help-0

[little drum]

Yeah thought so.. Can you show me the actual question?

[limpid garnet]

Number 12

[little drum]

Do you have to integrate it!?

[limpid garnet]

the average I got was the 1/2e^4 +1/2

yea

[little drum]

I think the question probably is asking you to find the area under graph?

what is the actual question lol, I got the function ✓

[limpid garnet]

I had to find the average value of f on the given integral

and the second problem is using the mvt

[little drum]

the average value of the function is that...

[limpid garnet]

yes that is what I did

use

[little drum]

I still don't get why you need to solve the equation

[limpid garnet]

well the second part of the problem ask to find c in the given interval that fave = f(c)

[little drum]

hmmmm

[limpid garnet]

so after evaluating the integral and multiplying by 1/2 the average comes out to -1/2e^4 + 1/2

then u set the 2ce^-c^2 =the average

and that where Im stuck

[little drum]

can you show me the answers to 11.?

I might get a hint on how to-

[little drum]

I think you're allowed to use Graphing calculator

Because this question can't be solved otherwise

I mean, you could try to roughly get to the part(also using a calculator) but otherwise, I don't think so.

[limpid garnet]

Ok but i dont think my calculator is able to solve it

I have a tin84

Ti

Unless i break it down

[little drum]

basically, this is the function

Use the approx value from the graph: here, approx
x = 0.27, and x = approx 1.3

(ヘ･_･)ヘ┳━┳ I see no other way.

[limpid garnet]

Thank you

[lone heart]

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[wide cradle]

I have created two distributions based on different time frames and would like to test if how those two distributions perform when using some new random time frames
are there any tests that do that?
I thought of Anderson-Darling test but I'm not really sure if that's its purpose...

[lone heart]

@wide cradle Has your question been resolved?

[lone heart]

@wide cradle Has your question been resolved?

[wide cradle]

<@&286206848099549185>

[lone heart]

@wide cradle Has your question been resolved?

[lone heart]

@wide cradle Has your question been resolved?

[lone heart]

@wide cradle Has your question been resolved?

[noble sinew]

Wdym time frames? Wdym how they perform?

[lone heart]

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[opaque inlet]

Draw a Venn diagram or two way table representing the data

[smoky jungle]

i have tried

[opaque inlet]

Show me

[smoky jungle]

i cant because my phone is dead

[opaque inlet]

Then how are u chatting to me

[smoky jungle]

pc

[opaque inlet]

I can’t do much then

Someone else can help

[smoky jungle]

okay

.close

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[plucky crow]

,tex how would i differentiate $ x\frac{dy}{dx} $ ?

[ocean seal]

Syphax

[plucky crow]

,tex is it product rule so $\frac{dy}{dx} + x\frac{d^{2}y}{dx^{2}} $ ?

[ocean seal]

Syphax

[vale wigeon]

yes

[plucky crow]

alright thanks

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[dull storm]

hi guys

if sinx/cosx=tanx

does it mean sinhx/coshx=tanhx?

[plucky crow]

yes

,tex all of the identities are the same except for when you have $sin^{2}(x) $ in a normal identity you get $-sinh^{2}(x)$ in its respective hyperbolic one

[ocean seal]

Syphax

[plucky crow]

,tex e.g $$sin^{2}x + cos^{2}x = 1$$ $$ cosh^{2}x -sinh^{2}x = 1 $$

[ocean seal]

Syphax

[lone heart]

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[alpine sable]

How do I do this

[alpine sable]

I am clueless

pls ping when answering

<@&286206848099549185>

[plucky crow]

aq is 3*bp

so x is 3*y

can you do part (i) now?

[alpine sable]

Let me trie

[alpine sable]

The book answer says its 4y m

*it's

[plucky crow]

what is pa in terms of x and y?

(hint: its pm + ma)

[alpine sable]

AH wait

I didnt solve that

Yeah

It's correct

[alpine sable]

How about part (ii)?

[plucky crow]

you can find a relationship between the triangles because you know PM (y) and PA (you found this out in part 1)

[alpine sable]

Ah okay

So the base triangle

QAP is 4y meters as well

Which means that triangle TPM is 4x smaller than QPA

So the height of QPA is 6m

Hence the height is 6/4

or 1.5m

Thanks for the help @plucky crow !!!

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[terse barn]

Can someone help me with this?

[lone heart]

@terse barn Has your question been resolved?

[terse barn]

<@&286206848099549185>

[gray isle]

what have you tried

[terse barn]

Ik you have to find out how to find the y intercept by looking where it crosses the line first

But idk how to do the gradient

[willow pewter]

Anyone can help me with Differential Equation?

[terse barn]

You can use this channel gela

I found out of how to do gradients

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[sinful glacier]

yáll im a bit confused

[sinful glacier]

i got e^(xy)+x-y-1=0

and i need to find the dy/dx

that means that y is a function of x right?

[marsh shore]

yep

[sinful glacier]

and how would i go about that

[marsh shore]

Have you used implicit differentiation before?

[sinful glacier]

i have yeah

oh

oh partial derivative?

[marsh shore]

not really

Implicit differentiation is just using the chain rule

[sinful glacier]

i'd use the chain rule right

just plit it into to

but

wait the derivative of e^(xy) in this case would be ye^(xy)

[marsh shore]

except y is a function of x

[sinful glacier]

e^(xy)(xy'+y)

?

[marsh shore]

seems about right to me

[sinful glacier]

would the x and the 1 term dissapear and the y term become yy'

[marsh shore]

the derivative of y with respect to x is just y'

the derivative of x with respect to x is 1

[sinful glacier]

oh right lmao

so x becomes 1 and y just y'

[marsh shore]

yep

[sinful glacier]

and i need to solve for y'

[marsh shore]

indeed

[sinful glacier]

thanks

.close

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[clear plume]

Yeah hi. People are saying this man just robbed the guy behind the register for $10 but my brain isn’t computing it. Can someone please explain this to me because it’s keeping me up & I want to go to sleep

Ok rewatching it I actually understand now

.close

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[ionic sand]

any ideas?

[wintry wadi]

derangements or subfactorial or !n would work i think

those 3 are the same thing btw

[ionic sand]

is the answer 9

[wintry wadi]

yup

[ionic sand]

thankq

[pale kestrel]

overkill???

[wintry wadi]

oh sorry, what would you do?

[pale kestrel]

Well yes, basically work out the derrangement, but from first principles.

And give hints on how to count

Because that appears to be the point of this question.

[wintry wadi]

ah, yeah, jumped to how to get it too quickly

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[quiet summit]

I need help with 7(t^2+5t-9)+t=t(7t-2)+13

[fluid eagle]

what have you tried already?

[quiet summit]

I am stuck

like Im in 35t-63+t=-2t+13

then idk what to do-

[fluid eagle]

this is a normal linear equation, the easiest way of solving it is to bring the equation to the form at = b such that t=b/a

[quiet summit]

so what do I do exctaly ;-;

[fluid eagle]

well, first you cleanup to 36t-63 = -2t+13

do you see what to do next?

[quiet summit]

I have to move the +13 then it well turn into -13?

[fluid eagle]

you could do that, but i think it's easier to put the t on the left hand side and the constant term on the right hand side

because 36t, a big term, is already on the left

[quiet summit]

mhm

[fluid eagle]

so you are probably better off moving the -63

so you get 36t = -2t+13+63

[quiet summit]

okay

wait let me write it down mate T-T

okay then

what do we do?

[gray isle]

recall basic algebraic manipulation principles,
apply the same operation to both sides of the equation etc.
at this point i'd recommend that you do a review on something like khan

[quiet summit]

khan?

[gray isle]

khanacademy

[quiet summit]

and is that a way of doing maths or sum?

;-;

[gray isle]

its a free online resource to learn basic → intermediate math

[quiet summit]

aha-

[lone heart]

@quiet summit Has your question been resolved?

[quiet summit]

https://tenor.com/view/sad-pablo-lonely-alone-gif-12928789

[lone heart]

@quiet summit Has your question been resolved?

[quiet summit]

T-T. . . .

[dull storm]

@plucky crowthank u so much, God bless

[plucky crow]

?

[quiet summit]

;-;?

[lone heart]

@quiet summit Has your question been resolved?

[lone heart]

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[thick star]

I got to the point where i established the relationship between y3 and y2, y1

it's y3 = (y2-y1)/2

and so substituting it back in C

id get

C (x3, y2-y1/2)

[little drum]

Actually

your y3 value is also wrong

Are you sure you used the mid-point formula correctly?

[thick star]

yeah, im positive

[little drum]

hmm?

what should be your y - coordinate for C? according to this formula?

[thick star]

oh, one second ill graph it and show

where A (x1, y1)
B (x2, y2)
M (x1+x2/2, y1+y2/2)
C (x3, y1+y2/2)

[lone heart]

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[lone heart]

@thick star Has your question been resolved?

[lone heart]

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[empty terrace]

is there a polynomial which outputs 0 if the input is even integer and outputs 1 if the input is odd integer?

[wary stream]

I'm not sure about a polynomial but a square wave might do that

[empty terrace]

thanks but i need a polynomial

[tacit arch]

for all integers? no there isn't

for finite range of integers? yes

[lone heart]

@empty terrace Has your question been resolved?

[pale kestrel]

If the polynomial outputs 0 for all evens, then it has infinite roots. Which is impossible.

[empty terrace]

for finite integers say from 1 to 10?

can i have an example please

[tacit arch]

https://en.wikipedia.org/wiki/Lagrange_polynomial

[empty terrace]

thanks will take a look into this

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[alpine sable]

How do I solve this?

[pale kestrel]

Count how many triangles are in each square

And also, note what the side lengths of each square is

[alpine sable]

yes, but in words how can I prove pythagroas theorem with it?

[pale kestrel]

🤷‍♂️

What I gave is a hint how

Tell me --- how many triangles are there in each square

[alpine sable]

8

[pale kestrel]

There are different sized squares there.

[alpine sable]

2 squares which are 8
1 big one which is 32
and 1 half one which is 4

[pale kestrel]

huh?

I don't think I agree with you there

I'm talking about how many triangles are inside

Small trianlges

[wary stream]

Are you saying half one as in the triangle?

[alpine sable]

yes

[wary stream]

That's in the middle

[alpine sable]

yes

[pale kestrel]

ok lets slow down

There are 3 squares in the diagram

[alpine sable]

yes

[pale kestrel]

I mean these 3

[alpine sable]

yes

[pale kestrel]

And I was asking how many triangles in each

1: ?
2: ?
3: ?

[alpine sable]

1: 8
2: 8
3: 32

or

[pale kestrel]

no

3: isn't 32

count again

wait wait

you mean 2: right?

Go by this numbering lol

And none of them are 32

[alpine sable]

16

[pale kestrel]

yes ok

8, 8, 16

[alpine sable]

yes

[pale kestrel]

Notice anything then?

[alpine sable]

nope

[pale kestrel]

In terms of area

8 + 8 = 16, no?

[alpine sable]

OHHH

yes now i do

[pale kestrel]

Now you can say something about the sum of areas

[alpine sable]

yes

[pale kestrel]

Notice what the side lengths of the squares are

[alpine sable]

2 triangle for the little ones

and 4 for the big one

[pale kestrel]

huh?

The diagram is marked with the letters a b c

I'm referring to that

[alpine sable]

oh

i'm unsure what the side lengh is

[alpine sable]

Wdym by side length?

[pale kestrel]

Side

[wary stream]

The length of the side

[pale kestrel]

https://i.imgur.com/NV2r7yW.png

[alpine sable]

ohh

2

[pale kestrel]

2?

No

The diagram uses the letters

a b c

[alpine sable]

and?

[pale kestrel]

Do you know what these letters are meant to represent?

Maybe it isn't clear

[alpine sable]

I think the length of each side?

[pale kestrel]

Yes.

So how long is the side of square (1)

[alpine sable]

2

[pale kestrel]

???

[alpine sable]

2 triangles

[pale kestrel]

.

You just told me the letters are marking the 'length of each side'

use the letters

[alpine sable]

then its A

[pale kestrel]

yes.

The square has side a

so what is it's area?

[alpine sable]

a squared

[pale kestrel]

indeed.

Now write down the areas of the other squares

And think about what we just showed

8 + 8 = 16

[ocean seal]

Shuri2060

[alpine sable]

ohh

yes

the area of square 2 the same

and the area of square 3 is c squared?

[pale kestrel]

yes

[alpine sable]

so?

[pale kestrel]

Remember what you are trying to prove???

Pythagoras???

[alpine sable]

yes

[pale kestrel]

think how this diagram helps.

[alpine sable]

OHHH

the 2 squares squared make the other side

[alpine sable]

yes that the two sides squared make the other one

in this case the 2 squares squared make the other square

[pale kestrel]

Yes. So I think you can do the question, now.

[alpine sable]

yes

thank you

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[edgy sparrow]

uh...

[lone sandal]

shit mb

[edgy sparrow]

sorry mate, occupied

[lone sandal]

lmao

[edgy sparrow]

this is the diagram provided ^

i am aware to apply N2L

which is F - E = ma

given --> = +ve

somehow this isnt right ;-;

NO WAIT I THINK I SEE THE PROBLEM

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[alpine sable]

Hello

[alpine sable]

Sorry for the stupid question

In this video what is x?

Is it degree or radian? 😀

[marsh rapids]

always radians. As soon as you're doing maths without context, radians

unless specified otherwise, radians

[edgy sparrow]

bruh... rads > degrees for sure, but like why did sec sch teach us in degrees

[alpine sable]

I see. But then I don't understand algebra after this.

I know:

x = yz
z = x/y

But here we have radian as x then how we can set that aside and do the algebra? 😕

[marsh rapids]

wdym "set that aside" ?

[alpine sable]

Here we have radians

Then how we can do calculation like this? :

y = sin^-1(pi/2)
sin(y) = pi/2

Ohh!

I realized my mistake

I am so sorry. Thank you guys

[marsh rapids]

units are coherent if that's what you're having trouble with. You can also view the functions as going from radians to "standard" and vice versa

[alpine sable]

May I keep open this thread for some minutes?

Thank you guys @marsh rapids @edgy sparrow 😊

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[odd obsidian]

I understand how to do the computations, I just don't understand what it means to write it as the product between a matrix and a vector

I have this so far, I just don't know what they mean by "write w as the product between a matrix and a vector"

[marsh rapids]

technically you can cheese question 2 by saying w is the product of itself and the identity matrix. I think the expected answer here is to use this matrix x vector form to express w as the linear combination of vectors v1, v2 and v3

[odd obsidian]

okie, but how would you write the identity matrix for a non-square matrix? Also, "use this matrix x vector form to express w as the linear combination of vectors v1, v2 and v3", I'm not sure what you mean by this

I don't think I've learned what a linear combination means yet

[tacit arch]

random internet definition. there should be a definition in your book too

so your scalars are 3, 2, and -1.

[marsh rapids]

for the product part, if you write the matrix with columns (v1, v2, v3) (or lines, depending on the side on which you put the vector), how can you use the definition of the matrix product to multiply it by some coefficients such that the result is w ?

[lone heart]

@odd obsidian Has your question been resolved?

[deep creek]

.reopen

.open

[marsh rapids]

@deep creekwrong channel

[lone heart]

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[lone heart]

Please don't occupy multiple help channels.

[smoky schooner]

what's equation for this graph

[odd obsidian]

looks like a transformation of $\sqrt{y}=x$

[ocean seal]

QLightningWolf44

[smoky schooner]

this looks close what am i missing

nvm i figured it out

[smoky schooner]

ok so the inverse for this would be √x+5=y

?

[odd obsidian]

No

The inverse of a square root is what?

How do you "undo" a square root

[smoky schooner]

to the second power?

[odd obsidian]

yes

so what happens if you square both sides

[smoky schooner]

y=1+\sqrt{4+x}

?

[smoky schooner]

ok i think this is the right answer

[lone heart]

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[odd obsidian]

hey, sorry, I think I'm starting to understand it a little more

[odd obsidian]

But I'm still not entirely sure how to go about it

[lone heart]

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[static copper]

I'm confused how to get past here if that definite integral from 0 to x of 1/t is divergent

The answer key just looks like it ignores it?

.close

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[loud oriole]

why does integral ((7/6 * dy)/y) = 7/6 log |y|

[loud oriole]

in this case y is a substitution for another expression btw (calc 2)

[wintry lotus]

What is the integral of 1/x *dx?

[loud oriole]

.close

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[marsh olive]

Tell me if i'm wrong but shouldn't the missing angle be the top one based on the word problem? This is the answer key but i'm 99% sure the teacher did it wrong

[alpine sable]

No

Because the ladder is 40ft long

Ladders don't go straight up

and its 36 feet off th ground meaning height = 36

[alpine sable]

• hypotenuse is always the largest

[marsh olive]

I know but the 36 side is the wall and the diagnol line of 40 is the ladder

so shouldn't the angle be between them

[alpine sable]

so your saying x should be $cos^-1(36/40)$?

[ocean seal]

raw

[alpine sable]

Because the answer is correct

[marsh olive]

Yes

I know that but i'm asking if they drew it out wrong

[alpine sable]

They didn't

[marsh olive]

but the word problem says the angle the ladder makes with the wall not the floor

So the angle should be inbetween the ladder and the wall

Correct?

[marsh olive]

Yeah but it's saying the one the ladder makes with the wall

[alpine sable]

Are you saying that x is in the wrong spot?

[marsh olive]

Yes

[alpine sable]

Draw where you think it should be

[marsh olive]

Let's preted there's no floor for a second

It's just the ladder line and the wall line

If somebody said the angle that the ladder makes witht he wall

It would be the one between them, correct?

I'm just asking if the teacher misplaced the x when solving it themself

[alpine sable]

They didn't misplace it

Since the x is where the floor and the bottom of the ladder touch

making the angle toward the wall

[wintry lotus]

They did imo

[alpine sable]

It could be both ways

[marsh olive]

But it's asking for the ladder and the wall

not the floor and the wall

[alpine sable]

Yeah but facing the wall

[marsh olive]

But it didn't say facing the wall

[alpine sable]

Its making a 64 degree angle with the wall

[marsh olive]

It said with the wall

[alpine sable]

Ask your teacher, either way its a poor worded question

[marsh olive]

True

.close

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[ember sky]

can someone help me understand what was done in these last 3 steps

[lone heart]

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[raw citrus]

If A is the set of all real numbers x ≠ 0,1,2, what is the order of f(x)=2/(2-x) in SA?
I'm new to this subject and am very confused

[pale kestrel]

S_A ?

symmetric group of A

You are basically finding out how many times you need to compose f with itself to get the identity

fof = ?

fofof = ?

fofofof = ?

...

[raw citrus]

Oh

Can it come out as an equation or as a number?

Wait, it ends up as x? When we do f composed with itself?

[pale kestrel]

f(x) = x is the identity function

[lone heart]

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[lethal dock]

Don't u think this question is missing information

[lethal dock]

Like they didn't mention how much time it takes for a crab to make a new shell

Wasn't the size of the shell unrelated information?

[blazing saffron]

That is irrelevant

You know it is 10cm at the final time

It needs to go from 1cm to 10cm

And each shell is 1/3 bigger than the previous hence it is compounded growth

1cm, 4/3cm, 16/9cm,...,10cm

You can either keep doing this iteratively until you get an answer or use a compounded growth formula to find the n times needed to reach 10cm

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[raw urchin]

Hello

[raw urchin]

I have a probability question which I've solved but I think is wrong... can someone trace my steps and tell me where I went wrong?

[remote heron]

woah rotating star

[raw urchin]

.close

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[crystal tiger]

Show that if f is a borel function on R and A $\in B$, that ${x: f(x)\in A}\in B}$. Conclude that if X is a r.v. and f is a borel function, that f(x) is also a r.v.

[ocean seal]

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

[lone heart]

@crystal tiger Has your question been resolved?

[crystal tiger]

please ping me

[lone heart]

@crystal tiger Has your question been resolved?

[crystal tiger]

@crisp iron

please help

@crisp iron

[little drum]

@crystal tiger @ helpers

lol

Helper is a random user

[crystal tiger]

<@&286206848099549185>

I think i got it now

.close

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[mellow fossil]

I just started math and I was wondering if someone could help me understand how to create a function given these properties?

[lone heart]

@mellow fossil Has your question been resolved?

[mellow fossil]

<@&286206848099549185>

[lone heart]

@mellow fossil Has your question been resolved?

[lone heart]

@mellow fossil Has your question been resolved?

[noble sinew]

1 at a time

For example c, d, e, f, b, a or whatever

[lone heart]

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[foggy charm]

i need help

[foggy charm]

how would i sketch the graph

[jagged imp]

sketch the graph of y=sqrt(16-x^2)

do you know how to do that?

[foggy charm]

yea but do u not have to find the anti derivative first?

[little drum]

Yeah I'm interested too

[jagged imp]

not at all. the point of the question is to do it without an antiderivative

y=sqrt(16-x^2) forms a specific shape

[foggy charm]

a circle?

[jagged imp]

almost

[foggy charm]

half of a circle

[jagged imp]

yuh

[little drum]

Yes but the antiderivative (ヘ･_･)ヘ┳━┳

how.

[jagged imp]

idk trig sub maybe?

[little drum]

Anyways, in this question it asks to sketch a graph of each definite integral

[echo socket]

integrand I'd say

[foggy charm]

thanks for pointing that out Ansh, im kinda illiterate my self

[jagged imp]

ansh i understand your issue with the wording but its pretty obvious it means the integrand

considering the area formula thing

[echo socket]

The integrals themselves are constants

[foggy charm]

@jagged imp for the calculation part i found the antiderivative and solved the integral, but i got 15.0849...

the answer is 8 pi

how did they get that

[jagged imp]

so it forms a semicircle

whats the area of a semicircle

[foggy charm]

$Area = \frac{\pi r^{2}}{2}$

[ocean seal]

breadiculous

[jagged imp]

from your graph would you agree that the integral here is just the area of the semicircle y=sqrt(16-x^2)?

[foggy charm]

yea

would u then substitute it with area

[jagged imp]

I don't know what you mean by that. You can get the radius of the semicircle from your graph and plug it into the area formula though.

[foggy charm]

oh ok

this makes more sense

thanks for ur help

.close

[lone heart]

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[astral mist]

how do i do this

i know the other root must be -1+2i

(z+1-2i)(z+1+2i)

[hasty elk]

hint: simultaneous equations

[astral mist]

mmm

got it

[little drum]

Vieta's is another good way out :o

[astral mist]

vieta's?

[little drum]

Gives the relation between sum of roots taken n at a time and the Coefficients of the polynomial given

Here for example, you can quickly spot that "3" is the third root, and consequently, the values of "c" and "d"

=========================

sum of roots of polynomial = coefficient of term with (n - 1)th degree/leading coefficient

= ( 1 ) in this case, and so on

Want to see it!?

[astral mist]

yes please

im confused abit

[little drum]

Okay

Let's say, the roots of your given polynomial were $\alpha, \beta, \gamma$

[ocean seal]

Ansh

[little drum]

okay?

[astral mist]

okk

[little drum]

Then you can write your polynomial as: \

$z^3 - z^2 +cz +d \equiv (z-\alpha)(z-\beta)(z-\gamma)$

[ocean seal]

Ansh

[little drum]

okay!?

[astral mist]

ye okk

yes

[little drum]

now, expand the right hand side, and compare:

Right hand side is: \
$z^3 - (\alpha + \beta + \gamma) z^2+ (\alpha \beta + \gamma(\alpha + \beta))z - \alpha \beta \gamma$

[ocean seal]

Ansh

[little drum]

okay?

[astral mist]

yepepe

[little drum]

compare with the given polynomial, and you'll have sum of roots = 1

See it?

$z^3 - z^2 +cz +d \equiv z^3 - (\alpha + \beta + \gamma) z^2+ (\alpha \beta + \gamma(\alpha + \beta))z - \alpha \beta \gamma$

[ocean seal]

Ansh

[little drum]

sum of roots = coefficient of z^2 in right hand side = 1 in left hand side

see it?

[astral mist]

not XD wait

give me sec

[little drum]

hmm, we're only comparing the coefficients

[astral mist]

yes

[little drum]

Got it?

[astral mist]

but z^2 = (a + b +r )z^2

?

so 1=a+b+r

im confused sorry

[little drum]

Yeah, we're only comparing the coefficients afterall

[astral mist]

XD mmm

[little drum]

Don't question it right now, just trust me with it atm and you can question it after we're done.

[astral mist]

okkk

[little drum]

For right now, can you understand that we got
(a + b + r) = 1 by comparing the coefficient of z^2 on both sides?

[astral mist]

okkk

[little drum]

great

now, we also know two of the roots

-1 - 2i, and -1+2i

[astral mist]

yupp

[little drum]

since sum of roots = 1, and sum of two of the roots = -2, we must have the third root be: 1 - (-2) = 3

Got it!?

[astral mist]

ohh

wait

umm wait so

[little drum]

so!?

[astral mist]

-2 + b = 1

[little drum]

hmm? what's with the choice of variables

[astral mist]

i dont get it

wait

so a + b+ c = 1

2 root sum = -2

so -2 + varaibel = 1

?

ok

[little drum]

Yeah

[astral mist]

ohh

[little drum]

hence, varaibel = 3

[astral mist]

okkk

yup i was thinking sometinh else mbb

[little drum]

therefore, you have the third root 👀

Now, back to the comparison part-

[astral mist]

the third root is 3?

oikkkokook

oghh

[little drum]

Just... relax and see this without any criticism and you'll understand lol

$z^3 - z^2 +cz +d \equiv z^3 - (\alpha + \beta + \gamma) z^2+ (\alpha \beta + \gamma(\alpha + \beta))z - \alpha \beta \gamma$

[astral mist]

okkk

soz

[ocean seal]

Ansh

[little drum]

so, on the left hand side, we have a polynomial whose roots are alpha, beta and gamma

on the right hand side, we also have a polynomial whose roots are exactly alpha, beta and gamma

and both have same leading coefficients

[astral mist]

o

okkk

[little drum]

therefore, we're allowed to say that both the polynomials should be one and the same

[proud basin]

what is happeningg 0-0

[little drum]

Is why you can without doubt compare the coefficients

[astral mist]

oh

[little drum]

||check the pinned question.. also, tell me how much time it takes for you to solve :p||

[little drum]

Now

[astral mist]

uhumumum

[little drum]

$z^3 - z^2 +cz +d \equiv z^3 - (\alpha + \beta + \gamma) z^2+ (\alpha \beta + \gamma(\alpha + \beta))z - \alpha \beta \gamma$

[proud basin]

uhm

[ocean seal]

Ansh

[proud basin]

i think you guys are over complicating it

[little drum]

After comparing the coefficients, what do you think about "c" ?

[hasty elk]

||about one minute tbh||

[little drum]

about few secs is all it takes

[proud basin]

just plug -1-2i to z and then separate the imaginary and real part then solve for c and d

t^t

[hasty elk]

||i still say simultaneous equations in two unknowns is much faster, though viete's is cool||

[little drum]

mhmm

[proud basin]

agreed

[little drum]

||this tho (╯°□°）||

[alpine sable]

Lol

[astral mist]

c is just a * b *c

?

[little drum]

nope,

looking back at the comparison

$z^3 - z^2 +cz +d \equiv z^3 - (\alpha + \beta + \gamma) z^2+ (\alpha \beta + \gamma(\alpha + \beta))z - \alpha \beta \gamma$

[ocean seal]

Ansh

[astral mist]

oh

wait

no thats d

mb

[alpine sable]

Look at the coefficients again e

[astral mist]

soz soz

[little drum]

c is the sum of roots taken two at a time

[astral mist]

c = (ab+r(a+b)

[little drum]

and d is negative times the product of roots

[astral mist]

ye

[little drum]

and you have all the three roots with you now

[astral mist]

huh

so

[little drum]

So \
$c = (-1-2i)(-1+2i) + (3)(-1-2i -1 + 2i)$
\ and \
$d = - (-1-2i)(-1+2i)(3)$

[ocean seal]

Ansh

[astral mist]

ohh

[little drum]

that easy-

[astral mist]

oohooh

okkk i think i got it, ill do more practice on this

thanksksksksks so much

this seems alot faster

[little drum]

Yup, more questions like this might come up and if it's MCQ, 10-15 secs should be at max it takes

(ヘ･_･)ヘ┳━┳

[astral mist]

ooo okosokssk

Thanksksksksk alottttttt

[little drum]

Yw, read brilliant.org on Vieta's for appropriate reference

[astral mist]

oo okkk

[lone heart]

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[lone heart]

@restive haven Has your question been resolved?

[lone heart]

@restive haven Has your question been resolved?

[restive haven]

yeah i just figured it out

thanks anyway

[astral mist]

okk

[lone heart]

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[void estuary]

Is there a way to turn a function into a... "Broad sense" function (translated that)?

[lone heart]

Please don't occupy multiple help channels.

[void estuary]

I can't close the other one aaa

Anyways my function is 10y=x³-5x²+15x+0

If broad sense isn't correct, i mean when the function gradually stops going up in the Y axis and rather just flattens

[pale kestrel]

NO

@restive haven @astral mist thats not how you square the left side

@void estuary maximum minimum inflection?

You differentiate to find extremum

[void estuary]

Lemme check in google

[alpine sable]

What??

$(a+b)^2$ ≠ $a^2 + b^2$

[ocean seal]

Pencil

[void estuary]

As far as google has shown, nope. It's dis

[pale kestrel]

asymptote

not sure i can answer your question though

[void estuary]

yep yep yep that's it xP

Its alright

[lone heart]

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[livid bone]

Oskar has driven 182 km of a 500-km trip. What percent, to the nearest percent, of the journey does he still have to drive?

[livid bone]

how do I get the percent and to the nearest?

[gray isle]

what have you tried so far?

[livid bone]

I tried subtracting 182 from 500

then divided by 100

so 318 / 100

which gave me 3.18

[hidden jetty]

Shouldn't it be (182 / 500) * 100?

Not sure tho...

[livid bone]

wait

let me try

[hidden jetty]

100 % -> 500
x% -> 182

Should be something like this

500 km is 100% of the journey

how much is the percentage of 182 km

then you multiply in cross

[livid bone]

thanks

.close

[lone heart]

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[young spear]

how should i understand this?

[glass lichen]

the function's 1 when |Omega| is within those ranges
0 else

[young spear]

ahhh okay

THANKS

.close

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[vocal tapir]

help

[vocal tapir]

"Given:
Triangle ABC (angle ACB less than 90 degrees)
Angle BAC = alpha, angle ABC = beta
Symmetrical bisector of AC crosses AB at point M," etc

I need help proving

angle MCN = 180 degrees - 2a - 2b

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

[red plinth]

U have the angles MNC and NMC

@vocal tapir u can solve it easly cuz u have MNC = 2B and NMC = 2 a

[vocal tapir]

how?

[red plinth]

U know the total of angles is 180

[vocal tapir]

yea?

for triangle MNC you have 2 more angles which you don't have values for

I don;t*

[red plinth]

U have 2 b and 2 a

[vocal tapir]

yea?

[red plinth]

180 = mnc + nmc + mcn

And we have mnc and nmc

Nmc

[vocal tapir]

180=2a+2b+x

[red plinth]

Yes

Continue

[vocal tapir]

180-2x-2b=x

?

[red plinth]

Yes

[vocal tapir]

ffs

[red plinth]

Thats the answer

[vocal tapir]

why does my brain just refuse

to do some very simple stuff

[red plinth]

Lol

[vocal tapir]

I guess I'm overloaded on info

btw

I have some more problems

in regards to the same problem

conditions if you will

[red plinth]

Post em

[vocal tapir]

I have to prove that triangle ABO is isosceles

that AMO and CMO are congurent

an that CO is bisector of MCN

so AB is the common segment

and the one halving ABO is also a common segment

but how do I find the angle which shoulders are the two common segments

[red plinth]

I can't solve it xd

[vocal tapir]

<@&286206848099549185>

[red plinth]

I think the drawing is a bit confusing cuz it shows angle a = b

[vocal tapir]

angle BAC (a) = alpha and angle ABC (b) = beta

but not equal

or least I don't see it

[red plinth]

Wait

Is the line Sbc crossing bc in the middle

?

Oh im stuped

Ofc it does

@vocal tapir u have to prove that Bc = CO then co = ac

[vocal tapir]

ohhh I see it

[red plinth]

Easy proof

[vocal tapir]

how do I prove that BC=CO

[red plinth]

U have the line $S_(ac)$

[vocal tapir]

I can prove that CO=BO

[red plinth]

Lol thats what i meant

Sry

Bo = oc = ao

Do u know how to solve the rest ?

[vocal tapir]

how do I prove that OC=AO?

[red plinth]

So u have the angle oca = cao

Thats ur proof

[lone heart]

@vocal tapir Has your question been resolved?

[lone heart]

@vocal tapir Has your question been resolved?

Channel closed

Closed by @vocal tapir

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

Hey! I'm sure this is a silly question but somehow I'm stuck so here I am 😭
Soo, I was solving this inequality, and below is what I've done.
My book says the solution is x ≤ -2, but I have checked my passages like a hundred times and I can't figure out why I get x ≥ -2.
Clearly, I'm missing some obvious point, but... can someone help me? Thanks a bunch!

[alpine sable]

?

[wary stream]

Don't ask in an occupied channel

[vast hare]

shoot

sorry

[alpine sable]

ohh dw

i thought it was related to my problem and i was like what xD

[vast hare]

when i took th epicture it wasnt occupied

[alpine sable]

i see

[wary stream]

Out of curiosity, since you're doing a t sub, why did you sub for the first two terms and not the last one?

[alpine sable]

hmmm not sure, ig i did it because (-1/2x)*2 is -x

[wary stream]

Shouldn't you do all the terms?

[alpine sable]

i think not? because i can't do anything else with the final "+2"

if it wasn't for that method, i'd have no idea how to solve it tbh

[wary stream]

Wait, you might be right about that

[alpine sable]

i think i have solved other inequalities by only substituting some terms, so that shouldn't be the problem

maybe something's off with the t<=-1 or the t>=2 solution

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

<@&286206848099549185>

so, so sorry to ping, it's not urgent at all, i'm just super curious

[lone heart]

@alpine sable Has your question been resolved?

[tacit arch]

Your error's just in your last few lines. Keep the inequality when subbing back for t.
t>=2, -x/2 >= 1, -x >= 2, x<=-2

[alpine sable]

ohhh i see!!

thank you so much for your help!

.close

[lone heart]

Channel closed

Closed by @frozen wing

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ancient coral]

<@&286206848099549185>

[tacit arch]

• After 15 minutes, feel free to ping @Helpers.```

[ancient coral]

what is 12 divided by 84

[alpine sable]

1/7

[ancient coral]

its ok

[echo socket]

Try prime factorising 12 and 84 if you're having trouble

[ancient coral]

is it 7?

[alpine sable]

if I understand you question correctly
12/84 = 6/42 = 3/21 = 1/7 (what I did is I divided by 2 three times and by 3 one time)

1 over seven

[ancient coral]

oh ok

thx .close

oops

.close

[lone heart]

Channel closed

Closed by @ancient coral

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[terse canyon]

Hi

[terse canyon]

If in 100g 479 calories how much in 22g?

[alpine sable]

One message removed from a suspended account.

One message removed from a suspended account.

[terse canyon]

So im tryna gain weight and get fat ass

But idk this chocolate im eating its 22g

And idk how much is the fucking calories

[supple tundra]

[echo socket]

Pensin already said that the answer is (479/100)*22

[terse canyon]

I dont understand

[sterile idol]

22/100 * 479

[terse canyon]

Just say how much in 22 g

[echo socket]

Just put it in a calculato

r

[sterile idol]

Take hundred parts of 479, multiply by 22

[terse canyon]

Not points and shit a

[sterile idol]

No one's going to do it for you

Use a calculator

Or ask us if you need help using a calculator

[supple tundra]

If in 100g = 480 calories

how many in 10g

[alpine sable]

One message removed from a suspended account.

[terse canyon]

English isnt my first lang

[echo socket]

Calculator, write (479*22)/100

[terse canyon]

So idk how tocalcuate when u explain in eng

[echo socket]

That's it

[terse canyon]

Just say the answer

Ok

[sterile idol]

What?

[terse canyon]

Thqks

Thanks

[supple tundra]

see when did this become a weight loss discord server

[terse canyon]

No

Irs gain weight

Its

[sterile idol]

Weight gain

[terse canyon]

Imt tryna get a fat ass

[supple tundra]

oh weight gain

oh fat ass

oh yes i see

.close

[terse canyon]

So i had to join this math discord cuz my friends dont know math like me

[wary stream]

If you know math, you couldn't determine the math for your problem?

[terse canyon]

No i hate math

Thats why i joined this shit to ask

[sterile idol]

Why did you go through the trouble of calculating all this if you could have eaten the whole chocolate?