help-0

[zealous lichen]

oh I meant pi

sry

[sage ore]

oh right

when i did B) what are the x intercepts I did:

ohh

[zealous lichen]

,rotate

[zealous lichen]

the function is not defined at pi

[sage ore]

i get it

[zealous lichen]

so the x intercept doesn't include pi

[sage ore]

yeah so i should do it seperately so sinx = 0 and 1+cosx=0

wait na

wait so hows a good way to show that and sorta see it coming before?

[zealous lichen]

find out the domain of the function first

[sage ore]

oh yeah

okay thanks

.close

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[worn hinge]

Am I missing something? how can I simplify this further?

[modern sedge]

You're missing parenthesis in wolfram

it should be d/dx (something something)

[worn hinge]

oh

[modern sedge]

,w differentiate 5x^2-4x+9-2/(3x^3)+4/x^5

[ocean seal]

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[modern sedge]

Your solution seems to be correct, if you wanted to, you could factor out 2 but it's not necessary

[worn hinge]

yep

how about the ordering of my values?

should I change it?

[modern sedge]

no, your ordering is good

[worn hinge]

I think I'll do the factoring cause my prof wants it to always be at it's simplest form

[modern sedge]

You can do that, it depends on your profs preferences.

I personally think that leaving it as you wrote it is good enough

[worn hinge]

okay okay thanks!!

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[halcyon ore]

how do i find the value of x?

[halcyon ore]

i did x^4-4x^2=525

im thinking of dividing it by 4 but then i would have a weird equation which idk how to solve

um?

[full garnet]

Oh, you took the channel before I was able to write my question. Hahah. Sorry.

[halcyon ore]

oh ok lol

i apologize for stealing ur channel

[vale wigeon]

not gonna be of much use

are you familiar with quadratic equations?

[unkempt vapor]

use t = x^2

[halcyon ore]

a little

[vale wigeon]

use timK's suggestion to turn yours into a quadratic.

[halcyon ore]

ok

[unkempt vapor]

then $t^2-4t-525=0$

[ocean seal]

TimK

[halcyon ore]

would adding 525 to the other side now

be of help?

[unkempt vapor]

no

[halcyon ore]

o

[vale wigeon]

this is a quadratic equation, solve it like you would any other

[halcyon ore]

i forgot i did them earlier this year

ill search it up on yt

thanks for the help

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[lilac stratus]

I'm not sure what (a) means.

[lilac stratus]

I mean, it's the derivative, but evaluated in each direction, so I'm not sure option (d) works.

The vector is indeed perpendicular to the surface, but I don't know what the "equiscalar surface" thing is about.

[glad socket]

i think thats referring to the tangent plane

[lilac stratus]

Then it's (a), right?

Because the gradient is indeed perpendicular to the surface that the tangent plane represents.

@glad socket

[glad socket]

im pretty sure thats not the case

[glad socket]

im really not sure

if thats ur source then yh

[lilac stratus]

Alright, thanks. Hopefully someone else weighs in.

<@&286206848099549185>

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[fast crypt]

Pretty dumb but is there an efficient method of getting the answer when the questions get bigger

[vale wigeon]

not really you just need to recognize powers of some small numbers

[fast crypt]

so like for instane i can tell the powers for the earlier ones but i literally cannot wrap my head around 2401

like how would i do that without wasting time

[vale wigeon]

ah uh

i don't really know

i happen to recognize it as 7^4

[fast crypt]

alright

thanks

i'll still keep it open just in case someone has a method

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@alpine sable Has your question been resolved?

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<@&286206848099549185>

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[cedar hare]

I think I did something wrong...

[keen pasture]

Is that 4q or 49?

[cedar hare]

49

[winged cloak]

any ideas please?

[glacial patrol]

!help

[lone heart]

To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.

[mortal trellis]

sqrt(a-b) is not the same as sqrt a - sqrt b

[bleak geyser]

Can u send the pic again I wanna rotate it

Nvm u got the way 👍

[cedar hare]

oops, thanks

i completely overlooked that

[keen pasture]

I'd take a look at the problem mod 4

[lone heart]

@cedar hare Has your question been resolved?

[keen pasture]

@cedar hare Did you try what I suggested?

[cedar hare]

i don't understand what u meant, sorry

managed to expand the expression to (2p+q)(2p-q) = 49, and couldn't figure out where to go from there

[mortal trellis]

consider the prime factorization of both sides

they have to be equal

that gives you only a very small amount of cases you have to check

[cedar hare]

1, 7 and 49, right?

[mortal trellis]

yes. so the product on the left is either 1*49, 7*7 or 49*1

or with -

[cedar hare]

yeah, i'll give that a try :)

ty

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[thick surge]

How do I find f(-2) for graph number 12

[lethal citrus]

I don’t think you can

[wanton umbra]

if it's periodic f(-2) is 0

sorry, 1

[thick surge]

Is there like an equation or mathematical way I can do it without just drawing out the rest of the graph

[lethal citrus]

If you know the degree of the function then yes you can

[thick surge]

Ok ty

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[kind oyster]

What do I do? idk where to start, I got help from a classmate but I still don't understand how they got to "e" and all that

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[kindred swallow]

hi, I am very confused about the last 2 of the question, my understanding of question is that for all real number a that is not zero, and for all real number b, there exists one and only x which is a solution for ax + b = 0. and I think since the order is mattered for this, I think putting the x at the last should meaning that there is only x that corresponding the solution of for all a that is not zero and for all b. So matter no matter what a and b is, there should be only one x that is solution of ax + b. so I think the statement is true.

In addition, I think if the order changed and there is one and only x to the front, then the statement should be wrong

[kindred swallow]

Same meaning for the question 4, I think the statement should be correct too, there exists a b, such that for all x that is not 0, there exists one and only one a, which is solution of ax + b = 0

because the for that one and only one is the last, I think the statement should be correct

so I think both (iii) and (iv) are correct

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[thick lynx]

When determining the volume of a tetrahedron,

[slow silo]

help

[leaden thicket]

hi

I was wondering if u could help me on ratio?

[violet urchin]

@thick lynx sorry, what is the question here

[thick lynx]

What's wrong with it? Wikipedia provides a different answer

[violet urchin]

ah ok so you're wondering why wikipedia got a different answer

[rich escarp]

the mid point of the perpendicular of the base doesn't have to form a perpendicular from the apex

[violet urchin]

@rich escarp this shouldn't be (d/2)2 should it

[rich escarp]

Yea

[violet urchin]

since the centroid is 1/3

or actually he'd be using the 2/3

yeah

[thick lynx]

What do you mean?

[violet urchin]

@thick lynx it should be ((2/3)d)^2

[thick lynx]

Where?

[rich escarp]

Try projecting the apex onto the base

[violet urchin]

in the expression = to h

[thick lynx]

Why? Because of what Arkos said?

[violet urchin]

because the perpendicular from the apex will intersect with the base at the centroid of the base

[thick lynx]

Yes, so shouldn't it be d/2 exactly because of that?

[rich escarp]

Why should it?

[violet urchin]

the centroid is not at the mid points of the medians

it is at the 2/3 point

[thick lynx]

Wouldn't it have a different position then, depending on from which median you go?

[violet urchin]

no, because the base is an equilateral triangle

and the medians all intersect at the same point

[thick lynx]

How do we derive that it's at the 2/3 point?

[violet urchin]

that's a whole proof on it's own

you can find that online if you want

[thick lynx]

Well, we strictly need that, if we want to find the volume of it, right?

Or is there another way?

[rich escarp]

You can take a slice of the solid which contains the median of the base and the apex then try working out what h should be

[violet urchin]

using that fact is the closest way to what you did originally

you can prove it on your own if you want, but to do this problem, we can just assume it

[thick lynx]

Would there be other, faster ways?

[violet urchin]

I assume there are but i'm not sure but the straightforward way is just what you were doing

so stick with that

if you correct the (d/2) to (2d/3) your method should work

[thick lynx]

Thanks, I should first derive that it's at 2/3 d first, though

[violet urchin]

sure, gl then

[thick lynx]

Do you mean a slice like this?

Oh, found a derivation, thanks

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[mighty brook]

Can someone explain why the integral between 0 and -5 of this function isn't -8

[vapid shuttle]

looks like a rectangle with base 3 and height 1. Plus 2 triangles with base 1 and height 1.

what does that area evaluate to?

[mighty brook]

Shit

-4

Thank you

[vapid shuttle]

np

[mighty brook]

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[thick lynx]

The numbers between 440 and 880 are divided by 11 pieces in a way so that two consecutive ones have the same ratio. Find the ratio and the pieces.

[thick lynx]

So we need a_n+1/a_n = k

That means that a_n+1 = k * a_n

So this will be an exponential function, right?

[west girder]

what does it mean by divided?

are the groups summed?

[thick lynx]

Solved it, k is sqrt12.

[thick lynx]

There will be 12 parts

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[rustic lily]

does that f :x

[rustic lily]

notation

does that just mean f(x)

[strange meadow]

No

[rustic lily]

what

[strange meadow]

f maps x to x/x+3

But yeah basically I guess you can think about it as f(x)

[rustic lily]

ok lol

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[somber flume]

From the top of a 30m building we drop a body of mass 50g that reaches the ground at a speed of 20m/s. What is the energy that has been dissipated by friction with the air?
I've tried:
Initial Em = Initial K (kinetic energy) + Initial U (potential energy)
Initial Em = (1/2)mV^2+mgh
and as at the beggining velocity = 0; Initial Em = mgh
Final Em = Final K + Final U
Final Em = (1/2)mV^2+mgh
and as at the end the height is 0; Final Em = (1/2)mV^2
and I got; Initial Em = 14700 | Final Em = 10000
and as Final Em = Initial Em + friction; 10000 = 14700 + friction; friction = -4700
but i think negative friction isn't a thing, and on top of that the solution book says that E = 4.715 J
(excuse my english, I'm spanish)

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[wraith cave]

I need help with the steps to solve the problem, I cannot understand how to solve the distrubutinmg part with 28 and the fractions, please help;;.

[mint robin]

distributing is multiplying the stuff inside the brackets by the thing outside it

in this case 2x/7 and -1/3 are inside

28 is outside

thats just how brackets work right, that's what they imply

[wraith cave]

I understant that, but im confused how they multiplied it and got 8x

bc when I multiply it im getting high numbers

[mint robin]

they multplied and that the fraction got simplified

[wraith cave]

so would I multiply 28 x 2, and 28 and 7??

[mint robin]

no 28 * 2/7 = (28*2)/7

not the seven as well

[wraith cave]

why was I not supposed to multiply the 7 is their a reason? And do i do that now for all the problems in the future?

[mint robin]

yes

you shouldve learnt this when multiplying fractions

also you'll see that multiplying both the top and the bottom doesn't change the fraction, it'll just stay the same number, which doesn't makes sense if you're multiplying it by smth right

[wraith cave]

its been a long time since I have taken a math class

So ty

[mint robin]

np

[wraith cave]

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Show your work, and if possible, explain where you are stuck.

[wary stream]

That's the formula you should use

That table is the $(x - \bar{x})^2$ values already

[ocean seal]

dldh06

[wary stream]

Yes because it's sample SD

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[wet linden]

So you are given that the common factor is z ^ -1/4 right

[keen bluff]

yes

[wet linden]

so if you take z ^ -1/4 out of 9z ^ -1/4

what are you left with?

[keen bluff]

9

[wet linden]

alright

wait this shit lowkey hard

[keen bluff]

thats what im saying 😭

[wet linden]

p sure its the 1/4 turns into 1/2

idk if it becomes pos or neg tho

[keen bluff]

hm ok

[wet linden]

ye tbh idk what to do for the second one

[keen bluff]

yea, ive been stumpted on this for a bit

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[keen bluff]

.close

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[versed zinc]

5x3

[wary stream]

Don't troll

[versed zinc]

no troll

i need help

[wary stream]

Then post your actual math question

[versed zinc]

im autistic and exam coming up

[wary stream]

.

[versed zinc]

5 take away 5 is the answer 2?

[wary stream]

Are you trolling

[versed zinc]

no

can you help me with elimination method

algebra tingz

please

i need the helps

PLEQASE

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[wary stream]

Because that's not an equation

That's an expression

[worldly bolt]

Thank you

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[ebon torrent]

I split it to 27 < 2x - 7 , 2x - 7 < 45

and got 17 < x < 26

but the answer says its 2 < x < 26

[solemn juniper]

where the heck does 2 come from

I agree with your answer

[ebon torrent]

here's the answer to question 21

[alpine sable]

you had I believe question no.20 right?

[wary stream]

@alpine sable 21

It's the .21 at the end, the number format is weird

[ebon torrent]

I did question 20 already , this is 21

is this a mistake ?

[solemn juniper]

,w solve 27 < 2x-7 < 45

when in doubt

[ocean seal]

Results provided by WolframAlpha

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Requested by steakanator

[alpine sable]

Yes I know. but if he had 20 right with the same steps I dont see why this is right.

yea exactly.

[ebon torrent]

and this is the solution

I got 1 < = x < 8

oh this one actually is my mistake

[wary stream]

I was about to say that the key is correct on that one

[ebon torrent]

so they just wrote the wrong solution on one of the questions and it threw me off

thanks.

.close

[lone heart]

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[dire terrace]

am i wrong for hours?

[violet nova]

im a bit confused with my calculus hw can som1 help me rq?

[lone heart]

@dire terrace Has your question been resolved?

[dire terrace]

<@&286206848099549185>

[wanton umbra]

,w simplify 21(2t+1.2)^2-83(2t+1.2)+40

[ocean seal]

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Requested by _ils

[dire terrace]

I got the first part right

2nd part is wrong for some reason

[lone heart]

Show your work, and if possible, explain where you are stuck.

[dire terrace]

^

stuck on why i got 7.891703728

im just confused how to to get hours tbh because I know its wrong

[wanton umbra]

you can leave the thing below 34 and number of bacteria will be const

[dire terrace]

wym thing

[wanton umbra]

how long was it in the fridge?

do you put it back in

ambiguous question

what's the temp in the fridge

[dire terrace]

2t+1.2 ?

[wanton umbra]

Product

[wanton umbra]

that's removed

From the fridge

[dire terrace]

wouldnt it be 84t^2-65.2t-29.36

.close

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[sage hedge]

im confused on what this is even asking

[zealous lichen]

do you know what limit is

and the meaning of limit not exist?

[sage hedge]

I think

[zealous lichen]

why are you confused?

[sage hedge]

what is it asking me to do

wait

is it asking me to make a function?

[zealous lichen]

yes

[sage hedge]

like invent a function?

like albert einstein?

[zealous lichen]

yes

[zealous lichen]

no

[sage hedge]

I realized when I re read it sorry im so tired

well it wouldnt have a limit if the denomoniater was undefined or it went to an infinite point

[sage hedge]

wait is it asking for the combine functions

or 2 dif functions

[zealous lichen]

add

combine sounds more like composition

[sage hedge]

oh ok

[lone heart]

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[lone heart]

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[dusk umbra]

hey notation question

[dusk umbra]

this guy

does it mean that only a'' is varying, and that it skips being equal to a'?

or am i meant to take from this that a

a' is varying too?

[vapid shuttle]

if a''=a' then we have division by 0

[dusk umbra]

yes

[vapid shuttle]

so we can't have that

[dusk umbra]

but, what im saying is

is a'' the only thing that is increasing with each step?

or is a' supposed to be increasing too?

[vapid shuttle]

where is this from?

[vale wigeon]

i'd read this as only a'' varying

[dusk umbra]

Problem 1.9 Sakurai quantum mechanics 3rd edition lol

[weak field]

Nothing is increasing
They r taking the product of all possible values of this expression
Here ig a' and a" both r variable

[vale wigeon]

but need context

[zealous lichen]

I think they take all possible a' and a''

[dusk umbra]

uhh basically a' and a'' are possible eigenvalues of a state

err eigenvalues of an operator, rather

specifically A

[weak field]

So r both variables ?

[dusk umbra]

these people seem to interpret it as just j is changing i think

this is in reference to the same problem

[weak field]

Ic
j is variable from 1 to n

But j≠i

What's i tho

[dusk umbra]

a specific eigenvalue of operator A

the point of this is to show it reduces to the projection operator

because if a_i remains the same, I can make this the projection operator using the closure relation, if peeps are familiar with that

[weak field]

Sorry
I have no idea about these
But a_i is not defined to be a constant
It shud be variable as well

[dusk umbra]

life is so hard

uhhh ok

[twilit gull]

fr

Steins gate is really good

[dusk umbra]

el psy congroo

god this problem is a bitch

[weak field]

But then the expression shud be looking something like this

[dusk umbra]

this screenshot leads me to believe a_i stays constant

[weak field]

Here both r variables but with different limits

Unless a_i is constant
It shud be variable

Well
That's obvious

[dusk umbra]

hnggg

[lone heart]

@dusk umbra Has your question been resolved?

[dusk umbra]

thank you for your help. i think i got it now.

.close

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[keen fossil]

help pls

[keen fossil]

dam, alr

[weak field]

..

[keen fossil]

yoo hello

:D

[weak field]

Close the channel

[keen fossil]

I NEED HELP THO

[tribal haven]

ask a question, don’t ask to ask

[weak field]

Then ask

[keen fossil]

ok

one sec its a hard one

[vale wigeon]

are you deliberately spreading misinfo, or what

[weak field]

He said dam alr
So I thought his doubt is solved

[keen fossil]

\left(2y^{-5}\right)^3\left(x^{11}y^{-10}\right)^2

dan ghow do i

[vale wigeon]

put dollars at the start and end

$\left(2y^{-5}\right)^3\left(x^{11}y^{-10}\right)^2$

[ocean seal]

Ann

[vale wigeon]

ok

!status

[keen fossil]

YES

[lone heart]

What step are you on?
1. I don't know where to begin
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

[keen fossil]

1 essentially

[vale wigeon]

do you know exponent laws

[keen fossil]

not that well

can you help me sovle this

[vale wigeon]

here is a reference

try something on your own first

[keen fossil]

yes but there's so much stuff

how do i know where to start

ok uhh

guess i gotta solve this myself

lets see

[vale wigeon]

do you have paper btw

[keen fossil]

yes

can u help

<@&286206848099549185>

[dusk umbra]

lool there was no need to ping helpers someone is here helping you

[zealous lichen]

first use power of power rule

get rid of parenthesis

then combine like termsw with product rule

[keen fossil]

okay let me try it out

[keen fossil]

how does that work though

[zealous lichen]

oh yeah

use power of product rule to seperate them first

[keen fossil]

ok

[wooden moon]

yes

@keen fossil

[lone heart]

@keen fossil Has your question been resolved?

[lone heart]

@keen fossil Has your question been resolved?

[undone hornet]

ok pretty much

a - exponent

means reciprocal

u distribute the big exponent on top to num and den

and do stuff

GL

[undone hornet]

Ann sent a image that practically helps you solve it step by step

[lone heart]

@keen fossil Has your question been resolved?

[lone heart]

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[vale wigeon]

this is a 30° rotation matrix

how many times do you need to rotate by 30 degrees until you are back where you started

surely not 3

it's in the form of a rotation matrix and the angle is pi/6

[lone heart]

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[silent linden]

would anyone mind verifying something for me ?

[alpine sable]

[vale wigeon]

show us what you want verified

[silent linden]

one sec

[vale wigeon]

oh ugly.

[silent linden]

im trying to evaluate by partial fraction

was wondering if the solution at the bottom was spot on

[tardy tapir]

it is correct

still lemme check

[silent linden]

tysm, its 4:38 and i wanted to sleep but the anxiety is killin me

[tardy tapir]

,w integral (4x^2 + 7x - 5)/(x^2 + x - 6)

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by oldieidlog

[tardy tapir]

yup

[tardy tapir]

dw, you can sleep now

[silent linden]

omg i wish i could like commend you or something lol

[tardy tapir]

lol np

do you have any other questions?

[silent linden]

can you run , (2x-1)/(4x^2+4x+1 )

[tardy tapir]

integral?

[silent linden]

yes

[tardy tapir]

send it

ill check

[lone heart]

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[lone heart]

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[ember needle]

This book has a lot of exercises in 3D

and the author has not taught anything about it, it wants me to solve it by using my knowledge in 2D

and I can't, for the love of it do it

can someone please, walk me trough this step by step

considering that I have never, ever done anything with 3-space?

[opal jolt]

okay. start by the most basic case.
draw a box in 3d. mark the point A(0,0,0) and the opposite corner B(b1,b2,b3)

[ember needle]

okay hold on

just to make sure

how to draw a box in 3d?

I'm a humanities guy to the max

so basically, I'm an idiot when it comes to mathematics

absolute idiot

[opal jolt]

https://images.app.goo.gl/WBmsfJCoCWauPe3g9

[ember needle]

alright, hold on

[opal jolt]

something like that

you also want to draw the axes

[ember needle]

sending a pic

what do you mean the axis?

[opal jolt]

,rotate

[ember needle]

mine looks a lot like a rectangle

I'll get to the notating part now

[opal jolt]

now, with what you know in 2d, can you get the distance between A and C?

[ember needle]

hold on, where should I put the origin here?

[opal jolt]

on any corner. just be careful of where each goes

look at your box and mine for reference

[ember needle]

how is the corner in the lower-middle sound?

I've got no idea how to draw the axes on this oh my

[opal jolt]

basically you want to work in 2d to get the distance between A and C, the distance between C and B, and those are the sides of a 3rd right triangle

the hypothenuse will be the distance from A to B

[ember needle]

alright, hold on

how's this?

[opal jolt]

good enough, but your components will be in different parts of the drawing

[ember needle]

alright screw this, I'll go with your drawing

so, A to C, right?

[opal jolt]

anyways, gtg

[ember needle]

oh, bummer

I'll open a question later then

.close

[lone heart]

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[tardy tapir]

that is correct!

[silent linden]

for the first one i sent, does it matter if -2ln is before positive 5ln, arent they equivalent ??

[tardy tapir]

i dont remember the first one tbh

[silent linden]

this guy

4x+5ln(2-x)-2ln(x+3) is equivalent to , 4x-2ln(x+3)+5ln(2-x)

?

[tardy tapir]

yeah totally

[lone heart]

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[alpine sable]

2x-x+96

[subtle birch]

what is your question

[alpine sable]

the answer is x+96

[alpine sable]

this

is the answer X+96

[tardy tapir]

2x -x = x so yes, if you want to simplify the expression, its x + 96

[alpine sable]

thanks a lot

bye

.close

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[subtle birch]

that was quick

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[silk crag]

Write the formula of this function

[silk crag]

Also please explain if possible

[alpine sable]

Is it meant to be a straight line or is it just my eyes that see it curved

[silk crag]

Curved

Straight line is easy but I don't understand curved

[mellow grail]

Looks like some logairthm

[silk crag]

It doesn't involve log

[mellow grail]

ah right it goes into -ve

well f(1)=0, f(-3)=-2

[alpine sable]

I personally think there isn't enough information

[mellow grail]

u need to sorta guess what type of function it is

[silk crag]

There is no other info

[ember lichen]

yeah me too

[mellow grail]

is the derivative given

[silk crag]

The only info it has is the picture

Nothing else

[alpine sable]

There has to be some context as to what you were learning in that chapter

[silk crag]

There's no

[mellow grail]

yeah what chapter is this in

[silk crag]

It's not like a new thing so my book doesn't have any formulas

Function and it's graph

I can do parabola and linear but this idk

[alpine sable]

Take a picture of the full question please

[silk crag]

It's not in English

4th one

I tried to look for an answer in the back of a book but it only had answers for 1 2 and 3

[ember lichen]

my eyes are getting bent for the graphs

[wanton umbra]

sqrt

translated by (-3,-2)

[silk crag]

?

What's the formula

[lone heart]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[bitter hemlock]

do you know what a sqrt graph looks like?

it usually starts from the origin, and try translate that graph

[silk crag]

I just looked it up and I'm not really familiar with it

[bitter hemlock]

i would recommend desmos if you wanna play around with it

a basic square root graph/relationship is like y=√x

and you can translate that like you would any other graph

ie. adding/subtracting to the whole function, to x, stretching by multiplying x or the function etc.

[silk crag]

I think i got it

So it's y = (√x-h)+k?
Meaning y=(√x+3)-2

Right?

[bitter hemlock]

sounds about rught

[silk crag]

Thanks

.close

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[alpine sable]

I am extremely stuck.

Flux = E*A in this scenario

So I took E1 = k*|5uC| / (0.09^2) and E2 = k*|-1uC| / (0.09^2).

E1 = 5.55 x 10^6 and E2 = 1.11 x 10^6

i have no idea where to go from here 💀 I tried reverse engineering a practice problem and I'm still not getting anywhere

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

.close

[lone heart]

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[jaunty turret]

help pld

<@&286206848099549185>

[lone heart]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[lone heart]

Show your work, and if possible, explain where you are stuck.

@jaunty turret Has your question been resolved?

[main viper]

<@&286206848099549185>

[empty moth]

I’d help

But youngboy profile pic

[wanton umbra]

#help-0 message

[lone heart]

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[wanton umbra]

( can be anywhere after an operator or at the beginning

[gray isle]

they do indeed seem to be missing a (

number of ( \neq number of )

[lone heart]

@alpine sable Has your question been resolved?

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[alpine sable]

How do i put squareroot(4i) in the form of x + iy ?

isnt sqrt(4i) already the imaginary number

so isnt this already the solution : 0 + sqrt(4i)

[rancid hazel]

the form x+yi means that i needs to be a power of 1 however in this case it's to the power of 1/2

[alpine sable]

so i need to multiply it with itself?

[rancid hazel]

it's not going to be the same then

[alpine sable]

wym..

[rancid hazel]

sqrt(4i) has one value, if you multiplie by itself then it's gonna get a different result

like sqrt(2)=1.41 but if we multiply by itself it's gonna be 2

[alpine sable]

agree

what else is there

what should i do

[rancid hazel]

well you should start by seperating the 4 and i in the square root

[rancid hazel]

yep

so now we need to find the value for sqrt(i)

[alpine sable]

so this is then yi

hm

well i = -1

no

i = sqrt-1

@rancid hazel

[rancid hazel]

i mean yeah but does it lead to the form x+yi?

[alpine sable]

nooooo

but then why must i fid out what sqrt(i) is

[rancid hazel]

because we want to know what 2sqrt(i) is in x+yi form

we know what 2 is ofc but sqrt(i)?

we don't know the value of sqrt(i) and that is what we're going to figure out

[alpine sable]

yeah...

[rancid hazel]

and i'm going to say this

the value of sqrt(i) is in the form a+bi

think about it...

[alpine sable]

weeeeeeeell..............

may you give me another tip..

[rancid hazel]

maybe put sqrt(i)=a+bi and play with the equation a little bit?

[alpine sable]

substitute sqrt(i) for i?

[rancid hazel]

so what you are saying is sqrt(i)=i?

[alpine sable]

nooo..

but where else am i gonna put it

[rancid hazel]

well you want to get rid of that annoying square root?

agree?

[alpine sable]

yes!!

[rancid hazel]

how do we do that in an equation mmmmm

[alpine sable]

skuair!

[rancid hazel]

oui

[alpine sable]

()^2

[rancid hazel]

yes

[alpine sable]

skuair a + bi ???

and then solve for..

...

[rancid hazel]

both a and b

[alpine sable]

..................

[rancid hazel]

don't worry just square both sides and see what happens

[alpine sable]

and then plug in 2sqrt(i) forrrrr

okk lemme tryyyyyyyyy

@rancid hazel

can i now plug in b=2sqrt(i) and calculate a ?

[rancid hazel]

and how do you know that b=2sqrt(i)?

[alpine sable]

bkuz imagineiry numbre

a + bi
bi is imaginary

just like ... 2sqrt(i) ??

[rancid hazel]

what do you think...

[alpine sable]

i think im probly wrong..

[rancid hazel]

yeah...

[alpine sable]

i am pyro main ..

[rancid hazel]

what weapons you use

don't say phlog...

[alpine sable]

the flair gun

[rancid hazel]

based

[alpine sable]

im jk tho i main skout

[rancid hazel]

xd

[alpine sable]

but prefer playin vsh

irrelevan!!

help me pls with meth..

[rancid hazel]

vsh is gone : (, ok let's continue

the b in bi needs to equal to a real number

[alpine sable]

2

[rancid hazel]

don't guess it is not gonna help xd

[alpine sable]

😦

[rancid hazel]

but let's go back to your equation,

it is right btw

[alpine sable]

yay

[rancid hazel]

i = a² +2abi - b²

do you see something in this?

[alpine sable]

i see real nunmbers and imaginary numres

[rancid hazel]

mmmm let's change it a bit

i = a² - b² +2abi

what about now

[alpine sable]

uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuumm..

[rancid hazel]

still not?

[alpine sable]

binomial

[rancid hazel]

that's gonna make this alot more complicated

it is a lot more simple than that

[alpine sable]

:::::::(((((((((

value for i

[rancid hazel]

elaborate

alright let's change this one more time

maybe this helps

do you agree that i = 0 + 1*i?

[alpine sable]

yes

[rancid hazel]

here we go:

[alpine sable]

so a is zero in our case?

[rancid hazel]

0 + (1) i = (a² - b²) + (2ab) i

[rancid hazel]

why that

[alpine sable]

you rewrote the eequation

with brackets

..

[rancid hazel]

it is this the same equation, with brackets or without brackets

(2+5)=7 , 2+5=7

nothing changes

[alpine sable]

(a² - b²) tis real number

[rancid hazel]

YES

[alpine sable]

(2ab) i tis imagner

[rancid hazel]

so what does that mean

[alpine sable]

2ab = 2sqrti ?

[rancid hazel]

you should ignore the 2sqrti

[alpine sable]

a² - b² = 2 ??

[rancid hazel]

a²- b² =?

[alpine sable]

haaa

[rancid hazel]

look at the equation closer

[alpine sable]

i = 2ab

[rancid hazel]

both a and b must be real numbers

[alpine sable]

yef

[rancid hazel]

but you are so close

[alpine sable]

where do iget real numbers fromm...

the information i have is 2sqrt(i)

[rancid hazel]

1 x i = 2ab x i

right?

[alpine sable]

jahhh

[rancid hazel]

so cancel out the i ...

[alpine sable]

1 = 2ab

[rancid hazel]

YES

and what is it for a²-b²=?

shit

[alpine sable]

1

[rancid hazel]

why that

[alpine sable]

1i...

real number 1..

[rancid hazel]

we know that a²-b² must equal a real number right?

[alpine sable]

yeas..

[rancid hazel]

but on the left side is there no real number

it is only 1 i

[alpine sable]

shyey

yes

2ab?

[rancid hazel]

we already figured it out for 2ab

[alpine sable]

what else is there

if not 2

[rancid hazel]

0 + 1*i

[alpine sable]

ZERO?????

[rancid hazel]

there we go

you are right

a²-b²=?

[alpine sable]

zero

buttt

[rancid hazel]

yeah?

[alpine sable]

but now what...

[rancid hazel]

we know that a²-b²=0 ; 2ab=1

[alpine sable]

a² = b²

substitute method

[rancid hazel]

yep

you already know it

[rancid hazel]

solve for both a and b

[alpine sable]

i hope God blesses you

[rancid hazel]

me?

inshallah

[alpine sable]

you

i pray for your success

[rancid hazel]

why so are you grateful

[alpine sable]

youve shown me more kindness and patience than my own parents

[rancid hazel]

dunno if i am sad or happy reading this

[alpine sable]

dw i have nice parents but they are not good teachers

[rancid hazel]

see i always wanna help the person by letting them think and taking their time

[alpine sable]

youre insaneeeeee dawg

[rancid hazel]

giving the answer does nothing

[alpine sable]

like positively

bro..

[rancid hazel]

aight

let's solve for both a and b

[rancid hazel]

don't forget

i also do forget it sometimes

but b can also equal something else

[alpine sable]

oh yeah plus and minus

[rancid hazel]

yep

i failed an exercice because of that

: (

[alpine sable]

its the goeverments fault

[rancid hazel]

fact

[alpine sable]

i tried calculating a now

i got a weird ah number

0.707

[rancid hazel]

that is 1/sqrt(2)

[alpine sable]

aaahhh

but in conclusion squaring these two and subtracting them should give me the x value?

[rancid hazel]

not particarly

go all the way back to our equatin

we defined sqrt(i) = a +bi

[alpine sable]

btw how come thats true? ..

why are we allowed to do that

[rancid hazel]

in what way

[alpine sable]

sqrt(i) = a +bi

since when

[rancid hazel]

well we know that with complex numbers the form is always x+yi. we both know sqrt(i) is gonna be a complex number,

because what else will it become?

[alpine sable]

sqrt (i) could also just be an imaginary

i mean it cant but why not

[rancid hazel]

imaginary numbers are complex numbers xd

[alpine sable]

i thought imaginary is only the bi part of a + bi

[rancid hazel]

yeah you are right

made big mistake on my part

[rancid hazel]

so what is our final answer

what does sqrt(i) =?

[alpine sable]

bi

im not sure now whether its complex or imaginary

[rancid hazel]

it it is imaginary if a=0

but in this case it isn't

[alpine sable]

we know thats the case because

because the task asks us to calculate x + yi ?

[rancid hazel]

yep

[alpine sable]

and why do we leave out 2

[rancid hazel]

no first we calculate sqrt(i)

and later 2sqrt(i)

i'm doing this because if you have a later problem with sqrt(i) in it

[alpine sable]

let me recapitulate rq

[rancid hazel]

you ca directly know the value of sqrt(i)

[rancid hazel]

aight is good

@alpine sable you back?

[alpine sable]

im writing it down more understandably 1 sec i almost got it

[rancid hazel]

aight

[rancid hazel]

don't forget

a can also have a different value...

[alpine sable]

wow the screenshot extended wth

but wait

is that it? the solution?

[rancid hazel]

it misses something

[alpine sable]

2

its missing two

the nunbmer

hmm

whatt

[rancid hazel]

alright

[alpine sable]

whaaaaaaaaaaaaaat

[rancid hazel]

a can equal 1/sqrt(2)

or ...

[alpine sable]

meinus

min us

[rancid hazel]

yes

-1/sqrt(2)

[alpine sable]

yes

hey

do i have to do the entire thing again

[rancid hazel]

don't forget that sqrt(i) can not only equal 1/sqrt(2)+ 1/sqrt(2)i but also -1/sqrt(2) -1/sqrt(2) i

[alpine sable]

but with 2 this time

[rancid hazel]

hell no

you can just do 2[sqrt(i)=+- 1/sqrt(2) +-1/sqrt(2) i

[alpine sable]

ok!! nicely

[rancid hazel]

so what do you get?

[alpine sable]

when i multiply this stuff by two

[rancid hazel]

yeah you geet +2/sqrt(2) + 2/sqrt(2) i or - 2/sqrt(2) - 2/sqrt(2) i

[rancid hazel]

but you can simplify this

2/sqrt(2) is also equal as?

[rancid hazel]

yep

so it equals sqrt(2)

[alpine sable]

if i want to put a number into square root

i have to square it ?

if i wanna put 2 into the square

[rancid hazel]

oh i see what you mean

yes

[rancid hazel]

absolutely

[alpine sable]

thats the solution isnt it

square root 2 + square root 2 * i

it is the solution

why were we allowed to just multiply the thing by two ?

at the end

so we split it in the first place to make it easier?

[rancid hazel]

yep

[alpine sable]

i mean the 2 sqrt(i)

[rancid hazel]

it makes the equation easier

to solve