help-39

[snow skiff]

can you answer the question now?

[drowsy tangle]

so the population of the eabbits can never go past 3000

[snow skiff]

very good

[drowsy tangle]

thank you

while you are here coulkd u help me find real zeros?

[snow skiff]

of?

[snow skiff]

Ok

When does a quadratic have real zeros?

that $\sqrt{-4}$ should be tipping you off very heavily

[jolly parrot]

DerpZ

[drowsy tangle]

Because there cannot be any - sqrts?

[snow skiff]

not in the real numbers

[snow skiff]

^

[drowsy tangle]

So what do i have to do?

[snow skiff]

Oh are you asking if Q(x) has real zeros?

,w x^3 - 7x^2 + 17x - 15 = 0

[jolly parrot]

Results provided by WolframAlpha

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

Requested by DerpZ#9141

[snow skiff]

well I see you got x=3

[drowsy tangle]

Yes

O found it yes by pluggin in the potential zeroes

Then i used synthetic division to get me the quadratic

[snow skiff]

Do you know the criterion for when a quadratic has real zeros?

[drowsy tangle]

And i asked a classmate what i have to do after and she responded use the quadratic formula

[snow skiff]

Yup that is correct

[drowsy tangle]

I dont think so

[snow skiff]

Notice how when the sqrt is negative you "can't solve it"

[drowsy tangle]

Yes

[snow skiff]

So if you "can't solve it" can there be real zeros?

[drowsy tangle]

So do i like cancel it out with squaring?

[drowsy tangle]

Oh no?

[snow skiff]

Good

So there is no x such that....

[drowsy tangle]

Bcz i would get a complex number

No real zeros

[snow skiff]

Good

Which means that

[drowsy tangle]

But then what is 3

[snow skiff]

Which means that x=3 is....

[drowsy tangle]

The only zero

[snow skiff]

Good

[drowsy tangle]

But x is in the 3rd degree i thought it MUST have 3 zeros

[snow skiff]

Absolutely not

It has 3 solutions

(real or complex)

[drowsy tangle]

Ahhh ok

So for my answer i could include the three like i showed above and then write there are no more zeros?

[snow skiff]

a polynomial of degree n has n complex solutions but not necessarily n real solutions

[drowsy tangle]

Bcz theyre complez

[snow skiff]

Well clearly x=3 is a real solution

The other ones are not real

[drowsy tangle]

Ah ok

[snow skiff]

You should be able to do the rest on your own I think

[drowsy tangle]

Ok thank you again

[pearl pond]

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[toxic wigeon]

stuck on last part

[coarse dawn]

It wants you to write the rule

[toxic wigeon]

oh

so its n+4/n+5

i mean times

[coarse dawn]

That's horribly typed

[toxic wigeon]

lol i was thinking of

4n/5n

but its wrong too

[coarse dawn]

Because it wants this form

[toxic wigeon]

oh

[coarse dawn]

It's a geometric sequence

[toxic wigeon]

so

(4)^n-1

but um

that doesnt make sense either...

[coarse dawn]

Use this to write the rule

a1 is the first term, what's the first term?

r is the common ratio, what is that common ratio?

[toxic wigeon]

4/5 is the common ratio

the firs term is 8

so 8+(4/5)^n-1?

noo thats wrong too

[coarse dawn]

Why is there a plus sign?

[toxic wigeon]

oh

yeah ur right lol

thanks!!

[coarse dawn]

And you need parentheses around the exponent

[toxic wigeon]

its correct!!

woah

.close

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[real chasm]

Hi I need help with a problem. It is an inequality equation. So there is 10000 coconuts and 2022 pirates. Each pirate goes to a the pile of coconuts and takes the number of coconuts divided by the number of remaining pirates. I need to know, how many coconuts pirates number 1803 and 1804 get.
and also the last 2 pirates
also you round normally
below 0,5 down and above etc.

[grave thistle]

Sounds like a python problem

[real chasm]

Yeah

Thats what my guy in math class said

He tried that but an inequality equation worked apparently

[grave thistle]

Let me run the code

[real chasm]

Thanks

Also could you send the code

Not that I will understand it but I would like to see it

[grave thistle]

!e
p = 10000
n = 2022
for i in range(1, p+1):
a = n // p
b = n % p
if b > 1:
print(f'{n} nuts = {a} nuts for pirate#{i} and {b} nuts for the monkey')
elif b == 1:
print(f'{n} nuts = {a} nuts for pirate#{i} and 1 nut for the monkey')
else:
print(f'{n} nuts = {a} nuts for pirate#{i} and no nuts for the monkey')
n -= a + b

a = n // p
b = n % p
if b > 1:
print(f'each pirate gets {a} nuts and {b} nuts for the monkey')
elif b == 1:
print(f'each pirate gets {a} nuts and 1 nut for the monkey')
else:
print(f'each pirate gets {a} nuts and no nuts for the monkey')

Bruh no python bot

p should be 2022 and n 10000

[pearl pond]

@real chasm Has your question been resolved?

[real chasm]

uh

my initial question was how many coconuts pirate 1803 and 1804 get

also the last 2

[pearl pond]

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[muted sage]

Hey guys, I need help understanding how this was simplified from line 1 to 2

[muted sage]

Then how line to was simplified to this

[queen schooner]

,, \frac{n!}{2!\cdot(n-2)!} = \frac{n\cdot(n-1)\cdot(n-2)!}{2!(n-2)!} = \frac{n \cdot (n-1)}{2!}

[light helm]

definition of the factorial

[jolly parrot]

illuminator3 (#eric4honorable)

[muted sage]

So, basically what I am getting is you want to get rid of (n-2)! on the bottom, so you go from (n-1)on the top until you reach the factorial on the bottom to cancel out?

If it was (n-3)! on the bottom it would be n*(n-1)(n-2)(n-3)! on the top?

[pearl pond]

@muted sage Has your question been resolved?

[muted sage]

<@&286206848099549185>

[light helm]

yeh

[pearl pond]

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[midnight haven]

Please explain me this definition:

[pearl pond]

Please don't occupy multiple help channels.

[midnight haven]

.close

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[quick edge]

<@&286206848099549185>

[pearl pond]

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.

[quick edge]

x²+15x+36 (factorising quadratic expression) <@&286206848099549185>

Asap

[ember bay]

1. Read the rules
2. Why asap

[quick edge]

Oh sry

[ember bay]

Is it a test?

[quick edge]

No

[ember bay]

Have you already tried something?

[quick edge]

Yh

[ember bay]

Send your work then

[quick edge]

This is what I got x2-18x+36

So far

[ember bay]

How did you get that?
The original problem was x²+15x+36

[quick edge]

Yh ik

I'm stuck on the question that's why am asking for help

[ember bay]

Yeah, and I asked if you had already tried something, and you sent me that. That's why I asked how you got to that expression

So, you have:
x²+15x+36
If you want to factorize it your goal is to find two numbers whose product is 36 and whose sum is 15, right?

[quick edge]

Ye

[ember bay]

You should try with some numbers then. For example, 6×6 obviously gives 36, but 6+6 is not 15 so that's not it. Try to see whether you can find those two numbers by trying like I just did. That's the fastest way to do it.

The other way is to find all the possible dividers of 36 which together give 36 as a product, and see whehter their sum is 15

[quick edge]

K I will give it a go thx

[pearl pond]

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[buoyant saddle]

@midnight haven sorry for the ping, but... I have this

[buoyant saddle]

wouldn't I need to have f(z_1), f(z_2) and f(A) to be z_1, z_2 and A?

[midnight haven]

wdym?

z_1,z_2 are both in A

and you found that z_1≠z_2

thats enough to show that the composition is not injective

[buoyant saddle]

oh ok

.close

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[hollow plover]

Hello, I am unsure of the result of a multiplication... I'd appreciate if someone could help :)

[tacit mulch]

Multiply the roots, consider the negative sign separately

-(x+5)

which is equal to -x-5

[midnight haven]

yeah

[hollow plover]

ok thank you

[midnight haven]

note that square root of x multiplied by another square root of x is equal to x

[hollow plover]

yeah, knew that one, was just unsure about the procedures for the sign

.close

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[broken rivet]

√7 √28

[broken rivet]

I am not sure how to love this.

[abstract locust]

is that √7 x √28 ?

[broken rivet]

In the text book they are just beside each other, no symbols.

[abstract locust]

ok yeah I guess it means that then

28 = 4x7

so √7 √(4x7)

4 is a square number

so you can take it out the root

√(4x7) would become 2√7

and then mutliplying that by √7

is just 2x7

[broken rivet]

wait how did you get 2 instead of 4 when moving out of the square root?

wait

nvm

square root of 4

got it

[abstract locust]

yep 👍

[broken rivet]

so if square root of a number is indivisible like 7 it becomes itself?

[abstract locust]

hm?

[broken rivet]

not 1/7

[pulsar lark]

√a * √b = √(a*b)

√a * √a = √a^2 = a

[abstract locust]

ye

[pulsar lark]

These are stuff you need to know

[broken rivet]

I think I understand kind of. Thanks guys.

.close

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[fiery vortex]

aye aye

wassup

so

have u

tried anything

ye maybe

let x+y =17

basically

$\sqrt{17-\sqrt{240}} = \sqrt{(x+y)-2\sqrt{xy}}$

[jolly parrot]

Springsskateboard

[fiery vortex]

express in that form

then ur answer

will be

$\sqrt{x} - \sqrt{y}$

[jolly parrot]

Springsskateboard

[pearl pond]

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[empty basalt]

My teacher gave me this exercise if I should get bored but now I'm having trouble on how to calculate the surface area of the square bordering D. The only thing given information are the surface areas of the other 7 squares.

[minor vortex]

Kannst du Deutsch?

[empty basalt]

ja

[minor vortex]

Das ist von der Mathe-Olympiade. Ich will dir nichts unterstellen, aber für manche ist der Abgabetermin erst am 28.10, als frag erst danach nach der Lösung.

[empty basalt]

wirklich? bei uns wurden die von allen Teilnehmer schon eingesammelt weil morgen der letzte Schultag ist und der verantwortlich Lehrer nicht mehr da ist, deswegen haben wir diese heute in Mathe als Übung bekommen

[minor vortex]

Okay

Ich wollte nur sichergehen.

@fallow cosmos Just another example for this problem. She had to hand it in today.

[empty basalt]

wohne in RLP hier sind schon wieder Ferien

[minor vortex]

Ja

Hier in NRW auch.

Aber ich muss das zum Beispiel erst Montag abgeben.

[empty basalt]

ich hatte keine Lust mitzumachen weil ich eh nicht weiter komme aber ich hänge hier ein bisschen dran und es lässt mich nicht schlafen

[minor vortex]

Ich habe gestern schon mit einem Moderator darüber gesprochen weil 6 Leute nach der Lösungf für Aufgabe 3 gefragt haben.

[empty basalt]

wir haben nur diesen Würfel und die Werte von unserer Lehrerin bekommen sonst nichts

[minor vortex]

Achso

https://www.mathematik-olympiaden.de/aufgaben/62/1/A62121.pdf

Das ist Aufgabe 1

[empty basalt]

das weiteste was ich herausfand ist das ich die Gesamtoberfläche fast bekomme wenn ich alle werte durch zwei Teile, da 3 Seiten immer innen und außen sind

[minor vortex]

Bitte keine Spoiler

Ich möchte das selbst herausfinden.

[empty basalt]

ok

wie schließe ich dann den channel?

[minor vortex]

.close

[empty basalt]

.close

[pearl pond]

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[proven moon]

130 feet per second means dh/dt = 130

so find the derivative of h and equal it to 30 and rearrange to find the value of v_0

initially the height is 3 feet so h(0) = 3

use that information to find the value of h0

once you have those values, you need to work out when the height is 256 feet

so you let h = 256

i.e -16t^2 + (the value u calculated for v0)*t + (the value you calculate for h0) = 256

which'll be a quadratic equation

and u solve for t

[tame mica]

ogm sorry that was the wrong question

i had already done that one

it was this one ;-;

[proven moon]

;-;

[tame mica]

ty tho

like

i sorry

[proven moon]

nws it happens to the best of us

the x^2 term has a positive coefficient, therefore you'll have a minimum point rather than a max

do you know how to complete the square?

[tame mica]

i do know

[dry shard]

Wouldn’t we just do dy/dx=0?

[proven moon]

there's lots of ways to do it, i don't know what methods they would or wouldn't know

you can complete the square to find the x co-ord of the minimum point

then plug that number into f(x) to find the y value of the minimum point

[dry shard]

Oh lol I didn’t even know that I’ll have to use it

[pearl pond]

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[cursive dagger]

Can someone help me prove this, it's a First Order Logic natural deduction problem: https://proofs.openlogicproject.org/

[grim patrol]

whats Ljx

[cursive dagger]

The conclusion that I need to prove

I think this is more related to discrete mathematics

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@cursive dagger Has your question been resolved?

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[midnight haven]

How did that become 2m1 m2

M1g x 2m2 should be: 2m1g m2

[old marsh]

Commutative property

a * b = b * a

[patent yew]

g is just placed at the end of the fraction

[midnight haven]

Oh yeah because then it would still be the same

Thank you❤️

[patent yew]

np

[midnight haven]

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[rare sail]

Hey. What am I doing wrong here?

[pearl pond]

@rare sail Has your question been resolved?

[ivory swallow]

Your pfd has a wrong sign i think

B = - 1/2

@rare sail

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[vestal lodge]

Is someone able to steer me in the right direction with this problem? I don’t even know where to begin

[pearl pond]

@vestal lodge Has your question been resolved?

[rare sail]

Why is b = -1/2

[ivory swallow]

Algebruh

Take a closer look at what happens when x=-1

[rare sail]

On the second line

I made a mistake

There was supposed to be + in the middle

@ivory swallow

[ivory swallow]

1/[(1-x)(1+x)] = A/(1-x) + B/(1+x)
1 = A(1+x) + B(1-x)
x = 1, A = 1/2
x= -1, B = 1/2

Yeah so the Pfd looks good now

But I think you didn't integrate
1/(2(1-x)) correctly

The integral of that should be
-1/2 ln(1-x)

[rare sail]

Ah you’re right

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[midnight haven]

im confused about the yellow bit

[pearl pond]

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[wind wigeon]

why should theta_0 be an interior point?

[wind wigeon]

i understand theta_0 being an interior point makes it easier to show that this sequence of sets is the full space R

but suppose a binomial distribution and youre testing theta_0 = 1 against theta_0 != 1

then theta_0 wouldnt be an interior point

but that is still a valid test right?

am i missing something

ahh nvm theta_0 should be an interior point to make sure the other conditions for wilks theorem hold

well

usually hold

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[plain turtle]

does x:y equal x/y?

[grim patrol]

i mean

kinda?

i wouldnt say they are exactly the same

but similar

[plain turtle]

please could I ask you in reference to a question?

[hollow cobalt]

x:y = x/y

[plain turtle]

thanks

.close

[pearl pond]

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[shell perch]

But. The quadratic dont add up

[shell perch]

For question 10, i assume i have to do some quadratic stuff to get (something)(something)ˆ4

[pearl pond]

@shell perch Has your question been resolved?

[shell perch]

.close

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[shell perch]

How does this part work

[fiery vortex]

aye aye

wassup

hm

eh

maybe

they skipped

a few steps

they used

sine rule

I think

aye

ye*

also

ur teacher

forgot

to put r

next to the 1/2

in the last step

for area

one of the 1/2

should have an r

$\frac{sin(\fracπ6)}{BD} = \frac{sin(\fracπ2)}{r}$

damn

is the bot

still sleeping

[pearl pond]

@shell perch Has your question been resolved?

[shell perch]

Like a/SinA = b/SinB

?

[fiery vortex]

mhm

yeye

idk why

the math bot

isn’t working

[shell perch]

This ain’t adding up

[fiery vortex]

why not

should be

[shell perch]

So im tryna find BD right

[shell perch]

Ill use the sin rule.

BD/(sin 1/6 pie) = r/sin 1/2 pie)

Hold up

[fiery vortex]

yeye

[shell perch]

I get some cracked up decimal from sin (pie/2

[fiery vortex]

bro

don’t let it

into

your calc

also

are u

in radians mode

or degree mode

[shell perch]

Degree

[fiery vortex]

ye that’s why

pi/2 is radians

if u want to

use degree

key in

sin90

not sin(pi/2)

[shell perch]

Ok lets try

[fiery vortex]

yeye

[shell perch]

This shit makes sense yo

[fiery vortex]

ayeeee

niceee

let’s go

sweet

simple

bitter

💥

[shell perch]

Bro whats going on with AD? Using the cos rule but i may have mucked up

[fiery vortex]

eh

no need

just use

sine rule

boom

[shell perch]

Oh

[fiery vortex]

this is how

ur teacher

got the ans

[shell perch]

Yeah i gotchu

Fuck cos

!!

[fiery vortex]

ayeee

nice

sine rule

for the W

[shell perch]

Thanks for the help bro

[fiery vortex]

npnp

[shell perch]

.close

[pearl pond]

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[pearl pond]

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[bright lark]

Anyone tell me about, how can I PDE by solve neural network?

[pearl pond]

Please don't occupy multiple help channels.

[coarse dawn]

Don't open multiple channels

.close

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[pearl pond]

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[steep pebble]

just a quick yes and no question: Can vertically opposite angles be equal on non-parallel lines?

[winter otter]

Vertical angles don’t exist on parallel lines

Vertical angles are always congruent otherwise

[pearl pond]

@steep pebble Has your question been resolved?

[steep pebble]

then how would this question be proved:

[pearl pond]

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[steep pebble]

.reopen

[pearl pond]

✅

[pulsar lark]

I think it's fine

[pearl pond]

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[regal stirrup]

i need to find concavity and points of inflection

how ever

when i take the double deriv and solve for x theres no solution.. which typicaly means theres no point of inflection, but when i look at the graph x = 3 is a point of inflection

isnt it supposed to be an asymptote ?

[vital estuary]

if f" is undefined at a value of x, you need to do local testing to check if its a POI

[regal stirrup]

local testing whats that

[vital estuary]

do you know what a sign chart is?

[regal stirrup]

Yes i do

[vital estuary]

that

[regal stirrup]

but what number do i put in?

[vital estuary]

any number around the value

one above, one below

[regal stirrup]

whats the value lol

bc x is undefined

typicaly you would do a sign chart on what ever x you got

[vital estuary]

what x value makes it undefined

[regal stirrup]

3

[vital estuary]

that value

[regal stirrup]

but in some situations concavity changes over an asymptote, but it isnt considered a point of inflection

so is the 3 i have an asymptote?

[vital estuary]

is f(3) defined and differentiable at that point

if yes, its a POI

[regal stirrup]

its not differentiable

right?

[vital estuary]

oh

its defined and continuous

[pearl pond]

@regal stirrup Has your question been resolved?

[pearl pond]

@regal stirrup Has your question been resolved?

[pearl pond]

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[pearl pond]

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[tiny igloo]

helloo

[toxic lichen]

What is the probability that the city shall be rated at least very poor?
is 0.05 meant to be the answer to this question?

[tiny igloo]

i don't know too.

[toxic lichen]

???

you wrote something but you yourself don't know what it's for?

then nobody can verify your answers

[tiny igloo]

my answers below are my answers for probability of very poor, very good, and excellent

[pearl pond]

@tiny igloo Has your question been resolved?

[tiny igloo]

no

.close

[pearl pond]

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[pearl pond]

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[midnight haven]

when should i study linear algebra before or after calculus?

[sick adder]

I think you could do either as prerequisites for linear alg are usually just other algebra classes

I would probably take it before multivariable calculus, but I think it can be mixed into the univariate calc classes anywhere

Before or after either of them

[midnight haven]

so you think its best to study before multivariable?

why tho?

[sick adder]

Because multivariable calc uses vectors and matrices from my experience

I took Calc III before Linear Alg and I had to crash course some stuff

[midnight haven]

okay ill do that

[sick adder]

If I could go back I would have taken Linear Alg first

But I don't think it matters as much if you take it before/after differential and integral calc

[midnight haven]

its okay to study this after calculus 1 and 2?

[sick adder]

Yeah that should be fine

You likely won't use linear algebra in calc 1 and 2, but you do use it in calc 3

[midnight haven]

okay thanks! im trying to make a study path before starting studying

is multivariable calculus 3?

[sick adder]

Yes

[midnight haven]

differential is calculus 1
integral is 2
then multivariable is 3 am i right?

[sick adder]

Yup

[midnight haven]

.close

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[primal bluff]

do I just set β anc x in the augmented matrix and reduce?

[primal bluff]

Anybody knows what is meant in the Linear Algebra problem?

do I just set β anc x in the augmented matrix and reduce?

[pearl pond]

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[pearl pond]

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[junior pawn]

an idea to integrate : $\int \frac{dx}{e^x + 1}$?

[jolly parrot]

Max.cc

[tropic saddle]

add and subtract e^x in the numerator

[junior pawn]

ok i see

[hollow cobalt]

Or simply rewrite the integrand as e^(-x)/(1 + e^(-x))

[junior pawn]

why -x

[shrewd basin]

Derivative of 1+e^(-x) is -e^(-x)

So we have f’(x)/f(x) situation

[junior pawn]

There must be something wrong

[old marsh]

There’s a 1 in the numerator right

[junior pawn]

yeah i forgot the +1

[old marsh]

We start out with int(1/(e^x + 1))

[junior pawn]

with the +1 it doesn't work

[old marsh]

Lemme try

@junior pawn

Is this what u were trying to get

[junior pawn]

yeah

but as u can see the left expression is a problem

[old marsh]

The first integral on the last line?

[junior pawn]

yeah

[old marsh]

How so?

(1+ e^x)/(e^x +1)

[junior pawn]

ah no i'm dumb

[old marsh]

= 1

[junior pawn]

it's 1

[old marsh]

Yes

[junior pawn]

.close

[pearl pond]

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[primal bluff]

Linear Algebra: Who knows how to perform a transformation, and produce the standard matrix?

[primal bluff]

Pretty Please?

[pearl pond]

@primal bluff Has your question been resolved?

[pearl pond]

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[junior pawn]

an idea to integrate $\int \frac{1}{x^2 + 2x + 3}$

[jolly parrot]

Max.cc

[junior pawn]

because we can't factorize x^2 +x +3

[mossy canopy]

x^2+2x+3=(x+1)^2+2

[junior pawn]

how do you found it

[mossy canopy]

complete the square

basically

we have x^2+2x+3

we want

(x+a)^2+b

this makes it

x^2+2ax+b

therefore 2a=2=>a=1

so we hav

(x+1)^2+b

which is x^2+2x+b+1

so b+1=3=>b=2

then we have integral of 1/((x+1)^2+2)

now we want to get a substitution

if we try u=x+1 we will surely get somewhere

but there is a better one

if we take u=(x+1)/sqrt(2)

it will make it prettier

then it will resolve into an integral that you may have seen

1/(u^2+1)

[junior pawn]

hum

so it's = du / u^2 + 2

[junior pawn]

i don't get this u

[mossy canopy]

do you know what we try to do with u?

have you seen this before?

[junior pawn]

ye

[mossy canopy]

ok

so basically

we know that 1/(x^2+1) integrates to arctan(x)

so we want to get it to this

at the top, we can just pull scalars out of the integral

at the bottom we have (x+1)^2+2

[junior pawn]

i didn't thought about that

[mossy canopy]

so our first idea is to set u=x+1

but that would not make the +2 go to +1

i can't explain further how to get to the exact u, i would just try out stuff

there are surely some ways to calculate u here but i haven't had calculus yet so...

[severe quartz]

When theres just a quadratic in the denominator the integral is always in the form of either a tan inv or a logarithm

[junior pawn]

quadratic?

[severe quartz]

The original question has x^2 in the denominator

[junior pawn]

ah that's what your talking about

but we're still blocked because 1/(x+1)^2 + 2 is not 1/(x+1)^2 + 1

[severe quartz]

write it as (x+1)^2 + (root (2))^2

and then theres a general result for integration when u have x^2 +a ^2 in the denominator

[junior pawn]

root(2)?

[severe quartz]

sq root 2

[junior pawn]

ah sqrt

$\frac{1}{(x+1 + \sqrt{1})((x+1 - \sqrt{1})$

[jolly parrot]

Max.cc
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[junior pawn]

am i right?

[pearl pond]

@junior pawn Has your question been resolved?

[severe quartz]

Not checking this, but why are you calculating this

[pearl pond]

@junior pawn Has your question been resolved?

[pearl pond]

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[vital bluff]

Find the limit

[vital bluff]

the answer is 0 but i don't know how to get to it

tried getting n before the brackets but it doesn't work

[old geyser]

(2n-1)^14 > (n+1)^10

So like

I mean unless you need to show work it's pretty obvious it's 0

Denominator is gonna get bigger than the numerator

[vital bluff]

yeah but i want to find the method to do different examples

like this

[old geyser]

To infinity?

[vital bluff]

answer is 1

[vital bluff]

yes

[old geyser]

,w calc 3/2 times 8

[jolly parrot]

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[old geyser]

Too lazy to use my brain

,w calc 8(3+0.5)

[jolly parrot]

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[old geyser]

,calc 4 times 7

[jolly parrot]

The following error occured while calculating:
Error: Undefined symbol times

[old geyser]

Well

28

Either way

Here

Lemme latex this

$$\lim_{n\to \infty} \frac{(n^3\sqrt{n}-2n^2 + 1)^8}{(n^4-2n+2)^7} \equiv \lim_{n\to \infty}\frac{(n^{3.5})^8}{(n^4)^7} = 1$$

[jolly parrot]

Umbraleviathan

[old geyser]

Notice anything interesting?

[vital bluff]

yeah

[old geyser]

So when we take limits to infinity, we can literally erase what we call low-order terms

These low order terms don't get as big as the leading term

You can think of them as a pebble to a mountain

So we only focus on the largest terms

In this case, (n^3.5)^8 and (n^4)^7

Both are n^28, and n^28 / n^28 = 1

[vital bluff]

thanks :)

i didn't think about it in such a way

[pearl pond]

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[lament junco]

I need help with this question but it's in french tho

[woven perch]

translate it and people will help you

[pearl pond]

@lament junco Has your question been resolved?

[lament junco]

find all the common divisors of a and b

[lament junco]

<@&286206848099549185>

How do i find all the common divisors of a and b if idk the value of a and b

@woven perch

?

Anyone?

The highest common divisor is 18

And a<b

.close

[pearl pond]

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[midnight haven]

Can someone explain this please?

[coarse dawn]

Plug in the given values

[midnight haven]

wdym?

[coarse dawn]

You're given values for c and d, plug it into the expression

[vital estuary]

5□+□○
□=5, ○=1/15

[coarse dawn]

Fyi, when it's written cd that's multiplication, c * d

[vital estuary]

Yeah

[midnight haven]

The how does ed = 3

That’s the rest of it but it makes no sense to me tho

[coarse dawn]

What's (1/5) * 15?

[coarse dawn]

.

[midnight haven]

1.5

[coarse dawn]

Explain how you got that

[midnight haven]

well I did 1/5 as 0.5 but now that I think idk how I made it = 1.5

[coarse dawn]

$\frac{1}{5} \neq 0.5$

[jolly parrot]

dldh06

[midnight haven]

So what does 1/5 =

[coarse dawn]

Can you use a calculator?

[midnight haven]

I don’t have one but I can use my phone one

[coarse dawn]

I suggest that

[midnight haven]

I thought of away for it to be 3, I thought how many 5 could go into 15 and that was 3

[coarse dawn]

Yes that's how division works

[midnight haven]

wait so do I just forget about the 1/5 and just divide it instead?

[coarse dawn]

No

(1/5)(15) = (1/5) * 15
Do you know how to multiply fractions?

[midnight haven]

I’m was alr with it but I haven’t been in school for like 5 years so I’m not the best

[coarse dawn]

Then I suggest reviewing that because that's an important step

[pearl pond]

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[zenith trench]

I'm very lost

z = a + ib is standard form

and I think Im(z) = b?

kinda lost here

z = re^iθ

is polar form

no clue where to begin here

[grave thistle]

Yeah so z=a+I ots give modulus is sqrt(2)
So sqrt(2)=sqrt(a^2+1^2) solve for a

U will get 2 sølutions

Quadrant III will tell u the cōrrect onë

[zenith trench]

hm

so sqrt a^2 + 1^1 = sqrt 2?

[grave thistle]

Yes

[zenith trench]

a = 1 or a = -1?

[grave thistle]

Да

Yes

[zenith trench]

since its third quadrant its -1?

[grave thistle]

Huhhh

Ohhhh

Z overtime lies in rd

Z overlines lies in 3rd*

So z overline is a-i

So yes -1

[zenith trench]

gotcha

then for polar form

[grave thistle]

.ake a teiqngle

Make a triangle

Find r then u can find angle

[zenith trench]

isnt r = sqrt(2)?

[grave thistle]

Yes

[zenith trench]

y= -1/sqrt(2) and x= 1/sqrt(2)

so its pi/4?

uh wait

sqrt(2)e^iπ/4?

or something?

[grave thistle]

,w arctan(1)

[jolly parrot]

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[grave thistle]

Sqrt(2)*(cos(pi/4)+isin(pi/4))

,w cos(pi/4)

[jolly parrot]

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[grave thistle]

sqrt(2)*(i/sqrt(2)

i

Lol

Wait

[zenith trench]

thats...a little sus

[grave thistle]

Sqrt(2)*((1+i)/sqrt(2))

1+i

[zenith trench]

so polar form is sqrt(2)e^ipi/4?

[grave thistle]

z=-1+i standard
z=1+i polar

Isn't that exponential form

[grave thistle]

Yeah then

[zenith trench]

r = sqrt(2)

yeah?

[grave thistle]

Yes

https://tenor.com/view/oh-yeah-mochi-peach-cat-corean-gif-24678746

[zenith trench]

and cos(1/sqrt(2)) = pi/4

[grave thistle]

,w sqrt(2)*e^(ipi/4)

[jolly parrot]

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[grave thistle]

,w cos(1/sqrt(2))

[jolly parrot]

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[grave thistle]

,w cos(pi/4)=1/sqrt(2)

[jolly parrot]

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[grave thistle]

U meant?

[zenith trench]

yeah

[zenith trench]

so is this the polar form?

[grave thistle]

Yeah worked our

Out

[zenith trench]

but if its in third quadrant

should the pi/4 be different

?

[grave thistle]

Z overline is in third

[zenith trench]

it would be uhh

pi+pi/4 no?

[grave thistle]

,w sin(pi/4)

[zenith trench]

5pi/4?

[jolly parrot]

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[grave thistle]

Sin(pi/4)=cos(pi/4)

[zenith trench]

but if z overline

is in third quadrant

doesnt that mean pi/4 becomes 5pi/4?

so the final answer

is sqrt(2)*e^i5pi/4

[grave thistle]

It asks the forms of normal z not overline

Z overline was just to help find a

[zenith trench]

hm ok

[zenith trench]

ooooooooh

i get it

im stupid

thank you lmao

[pearl pond]

@zenith trench Has your question been resolved?

[pearl pond]

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[pearl pond]

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[bright flint]

How do I solve 7a

[midnight haven]

try factoring by 3

[bright flint]

what do u mean

[midnight haven]

you have 3x²+12x+9

The greatest common factor of 3,12,9 if 3

So you can rewrite it 3x²+12x+9 = 3(||x²+4x+3||)

[bright flint]

ohhh

dividd all by gcf

right?

[midnight haven]

yeah

[bright flint]

and then proceed to solve

Ok

thx

.close

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[pearl pond]

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[buoyant sun]

This is a fairly easy question i think I just need an explanation of everything that is happening.

[small spruce]

A = xy

x+2y = 120

find x in terms of y from 2nd equation and plug into ur area function

then just find maximum of it

[buoyant sun]

maximum?

what math do u think im taking?

lmfao

[small spruce]

wdym

is this not calc

or like pre calc?

[buoyant sun]

Im in algebra 2

[small spruce]

oh

[buoyant sun]

yeah

im freaking out

[small spruce]

u could graph function and see highest value of x that way

[buoyant sun]

that might be what they want us to do

Bc we have TI-Inspires

what would the function be?

[small spruce]

A=xy

x+2y = 120

y = (120-x)/2

A=x((120-x)/2)

[buoyant sun]

alright thanks appreciate it

[small spruce]

np

[buoyant sun]

thanks that worked on the graphing calculator

@small spruce

[small spruce]

nice

theres a maximum function on ur TI

or there should be on like ti-84's

[buoyant sun]

I just used it. I got 60,1800

the answer is 1800

[small spruce]

urm

how did u get 601800 lol

[buoyant sun]

(60, 1800)

coordinate

[small spruce]

ohhh

[buoyant sun]

haha theres a comma

i have one question though

[small spruce]

shoot

[buoyant sun]

when you had y = (120-x)/2

how did you go from that, to A= x((120-x)/2

wait

im an idiot

[small spruce]

our area function is A=xy

[buoyant sun]

dont answer that

[small spruce]

yeah lol

[buoyant sun]

im overthinking everythingf

.close

[pearl pond]

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[exotic plume]

hi

[exotic plume]

I'm trying to find out how to find the derivative of this function:

[hexed crypt]

Ok, this is chain rule

In this case, the outside function is x^(-1) and the inside function is 8x-1

[midnight haven]

maybe it's better if we write it $\dfrac{1}{8x-1}^$

[jolly parrot]

Zamarus
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[toxic lichen]

it does not make much difference to write it this way

[hexed crypt]

wtf I swear TeXit just tried to crash my Discord or smth

[fiery vortex]

aye aye

[fiery vortex]

happened

before to me

[fiery vortex]

yeye use chain

rule

[hexed crypt]

Honestly I think it might actually complicate stuff

[fiery vortex]

eh rly?

i mean

u could do

[hexed crypt]

Just do power rule and multiply by the derivative of the inside stuff, which is just 8

[hexed crypt]

Well, it depends on the person ig

[fiery vortex]

yeye

[safe prairie]

plug into top

[exotic plume]

I'm still confused as to exactly why I'm multiplying this:

[safe prairie]

You see the top formula right?

f(x)=(8x-1)

n=-1

this is what you get

exact same answer

[exotic plume]

so the one on the right is considering 8x and not the whole thing?

[safe prairie]

You multiply by the derivative of f(x) which is just 8

derivative of (8x-1) is just 8

[exotic plume]

ok

let me just recap so if I know if I'm right

you take the derivative of f(x) including the power,

then multiply it by f(x) without the power

right?

[safe prairie]

Uh

You do the power rule on the exponent

times that by the orginal f(x)

I suck at explaning

The top formula shows the exact steps

[exotic plume]

I think I can understand how it works now

[safe prairie]

The top formula is for when you have an exponent

the bottom is for when you don't

[exotic plume]

its just so freaking confusing at first

[safe prairie]

you know how to do the chain rule on one without an exponent?

[exotic plume]

I think so???

[safe prairie]

How would you do this

[exotic plume]

I'm not exactly sure cuz I don't know the derivative of ln

[safe prairie]

it's 1/x

[exotic plume]

ok

so would it be something like 1/(x^2-1) ???

[safe prairie]

You need to multiply that by the derivative of the inside

You did the f'(g(x) part

you need to multiply that by g'(x) to complete it

[exotic plume]

so it would be

2x/x^2-1

is that right?

[safe prairie]

exactly

[exotic plume]

ok

but what if it was something like 2 instead of ln

[safe prairie]

It would just be 4x/x^2-1

you can take the constant out

and multiply it at the end

would just be 2 * 2x/x^2-1

or you can just solve it with it in makes no difference

Or are you asking about 2(x^2-1)?

[exotic plume]

yea that one

[safe prairie]

The answer would just be 4x

no chain rule