help-4

[north scarab]

but we’re solving it for when k = 2, right?

[tawny moon]

no?

why are we solving for a "particular k value"? we wanna know for what k it works

[nimble crypt]

For what values of k is the equation true?

[tawny moon]

also, you can treat this as solving a quadratic

[junior ore]

yeah 2 values which u will get from the above expression u solved

[north scarab]

wait wait so how do we solve for unknwon integral limit?

after I integrate

[tawny moon]

solve the quadratic

[jovial edge]

Am I the only one thinking of solving this using geometry

[nimble crypt]

Its just like the x variable

X,k no difference

[lyric sundial]

Me too, but only because it's a line oc

[hearty belfry]

Yeah you can do it that way

[north scarab]

x=0,3

[tawny moon]

why is the answer the same?

and why is it x now?

the answers are wrong, not the variable!

[junior ore]

werent we talking about k?

[north scarab]

because the integrand is

in terms of x

[junior ore]

0,3 is wrong

[tawny moon]

but you're substituting k as a bound

[junior ore]

but need to find k not x

[north scarab]

so i make

x - k

x =k*

[junior ore]

ahhh noooo

[junior ore]

just put the limits in the integration and get the answer

[junior ore]

u wont get those values

u calculated wrong

[lyric sundial]

See, you just need to solve this quadratic inequalities

[junior ore]

there is a 2 on the RHS

[lyric sundial]

Solve properly of course, not as you did

[north scarab]

ohh

[junior ore]

u can transpose 2 to the LHS and use the quadratic formula if u like but u can also find the values from hit and trial just like i did

[lyric sundial]

Yeah, you should know well how to solve quadratic inequalities if you're doing integrals...

[north scarab]

Is there any videos on youtube that covers this?

I tried finding but coudnt

[tawny moon]

this is just definite integrals though

[junior ore]

integrals or quadratics?

[north scarab]

integrals

[tawny moon]

if you understand definite integrals, you understand this

[north scarab]

yeah I understand integrals

[tawny moon]

so why not this?

you're already correct up to that highlighted step

[junior ore]

u dont need to watch integrals video to solve a quadratic

[tawny moon]

just solve the quadratic for k

[north scarab]

I keep getting k=0,3

[tawny moon]

because there's still the 2 on the right!!

[junior ore]

nooo

[tawny moon]

move it over to the left and factor the quadratic again!

[junior ore]

just put 0 in the equation and compare LHS and RHS

[junior ore]

u will see that LHS=0 and RHS =2

[tawny moon]

now what happened to the 2?

why did you put = 0?

[lyric sundial]

And where did the 2 disappear????

[junior ore]

nope there was a 2 in the RHS

[tawny moon]

that expression is supposed to be = 2

you can't just thanos snap the 2 just because you feel like it!

[north scarab]

ohh alr

[junior ore]

fr fr

[north scarab]

so

-k^2+3k-2=0

[lyric sundial]

There you go!

Now use whatever method you like

Quadratic formula, completing the square, factorization, ...

[north scarab]

well I cant use factorisation in this case

[tawny moon]

why not

if it's because a = -1, just flip all the signs by multiplying the equation by -1

[north scarab]

factors of 2

oh wait

[tawny moon]

what's wrong with factors of 2

[lyric sundial]

Yeah

[north scarab]

nvm

[tawny moon]

-2 -1?

[north scarab]

(-k+1)(k-2)

k=2

and

[lyric sundial]

Yes, don't forget the = 0

[tawny moon]

ok good

don't forget your = 0 as mentioned

[north scarab]

and 1

[lyric sundial]

Yep

[tawny moon]

now those are the correct values of k

[north scarab]

wdy,

wdym

[tawny moon]

this expression is supposed to be = 0

[north scarab]

yep

so basically k is the

x value

[tawny moon]

k represents the two possible upper bounds, yes

[north scarab]

why are there two possible

uppoer bounds

[tawny moon]

i will invite you to think again about what you learnt regarding signed areas

esp from licht earlier

[green urchin]

I think

Op needs some advice on that

[vale dock]

@north scarab Has your question been resolved?

[north scarab]

above the x axis = positive

below x axis = negative

[tawny moon]

mhm

[green urchin]

Finally

So when you sum up regions which are present in both sides of the axis, you don't get the actual area, instead you get the reduced area

Suppose p sq units above the x axis and q sq units below the x axis

What you receive upon blindly substitute, is p-q

Whereas you're asked to find p+q

[vale dock]

@north scarab Has your question been resolved?

[vale dock]

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[wet tundra]

from this how do I find P?

[hearty belfry]

you're missing a +c btw

also

!xy

[vale dock]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[hearty belfry]

wait do you mean like find the value of P, or rearrange it to make p the subject?

[wet tundra]

umm make it P=

[hearty belfry]

ah okay

[hearty belfry]

okay, so you're meant to substitute t = 0 and p = 100 first to find c

[wet tundra]

oh..

[hearty belfry]

yeah, then you rearrange it

[wet tundra]

at what stage am i supposed to substitute it

[hearty belfry]

although I guess you can rearrange it first, and then find c

[red tulip]

shouldnt the constant just be 50 not 1/50

[wet tundra]

wat

[red tulip]

when you took the integral you made 50 into 1/50

[wet tundra]

should iot..

i forgot how to do it

i think ur right

y ea

[red tulip]

i mean its an understandable mistake considering youre turning 1/p into lnp

[wet tundra]

thanks

[wet tundra]

hi I’m still kinda lost

[hearty belfry]

times both sides by (500-p)

[wet tundra]

wait

i see it

i can move

it over

and take

p out

[hearty belfry]

yeah

[wet tundra]

IM GONNA CRY

I GOT IT WRONG

wait

whats 1/50

OMG

I GOT IT RIGHT

OMGMOGMGOG

[tawny moon]

0.2

[wet tundra]

MOGMKLGOGMGMOG

OGMOGMGOG

[tawny moon]

0.02*

[wet tundra]

YASS

QUESTION 2 COMPLETED!!

[hearty belfry]

good job

[wet tundra]

wait why do they give me this formula

what is it for

[tawny moon]

well done

[wet tundra]

this one

[hearty belfry]

I presume it's just the general form for when you solve the differential equation

[wet tundra]

im confused

would that help me answer this question?

[hearty belfry]

not really?

I mean you can memorise the formula but I wouldn't recommend it

[wet tundra]

noo i have the formula

[hearty belfry]

it's just a logistic equation of a mathematical model usuaully used to describe population growth

[wet tundra]

its in my formula sheet

[hearty belfry]

oh

[wet tundra]

how would i use it to solve this question

instead of using separation of variables

[novel canyon]

ballus riggidus unc i found you @hearty belfry

[hearty belfry]

well your 0.02 would be your r, and the k is 1. Your p(0) is 100 so you just substitute all of that into the formula

[wet tundra]

wait..

thats sm easier..

[hearty belfry]

[novel canyon]

sully yourself

[hearty belfry]

I mean it is

if they've given you the formula for it

[wet tundra]

um

Did I do it wrong

[spring jackal]

the exponential should be $e^{-rkt}$, not $e^{-kt}$

[rocky lotus]

haseeb

[wet tundra]

oh ok

i see

[wet tundra]

Yay

Thanks

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[vale dock]

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[plush pawn]

What's the purpose of differential equations, and what are we typically trying to give as an answer? Do we try to give the answer as x = ... or y = ...

[hearty belfry]

You can use differential equations to model various physical phenomena. Mainly systems that evolve over time or space, such as population growth, heat transfer, motion, etc

[severe verge]

Differential equations specify a function, or a family of functions. So in trying to solve them you are looking for a function which satisfies the equation, or all of the functions which do so

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[dusky eagle]

How can I find the vertex of a parabola if I have it in the general 2nd degree equation form ?

[hardy coral]

Complete the square

[hearty belfry]

or you can just know the fact that the x - coordinate of the vertex is -b/2a (but that comes from completing the square anyways)

then use that x-coordinate to find the y-cordinate

[dusky eagle]

And then keep it in a y^2 = 4ax form ?

[dusky eagle]

Mb I forgot to mention I meant 2nd degree in 2 variable form not one variable

[hardy coral]

What

Ok what do you mean exactly? Write down the equation

[dusky eagle]

I have x^2 + y^2 - 2xy + 14x + 2y + 1 = 0

[hearty belfry]

oh, thought you were talking about quadratics

[hardy coral]

I see

[hardy coral]

Well it's a quadratic form

[hearty belfry]

actually yeah it is

[dusky eagle]

Haha it would be much easier if It was in one variable tho

[hearty belfry]

Yeah, I initially thought you meant something like this. y = ax^2 + bx + c

[hardy coral]

Find the axis of symmetry
https://math.stackexchange.com/questions/2042028/axis-of-symmetry-for-a-general-parabola
and then find the intersection

[dusky eagle]

Oh alr thnx

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[jade bough]

@stark wedge

[stark wedge]

yeah ok lets see here

so we got two columns both of the form (_ + _) / _ = 1

[jade bough]

indeed there's some element of symmetry im seeing

also the + - = and - + =

[stark wedge]

is this the same rules as the previous grid btw

[jade bough]

yes

[stark wedge]

1-9 once each

ok

[hardy coral]

There's a 1 in either top-right or one below

One of the parentheses sum to 6

[jade bough]

No way

then there would have to be a 6 below the parenthesis to get the 1 on the colum

[hardy coral]

Yeah

Hm hold on

[stark wedge]

wait why does one of the brackets have to sum to 6

[hardy coral]

Never mind I'm just wrong

[jade bough]

it can't sum to 6

[stark wedge]

idt thats possible cause then row 3 would be unsatisfiable without repeats

[jade bough]

yes

[stark wedge]

also 1 can't go into col 3 at all i think

it can't be one of the addends cause thatd force a repeat

[jade bough]

yep

ann

maybe we should focus on bottom of first two column possiblities

if one is a 3

[terse hemlock]

1 also cant be bottom left or middle

[jade bough]

if bottom left is a 3

then bottom middle cannot be a 4, or 5, or 6, or 7, or 8

nvm we cannot have 3 and 9 on the bottom two left columns

seems pretty hard

this is the one I initially meant to send

this was the side I had worked on a long time ago and couldn't figure out

[stark wedge]

ok sorry i was away

so the 1 can't appear in row 3 or col 3

[jade bough]

true

[hardy coral]

Neither can the 2

[jade bough]

thats not true

[stark wedge]

why no 2

[jade bough]

if that was the case the puzzle would be unsolvable

[hardy coral]

Same reasons

[jade bough]

the two can go into column 3

2 + 3 - 4 = 1

[hardy coral]

Sorry, just row 3

Man I'm not thinking straight

[jade bough]

true

no 2 in row 3

a powerful deduction is that we cannot have a 3 in either bottom of the leftmost 2 columns

[hardy coral]

Why?

[jade bough]

sorry its complicated and i'm working something out

i'll get back to you soon

we cannot have a 1, 2, 3, or 4

in either bottom of the leftmost 2 columns

for some understanding

if we have a 3 in one of them

then we must use 1 and 2 above

therefore any other number in one of those spots must be composable with numbers other than 1,2,3

9 is the first one

and it leads to a contradiction because the otop row cannot be satisfied if we use 9 = 4+5

or 5+4

same sorta thing applies with 4

[terse hemlock]

ithink i got it let me double check

[hardy coral]

I agree for 3 but not for 4

[jade bough]

i think i'm onto something rn

[hardy coral]

If you put in 4, you get 1+3 above, but then you have a 2 so you can make 7 or 8

[jade bough]

yes

the 9 and 5

I figured out those had to be in the bottom left corner

great job though

crazy that this was expected

of my 5th grade brother

[terse hemlock]

that was a 5th grade question?

[jade bough]

yes

lol

extra credit

[terse hemlock]

i knew 9 had to be bottom left and then i knew the bigger number in the addition on the left column had to be in the top and just went from there

[jade bough]

yeah

nice job

thanks

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[limpid wind]

hi can I send my question here>

[hearty belfry]

you can, since you opened a help channel

[limpid wind]

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[dawn axle]

how to do this

[frozen ledge]

$\int_2^4 \frac{4}{t^3 + 1} \dd{t} = x(4) - x(2)$

[rocky lotus]

knief

[dawn axle]

And u substitution ?

[frozen ledge]

you can use a calculator

seems like a calculator question

[dawn axle]

I see thx

[opal pendant]

How do u integrate this 😭

[dawn axle]

Caculator

[opal pendant]

Huh calculator for integrating?

[frozen ledge]

probably factor the denominator

[dawn axle]

Yeah

[opal pendant]

Didn't know that was a thing

[frozen ledge]

but this seems like a question theyd let you use a calculator for

the answer choices have 3 decimal places

[dawn axle]

The answer is C

[frozen ledge]

no chance theyd want you to find that without just plugging the integral into a calculator

[opal pendant]

Alr alr cause we just finished doing indefinite integration and I was wondering why I wasn't able to do this one

[dawn axle]

https://tenor.com/view/thank-you-thankyou-thanks-dance-gif-12076259571370395144

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[jagged zephyr]

A satellite is initially in a circular low Earth orbit (LEO) of altitude h_1 = 300 ,\text{km}. The satellite must transfer to a higher circular orbit of altitude h_2 = 900 ,\text{km} using a two-impulse Hohmann transfer.

Take Earth’s radius R_E = 6371 ,\text{km} and gravitational parameter \mu = 3.986\times10^{14},\text{m}^3/\text{s}^2.
1. Compute the orbital radii r_1 and r_2.
2. Compute the orbital speeds v_1 and v_2 in the initial and final circular orbits.
3. Compute the velocities at perigee (v_p) and apogee (v_a) of the transfer orbit.
4. Compute the delta-v for the first burn (\Delta v_1) and second burn (\Delta v_2), and the total delta-v.
5. Compute the transfer time t_{trans} for the Hohmann transfer.

Can anyone help me in 3??

[woven maple]

@jagged zephyr perhaps you should post this on the physics discord instead

Or physics forum

[jagged zephyr]

Can you DM me the physics channel?

[woven maple]

Question 3 requires specific physics knowledge

https://discord.gg/physics

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[jagged zephyr]

Thanks

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[cosmic crest]

I don't get how stuff is being simplified

only thing that gets simplified here that makes sense is the x

how do you expand (2n+2)! ?

same for (n+1)^(2n+2)

[autumn lantern]

$(2n+2)!=(2n+2)(2n+1)(2n)!$

[rocky lotus]

tm

[cosmic crest]

hmm

so you expand until the constant is at 0

[autumn lantern]

hm no $n!=(n-1)(n-2)…2*1$

[rocky lotus]

tm

[autumn lantern]

only the x and the factorial are simplified i think

[cosmic crest]

okay bet

alright cool I'll make note of how you simplified

tysm

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[autumn lantern]

u welcome :))

[bitter timber]

a

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[void shard]

guys can you tell me how to memorie all the formulas of trignometric eqn , do i just memorize them or what it too hard memorizing them

[void shard]

help

?

[wraith heart]

#study-discussion

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[wraith heart]

answered in #study-discussion

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[dire helm]

Am I missing anything?

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@dire helm Has your question been resolved?

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[leaden whale]

Hi need help with this can someone simplify this pls

[wraith heart]

,rotate

[quasi valve]

did you try factoring the numerator?

[leaden whale]

No

Tryed alot to know how we did get this result but was hard for me

[quasi valve]

you mean, how to go from the first line to the second?

[leaden whale]

Yes

[quasi valve]

try multiplying the numerator and denominator by 3eps

[leaden whale]

Can u show me pls

[quasi valve]

^

try it and show what you get, if you can't get the second line from the first

[leaden whale]

Got this

@quasi valve

[quasi valve]

this doesn't look right, it appears that you multiplied the denominator by 3 but not the numerator

to get this, i mean:

[leaden whale]

So whats the right

[quasi valve]

you need to multiply the numerator by 3 as well

so do that

[leaden whale]

Same shit brother

@quasi valve

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@leaden whale Has your question been resolved?

[delicate parrot]

does this help you?

[leaden whale]

Man u r a hero thanks alot

[delicate parrot]

no problem

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[spice tartan]

Is 2) wrong?
Déduire que= deduce that
So we have to use the previous question but shouldn't the 0 and (1-cosx)/sinx be flipped

[normal hollow]

Multiplying with conjugate might help

[turbid valve]

,rccw

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[quasi valve]

1-cos(x) and sin(x) are both positive in that interval, it wouldn't make sense if you said (1-cos(x))/sin(x) < f(x) < 0

(if that's what you meant)

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[vital island]

can someone help me real quick idk how to calculate % can someone like tell me real qucik what 17% of 5hours and 30 minutes is

[normal hollow]

(17/100)×(5 hours and 30 mins)

[vital island]

and why /100?

[normal hollow]

Percentage refers to the amount with respect to 100

[vital island]

so that would be 56 minutes and 10 seconds

[normal hollow]

For example u had 8 slices of pizza ,u ate 2

Out of 8 slices u had 2
Out of 100 slices ,u had (2/8)×100=25%
So u ate 25% of the pizza

[vital island]

oh ok

so

17/100 = 0,17 --> 0,17x330=56,1

[normal hollow]

10 secs?

56 mins is ryt

[vital island]

ryt?

[normal hollow]

Right

[vital island]

ohhh

ok

thanks

i need to wait 56more mins till my package is here

[normal hollow]

It's 56 mins and 6 secs

Not 10 btw

[vital island]

how u got 10 secs

its 56,1 am i mistaken?

[normal hollow]

U wrote it here

[vital island]

oh i meanty 6

[normal hollow]

If 56.1 minutes ,then yes

[vital island]

ok

[normal hollow]

Welcome to mathcord btw

[vital island]

i get it

thanks

ive been in here before

[normal hollow]

Oh ic

[vital island]

but i left bcs my dad wanted me to try math myself without help

[normal hollow]

We dont reveal answers directly tho

Guiding u through maths should be okay

[vital island]

true

but he was very strics

until i got a 87 on my math examn

[normal hollow]

Woah thas impressive

[vital island]

it wasnt that hard

[normal hollow]

Still efforts matter

[vital island]

it was some wierd math law and the rule of 3 and some other things like first degree function and General Stokes theorem

[normal hollow]

I see ,well u did good

[vital island]

im proud lol

finally going to my last year

its just been like 4 years since i did calculations with %

so i didnt know it anymorer

[normal hollow]

As u should be

[normal hollow]

I see

[normal hollow]

Gl w it

[vital island]

thanks

have a good night/day

[normal hollow]

U too

[vital island]

how do i close this?

[normal hollow]

Type .close

[vital island]

.close

[vale dock]

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[valid pilot]

how do you find the domain of the derivative function. where did it come from? does the domain just stay the same as the original function i dont understand

[jovial scarab]

Remember that the derivative is basically a limit, so we need it to look the same when approached from either direction

if you’re in an open interval, the derivative will just look the way it normally does, because the function behavior is consistent in a neighborhood of the point you’re looking at

but, if you’re at an endpoint where behavior switches, you have to manually check that the limit is the same in all directions

for instance, wherever x > 0, the function looks like x^2 + 2x + 1. that means that if we pick any point > 0, then the function looks like x^2 + 2x + 1 from either direction if we get close enough to that point.

We can apply similar logic when x < 0.

But when x = 0, there’s switching behavior. From the right, it looks like x^2 + 2x + 1, while from the left, it looks like 2x + 1. we need these to line up at x = 0 for the function to be differentiable at x = 0. Otherwise, it won’t be differentiable there

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[rustic knoll]

Does Muirhead inequality work if the sequence of exponents contain negative numbers?

[rustic knoll]

I feel like it should, because I can multiply both sides (abc)^... so the negative numbers get removed

[vale dock]

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[rustic knoll]

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[vocal fossil]

Q5

[vocal fossil]

<@&286206848099549185>

[green urchin]

!15m

[vale dock]

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.

[green urchin]

I'll help you once I'm done with the previous channel

Please wait

[vocal fossil]

I have been waiting since 30 minutes! @green urchin

Ok
K

[green urchin]

It's a new help channel so yeah

Looks like the previous helpee is inactive

[vocal fossil]

Fine

[green urchin]

Yeah

Where are you stuck

Tell me the question no.

[vocal fossil]

Bro, I give you my solution. I am getting my answer. 62, that’s not right.

It’s question number five

[green urchin]

Oh yeah

[vocal fossil]

I am talking that how can I find the derivative of integration of a function?

[green urchin]

You applied the fundamental theorem wrong

First let the antiderivative of f be g

Such that g'=f

So integrating g' from 0 to x

It'll result it g(x)-g(0)

Right? Integrating the derivative of a a function results in that function only

[vocal fossil]

Like this

[green urchin]

Yes

[vocal fossil]

Wow

[green urchin]

Now

[green urchin]

Why'd

You

Denote the LHS as g

[vocal fossil]

Then

[green urchin]

I said

g can be any function

Such that

If we differentiate g

We'll get f

Keep your LHS as F(x)

As you've told

Now we have

F(x)=g(x)-g(0)

[vocal fossil]

Yeah

[green urchin]

Differentiate both sides

[vocal fossil]

I got there

[green urchin]

What g'(x)?isn't it f

So F'(x)=f(x)

[vocal fossil]

Hssss

Yesss

See like this

[green urchin]

Oh so @vocal fossil you're differentiating F(x²)? That'd be a different story

[copper stump]

I dont wanna interrupt, but when you tried calculating F'(x), you used F'(x^2) for that. Which is different, making it wrong.

[green urchin]

F(x²)=g(x²)-g(0)

[vocal fossil]

Yess

[vocal fossil]

U r also right

[green urchin]

True

[copper stump]

Dont use sqrt here. That induces positive and negative values of sqrt(x) and you end up considering only half the possibilities

[vocal fossil]

Can you just tell me what’s thequestion demands because I’m really confused on

[copper stump]

instead directly use F'(x^2) with chain rule

[vocal fossil]

Ok

[green urchin]

Yeah

[green urchin]

@vocal fossil substitute your function for F(x²)here

Then differentiate

[vocal fossil]

Bro I am confused 😭

[green urchin]

Look

What is F(x²)

[vocal fossil]

X square into one plus X

[green urchin]

So x²+x³=g(x²)-g(0)

Differentiate both sides

[vocal fossil]

Ok

W.r.t. X or X squared.

?

[green urchin]

ofc x

Wild typo

[vocal fossil]

Hmm

Nxt ?

[green urchin]

What is g'(x²)

It's f(x²) right

[vocal fossil]

f(x2)

Yeah

[green urchin]

Now what'll you do to obtain f(4)?

Put x=2 right

[vocal fossil]

Like this

[green urchin]

Were are you getting square roots?

Don't substitute that

It'll be confusing

[green urchin]

Directly substitute x=2 into that equation

[vocal fossil]

No, I just change the formula in terms of route X so that the function of X

Okay, I understood your approach option. That is also fine to me.

[green urchin]

you don't know yet

If it's -√x

Or √x

[vocal fossil]

Oooo

Yeah

[green urchin]

As someone said, it'll limit the function to half

[vocal fossil]

Fine

Thankssssss @green urchin

😌😌

.close

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Channel closed

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[green urchin]

No worries

[vale dock]

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[shell moss]

Based on the 1st image there are 2 white quadrilatirals and 2 black quadrilatirals.

Using this concept, identify how many Quadrilaterals are found on here? Consider overlaps as one quadrilateral (ex. The long white rectangle at the innermost part of the image)

[vale dock]

@shell moss Has your question been resolved?

[shell moss]

<@&286206848099549185> hi i need help with my hw

[radiant prawn]

yeah sure!

whats the question?

[pale scarab]

Uni?

[radiant prawn]

a

a counting problem

interesting

[radiant prawn]

im a bit confused, how are there 2 white quadrilaterals and 2 black quadrilaterals?

is a white quadrilateral a quadrilateral that is coloured white or a quadrilateral that has white edges?

@shell moss you.. there?

[sharp whale]

you left out the part where you were supposed to get an answer for the 'next meeting'

when is this due?

[radiant prawn]

i have no idea

[radiant prawn]

yk what im just gonna roll with it, i suppose the white inbetween the black regions is 1 white quadrilateral, the 2 black regions are 2 black quadrilaterals, and the inside is another.

but using that logic

every black quadrilateral

has a white quadrilateral inside

and what if its a blank canvas?

does the ever-lasting white space count as a white quadrilateral??

[sharp whale]

as seen from here, no

there may be a varying number of quadrilaterals depending on which ones you separate out of view

[radiant prawn]

right now, i dont even know what the question defines as a 'white' or 'black' quadrilateral

[sharp whale]

presumably it was gone over during the 'meeting'

[radiant prawn]

yeah

[sharp whale]

@shell moss you have to actually talk in the channel for us to help you figure it out, the server isnt here for us to give you a solution

[radiant prawn]

also nice to meet you mtt

[sharp whale]

hello

[radiant prawn]

i am perpetually playing minecraft

gregtech is peak

[misty moat]

hi

[vale dock]

@shell moss Has your question been resolved?

[vale dock]

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[signal chasm]

can anyone

[signal chasm]

explain the unique logic part

ik how to solve it

but how do you see how the side is unique

like what angle has to be unique so that side is unique

[jovial edge]

My guess is if you use cosine law to solve the problem you will get a quadratic

And they want it to have only one root

[vale dock]

@signal chasm Has your question been resolved?

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[ruby oriole]

Hi,how do I solve this

[rough talon]

say you fix theta, then it would become a silmutaneous linear equation with variables x and y correct?

[ruby oriole]

Yh

[rough talon]

do you know when a two variable simutaneous linear equation has no solutions?

[ruby oriole]

I’ve done a bit of substitution but it doesn’t cancel down to what it’s supposed to

[rough talon]

(what property would two lines need to have to not intersect?)

[ruby oriole]

Same gradient different intercept

[rough talon]

yes!

[stark wedge]

that or you could look at the determinant

[ruby oriole]

Isn’t determinant for quadratics

How does a linear determinant work

[swift magnet]

that's discriminant

[stark wedge]

no, you're thinking of the discriminant

[ruby oriole]

Damn

[stark wedge]

i mean for a linear system

[rough talon]

something something matrix id presume

[ruby oriole]

I got 2 hours of sleep my brain’s a bit slow

Yh yh

[stark wedge]

go get some more sleep and then come back here

[swift magnet]

honestly i would just recommend elimination for this problem

[stark wedge]

or admit you're on a deadline

[light saddle]

Damn you should really sleep

[ruby oriole]

Determinant =0 was it?

[ruby oriole]

I tried

[stark wedge]

det=0 means no sols

[swift magnet]

(or infinitely many)

[ruby oriole]

I’m not this is revision not homework

It’s 9 am I can’t be sleeping anyways

[ruby oriole]

I was on my bed for 8 hours

Only managed to be asleep for 2 of those hours

[stark wedge]

anyway, something very curious will happen if you calculate the determinant for this system

[ruby oriole]

I’ll try this

Smth like this,I kinda forgot matrices a bit tbh

[sinful obsidian]

correct

has something curious happened yet

[ruby oriole]

=1 or smth like that

[sinful obsidian]

that is something curious

[ruby oriole]

That means it’s true for all values of theta

So that’s the answer?

[sinful obsidian]

that sounds right to me but it's only right if ann says it's right

[ruby oriole]

😭

The solution seems to say it’s correct

Thank you for the help guys

.close

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[sinful obsidian]

nice work and np!

[stark wedge]

don't hinge truths on me

[sinful obsidian]

i wanted you to come back and check 😔

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[tidal terrace]

what is the best strategy to solve something like
$e^{4-5x}=11^{7-3x}(7^{2x+1})$ ?

[rocky lotus]

qimmah

[stark wedge]

logs

either that or pull everything apart w exponent laws and put it into the form A^x = B

[tidal terrace]

doing logs would result into some kind of factoring yeah ?

[stark wedge]

i guess?

[tidal terrace]

icic thanks

.close

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[tawny crane]

help what is this

[tawny crane]

i get that i is the square root of -1 but what the hell are these answers

[frank salmon]

did u study complex numbers?

[tawny crane]

no

[frank salmon]

alright basically any complex number is writen in form of $z = a + bi$ where a is called real part and b imaginary part

[rocky lotus]

Ryne___np

[frank salmon]

a and b are both real numbers

[tawny crane]

do i calculate a and b separately

[frank salmon]

no when simplfying an expression you need just factorise the i so you can have an imaginary part next to i and real part

for exemple

[ivory valley]

A quicker way to do this is notice that multiplying a complex number with itself is just a rotation, so you only need to figure in which quadrant you land when you calculate the argument (angle), and how multiplying that by 3 affects the new complex number.

[frank salmon]

$ai + z + (x+yi)^2 = ai + z + x^2 + 2xyi - y^2= (a+2xy)i + z +x^2-y^2$

[rocky lotus]

Ryne___np

[tawny crane]

i'm cooked i didn't get that at all
okay i'll search up like a 30 minute yt video and pray i pass my exam in a week
thank you all

[frank salmon]

what part you didnt get

[ivory valley]

At first you are in the first quadrant and the argument is $\arctan(4/3)$, now the power of 3 changes the argument to $\arctan(4) \approx 76^{\circ}$ which implies your new complex number lies in the second quadrant which means $\mathfrak{R} < 0$ and $\mathfrak{I}>0$.

[tawny crane]

i have heard these terms being used like, once total

[frank salmon]

bro relax he didnt study complex numbers yet

[tawny crane]

i will now email my maths teacher in hopes that he can revive my failing notice

.close

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[ivory valley]

There is nothing wrong with what I shared

[frank salmon]

well he wont understand it

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[frank salmon]

.close

[gusty jasper]

how do i find the exact equation?

[jovial edge]

uhh, the equation is tan(2sin(x)) ?

[gusty jasper]

yes

[jovial edge]

you have to limit the value for x tho

[gusty jasper]

tan = sin/cos

hm?

[terse compass]

I assume the part with pi there

[terse compass]

X shouldn’t go below negative π or above positive π

[gusty jasper]

yes but they need the equation for x

as in x = pi/2 + npi

for tan(x)

but this is tan(2sinx)

[jovial edge]

for asymptotes not x

[gusty jasper]

yes

[jovial edge]

well what have you tried?

[gusty jasper]

cos(2sinx) has to be zero

[jovial edge]

yes

[gusty jasper]

for cos to be zero it should be cos(pi/2 +npi)

so...

2sinx = pi/2 + npi

[jovial edge]

yup

what's the problem here?

You can just solve for x

[gusty jasper]

so

cos(2sinx) approaches 0 as 2sinx approaches pi/2 + npi

but x is arcsin(pi/4) +npi

[jovial edge]

and also pi-arcsin(pi/4) +npi

remember x can only be in [-pi , pi]

[gusty jasper]

this doesn't tell me much to be fair

[jovial edge]

well arcsin(pi/4)+pi>pi

so x can't be larger or equal arcsin(pi/4)+pi

and arcsin(pi/4)-2pi<-pi

[gusty jasper]

is this really the way to find the asymptotes?

[jovial edge]

see for yourself

[gusty jasper]

this can't be this hard, i just learnt the definiton of asymptotes ;-;

[jovial edge]

It's just trig tbh

[gusty jasper]

alright got it

thanks

.close

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[wooden bridge]

Hello I am in 9th class and it's the first time in maths my chapter is linear equations in two variables , till 8th it was one , so pls explain me what the heck is this , I am confused how can we assume x , if it is not given , random assumption means changing value of a particular equation??

[stark wedge]

where do you see "assume x"?

are you looking at a fully worked solution of some particular question?

[wooden bridge]

Like in ques 2x+3y = 0 find two solution of equation

We put x = anything like 0 and find y

[stark wedge]

oh, you are just given one equation and they ask you to find any two solutions of that?

[wooden bridge]

So how can we put it anything ourselves

[wooden bridge]

Yes

[stark wedge]

you have a lot of freedom of choice here bc this equation has infinitely many pairs of (x,y) that satisfy it

so it is a little strange yes

but you aren't finding the entire solution set but just picking out your favorite points from it

[wooden bridge]

So you mean it cannot be perfectly satisfied like we solve linear equ in one variable

[stark wedge]

dunno what you mean by "perfectly satisfied"

[wooden bridge]

Is there a way to find entire ? 🤩

[stark wedge]

well you can graph it on the coordinate plane

it'll give you a straight line of some kind

[wooden bridge]

Means in linear equ in one we get same Sol always

[wooden bridge]

And It will always be same ?

[stark wedge]

yes

(unless you fuck up)

[wooden bridge]

Ok thanks , graph is not in my syllabus

.close

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[brave bay]

Hi could someone help me? I don’t understand how the unit circle works or how I’m supposed to be solving these questions 😭

[quick rose]

,rccw

[hearty belfry]

<@&268886789983436800>

[final adder]

@brave bay any one in particular?

[brave bay]

Any one is fine I just want to know how to solve them 😓

[final adder]

alr lets start with a) then

how would you start?

[brave bay]

I would determine which quadrant it’s located in (?)

[final adder]

good!

if cos is positive, which quadrants could it be in?

[brave bay]

I think 1 or 4

[final adder]

yep!

ok, if theta is in quadrant 1, can you determine its value?

[brave bay]

60 degrees?

[final adder]

yep!

[brave bay]

Oh is that the answer

😰

[final adder]

there's one more!

in quad 4

[brave bay]

300?

[final adder]

yes!

[brave bay]

Ohhhh I get it now

Tysm!!

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[final adder]

do you still need help with the other two?

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[midnight pier]

How to do this? h^2 = ab in my book.

[tidal terrace]

i don't think h^2=ab is relevant in the parabola question

[midnight pier]

any advice on how to takle this?

[tidal terrace]

you know the general form of a parabola ?

[midnight pier]

not rly no

[tidal terrace]

not even (x-h)^2=4c(y-k) nor (y-k)^2=4c(x-h) ?

[midnight pier]

no i havent come across this

ive done engineering maths first year only

[tidal terrace]

anyways for every conic stated here they have a general form the summarizes most of their properties
for the parabola it can give you a lot
coords of vertex , focus , the direction , directrix and much more
length of the latus rectum is 4c for any parabola in either form

if you want to show it then first off find the focus point then find the distance between (8/3 , y^2) and (8/3 , -y^2) which should be the latus rectum

[midnight pier]

why 8/3

im new to conics

[tidal terrace]

focus coords of a parabola of the from y^2=4cx
is (c,0) and the directrix equation is x=-8/3
other properties would show themselves

[midnight pier]

do u recomend any resources to learn more? my book doesnt go into much depth

[tidal terrace]

there is a lot but i'd say khan academy and organic chemistry tutor
learn specific conic sections first and properties then go for the general equation
some will teach the topic differently
like for example to determine the conic sections you must know if B^2-4AC is bigger than 0 or equal or less than 0 where B is the coefficient of xy and A and C coefficients of x^2 and y^2 respectively to determine the conic

[midnight pier]

thanks ill do it now

[daring elm]

hi my name is hicham please help me

@daring elm

[tidal terrace]

!occupied

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[midnight pier]

.close

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[spark burrow]

So what went wrong?

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@spark burrow Has your question been resolved?

[jovial scarab]

these look consistent to me, f'(g(x)) treats g(x) as the variable you're differentiating with respect to. it's like you're plugging y = g(x) into f'(y). so we can think of f'(\lambda x) as df(\lambda x) \ d(\lambda x), and then we just get the jth coordinate

[spark burrow]

Isn't f'(g(x)) = d f(g(x)) / dx?

[jovial scarab]

no, f’(g(x)) should be interpreted as “find f’(y) and then plug in y = g(x)”

the right hand side there equals f’(g(x)) g’(x), that’s just chain rule

[spark burrow]

Oh, you're right...

[spark burrow]

Thanks!

.close

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[stoic yew]

ya'll. what grade do you have to be in to get help?

[turbid valve]

#rules ; #❓how-to-get-help

There isn't really an age limit imposed on this server beyond Discord's ToS

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[left quest]

😭 what’s wrong w/ it??

[left quest]

HA and VA don’t exist.
Hole - (3,-1/4)
x intercept - (x=2)
Y intercept - (y=1/2)

Anything wrong w/ my numbers…? 😕

[gaunt lark]

I will answer here, also answered innthe algebra channel

[gaunt lark]

the function is (-1/2)(x - 2) with a hole at x = 3, you're really close actually

[left quest]

I am? 🥹🥹🥹🥹

What’s the (-1/2)?

Y intercept?

[gaunt lark]

ah no, that's not a normal form

how could you turn y = (-1/2) * (x-2) into slope - intercept?

[left quest]

Mx+b …?

[gaunt lark]

yes, so what's M here

[left quest]

Hm..

-1/2..?

[hazy pivot]

Yes

[gaunt lark]

yes, and that's correct to your original answer

[hazy pivot]

And what is b

[left quest]

I don’t get it..? What do I do with it..?

[left quest]

B wud be -2, right?

[gaunt lark]

no

[left quest]

Oh

[hazy pivot]

y = mx + c

Not m(x+c)

[left quest]

Oh

Right

So no b?

[hazy pivot]

Oh right b, not c

Either way my point is

Do the multiplication

[turbid valve]

The b or c are just constants; what you call them isn't that important

[hazy pivot]

Ye

[turbid valve]

What is important is that in this form, that addition comes after the multiplication

[left quest]

I’m like…lost rn 😭. Should we js start from the top?
Idek what we’re getting at..?

[turbid valve]

Not before

[hazy pivot]

But it's always better to have consistency

[turbid valve]

True

[hazy pivot]

You have y = (-1/2)(x-2)

This doesn't look like y=mx+b

[left quest]

Where..? 😭

[hazy pivot]

^^

[gaunt lark]

Maybe starting from the top would be instructive tbf

[left quest]

We’re talking abt the function?

[hazy pivot]

Actually yeah

Let's start from the beginning

[left quest]

Alright

[hazy pivot]

What's HA and VA

Just so I understand your question

Oh asymptotes

[turbid valve]

Horiz. and Vert. asymptotes; see the image

[left quest]

Yeah

[hazy pivot]

Yeah my image blindness continues

Either way

You have a ratio of two polynomials

First step should be factorising

[left quest]

Yeah

I did that

Final result was (x-2)/-4

The (x-3) had to be canceled out

[hazy pivot]

How do you still have a -4

It should cancel out to be -2

Write out the factorization properly

[left quest]

Maybe that’s the issue 😭.

[hazy pivot]

Write the thing out properly

[left quest]

Canceling it out with -2 right?

I mean 2

[hazy pivot]

Yes the latter

Good, now you have (x-2)/(-2)

[left quest]

Ah YESS

😭

[hazy pivot]

And since you cancelled out an x-3 on numerator and denominator

What happens at x = 3

[left quest]

Hole

The x value of the hole

[hazy pivot]

Yes

[hazy pivot]

Now we have this

And we want to write this as y = mx + c to get slope

[left quest]

You lost me. What’s the slope for..?

I usually js find all the features then graph them

[hazy pivot]

Oh right your question doesn't ask for slope at all

But essentially slope is just the steepness of the graph

Cool we don't need it

For the intercepts, just plug in x = 0 to get the y-intercept

And then solve for y = 0 to get the x-intercept

[left quest]

I think it got this from here

🥹 thank you so much, kind stranger!!

[hazy pivot]

No worries :D

[left quest]

😭 math ain’t my strongest suit but..im trying 😮‍💨✊

@gaunt lark thank you too!! 🙏☺️

Really appreciate it

[gaunt lark]

Sure, I figured at some point one helper is better than two lol

[left quest]

I finally got it down. You came first tho and it was urgent so..im really grateful 🥹🙏

[gaunt lark]

You're welcome! I'm a bit speedy and help many with math. brw, it's proper ettiquette to do .close when you're done with a channel, so it can open again (not clutter the list)

[gaunt lark]

ig you know where to ask if you have math questions.

[left quest]

Aww, that’s kind of you.
Yeah, I will. Thanks for letting me know.

[left quest]

Ofc!! 🙏

.close

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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.

[ivory tree]

can someone explain how to do this with combinatorics?