help-23

[sour mica]

how do u graph one of these anyways? what is z

[jolly shard]

Just picking those row operations is all you need to do to solve those (and bigger systems)

[jolly shard]

Write them in the form z=ax+by+c then drop the z= and this will show you the planes

https://www.desmos.com/3d

Then the solution is the point where they all meet

[sour mica]

i see...

that must be horribly hard to do by eye

[jolly shard]

Yeah, now try doing that with 10 variables or 100.

[sour mica]

is that a thing ppl do

[jolly shard]

But by using row operations, your computer can that millions of times a second

It’s called linear algebra and it’s fundamental to the way computer graphics and machine learning works

[sour mica]

math man...

[jolly shard]

It’s life changing stuff

[sour mica]

anyways thanks a lot for the help

rlly appreciate it

[jolly shard]

Good luck out there

[sour mica]

tyty

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[unborn canopy]

what's the next step here ?

[safe radish]

Please don't occupy multiple help channels.

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[charred lark]

can some one explain why it's 202 choose 2

[stoic dune]

We use stars and bars to get this

Take 200 stars, and 2 bars. Arrange them into any sequence you want.

The number of stars to the left of the first bar represents the value of x - 1, the number of stars between both bars is y - 1, the number of stars to the right is z - 1

So any sequence corresponds to a solution to x + y + z = 203

How many ways are there to create such a sequence?

[safe radish]

@charred lark Has your question been resolved?

[charred lark]

oops

[charred lark]

oh okay I kinda get it

[stoic dune]

You'll see this method used for counting choices, without order, with repetition.

We can think of this as "choosing a bunch of xs, choosing a bunch of ys, choosing a bunch of zs, such that we get 200 of them"

[charred lark]

okay, so it's just called stars and hard?

bars*

okk thanks kaynex

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[brittle stone]

whats the length of az?

[brittle stone]

trying to find the equation of the porabola using the focus and directrix

!status

[safe radish]

What step are you on?
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2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[brittle stone]

3

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[vapid python]

Hi is this correct?

[woven hound]

Yes but I'd change 6i^2 to -6

[vapid python]

Ok thank you!

So -6-8i?

Does anyone know what to do after this? Step by step

[safe radish]

@vapid python Has your question been resolved?

[vapid python]

<@&286206848099549185>

[willow gust]

If u r supposed to get the value of x then
It should be..
2x - 4 = 3√3
=> 2x = 4 + 3√3
=> x = (4+3√3)/2

[vapid python]

Oh no I’m sorry it’s the square root method I forgot to mention

[lunar rampart]

do you mean completing the square or?

because beside what he said i dont see why theres a different “method” to solving the given eq

[vapid python]

Idts cus isn’t it a completely different thing? Completing the square gives me only 1 x answer (as there’s a bottom page for this page) but square roots you have 2 x answers

@lunar rampart

[lunar rampart]

sometimes only 1 answer but usually 2. the square root operation when applied should be applied as +- sqrt()

so it would be +-3sqrt(3)

the positive and negative root

you get only one answer if 0 is in the sqrt operation

just like you took the positive and negative root of 10, do the same here but with 27

@vapid python does this help?

[vapid python]

Kinda, the square root part is familiar with there being sometimes 1 andwer but Photomath is showing 2 and I don’t know the steps to get there

Could I apply this to the problem and make it easier?

[lunar rampart]

how did you get 2 values here?

[lunar rampart]

this is just the determinent- it tells you how many solutions are there, but it wont help you solve them

[vapid python]

Here’s my work

[lunar rampart]

im aware, im asking how you went from sqrt(10) to having 2 answers

[vapid python]

I don’t know, my teacher always makes us separate the answers into neg and pos

I always assumed it’s bc a negsqrt equals a positive still and the positive answer is a given cus ofc it equals x

[lunar rampart]

yes, basically. when solving for a value x^2 = a (where a js positive) you have two roots (unless a = 0, then you have 2 equal roots.
there js always a positive and negative root. so when solving both should be considered as a solution

both are roots

so when taking the root of 27, both the positive and negative squar root must be considered

[lunar rampart]

which is why here one is postive and one is negative

you get two solutions

[lunar rampart]

thats where this comes from. for any quadratic, the discriminant,( b^2 -4ac) is what is put into the sqrt operation. so if discriminant > 0, its a positive number and has 2 unique roots. if its 0, the +0 and -0 are the roots, which are equal. if its negative, sqrt() operation doesnt yield real solutions

[vapid python]

I think I got it, thank you!

[vapid python]

Thank youuu so much this really ties in all the formulas together 😭😭

[lunar rampart]

ofc

[vapid python]

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[crisp kiln]

I got 3sqrt(3) + 2 and -3sqrt(3) + 2

Do you can’t the steps as well?

Oh mb

It was closed

Lol

Here I will do yours

So you need the other root right?

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[barren brook]

anyone know where i went wrong?

sorry not good at this

trying to convert it into $f(x)=(x+h)^2+k$

[thin bridge]

the leading coefficient is negative,
you should've first factored out -1

[flat frigate]

x927373

[barren brook]

ok let me retry rq

would this be it?

[thin bridge]

no

you didn't factor out -1 properly

[barren brook]

oh damn

can you walk me through that or is it too long

[thin bridge]

don't try and do patchwork

restart from the beginning

[barren brook]

okay

[thin bridge]

factor -1 out of
-x^2 - 4x
whether you include that +4 is optional/up to personal preference in this step

[barren brook]

im adding it because thats how were taught in class, so im tryna get used to it

ok il reset it and send my progress

@thin bridge

[thin bridge]

$x^2+4x + 2^2$ isn't $x+4$

[flat frigate]

ℝam()n()v

[barren brook]

i forgot the ^2 on the (x+4)

[thin bridge]

isn't (x+4)^2 either

(x+4)^2 expands out to x^2 + 8x + 16

[barren brook]

hmm

ok one sec

ye im lost, where should i go from here?

[thin bridge]

$x^2 + bx + \br{\frac{b}{2}}^2 = (x + \what)^2$

[flat frigate]

ℝam()n()v

[barren brook]

b?

[thin bridge]

no

this should be in your notes

[barren brook]

nobody told me to put this damn

[thin bridge]

,tex .cts

[flat frigate]

ℝam()n()v

[barren brook]

so b/2?

oh i know

i for some reason added 4 instead of the 4/2

[thin bridge]

looks ok now

[barren brook]

thank you 🙏

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[teal finch]

Is 2^2n = O(2^n)? what are the steps i need to prove this?

[torpid fable]

Yes

[marsh walrus]

hmm i dont believe you are correct

this would require $\lim _{x\to \infty} \frac{2^{2x}}{2^x} = 0$ right

[teal finch]

wait but if i simpify that wont it be (2^2)^n?

[flat frigate]

jan Niku

[teal finch]

wait is it possible to solve without lim

i have 0 clue about those

[marsh walrus]

just use the limit, it tells you exactly what you need

$$f(x) = O(g(x)) \leftrightarrow \lim_{x \to \infty} \frac{f(x)}{g(x)} = 0$$

[flat frigate]

jan Niku

[teal finch]

are there no other ways because we wont be using lim in our curriculum

[marsh walrus]

i wanted the longer arrow damnit

hmm well I don't know another way personally, no

i can tell you what you said is incorrect, I think

the limit is 2ln2

not 0

err

actually thats not true either

but definitely not big O

[teal finch]

my prof did something like (2^2)^n

[marsh walrus]

[teal finch]

but im not sure what happened after that

[marsh walrus]

if not interpreting big Oh as a limit im not sure how to think about it

to be honest

[teal finch]

it was (2^2)^n = a^2

[marsh walrus]

other than just memorizing growth rates

[teal finch]

i see

[marsh walrus]

and you can think about what big oh is saying

ive been thinking of it like, we are putting a cap on the growth of another function

so 2x = O(x^2) because x^2 is an upper bound on the growth of 2x

its much bigger than 2x, for big x

,w graph 2^(2x) and 2^x

[flat frigate]

Results provided by WolframAlpha

Click here to refine your query online
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Requested by janniku

[marsh walrus]

2^x is not a good bound on 2^(2x)

[teal finch]

is the 2^2x the blue one?

[marsh walrus]

it is

[teal finch]

ngl i dont fully understand the theory of big O, might try to understand that first

thank you tho

[marsh walrus]

sure

im reading now that limits are the wrong way to think about big Oh

so maybe i need to know something else too

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[dense wadi]

how can the first line become 2sinθcosθ?

doesnt it just equal to 0

considering sinθcosθ-cosθ-sinθ

[pseudo scroll]

That just seems plain wrong

[dense wadi]

the equation?

[pseudo scroll]

yes

Unless there's missing context

[dense wadi]

this is whole context

[pseudo scroll]

yeah it should be sincos + cossin

And since summation identity instead of difference

[dense wadi]

so this is wrong? 😅

[dense wadi]

yeah this

idk whats going on

[pseudo scroll]

Its wrong

Yes

[dense wadi]

possible teacher messed up ty

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[muted pewter]

Not sure how to do this

by trees they mean leftist heaps

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<@&286206848099549185>

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[prisma hamlet]

can someone please help me with 8?

[prisma hamlet]

I did 7 correctly

but for whatever reason, I jut can't do 8

[tidal imp]

Show your work

[prisma hamlet]

hold on a second, I'm writing it down right now

so alright

the line PA is (-4, -2) + t(5, 1)

QB is (-1 , 1) + s(2, - 5)

which results in these following equations:

-4 + 5t = -1 + 2s
-2 + t = 1 - 5s

I'm stuck from here onwards

[tidal imp]

Ok so my initial thought was to generate lines

[prisma hamlet]

hmm

I think he wants me to sovle it without graphing first, and graph it second

to note that, he wants me to use the parametric representation

[tidal imp]

Taking slopes

[prisma hamlet]

so P + tA is the definition of the line

such that int he case of PA, the line is (-4 + 5t, -2 + t)

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[thin crescent]

I am so lost, I was able to do every other problem but this one. The fractions on the x-axis confuse me

[icy lance]

what have you tried

[thin crescent]

I dont know what to try, the only thing i got is the amplitude and center line finding the period is whats confusing me

[icy lance]

i see, well, if we compare it to cos(wx) graph,
the point x=5/6 would have corresponded to cos(wx)=-1
we can infer then that 5/6 w=pi

(because its flipped and translated down)

or you could see the period is 5/3, so dividing 2pi by 5/3 gets you 6pi/5 for w

either works

[thin crescent]

I see

So it would come out to y = -1 cos (6pi/5 x)-1

Oooooh now i get it

Thanks

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[stable inlet]

write out the truth tables

[safe radish]

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[signal aspen]

The second sentence is like $(A \vee B) \wedge \neg(A \wedge B)$ (Wherein we De Morgan'd $\neg(x \in M) \vee \neg(x \in N)$). Just truth table $(A \vee B) \wedge \neg(A \wedge B)$, the first sentence should make sense.

[flat frigate]

poypoyan

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[cunning thistle]

hi

[cunning thistle]

i tried multiple answers and i used up 4/5 of my chances My tutor didnt know the answer either. the closest ive gotten was the second and third options

tried just the second one and just the third one as well

and just the first one

[split ether]

Would go with the second, third and the fifth

[snow robin]

i agree

those are all true and combining them means P(0) is true

[split ether]

Right, and the rest are just irrelevant

[wild lily]

can anyone help me ,how to find eigen vector when all rows and columns are propotional..

[snow robin]

Please open a new channel

[wild lily]

huh?

how

[cunning thistle]

help 31, 32 and 33 are avaliable

[snow robin]

Go to available and pick one

[wild lily]

okay ..sry

[cunning thistle]

its ok

ok the second third and fith. last try here we go...

thank you guys

i need more help later but ill ocuppy a different channel later during the day once i get everything together

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[cold patrol]

<@&286206848099549185>

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<@&286206848099549185>

[cunning thistle]

,rotate

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[cold patrol]

<@&286206848099549185>

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[snow wren]

.

[safe radish]

Please don't occupy multiple help channels.

[icy lance]

why post again

[snow wren]

it didn't pop out of my screen

[snow wren]

.

<@&286206848099549185>

[lean otter]

yes?

[snow wren]

I don't know how to do this, can someone please help me? It's a frequency distribution

[elder silo]

Here are the marks sorted in ascending order:

12, 13, 14, 15, 15, 16, 17, 18, 18, 21, 22, 23, 23, 24, 25, 25, 26, 27, 28, 29, 29, 30, 31, 36, 36, 38, 39, 42, 43, 45

Now, let's calculate the range, class interval, and class size:

Range:
The range is the difference between the highest and lowest values in the data set.

Range = Maximum Value - Minimum Value
Range = 45 - 12
Range = 33

Class Interval:
To determine the class interval, you need to decide on the number of classes (groups or bins) you want to use. The choice of the number of classes can vary based on your preferences and the nature of the data. Let's assume you want to create 5 classes for this data set.

Class Interval = Range / Number of Classes
Class Interval = 33 / 5
Class Interval ≈ 6.6

Since you can't have a decimal class interval, you can round it up to the nearest whole number, which would be 7.

Class Size:
The class size is half of the class interval.

Class Size = Class Interval / 2
Class Size = 7 / 2
Class Size = 3.5

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[toxic elk]

can someone help me? i’m not sure if i started to do something wrong because this won’t work, and i’ve tried a lot of other methods too and my denominator always equals 0

[thin bridge]

attempting to multiply by (x+3)/(x+3) doesn't help here

to rid yourself of nested fractions, multiply the numerator and denominator of the main fraction by the lowest common multiple of the denominators of the smaller fractions

[toxic elk]

so multiplayer (1/x) by -(1/3)?

[thin bridge]

no

what are the smaller fractions in that whole expression?

[toxic elk]

(x/(1/x)-(1/3)) and (-3/(1/x)-(1/3))?

[thin bridge]

no

not what I'm looking for

don't split the fraction

[toxic elk]

3x/3x?

[thin bridge]

what's that supposed to be?

[toxic elk]

the denominaters of the smaller fractions multiplied

so -3x/3x

i think

[thin bridge]

that would be just 3x
3x/(3x) is what you could multiply by to simplify your fraction

[toxic elk]

but i still just get 0 in the denominator

[thin bridge]

after multiplication, you should see a common factor in the numerator and denominator

[toxic elk]

ohhh

i do

the issue i’m having with limits is that there are so many ways i have to try to solve them before i find the right one

[thin bridge]

usual approach would be to simplify until you cancel the common factor responsible for the indeterminate form

or apply a limit identity doing something similar

[toxic elk]

okay thanks

.close

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[dense basin]

Not sure how to do this, I found 7/2x^2-2x-27/14 which satifies the condtions, but it wants integer coeffients

[obtuse plover]

$\frac 72 x^2 - 2x - \frac {27}{14} = 0$

[flat frigate]

Stephen

[obtuse plover]

thats what u got right

@dense basin

COME BACK!!!!!

[dense basin]

yah

but it wants integer, and that means whole numbers

right, so no working

[obtuse plover]

how can u get rid of that 14 denominator

[dense basin]

ohh

okay

so algebra, multiply

let me try

wait no, after multiply won't it just become $7x^2-2x-27$

[flat frigate]

The Force

[obtuse plover]

what did u multiply both sides by

[dense basin]

by denominator?

[obtuse plover]

which is?

[dense basin]

2 and 14

[obtuse plover]

?

[dense basin]

but, that's like just dropping the denominators, would it work?

[obtuse plover]

no u cant just get rid of the denominators like that

a(b+c+d) = ab + ac +ad

[dense basin]

what?

[obtuse plover]

you said you multiplied both sides by 2 and 14

how exactly did you do that

[dense basin]

I don't know, algebra right, opposite of divison multiplication

[obtuse plover]

im asking, how did you multiply both sides by 2 numbers? what do u mean by that

[dense basin]

oh, they're fractions

multiply by 2 gets rid of denominator of 7/2

then multiply by 14 get rid of -27/14 denominator?

[obtuse plover]

if u multiply one term by 2, you have to multiply all terms by 2

if you multiply one term by 14, you have to multiply all terms by 14

[dense basin]

so if I were to multiply by 2 then the -2x and -27/14 also gets multipled by 2?

[obtuse plover]

of course

as well as the other side, 0

[dense basin]

Oh, okay let me try doing some work then

[obtuse plover]

thats why i said this

[obtuse plover]

btw i just checked this and im not getting the same fractions

so u probably wanna redo that first

[dense basin]

right, c should be -23/14

[obtuse plover]

i didnt get that either

show me ur work

[dense basin]

Okay
A should be = 3.5 which is 7/2 since 3.5*2 = 7
B = -2 since quad formula is -b +_
C = -23/14 since 4-4(3.5)(-23/14)= 23

[obtuse plover]

check the computation on that last line

u sure thats true?

[dense basin]

not true, let me redo

[dense basin]

I don't think I'm getting it, I keep getting -23 using 27/14

[obtuse plover]

show me ur step by step work

[dense basin]

I just kinda plugged in numbers, -4(a)(c)
a = 7/2
-4(7/2)= -14
27/14 as a c value would give me 27
then b^2 = 4 minus 27 I get -23

[obtuse plover]

b^2 - 4ac = 23

(-2)^2 -4(3.5)(c) = 23

Solve for c

Algebraically

Dont just plug in numbers

[dense basin]

-19/14

[obtuse plover]

Good

[dense basin]

🤦

Now I go get rid of fractions

It works now! Thanks for the help

.close

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[outer blade]

I endded up solving it question 3

in the box below the rectangle

i was wondering if that is the correct way of doing it

or if im just tottally doing it wrong

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@outer blade Has your question been resolved?

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[lean otter]

A function can be discontinuous

I'm still quite unclear as to why log cannot have negative base

radical functions have holes all the time

[plucky elk]

What

[lean otter]

rational

mb

rational function*

[plucky elk]

Rational functions have nothing to do with logs

[lean otter]

Im giving an example

to illustrate a concept I believe to be analogous

not equating the two as the same function, but generalizing a concept I believe to be uniform across function

[plucky elk]

It's not

[plucky elk]

It doesn't generalize

[lean otter]

The picture makes a statement that since a function is not continuous, it is not a function. Therefore, we cannot use negative base

But I believe discontinuity does not suggest anything about whether it is a legitimate function or not

This can be seen through examples in rational function

Why is it not generalizing, why is it not?

Your answers are really vague, if you could expand on the reasoning behind your statement

[plucky elk]

It's just telling you that your assumption is wrong

I don't need to demonstrate why you're wrong, you need to correctly demonstrate why you're right

And analogies don't do that

[lean otter]

If I am unclear why my statements and assumptions are wrong, I cannot correct them.

You merely pointed the fact that they are wrong without explaining why they are wrong, meaning I don't possess a solution to resolve my incorrectness.

[plucky elk]

It really is that simple. Analogies aren't proofs

[lean otter]

This still doesn't answer the question that I am asking. My question is really that given how discontinuity in other functions still make that function as a function, why is this not the same for Log.

I am not trying to prove a point. I am asking for an explanation for the values of the argument of a log function.

I am not attempting to prove why it isn't a function. I wish to understand some form of intuition that helps me with my current confusion

[plucky elk]

https://math.stackexchange.com/questions/2086540/can-we-take-negative-numbers-as-base-in-taking-log

[lean otter]

Ok, my question is. Do we only consider positive argument because we want to restrict the range to be real numbers, or is the reason that if we consider negative values of argument, the function becomes discontinuous which means it isn't a function anymore.

These are 2 justifications that seem to be distinct from one another that I have read on the internet, and are they compatible, or is one correct and the other is incorrect?

<@&286206848099549185>

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@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185>

[lean otter]

<@&286206848099549185>

[lean otter]

<@&286206848099549185>

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[timber atlas]

I need this in modulus-argument form

[timber atlas]

where do I start from?

I think I apply de movire’s?

[split ether]

Yeah, evaluate (3 + 3i)^4 using de movire's theorem

[timber atlas]

and then what

[split ether]

What did you get?

[timber atlas]

3 sqrt 2 [cos(pi/4) + i sin(pi/4)]

[split ether]

That's 3 + 3i, yes, now raise that to the 4th power using de movire's

[timber atlas]

wait

[timber atlas]

raise this to the 4th power?

[split ether]

Yes

[timber atlas]

ok

so that’s like (3 sqrt 2)^4 [cos pi + i sin pi] ?

[split ether]

Yes

Now what are cos(pi) and sin(pi) equal to?

[timber atlas]

so cos 90= 0 degrees

wait

[split ether]

pi radians is not 90 degrees

[timber atlas]

cos 180

[split ether]

Right

[timber atlas]

-1

and sin 180 is zero

[split ether]

So it's just -(3 sqrt2)^4

I.e., -81*4

[timber atlas]

right

so -324

[split ether]

And the answer will thus be -1/324

[timber atlas]

wait how did you get that?

oh nvm

ok makes sense

thankyou

.close

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[terse jackal]

Question A

Is this correct

[quasi bison]

you can copy paste directly from paint into discord btw

[terse jackal]

Im on my phone

[frigid locust]

seems good

id keep fractions only

no decimals cuz they can get tedious , but its preference

[terse jackal]

I use decimals so i dont get confused

[frigid locust]

if ur teachers fine then that is fine

but usually ppl use fractions

[quasi bison]

imagine using 0.33333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333333... instead of 1/3

or 0.142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857142857... instead of 1/7

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[royal wharf]

How would i solve this?

[pseudo scroll]

Write it in sigma notation maybe it would be easier for you to see

[flat frigate]

jan Nejon

[pseudo scroll]

Do you know these formulae?

[royal wharf]

yeah

i did that now

[flat frigate]

xd_senBugha

[pseudo scroll]

I see

$\frac 23 \sum_{k = 1}^n \frac{2k + 1}{k(k + 1)}$

[royal wharf]

am i correct

[pseudo scroll]

Evidently not

[flat frigate]

jan Nejon

[pseudo scroll]

$\frac 23 \sum_{k = 1}^n \frac{k + 1}{k} + \frac{k}{k + 1}$

[flat frigate]

jan Nejon

[royal wharf]

yeah

howd you get that

[pseudo scroll]

split the fraction

2k + 1 = k + (k + 1)

[royal wharf]

then what do we do?

[hushed kestrel]

J

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[royal wharf]

<@&286206848099549185>

.close

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[bleak juniper]

<@&286206848099549185>

[reef estuary]

bruh

[bleak juniper]

im forgot how to do long devision

.close

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[elfin bronze]

does anybody have python on their computer

[reef estuary]

yes

[elfin bronze]

could you run a code for me

[reef estuary]

no

use an online compiler

[elfin bronze]

oh....

[split ether]

I don't believe this to be an appropriate place for that

[reef estuary]

if you dont have python

[elfin bronze]

ok but im on mac 😭

[reef estuary]

online compilers dont use your computer

[elfin bronze]

??

[reef estuary]

use an online compiler

you dont need to install python

[signal aspen]

Just search "python online" or something

[elfin bronze]

ok ok thanks

[split ether]

.close

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[elfin bronze]

it doesn't work

is there a online compiler that can use tkinter

[safe radish]

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[elfin bronze]

☠️

[opaque bolt]

@elfin bronze close? or any que?

[split ether]

They are looking for someone to run their python code because they have mac

[elfin bronze]

i need help

[split ether]

Sure but it's not math-related

[opaque bolt]

but this is math help not general

[elfin bronze]

and no i dont anymore

[opaque bolt]

so GGz?

[elfin bronze]

so idk y ur saying tht

[split ether]

Then what do you need help with

[elfin bronze]

^^

[split ether]

https://onecompiler.com/python/3wnjbppaa

[opaque bolt]

@elfin bronze This Channel Is For Math Help Not General Help!!

[split ether]

Literally googled "python tkinter compiler"

[elfin bronze]

u think i didn't try tht??

if it worked i wouldnt be here 🤣

[split ether]

Anyway ask somewhere else

[elfin bronze]

is this not math tho? and if so where can i find help with this issue

[split ether]

You are wasting time here

[opaque bolt]

nah not math , idk ask in general

[split ether]

There's CS server in the #old-network as I remember and you may ask in #discussion

[elfin bronze]

ok ty

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[split ether]

.close

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[honest niche]

<@&286206848099549185>

[honest niche]

Is this question right

Kinda just guessed on what to do

It originally looked like this

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[eternal creek]

so im not sure if im doing the improper integral right

its been about a decade since i did one and took a calc 2 course

i set the limit as t right

[reef estuary]

can you show what you did

[eternal creek]

just making sure i did that right?

been awhile since i did an improper integral honestly

[reef estuary]

looks right to me

[eternal creek]

i guess the main idea here is that when you have a singulaity the value will change and there cant be uniform convergence

anyways great, im back on my A game 🙂

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[shut veldt]

Is this correct so far? (TRIGONOMETRY QUESTION )

[exotic bolt]

How did you get this?

Tbh this isn’t how I would to the problem but

[shut veldt]

Can you tell me which method do I use then?

Because when I used the above method I got the answer correct

[exotic bolt]

oh oops nvm

mb

i see what u did

[shut veldt]

Should I take a multiple of 90

[exotic bolt]

but i dont tink thats right

[shut veldt]

Yeah I understood that

Like this right!?☝️

[exotic bolt]

whats the probelm?

i cant really tell lol

[shut veldt]

Okay bro

[exotic bolt]

btw

cot -495 is 1

not -1

thats what u did wrong

[shut veldt]

Here

[exotic bolt]

why are u transforming it into sin

[shut veldt]

Oh okayy

[exotic bolt]

???

lol

[shut veldt]

My teacher told me to do so🌚💀

[exotic bolt]

ur teacher setting u up

tf

i dont know why ur seperating

it things of 90 at all

[shut veldt]

If was smart enough to teach us math I wouldn't have joined this channel tbh

[exotic bolt]

you literally could just find the terminal angles

just do your 405-360

aqnd thats 45

cosine of 45 degrees and cosine of 405 degrees are the same

lol

you arent doing half angle identites so theres no reason to do what ur doing

[shut veldt]

Well I only know allied angle formula

We haven't reached the terminal angle topic igig

So that's why I was converting it

[exotic bolt]

literally the first thing on my notes in precalc LOL

first topic introduced in the year

[shut veldt]

I am just learning

[exotic bolt]

your teacher is making that 10x more complicated than it needs to be

[shut veldt]

The so called basics

[exotic bolt]

literally just do theta-360

this is also wrong

[shut veldt]

What after this

[exotic bolt]

so do 405-360

[shut veldt]

I have to write a explanation for the next step

[exotic bolt]

and that gives u an equal ratio

405-360= 45

405 degrees and 45 degrees are going to give u the same trig ratios

This is what got u the wrong answer

[shut veldt]

Wait let me do it

[exotic bolt]

did u figure it out

[shut veldt]

Yeah

Okay thanks mate

@exotic bolt

.close

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[safe radish]

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[fervent pond]

h

[fervent pond]

i have a question

[proper swan]

how do I find c here

help

[fervent pond]

bruh

go find ur own channel

[hot gate]

💀

[fervent pond]

.close

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[proper swan]

oh sorry

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[zinc lintel]

<@&286206848099549185>

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[lean otter]

shouldnt that be +16?

[zinc lintel]

i got that one

need help with this one

that one was q= r+16

[lean otter]

not 6r?

[zinc lintel]

no

i need hekp with this one

[lean otter]

you need to get y=..

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[native epoch]

If I have a complex equations such as iz= 4+3i and I need to find z. Would it be just -4i+3 ?

[native epoch]

Since I just need to multiplicate it for its conjugate?

[mortal sandal]

i*(-4i+3) is 4+3i yes

it doesn't have to do with conjugates though

[native epoch]

well since I move the i to the right side, is a division, therefore I need to multiply for the conjugate

@mortal sandal if it makes sense

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[round marten]

A typewriter types 36 letters in 8 cm. How many letters could be typed in 35 lines, each 12 cm long?

[safe radish]

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[supple valve]

the claim is let p and q be distinct prime numbers

then the sqrt(pxq) is irrational

so im supposed to fill up this proof by contradiction

im confused on how we get from the Line 2 to Line 4

like what would LIne 3 be'

as of right now im sure u sqare both sides to get pxq = n^2/d^2

but how does that make n^2 divisible by pxq??

idk how to explain that

[livid dove]

Exactly like that

Youre proving that pxq is rational

Cuz n/d is rational, so is nsquared/dsquared

And n squared is divisible by pxq because there exist d squared such that pxqxdsquared is n squared

[supple valve]

ohhhh

ty

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[hollow crow]

Hello

[hollow crow]

Why is (a + b) (a - b) not equal A² - B²

In matrix

[icy lance]

BA doesnt necessarily = AB

so they wont necessarily cancel

in simple: matrix multiplication isnt commutative

AB!=BA most of the time

[hollow crow]

Ohh right

Thanks

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[tawdry acorn]

Need help wtih Complex Analsis question

[minor goblet]

context?

what specific subject were you learning when this question came up

[tawdry acorn]

Use of logarithms in complex analysis

[minor goblet]

can you take a screenshot without cropping everythng around the question?

i.e. what ist he "for instance" referring to

[tawdry acorn]

Oh ok

This is from the lars ahlfors textbook

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[karmic hedge]

Take 5^10 modulo 4

[lean otter]

you know 5 mod 4 = 1 so therefore 5^n mod 4 = 1, bec like 1 * 1 * 1... = 1

so its just i^1

which is i

wdym?

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[lean otter]

Is what I did in the end allowed?

[icy lance]

replacing 1/c with C?

[lean otter]

Yes

[icy lance]

yeah, C is just a constant

[lean otter]

Ok

Thanks

[icy lance]

could write A if you wanted

[lean otter]

Ill keep track don't worry

Thanks a lot

.close

It's already closed rip

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[fathom perch]

Can someone help q1?

[little barn]

!show

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[fathom perch]

Question f

For question 2 b

Is this right

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[hallow moss]

I do not understand

[hallow moss]

C superset S, C is a convex part

How is the expression saying the same thing as conv(S) is the minimal convex set that contains S

[thick otter]

Since the intersection of convex sets is a convex set, the ''minimal'' convex set is obtained by doing the intersection of all possible convex sets

[quiet juniper]

Show that if A is arbitrary convex set that contains S then all the elements in conv(S) are in A, which is ez to show by definition of convexity

[hallow moss]

Thank you, this helped

[hallow moss]

Does this show that conv(S) is necessarily the minimal convex set?

[quiet juniper]

If you also show it's convex (again, ez) then yeah

[hallow moss]

Ah got it, thank you two

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[lean otter]

Hello! I'm answering a questionnaire my trainer sent me and I'm struggling with this number;

If $a>b>1$ and $\frac{1}{log_ab}+\frac{1}{log_ba}=\sqrt{1229}$, find the value of $\frac{1}{log_{ab}b}-\frac{1}{log_{ab}a}$

[flat frigate]

Cerise Aurium

[lean otter]

My current solution:

Let $x=log_ab$
$$x+\frac{1}{x}=\sqrt{1229}$$
$$x^2-\sqrt{1229}x+1=0$$
$$x={35.028, 0.028}$$

[flat frigate]

Cerise Aurium

[lean otter]

$$log_ab=35.028$$
$$b = a^{35.028}$$

[flat frigate]

Cerise Aurium

[lean otter]

<@&286206848099549185>

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[lean otter]

<@&286206848099549185>

!!!<33

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[dry hinge]

do some log rules

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[karmic cobalt]

Hi

[karmic cobalt]

Can u help me pls ?

[dapper venture]

Find the function of the two lines

And combine them to a piecewise function

[karmic cobalt]

1.y= 2x-6

second function is y= | x-3 |

[dapper venture]

Why the absolute value

[karmic cobalt]

isn`t it absolute value?

[dapper venture]

It's just 3-x

[karmic cobalt]

idk is is one fuction or 2

[dapper venture]

Oh wait you want to write it as absolute value?

[karmic cobalt]

yeah

is there any way without absolute value?

I am new here, can you write on the paper then share it?

[dapper venture]

I thought you want a piece wise function

Oh a formula ok

[karmic cobalt]

idk what to do there

i need like this wait 1 min

[dapper venture]

Oh

That's a piecewise function

[karmic cobalt]

yep

[dapper venture]

Ok so you don't need to use absolute value here

[karmic cobalt]

okay

[dapper venture]

The first line is 3-x and what's the domain?

[karmic cobalt]

domain is -infinitive to 3

or how?

It is not R i guess`cause its piecewise

[dapper venture]

Not infinity

It stops at x=0

[karmic cobalt]

yes the x is between 0 and 5

like x greater and equal to 0

Also x is less than and equal to 5

like this ?

the mid point is (3,0)

[dapper venture]

Ya

So the first line is from x=0 to x=3 and second line is from x=3 to x=5

[karmic cobalt]

yes

[dapper venture]

Write down the line equations with their domain

[karmic cobalt]

it decrease and then increasing

[dapper venture]

Yes?

What's wrong

[karmic cobalt]

I couldn`t get that I need a formula

I have 3 point

0,3 3,0 5,4

[dapper venture]

Write in this form

[karmic cobalt]

the problem is idk know how to write😅

idk the piecewise function

is it possible not to tell just write on paper the solution and show me

[dapper venture]

List the functions and their intervals

[karmic cobalt]

so there are 2 linear functions that combined together

[dapper venture]

Ya

[karmic cobalt]

But i write 2x-6 and absolute valuse 3-x

its wrong ya ?

[dapper venture]

but it's not |3-x|

[karmic cobalt]

thank you I get it

Can I send u one pdf

?

its homework I did till 6 and 7 u helped me

Just I need to check the one Q

this one

I write the solution wait

is it correct ?

[dapper venture]

f(x) = -1 is a horizontal line

@karmic cobalt

[karmic cobalt]

yeah I write it in graph

y= -1

[dapper venture]

wait

why is there 3 lines

this is pretty wrong

[karmic cobalt]

hmm can u write it ?

[dapper venture]

try to correct it yourself

you can do this

[karmic cobalt]

I need to see mistake where I did it

[karmic cobalt]

let me try

wait

the one that y= -1 stops 1 ya ?

and i dont need the upper that i write its just like that. y= -1 stops at 1 point then it continues with point (2,3)

like this ?

[dapper venture]

yes don't need the upper line

[karmic cobalt]

wait I will rewrite on graph

Like this ?

I guess I did correct know

[karmic cobalt]

?

.close

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[teal finch]

T (n) = n^3 + 10n^2 − 5. Prove that T (n) = Ω(n)

[teal finch]

what is the formal way to solve this

without using limits

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[teal finch]

.close

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[lone crescent]

Lets say we have f(x)=f(x+y)+f(x) or whatever 3 functions then we have 1 constant solution right but then lets take function from both sides(it is legal), then
f(f(x)=f(f(x+y)+f(x)) f(x)=c infinity constant solutions. Then how we even can talk about proving all solutions if they are changing with each substitution?

[lone crescent]

I dont understand how it works tbh

[obsidian oracle]

Are you talking about functional equations? Your example is not the best to portray it

[lone crescent]

yes

I just wanted to show that number of solutions change with each my substitution

[obsidian oracle]

Also when you reach "f(x) = c constant" you might have not finished refining to only get correct solutions

Plug it in back to the first equation and c = c+c, so c = 0

[lone crescent]

yep but what How do I know which functions are valid and which arent

[obsidian oracle]

So until you're sure that every single solution you've reached actually works (you can prove it by plugging it back in the original equation), keep going

[lone crescent]

because by this logic I can get nearly infinite amount of solutions through substitutions

Checking them all is definetly not a way to do it

[obsidian oracle]

If you work your way through, you definitely will not have to check through all cases

[lone crescent]

Yep but how do I prove I found all functions if there is infinite amount of substitutions

[obsidian oracle]

Let's take for example f:Z->Z such that f(x+y) = f(x) + f(y)

[lone crescent]

for example I can get f(x)=0 and it will work but I have 2 or 3 more possible

[obsidian oracle]

If you managed to prove that you MUST have f(x) = 0 in your analysis, then there is nothing left to try finding

[obsidian oracle]

And we proved it here for example

[lone crescent]

no there is more solutions

and I even see that

[obsidian oracle]

Not in the original equation you wrote

[lone crescent]

it is some special equation I guess

[obsidian oracle]

You wrote f(x) = f(x+y) + f(x)

[obsidian oracle]

It's not the same equation as you wrote so yes there will be more

[lone crescent]

so no need to prove solutions in your example

[obsidian oracle]

Well : as soon as you prove (for this equation) that f(x) = xf(1)

[lone crescent]

yea bad example

[obsidian oracle]

You want to show that all of those work

Well let f(1) = a

So if we let f(x) = ax

We do see that f(x+y) = a(x+y) = ax+ay = f(x) + f(y)

And even though there is an infinity of functions that are potentially solutions, we just proved in 1 line that they all are solutions

[lone crescent]

Let me show my example P(0,x)then in my case
f(x)=f(0)*f(x)+0+xf(0)

I know that f(0) is either 0 or 2 so if f(0)=0 f(x)=0 but I know that there is at least one more solution

that I ironically found by my own mistake but it worked

[obsidian oracle]

f(0) = 0 or 1 you mean