help-0

[winter salmon]

<@&286206848099549185>

[true pulsar]

Is $\sqrt{z} = \sqrt{-48 + 14i}$ ?

[ocean seal]

hello2248

[shrewd topaz]

hello any clue

this is a mock test btw

[primal ether]

...

[winter salmon]

yea

[shrewd topaz]

[true pulsar]

Do you know De Moivre's formula?

[winter salmon]

uh nope

[true pulsar]

That's the only way I can think of to solve that problem

[winter salmon]

could you tell me how to work it out with the formula

[ashen oriole]

hey guys

[true pulsar]

Note that the sqrt is equivalent to raising to the 1/2th power

[ashen oriole]

would anyone be able to help me with understanding the level set of root(xyz) which contains 3,0,-5

[true pulsar]

#❓how-to-get-help

[winter salmon]

would n be 1/2

[true pulsar]

Yep, it's just another way to write the sqrt

[winter salmon]

im very confused could you show me how to do it step by step

[true pulsar]

So you first have to rewrite the complex number in polar form

Do you know what polar form is?

[winter salmon]

uh

no

[true pulsar]

Jees what class is this for? 😂

[winter salmon]

pre calc and im not even in high school

[true pulsar]

Ohh I guess they want you to do it the lame way

[winter salmon]

[true pulsar]

They want you to recognize that $-48 + 14i = 1 + 14i - 49$

[ocean seal]

hello2248

[true pulsar]

Which you can factor

[winter salmon]

oh

2(7i-24) right

[true pulsar]

No not that factor

The other factor xd

Like (x+1)(x+1) = x^2 + 2x + 1 factor

[winter salmon]

oh

lmao

my brain isnt working properly hold on

idk how would you factor it

[alpine sable]

just need help with these 2 questions

1. How much must we invest today to generate monthly $600 payments for 7 years at 4% compounded monthly?

and

2. Determine the amount we would have if we invested $850 every 3 months for 5 years into an annuity offering 6% per year, compounded quarterly

[primal ether]

i^2=-1

[winter salmon]

where did i^2 come from

[true pulsar]

So the 1 is obvious right, it has to be 1 * 1, meaning we know (1 + a) (1 + b), we just have to find a and b

-49 is (7i)^2

[alpine sable]

oh sorry i dint know this room was getting used

[true pulsar]

All good mate

[winter salmon]

ohhhh

[primal ether]

this would be in the form (1 + a)^2

because it has to be rooted

[true pulsar]

Yeah

I was just going for the general factoring process since he seemed confused on that specifically

[winter salmon]

so (1+7i)^2

and since its sqrt

[true pulsar]

Right

[winter salmon]

it would just be 1+7i

[true pulsar]

Yes

[winter salmon]

oh damn that was much easier than i expected it to be

thank

s

[true pulsar]

No problem

[south abyss]

hihi
https://gyazo.com/dcdf10590c81a61ee0ccf0fff488d8af

[still steeple]

oops

sorry

u can go ahead

[lapis valley]

do u have the answer with u?

im not good at combinatorics so i want to make sure that im right

[south abyss]

I'm being answered in #help-1 sorry for wasting your time

[lapis valley]

ohk

np

Ye its 7C4, because there is only one way to arrange the 4 digit in ascending order

so combination instead of permutation

[south abyss]

ohhhh

no like but

it can be

1279, 2479, 1457, anything

that's increasing

[lapis valley]

Yea

they correspond to 7C4

[south abyss]

it can't be like 1532

[lapis valley]

u are choosing 4 things from 7 options

[south abyss]

but you can't do 1532, 1952,

[lapis valley]

and all these numbers that u mentioned above are 4 distinct things

[south abyss]

oh

ok

[lapis valley]

is it confusing?

[south abyss]

kind of

i have more questions like this

[lapis valley]

suppose you take 1, 2, 3, 4

[south abyss]

for example

wait ill listen

[lapis valley]

there is only 1 way to arrange them

[south abyss]

yea

yeah

but you can also do

[lapis valley]

and there are 7 options

[south abyss]

1423

1324

4123

4132

[lapis valley]

yes but thats not ascending order

[south abyss]

but won't 7c4 include ALL of those?

[lapis valley]

ascending order means smallest digit first and gradually increasing

[south abyss]

i know

but 7c4 includes all of those

[lapis valley]

no beacuse its combination

[south abyss]

ohh

okay

[lapis valley]

7p4 will include all of those

[south abyss]

OH

I GET IT

[lapis valley]

lol

[south abyss]

i have 2 problems like this

[lapis valley]

ok

[south abyss]

https://gyazo.com/62ee344bc9eb543c07e7de14424f41be

oh and know a website where i can learn latex easy? so i can put it in the bot to make it easy to see

[lapis valley]

no im not good with latex either

[south abyss]

ohh

okay

[lapis valley]

ok give me a few min ill try

[south abyss]

nono

its fine

[lapis valley]

why

[south abyss]

i just want to know how to do the question

[lapis valley]

i like these questions

oh yea

i was talking about that

[south abyss]

OH i thought you were talking about the latex thing

LOL

[lapis valley]

lol

[south abyss]

ok

thank you 😭

[still steeple]

can anybody help me with this?

im not sure how to approach this

[south abyss]

5 = f(x)

start with that

[still steeple]

wouldnt it be f(1)=5?

[lapis valley]

do u know the answer to this

[south abyss]

no

[lapis valley]

ok

i got 5!*5

[south abyss]

ohh how tho?

[primal ether]

f(2x) stretches the graph horizontally (doubles the x)
2f(x) stretches the graph vertically (doubles the y)
-f(x) reflects the graph in the x-axis (flips sign of y)

[lapis valley]

suppose there are 5 gifts at first

use other channel plz

[still steeple]

THX

[south abyss]

but it's 6 gifts tho

[still steeple]

caps* (I thought u guys were done sorry)

[lapis valley]

so suppose there are 5 gifts, and they are each handed to one child. There are 5! ways to distribute the gifts keep in mind that everyone needs a gift

do u get this

[south abyss]

but there are 6 gifts tho

[lapis valley]

yes i know

[south abyss]

one child has to get 2

[lapis valley]

so i said suppose

to make it simpler

[south abyss]

ohh

[lapis valley]

im breaking the question in bits

[south abyss]

ohh

[lapis valley]

do u understand the 5!

[south abyss]

yeah

5! == uhh

120

[lapis valley]

but do u know why i did 5!

[south abyss]

i don't know but i do that with other problems

i just don't know why it works

[lapis valley]

ok so if there are n distinct things put in an order there are n! ways to rearrange them

[south abyss]

okay

[lapis valley]

and then since the last remaining gift can be handed out to any student

we multiply 5 with 5!

[south abyss]

ohhh

i understand

[lapis valley]

ok

nice

[south abyss]

so

that would be

25 * 24

which is uhh

like

600

okay thank you

[lapis valley]

cool

[south abyss]

and last one i promise LOL

[lapis valley]

its good

im enjoying

[south abyss]

https://gyazo.com/11ae32f4faf476e09c44262dd91b47a6

i think i know where to start

the first one can have like

8 possibilities

the second one is 7

third one is 7

and everything after that is 6, 5, 4, 3, 2,

is that right?

another channel pls

[lapis valley]

how are u approaching this

are u looking at contradiction?

[south abyss]

?

whats contradiction again

in math

[lapis valley]

so like false statement

[south abyss]

complementary counting?

[lapis valley]

so u are looking for ways to arrange in which twos e are next to each other

i think thats easier

[south abyss]

ohh

so there would be like

uhh

6 ways

[lapis valley]

why 6

there should be way more

the word is 8 letters

[south abyss]

O

7?

to put 2 E's together

[lapis valley]

suppose the two es are at front

[south abyss]

1 way

[lapis valley]

then the other 6 letters can be arranged in how many ways they want

[south abyss]

OH

OH

okay

so 6!

[lapis valley]

yes

[south abyss]

is uhh

[lapis valley]

ok this is quite hard

[south abyss]

720

[lapis valley]

and annoying

[south abyss]

so it would be 720 * 7

[lapis valley]

i might get the wrong answer

[south abyss]

which is 5040

no wait

yeah it is hard lol

[lapis valley]

6! is right

but two consecutive Es can only occur in 6 ways

in a 8 letter word

[south abyss]

yeah

no wouldn't be 7

[lapis valley]

so 1,2 2,3 3,4 4,5 5,6 6,7 7,8

oh wait

yea ur right

wtf i used my fingers lol

to double check

[south abyss]

_______
EE
aEE
aaEE
aaaEE
aaaaEE
aaaaaEE
aaaaaaEE

[lapis valley]

ok that was a noob alert

lets move on

[south abyss]

LOL

[lapis valley]

so u are ahead of me

[south abyss]

no i am not

so 6! * 7?

[lapis valley]

5040

[south abyss]

which would be 7!

which is 5040

so

[lapis valley]

yea

[south abyss]

i do 8! - 5040?

[lapis valley]

so that are the number of ways that doesnt work

we cant do 8! in this case because there are like terms

[south abyss]

ohh

[lapis valley]

remember this

the e is not distinct

[south abyss]

true

its uhh

i forgot the word

[lapis valley]

suppose we have 112, then the number of ways to arrange would be 3

[south abyss]

undistinguishable

[south abyss]

yeah

[lapis valley]

we use the formula n!/(number of like terms!)

so in this case

[south abyss]

8!/3!

[lapis valley]

the number of ways to arrange would be 8!/3!

[south abyss]

oh ok

3?

[lapis valley]

yea

there are 3 es

[south abyss]

OH

ok

im stupid lol

8!/3! is uhh

6720

[lapis valley]

wait

rly?

[south abyss]

i think so

[lapis valley]

did i mess up?

i think i did

wait give me sometime i need to go back

nvrmind i cant find the error

[south abyss]

okay

[lapis valley]

i might be right

50-50

ok so the answer is 6270-5040

total-contradiction

1230

[south abyss]

okayy

THANK YOU

[lapis valley]

can u DM me if i got any of the questions wrong?

np

[south abyss]

sure! you're awesome

[lapis valley]

thanks man

that was some good practice

[dark granite]

That isn’t the right answer @lapis valley @south abyss

[lapis valley]

yea

i noticed

i told him in the dm

is 2400 correct?

what did u get

[dark granite]

2400 is right

[lapis valley]

ok thanks dude

[dark granite]

Cuz it’s $5!\binom{6}{3}$

[ocean seal]

logician_pdx

[dark granite]

You’re welcome!

[lapis valley]

yea

no of ways to put in 3 E's such that no E's are consecutive* 5!

[dark granite]

Yeah it’s easier to see that if you place the non-E’s down in any one of 5! Then place the E’s as needed

[clever hare]

hey guys im wondering if i did this question right

[dark granite]

It’s hard to say without the question lmao

[alpine sable]

How could I solve this without using conjugates or imaginary numbers? Cause it's beyond the curriculum.

What I have tried:

Ignore the cross please

[alpine sable]

I am getting stuck on the last step because I can't figure out another equation to make a system

And even tho I tried making another system it didn't work, because it was probably pure randomness, handwriting too bad and unreadable for me too in that part so I can't send it

need some help with this to see if im doing it correctly

this channel already has a open question

please move

ok

@alpine sable I'm trying my best to decipher your handwriting. I'm not going to say I know how to solve it because I don't (at the moment, my brain is kinda flopped.)
Have you tried this:

sorry for bad handwriting lmao

$f(1+\sqrt{3})=0$\$0=a(1+\sqrt{3})^2+b(1+\sqrt{3})+c$\$f(2)=-2$\$0=a(2)^2+b(2)+c+2$

???

Oh

Oh

Oh damn

Ok one error in 2nd step

There's going to be c in the last

oop that was my bad lol

So this gives me a and b

[ocean seal]

Cicopath

[alpine sable]

And I can probably solve it now

But

Lemme try

Oh yes

I did try this

My initial attempt looks pretty much like this

Then again, to solve for 3 variables, you need 3 equations. I might be going about this the wrong way, I apologize

My brain is fried today, see if somebody else can help ya out

I just asked my math teacher

[alpine sable]

No problem mate

Hope tomorrow is a better day for you

Yes

It can easily be solved by taking the conjugate of the complex root 1 + root(3)

But it's outside the syllabus so I can't use that

[ionic jewel]

also it's not true

1+root(3) isn't complex

its (real) conjugate is not necessarily the other root

[alpine sable]

Oh

My grandpa said that actually I don't know about complex numbers

[ionic jewel]

ah i see

complex numbers only show up when you take the square root of a negative number

written as i

[alpine sable]

i = root(-1)

[ionic jewel]

$i^2 = -1$

[ocean seal]

bunny

[ionic jewel]

but yes

and yours doesn't have that

it's a real number

[alpine sable]

I see

So

[ionic jewel]

I'm fairly sure your problem is solvable but i rather don't see how either

[alpine sable]

We can't take the conjugate of 1 + root(3)?

[ionic jewel]

you can, it's 1-root(3) but it doesn't help you

[alpine sable]

Okay

Lemme show you what he did

This

[clever locust]

How are complex numbers even relevant to this problem?

[alpine sable]

Probably aren't

Cause - in a root doesn't come up here

[ionic jewel]

yeah his solution makes an assumption I'm fairly sure is wrong

[alpine sable]

Here

[clever locust]

One root being 1+√3 does not in any way mean the other root is 1-√3

[ionic jewel]

actually you just don't have enough information to solve this now that i think about it

[alpine sable]

Lemme Google search ig

[ionic jewel]

you can pick any arbitrary root to be the other root and you can find a solution

[clever locust]

This^

[alpine sable]

[clever locust]

But you should be able to find b and c in terms of a at least (or some other permutation of this)

[ionic jewel]

the relevent rule is for a polynomial with real coefficients, if it has one complex root, the conjugate of that root is another

but you don't have any complex roots, they are both real

so the rule doesn't apply

[clever locust]

Actually, this might be solvable due to a,b,c being rational and not just real

Though I haven't tried it lol

[alpine sable]

Uh

Basically what I have written in my solution

[ionic jewel]

that's 2 eqns 3 unknowns, it's not enough

[clever locust]

To summarize the important parts of the problem (at least as of right now), you know that:

$$p(x) =ax^2+bx+c$$
$$p(1+\sqrt{3})=0$$
$$p(2)=-2$$

[alpine sable]

Wo

[ocean seal]

Lorago

[alpine sable]

Wow

[ionic jewel]

yeah it gives you two points, and you need 3 (nonvertex) points to express a parabola

[analog fable]

What is a policy

[alpine sable]

Where did 4a go

And why is it - b

Oh

I sense a mistake here because you took 2 common but a is outside the bracket and there is no 2a for you to get that

[wise sigil]

Here's one way to solve it:
Since the sum of the roots x + 1 + sqrt(3) is rational, you have x = p - sqrt(3) for some rational number p
Now since the product of the roots (1 + sqrt(3)) * x = (1 + sqrt(3)) * (p - sqrt(3)) = p - 3 + (p-1)*sqrt(3) is also rational you find that p = 1 and so x = 1 - sqrt(3)

[ionic jewel]

vietas formula?

[clever locust]

Really nice solution

[alpine sable]

Is this channel free

I'll take that as a yes

Should we take 5 as an axiom, why should I agree to the assertion that it's a priori

[young granite]

help me unprove this if possible

[oak chasm]

@young granite Sorry, channel is busy.

[young granite]

kay

[alpine sable]

<@&286206848099549185>

[solid iron]

that's a long ass text

[alpine sable]

I'm just curious about the (5)

[warped phoenix]

oh boy

hes really going at it

[solid iron]

@alpine sable Now I don't know if whatever that text is, even related to maths but what I could deduce is that it's talking about naming things

From what I could understand (5) should be an axiom since X is just the name of the Φ's, viz, the properties X is made up of.

For example, you as a human being have some fundamental properties of life that are present in all living organisms, and you are also constituted of the unique DNA that you have which make up specifically just you, and no one else in the universe (probably), hence the unique DNA is also one of your properties BUT those unique properties aren't the only things that make you, YOU. The human brain excels at plasticity, thus if we were to clone you but raise your cloned twin in a different part of the world, fundamentally you both would possess the same properties but your brains and how they work needn't necessarily be the same even though you're both 99.99...% the same.

Thus you, Leonbukvan, are but a collection of properties and therefore that collection of properties will of course intersect with the collection of properties that you have, most, not necessarily all (as explained earlier), would.

Hence I would take (5) as a priori

but of course, I could also be wrong since I don't exactly know the context of those assertions or even the field to which they belong

[alpine sable]

I mean it's logic

[radiant island]

How I continue ?

[alpine sable]

Yes but looking at it like this. If leonbukvan exists then leonbukvan has most leonbukvan properties should be known a priori. But if someone doesn't know leonbukvan or what properties leonbukvan constitutes from to be defined as a human being could someone with no prior epistemological experience about that subject know this RIGHT AWAY. Again I might be going totally wrong about this.

[solid iron]

hm you make a good point

but I feel like that should be answered in the text

[alpine sable]

Kripke isn't very good at that

I can send you the text

I mean it's linguistic logic

Technically math but right at the edge

[warped phoenix]

bruhhhhhhhhhhhhhhhhh

wtf

what does this do

for like

[solid iron]

I think (5) just means that X has most of the properties which constitute X

[warped phoenix]

humanity's progress

i just read this whole conversation and feel like im in an alternate dimension

[solid iron]

rather than arguing about if you'll know the name of X, you'll know the properties of X

[viscid cove]

can someone help me

ignore the limits, what happened to the second sine ratio from the first to the second step?

it goes like this,

send help pls

nvm, its probably a typo

[cinder shard]

This is such an easy question so I don't understand how this is wrong

I know there's a solid square colored in, but it has no dimensions other than that 15 it shares. The other measurement could virtually be anything

[alpine sable]

hmm

[cinder shard]

I have no idea what I did wrong or what the question might be asking other than the area of the triangle

Okay I did something wrong, but the correct answer isn't even present

the 15x15 acts as a square

you cut it in half = triangle

so 15 x 15 x (1/2) = 112.5

But thats not even an answer

[alpine sable]

huh

[cinder shard]

Triangular face would just be the area of the triangle right?

[alpine sable]

you cant do that

[cinder shard]

A right triangle in a 10x10 is effectively half of the area

[alpine sable]

you could divide the triangle in half but what would the height be?

oooh

[alpine sable]

it is not a right triangle.

angle ABC is not a right angle

[cinder shard]

why is there a random rectangle not to it

wtf

[alpine sable]

if you want you can use herons formula for an overkill but just draw an altitude from B to AC and pythag to find the height

[vale sapphire]

gut check for why this can't be a right triangle : 15²+15² has a high likelihood of being divisible by 5

[cinder shard]

what is the rectangle for though

[alpine sable]

ohhh

hahaha its meant to be a 3d solid

its a really bad drawing lmao but try to think of the rectangle as like another side of a triangular prism

@cinder shard Have you figured out the answer?

I suppose the rectangle is there because ... it's there

Sooo

Doing maths

no

don't do math

how do you find the center point of this? i have the limits and know where the intercept is.

Ive just thought about the fact that x has a range of six. and since its starts at -2 the center has to be 1 on the x axis

is that the proper way to think about it?

[placid zinc]

Is there a set of values for t?

Either way, the center is (1,0)

Yeah you've got it

[alpine sable]

nah no set of values 🙂 was just to draw it

[lilac pollen]

you guys are loykey geniuses

[gaunt magnet]

hi

My answers

[gaunt magnet]

<@&286206848099549185>

[alpine sable]

someone explain what the fuck is going on

b

[upper furnace]

0.15 * 2 * 1000 + 0.15 * 1/2 * 8 * 1000

[mortal void]

is this channel free now?

so i can ask my doubts?

<@&286206848099549185>

[glass lichen]

why did you ping helpers if you never posted a question......?

[mortal void]

pls tell whats the fault i did here

[mortal void]

cause i was waiting for someone to arrive usually you dont get your answer if you post and left it there

[alpine sable]

guys if anyone know anything about "linear law" pls let me know what it is

[glass lichen]

why is there an x in between the brackets?

also no clue if the initial term is suppose to be .7x or just .7

[mortal void]

sorry thats multiplication sign there

[glass lichen]

and why you have .7+3 instead of.. 3.7

yeah, dont use x for times if you're using a variable...

()() implies multiplication

[mortal void]

just .7

[glass lichen]

ok so why didnt you simplify .7+3 first?

then you'd only have 4 terms in the expansion

[mortal void]

okay i will keep that in mind

[mortal void]

lol right thankyou sir

[glass lichen]

That should've been something taught but ok

[mortal void]

idk why i even ignore very basics all the times

[ruby current]

what about the derivative of |x|?

what am i missing?

[glacial hedge]

Hi i am a little confused with how to do this

how do i find the coposite of a mtrix??????????

[shut rampart]

um

\

which one did i get wrong????

huhhh

doesn't make any sense

[sage jacinth]

you got the last one wrong

its asking for the probably of her choosing to walk to school and her being late as a result of her walking to school

not the probability of her being late if she chooses to walk to school

@shut rampart

[shut rampart]

oh

so than it is um

0.025

@sage jacinth

[sage jacinth]

yup

[shut rampart]

ok

thanks man

[sage jacinth]

np

[shut rampart]

i always forget to read closely

@sage jacinth

i think im good at math but i never take the time

[sage jacinth]

yea with these probability problems its crucial to read closely

exactly why i dislike probability in general

[pearl marlin]

First make soT

[vapid seal]

Please help me get solution

[ionic jewel]

try #linear-algebra

[vapid seal]

I have no permission to ask answer there

Can you Please help me to get unlock there or getting me answer

[placid zinc]

@ruby current
Little late to the party, haha.
|x| does not have a jump discontinuity. In fact, it is continuous everywhere.

[alpine sable]

Is this channel still being used

Oh nevermind

multiplying a 2x4 matrix by a 4x3 matrix has a 2x3 matrix product

is that because

oh nevermind i got it

[severe socket]

what do i do when all channels are being used

[left echo]

anybody know how to do number 2

[glacial hedge]

use a double angle formula...

hint

sin^2(x) = 1/2(1-cos(2x))

[left echo]

okay thx

[glacial hedge]

I am a little confused.... isn't it D? because -t^3y^2 is always continuous and del (-t^2y^2)/del(y) is always continuous???

[glacial hedge]

represent 3.12 as decimal then represent 0.007 repeating as a decimal and add them

*hint

[alpine sable]

oh sorry the question is wrong

represent as fraction

lmao

[glacial hedge]

yeah i assumed that was what you meant

also hint

[wild marten]

let x = 3.127777....

[glacial hedge]

0.007 repeating is 7/9 / 100

[alpine sable]

oh

yeah

[wild marten]

multiply both sides by 100 to get 100x = 312.777...------(1)

multiply (1) by 10 to get 1000x = 3127.777...----(2)

[alpine sable]

oh i got it

[wild marten]

now perform, (3) - (2) to get :
900x = 2815
x = 2815/900
x = 563/180

[alpine sable]

we sud do 1000x-100x

[wild marten]

yes

[alpine sable]

yeah

okay

ty!

[wild marten]

welcome!

[ionic jewel]

the average rate of change is going to be the slope of the line between the two points

[severe socket]

1/2

?

[ionic jewel]

i cant read the axis but looks about right

[next hatch]

im working on 6i rn

and i think ive got it but it seems weird

like its not a satisfying answer

could someone confirm please

[rigid smelt]

the derivative of x^5 - 6x^2 + 4 isnt 5x^4 -48x

thats the only mistake in the problem

the other places look good

[next hatch]

right yeah thanks for that

[upper pebble]

any idea as to what the reason is for the difference in answers here?

the bottom one is Desmos

[ionic jewel]

,w arcsin(4/3*sin(40 degrees))

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[ionic jewel]

@upper pebble the first one computed it in radians, then converted the final result to degrees (incorrectly), the second one kept it in degrees the entire time (presumably what you want)

[upper pebble]

i see

thanks

[old swan]

Can someone explain how significant numbers work again?

Calculate 510.484 ft + 841 ft. Use the correct number of significant digits in the answer.

[upper pebble]

Rounding Significant Figures Rules

1. Non-zero digits are always significant
2. Zeros between non-zero digits are always significant
3. Leading zeros are never significant
4. Trailing zeros are only significant if the number contains a decimal point

For addition and subtraction, the answer should have the same number of decimal places as the term with the fewest decimal places.
For multiplication and division, the answer should have the same number of significant figures as the term with the fewest number of significant figures.

[old swan]

Thank you

[glacial hedge]

Is there a way to do this... without doing a crap ton of computations?

like a theorem i can use?

i wouldve tried using the PDP-1 diagonalization thing

but

um...

cant exactly diagonalize a non square matrix

[pearl marlin]

Can you find sot?

[alpine sable]

help i don’t know how to find the measure of angle ABC and ABC

[rigid smelt]

ACD = 180

because A,C and D are linear

[alpine sable]

oops i meant ABC

sorry

[rigid smelt]

can you find ABD, CBD and BCD?

[glacial hedge]

yes... i found it

just have to multiply the 2 matrices first before plugging in the basis'

[zenith hemlock]

Did I do something wrong? idk how to find numerical value of cos^2. I found tan(pie/2)=1 using calculator

[rigid smelt]

tan(pi/2) != 1

it is undefined

i supposed you mean tan(pi/4)=1 which is correct

for the rest just plug pi/4 into x^2 and then simplify if possible

[ruby current]

find the numerical value of cos(pi/4) and then square it

cos^2(pi/4) is the same thing as (cos(pi/4))^2

[zenith hemlock]

oh yeah....

[ruby current]

it's just a notational thing

[zenith hemlock]

hahahahahha

[zinc stirrup]

how to prove this rigorously? the limit with upper bar is supremum of limit set

i was trying to proof by contradiction ,i have no idea what should i do next. i let the X, Y as corresponding limit set of xn and yn

[noble sinew]

Is it lim sup or sup?

[zinc stirrup]

lim sup

[noble sinew]

Okay so you started with suppose for contradiction? Then we have lim sup X_n < lim sup Y_n. From definition we then have a subsequence for X_{n_k} that converges to some x< lim sup Y_n

Should end up with a contradiction if you think about what that implies

[zinc stirrup]

you mean $x_{n_k}$ will smaller than a $y_{n_k}$ that converge to some $l>limsup{x_n}$ , so i can say contadiction occurs by order rule?

[ocean seal]

mikeqwertyuiop

[zinc stirrup]

will there be any problem about the indices? actually the statment did not mention $x_n \geq y_n \ \ \forall N$

it only saids $x_n \geq y_n$

[ocean seal]

mikeqwertyuiop

mikeqwertyuiop

[noble sinew]

Not sure what you mean by order rule. But yes you will reach a contradiction

And x_n>=y_n implies it is for all n

Otherwise it isn’t even true

[zinc stirrup]

sorry its non official name, i mean if $x_n>L$ where $x_n$ converge to M then $M \geq L$

[ocean seal]

mikeqwertyuiop

[noble sinew]

Well true if it holds for any n>=z but doesn’t change the proof

[zinc stirrup]

okay, but what i concern is how do I know the $x_n < y_n$ for the same n, this contradiction only shows there $\exists N>0$, $m,n>N$ such that $x_m<y_n$

[ocean seal]

mikeqwertyuiop

[noble sinew]

Oh ye we have for every subsequence the above right

[zinc stirrup]

what do you mean?

[noble sinew]

For every subsequence of X_n we have that they converge to a x_i which is less than a subsequence in Y_n

[zinc stirrup]

oh ye

🤪 are there easier way to prove🤣

[noble sinew]

But pretty sure you can say just say that for m>=w that y_m<=x_m<=sup_{n>=w} x_n

Since this is true for all m>=w you get sup_{m>=w} y_m<=sup_{n>=w} x_n

Now just take limit on both sides as w->inf and you are done

[zinc stirrup]

wait are we talking about sup of the limit set?

[noble sinew]

Sup at the start

[zinc stirrup]

is it still the same thing

[noble sinew]

Assuming you can use if x_n>=y_n then sup x_n>=sup y_n

[zinc stirrup]

but i am talking about a set containing all the limit that subsequence of x_n converge to

and the sup of that set

[noble sinew]

Yes

You take limit on last line

So now we have lim sup

[zinc stirrup]

oh yea

sorry i have just started the chapter of limsup , i havent prove the statment you hv mentioned🤣 so it takes me a while to think of that

@noble sinew btw is there any further condition regarding your definition? the take sup then take limit one

Anyway thanks so much

[noble sinew]

Not really - an inequality is perserved (if it was less than before it comes less or equal to after tho) when taking limits

Similar to squeeze theorem if you have heard of that

[zinc stirrup]

oh i see

[minor dagger]

Can I get help on these please

[pearl marlin]

which one?

[minor dagger]

All of them

Sec is sin/cos?

No, 1/cos

I'll paste the unit circle here

Would the line be at pi/3? @pearl marlin

[pearl marlin]

just solve sec(240 degree)

[minor dagger]

-1/2?

[pearl marlin]

sec(240)= 1/cos (240)

[minor dagger]

1/(-1/2)=-2

[pearl marlin]

yes

do you know how to convert radian into degrres?

[minor dagger]

Kinda

For b isn't it just sin(210) deg

1/2

[pearl marlin]

because for me deggre works very well ( but thats upon you )

[minor dagger]

Ooh it's a negative

It asked for the exact value

[minor dagger]

Sin(30) deg

[pearl marlin]

sine take out negative

[minor dagger]

Ok

For c, cot is 1/tan

[pearl marlin]

yes

[minor dagger]

C confuses me

[pearl marlin]

cot(240)= cot(180+60) , third quadrent

[minor dagger]

-sqrt3/2 and -1/2?

[pearl marlin]

tan is positive so cot is cot(60)= 1/tan60 =1/sqrt 3

[minor dagger]

1/sqrt (3/2)?

[pearl marlin]

1/tan 60 = cos60/sin 60 = (1/2)/sqrt(3)/2 = 1/sqrt 3

soory i MADE SOME MISTAKE THERE (I EDITED)

[minor dagger]

It's ok

1/sqrt(3)? Why not sqrt(3)/3?

[pearl marlin]

yes it can also be true

just multiply sqrt 3 in deno and nemo

[minor dagger]

Okay

Cos(-300) deg

[pearl marlin]

cos is even function it eats negative

[minor dagger]

1/2?

[pearl marlin]

cos (300)= cos(360-60) , fourth quadrent , cos is postive so cos60=1/2

[minor dagger]

Thank you, I also have other questions I'm a bit lost with

[pearl marlin]

you can post ( some other will help)

[pearl marlin]

just try to make the function

[minor dagger]

I struggle with these, I'm terrible at transformations

[pearl marlin]

dm me(if you want)

[vapid seal]

Please help me solving this

[vale wigeon]

this sure is a long paragraph

have you done any progress on this or do you expect someone to (a) read through all this and (b) give you the answer on a silver platter with zero effort on your part?

[ionic jewel]

i read it and there's not even a question attached, it's a bunch of costs for a business

[vale wigeon]

lmao

@vapid seal you haven't even posted a question

[vapid seal]

Amm

[ionic jewel]

i imagine there's like another screenshot thats supposed to be below it

but that involves more reading

[vapid seal]

Please try I'm confused in solving this

[vale wigeon]

there's nothing to solve here sumit

[ionic jewel]

^

[vale wigeon]

did you mean to send multiple screenshots?

[alpine sable]

can someone help me with this please

i solved 2 parts the 3 i can't

[jagged imp]

it wants you to use pythag identity to simplify 9sin^2(t)+9cos^2(t)

[jagged imp]

this sentence makes 0 sense btw

oh... "I solved the first two parts, I can't solve the third"?

irrelevant regardless ig

[ionic jewel]

$\sin^2(x) + \cos^2(x) = 1$

[ocean seal]

bunny

[alpine sable]

btw fam it does not matter how something is written so as long as you get the point

like Einstein said there is more then one way to do something and i prefer the way i am

btw thx for the help

[jagged imp]

what i said was that i dont get the point

lmfao

so that kinda did matter

[carmine lion]

how to solve part (d)

[vale wigeon]

have you done parts a through c?

the strategies are similar for those

[carmine lion]

https://cdn.discordapp.com/attachments/818739351399825459/869507048738541568/473221703418511360.png

i've gotten 3 simultaneous eqns

[vale wigeon]

have you done parts a through c?

[carmine lion]

missing a 4th cuz theere are 4 eqns

[carmine lion]

yes

[vale wigeon]

okay

[sage summit]

why do you expect there should be a 4th equation ?

[vale wigeon]

so you know that an even polynomial will have roots symmetric about zero, yes?

[carmine lion]

because 4 vars needs 4 eqns to solve them?

[vale wigeon]

also, 4 vars?

[carmine lion]

$ax^6+cx^4+ex^2+g=0$

[ocean seal]

abe

[carmine lion]

because eveen

[vale wigeon]

overcomplicated

[vale wigeon]

.

[sage summit]

well have you read the second part of question d)

asking whether there is a unique polynomial satisfying those conditions

[carmine lion]

no, there isn't?

[sage summit]

right

there are not enough equations

[carmine lion]

because the y-int not given

[sage summit]

so just pick any of the infinitely many possible ones

or maybe just leave one parameter

tbh the question is unclear on what to do there

[carmine lion]

i have to find a faactored polynomial that satisfies part(d)'s requirements

i assume there will be 1 var remaining

like we discussed

because not enough info is given

[vale wigeon]

.

[carmine lion]

yes

i didn't consider it, but that makes sense

[sage summit]

what are the factors you found so far

[carmine lion]

uhh none

[vale wigeon]

so there are double zeros at ±1 and single zeros at ±2

[sage summit]

since apparently they want the answer in factored form

[carmine lion]

yes

[sage summit]

wdym none

[carmine lion]

i only have the 3 roots given

[sage summit]

that should be 3 factors then

[carmine lion]

yes

[sage summit]

so what are the factors you found so far

and lol I misread the question

[carmine lion]

$P(x)=a(x+2)(x-1)^2(x-b)(x-c)(x-d)$

[ocean seal]

abe

[sage summit]

I read double root at 0

xD

so yeah go read what Ann said

[carmine lion]

so there will be roots at -2 and 1?

then use the equations to find d?

[vale wigeon]

.

i have to say im a bit upset at how my messages get no reaction at all not even a "what did you mean by this"

[carmine lion]

sorry my bd

i was just thinking that you were reiterating my response

[carmine lion]

.

so there are 4 roots, 2 at -1 and 2 at +1?

and 2 roots, 1 at -1 and the other at 2

is that correct Ann

[carmine lion]

sorry

[vale wigeon]

man what a mess youve said up there

[carmine lion]

uh oh

[carmine lion]

what do u mean

[vale wigeon]

i mean exactly what i said

1 and -1 are each a double root
2 and -2 are each a single root

you have f(x) = a(x-1)^2(x+1)^2(x-2)(x+2)

[carmine lion]

alright

[carmine lion]

ty ann

[night sigil]

I have found that the values of M are 1,3,7,15 now how can I figure out what the formula is?

[blissful tinsel]

can someone help me with calculating the area of an helix?

[blissful tinsel]

<@&286206848099549185>

[sage summit]

so is your helix the set of points (r cos t, r sin t, t) for r in [0;1] and t in [0;2pi] ?

your picture looks like [0;3pi] for t

[blissful tinsel]

yes i believe so, my drawing is wrong

[sage summit]

then you just need to set up an integral and compute

[blissful tinsel]

i am a bit confused, should i use a line integral of a scalar field? and then set f = 1

or how do i set up the integral?

[sage summit]

what

you want to compute an area of a parametrized surface

so you have to integrate small areas

the small areas of the small helix pieces that are the image by (r,t) -> (r cos t, r sin t, t) of small rectangles [r ; r+dr] * [t ; t+dt]

[blissful tinsel]

mhmm

so i need a surface integral

[sage summit]

yes

[blissful tinsel]

like that? @sage summit

[sage summit]

yeah

isn't there a more explicit answer

wait why the + sqrt(2)

[blissful tinsel]

i used this

[sage summit]

,w integral from 0 to 1 of sqrt(1+x^2) dx

[ocean seal]

Results provided by WolframAlpha

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

Requested by Zef Klop 🍃 🌿 🌻#6420

[sage summit]

I guess it's true

idk a primitive of sqrt(1+x²) by heart

[blissful tinsel]

me neither

thank you 🙂

[pearl marlin]

F(G(4))=H(4) so F(2)=?

This will help

[alpine sable]

how would i do a question like this?

[blissful hamlet]

thank u

[sage jacinth]

find an equation that has a rate of change of 2

then you can just use point slope form and solve for y

[ocean seal]

(バカ) baka

[velvet condor]

baka~

[sage jacinth]

baka??

[velvet condor]

we bakas

[sage jacinth]

is that really you

[placid stag]

can someone please help me with this

[ruby current]

(x_1 + ... + x_25) / 25 = 36
(x_1 + ... + x_13) / 13 = 32
(x_13 + ... + x_25) / 13 = 40

[ruby current]

do you see why?

[placid stag]

yeah ik I'm getting stuck when i get here

[ruby current]

okay try multiplying each equation by the denominator

so that you just have the sums on the left side

[placid stag]

ohhh

thanks a lot

[ruby current]

happy to help

[placid stag]

I solved it as a system of equations with 3 unknowns

a = x_1 ... x_12

b = x_13

c = x_14 ... x_25

[ruby current]

nice

[rigid smelt]

what have you tried?

[blissful hamlet]

is the tangent line 2x/25=0?

cause then x would just be 0

meaning y has two solutions

and from there i get stuck

[rigid smelt]

there isnt a specific tangent line

but anyway, thats not what we are finding

we just need the slope of the tangent line

can you guess what that is?

[blissful hamlet]

2/25?

[rigid smelt]

no again, we dont need a specific tangent line

so there isnt a specific slope that we are finding

for example, with a problem like x^2 + 1, how do you find the slope of the tangent line to this?

[blissful hamlet]

you find the derivative

[rigid smelt]

yes

so the slope of the tangent line to the ellipse at (x,y) is the derivative of that equation at (x,y)

can you find the derivative at (x,y)?

and notice here that (x,y) is not known, hence there is no substituting and such

[blissful hamlet]

yea

i thought the derivative was 0=2x/25 tho

or am i doing that part wrong

[rigid smelt]

thats wrong

[blissful hamlet]

oop

[rigid smelt]

thats not any derivative either

thats just some random equation in x

[blissful hamlet]

so is it just 0

[rigid smelt]

no?

[blissful hamlet]

but 1 is a constant

[rigid smelt]

have you heard of implicit differentiation?

[blissful hamlet]

yea but i'm not good at it

[rigid smelt]

yeah but you need to do it

anyway

differentiate both sides of the equation

the right hand side is easy, as you said, derivative of 1 wrt x is 0

the hard part is the left hand side

can you do that for me?

[blissful hamlet]

yea i'll try

brb lol

i mean wouldn't you just use the power rule

[rigid smelt]

yeah ofc

but not just that

theres a reason i said implicit differentiation

derivative of y^2/9 is not as easy as it seems

[blissful hamlet]

i see

is it (2yd/dx(y))/9

[rigid smelt]

uh yeah

or 2y/9 * dy/dx

[blissful hamlet]

ok

so now i have 2x/25+2y/9*dy/dx=0

[rigid smelt]

yes

so find dy/dx

[blissful hamlet]

is that y/2x-4x/50y

[crude hazel]

how do you solve for p(x), q(x), and r(x) if √(x^3 + 2) = p(q(r(x)))

[rigid smelt]

channel is occupied please move

[rigid smelt]

no

its just algebra manipulation

"solve for dy/dx"

[blissful hamlet]

ohh i see. i guess i was thinking differentiation

k one second i'll solve that

so -18x/50y

[rigid smelt]

or dy/dx = -9x/(25y)

anyway thats the first part

now can you find when the slope is undefined?

[blissful hamlet]

would it be any point where y is 0

[rigid smelt]

yeah

[blissful hamlet]

ok! thank you so much bro i really appreciate it

[dense aurora]

Can someone help me with an inequalitie?

I need to prove the 3rd inequalitie

[upper pebble]

gotta get those 10 euros

[rigid smelt]

nice catch

[bitter sage]

can anyone help me find the local max and min of this equation?

y = 4/x - (cos0.1x^2 + 120)

[dense aurora]

The award time expired at 15th july 😭☠

[rigid smelt]

Yes definitely worth a ping

[neon igloo]

heyyy

help pls!!

any one here

[ocean seal]

Chai T. Rex

[oak chasm]

@neon igloo

[rare patio]

did you write those script from memory?

[wary zephyr]

hey can someone help me with this?

[oak chasm]

@wary zephyr Sorry, channel is busy.

[wary zephyr]

oh sorry :(

i thought they completed it

[hexed abyss]

hello?

i need help with a question

[oak chasm]

@hexed abyss Sorry, channel is busy.

[hexed abyss]

oh ok

[native temple]

if In conditional Probability

[oak chasm]

@native temple Sorry, channel is busy.

[native temple]

P(A | B) = $ \frac{P(A and B)}{P(B)}

[native temple]

No it isn’t

[oak chasm]

Yes, it really is.

The question was asked 13 minutes ago.

[native temple]

someone else asked a question before

so that overrides the other one

anyway

P(A | B) = $ \frac{P(A and B)}{P(B)} $

[oak chasm]

OK, so that question has the channel.

[native temple]

sigh where’s latex

no because they lef

as they were conviced the channel was active

P(A | B) = $ \frac{P(A and B)}{P(B)} $