help-27

[feral bobcat]

its just solved by intuition ?

[dull loom]

No by using newton’s laws

I think his first and third but I’m not sure

[dull loom]

A I think

Because the bus keeps moving to the west it just goes slower

It doesn’t go backwards (to the east)

When the driver hits the break, the passengers in the bus will keep moving the same way as the bus, (west) until an external force works upon it (the muscle force of your legs)

But I might be tweaking

[devout snow]

@feral bobcat Has your question been resolved?

[feral bobcat]

what about the passengers

i feel when a car is accelerating, i am like moving the opposite direction

like you are stuck to the chair

why does this happen

[wicked turtle]

the question is kind of dumb because it doesn't specify in what frame

[dull loom]

Because you stay stationary until the force of the chair acts upon you

[wicked turtle]

obviously in a frame that is fixed to the ground outside, both continue moving west

[feral bobcat]

so I move eastward when the bus accelerates?

[dull loom]

That’s why you feel a pressure in your back

[dull loom]

Yes

[feral bobcat]

mhm

can u help with this

[dull loom]

what’s a bearing

I’m not English

[feral bobcat]

i dont know lol

[devout snow]

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[devout snow]

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[zealous token]

If x>3 and y<2 then prove (x-3)(y-2) < 0

[zealous token]

can someone explain how to solve this?

[supple knot]

do you know the signs of x-3 and y-2

[zealous token]

huh

[supple knot]

sign of something nonzero is either positive or negative

[zealous token]

nah it's unknown

[supple knot]

if x > 3, then the sign of x - 3 can be deduced

[zealous token]

so what does this mean

[supple knot]

subtract 3 from both sides of x > 3

[zealous token]

x-3>3-3

[supple knot]

yes

[zealous token]

?

then?

[supple knot]

3 - 3 = ?

[zealous token]

0

[supple knot]

put it all together and deduce the sign of x - 3

[zealous token]

so repeat what we just did?

[supple knot]

sure

[zealous token]

x>3 then x-3>3-3 then x-3 > 0

this?

[supple knot]

that's right

so what's the sign of (x-3)

[zealous token]

• ?

wait what do you mean by sign

ohhh

wait

it's got to be positive

because it's larger than 0

[supple knot]

yes that's the meaning of positive

[zealous token]

yea...

what now tho

[supple knot]

do the same thing for y<2 to find the sign of y-2

[zealous token]

and once i find it?

oh it's also positive because it's the same y-3

[supple knot]

find the sign of the product (x-3) (y-2)

[zealous token]

wym x 😭

oh

it's y<2

[supple knot]

yes

it's important to read the information given in the problem

[zealous token]

y-2<2-2 then y-2<0 so the sign is negative

and then the sign of the entire thing is negative

that was more simple than i thought

thanks

@supple knot the next one is a bit more confusing if you can help me

xy +6 < 2x + 3y

same info

[zealous token]

(x> 3 y<2)

[devout snow]

@zealous token Has your question been resolved?

[devout snow]

@zealous token Has your question been resolved?

[devout snow]

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[cosmic yacht]

Are my solutions right ?

[cosmic yacht]

and I have 2 more questions, if my solutions are right

[sour thunder]

Naja die Frage hast du jetzt nicht beantwortet, für welche a gilt das denn jetzt?

[cosmic yacht]

a darf nicht 2 sein

sonst für alle, nh?

wenn meine rechnungen stimmen

[sour thunder]

Ist das die ganze Aufgabe?

[cosmic yacht]

warte ich kann dir das original zeigen

[sour thunder]

Sekunde ich rechne kurz nach

[cosmic yacht]

dankeee

[sour thunder]

Ja genau für alle a ungleich 2

Was für Fragen hattest du noch?

Deine Rechnung ist auch Top

[cosmic yacht]

yaay

warte

die Frage war, ob ich das direkt dort ablesen kann, oder ob ich etwas neu berechnen muss

[sour thunder]

Theoretisch hast du das schon beantwortet

Auch für a ungleich 2

[cosmic yacht]

ufff

but why?

also ich kann glaube noch nicht soviel mit injektiv anfangen und umkehrbar

[sour thunder]

Wenn die nach injektivität fragen musst du immer daran denken dass eine abbildung nur injektiv ist wenn ihr kern = {0} ist

[cosmic yacht]

Also ist es nur injektiv, wenn ich a=2 einsetze?

[sour thunder]

Also für welche fälle phi(x)=(0,0,0)^T ist

Ne dann eben nicht

Das ist LA nehme ich an oder=

[cosmic yacht]

LA?

😓

[sour thunder]

Lineare Algebra?

[cosmic yacht]

Achso ja

Mathe 1

[sour thunder]

Weißt du was der Kern einer Abbildung ist?

[cosmic yacht]

irgendwas mit nullvektor

[sour thunder]

yes yes

Der Kern ist die Menge aller Vektoren für die phi(x) null ergibt

Du hast bei deiner Rechnung bestimmt gemerkt dass die die unteren zwei einträge des Vektor immer 0 sind oder=

[cosmic yacht]

meinst du das?

[sour thunder]

ja genau

[cosmic yacht]

yes

[sour thunder]

Oder machen wir das mal so das kannst du allgemein anwenden

Du setzt deinen Vektor gleich null und löst nach a auf

[cosmic yacht]

Ich glaube jetzt fürs üben würde ich es mal richtig machen und nicht nur hinschreiben a!=2 fürs verständnis

[cosmic yacht]

yess mach ich

2 = a

[sour thunder]

Genau 🙂

Also das ist wichtig zu wissen für sowas

Die abbildung ist injektiv wenn im kern nur der 0 vektor liegt

Also wenn phi(x) nur dann gleich 0 ist wenn ich in phi(x) die null einsetze

[cosmic yacht]

wie kann ich diese 2 jetzt genau interpretieren? Was sagt sie mir? :3

[sour thunder]

Wenn dein a=2 ist dann ist das immer null

[cosmic yacht]

alle vektoren

[sour thunder]

Also ist die gleichung in mehr als diesem fall null

ja du hast ja beim rechnen bestimmt irgendwann (2-a)x_3=0 da stehen gehabt oder?

[cosmic yacht]

yes

[sour thunder]

Also das ist null wenn x_3=0 ist oder wenn a=2 ist oder?

[cosmic yacht]

genau

[sour thunder]

Aber die abbildung ist nur injektiv wenn nur null rauskommt wenn (x_1,x_2,x_3)=(0,0,0) gilt

Das mit dem Kern musst du dir vielleicht in ruhe anschauen

[cosmic yacht]

Wenn ichs richtig verstehe, kann es nicht injektiv sein, wenn nur x3 0 ist

[sour thunder]

Aber solche ist es injektiv/surjektiv fragen kommen 100% dran und injektivität argumentiert man am leichtesten mit dem kern

[cosmic yacht]

jap... Klausur am Donnerstag ohoho

[cosmic yacht]

jop. Ist in jeder Klausur

war nur noch nicht soweit bis jetzt

[sour thunder]

Also die idee im groben ist so

Phi(x) ist ja deine Abbildung

[cosmic yacht]

yes

[sour thunder]

Wenn ich da den Nullvektor reinmache, dann ist die immer null oder?

Wenn x_1=0 ; x_2=0 ; x_3=0 gilt

[cosmic yacht]

jap

würde ich jz sagen weil alles 0 ja 0 ergibt

[sour thunder]

Genau

Wenn phi(x) für was anderes als den Nullvektor null ergitb dann ist phi nicht injektiv

Also wenn phi((1,1,1)^T) jetzt null ergeben würde z.B.

[cosmic yacht]

wäre es nicht injektiv

Aber dann würde man die Antwort ja schon wissen, bevor man überhaupt irgendwas an der Aufgabe rechnet oder nicht

in dem fall nie injektiv außer da steht 0,0,0

[sour thunder]

nein nei

injektiv ist es wenn es nur genau dann null ist wenn ich null einsetze

Aber das gilt ja immer

[cosmic yacht]

Ja ich glaube diesen Satz checke ich, aber ich glaube nicht das übertragene xd

[sour thunder]

Wenn ich in eine lineare abbildung 0 einsetze ist die immer null

[cosmic yacht]

Mir fällt noch iwas damit es check macht

[cosmic yacht]

ja

[sour thunder]

Besonders ist es wenn bei etwas anderem 0 rauskommt

Dann ist sie nicht injektiv

Würde dir die hintergründe erklären aber ich glaube das verwirrt dich nur noch mehr

[cosmic yacht]

okay, aber laut meinem jetzigen Verständnis: kann es ja dann nie injektiv sein, außer man rechnet mit 0,0,0

Ich glaube das wäre jetzt hier ein ewiges gespräch, weshalb ich mich lieber doch ein wenig auf yt umschaue

haha

[sour thunder]

der Kern ist quasi die lösungsmenge wenn ich da null setze

Ja gute Idee

Viel Erfolg

[cosmic yacht]

Ich danke dir für deine Hilfe und Zeit peppoHappy

[sour thunder]

Immer gern 🙂

Hauste rein

[cosmic yacht]

.close

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[sage pagoda]

I need help asap:

What is distributive property in exponents?

[tropic skiff]

Do you mean $(ab)^m$

[woven radish]

King Leo [Ping For Help]

[tropic skiff]

$$(ab)^m = a^m b^m$$

[woven radish]

King Leo [Ping For Help]

[iron kindle]

,rccw

[sage pagoda]

Yep

[devout snow]

@sage pagoda Has your question been resolved?

[sage pagoda]

?

[devout snow]

@sage pagoda Has your question been resolved?

[thin basin]

whar have you tried?

[devout snow]

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[versed wyvern]

Solve this in the simplest way possible $\left{ yz=-200,y+z=-10 \right}$

[woven radish]

Elliot Pixel

[tropic skiff]

@versed wyvern try making a substitution. in the second equation, solve for (or isolate) z or y

One thing i despise about this equation is that z and y are interchangeable

[versed wyvern]

I did that and got $\frac{-200+z^{2}+10z}{z}=0$ but that's not the simplest way is it

[woven radish]

Elliot Pixel

[versed wyvern]

yeah so I'm trying to avoid quadratics

challenging myself not to use them lol

[trail apex]

Upon looking at it quadratic solves to 20 and -10 I think

[versed wyvern]

Yeah

.close

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[bitter mantle]

What is the answer for the right steps for this one.

[ionic coyote]

I would say 1, 2, 5, 3, 6, 4

[bitter mantle]

Okay as how were you able to determine that

[bitter mantle]

Your right as well

[ionic coyote]

Because that is approximately what a proof by induction does, you start from m = 1

and then you check if it holds

so you assume that it does not hold and then proof that this assumption is wrong

you understand?

[bitter mantle]

Yes I do better now as could it be like k = 1 as well as any letter = 1

[ionic coyote]

yes!!

[bitter mantle]

Thank you for that as I am a CS major student and so I ablout about to completye my course and so hope to keep doing well

What is your major and was it easier for you to understand this stuff the first time you saw it

@ionic coyote

[ionic coyote]

good luck!!

I have a bachelor in Maths and master in statistics, so I am a bit familiar with these yes 🙂

[bitter mantle]

Next class for me is Theory of Computations

[ionic coyote]

sounds difficult xD

[bitter mantle]

Makes sense for that then as I need like 6 more classes before graduation as am wanting to go into embedded systems

Agreed to that idea

[ionic coyote]

good luck!

[bitter mantle]

I done recursion with programming but not abstract ideas before

[ionic coyote]

yeah it is not easy to undersand then

[bitter mantle]

Agreed to that idea and all

I hope to keep doing better with it as I just understand the way it is setup

How about this one @ionic coyote

<@&286206848099549185>

[devout snow]

@bitter mantle Has your question been resolved?

[bitter mantle]

<@&286206848099549185>

[wet torrent]

hello

[bitter mantle]

Hello

Can you help me out

I am trying to figure out why for the right steps here

.close

[devout snow]

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[bitter mantle]

.reopen

[devout snow]

✅

[bitter mantle]

Please do help me out

[bitter mantle]

.close

[devout snow]

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[jaunty dagger]

For the transitivity proof, why can i just not do f'(x) = g'(x) = h'(x)?

[jaunty dagger]

would that not be valid?

[supple knot]

f' = g' and g' = h' implies f' = h' therefore f ~ h is perfectly valid

[jaunty dagger]

ok good throught i was loosing my mind

is what they did more accepted?

or is there any reason to it

[supple knot]

no reason really

[solar goblet]

i suppose this is a way more convoluted way to say that f(x) ~ g(x) means f(x) = g(x) + c for some constant c

[jaunty dagger]

can you kinda explain what they did

im a little lost

[supple knot]

lots of ways to do multiple problems

[jaunty dagger]

^

Oh are they just integrating both

and adding some constant

@solar goblet wait rq

are they just integrating

getting some cosntant

how did they get
f(x) − h(x) = (f(x) − g(x)) + (g(x) − h(x))

[solar goblet]

from thin air

note that -g(x) + g(x) = 0

[jaunty dagger]

oh

ok yeah

then when u integrate constants go to 0 so there is no diffence

annoying way to do this but makes sense ig

[devout snow]

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[strong tiger]

what did you try?

[sharp token]

$u=1-tan^2(t)$
$\int\frac{sec^2(t)}{\sqrt{1-tan^2(t)}}dt=1/2*\intu^(-1/2)*\frac{1}{tan(t)}du$

well

that doesnt work

[strong tiger]

try

tan(t) = u

you want to use substitution

in such a way that

how do i explain

[sharp token]

doing u=1-tan^2(t) gets rid of the sec^2(t)

[strong tiger]

it will give you an extra term of tan(t)

if you do tan(t) = u you won't have to deal with extra tan(t) term

start with elementary substitution first

its much better that way

[sharp token]

im not sure how you can just know these things

[strong tiger]

it comes with practice

when you have practiced enough integrals you'll know it too

[sharp token]

ill try that u then

[strong tiger]

as a beginner to integrals i would recommend trying more elementary substitution first

[sharp token]

what do you mean elementary substitution

[strong tiger]

like just a single trignometry or algebraic term as u

instead of the entire equation

in this case tan(t) = u

instead of 1-tan^2(t) = u

[sharp token]

alright

so does elementary substitution work in the same situations where bigger substitutions can be used just slower?

[strong tiger]

elementary substitution works in basically all situations
here the bigger substitution actually makes the integral harder to solve

key rule to using substitution is that the derivative of your substitution must be present in your integral

derivative of tan(t) is present [sec^2(t)] but not of 1-tan^2(t)

[sharp token]

yeah alright

thanks thats really helpful

$=\int[1-u^2]^{-1/2}$

[woven radish]

BlackWizard

[sharp token]

im not sure where to go from here

[junior flax]

U sub probably doesn’t work in this case actually

Lowkey this integral seems pretty hard (for me at least)

[devout snow]

@sharp token Has your question been resolved?

[junior flax]

Hold up never mind

U sub does work

I’m lowkey goofing

[junior flax]

This the derivative of arcsin(u)

I lowkey remember non of the trig integrals

[devout snow]

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[dawn ginkgo]

Fast math people please help me I’m doing question 17

[devout snow]

@dawn ginkgo Has your question been resolved?

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[sullen karma]

Can someone help me out. I’m not sure if I’m allowed to ask anymore as I asked earlier. But no one replied to me

[devout snow]

Please don't occupy multiple help channels.

[sullen karma]

Nvm then. I’ll just ask another time 😭

.close

[devout snow]

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[iron kindle]

probably better to close your previous channel and start a new one

[sullen karma]

Can I talk here now I closed my old one

[iron kindle]

you already closed this one

[sullen karma]

.reopen

[iron kindle]

just start a new channel with your question as the first message

[devout snow]

✅

[iron kindle]

if you start the channel with your question itll show up in the pins which makes it easier to look back to

[sullen karma]

Oh

.close

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[scarlet wave]

hello

[devout snow]

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[solar silo]

can someone help with q 4c?

[devout snow]

@solar silo Has your question been resolved?

[devout snow]

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[feral bobcat]

help pls

[feral bobcat]

idk how to start

[feral bobcat]

area = pi * r^2 🙂

[feral bobcat]

bro idk how to start

what is A1, A2 , A3..

i dont understand what they mean

[iron kindle]

A1 means there is 1 circle

A2 means there are 4 circles

the square is 1m^2 thus r_1=0.5

r_2=0.25

r_3=1/6, etc

[feral bobcat]

how did you know

that A2 = 4 circles

a33 = 8 circles?

[iron kindle]

right here

[feral bobcat]

i didnt understand this statement ngl

i just did this

1 1 1 1

but i didnt know what means A1, A2 , A3

[iron kindle]

this is wrong

[feral bobcat]

why

[iron kindle]

the area of hte square is 1m^2

[feral bobcat]

they said area = 1

[iron kindle]

thus the sidelength is 1

[feral bobcat]

oh

[iron kindle]

of the square

[feral bobcat]

let me try again

1.5 circle =. 0.5

[iron kindle]

this is A1, which has 1^2=1 circles

[feral bobcat]

1.5 circle = 0.5

3/2 * r^2 * pi = 0.5

[iron kindle]

this is A2

[feral bobcat]

bruh this confusing as hell

can you complete

ill try to understaand

[iron kindle]

A2 has 4 circles

each with radius 1/4

what is the area?

[feral bobcat]

why raduis 1/4

how did u know

nvm from this?

[feral bobcat]

this

[iron kindle]

the diameter of 2 circles is equal to the sidelength of 1

the drawing is shit

but you get the point

[feral bobcat]

yes i do

but i think your wrong

[iron kindle]

i disagree

[feral bobcat]

each 3 circles = 1 diameter

[feral bobcat]

.

[iron kindle]

A1=pi/4

[feral bobcat]

oh

[iron kindle]

A2=4 * pi * (1/4)^2=pi/4

[feral bobcat]

so we make it 1 circle

[iron kindle]

this doesnt make any sense and is wrong

[iron kindle]

what?

the diameter of each circle is 1/n

thus the radius is 1/(2n)

[feral bobcat]

mhm

so A4= 8 * 0.5^2

A3 = 4* 0.5^2

[iron kindle]

where did pi go

and why do they all have radius 1/2?

[feral bobcat]

i mean they cancel out

[iron kindle]

what?

please think about what youre doing

dont just write out random equations

[feral bobcat]

didnt you say 1 circle = 0.5

ok

ill try again

sorry

[iron kindle]

for A1, yes

but if you are at A2

then you have 4 circles

in a 2x2 grid

[feral bobcat]

ok i am trying again

sorry

A1 = 0.5^2 * pi
A2 = 0.25^2 * pi

[iron kindle]

look at the given example

[feral bobcat]

i am now trying A3(4 circles) and A4(8 circles)

[iron kindle]

the sidelength is 1

what is the diameter of 1 of the circles

[feral bobcat]

depends on how many circles

here there is 3 in a row

so 3 circles = 1

diameter of 1 circle = 1/3

raduis = 1/6

right?

[iron kindle]

perfect

[feral bobcat]

that is A4

[iron kindle]

now imagine there are n^2 circles in thet square

[feral bobcat]

now when we have 4 circles

Each circle has a diameter of 1/2

so raduis = 0.25

[iron kindle]

yup

and when we have 16 circles?

[feral bobcat]

when we have 2 circles , it is also 0.25

1/32 = raduis of 1 circle

[iron kindle]

and when we have 5^2 circles?

[feral bobcat]

1/50 raduis

so A2 = A3
2 circles = 4 circles

[iron kindle]

try writing more general

like, when you have n^2 circles

[feral bobcat]

A2 = A3 = 0.25^2 pi = 1/8 pi

A1 = 0.25 pi

A4 = 1/6 ^ 2 pi

am confused , what do you mean

[iron kindle]

we want to go to An

[feral bobcat]

is this wrong?

[iron kindle]

yes?

A1=pi*(1/2)^2

[feral bobcat]

yes

1/4

pi

[iron kindle]

A2=4 * pi * (1/4)^2=pi/4

A3 = 9 * pi * (1/6)^2=pi/4

etc

[feral bobcat]

oh right , we multiply 4 because we have 4 circles

[iron kindle]

do you see the pattern here?

[feral bobcat]

we want the area of the entire square

let me figure out the pattern

i dont see a pattern

[iron kindle]

what is A4?

[feral bobcat]

i just see you multiply

the number of circles

with the area of 1 circle

[iron kindle]

the number of circles is n^2

and what is the radius of the circle?

[feral bobcat]

So if we say A4, that means 16 circles?

[iron kindle]

yes

[feral bobcat]

dang i didnt even understand this from the question

A4 = 16 circles

how do i know each row has how many circles?

[iron kindle]

there are n^2 circles in a grid

that means each row has n circles

[feral bobcat]

oh kinda makes sense

1/8 = A4

[iron kindle]

if there are n circles in a row, what is their radius?

[feral bobcat]

1/8

1/2n

[iron kindle]

BRACKETS

[feral bobcat]

what do you mean

[iron kindle]

1/(2n)

1/2n = n/2

[feral bobcat]

oh ok

[iron kindle]

so the radius is 1/(2n)

and there are n^2 circles

what is the area of all the circles?

each circle has pi*(1/(2n))^2 and there are n^2 circles

@feral bobcat

[devout snow]

@feral bobcat Has your question been resolved?

[feral bobcat]

hello

sorry my internet disconnected

i think i got it, ill retry when my internet is back

thank you so much

[iron kindle]

its okay

[devout snow]

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[devout snow]

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[void ember]

how does this quadratic equation factor to -3,8?

two numbers is supposed to multiply to 24 and add to -5

-3*8=24 but -3+8=5 (not -5)

is this an error on KA?

[dense jay]

you want 5

also -3*8=-24

they factored out -1 so we had -[x^2+5x-24]

[void ember]

its -5

check again

[dense jay]

thanks, i can read

they are factorising x^2+5x-24

[void ember]

yea...so its -5

[dense jay]

look at it properly

[void ember]

am i posting a different image?>

[dense jay]

no

they had -x^2-5x+24

they factored out -1

-[x^2+5x-24]

they factored the interior of the []

thats it

[void ember]

i must be looking at something else

ok thanks anyway

[dense jay]

[void ember]

if anyone can help, would be much apprecaited. i'll be on for a little more if anyone sees this

thanks

[alpine python]

i think it means that x^2+5x-24 factors to (x-3)(x+8)

[void ember]

yea but -3+8 = 5

isn't it supposed to add up to -5?

or is it always supposed to add up to a positive number?

[alpine python]

not if you're factoring x^2+5x-24

[void ember]

regardless if there's a negative sign?

[dense jay]

if it were x^2-5x+24 you would be right

[alpine python]

it can be positive or negative

[void ember]

dude just leave, you're not helping at all...sorry

[void ember]

so even though the question says -5....it should always add up to +5?

[dense jay]

👋

[void ember]

is that what you're saying?

[void ember]

bye

[alpine python]

no

[void ember]

so basically the absolute value?

[alpine python]

no

[void ember]

look at this

it's minus -11x

[alpine python]

yes

[void ember]

so makes sense that answer is -3,-8

[alpine python]

yes

[void ember]

but other question doesnt make sense

cause -3+8 = +5

i think its an error on KA

[alpine python]

well the answer isn't complete

they only wrote -3, 8

but they didn't write the answer

[void ember]

that's the answer

(x-3)(x+8)

but it doesnt add up to -5

[alpine python]

no the answer should be -(x-3)(x+8)

[void ember]

that's not what's written

[alpine python]

what's the question?

[void ember]

that's the question

[alpine python]

that's not a question

i'm guessing the question is "factor -x^2-5x+24"

[void ember]

yea

[alpine python]

then the answer is -(x-3)(x+8)

[void ember]

ok well that's not what he wrote as his final answer

[alpine python]

what did he write as a final answer?

[void ember]

i'm just going to assume the site is wrong

[alpine python]

it's possible

[void ember]

(x-3)(x+8)

[alpine python]

that seems wrong

seems like they forgot the -1 that they factored out

unless i'm misunderstanding what the question is

[void ember]

what do you mean by "factored out"?

[alpine python]

i mean it seems like they forgot that they did this

[void ember]

oh I see....

Ok I'll double check their answer maybe I missed it

thanks for the help

[devout snow]

@void ember Has your question been resolved?

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[cosmic yacht]

How do I get from the equation at the bottom to the equation at the top?

[faint gorge]

2a = sqrt(4a^2)

[vital dagger]

yes you put it into the root and square it to "cancel" the root

[cosmic yacht]

okay nvm

can you say how it works?

[faint gorge]

wurzelgesetze mein freund

[cosmic yacht]

hab ich in 13 jahre schule nie gebraucht

[faint gorge]

wurd dann zeit

[cosmic yacht]

okay ja doch checke

aber wieso steht eine 1 im zähler?

[faint gorge]

weil die 2a im nenner steht

a/b = 1/b * a

1/b * a = 1/b * a/1

[cosmic yacht]

ahh okay habs

dankeschön

[devout snow]

@cosmic yacht Has your question been resolved?

[cosmic yacht]

yes

[devout snow]

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[solid osprey]

find real positive solutions $(x,y,z)$ to
$$xy+xz+yz=12$$
$$xyz=2+x+y+z$$

[woven radish]

skissue.in.a.teacup

[solid osprey]

immediately this screams to change it into a cubic, so $t^3+(2-xyz)t^2+12t-xyz=0$

[woven radish]

skissue.in.a.teacup

[solid osprey]

but im not really sure how to continue ;-;

3d graph looks like this, by the looks of it thered a tiny intersection at (2,2,2) which is a solution

ok ill close this why did i even open it im going to school in like 20

.close

[devout snow]

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[crude wasp]

ok i'm going to bed like now

[solid osprey]

damn

[crude wasp]

might not be intended, but you want the cubic to have 3 +ve roots (may be repeated)

so like differentiate and find turning points potentially

[solid osprey]

and what willl i be looking for in the turning points?

[crude wasp]

sketch a cubic

and see what it means for said cubic to have 3 roots assuming no repeated roots

[solid osprey]

do i want the y coordinates for the turning points for one of them to be >=0 and one to be <=0

(in my head) i think if they are both "at the same side" of the x axis it will only have 1 sol

[little totem]

correct

i dm'ed you a hint

notice that the turning points are where f'(x) = 0

youll find that youll be able to restrict some of what xyz can be by only looking at cubics such that f'(x) even has real solutions

[solid osprey]

ah sorry i didnt see, discord sends them to message requests and doesent notify me of it

[little totem]

np, just wanted to make sure you saw it since I figured typing it here it would get buried

now we just need to figure out how to show that xyz cant be >8

[devout snow]

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[cold meadow]

This is the problem but where I’m confused is the 0

[cold meadow]

So if I understand correctly the limit for g(x) is 0

And uhh

[little totem]

actually all 3 of those are wrong

[cold meadow]

I forgot my question 😭

[little totem]

to see why, pick a point VERY close to x=3

[cold meadow]

My savior

[little totem]

and try it

[cold meadow]

Uhh

[cold meadow]

Like 2.99?

Oh wait it’s negative

So negative/negative is positive

And that applies to both side of the limit?

[little totem]

yep

[cold meadow]

Uhh, this is kinda a weird question but what is the result or what would the answer be if it was (-infinity)/0

Wouldn’t it just be -infinity

[little totem]

divide by zero depends

on which side

but otherwise yes

[cold meadow]

I understand, thank you 🙏

[devout snow]

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[outer flume]

Hello do you guys think using a hyperbola to model a water bottle cap is okay if I restrict domains properly (Using the function I get and inputting to the Formula of Surface Area of Revolution)

[devout snow]

@outer flume Has your question been resolved?

[outer flume]

<@&286206848099549185>

[forest yarrow]

ye

it should be ok

but

a hyperbola extends infinitely

[devout snow]

@outer flume Has your question been resolved?

[outer flume]

Thx

[forest yarrow]

np

[devout snow]

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[gentle sundial]

i have the short answer but can i have step by step solution?

[devout snow]

@gentle sundial Has your question been resolved?

[tropic skiff]

First, lets define our hypotheses

$$\mathrm H_o: p = \frac{450}{3,000} = 0.15$$
$$\mathrm H_a: p > 0.15$$

[woven radish]

King Leo [Ping For Help]

[tropic skiff]

$$\hat p = \frac{351}{1,800}$$
$$\mathrm{SE} = \sqrt{\frac{\hat p( 1 - \hat p)}{n}} = \sqrt{\frac{0.195(1 - 0.195)}{1,800}} = 0.00933$$

[devout snow]

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[tropic skiff]

Are you serious

.reopen

[devout snow]

✅

[tropic skiff]

Then you can normal cdf

Hmm i did smth wrong

Oh i completely messed up

New hypotheses:
$$\mathrm{H_o} \implies p_1 = p_2$$
$$\mathrm{H_a} \implies p_1 < p_2$$
$p_1$ refers to the true proportion of teenagers in 1990 who showed hearing loss. \
$p_2$ refers to the true proportion of teenagers in 2010 who showed hearing loss.

[woven radish]

King Leo [Ping For Help]

[tropic skiff]

We'll used the pooled proportion to calculate our standard deviation

$$\hat p_c = \frac{x_1 + x_2}{n_1 + n_2} = \frac{450 + 351}{3,000 + 1,800} = 0.166875$$

[woven radish]

King Leo [Ping For Help]

[tropic skiff]

Now lets calculate the standard error:

$$\mathrm{SE} = \sqrt{\hat p_c(1 - \hat p_c) \qty(\frac 1{n_1} + \frac 1{n_2})} $$ $$= \sqrt{0.166875(1 - 0.166875) \qty(\frac 1{3,000} + \frac 1{1,800})} $$ $$= \boxed{0.0111}$$

[woven radish]

King Leo [Ping For Help]

[tropic skiff]

Now lets find our z-score

$$z = \frac{\hat p_2 - \hat p_1}{\mathrm{SE}}$$
$$z = \frac{\frac{351}{1,800} - \frac{450}{3,000}}{0.0111}$$
$$z = 4.048$$

[woven radish]

King Leo [Ping For Help]

[devout snow]

@gentle sundial Has your question been resolved?

[devout snow]

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[icy spade]

I got y=-3cos(1/2x) but it says its wrong. Where did I make a mistake? Cant figure it out

[alpine python]

it's the 1/2

[icy spade]

is the period not 4pi?

then 2pi/4pi=1/2

[icy spade]

.

[alpine python]

looks to me like the period would be 8pi

[icy spade]

so the equation would be y=-3cos(1/4x)?

[alpine python]

that seems right

[icy spade]

it was, thanks!

.close

[devout snow]

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[obsidian plank]

Can anyone help me I don't know where to start

[tropic skiff]

It says horizontal

Can you try drawing a horizontal line

[obsidian plank]

oh is it 0

[obsidian plank]

so what if it is vertical

[tropic skiff]

Undefined, because in rise/run, you have run = 0, but you cant divide by 0

[obsidian plank]

ok so does this apply to everything like if I changed it to (2, 5) would that change anything ?

[tropic skiff]

If you changed the point, but the line was still horizontal/vertical, the above properties apply

[obsidian plank]

got it thanks

.close

[devout snow]

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[reef cedar]

How can I learn basic arithmetic? like basic addition, subtraction, multiplication and division. And I mean real basic like 8x11, 7+12, lol.

[reef cedar]

And not Khan Academy because that website has a horrendous layout.

[slate pawn]

I reccomend practice and then more practice

[reef cedar]

How do I practice

[tropic skiff]

IXL

[slate pawn]

if we're working on basics such as addition and multiplication, I would reccomend using a sheet of paper and a calculator as well as https://www.wolframalpha.com/problem-generator/ or similar to get problems.

from there, some helpful aids may be a number line or a group of objects to count and move such as marbles or dried beans, however it is best to move away from these after a bit of time.

at this stage it is probabaly best to stay away from a digital learning tool aside from getting problems or using a calculator to check work

[reef cedar]

So is it just a memory thing with addition and subtraction?

and multiplication

[slate pawn]

you get a feel for it over time but with small integers it is a memory thing.

as you get into larger numbers it is helpful to break it down into a series of smaller questions

[tropic skiff]

Also are you really learning basic arithmetic at 13 years old?

[reef cedar]

I'm an adult but somehow i made it to 3rd year of college without knowing basic arithmetic.

[slate pawn]

and then carry the extra bits to the next set for addition

[reef cedar]

sadly im a lot older lol

I have a 4.0 in college and aced symbolic logic meanwhile i dont know 8x8

[tropic skiff]

Multiplying two numbers that have each are less than 10 is something you will have to do very fast. You might even have to memorize

[slate pawn]

assuming you spend a bit of time with it, it should come decently easily then

[ancient sluice]

Memorize tables till 10 or 20

[tropic skiff]

The highlighted numbers (1, 2, 4, 9, etc) are square numbers btw

[tropic skiff]

10. Beyond that, its easy to solve

[reef cedar]

that have each?

[slate pawn]

thats a bit overkill, 10 is normally enough since after you can break up problems

[young spade]

may i ask how this happens

[tropic skiff]

You basically just need to memorize every combination

Alternate

[young spade]

also, before learning multiplication, you prob wanna get a hold of the concept of the "number line" and addition being somewhat related to the idea of "moving to the right"

basically, understand base-10 and the how the digits go

[reef cedar]

I never was good in math and would fail every math class, i got an F in literally every math class ive ever been in since a kid, im not joking. And my school never cared to help me so by the time i was in Jr High math class was gibberish to me so i stopped caring about school because i thought i was just stupid.

Years later i got interested in philosophy and did a lot of self study and got my GED, and went back to school, now im on honors list at my uni, but i take philosophy so it involves basically 0 math for undergrad.

[reef cedar]

And this is just for multiplication right?

[tropic skiff]

Ya. Ik it looks daunting, but you can technically ignore about half of the table

[reef cedar]

So for addition and subtraction, just do problems. For multiplication, memorize this chart. And then for division what do I do?

[tropic skiff]

Everything to the left/below the red line, ignore

[tropic skiff]

For multiplication also, you need to practice some problems

[reef cedar]

Okay thank you

[tropic skiff]

Simple Division can also be done with that multiplication table

For harder division, either

• long division
• approximate (in the real world, no one gaf if youre slightly off)

[young spade]

or pull out a calculator once you learn the actual methods

[tropic skiff]

Basic arithmetic should be done w/o a calculator tho

[reef cedar]

So how do i know when to move onto multiplication and division?

I guess my main question is about the mental process of doing math. Is it supposed to feel like youre just memorizing stuff or is there some reasoning that goes into it?

Some stuff i know but i feel like I don't know it. Like for example, i know 5x6 but if someone asks it as 6x5 i wont know it, which makes me think it must be more than just memorizing lol.

[young spade]

As for my experience, the visual representatios of it help a lot.

[tropic skiff]

So how do i know when to move onto multiplication and division?
when you can add a two-digit number and a one-digit number very quickly (meaning if youre repeating the problem out loud, there shouldnt be a pause after "equals")

[young spade]

Like, some things obviously youll have to memorize

[slate pawn]

Consider looking into Dyscalculia

[young spade]

but understanding the basic concepts behind them is really useful, ive had my share of little kids i had to explain to, and making it seem somewhat intuitive helps

[reef cedar]

will do

[slate pawn]

id say moving on its safe to do after you get a good idea of each topic, then just keep coming back to it.

[tropic skiff]

I guess my main question is about the mental process of doing math.
Most of the students in this server had time to do math when they were young, so all the stuff im telling you to memorize was easy for many others to to by-heart with enough practice. In your case, you might have to force it into your brain, because i assume you dont have as much free time as a child

[slate pawn]

it helps alot to try and teach a pet/object the topic as well ive found

[tropic skiff]

Like for example, i know 5x6 but if someone asks it as 6x5 i wont know it, which makes me think it must be more than just memorizing lol.
there are some basic properties that come with logic/intuition. For example:

• transitive property
• commutative property (this is the one that says 5 * 6 = 6 * 5)
• distributive property

[reef cedar]

Maybe learning that would help me because I like logic a lot

[young spade]

commutative property (basically the fact that the order doesnt matter)

applies, in what you will first encounter, only to addition and multiplication. like
3+2 is the same as 2+3
5x7 is the same as 7x5

but

3-2 is not the same as 2-3
5/7 is not the same as 7/5

[slate pawn]

it could be fun to try and pick up a book of proofs after you get the basic idea for you. Proofs are the logic/reason behind doing things, which are built on a series of core ideas called axioms.

[reef cedar]

😳 why the skulls LOL

[tropic skiff]

Bro now is not the time 😭

[slate pawn]

basic arithmetic isnt normally taught w proofs to kids as they dont have abstract thought developed yet

but

[reef cedar]

Thank you

[slate pawn]

that could make it stick better

[tropic skiff]

Bc in american education, proofs with axioms are taught in high school/college

[slate pawn]

due to development of abstract thought happening at a later age.

[tropic skiff]

Fair point

[reef cedar]

yeah well i took well to the square of opposition in logic which helped me a lot

Thank you everyone, I appreciate all of the advice, this is really helpful! Before I was searching youtube for an hour and every book recommended for "super beginners" was still way above my level lol

🙏

[tropic skiff]

Btw do you natively speak a different language

If so, i highly encourage you to decide quickly which language you want to learn math in

[reef cedar]

No, just english 😂 lol

[tropic skiff]

https://youtu.be/mjlsSYLLOSE?si=MJneCr4eYgbxIbyS you can prob watch at 2x or 1.5x speed

[reef cedar]

Thank you!

[tropic skiff]

Np

[slate pawn]

learn it in latin 😼

(please do not)

[tropic skiff]

I initially started learning math in my native language, and I hated it because of the unpredictable combinations of English + Tamil (native language)

It was honestly easier for me to just go to a fully English school even in a Tamil-speaking area lol

[slate pawn]

that wouldve also made it very difficult at most universities/schools out of your area

[devout snow]

@reef cedar Has your question been resolved?

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[umbral coral]

question about peicewise (calc 1). I'm not understanding what they mean by limit condition?

[umbral coral]

Are they saying text the value under 4 to see if it's going to be positive or negative?

[rapid merlin]

In my opinion instead of testing
The quadratic equation can be factorized to know it's zeros then you can see when it would be positive or negative

[umbral coral]

yeah I know that it can break down into 1/x^2

well on both 1/2 would be a zero (for top and bottom).

[rapid merlin]

That's not what I said
Also how it can be down into 1/x^2

[rapid merlin]

the quadratic denominator can be factorized into
(x-3)(x+4)
And because the sign of the x^2 is positive the quadratic is negative between the roots so the bottom quadratic is always negative for the values between -4 to 3

[rapid merlin]

This needs more clarification what did you do to get 2x-1 on the nominator
And get out x^2 on the denominator

[umbral coral]

ohhh hold up lol

that was a totally different problem, let me go back

Sec on my side

[rapid merlin]

About that the quadratic would be positive other wise meaning it will be positive for x less than -4 or bigger than 3

[umbral coral]

So I can either manually test it or do it that way?

by getting the zeros

[rapid merlin]

You can test it after factoring or getting the roots

[umbral coral]

I don't understand how you know it can be negative always between 3, -4

what leads you to understanding that.

[rapid merlin]

This way if a value between the 2 roots output positive value you would know that any value between the roots would output positive and negative otherwise

[rapid merlin]

Properties of quadratic equation or parabola specifically

[umbral coral]

for me I don't understand how you get it from that at all. all I know when I have it factored down in that position that I just can't have x= 3 or -4

So if I want to do it the manually testing way.

my question is.

can I tell if it will be - or + via the side of the limit I'm checking?

because we keep getting told if x is lower than the limit (we are going under it) it will be negative, if it's above the number we are approaching we are going to have it be positive.

[rapid merlin]

If a parabola intersects the x-axis at two points (aka. there are 2 values making it equal to zero) the part between the roots of the parabola is either positive or negative, depending on the co-effitient of the x^2 of the quadratic equation. If it is positive then that part is negative, and vise versa.

[umbral coral]

I don't really know what that means.
Do I need to check if it will be positive or negative if I have which side of the limit I'm looking at?

[devout snow]

@umbral coral Has your question been resolved?

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[lost laurel]

How would I find a path length parametrization of say $(t,t^2)$ where t is in [0,1]

[woven radish]

What a wonderful world it is !

[acoustic leaf]

well you can find the arc length as a function of t, then you would have to invert that relation

[iron kindle]

why is the ] cut off?

[lost laurel]

I know $\mathcal{L} = \int_{0}^{\tau} \sqrt{1+ 4t^2} dt$

[woven radish]

What a wonderful world it is !

[lost laurel]

wht does that work

[lost laurel]

Ouch

,w integrate sqrt{1+4t^2}

[woven radish]

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[acoustic leaf]

because if you find s as a function of t, then inverting that would give t as a function of s (which you can then substitute into the parameterization)

[lost laurel]

Yeah, no this is going to be really nasty

[acoustic leaf]

which is why the arc length parameterization is mostly of theoretical importance

[lost laurel]

I do suppose in [0,1], an alternate paramatization is sin(t), sin^2(t)

which could help

$(cos(t), sin(2t)$

[woven radish]

What a wonderful world it is !

[lost laurel]

,w integrate sqrt{ cos^2(t)+ sin^2(2t)}

[woven radish]

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[lost laurel]

Do you have examples of any easily arc-length parametizable functions

other than a circle

[acoustic leaf]

another simple one would be the helix (r cos(at), r sin(at), bt) for constant a,b,r

[lost laurel]

hmm, okay

so uh, the integral would work out to be $\sqrt{1+b^2}t$

[woven radish]

What a wonderful world it is !

[lost laurel]

the inverse function is $\frac{t}{\sqrt{1+b^2}}$

[woven radish]

What a wonderful world it is !

[acoustic leaf]

you ignored a couple of the constants there

[lost laurel]

$\int \sqrt{1+b^2}$

[woven radish]

What a wonderful world it is !

[acoustic leaf]

that's true if we're setting a,r = 1 i suppose

[lost laurel]

oops

okay but I essentially just invert the function and differentiate it, right

I should get $\sqrt{ a^2r^2+a^2r^2+r^2}$

[woven radish]

What a wonderful world it is !

[acoustic leaf]

do you?

[lost laurel]

Yes

[acoustic leaf]

where did b go?

[lost laurel]

Shit

Okay

Have a class now , sorry

.. close

. close

.close

[devout snow]

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[devout snow]

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[summer timber]

is it ok to do this where the natural logging and raising e to the power of does not affect the 64/5

the answer is correct just not sure if my work is fine

[pseudo basin]

yeah this is fine

[summer timber]

ok ty!

.close

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[devout snow]

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[distant helm]

the integral

[distant helm]

i have solved it, but with help of MSE. i wanna try a different way tho

the solution is pi*ln(ln2)

this should also be the great opportunity to use contour integration for the first time in my life

[iron kindle]

complex analysis?

[distant helm]

ye

[cyan laurel]

What is MSE?

[distant helm]

math stackexchange

pretty good forum

[cyan laurel]

Oh

Ik mathstack

thanks

[distant helm]

$\int_{0}^{\frac{\pi}{2}}\ln\left( x^2+\ln^2\cos x \right),dx=2\Re\left( \int_{0}^{\frac{\pi}{2}} \ln\ln(\frac{1+e^{2ix}}{2})\right)$

[woven radish]

TargetVN

[distant helm]

so i got this

which is cool

[iron kindle]

$\mathfrak{Re}$

[woven radish]

Bonk

[iron kindle]

where did the dx go?

[distant helm]

i would rather not write that

[distant helm]

i forgor

$\int_{0}^{\frac{\pi}{2}} \ln\ln(\frac{1+e^{2ix}}{2}),dx=\int_{\mathcal{C}}\ln\left( \ln\left( \frac{1+z}{2} \right) \right)\frac{dz}{2iz}$

[woven radish]

TargetVN

[distant helm]

where z=e^(2ix)

[coral tulip]

What is ln² ? is it (ln(cosx))²

[distant helm]

yes

[coral tulip]

Can i do this question without using complex analysis?

[distant helm]

well... afaik there's only 1 solution without complex analysis

it uses feynman and the form is very disgusting

[coral tulip]

ok

[distant helm]

do i just need to consider C being the contour from z=1 to z=i along a quarter of unit circle

.. or i have to do something else?

[iron kindle]

where is your singularity

[distant helm]

is it z=0

[iron kindle]

no?

what happens at ln(0)

thats a singularity right

so at ln((1+z)/2)=0 theres a singularity

so (1+z)/2=1

i think you can figure it out from here lol

(what the singularity is)

[finite briar]

how?

[finite briar]

send mse link btw?

[distant helm]

https://math.stackexchange.com/questions/5020784/how-to-evaluate-int-0-frac-pi2-ln-leftx2-ln2a-cos-x-right-dx?noredirect=1&lq=1

[finite briar]

still dont get this

[finite briar]

also why isnt z=0 a singularity?

[distant helm]

But then, z=0 also makes it undefined tho?

z=1 is a singularity indeed

[distant helm]

Hold on a sec

[iron kindle]

no, then it becomes complex

ln(x) for x<0 its complex

ln(x) for x>0 is real

ln(x) for x=0 its undefined

[finite briar]

what about the 1/2iz

[iron kindle]

oh...

😂

[finite briar]

💀

[iron kindle]

mb 😅

[distant helm]

... I hope i dont violate some kind of complex logarithm rules

Also forgor the i before arctan

[finite briar]

ic got it

thanks

sheesh thats new to me

[devout snow]

@distant helm Has your question been resolved?

[finite briar]

whatever helps, I guess

[devout snow]

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[thin brook]

Hello sorry, I don’t know how to do this question especially part c (btw this isn’t a homework assignment or exam it’s a practice sheet I found)

[iron kindle]

did oyu do a and b?

[devout snow]

@thin brook Has your question been resolved?

[thin brook]

Uh no😓

[fossil locust]

IB maths spotted

[thin brook]

Did you take IB/are you in IB?

[fossil locust]

if $g'(x) = f'(x)$, upon integrating both sides, what do you get?

[woven radish]

south

[fossil locust]

yes

[thin brook]

Wait actually I think I figured it out

Thank you for asking me that !!!

I will integrate it after equating it

Since I know that f’(x) = g’(x)

[fossil locust]

the really important thing is don't forget your constant of integration

so g'(x) - f'(x) = c for some constant c