help-19

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[light zodiac]

Idk if it's 5 or 25 😭

It's 5 right

Number of mosquitoes as a function OF rainfall in centimeters

So like

Centimeters is 5

[silent raptor]

U want the -(x-5)^2 to be as small as possible

because its negative

[light zodiac]

Wat

[silent raptor]

Is this a optimization question?

or like algebra

[light zodiac]

But I want the most amount

Fr

The highest

[light zodiac]

Algebra 1

[silent raptor]

You are thinking right

[mint mirage]

You know it's a parabola, and the question asks the max number. The max/min of a parabola is where the vertex is

So you just need to find coordinates to the vertex

[light zodiac]

5, 25

I was ask which it is fr

I think 5

Right

[silent raptor]

Why

do you think it is 5

[light zodiac]

I said 😭

[light zodiac]

.

So like m(x)

X is centimeters I think

5 centimeters

Makes it that thingy squared 0

So it's the highest it can be

[silent raptor]

Yeah

Cool

cuz if u plug 25 in, it would make that left part big negative

which would lower the 25

compared if it was just 0

[light zodiac]

Who do u think would win soldier boy vs homelander

[mint mirage]

Functions can be thought as a cause and effect situation, the rainfall causes more mosquitoes

So the input is rainfall, output is mosquitoes

[light zodiac]

Did I interpret the first sentence thing right

Fr

[mystic saffron]

the equation is in vertex form

[light zodiac]

Fr

[mystic saffron]

its of the form f(x) = a(x – h)^2 + k

[light zodiac]

So like the answer is 5 right

[mystic saffron]

yes

[mint mirage]

Yes, people said it was 5 already

[light zodiac]

Ez

[mystic saffron]

when x=5, m(x)=25 which is maximum

[light zodiac]

.close

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[opal wren]

I was wondering if anyone has a 6 by 6 grid. 6 on top 6 on bottom

[silent raptor]

Huh

[opal wren]

I couldn't find one

[silent raptor]

Use excel

[opal wren]

Fine...

[silent raptor]

Its good to ask for help

but bruh

[opal wren]

I'm too lazy

[odd edge]

@opal wren Has your question been resolved?

[odd edge]

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[obtuse rivet]

Just wanted to see if I did this right. I’m supposed to condense this problem and I did log 2m^3 (log m^7)/ log(3m)

[random stirrup]

Show work

[obtuse rivet]

I used the logarithm rules

[flint heart]

hiw did u get m^7 there

[obtuse rivet]

Underneath is my condensed version

[flint heart]

its wrong

[steady tide]

simplify everything to log(m)

[digital matrix]

it would be m to the power do 2*5

since it’s 5 log m^2

[obtuse rivet]

I added 5 to 2 to put that 5 back up to the exponent place

[flint heart]

nooo

[obtuse rivet]

Oh

[digital matrix]

if u put an exponent on an exponent u multiply them

[flint heart]

its (m^2)^5=m^10

also in the first one , it should be (2m)^3 not just 2m^3

[obtuse rivet]

Oh gotcha

Other than that is the log(3m) correct?

[flint heart]

yes

[obtuse rivet]

Alright I think I get it then 👍

Thank you

.close

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[wanton escarp]

so in did how do i put into words how many days they are losing followers?

[wanton escarp]

so the maximum followers is at 38 days and min is at 74

that means its decreasing during those days

am i right or wrong?

[silent raptor]

well I mean

The overall trend is decreasing, yes.

[wanton escarp]

its a cubic

[silent raptor]

Though it could still increase between that but not above the max

Ahh

[wanton escarp]

anywas do i just do 74-38 for this to find how many days are dereasing?

[silent raptor]

Sounds abt right

[wanton escarp]

but i was compensating about including 74 and 38 casue they arent when they are decreasing

[silent raptor]

like including the end bounds?

[wanton escarp]

yea

[silent raptor]

well I mean

I dont think you should

[wanton escarp]

38 and 74 arent decreasing folllowers

[silent raptor]

But 74-38

Does not include those days

36 doesnt include the end bounds

already

38 would include the bounds

if you added 2

74-38+2

[wanton escarp]

what if i did 73-37 tho....

[silent raptor]

That is the same thing

You just subtracted one from both sides bro

[wanton escarp]

but its 35 instead of 36

[silent raptor]

No

73-37

is not 35

[wanton escarp]

oh i mean 73 - 39

[silent raptor]

you are overthinking this

[wanton escarp]

casue those are the days that they actually lost followers

[silent raptor]

yes

but then you lose

the 73rd

day

[wanton escarp]

it was in an exam so i hope i was right tho

[silent raptor]

Like logically you are overthinking it

Just draw a numberline and visualize the subtraction

and you will see your fault

like 2-0 just shows the stuffhappening between 0 and 2

not on 2

[wanton escarp]

but

therees 35 days from day 39 to 73 inclusive
think about it
for example
how many days from 3 to 5 inclusive
day 3, day 4, day 5
3 days
so basically
if youre including
its the difference+1

caue they wern losinf follwers on day38 and day74

[silent raptor]

yes but when you subtract 73-39

You lose the 73rd day

[wanton escarp]

or not subtracting

[silent raptor]

all the hours btwn 73.00001 - 73.99999 which are losing followers

[wanton escarp]

• 1 it

[silent raptor]

which is the same thing

as 36

74-38

[wanton escarp]

<@&286206848099549185> can someone reassure me please

[silent raptor]

[wanton escarp]

i dont know who to belive. myself or u

[noble hull]

reassure what exactly

[wanton escarp]

@noble hull

so the max followers is on day 38and min is on 74

so taht means they are losing followers between day 38 and 74

[noble hull]

and you say its a cubic?

[wanton escarp]

yeah

[noble hull]

like wdym exactly, like every day they are losing followers or smth?

coz obviously overall between those they are losing followers

[wanton escarp]

yeah between day 38 nd 74

[noble hull]

so every day between days 38 and 74, they are losing followers? is that what ur asking

[wanton escarp]

well 38 is max folowwers in the first 90 and 74 is min followers

so the days in between 38 and 74 they are lsoign followers

[silent raptor]

so like the question is if you count the end points

[noble hull]

well if day 38 is the max and 74 is the min so like of course overall there will be a decrease from 38 to 74?

[wanton escarp]

so what would u do to find how many followers tehy are losing in words

like they are losing xx followers in toal in the first 90

days

[noble hull]

wait isnt the question asking how many days the accoutn is losing followers?

[wanton escarp]

yeah

oh i worded it wrong

like xx is the amount of days they lost followers

@noble hull

[noble hull]

are you asking how to find the answer?

[wanton escarp]

yeah

casue idk if its 35 or 36 days that they lost followers

[noble hull]

so you find the derivative of the cubic right? then you solve for the days when the derivative quadratic is under 0 (i.e. the followers is going down), then you would count the amount of days that satisfy the inequality

[wanton escarp]

ive already done all that

[noble hull]

oh are you asking my opinion whether its 35 or 36

[wanton escarp]

yeah like do u count day 38 and 74 ?

casuse they are min and max points

[noble hull]

no i wouldnt include the end bounds as that is the inequality

that inequality tells u that they are losing followers between 38 and 74 but not including 38 and 74 which would be still

so 74-38-1 would be the answer

[wanton escarp]

so it was 35 @silent raptor

[noble hull]

well the wording is a bit weird, because ig they could include the 74 as the followers would be decreasing until it reaches that turning point but 🤷‍♂️

[wanton escarp]

well thanks .close

.close

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[quick wharf]

Wth is that

[brave thunder]

Thats what Im saying

[quick wharf]

What grade are you even in

[viral frost]

Well, if you add the rhs by considering LCM and stuff, you'll get something like lhs.

This is probably grade 11? I think??

[brave thunder]

This is NCEA level 3

[tulip laurel]

so make denominatior same on both sides

then cancel them

then compare coefficients

[brave thunder]

How was this the first working in the answer schedule

[quick wharf]

😭

[tulip laurel]

they are making denominatior same

[viral frost]

And then equating the numerators.

[tulip laurel]

so they are muliplying by each orthers denominatior

[brave thunder]

Oh ic

Then all have same denominator

So denominator is gone

[tulip laurel]

yes

[brave thunder]

Ah okayy

How do I get the values now

[viral frost]

Now equate the coefficients.

Like the coefficient of x^2 in both sides, then x, and finally the constant term.

[brave thunder]

I dont get that

A = C?

[viral frost]

no.

What's the coefficient of x^2 in rhs?

[brave thunder]

RHS of original q or what I got rn

[viral frost]

What you got rn

[tulip laurel]

so it's like 0x^2 on lhs

[brave thunder]

A + C

[tulip laurel]

so compare it with rhs

A+C=0

-B=1

[brave thunder]

B - A = 0 too?

[tulip laurel]

constants comparing

yes

[brave thunder]

What was it compared to

I dont get that

[viral frost]

B-A is the coefficient of x in rhs, which is equated to the coefficient of x^2 in lhs, which happens to be 0.

[brave thunder]

Where is the coeffecient of x^2 in lhs

Can you point it out

Because Idk where it is

[viral frost]

Lhs or rhs?

[brave thunder]

LHS

[viral frost]

There isn't.

If there is no x^2 term, it means it is the same as 0x^2

[brave thunder]

Ohh

[viral frost]

The coefficient being 0 in that case.

[brave thunder]

So A + C = 0, B - A = 0, B = 0?

[viral frost]

No.

Why is B zero?

[brave thunder]

Theres no constants

[viral frost]

There is

1 happens to be a constant, you know.

[brave thunder]

Ohhh

Do we not take into account the denominators

[odd edge]

@brave thunder Has your question been resolved?

[brave thunder]

<@&286206848099549185>

[odd edge]

@brave thunder Has your question been resolved?

[warped glacier]

where are you stuck?

[brave thunder]

How is 1 a constant

[warped glacier]

it doesn't contain x

[brave thunder]

https://cdn.discordapp.com/attachments/903463355619110912/1173138401671778384/image.png?ex=6562dd46&is=65506846&hm=43b2fbf7f64e0a50fcb3c829b14325d84827bde39781271c904a39f0d010b04f&

No in here

[warped glacier]

do you understand comparing the terms from before?

[brave thunder]

Yeah I do

[warped glacier]

$(A + C)x^2 + (B - A)x - B$

[clever fjord]

south

[brave thunder]

But how does a constant compare to any of these

When all have x in them

[warped glacier]

-B is a constant

-B doesn't have any x

[brave thunder]

Yeah

What do we compare B to https://cdn.discordapp.com/attachments/903463355619110912/1173138401671778384/image.png?ex=6562dd46&is=65506846&hm=43b2fbf7f64e0a50fcb3c829b14325d84827bde39781271c904a39f0d010b04f&

[warped glacier]

you compare -B to 1

[brave thunder]

Wheres the 1

[warped glacier]

the 1 in the numerator of 1/(x^2(x - 1))

think of $1 = 0x^2 + 0x + 1$

[clever fjord]

south

[brave thunder]

Ohh

So we dont care about denominator

[warped glacier]

yes, for the purposes of comparing the coefficients

[brave thunder]

Oh okayy

Icic

[warped glacier]

npnp

[brave thunder]

Okayy

Thanks

[warped glacier]

nw

[brave thunder]

.close

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[mystic saffron]

Can someone explain to me what happened in second step ?

The series was broken into different intervals that have no effect on the sums, and n! Was factored out

@mystic saffron

Can you expand few terms ?

How will it change the lower limit ?

Like how did k change from 0 to n+1

Is it correct?

I expanded the terms

@mystic saffron

<@&286206848099549185> have I expanded terms correctly?

,step

,steps

<@&286206848099549185>

[odd edge]

@mystic saffron Has your question been resolved?

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[frank wave]

how do i find this

[frank wave]

i found that the standard deviation is 200

but i dont understand what do they mean by "the sample is used to estimate the mean water consumption of each family in that country

[odd edge]

@frank wave Has your question been resolved?

[odd edge]

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[crisp flume]

The matrix A ∈ C^(n×n) is called antihermitian if A = -Ā^T, where Ā = (Āij) is the matrix obtained from A by taking the complex conjugate of all its elements. Show that the set of all antihermitian matrices of type 2 × 2 forms a vector space over R (the set of real numbers). Find a basis for this vector space and determine its dimension. Explain why it is not a vector space over C (the set of complex numbers).

[crisp flume]

how can i show that two antihermitian matrices A and B are closed under aditioin?

[tall veldt]

Take two antihermitian matrices, A and B, and compute $\overline{(A+B)}^T$

[clever fjord]

ΣΑCu

[crisp flume]

but what two antihermitian matrices? they shoudl be in general form shouldnt they?

[tall veldt]

Yes just call them A and B

[crisp flume]

alright and is this general from?

[tall veldt]

Don't need to actually write out a matrix here

[crisp flume]

hm

[tall veldt]

Just try and simplify this expression

[clever fjord]

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

[crisp flume]

u mean something like this? $A+B={-}{\overline{A}}^T{-}{\overline{B}}^T={-}({\overline{A+B}})^T?$

[clever fjord]

Slowaq

[crisp flume]

@tall veldt

[tall veldt]

Don't listen to GPT

But sure

[crisp flume]

yes i deleted it because it is not reliable

[crisp flume]

but does this show that A+B is also antihemirian?

[crisp flume]

and to show Closure under scalar multiplication i just do this? $Ac={-}{\overline{A}}^Tc$

[clever fjord]

Slowaq

[crisp flume]

but how do i prove it that itll still be antimermitrian matrix

.close

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[gilded bluff]

25c)

?

[cyan dragon]

|z + a| = b <= |z| +|a| = b, |z| = b - |a|

Triangle inequality

[gilded bluff]

uh what

what is triangle inequality

[cyan dragon]

Put a = 3-3i

[gilded bluff]

im so confused

[cyan dragon]

|a+b| <= |a|+|b|

[gilded bluff]

is that the only way to do it

ive never been taught that

[cyan dragon]

Okay

Lets do it in a simpler way

Assume z = a + ib

Now |a + 3 + i(b-3)|=2

[toxic rose]

|z| is the magnitude of z right? Well it will be very painful but you can substitute z=a+bi, and then isolate the magnitude of z from the given equation

[cyan dragon]

Now you evaluate it further

[toxic rose]

I.e. this

[gilded bluff]

i had something like this before

[cyan dragon]

You should learn triangle inequality it's very easy and intuitive and would solve most ques like this

[gilded bluff]

idk how to find min of z tho

[toxic rose]

I can't see 💀

[gilded bluff]

answer book says it's 3 square root 2 -2

[gilded bluff]

b

[gilded bluff]

how

[cyan dragon]

Z can be a complex no thats how, of form a+bi

[toxic rose]

She's asking how to isolate magnitude of z

[gilded bluff]

yes

[cyan dragon]

Triangle inequality again

[gilded bluff]

please no

[cyan dragon]

This

[gilded bluff]

i swear i don't need to know that

it doesn't show up anywhere in my book

[cyan dragon]

You are in which standard?

[gilded bluff]

?

[cyan dragon]

I was taught triangle inequality when i started complex i mean its necessary inequality to isolate magnitude

If not for that, you have to do like manually check for a, b values

[gilded bluff]

idk but we were never taught

[cyan dragon]

To find min and max

Okay let's talk about min

Basically we have to z=a+ib for which eq is also true and |z| is min right

[gilded bluff]

yes

[cyan dragon]

Let me do it on paper

In a simpler way

[gilded bluff]

ok

[cyan dragon]

You know calculus?

A little bit like maxima and minima?

[gilded bluff]

probably

idk what the things I do r called

[cyan dragon]

You take derivative of an equation

And check if it's equal to 0

[gilded bluff]

yes

i can do taht

[cyan dragon]

Nice

[gilded bluff]

👍

[cyan dragon]

Dayum its looks more complicated using calculus

Lol

[gilded bluff]

great! 😀😀

[cyan dragon]

What's the answer for c?

[gilded bluff]

3 square root 2 minus 2

[cyan dragon]

You have like similar solution to such problems, like examples which teacher made you do etc

Which method did they used?

[gilded bluff]

no

I studied ahead

[cyan dragon]

Ahh

Makes sense

[gilded bluff]

also there r no examples

[cyan dragon]

Tf lol

[gilded bluff]

but school is too slow

[cyan dragon]

Yeah i did the same

But i used better book which provided examples and methods such

[gilded bluff]

this is our official book

for our final exam

its so shit

[cyan dragon]

You should always use another reference book for studies

[cyan dragon]

Exactly

[gilded bluff]

i looked but their all too hard

[cyan dragon]

Even better use chatgpt

For better overview

[gilded bluff]

CHATGT IS SO BAD

[cyan dragon]

Yup but you can ask it provide references

Anyway

You can solve this using calculus

But the eq is not worth it

[gilded bluff]

i bought all the books u could find in my country

[cyan dragon]

Which grade are you in?

[gilded bluff]

uh

Next year 12

but I'm starting 12 now

[cyan dragon]

Ahh makes sense

That's what i thought

Okay if you are learning complex no

Let me give you a list of topic

That basically serve as prerequisite alright

It will help you a lot

[gilded bluff]

we already finished y11 tho

teachers r just stalling

[cyan dragon]

Thats why I'm worried they should have taught you inequalities and stuff

Which is like first thing we do in complex

[gilded bluff]

that sounds familiar

what do u do inequalities

[cyan dragon]

To solution eq like above isolate |z| and find max and min values

[gilded bluff]

how do u isolate z when it is in between the lines

[toxic rose]

$|(a+3) + (b-3)i| = 2$\
$\Rightarrow \sqrt{(a+3)^2 + (b-3)^2} = 2$\
$\Rightarrow (a+3)^2 + (b-3)^2 = 4$\
$\Rightarrow a^2 + b^2 + 3a - 3b = 4$\
$\Rightarrow a^2 + 3a + (b^2 - 3b - 4) = 0$

[clever fjord]

ItzKraken

[cyan dragon]

The calculus way

Now put a in terms of b or vice versa

[gilded bluff]

that looks great

[cyan dragon]

And minimize a^2 + b^2

[toxic rose]

theres a non-calculus way

[cyan dragon]

That the issue

[toxic rose]

but that would require a head ton of guessing

[cyan dragon]

Like manually?

[toxic rose]

because u can do some factorization there to make it easier

$\Rightarrow a^2 + 3a + (b^2 - 3b - 4) = 0$\
$\Rightarrow (a+2)(a+1) + (b+1)(b-4)= 2$

[clever fjord]

ItzKraken

[gilded bluff]

what do i do with that

[cyan dragon]

Now u hit and try lol

[toxic rose]

guess 🙂

[gilded bluff]

😭😭😭

i actually cant

where is the z im that

[toxic rose]

if u know a and b u know z

guess for a and b

[cyan dragon]

Yess you have to guess min values of a, b for which this true

Because u want |z| to be min

Which means u want a^2+b^2 to be min

[toxic rose]

wait iirc wasnt |z| some irrational crap

[cyan dragon]

Which means u want a, b to be min

[gilded bluff]

i looked at worked solutions

this is what they have

how does that equation become this

[toxic rose]

I am getting triangle inequality feels

[gilded bluff]

😬😬

[cyan dragon]

Exactly

Let me show without inequality its not worth it

[gilded bluff]

👌

[cyan dragon]

Look at f(b) its not worth it

[gilded bluff]

wtf

[cyan dragon]

With inequality it would be like 2 lines lol

Exactly

[gilded bluff]

what are all these

like

i cant find on my keyboard wtf

[cyan dragon]

Triangle inequality you know sum of of sides of triangle is greater than third side A+B>C

[cyan dragon]

Latex bot

[clever fjord]

ItzKraken

[gilded bluff]

y is it like that

[cyan dragon]

Greater or equal

[gilded bluff]

OK

[cyan dragon]

Like 2>=2

[gilded bluff]

OH

[cyan dragon]

Is true because 2=2

Yup

[gilded bluff]

what was the triangle rule again

[cyan dragon]

Anyway learn triangle inequality okay

Let me paste a learning source here

https://www.google.com/url?q=https://m.youtube.com/watch%3Fv%3Db5WdpOp4r8A&sa=U&ved=2ahUKEwiWoouLuL6CAxXt1zgGHYKPDFsQtwJ6BAgCEAE&usg=AOvVaw2fqz-7-FZmfXZx6ZiNyGoz

Here

[gilded bluff]

ill go watch that cute video

thanku for ur help 👍

.close

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[lean parcel]

Hello! I am having trouble with the following problem:

If I define a variable n as a whole number, then I can guarantee that

x= b + 2π n on the function f(x)=sin(x) will descripe all points equal to b on the function

[lean parcel]

Now the problem is how do I create a x so that all points equal to π /4 degrees and 3π /4 degrees on the infinite function are reppresented using help of n and other variables if needed

[valid thorn]

solutions=pi/4+2pi n or 3pi/4+2pi m for n,m in integers.

[lean parcel]

yeah

but

how do i combine those 2 functions as 1

which represents both points as 1 continuous x value

So basically I want a function that represents only the points equal to 45 and 135 degrees

on the sin(x)

[glass wedge]

½(1+sgn(sin(π/4+nπ/2))*(sin(π/4+nπ/2)

[lean parcel]

what is sgn

[glass wedge]

1 if x>0
-1 if x<0

[lean parcel]

but that solution also represents negative values

[glass wedge]

Starts at 45 degrees, moves by 90 degrees (π/2) for each n, but when the sin function is negative, 1-1 gives 0

[lean parcel]

i only want the values 45 and 135

[glass wedge]

It doesnt

It gives 0 for negative values

[lean parcel]

ok what is sgn

cuz im dumb

[glass wedge]

.

sgn(5)=1

sgn(-π) = -1

[lean parcel]

ohhh

[glass wedge]

Its a filter so to say

[lean parcel]

ohk

[odd edge]

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[peak pollen]

The sum of square numbers from a previous part of the question is given. 1/6(n)(n+1)(2n+1)

so am I right in just saying it's 1/6(n)(n+1)(2n+1) - n^2 - (n-1)^2 - 5?

Also n is >= 5

[mystic saffron]

The sum of the squares of all the numbers from 1 to n is n(n+1)(2n+1)/6

[peak pollen]

yeah

[mystic saffron]

Other than that, yeah, your solution works

Though it lacks some simplification

[peak pollen]

yeah I can't think of anything else other than expanding out brackets?

[mystic saffron]

One thing you could do instead is take n(n+1)(2n+1)/6 and replaces n with n-2

This'll naturally simplify down

[peak pollen]

oh yeah

idk why I didn't think of that

also include a -5 tho?

[mystic saffron]

Yes

[peak pollen]

perfect, thank you ❤️

[mystic saffron]

@peak pollen Don't forget to .close

[peak pollen]

.close

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[serene shore]

hello, I'm doing a python code about file I/O and directory exploration. I'm limited on just using OS and i'm wondering if anyone could help me understand where to optimize my code. Thanks in advance!

[zenith tartan]

not sure if that's a math question

but https://discord.gg/eF3Wjsd this might help

[serene shore]

oh, i'm very sorry, wrong channel!

[zenith tartan]

np

!close

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[rotund hawk]

.close

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[mystic saffron]

how do i write XY in complex number Z form similar to X^2 + Y^2 that i did above it? (sorry English is not my language)

[cold urchin]

you can expand (x+iy)(x+iy)

Hm nvm

Well idk what exactly you’re looking for but xy = Im(z) • Re(z)

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[mystic saffron]

.reopen

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✅

[mystic saffron]

i want it similar to this form but the correct version
z^2 doesn't equal xy

sorry i forgot to write the numbers in english

does it make sense now

i want xy similar to the form done above it
written in z or/and z bar form

[sudden shadow]

How do you get x with z and z bar？
How do you get y with z and z bar?

[spiral raven]

if i were teacher i would change x to a and y to b

z = a+bi and z bar = a-bi

[odd edge]

@mystic saffron Has your question been resolved?

[mystic saffron]

there has to be some sort of operations on them that results in xy

[sudden shadow]

Yes this is what I want you to think
Remaining x→y is cancelled

So what will you do to cancel y using z and z bar

[mystic saffron]

u mean like this?

[sudden shadow]

Yes

So you can express xy with z and z bar now

[mystic saffron]

but i think i have to remove i too

[sudden shadow]

There is no way to simplify it

i is the complex constant
So I think it's enough

[mystic saffron]

ok

thank you

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[spiral raven]

a and b is real number
u = 2i-3j+k , v= -i+aj+bk , w = 3i-j ; u // v
I 4v x w I ^2 = ?

[spiral raven]

<@&286206848099549185>

[stuck rock]

I'm sorry, I don't quite understand the notation. does u//v mean where u and v are parralel?

[spiral raven]

yes

[stuck rock]

well with that you can find the values of a and b

[spiral raven]

idk if it right i got a = 3/2 and b =1/2

and the answer is 269

i wanna check if it correct

[stuck rock]

ok

[stuck rock]

hmm I get 236, one sec

[spiral raven]

ah i see

[stuck rock]

for my value of b I get -1/2

[spiral raven]

ye it minus i forgot to put

[stuck rock]

ok

what did you get as your cross product?

[spiral raven]

-2i -6j -14k

ye i get 236 now

thank you

[stuck rock]

np

[spiral raven]

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[stark ravine]

How to find derivative of fog(X)

[stark ravine]

Composition of f(X) and g(X)

[mystic saffron]

use chain rule

[stark ravine]

Huh

[mystic saffron]

$\frac{d}{dx} f(g(x)) = f'(g(x)) \cdot g'(x)$

[stark ravine]

Ah

[clever fjord]

notamy

[stark ravine]

Yo

Got it

Thanks

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[mystic saffron]

i dont get this can someone help please

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[storm wharf]

The answer I get here is 0, but in reality the answer should be 1

What am I doing wrong?

Btw the last one there is sin pi/4

[flint heart]

answer should be 0 not 1 if i am not wrong

[storm wharf]

Book says it's 1

Book could be wrong

[mystic saffron]

use cos(a-b)

[flint heart]

that gives cos3pi/2 which is 0

[storm wharf]

Yeah checked it's 0 I'm right

[mystic saffron]

,w cos(7pi/4 - pi/4)

[clever fjord]

Results provided by WolframAlpha

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Requested by yozo_1211

[storm wharf]

Ok I'm good here thanks everyone

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[still axle]

need to find function from derivative

[still axle]

not 100% on what to do on this one lol

[hoary marsh]

Start with using chain rule

The outer function being () squared

[still axle]

idk how to use chain rule in reverse

so im not sure what im doing

[mystic saffron]

what's the function whose derivative is cosec²(x)?

[still axle]

-cot

[mystic saffron]

yep

so what would be differentiation of -cot(3x)?

[still axle]

Idk

[mystic saffron]

apply chain rule

[still axle]

csc^2(3x) x 3

[mystic saffron]

yep

so you need a function whose derivative is csc²(3x)

so what would it be?

if d(-cot(3x))/dx = 3csc²(3x)

[halcyon vector]

ur the best teacher ive seen

[mystic saffron]

i'm legit confused if that was sarcasm or was it an actual compliment?

[halcyon vector]

hahah dw its a compliment mate

[mystic saffron]

ahh, ty!!

[still axle]

Idk

is it -1/3cot(3x) + c

[mystic saffron]

yep

(-cot(3x))/3 + c

well btw are you familiar with integration?

[still axle]

no

[mystic saffron]

ah alright, no worries

[still axle]

but i’m still kind of lost

cus the method i was using originally was taking the function adding 1 to the exponent then dividing by the new exponent

and like i tried it with this

and it doesnt work i dont think

since it involves chain rule

[still axle]

^

i think i would need to start from the inside first right

idk

[mystic saffron]

as you're not familiar with integration, here's what i'd suggest to solve such questions - see each term and think "what could be the possible function whose derivative is that term"

well, you might not directly get the idea for terms like 1/x²

it'd just take some time

[still axle]

ones like these are fine for me

[mystic saffron]

you'd get more comfortable when you start learning integration

[still axle]

okay

but just like chain rule ones i havent gotten too in depth with

so yea

just kinda lost doing hw for stuff that wasnt covered in class yet lol

but thank you

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[pliant glade]

i managed to finish the questions, but i kinda guessed on the last blank. could someone explain to me how it became that?

[cold urchin]

[flint heart]

uh they separated cosx/sinx from cosx/sin^2x

[pliant glade]

o ok thanks

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[slender crescent]

hi

[slender crescent]

calc is hard

what would an appropriate jacobian matrix be ??

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@slender crescent Has your question been resolved?

[slender crescent]

yo nvm i got it tbh

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[viral osprey]

$$U_{n} = \int_{0}^{\frac{\pi}{4}}\tan^{n}(x)$$

[viral osprey]

Study the convergence of Un

[clever fjord]

zarblug

[viral osprey]

I tried to do Un+1 - Un but no can do

[mystic saffron]

try $U_{n + 2} + U_{n}$

[clever fjord]

notamy

[viral osprey]

Yeah we get 1/n+1

That was the first question of the problem, but I don’t know how to use it

[mystic saffron]

oh i didn't even see this. i saw the latex and thought you are finding relationship between different U_n's and n

[viral osprey]

Ahah no worries x)

[mystic saffron]

have tried it for a while but wasn't getting any kinda result :/

[viral osprey]

Thx for trying anyway, have a nice day!

<@&286206848099549185> if you guys think you can help you are welcome ^^

[odd edge]

@viral osprey Has your question been resolved?

[viral osprey]

So I’ve found it is decreasing, now I need to find the limit (and to prove it is converging),

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[ruby latch]

Ok so

[ruby latch]

The diff eq is y''-y'-6y = e^3t - 3t^2

Ive done the assoc homog and got c1e^-2t + c2e^3t

Ive done the particular sols for y''-y'-6y = e^3t and y''-y'-6y = -3t^2

Ive gotten Yp1 = 1/5t*e^3t

And Yp2 = 1/2t^2 - 1/6t + 1/36

So the gen sol is: y(t) = c1e^-2t + c2e^3t + 1/5t*e^3t + 1/2t^2 - 1/6t + 1/36

I plugged it into a calculator and it gave me y(t) = c1e^-2t + c2e^3t + 1/5t*e^3t + 1/2t^2 - 1/6t + 7/36

Where could I have missed a 1/6

Ping me whenever possible pls

<@&286206848099549185>

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@ruby latch Has your question been resolved?

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@ruby latch Has your question been resolved?

[ruby latch]

Oof

<@&286206848099549185> Anyone?

[odd edge]

@ruby latch Has your question been resolved?

[ruby latch]

Rip

[ruby latch]

Sike I finally found my mistake lol

I dropped a 2A

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[rotund forge]

is the inverse laplace of 1/s = 1 or H(t) or both? Does it matter what I use?

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[grave garnet]

yo

[grave garnet]

Does anyone know a good trick to memorize math specifically polyrythms?

nvm thanks anyways

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[radiant shell]

Does this epsilon delta proof look alright?

[radiant shell]

$\lim_{(x,y)\to (0,0)} \frac{x^3y^3}{(x^2+y^2)^2} = 0$

[clever fjord]

omgatriple

[radiant shell]

,tex
let $\delta = \sqrt{E}$ then, we can convert it to polar coordinates and we get $0 < \sqrt{x^2+y^2} = r < \delta$ and $|\frac{r^3\cos^3 \theta r^3\sin^3 \theta}{r^4}$. We can simplify this to $\frac{r^6}{r^4} \cos^2 \theta \sin^2 \theta |\cos \theta| |\sin \theta|$. All these trig terms are $\leq 1$ so $|f(x,y)| \leq r^2 \leq \delta^2 = \sqrt{E}^2 = E$

[clever fjord]

omgatriple

[radiant shell]

the proof in the solutions used \sqrt{2E} and did not go about it with polar coordinates so i'm unsure if im wrog or still right

[ember oak]

what is E? Is that your epsilon?

[radiant shell]

yeah

[ember oak]

$\varepsilon$, for future reference.

[clever fjord]

SWR

[ember oak]

This proof looks good. I'm curious what the solution did different.

[mystic saffron]

hi im sorry to bother you but i have another active channel and my current helper hasnt responded in 15 minutes, what should i do?

[ember oak]

You can try the @Helpers ping every 15 minutes if no one is around.

[mystic saffron]

is it ok if i post my question here?

[ember oak]

Nah you gotta stick to your original channel. This channel is in use

[radiant shell]

but if it looks good i'll go ahead and close the channel

.close

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[mystic saffron]

Find the identity element for the 11 hour clock.

[mystic saffron]

this is part 2 to a question with 3 parts. the first part was to create an addition table which i already did

[mystic saffron]

do you know how to answer that part?

[ember oak]

Show the whole problem

Also, it is bad form to ping individual helpers.

[mystic saffron]

sorry i didnt realize ping was on when i replied

[ember oak]

Guessing it's identity element for addition.

[mystic saffron]

i did the first part on help-31

[ember oak]

So you need a number, e, such that, for any given number, n, the sum n+e always equal n

[mystic saffron]

i still dont really understand

[quasi sparrow]

Pretend n=11

What number e satisfies 11+e=11

[mystic saffron]

0

[quasi sparrow]

Which one of the rows in your table satisfies this for all n, including n=11

[mystic saffron]

it wraps after 10 so idk

[mystic saffron]

ik im not supposed to ping but im actually still confused

[ember oak]

Can you show your table?

[ember oak]

0 would work here, yes.

but!

does a 12 hour clock have a 0?

[mystic saffron]

no but the other helper i was working with said i should use the system that wraps back to 0

[ember oak]

For an 11 hour clock, I recomment replacing 0 with 11

The sum table will all be the same, just replace each 0 with 11

[mystic saffron]

i dont feel like changing it rn since its late and im trying to go to sleep soon

[ember oak]

Well get some sleep then

[mystic saffron]

its fine i can stay up a bit longer

i aint that tired

[ember oak]

hard to explain your identity element then if you don't want to update your table.

[mystic saffron]

ok ill replace 0 with 11

does it wrap from 11 to 1 then?

[ember oak]

wdym

[ember oak]

oh. Yes it does.'

just like how 12 hour wraps from 12 to 1

[mystic saffron]

my table looks a lil weird because it starts at 11 instead of 1 but i dont think that should matter too much

ok i just changed the 0s to 11s

what's next?

<@&286206848099549185>

.close

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[west merlin]

u h h o w. help is greatly appriciated, thank you!

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[cold barn]

Trying to decipher how you do this

So I understand step 1

but after doing step 2 and then trying step 3...it just turns out wrong

I don't understand what I'm doing wrong

Because for z_upper - z_lower to be 0.95, that means that z_upper must be greater than 0.95 since z_lower can't have a probability less than 0 right

and on a z-score table

that corresponds to z = 1.65 or so

and that just...doesn't make sense to me

[tropic hazel]

what values are you getting for the upper boundaries and lower boundaries

[cold barn]

+/- 0.796

Lower z = -0.796
Upper z = 0.796

I just plugged in what they gave (which is what the formula is)

wait...

why is it square root 30

wait what.

wait isn't that...not what the formula is

0.9756 - 0.0244 is about 0.95 ok

Nevermind I answered my own question

The practice problems my prof gave use the solution formula incorrectly

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[polar locust]

There are numbers 1...n, where n>= 3. We randomly choose 3 numbers of them. What is the proability that that two of them are adjacent?

[polar locust]

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[old path]

hello

[old path]

is there any formula for the above sum?

[flint heart]

hi

[old path]

in computer terms, I want to do that in O(1), precomputation can be done too.

[low locust]

what is k?

[old path]

k is a constant

and n is a constant too

[old path]

I wonder if it's even possible to do that in O(1) with some precalculations

[low locust]

well what do you call precalculations and what do you call actual calculations

[old path]

precalculations means like factorial calcuations

or even 1/r! things

[low locust]

yeah but of which numbers

[old path]

or even the summation sigma (1/r!) till some k

[old path]

um wdym?

[low locust]

well in general the expression depends on n and k

can the precalculations depend on those?

[old path]

ok what's the expression?

yes it may prolly

it depeds, tell me the expression

[low locust]

WA gives it as k! U(k+1, k+n+2, 1) where U is some weird function

so not really helpful to you probably

[old path]

ohh

nothing else can be done?

ok if you wanna know the problem statement in easier words, i can tell

like suppose there are k items, and other n items

and you want to find all the permutations of (k items + any number of n items)

so the answer would be :

(k+0)! + (k+1)nC1 + (k+2)nC2.....

@low locust

[low locust]

no need to ping

[old path]

ok

[low locust]

hmm nothing that comes to mind

you could look up that weird function U and see if it has some special values but I doubt it

[old path]

ok

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[merry kestrel]

When we say two groups are isomorphic, we say they preserve the operation

[merry kestrel]

What all can it mean?

looking for motivation of the concept

[low locust]

it means its the same structure, just different names for all the elements

[merry kestrel]

structure as in?

say, if G is a cyclic, then G’ which is isomorphic is also cyclic?

[low locust]

"same thing"

yes

G and G' have all the same properties. just the elements are called differently

[merry kestrel]

so even I those element names were some gibberesh, ill get the operation same

like i can safely relabel them?

[low locust]

your isomorphism is basically that

it relabels the elements

and you get the same result if you first apply the operation and then relabel, or first relabel and then apply the operation

[merry kestrel]

so, simply their group tables are same

After i map

[low locust]

yes

[merry kestrel]

Makes sense

why did they bring up calculus here?

is it just analogy of limit after product or product of limits are equal

or is there something more?

[low locust]

just two examples of a similar kind of process

first doing this, then doing that vs first doing that and then doing this

[merry kestrel]

My textbook starts with isomorphism

[south plume]

oops

i wrote a wrong thing

[merry kestrel]

This is really intuitive

[south plume]

they use $\int_a^b (\text{something}) dx$ as an example of $\phi$

[merry kestrel]

thanks

[clever fjord]

artemetra

[merry kestrel]

oh

idk how to see it as a proper bijection

I think i only get the analogy

[low locust]

its not a bijection

just a homomorphism

just take it as an analogy

thats the only thing thats meant here

more precisely, you have the groups of all the integrable functions and the group of real numbers

both groups under addition

and then phi(f) = int_a^b f(x) dx

and then phi(f+g) = int_a^b f(x)+g(x) dx = int_a^b f(x) dx + int_a^b g(x) dx = phi(f) + phi(g)

[merry kestrel]

makes sense

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[neon swan]

Hi, my question isnt in english so I’ll try my best to translate it.
“You are given Points A(3,11) and B(7,1). The line y = 2x + k intersects point AB. Find the value of K”

Im not really sure what to do, or how to even start, as its been a few months since ive done any math, so im asking here

[neon swan]

Not 100% sure if i used the right word on “intersects”
like “cuts” or “slices”? Idk

My textbook has the answer already written down (to check if you’ve gotten the correct answer i think?) but I need to show my work
If it helps understand the question, i could send the answer

[snow marten]

you need to find the midpoint of ab

[neon swan]

Midpoint?

Is like that a point where they meet or something? Sorry, ive never done math in english so idrk the terms

Or is it just the middle of the point they gave and (0,0)?

[snow marten]

it is the middle point of A and B

[neon swan]

How do i draw the function
Would points A and B be going up/down? How can i find that out

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@neon swan Has your question been resolved?

[neon swan]

<@&286206848099549185>

um

Help?

..ill just google it again

.close

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[proven grail]

I still dont get this TT

[proven grail]

<@&286206848099549185>

[dusk osprey]

yup

tell me

[proven grail]

This

[dusk osprey]

which one

can u repost the question

[proven grail]

Reciprocal then?