help-0

[earnest saddle]

yes

[limpid turret]

Yes

[latent magnet]

Thank you so much!

[earnest saddle]

as long as o is centre of base

[limpid turret]

Assuming the base is a circle

[latent magnet]

O is a centre

1 more

From this exercise

[earnest saddle]

obviously also assuming given figure is right circular cylinder

[latent magnet]

Can I solve it like this?

I dont know if the system of equations is right

@earnest saddle

[vale wigeon]

почерк трудночитаемый...

[latent magnet]

Знаю )

[vale wigeon]

можешь расшифровать или переписать в более читаемом виде?

а то прямо как врач...

[latent magnet]

S=2 * pi * r * h + 2 * pi * r^2
AB * AD = 16*sqrt(3) -> AB = x; AD = y

x * y = 16*sqrt(3)
tg60° = x/y

[vale wigeon]

то есть вот эта закорючка -- икс?!

ни в жизни бы не догадалась. разве что u, например

[latent magnet]

Это икс )

[vale wigeon]

боже мой

[latent magnet]

Меня кстати на шейха хотели взять

[vale wigeon]

ну таки да, xy = 16sqrt(3), x/y = sqrt(3)

[latent magnet]

Получается я правильно сделал эту часть?

[vale wigeon]

да

и получилось y = 4, x = 4 sqrt(3)

[latent magnet]

Если честно, первый раз такую задачу правильно решил

Но там нужно было найти еще площадь

Вот это получилось

Могу переписать, чтобы было читаемо

[vale wigeon]

да, пожалуйста, так и сделай

[vale wigeon]

какую площадь?

[latent magnet]

AK = 1/2 * AD = 2
AOK = 60°
tg60° = AK/OK
sqrt(3) = 2/OK
OK = 2/sqrt(3)
r = OA = 2 * OK = 4/sqrt(3)
S = 2 * pi * (4/sqrt(3)) * 4*sqrt(3) + 2 * pi * (4/sqrt(3))^2

[latent magnet]

Площадь полной поверхности

[vale wigeon]

так

а что за точка K?

[latent magnet]

Эту точку я дорисовал позже, эта точка лежит на середине AD

[vale wigeon]

ок

тогда вроде все ок

[latent magnet]

Спасибо, и нужна помощь еще с одной задачей

Не пойму как сделать

Условие:
Через конец радиуса шара проведено сечение, плоскость которого создает с этим радиусом угол A. Найти площадь сечения, если объем = V

[lone heart]

@latent magnet Has your question been resolved?

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[latent magnet]

Hi newbie

[lone heart]

Available help channel!

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[alpine sable]

c/2+3=10

[vale wigeon]

!status

[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

[alpine sable]

1

1. I don't know where to begin

[long axle]

So u have

[ocean seal]

Stephen

[alpine sable]

yea

[long axle]

Ultimately we want to isolate the “c”

[alpine sable]

then

[long axle]

What do u think we can do first

[alpine sable]

put the c/2+3 in a bracket?

[long axle]

What would that do?

[alpine sable]

i really dont know

[long axle]

If I gave u this problem: x + 4 = 7, how would u solve?

[alpine sable]

the 4 would go to the other side and it would be subtracted with 7

andx=3

[long axle]

Right, we subtract both sides by 4, and find that x=3

[alpine sable]

yea

[long axle]

We are in a similar situation here

[alpine sable]

so what do we do here?

[long axle]

let me replace the c/2 with another arbitrary variable, and let me see if u can get it

[alpine sable]

okay

[long axle]

Let c/2 = k

So k + 3 = 10

How would u solve this

[alpine sable]

k=10-3?

[vale wigeon]

yes

so now you have k = 7
and remembering what k was, we have:
c/2 = 7

how do you proceed?

[alpine sable]

7+3=10?

oh yea

[ocean seal]

Stephen

[alpine sable]

c=7x2

c=14

i still didnt get it

[vale wigeon]

what didn't you get?

we go from c/2 + 3 = 10 to c/2 = 7, and from that to c = 14

[alpine sable]

c/2+3=10

hmm

[vale wigeon]

which part of this process escapes you?

[alpine sable]

fine yeah i got it

c/2=10-3=7

then c=7 x 2

c=14

got it

[lone heart]

@alpine sable Has your question been resolved?

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[alpine sable]

.reopen

[lone heart]

✅

[alpine sable]

<@&286206848099549185>

[slender quiver]

wat

[alpine sable]

w+3/4=6

[gray isle]

!15m

[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.

[velvet cliff]

pings helpers before asking

[gray isle]

anyway exact same idea as the previous question you had

[slender quiver]

w

[alpine sable]

i used the same idea and i got the wrong answer

[gray isle]

show work

[alpine sable]

no i didnt start it yet

i did w/4=6-3

[gray isle]

that conflicts with what you just said

[alpine sable]

and so on

[gray isle]

and again conflicts with what you just said

[alpine sable]

hmm?

[gray isle]

no i didnt start it yet
what was that abouit

[alpine sable]

wait im doing it

w/4=6-3

w/4=3

w=3x4

[gray isle]

you're not doing valid manipulation there

[alpine sable]

w=12

which is wrong

what am i supposed to do there

[gray isle]

firstly do you mean
$$w + \frac34$$
or
$$\frac{w+3}{4}$$
(btw neither of which results in $\frac w4$ after subtracting 3)

[ocean seal]

ℝamonov

[alpine sable]

wait

this

w+3=6x4?

[gray isle]

that would be ideal

[alpine sable]

yea i got it

[gray isle]

although immediately subtracting 3 from both sides would be a valid step,
you didn't do it properly, it wouldn't have helped much regardless.

[alpine sable]

hmm

[lone heart]

@alpine sable Has your question been resolved?

[magic bison]

You have to find w?

Multiply both sides by 4

Then subtract both sides by three

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
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[dusky kernel]

ABC is a triangle inscribed in circle O, with altitude AD, orthocenter , U and V are the feet of the perpendicular from D to AB and , I is the center of the circle inscribed in the quadrilateral.
how to prove I is the midpoint of DK?

[dusky kernel]

i can already prove M is the midpoint of HK

[mellow grail]

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

are all these lines drawn by you? or were ALL of them given in the question

[dusky kernel]

i mean there is just an extra M ?

[mellow grail]

Huh

[dusky kernel]

i just edit it

@crisp iron 😭

[lone heart]

@dusky kernel Has your question been resolved?

[lone heart]

@dusky kernel Has your question been resolved?

[lone heart]

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[short wave]

how do i prove this ?

[short wave]

,tex tan^2\theta \cdot sin^2\theta = tan^2\theta - sin^2\theta

[ocean seal]

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

[craggy token]

Try substituting tan = sin/cos for both sides

And use the fact that sin^2 = 1 - cos^2

It should be trivial from thereon

[short wave]

alr lemme try

[lone heart]

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[lone heart]

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[fierce meteor]

guys i havent done math in a while so its a bit of a dumb questio but can anyone make n the subject plz?

[fierce meteor]

7n-2 <= cn

<@&286206848099549185>

[slender quiver]

!15m

[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.

[slender quiver]

hm

[fierce meteor]

my bad

[fierce meteor]

what does that mean?

[slender quiver]

what would you do

first

[fierce meteor]

ive been stuck on dis for an hour

[slender quiver]

wait what is c

[fierce meteor]

doesnt matter

just neeed to make n the subject

u get me?

[slender quiver]

ok

[fierce meteor]

would u be able to help?

[slender quiver]

ok

subtract 7n

[fierce meteor]

-2<=7n +cn

-2<=n(7+c)

[slender quiver]

subtract

[fierce meteor]

n=>-2/(7+c)

[slender quiver]

c-7 or -7+c

[fierce meteor]

how tho?

[slender quiver]

7n-2 <= cn

-2 <= cn-7n

[fierce meteor]

oh yh

-2<=n(c-7)

[slender quiver]

yep

[fierce meteor]

-2/(c-7) = n

[slender quiver]

yep

[fierce meteor]

<=*

[slender quiver]

ya

are you done

[lone heart]

@fierce meteor Has your question been resolved?

[lone heart]

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[white nebula]

hello i am CS student from India , most of the classes i took in uni where not math intensive and the few that was compulsory where also taught in very poor way and i studied enough to get decent marks . but i am trying to learn math again from basic (high school to uni level) particularly for AI/ML what books / courses would you suggest i go through thanks

[modern sedge]

https://khanacademy.org

free, online. Not AI/ML but it taught me algebra and calculus which are really important topics in AI/ML

[lone heart]

@white nebula Has your question been resolved?

[lone heart]

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[violet ore]

is there a way to see if this converges to diverges by transforming it into a geometric series

[violet ore]

intuition it looks like it diverges because the overall power is 1. also i could just do root test probably

[slender quiver]

but it is ^n

[vague coral]

$\exp(n\ln(\frac{4n^7}{n^7 + 3}))$

[ocean seal]

Ｈｅｒｅｌｓ

[slender quiver]

so it is bascially 4^n

ye

[vague coral]

at infinity it should be equivalent to this :
$\exp(n\ln(4))$

[ocean seal]

Ｈｅｒｅｌｓ

[vague coral]

4^n diverges

[violet ore]

alr

i guess that is a cool way to see it

thank u

.close

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[lone heart]

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[shell tusk]

I want to solve the following cubiq equation : $2x^3-x^2+4x+2=0$
Tbh I have zero intuition on how to solve these, I would appreciate some input on how to approach to solve them.

[ocean seal]

aabb

[alpine sable]

so

the cubic equations has a methode

first u have to find one of the roots

[gray isle]

this doesn't seem to have nice solutions

[alpine sable]

by trying the factors of the constant over the x^3 constant

like

[gray isle]

what grade are you in?
did you copy down the equation correctly?

[modern sedge]

no rational root and single real root

[alpine sable]

2/2,-2/2,1/2,-1.2

does it have imaginary solutions?

sec

[gray isle]

are you expected to use stuff like cubic formula

[alpine sable]

this one has a complex answers

[gray isle]

usually you'd approach degree 3+ polynomials with rational root theorem
if there doesn't seem to be obvious grouping and hope for the best
but that's not going to help here

[shell tusk]

So its a algebra course and 1 exercise on the problem sheet is solving these type of polynomials.
Probably because we touched up on the history (polynomials for n=1,2,3,4,) before doing group theory.

I think im allowed to do whatever, but I have never solved these and I wanted to ask if there is a "easy" way

[alpine sable]

this one specially

is hard

[gray isle]

did you copy down the equation correctly?

this isn't something that's likely to come up in an alg1 course

[alpine sable]

it appears like defferential equations course

[shell tusk]

okay I hope I didnt fuck it up, originally its 2x^4-x^3+4x^2+2x=0
and I read on wikipedia: If the constant term a4 = 0, then one of the roots is x = 0, and the other roots can be found by dividing by x, and solving the resulting cubic equation,

is the quartic equation easier?

[alpine sable]

its the same methode

still gonna give imaginary soulutions

[shell tusk]

im very sorry its -4x^2

[gray isle]

zzz

[shell tusk]

bruh legit im sorry, i copied it down wrong the first time

[gray isle]

huge difference

the proper polynomial does indeed have nice roots

usually you'd approach degree 3+ polynomials with rational root theorem

[alpine sable]

now this one has real roots

[coral thorn]

lmao

[shell tusk]

okay ill check out rational root theorem, Im positive I can carry out the calculations
I just needed a starting point

[gray isle]

when people say

did you copy down the equation correctly?
you should quadruple check immediately

[alpine sable]

well use the rational root theorem

x=1.41......

x=1/2

x=0

x=-1.41....

[shell tusk]

lesson learned...
again sorry
And thank you for the help
Also thanks attacker 🙂

.close

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
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[regal dirge]

can i get help with this?

[alpine sable]

is that optimization problem

[regal dirge]

i'm quite new, what does that mean?

[alpine sable]

is this in differentiation

[regal dirge]

you are supposed to calculate the surface of the cylinder, and calculate the cost for each surface top and wall

k(x) = cost(x)

[alpine sable]

i get it

[regal dirge]

what do you think

[alpine sable]

the thing is i know this but i took it in arabic

finding some difficulties to understand the question

[regal dirge]

yeah, i find it quite hard

1 L = 1000cm^3

[alpine sable]

yeah i know it

but i told u took it in arabic language

[regal dirge]

so you cant help me?

[alpine sable]

im sorry

[regal dirge]

ok

[alpine sable]

maybe someone else can

[regal dirge]

how can i ask them

[stark yew]

what exactly is your question?

[regal dirge]

you are supposed to calculate the surface of the cylinder, and calculate the cost for each surface top and wall
k(x) = cost(x)

[stark yew]

I understand that but what exactly do you need help with?

[regal dirge]

how do i prove the surface of the top and bottom. And the wall with the formua i was given?

[stark yew]

are you referring to the question a?

[regal dirge]

yes

because later i can ust multiply the cost to the surface

that i can manage😆

[stark yew]

do you know what the area of a circle of radius x is given by?

[regal dirge]

pir^2

[stark yew]

well, not quite

i don't see an x in there

[regal dirge]

pixr^2

no

pix^2

[stark yew]

very good

now, what is the circumference of a circle of radius x given by?

[regal dirge]

pi*d

[stark yew]

again, i don't see an x in there

[regal dirge]

2pix

[stark yew]

good job

now, a cylinder has two kinds of surfaces. two circular surfaces, and a curved surface

the circular surfaces are simply that - circles

[regal dirge]

yes

[stark yew]

and the curved surface's area is found by multiplying the circumference of the circles that enclose it by the height of the cylinder

that is, if the height is h, the area of the curved surface is given by 2*pi*x*h

[regal dirge]

yes '

so then i get the volume?

no

[stark yew]

the volume is found by multiplying the area of the circular surfaces by the height

while the surface area of the curved surface is found by multiplying the circumference of the circular surfaces by the height

[regal dirge]

pixh is the circle without the area?

ahh i understand

[stark yew]

i'm not sure what you mean

[regal dirge]

forget it, it was bad written

[stark yew]

i believe you can solve question a now?

[regal dirge]

so 2 pix*h is the surface area?

[stark yew]

of the curved surface, yes

[regal dirge]

how do i find h

[stark yew]

by using the fact that the volume must be 1 liter

[regal dirge]

1000cm^3?

[stark yew]

yes

[regal dirge]

but the read text is not actually in the question, my teacher wrote it

[stark yew]

that's not the height, if that's wht u meant. note that i said u have to use that fact.

what's the volume of a cylinder of radius x and height h given by?

[regal dirge]

2pix*h

[stark yew]

that's not the volume. that's the area of the curved surface

[regal dirge]

ohh

pix^2*h

[stark yew]

very good!

and what must the volume be equal to?

[regal dirge]

1 L

[stark yew]

or 1000cm^3

so what must pi x^2 h equal?

[regal dirge]

1000 cm^3

[stark yew]

precisely

then you can express h in terms of x

go ahead, show me the expression for h in terms of x

[regal dirge]

i did not understand

you mean to make x = .... ?

[stark yew]

no, make h= ...?

[regal dirge]

ahh

h = 1000cm^2

/pix^2

[stark yew]

$h = \frac{1000}{\pi x^2}$

[ocean seal]

waris

[stark yew]

Is that what you mean?

[regal dirge]

h=(1000cm^3)/pix^2

yes

[stark yew]

good

[regal dirge]

but how can i solve that if i dont know x?

[stark yew]

well, i guess you can proceed from here now?

[stark yew]

ah

you're asked to find the best x (and h)

it's an optimization problem

i believe it's part of calculus course, isn't it?

[alpine sable]

yeah u need to use extreme values theorem

[regal dirge]

its a first year high school in norway

question

from a test my class had last week

but i was sick

[stark yew]

sorry to hear that

[regal dirge]

it's ok, I am much better now

so this is basically the answer to a?

h = ...

[stark yew]

Okay let me clearly state the problem we're trying to solve. The material making the curved surface costs less than the material making the lid and the bottom; so we wanna use less of the material making the lid and bottom, and more of the material making up the curved surface. And we must obtain a cylinder of volume V.

we'll come back to the actual problem later

i would like to teach you how to solve optimization problems like this, if you want.

[regal dirge]

yeah sure

[stark yew]

hmm. would you be able to come onto a voice channel?

huh. odd. apparently we don't have any.

well nvm.

[regal dirge]

sorry, can't talk right know, I am on vecation in my lodge

with my fam

[stark yew]

it's alright, there aren't any voice channels anyway.

So we're told to produce a cylinder of volume V. Let's not worry about the number yet, we'll introduce numbers later.

Now. Let's assume the volume of the material making up the lid costs more than the material making up the curved surface.

We would like to save money. So which material would we want to use more of, and which one would we like to use less of?

[regal dirge]

we would use more of the curved surface

[stark yew]

very good

now, the cost depends on the area. so if we increase the curved area, we'll be using more of the material that costs less.

and similarly, if we reduce the circular areas, we'll be using less of the material that costs more.

common sense so far.

[regal dirge]

yes 🙂

[stark yew]

now, consider the radius $x$ and the height $h$ of the cylinder. the area of the curved surface is then given by
$$ A_{cur} = 2\pi x h $$
and the area of the circular surfaces is given by
$$ A_{circ} = 2\pi x^2 $$

[ocean seal]

waris

[stark yew]

do you follow?

[regal dirge]

let me check

yeah

[stark yew]

hm. now remind me: what's the area of a circle of radius x?

[regal dirge]

pix^2

[stark yew]

but i used 2pix^2 here. why is that?

[regal dirge]

because there is a lid and a bottom

[stark yew]

very good!

[regal dirge]

so you get the area of both surfaces

[stark yew]

indeed, indeed

now. let's say we have a function $f(x) = x^2$. how do we find the minimum value of the function?

[ocean seal]

waris

[regal dirge]

?

sqre root?

[stark yew]

hmm.. no

how many classes did you miss exactly?

[regal dirge]

1 week

[stark yew]

hmm.. i'm afraid you've missed more material than you think.

anyway.

[regal dirge]

ohh

ofcourse

[stark yew]

let's say $y=x^2$. what is the smallest possible value $y$ can have?

[ocean seal]

waris

[regal dirge]

f'(x) = 2x

[stark yew]

keep going

[regal dirge]

can i do more

[stark yew]

you didn't find the minimum value yet

[regal dirge]

f''(x) = 2

[stark yew]

you're just differentiating

i asked for the minimum value

[regal dirge]

i dont quite understand what you mean

[stark yew]

https://www.khanacademy.org/math/ap-calculus-ab/ab-diff-analytical-applications-new
i'd suggest you watch this entire unit from khan academy.
you have to learn how to maximize/minimize a given function. only then can you work on optimization problems.

[regal dirge]

this is what my teacher has written

but i think I'm over complicating it

[stark yew]

i could simply give you the worked out solution to your problem, but that won't benefit you at all. you must learn the content. and it's too much to teach by text within the time we have right now. it'll take around an hour.

[stark yew]

so i'd suggest you go through this entire unit, not skipping a single video or quiz. then go through the problem you asked for help with, and i'm confident you'll be able to solve it yourself.

[regal dirge]

yeah, i need to go to bed also

thank you

[stark yew]

well, going through that unit is gonna take a while too. perhaps you can watch it tomorrow.

feel free to dm me if you have any confusions while going through the khan academy unit

[nimble latch]

this community is so wholesome-

[regal dirge]

yes, thank you

[nimble latch]

@stark yew I have a question too, are you free to help

[stark yew]

sure

[nimble latch]

I'll dm you then

[lone heart]

@regal dirge Has your question been resolved?

[lone heart]

@regal dirge Has your question been resolved?

[lone heart]

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[lunar lintel]

how does this make sense

[lunar lintel]

how do they get rid of the +15x^2?

[solemn juniper]

They factored out a 5

[lunar lintel]

oh

lo

.close

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[robust jungle]

Hi, i need help with a kind of problem, i don't want the answers, i just want to understand how to solve it:
Example (i used different numbers):

The sum of the first 3 consecutive terms of the arithmetic progresion is 252, if to the 1st term we substract 7 and to the 3rd term we add 34, the terms form a geometric progresion.

Determine:

-the difference (d) of the arithmetic progression:
-the ratio (r) of the geometric progression:
-the 1st and 9th term of the arithmetic progression:
-the 1st and 7th term of the geometric progression:

[uncut tartan]

You can find the first 3 terms from the info provided

Then see what's the relation between then to determine what's asked

[robust jungle]

but how can i find the first 3 terms of the arithmetic progression?

ive been trying all day

[uncut tartan]

Write them as a, b and c

So the sum would be a+b+c

What's the relation between consecutive numbers of a geometric progression?

[robust jungle]

so i have that the A. progression is
a + b + c = 252
and the geometric progression is
a-7 + b + c+34 = 279

but im stuck at that

[uncut tartan]

If a B and C are consecutive în the progression how do u write C using B (for example)

[robust jungle]

but they are consecutive terms, not consecutive numbers

so it wouldn't be b+1=c

[uncut tartan]

C can be written as the term before (in this case B) multiplied by the ratio

[robust jungle]

so it would be:

arithmetic progression:
a + b + c

Geometric progression

a-7 + (a-7)xr + ((a-7)xr)xr

but i still dont understand how to infere the terms a b and c of the arithmetic progression

sorry, i used 2 when i should have used r

[uncut tartan]

So if we have the first 3 terms we can write them all by using only one

[robust jungle]

yes

but i still dont understand how to get the terms with the relation between the 2 given

[uncut tartan]

Let the first one be a

The next one would be ar

And the third one would be (ar)r

[robust jungle]

ok i understand that

[uncut tartan]

U know the sum of those term

And another relation between them

So u can find a and r

[robust jungle]

i know the sum, it's 279 but i dont know the relation

i have
a + a+x + a+2x = 252 for the arithmetic progresion
and
a + ar + (ar)*r = 279 for the geometric one

[uncut tartan]

You have the sum a+b+c

[robust jungle]

i dont understand

[uncut tartan]

Ok so u know that a-7,b and c+36 are în a geometric progression

[robust jungle]

yes

[uncut tartan]

U can write the second term in function of the first as "second term" = ratio * first term

Oh yah I think I messed it up before it's supposed to be devided

[robust jungle]

so a-7, b = (a-7)*r ?

[uncut tartan]

Yes that's true

And the third term can be written in with the second using the same rule

So c+36=b*r

But we know b from the previous

So we write it using a to have only one unknown number

[robust jungle]

so we have:

a-7 b=(a-7) x r c+36= b x r = ((a-7) x r) x r ?

but how do we know b?

[uncut tartan]

I meant we know how to write it using a

[uncut tartan]

This is exactly what I meant

[robust jungle]

ok ok, im following

[uncut tartan]

But your third term is actually c+36

[robust jungle]

ok ok fixed it

a-7 b=(a-7) x r c+36= b x r = ((a-7) x r) x r

[uncut tartan]

Now u only have a and r if u put it in the sum

[robust jungle]

i dont know a or r

i only know that a + b + c is 252

that's all the info given

[uncut tartan]

Now u have to do the same thing (writing all the numbers using the first) for the arithmetic progression

[robust jungle]

a b= a + d c= b+d = (a + d) + d

d is distance*

[uncut tartan]

Yes

[robust jungle]

ok so we have both progression expressed, how do we determine the numbers?

A.P. = a b= a + d c= b+d = (a + d) + d

G.P. = a-7 b=(a-7) x r c+36= b x r = ((a-7) x r) x r

[uncut tartan]

sorry for letting u wait

The sum of the first n terms in an arithmetic is
(n/2)⋅(a₁+aₙ)

[robust jungle]

Yes

[uncut tartan]

So 256= 3/2(a+a+d+d)

That's just the same thing huh..

[robust jungle]

Thats not correct i believe...becau

[uncut tartan]

I'm not sure where are u supposed to get a third relation

[robust jungle]

Because we dont have a_n

Nor a

[quick peak]

Can I help

[uncut tartan]

Yah

[quick peak]

I just did a system of equations

[uncut tartan]

I'm trying to get the same thing but u get 3 unknown and 2 equations

[quick peak]

You know 3 relations , the add up to 252, they are an arathmetic seq, and if u change it it is geometric

For geometric you know an/an-1 is same for any n

So I set the relationship between a and b equal to b and c

And same thing for the arithmetic one

And the third is just they add to 252

[robust jungle]

i dont understand

[quick peak]

Which one sorry

[robust jungle]

both lol

[quick peak]

So what would c-b be equal to

[robust jungle]

we have a, b, c for the arithmetic
and a-7, b, c+36 for the geometric

so what did u do?

[quick peak]

I mean I kinda did the same thing

[quick peak]

But try this

[robust jungle]

c-b would be equal to... b - a?

[quick peak]

Uh

Flip them

B-a

[robust jungle]

ok ok

[quick peak]

Now the ratio between c altered and b altered should be the same for b altered and a altered

[robust jungle]

c-b --> b-a
c'-b' --> b'-a'

[quick peak]

Nah the ratio

It’s gonna be one over the other

[robust jungle]

aaah ok

c/b = b/a?

[quick peak]

Ya

And the third is that they add up

I plugged those into wolfram but u can try doing them by hand

[robust jungle]

c/b = b/a, a+b+c = 252

[quick peak]

Wait

You have to change the ratio

Cuz you have to add some numbers

To make it geometric

C plus smth and a - smth I think

[robust jungle]

so we have:

c+36/b = b/a-7 =252
c +36 = (b/a-7)b
c + 36 = (b^2)/ab -7b

idk i got stuck

[quick peak]

The first one does not equal 256

[robust jungle]

252

[quick peak]

C+34/b=b/a-7

C-b=b-a

A+b+c=252

[robust jungle]

but i still don't know a b or c

like, their value

[quick peak]

3 equations and 3 variables

You should be able to find them

[robust jungle]

idk, sorry

i started uni with little to no previous math knowledge, idk what to apply

maybe a system of eq

[quick peak]

I have to drive home

If no one else try’s this I’ll do it later and can dm u

[robust jungle]

thanks for all of you help

thanks @uncut tartan too c:

i'll see what i can do

[uncut tartan]

I didn't follow what u did but c+a=2b doesn't seem right 😅
Nvm c-B has to be equal with b-a from the arithmetic progression, both terms being equal with the ratio

But if it is u can find B from the last two relations

C+a=2b
A+b+c=252
=>3b=252 =>b=84

C+a=168=>a=168-c
Now coming back to the first
C+34/84=84/(168-c)-7
Then u find c

[lone heart]

@robust jungle Has your question been resolved?

[lone heart]

@robust jungle Has your question been resolved?

[robust jungle]

let's just give the oportunity to other question

.close

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[vital forum]

I don’t know how to find k, my answer is not correct I don’t think so, can someone show me how to find k please

[cursive badger]

You can solve for a and b

[cursive badger]

use 1=ab^3/2, divide by b^3/2, plug in the value of a into the second equation 32=ab^4

[vital forum]

Pls can u explain how u would make b the subject of 32 = 1/b^3/2 x b^4

Nvm

Thx

[lone heart]

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[fallen estuary]

Can someone please help with this

[long axle]

Second line is correct

But set it equal to 0

Then solve for y’

Because derivative of 25 is 0

That’s how u do implicit

[fallen estuary]

so y' = 2x/2y

wait no

-2x/2y

so -x/y

[long axle]

Nice, now do what u need

[fallen estuary]

plug it in

so its -3/4

[long axle]

Ye

[fallen estuary]

what is that value though

[long axle]

The slope at that point on the circle

Or “gradient”

[fallen estuary]

so the gradient?

alr

do i use this now

[long axle]

Ye

[fallen estuary]

y-4 = -3/4 * (x-3)

lemme expand it

[long axle]

Do u rlly need to?

Doesn’t ask for it

Unless ur teacher said ig

[fallen estuary]

ig i dont

[long axle]

Ye this is perfectly valid as it as

[fallen estuary]

thanks 🙏🏿

[long axle]

U can check on Desmos if u want

Np

Mr 🫘

[fallen estuary]

.close

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[wintry panther]

please help metra train keke palmer something idk

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[rotund crater]

this is alchimides method ?

[gleaming granite]

I think it's just a Riemann sum

[rotund crater]

u sure?

[gleaming granite]

yeah it should be a Riemann sum

why do you think it's not?

[rotund crater]

I don't know, tell me about it the rienman sum

[gleaming granite]

It's just using rectangles to approximate the area under a curve:

there are left and right types of Riemann sum's (depending on which corner touches the function)

[rotund crater]

the first is integral?

interval a and b

[gleaming granite]

yup

[rotund crater]

you can help me with an integrasl?

[gleaming granite]

sure, just post your question

[rotund crater]

if it derives the result it will not give that result

[gleaming granite]

what do you mean by deriving the result?

[rotund crater]

integrals are inverse of derivates

[gleaming granite]

oh you take the derivative to check the answer?

[rotund crater]

mean yea

[gleaming granite]

,w derivative of sqrt(8) sinx

[ocean seal]

Results provided by WolframAlpha

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

Requested by keto11#8349

[gleaming granite]

,w 2 sqrt(2) cos(x) = sqrt(4+(4cos(2x)))

[ocean seal]

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[rotund crater]

how

[gleaming granite]

did you get the same answer when you took the derivative?

[rotund crater]

mathway say this

[gleaming granite]

yeah that's right

what's the problem then?

[rotund crater]

Does that mean that the exercise is wrong?

[gleaming granite]

no they're the same value

[ocean seal]

keto11

[rotund crater]

how you can rewrite

to

[gleaming granite]

you'll have to use a trig identity

likely the double angle identity

[rotund crater]

in both?

[gleaming granite]

wdym?

[rotund crater]

Do I have to apply the double angle in both exercises?

[rotund crater]

.

[lone heart]

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[mortal delta]

Can someone help me graph this

[mortal delta]

<@&286206848099549185>

[sage jewel]

.help

[lone heart]

Commands:
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help: .help

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[coral thorn]

do you know what the derivative tells us about the original function?

[mortal delta]

No

[coral thorn]

what does the derivative give us?

[mortal delta]

That it’s less than 0 over the intervals (-oo,-5),(4,oo),(-5,4)

Greater*

And less on (-5,4)

[coral thorn]

what does that tell you about the original function on that interval?

[mortal delta]

That it’s increasing on thoes intervals and decreasing on the other one

[coral thorn]

yes

now

what does it mean when the second derivative is less than or greater than 0

[mortal delta]

If it’s less then in concave down and greater it concave up

[coral thorn]

yes, good

now you know the behaviour of the function

you can sketch it

you know where it’s increasing/decreasing and where it’s concave up/down

[mortal delta]

This look correct?

[coral thorn]

yes

you can label y-axis as well

they’ve given you values for that

[mortal delta]

Ok thank you

.close

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[void whale]

I need a bit of help with this. I think I’ve got it after the asymptote but would like that checked as well. Just not sure what’s going on to the left of it

[coral thorn]

what’s happening to the function as it approaches the VA from the left?

i.e. -inf

[void whale]

It is decreasing

So it should be moving negative, correct?

[coral thorn]

what about the concavity

up or down?

[void whale]

Concave down

[coral thorn]

yup

[void whale]

So it’s like an upside down parabola?

Cuz that would be increasing as it gets to the max. That’s why I’m confused

[coral thorn]

hmm

you’re right

maybe it’s like a

[void whale]

What were you going to say it was?

[void whale]

I see. And would that count as concave down?

[coral thorn]

i guess

[void whale]

The green side

Yeah that’s all I can think bc the directions make it seem like the graph needs to cross through the asymptote which makes zero sense

[coral thorn]

yes i think that’s how you’d draw it

try visualising a similar function

green part should count as concave down

[void whale]

I got you

[void whale]

Yes. So is everything on the right side of the asymptote fine?

[coral thorn]

yes

looks good

[void whale]

Appreciate it man

[lone heart]

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[candid garnet]

i need some help getting started with this problem, Im not sure what to do first

I need to find x and H

[sour verge]

What is the cosine of an angle?

And the sine of an angle?

[candid garnet]

isnt it like, The adjacent side divided by the hypotenuse? so 10 divided by H right? this is pretty new to me

[sour verge]

So cosine is adjacent/hypotenuse

[candid garnet]

yeah.

[sour verge]

Sine is opposite/hypotenuse

So on your triangle, what is sin(51)

[candid garnet]

hold on, my dad is calling me

13 i think

i think i had to divide sin(51) by 10 and that equals 12.86 blah blah blah

oh wait, i got it.

thanks for the help.

.close

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[vestal hawk]

<@&286206848099549185>

i got 4/3

is that right?

@normal hedge do you know how to approach this?

[candid garnet]

Yup thats correct i think

but im not too sure

lemmie see what i get

[lone heart]

@vestal hawk Has your question been resolved?

[vestal hawk]

ok

let me know @candid garnet

[candid garnet]

ok, its good

[vestal hawk]

can you send your working out?

i wanna see how you did it

[candid garnet]

My camera doesnt work sadly and i gtg, but how did YOU get ur answer? although im still not too sure if mine is correct, I havent done this kinda stuff in a while

So try and get someone else to check cuz i gtg to sleep

[vestal hawk]

ur 13 u dont know this

good troll @candid garnet

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[ripe wigeon]

hello

[ripe wigeon]

how to prepare 4 chapters in 1 hour?

[cerulean garnet]

on what topic

honestly, doing 4 chapters in one hour is kinda mad

i personally only do 1 chapter in one hour, and still not fully understanding

[coral thorn]

this question is better suited for the jvscholz discord

[ripe wigeon]

1. Matrices and determinants, 2. real and complex numbers, 3. logarithms, 4. algebraic expressions and algebraic formulas.

[ripe wigeon]

actually i got an half hour for test i was sleeping and no one make me to wake up i told everyone in my home

to do it but sadly they didn't listen to me.

[earnest saddle]

taking time to study and properly prepare is generally better than trying to rush through a large amount of material in a short amount of time. When you take your time to study, you have more opportunities to review the material, ask questions, and clarify any areas of confusion.

Properly studying also allows for a deeper understanding of the material and better retention of the information. Additionally, taking breaks during study sessions can help prevent burnout and help you retain information better.

Rushing through a large amount of material in a short amount of time can lead to a superficial understanding of the material, which may not be sufficient for exams or long-term retention.

Therefore, it is important to set aside enough time to study and review the material properly to achieve the best possible results. However, if you are in a situation where you need to study a large amount of material in a short amount of time, following the steps outlined in my previous answer can still help you make the most of your time.

[cerulean garnet]

honestly in that time span, what i would do is jsut to insanely cram the lots of it

[ripe wigeon]

got 25 minutes now : (

[earnest saddle]

The fact is that you can't do 4 chapters in 1 hour properly

[vapid shuttle]

Let's not ChatGPT

[earnest saddle]

the question is so silly

[ripe wigeon]

bruh my teacher will fuck my ass

[earnest saddle]

chatgpt can answrr it

[vapid shuttle]

I should tag mods but this doesn't seem necessary, so I'll just tell you that

[ripe wigeon]

if i don't give good results

[vapid shuttle]

Using ChatGPT to give answers will get you banned

[ripe wigeon]

i was sleep and told my parents to wake me up in early in morning

but they didn't do it

[earnest saddle]

why may i ask

[vapid shuttle]

Let's not

[ripe wigeon]

i got still 30 minutes

[alpine sable]

Crazy school i guess

[ripe wigeon]

indeed

[vapid shuttle]

Then spend that time studying rather than using profanity here

[earnest saddle]

why

[vapid shuttle]

read the changelog

[ripe wigeon]

im here to get suggestions what to do

[vapid shuttle]

I suggest you start studying

[alpine sable]

Not if you work smart

[alpine sable]

How much time do you have

[ripe wigeon]

30 minutes

[vapid shuttle]

Alright this is off-topic. ChatGPT use is against the rules, I was trying to be lenient but if you all continue acting like this I will tag mods

[alpine sable]

What do you want to do ?

[vapid shuttle]

Just focus on the question (if there is one) from now on, please

[ripe wigeon]

4 chapters in 30 minutes; 1. Matrices and determinants, 2. real and complex numbers, 3. logarithms, 4. algebraic expressions and algebraic formulas.

[alpine sable]

All from book or abstract

[ripe wigeon]

i am not going to school fuck it

fuck the test

[alpine sable]

You can use gpt but you have to be careful

[alpine sable]

Ohh that's checkmate 😂

[vapid shuttle]

Don't encourage academic dishonesty

[ripe wigeon]

that's the last option lmfao

[terse canopy]

ChatGPT kinda sucks for math. Would not recommend

[vapid shuttle]

Agreed

[alpine sable]

Bro I am not ....

[vapid shuttle]

^

[ripe wigeon]

stop fighting here

[earnest saddle]

gpt is god at writing essays

[ripe wigeon]

you dumb guys

im in tension and you guys are fighting?

damn fuck it

[vapid shuttle]

Sayyid do you have a specific math question ?

[earnest saddle]

@ripe wigeon I think you should study now

[alpine sable]

Using it also requires efforts.... If finding answers is something then I am here to give you shortest and possible way to do it

[alpine sable]

20 mins seriously 😂 ....

Well topics are easy tough

[vapid shuttle]

Helpers are not here to give solutions or instruct others how to find answers from calculators or ChatGPT, didn't I mention this to you in another channel earlier?

[earnest saddle]

i think he's trolling

[terse canopy]

Choose two and focus on those

[vapid shuttle]

We are here to guide others through there problems and teach them how to do the math they are struggling with.

And we are espcially not here to encourage someone to use ChatGPT on a test they haven't studied for because "it requires efforts"

its cheating

don't encourage that

and this channel is completely off topic, so I will be closing it

[ripe wigeon]

im serious bruh

[vapid shuttle]

.close

[lone heart]

Channel closed

Closed by @vapid shuttle

Use .reopen if this was a mistake.

[alpine sable]

You are not going school right? .... ( Next time you want suggestions try it in discussion section... This is for solving maths problems

[ripe wigeon]

idk

.close

.close

[lone heart]

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[zenith marsh]

Prove that
120| n^5+n^3+5n+4n+240

How does one even simplify that polinomyal

[zenith marsh]

I am so confused

There is nothing in common for that entire thing

[gray isle]

did you copy down the expression correctly?

[zenith marsh]

Yes

It was on my recent NT exam

I was so lost

I still cant figure out

Actually i have to check, give me a min

[lone heart]

@zenith marsh Has your question been resolved?

[lone heart]

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• After 15 minutes, feel free to ping <@&286206848099549185>.
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• 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.

[restive ermine]

(x-3/x*x-7x+12)-(x-3/3-x)

[viral pagoda]

!show

[lone heart]

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

[gray isle]

$(x-\frac{3}{x}\cdot x - 7x + 12) - (x - \frac33 - x)$?

[ocean seal]

ℝamonov

[earnest saddle]

simpify the eqn

[lone heart]

@restive ermine Has your question been resolved?

[lone heart]

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Remember:
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• 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.

[hollow mesa]

Guys I want a 4 degree polynomial whose coefficients are integers between -5 to 5 (excluding 0) and whose derivative at a natural number (x<10) is 0

[golden canyon]

What have you tried?

[earnest saddle]

!show

[lone heart]

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

[earnest saddle]

!status

[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

[golden canyon]

ima guess its step 1

[surreal mason]

Is that for all x<10 for any x<10

[golden canyon]

should be impossible for all x < 10

[earnest saddle]

maybe

lets try

lets generalise it

[golden canyon]

it would give a cubic that's 0 for all integers < 10

and coefficients are non-zero

[earnest saddle]

ax^4+bx^3+cx^2+dx+e

please wait

[surreal mason]

A cubic with 10 solutions?

[earnest saddle]

wait

lemme try

[golden canyon]

I thought it was integers but even with naturals its still impossible

f(x) = a(x - 1)(x - 2) ... (x-9) = ax^9 + ...

[marsh rapids]

maybe he just wants it to vanish at one integer

[earnest saddle]

ax^4+bx^3+cx^2+dx+e derivate of this is
4ax^3+3bx^2+2cx+d

wait

please lemme explain

[surreal mason]

Bro are you trying to disprove factor theorum or something?

[marsh rapids]

like is ${P \in {-5, \dots, 5}_4[X], 0 \in P'({0, \dots, 10}} \neq \emptyset}$

[earnest saddle]

so x = 1, then 4a1^3+3b1^2+2c1+d = 0;
4a + 3b + 2c + d = 0

[golden canyon]

I think the solution to the original problem just is: f(x) = x^4

f'(0) = 4 * 0^3 = 0

[earnest saddle]

please stop

lemme xplain

[surreal mason]

0 is a natural?

[earnest saddle]

😭

[golden canyon]

Oh I forgot, im stupid

[ocean seal]

mateo713
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[marsh rapids]

anyways

[golden canyon]

f(x) = 3x^4 - 4x^3

f'(1) = 12 * 1^3 - 12 * 1^2 = 0

[earnest saddle]

at x = 5

its not true

[marsh rapids]

depends on the phrasing of the question

[golden canyon]

"Guys I want a 4 degree polynomial whose coefficients are integers between -5 to 5 (excluding 0) and whose derivative at a natural number (x<10) is 0"

a natural number not all natural numbers

[earnest saddle]

-5x^4 + 4x^3 - 4x^2 + 4x - 5

[marsh rapids]

ofc if it had to be every integer you'd be looking at something like a degree 10 hermite polynomial

[earnest saddle]

-5x^4 + 4x^3 - 4x^2 + 4x - 5

is this right?

please verify someone

[surreal mason]

Is there a way to systemically generate those off topic?

[marsh rapids]

see hermite polynomial

[surreal mason]

On it chief 💪

[marsh rapids]

doesn't work with constraints on coefficients afaik

[earnest saddle]

-5x^4 + 4x^3 - 4x^2 + 4x - 5 is this right?

!nosols

[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.

[marsh rapids]

did you just nosols yourself again

[surreal mason]

Bro is batman 💪

[earnest saddle]

nope

i was just asking if eqn was right

i was explaining

[surreal mason]

Well what f'(x) = 0 did you construct this for?

[earnest saddle]

no

what i did was

found out 4a + 3b +2c +d =0

and 3 more eqn and calculated it using online calc

16 a + 12b + 8c +4d = 0

[surreal mason]

Still has only three roots though right? The question is phrased wrong

[earnest saddle]

idk

i just guessed

wait i will come after 10 mins with solution

[surreal mason]

Bro you can not have a derivative of a 4th degree (i.e a 3rd degree) polynomial with 10 roots

[earnest saddle]

ig ur right

[surreal mason]

A n degree polynomial has n roots at most. You can prove it using a lot of methods. Vandermonde matrices, fundamental theorum of algebra etc

[earnest saddle]

can you close this question then?

[surreal mason]

It'll close by itself dw

[lone heart]

@hollow mesa Has your question been resolved?

[lone heart]

Channel closed

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[lone heart]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• 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.

[misty pivot]

why for a is denominator 2 x dT

[lone heart]

@misty pivot Has your question been resolved?

[lone heart]

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• 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.

[desert pine]

In this q when we did r2-r1

How did we get 0q

Shouldn't it just be 0

???

[gilded crypt]

i believe that is just a formatting error, it's meant to be 0, q-p, r-q

they're put very close together which is why it looks like 0q

[lone heart]

@desert pine Has your question been resolved?

[lone heart]

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• 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.

[atomic comet]

Hi,could someone please help me with question 8

[lone heart]

@atomic comet Has your question been resolved?

[lone heart]

@atomic comet Has your question been resolved?

[lone heart]

@atomic comet Has your question been resolved?

[lone heart]

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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.

[chilly dove]

How do I do this problem?