]

distributive property

that’s all it is

[timid silo]

I'll try it thanks bro

[timid silo]

Where chu pull that 2nd 32 tho

[worn yoke]

24 = 20 + 4 so 24 * 32 = (20+4) * 32 = 20 * 32 + 4 * 32

[timid silo]

Makes sense

At the end of times

It will be the same thing

😤

Thanks

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[tough cave]

need my answer checked on this.. im pretty sure its wrong tho

[hexed river]

can you rotate your laptop

[river falcon]

its 360 ig

[grand yoke]

Think its 180

[tough cave]

😭 ??

[grand yoke]

Isnt 360 a full circle

[river falcon]

nvm not 360

[hexed river]

how far do you have to turn your laptop to get one triangle to the other

[river falcon]

i was thinking smth else

[tough cave]

wouldnt it be 180

[grand yoke]

I think so

[river falcon]

its 180 yeah

[tough cave]

tyty

.close

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[uncut niche]

ok... I AM BACK

[uncut niche]

idk how to do these, teacher barely covered what it was too

[green sphinx]

find the slope -> plug slope & the two points on graph into point slope form -> simplify into slope intercept

[uncut niche]

okay ty bro

[uncut niche]

i found the slope

with m = y2 - y1 / x2 - x1

[green sphinx]

so what was your slope you found

[uncut niche]

2

[green sphinx]

this is for problem 24 correct?

[uncut niche]

3 - (-1)
0 - (-2)

4/2

2

yes

(-2,-1) (x1,y1)
(0,3) (x2,y2)

[green sphinx]

use this formula to plug in

[uncut niche]

idk what thats called but yes ik what that is

y - (-1) = 2(x - (-2))

is this correct?

[green sphinx]

yep, now simplify

[uncut niche]

y + 1 = 2x + 2
y = 2x + 1
y - 2x = 1

i think

idk

we only just now started learning this formula, two weeks later

but im trying to do late work and i was missing this page

[green sphinx]

gimme a sec

[green sphinx]

okay, this becomes y + 1 = 2(x+2)

make sure you not only multiply the x by 2 but also the 2 in the parenthesis

[uncut niche]

OH NO

im sorry i forgot that

y + 1 = 2x + 4
y = 2x - 3
y - 2x = -3

isnt this it?

a + b = c or something

[green sphinx]

y should be on one side

[uncut niche]

y = 2x - 3
can we multiply everything by 2 or something

or -3

i think thats a possibility

idk

[green sphinx]

y + 1 = 2x + 4 to y = 2x - 3 is wrong by the way

[uncut niche]

idk what to do

what

waht the

bro im tired sorry

y + 1 = 2x + 4
y = 2x + 3
y - 2x = 3

is that it?

[green sphinx]

y = 2x + 3
is what you're looking for

[uncut niche]

oh

[uncut niche]

this is the wrong equation

just use yeah

y = mx + b

why didnt we do that

[green sphinx]

you needed to go from this equation to the one i just posted

or wait

no actually you could

[uncut niche]

😭

were both cooked sam

[green sphinx]

well i accidentally did a more complicated problem

but anyways

[uncut niche]

its all good

[green sphinx]

you can get the slope and just look at the graph for the y intercept

[uncut niche]

25 is

y = - 1/3x + 1 right?

[green sphinx]

yep

[uncut niche]

alr ty

[green sphinx]

you know how to check your answers right?

[uncut niche]

not really

[green sphinx]

the slope is visible without doing the y2-y1 equation

if your teacher hasn't taught this, then maybe wait to advance to this step

[uncut niche]

thats just how i normally get the slope

i just learned that there were two ways

this one was faster so i usually use this one lol

ty though

i have another paper

this one idk how to do

[green sphinx]

i can try to explain it for you

[uncut niche]

2 = |x| - 1

it says solve each absolute value equation

14 = |x| + 2

|-2x + 8| = 20

2|x + 8| = 20

2 <= |x| -8

|x| + 5 >= 10

|2x + 5| >= 9

-2|x + 4| <= -6

[green sphinx]

ok for this one, make |x| on one side alone, and then
x = 3 or x = -3

[uncut niche]

and then these

[uncut niche]

so

2 = |x| -1
3 = |x|
x = 3 or x = -3

?

[green sphinx]

yes as |x| = 3 --> x = +/- 3 (plus or minus 3)

[uncut niche]

okay, thank you'

[green sphinx]

ive got to go now, good luck!!

[uncut niche]

ty ty

appreciate the help

idk how to close it

wait

[green sphinx]

do .close

[uncut niche]

before you go how do i do this

|-2x + 8| = 20

[green sphinx]

well i havent done those in a while

gimme like 30 sec

[uncut niche]

tysm

[green sphinx]

ok so
|2x+8|=20
is
2x+8 = 20 or 2x+8 = -20

and then solve

👋

[uncut niche]

👋

tysm

.close

[obtuse pebble]

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[gloomy vector]

ABCD is a quadilateral, O is the intersection of AC and BD, AB=OD, AD=OC, BAC=BDA, what type of quadilateral is ABCD

[gloomy vector]

i tried drawing and i have no idea

[deep shard]

I think ABC and ODA are similar triangles

but idk what that means

for the quadrilateral

[gloomy vector]

how do you prove that?

[deep shard]

SAS

[gloomy vector]

wait nvm

wait SAS?

AB=OD BAC=ODA where is the lasr side

also isnt simmilarity only like AA and SAS is for congruency or am i stupid

[obtuse pebble]

@gloomy vector Has your question been resolved?

[wooden cipher]

AOD+COD=180
AOD+OAD+ODA=180

BAO=BAD=BDA=ODA

AOD+COD=AOD+OAD+BAO

COD=OAD+BAO

COD=BAD

you get your SAS

[obtuse pebble]

@gloomy vector Has your question been resolved?

[gloomy vector]

isnt AOD=COD?

[gloomy vector]

also how is BAO=BAD

[wooden cipher]

i meant BAC

[gloomy vector]

how about this

[wooden cipher]

nowhere does it say that

[gloomy vector]

oh i misread that as AOB=COD

so BAD=COD

so like this ish

[rose scroll]

From this congruency, can you say something about AB and DC?

(they arent equal, but there is some relation between them)

[gloomy vector]

err like BD=CD so CD is related to AB?

[rose scroll]

Think of angles attached to the sides, and what conclusion you can make from that

[gloomy vector]

wdym

[obtuse pebble]

@gloomy vector Has your question been resolved?

[rose scroll]

well... ABD and BDC are equal

[gloomy vector]

wait whar

[rose scroll]

congruence of triangles

ABD and ODC are congruent

[gloomy vector]

oh right i forgot i derived that

CD=BD and i dont see how we can get BD from AB

[rose scroll]

|| AB and CD are parallel making this figure, at least a trapezoid|| idk how else to explain it so read at own risk

[gloomy vector]

yeah i actually have no clue

im tired as fuck ill close this

thabks

.close

[obtuse pebble]

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[wraith thunder]

How would one come up with the N = 2Max{N1, N2}? Like where does it come from? Ik where N1 and N2 came from: they're subsequences of N, but where does 2max come from? Why would we wanna take the max of both subsequences and double it when proving Zn converges to the same limit ?

[wraith thunder]

Sorry if it seems like it should be a straightforward answer, just trying to understand how they got the answer :) Ik I could prob just say "Oh its true by Bolzano-Weierstrass Theorem" but i wanna know how the answer above came to be ! (esp since at this point of the textbook, B-W hasnt been introduced yet)\

A lot of yapping mb LMAO

[zenith raft]

you have an N_1 and N_2 to play with. taking the max couldn’t hurt

[unkempt vault]

because we want both the x_k and y_k sequences to be close enough, so we take the max

and double it because we have to account for the values of the other sequence

[shadow dagger]

why is our statement true? well it's because intuitively, x_n and y_n both get really really close to x

so imagine such a sequence in ur head

[unkempt vault]

like if x_50 and y_100 onwards are close enough, then we can't guarntee z_k is close enough until z_200 onwards

becaus z_199 = y_99

[shadow dagger]

you wanna pick a point N where eventually 'x_n is close enough to x' and 'y_n is close enough to x'

maybe x_n gets there faster than y_n so we'd need to take the max

[wraith thunder]

wait

i think i misunderstood the max function then

does the max function take whichever sequence is bigger, as in like

takes the sequence that uses elements higher above N if that makes sense ?

[unkempt vault]

max {N_1, N_2} is the bigger of the two values N_1 and N_2

if N_1 = 4 and N_2 = 6 then max { N_1, N_2 } = 6

[wraith thunder]

wait im dumb N1 is in the set of Natural Numbers

ok i get it now

ill close this ina bit lemme just reread over what everyone said to make sure i get it

.close

[obtuse pebble]

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[crude skiff]

Someone please refer me a video from where I can learn this … it’s part of theoretical distribution basics… no advance stuff plz..

[obtuse pebble]

@crude skiff Has your question been resolved?

[obtuse pebble]

@crude skiff Has your question been resolved?

[obtuse pebble]

@crude skiff Has your question been resolved?

[crude skiff]

.close

[obtuse pebble]

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[twilit spear]

Help me with this

<@&286206848099549185>

[bold bane]

What is 3/4 in decimals?

[hollow palm]

divide by 100

the whole percentage

[twilit spear]

Pls show me the process

[hollow palm]

answer him first

[wild glade]

try convert the number into a improper fraction

[twilit spear]

converted

[wild glade]

what have you got

[twilit spear]

135/4

[wild glade]

actually have you done this

[hollow palm]

yes

[hollow palm]

now divide

by 100

[twilit spear]

ok

got this

what to do next?

<@&286206848099549185>

hey?

it's easy i know but i need to convert in decimal

so if i cross out 100 then how will i be able to convert into decimal

[hollow palm]

actually

just write 33 3/4 as 33.75

[twilit spear]

what

[hollow palm]

now divide

by 100

should be easier

[twilit spear]

oh

[bold bane]

A mixed number is a whole number plus a fraction. If you convert the fraction to a decimal value, you can just add it to the whole number.

[wild glade]

multiply top by 25

[twilit spear]

thx

done

[twilit spear]

thx

.close

[obtuse pebble]

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[gritty oracle]

Studying for a math exam. This is a practice problem. Question b and c I am stuck on.

Here is the thing

According to my peers, the professor said that there is no analytical solution, despite what the problem states. his answer he wants is: "use math cad and use a Give and Find algorithm" I don't understand why we can't treat the constant as a vector

Apparently there's no analytical solution because matrices.

Same confusion for c. Apparently it's non linear now. My classmates aren't explaining in a way I understand, so I was hoping I could get some insight here.

It's especially frustrating that the problem says "analytical solution", yet apparently there isn't one so it's a trick question. I'm wondering if the student misunderstood.

Thank you

Also, I showed my work for b). I only did quadratic formula, but to finish the problem, I would just treat the exponential part as a scalar, only constants are vectors. That shouldn't be an issue, right?

[pseudo swift]

I don't understand why we can't treat the constant as a vector
you mean the A and B right ?

@gritty oracle

[gritty oracle]

I mean like what I wrote in my work, provided below..I'm not sure if A and B are vectors

It doesn't say if A and B are vectors. I'm assuming they're scalar

Cuz that'd be vector * vector and we aren't using dot products / cross products / geometric products in this class.

[pseudo swift]

yeah if A and B are scalars it's completely fine, it's like solving 3 scalar ODEs at a time

[gritty oracle]

Same for c?

Sorry finish what you were saying

[pseudo swift]

but yeah you have 2 linear independent solutions c1 exp(s1 x) and c2 exp(s2 x), which means the general solution to this ODE is c1 exp(s1 x) + c2 exp(s2 x)

where s1 and s2 are your two roots

it's a second order ode still

I'd expect you to find c1 and c2 in terms of y(0) and y'(0) also

(or at least write the equations they must satisfy)

[gritty oracle]

This is exactly what I thought! I am frustrated that my classmates are saying I am wrong. I also used chat gpt (albeit, not always accurate) and it gave the same solution I thought

The reason why people are saying it's not analytical os because one student talked to the professor apparently and told everyone that's the answer but I am wondering if he misunderstood

We did this in class :/

Are you sure by the way? Is there any way you can prove it

Like, I don't want to suffer from conformation bias here

[pseudo swift]

well if A and B were matrices they're prolly right

even 1st order ODEs y' = Ay where A is a matrix are already a decent pain in the ass to solve in generality

[pseudo swift]

if A and B are scalars, it's just 3 1D equations in a trenchcoat, if you want to be sure just work with the 3 equations instead

[gritty oracle]

Yeah I agree. But the problem does state anything about A and B so it's an unfair problems

[gritty oracle]

Does the same hold for c?

Sorry if you said already

[pseudo swift]

I didn't say but same thing yes

[obtuse pebble]

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[craggy spear]

Hello I tried several times to solve a question, but I couldn't. So I checked the answer, but I wanted to know the teacher's answer is only answer

[cursive forge]

what's the question?

[twilit spear]

what's the question?

[craggy spear]

This is the question, and my answer is

[twilit spear]

ah

[twilit spear]

this is not in my course

well, seems like you gotta mention helpers

i can't help you with this

[craggy spear]

Ok thank you!

[twilit spear]

now someone will help

[high lily]

!15m

[obtuse pebble]

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

[high lily]

Do not ping for others.

[twilit spear]

oh

sorry

@craggy spear you gotta ping yourself

[craggy spear]

Oh

[final thunder]

It's helpful to write out the definitions of du/dx and dv/dx

[twilit spear]

i can't ping for others, so yeah

so call helpers on your own

[craggy spear]

ok

[twilit spear]

by mentioning

[cursive forge]

ok so what are you stuck at?

[craggy spear]

My teacher said "you have to explain why the approximation becomes an equality"

And I couldn't find answer

So I found a picture that includes the teacher's answer but i wanted to use that kind of way

This is the teacher's answer

<@&286206848099549185>

[void holly]

yep this checks out

[craggy spear]

So is that the only way to solve the question?

[void holly]

no

[void holly]

if its only limits and their properties then this is the only way

[craggy spear]

ok thank you!

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[lusty willow]

Hello everyone

[cursive forge]

hi what's your question?

[lusty willow]

Isnt the answer he supposed to be C? Why is the answer A then?

[cursive forge]

first graph y = f(-x+4)

[lusty willow]

uh

kay

done

got a linear graph though

[crimson pike]

if you have a function f(x)
graphing f(-x) would mirror that function around the y-axis

[lusty willow]

ik

and i did it

but

isnt f(x + 4) a 4 units shift to the left?

why wsa the answer A then? it was supposed to be C

also

i got this from a government website

so te asnwers arent wrong

or so i think

its a provincial test

im all ears

[crimson pike]

I think the shifting is done first then the reflection

[lusty willow]

it wouldnt make a difference

since it would be -8 then a y reflection

[crimson pike]

it would be -8 so reflected becomes 8

[lusty willow]

wait

fr??

[crimson pike]

yep when rotating around y-axis
all x becomes -x

[lusty willow]

ah i see

so my mistake was

relfecting before shifting? so shifting before reflecting

is there like a rule for that?

i need to remember it

[crimson pike]

I can’t word it tho

[lusty willow]

mm

but it seems plausible

ok

thanks man

i was stuck on this for a while

ah yes

it seems there was indeed a rule

thank you

have a good day

evening

orrrr

night

or afternoon

or midnight

yeah

have a good day, evening, night, afternoon and midnight

and dawn

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[light flume]

so my limited brain capacity tells me i just have to find original function

which i think is

$-x^{2n} \le \frac{1}{1+x^{2}} - \sum_{k=0}^{n-1}(-1)^{k}x^{2k} \le x^{2n}$

am i right in thinking that i just have to show this inequality holds true on interval x:[0,1] or is that insufficient

[warm shale]

Dootud

[obtuse pebble]

@light flume Has your question been resolved?

[light flume]

<@&286206848099549185>

[pastel berry]

yeah?

[reef adder]

What do u need

[reef adder]

That’s an alternating series, use Taylor series expansion for arctan

[light flume]

taylor series isn't taught in highschool here

i cant use

[reef adder]

Ur in HS?

[light flume]

im just wondering if my inequality is correct

[light flume]

yes

[reef adder]

AP calc?

[light flume]

i dont take US curriculum so idk how ap calc works

[reef adder]

Canadian curriculum?

[light flume]

australia

[reef adder]

Right I see

[reef adder]

This is right

[light flume]

ok thx

just needed to check that my logic was correct

thx for ur time

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[mighty agate]

I dont understand how we got this. Could someone explain?

[mighty agate]

Is it some formula in use or?

[tardy epoch]

,tex .exp rules

[warm shale]

riemann

[drifting wraith]

looks super wrong

so you do 4/3 − (−2/3), that's 6/3, so a² is right

but then −3/2 − 1/2 is −2

[obtuse pebble]

@mighty agate Has your question been resolved?

[mighty agate]

idk

[mighty agate]

Why are we subtracting tho?

[drifting wraith]

when we multiply we add the powers

[mighty agate]

Ohhh yeah

[drifting wraith]

this is division

[mighty agate]

oh right yeah the second one is wrong it looks like I looked at the wrong task that's why

Thanks for pointing it out

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[lost condor]

If the universe of discourse is the integers, determine the truth value the following statement

∃m∀n(m - n = 2)

Can someone please help me figure this out

[tardy epoch]

the ordering of quantifiers is important

[lost condor]

correct

There exists a real number m, such that for all real numbers of n, m -n =2

but my confusion lies in lets say we replace n with any real number right example -4

m + 4 = 2

m could be some number of -2, right so that would be true no?

[tardy epoch]

lets say we replace n with any real number right example -4

that's already contradicting what the statement $\forall n$ means

[warm shale]

riemann

[timid silo]

Hello

[tardy epoch]

!occupied

[obtuse pebble]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[lost condor]

in what way?

-4 is an integer

[tardy epoch]

m is already fixed

[lost condor]

ohhhh

so when fixed it must not be contridictory

m as a fixed number must make the statement true for all real numbers

@tardy epoch

[obtuse pebble]

@lost condor Has your question been resolved?

[obtuse pebble]

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[dapper current]

Could someone please help me with this?

[merry peak]

Which part

[dapper current]

Mostly the arcs

[trim portal]

Hint: Consider the arc MNP, what's its measure?

i mean the arc starting at M, going through N and ending at P

idk the right notation

[dapper current]

If it was arc MNP, it hold be 62 + arc MN, but I don’t know how to find MN

[trim portal]

I'd actually find arc MN through arc MNP

[dapper current]

How?

[trim portal]

does that configuration look familiar?

green is what you need to find

orange is 80

[dapper current]

So is the green angle 160?

Making the arc 160?

[trim portal]

Exactly

and now you can subtract 62

to get MN

and MQP is easy to find

[dapper current]

Thank you 😄

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[fierce ermine]

Just need help factoring m² + m - 90

[fierce ermine]

There's no gcf and idk how I could do difference of two perfect squares with this

[brave bramble]

https://www.mathsisfun.com/algebra/factoring-quadratics.html

[fierce ermine]

Oh thx

[fierce ermine]

Immm not seeing anything that could help with this tbh. Maybe I'm not looking in the right spot

[brave bramble]

The section "a method for simple cases" is where you should start

[fierce ermine]

Oh alrighty

Thanksss

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[woven robin]

So I have this problem and just wanna be sure. If lambda(A)<infinity, then 1_A is measurable and it is a positive function so 1_A is in M^+(B(R)) which also means 1_A is in L^1(lambda) right? but how do I get the scalar a into this

[obtuse pebble]

@woven robin Has your question been resolved?

[woven robin]

<@&286206848099549185>

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[craggy skiff]

Algebra question: how do I make this a compound inequality?

[obtuse pebble]

@craggy skiff Has your question been resolved?

[craggy skiff]

<@&286206848099549185>

[craggy skiff]

Nvm I got it

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[harsh remnant]

Hello

[harsh remnant]

Not sure where to start

[orchid wind]

and ivt

[harsh remnant]

How do I apply those

[frigid prawn]

nvm i don't think mvt works

[white horizon]

Yeah thats ivt

[orchid wind]

mvt works

nvm

not necesary

[unreal musk]

(not told that f is differentiable anywhere)

[lucid falcon]

true

oops

[harsh remnant]

So like

How do I apply IVT?

[unreal musk]

You may wanna consider the function g(x) = f(x) - x: this is continuous (why?), and so you can apply IVT to that instead

As the range of f is [a, b], f takes on the values a and b - what does that mean?

[violet slate]

i dont know if this right

[obtuse pebble]

@harsh remnant Has your question been resolved?

[harsh remnant]

f(a) = a?

[unreal musk]

Not necessarily at x = a, but there's some p between a and b such that f(p) = a

[lucid falcon]

@unreal musk (by the way, I'm doing the problem too, as an exercise) I noted that g(a)= f(a)-a ≥ 0 and g(b)=f(b)-b ≤ 0. Then of course there exists x' such that g(x')=0. How can I formalize that last part?

[unreal musk]

Be careful, it isn't necessarily the case that g(a) is nonnegative and g(b) is nonpositive

But, as before, g is continuous, and (upon a correction) either one of those are zero (in which case, you're done) or one's strictly positive and the other is strictly negative (in which case, what does the IVT tell you?)

[lucid falcon]

but since range(f)=[a,b] how come g(a) = f(a) - a is not necessarily nonnegative?

[unreal musk]

Because while the range of f is [a, b], you do not necessarily have f(a) = a nor f(b) = b (nor swapping them around neither, you don't have to have f(a) = b and f(b) = a)

What you \emph{do} know is that there are some $p, q \in [a, b]$ such that $f(p) = a$ and $f(q) = b$.

Using the fact that $p, q \in [a, b]$, what can you say about $g(p)$ and $g(q)$?

[warm shale]

@unreal musk

[lucid falcon]

that $g(p) = f(p) - p \in [0, b-a]$ ?

[warm shale]

Ze_Beeg_Almond

[unreal musk]

Well, g(p) >= 0, which you have

[lucid falcon]

is it that?

[unreal musk]

Cause a <= p, that makes f(p) - p = a - p >= 0

[unreal musk]

(but that's the statement we needed, for which you can replace in here )

Similarly g(q) can be considered and all...

[lucid falcon]

yes, $g(q) = f(q) - q \in [a-b, 0]$ ?

[warm shale]

Ze_Beeg_Almond

[unreal musk]

Yep, g(q) is nonpositive

[unreal musk]

Then, of course

[lucid falcon]

but i still don,t understand why my previous thing didn't work

at $x = a we have g(x) = f(x) - x = g(a) = f(a) - a and then, since f(x) \in [a, b], we have g(a) \in [0, b-a], no?$

[warm shale]

Ze_Beeg_Almond

[unreal musk]

Actually yea it's alright, coming to think about it

[lucid falcon]

okok

[unreal musk]

f(a) is at least a

[lucid falcon]

yes

[unreal musk]

Gotcha

[lucid falcon]

so the function, evaluated at the leftmost point in the interval, is nonnegative, and for the rightmost point, it's positive, but returning to my previous commment, how can i formally justify that there exists x' in [a,b] such that g(x')=0. do i use continuity or what?

[unreal musk]

Continuity and IVT

g(a) = f(a) - a is nonnegative (as above, f(a) is at least a), and g(b) = f(b) - b is nonpositive (as f(b) is at most b)

Either one of g(a) or g(b) is zero, in which case, whichever of those, you're done

[lucid falcon]

Yes

[unreal musk]

Otherwise g(a) is strictly positive, and g(b) is strictly negative, and of course 0 is between those, and it should be clear that g is continuous, so the IVT tells you...?

[lucid falcon]

that there exists $x' \in [a,b] s.t. g(x') = 0 <=> f(x') = x'$

[warm shale]

Ze_Beeg_Almond

[unreal musk]

There you go

[lucid falcon]

how do you do <=> ?

and "there exists"

and thanks a lot man

[unreal musk]

$\iff$ and $\exists$

[warm shale]

@unreal musk

[lucid falcon]

and for all?

[unreal musk]

$\forall$

[warm shale]

@unreal musk

[lucid falcon]

alright man thanks

[obtuse pebble]

@harsh remnant Has your question been resolved?

[obtuse pebble]

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[spare terrace]

Why are we allowed to say that final velocity is proportional to square root of displacement? Where did acceleration go?

[hardy widget]

the formula only works if acceleration is constant

$v_f =\sqrt{2a \Delta x}=\sqrt{2a} \sqrt{\Delta x}$ and $\sqrt{2a}$ is a constant

[warm shale]

Civil Service Pigeon

[spare terrace]

also why is it c?

[hardy widget]

you can just use this tbh

[spare terrace]

oh wait this is just a proportion

i got it now

thanks

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[twin spade]

Hello, I will first give conext to the problem and myself. I am a highschool student who has taken little calc working on rockety. Inside a rockey to find how much fuel is burned you must know the surface area of the fuel grain, which is where my issue arrises.

[twin spade]

finding the inner surface area of a shape like this is easy, it would be the permiter of the of the "top hole" * length

i cannot understand how to find the surfave area when it is rotated around a helix like this

Logic would tell me that it should be the same bc the permeter of the face is the same, but alas the surface area is differnet

apparent this is due to streching of the lateral face, which made some sense to me after I took a cylnder toy and twisted the top and bottom

the volume and surface is the same for the same object in real life, but the height goes down, but in my instance in my fuel the height stays the same therefore the surface area must be greater

Now i though I was just turning my shape, not twisting it, but appertly it must be twised bc with not other changes other than just twisting the surface area increases

so how can I calculate or esmiate this new surface area???

https://math.stackexchange.com/questions/2930241/surface-area-of-twisted-prism

I found a website that seems to be dealing with a simialr problem, but I dont qoute understand their soultion

I would need to also somehow be able to iteratlivly calculate this in exel

Thank you!

[bold bane]

Take a single slice. Has the shape inherently changed?

[twin spade]

this shape is always the same

if thats what your asking

i think so atleast

[bold bane]

Exactly.

[twin spade]

ok... why does my surface area change in that case?

[twin spade]

increases from here to

other one with equal volume

[bold bane]

It shouldn't.

[twin spade]

logic would agree, but it does

same volume different surface area

5% difference which can matter in rockets

supposeably this is the soultion, but these means nothing to me, I dont know how to use this

[fluid fulcrum]

damn that's pretty interesting

I have an idea of why

imagine you have a square

intially

[twin spade]

ok

[fluid fulcrum]

if you push the bottom side to the right

if would become a rhombus

but then

the vertical height would lower

as a result

do you get what I'm trying to say

[twin spade]

one sec let me draw

[fluid fulcrum]

just saying im also a high school student asw lmao

i just have an idea

[bold bane]

What you are interested in is Cavalieri's Principle.

[fluid fulcrum]

this what im trying to say

so originally when you have the cylinder, your surface area is formed by long vertical rectangles

but when you curve them

you lose some of the height because of the distance which you've slanted them

because the height of the cylinder obviously don't change, you gotta add extra surface area

[twin spade]

it would have a different area no? isnt parrallegram area base*height.

[fluid fulcrum]

to maintain the height

oh wait yeah

oh but still

that proves my point

cause then

you have to stretch the rhombus

vertically

[twin spade]

well yes, but my 2 shapes have the same area

[fluid fulcrum]

you're cross section does

but I'm talking about

if you look at it vertically

[bold bane]

The area of the rhombus remains the same no matter how far you stretch it.

[fluid fulcrum]

imagine looking at it like this

[twin spade]

ok

[fluid fulcrum]

like don't look from the top side, look at it from the side

cause when you twist it, from the top down, if you kept making cross sections, it would look the exact same as the original

but if you twist it

the intial long vertical rectangles

are twisted

[twin spade]

well yes , i can understand why it happens

how do I calcualte it now

[fluid fulcrum]

this 💀

I don't think there is a simple formula

cause it also depends

on how many turns your helix has

the more turns, the more surface area

[twin spade]

probably from 0.75 to 2

[fluid fulcrum]

you'd have to use calculus to calculate the curved surface area

[twin spade]

the most ive taken is calc bc this is with no help beyond my understanding

which is why im here lol

[fluid fulcrum]

why do you want to calculate it anyways

im curious

[bold bane]

Calc BC doesn't usually cover this type of calculus.

[twin spade]

yes

[fluid fulcrum]

cause you've already found the SA with your software

[twin spade]

hence why im lost

[bold bane]

Calc AB and BC covers the same topics in Business Calculus in college.

But not what you would find in engineering.

[twin spade]

its to calculate mass flow rate of fuel, ik how deep it burns, i just need the surface area

[fluid fulcrum]

I think you could approximate it

[twin spade]

i am making a engine model

[fluid fulcrum]

using what I just did

just calculate

how much

the perimeter to area ratio changes

when you go from a square to a parallelogram (with a base of 1m^2)

[twin spade]

yk i still dont qoute understant how you are streching it

[fluid fulcrum]

like you know how when I nudged the base of the square, I had to add extra height

wait can u call 💀💀

sounds ridiculous but I can explain

better w vc

[twin spade]

sure

[bold bane]

It would stretch it now that I think about it. Imagine two points on an untwisted cylinder. If you twist it some amount dx, it from a triangle whose hypotenuse would net be the same length as the untwisted length.

[obtuse pebble]

@twin spade Has your question been resolved?

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[obtuse pebble]

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[drifting wraith]

false

[timid silo]

Sorry, im new to proofs, but if its asking to determine if this is true, and to prove my answer

yeah, its obviously false

but would there be any further proof to show that

[drifting wraith]

can't think of anything

[timid silo]

yeah i figured, thanks though

.close

[obtuse pebble]

Channel closed

Closed by @hearty moth

Use .reopen if this was a mistake.

[obtuse pebble]

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Send your question here to claim the channel.

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

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[modern palm]

Can someone double check that this is the correct usage of permutations and n choose k

[tepid solstice]

for option (a) if its an ordered sample then just picking 2E A N is not enough u have to permute those 4 letters too

(b) looks good

[modern palm]

Should it be 5P2 * 4P1 * 3P1 in numerator?

[tepid solstice]

ummm not exactly because ur just permuting two same alphabets

it doesnt make sense

what u shud do is u shud think like

ah okay now i have picked 4 alphabets

in how many ways i can permute them

AKA how many words i can make with them

because technically each word is an order of alphabets right

if u find number of words u can take it as number of orders u have picked out the alphabets

[modern palm]

Hmm I'm still have trouble understanding, my logic was that the first 2 tiles drawn have to be E, so therefore out of 5 E's we are taking 2, and not replacing them, so its 5P2,

[tepid solstice]

u are correct

i am saying here u cant do 5P2

because the objects arent distinct

u cant differenciate between two Es so why use nPk

instead just ue

nCk

but then after choosing all Es A and N u have to permute them as a whole

[modern palm]

Interesting

[tepid solstice]

because the order in which u pick

Es As and Ns are different

like u can pick two es one a and one n

OR u can also one pick 1E 1a 1n and then finally 1e

u see they re diff events because the order is different

[modern palm]

Yes

I see

So how are we going to restrict it to that specific order?

[tepid solstice]

have u learnt finding number of words from a given number of letters?

[modern palm]

Let me think about that, could you be more specific?

[tepid solstice]

like suppose

i gave u 2As one B one C

how many distinct words can u make out of them

using all of them

i forgot to mention

[modern palm]

Wont it just be like 4 * 3 * 2 * 1

[tepid solstice]

yep that is correct but here i have given u duplicate letters too

if u consider both As as distint ull get extra cases

ABCA is the same word even if the As places interchange

[modern palm]

So the probability of getting ABCA at random is 2/(4 * 3 * 2 * 1) ?

[tepid solstice]

no not exactly

i think i am confusing u

like in this case that is correct

but not always

there is a way to find number of words without the 4* 3 * 2*1 method using nCp too

i am sorry if im wasting ur time XD im not very good at explaining

[modern palm]

No worries

I appreicate your help

[modern palm]

Perhaps you could explain this once more?

[tepid solstice]

okay sure

so see

they said

we have to picked as an ordered sample

which means

the order in which we pick the letters

will matter

[modern palm]

Yes

[tepid solstice]

so like u can take in the order A N E E or A E N E

[modern palm]

Yes

[tepid solstice]

both will be different events right

[modern palm]

Yes

[tepid solstice]

because the order of letters change

[modern palm]

Let me propose a revised answer one second

[tepid solstice]

okay

btw im just telling u the choosing part is correct

[dry tusk]

Skidibi toilet

[modern palm]

Thoughts on this>

?

14 tiles total, no replacing, and we are selecting E,E,A,N

Where there are 5 E tiles, 4 A tiles, 3 N tiles, at the start

and 2 B tiles

[tepid solstice]

yeah see the problem is