math-help

[cyan night]

that really is weird

welp its discrete maths

[pulsar turret]

Can anyone help me solve this? The answers are -1/2 and 0

[left knoll]

check the sign once
is it (x-1) in denomitor of rhs?

[ember kernel]

The picture lacks context, but I'd say it means i < j, with i and j being natural numbers (not 100% sure tho)

[cinder yacht]

multiply everything by (x-1)(x+1)(x+2) and solve the 2nd degree equation

[ember kernel]

3rd*

[cinder yacht]

and just keep in mind that x = -1, +1, and -2 are not OK answers (because at the start, [x-(-1)], [x-(+1)], and [x-(-2)] were in the denominator

[cinder yacht]

2nd

cuz in each term at least 1 factor gets cancelled out

so there are at most 2 factors (x-a) that remain

[ember kernel]

Yeah you're right, I'm just dumb

[cinder yacht]

nah it happens

btw you're in a faculty? or prepa?

[pulsar turret]

No it’s +1

[oblique siren]

Can anyone help me find the characteristic polynomial of the third quadratic form, please? I already found the matrix. I can't get the correct eigenvalues when I calculate the characteristic polynomial. I'm struggling with finding characteristic polynomials 😓 Thanks in advance.

[gleaming ridge]

please help... i dont get how a four sided die works and i dont know how to find the probability theyre asking for : (

[patent rain]

1/4 * 1/10

tetrahedron die is like a standard 6 sided dice

but you can only roll 1-4 since it only has 4 sides

[sharp grove]

hello .w.

does anyone know how to do trig..?

[fervent lagoon]

what kinda trig haha

[sharp grove]

basic easy trig with right triangles haha

uhh basically finding angles

i was given a right triangle, with no angles

but i was able to find all lengths

[fervent lagoon]

do u know SOH CAH TOA

[sharp grove]

yes

[fervent lagoon]

u can use ur calculator right?

[sharp grove]

yes, this is just homework

[fervent lagoon]

ah cool

so ur gonna have to use arctan/cos/sine to find an angle

[sharp grove]

hmmm okay

[fervent lagoon]

so like TOA = tan(x) = opposite/adj

arctan(o/a) will give u an angle

[sharp grove]

oh we havent gotten there yet xD

im in precalc

and basically we're just reviewing the basic trig functions

you know the pythagoream therom

[fervent lagoon]

ah okay haha

[sharp grove]

yeah..

i mean idk if i should use the 90 degrees as its angle?

[fervent lagoon]

its just inverse tan- arctan is just a funny name for it

[sharp grove]

inverse tan ohh

[fervent lagoon]

lmao

[sharp grove]

so does that go where A or B is?

[fervent lagoon]

so the angle CAB = inverse tan (a/b)

[sharp grove]

ah r ight

[fervent lagoon]

as a is opposite angle A

[patent rain]

since tan(A) = a/b, invtan(a/b) = A

[sharp grove]

ohhh

[sharp grove]

so like this?

[patent rain]

use inverse tan on ur calculator if u didnt

[sharp grove]

OH

[patent rain]

on most calculators it looks like tan-1()

[sharp grove]

i got 36.86

[patent rain]

let me check

[sharp grove]

im trying to find the angles

[fervent lagoon]

thennn do 90-36.86 and boom

[patent rain]

yep thats right

good job

just remember if ur looking for angle given sides, use inverse

[sharp grove]

but why couldn't I use angle B to find the other angle?

or, if i did that, would I still get the same answer

[fervent lagoon]

u can choose which ever one u want haha

when u know all the lengths anyway

[sharp grove]

im kind of confused why we had to use tan and not sin and cos haha

[patent rain]

u can use sin or cos

[sharp grove]

oh

[patent rain]

as long as u use inverse

[sharp grove]

o

same answerr

woahhhh

THANK YOU SO MUH

[patent rain]

ya np

[sharp grove]

is this still correct?

o

whoopsies wrong pic xD

[patent rain]

ur work looks right

[sharp grove]

it feels weird using sin alot xD

i feel like ots wrong

[fervent lagoon]

ull use it a lot more trust me haha

[sharp grove]

ahh okay okay

[sharp ferry]

can anyone guide me on how to approach this

[ember kernel]

Are we supposed to calculate the min value of y ? The first part of the question is out of pic

[sharp ferry]

yepp

its a question from application of derivatives but idek i have no idea

[ember kernel]

Local maxima and minima happen at points where y' = 0

Here there are 2 variables so you should look for alpha and beta such that dy/da = 0 and dy/db = p

[sharp ferry]

eh i didnt quite understand

i was thinking of distance between 2 curves

[deep kernel]

does anyone understand the notation here?

[ember kernel]

I guess it's "is approximately equal to ... when x is arbitrarily close to 0"

[maiden prism]

Hi guys, I don't know how to continue from a step in this problem a

How should I treat with the power n? because it's power n so use conjugate won't work

[ember kernel]

Have you learnt about Newton's binomial formula (a+b)^n = ... ?

[maiden prism]

haven't yet, so I should look it up first :v

[maiden prism]

How will this formula will be used is this problem? we don't know n so basically can't expand them out

[hardy hare]

help me omg

[cinder yacht]

the exact definition is :
1-cos(x) = u(x) * x²/2 where u is a function such that u(x)->1 when x->0

that notation means "equivalent"

you didn't study it yet i guess, but it'll be very useful for limits etc once you study it

[cinder yacht]

ehm

the remaining limit is 0 if (x-1)^n = (x+1)^n
AKA if x=0 and n is an even integer
otherwise it's +infinity or -infinity depending on whether h->0+ or h->0-

ohhh lol

you made a mistake in that last formula you sent, you meant -(x-1)^n not -(x+1)^n

lol i was solving a harder problem

for that one you have to use the formula of a^n-b^n, google it

[maiden prism]

tks bro, after expand a^n - b^n then (a-b) will make h disappear, also sr for my mistake

[frosty cairn]

Find an even function g defined on the interval [-2π,2π] such that g(x)=f(x) for all x in [0,2π].```
can i just make it ```f(x)=√|(x)|+|sin x|```

[sharp ferry]

i solved it finally but i used a completely different approach

i didnt quite understand your approach but it would be nice to know

also can u check my solution

im unsure if this method is fine or not because i used less of derivatives and more of coordinate geometry

[hardy hare]

help

[cinder yacht]

after you foudn P0, in order to find Q0

acutally nvm seems good to me as long as the formula of P0Q0 is correct

that's interesting i never saw exercises like this, which country are you from?

[cinder yacht]

if u call G the orthogonal projection of H on AT, then the angle HGT is equal to 90°. So 1/2 = sin(30°) = sin(HTG) = HG / HT
=> HG = HT/2 = 5/sqrt(2)
but we know that AGH is also equal to 90°, so sin(GAH) = HG / HA => HA = HG / sin(GAH)
knowing that sin(GAH) = sin(45°) = 1/sqrt(2), that means that HG = 5

[patent rain]

just use law of sins

[cinder yacht]

oh yea maybe that works, i was never taught law of sins in school

actually yeah that works immediately, what i did is the proof of law of sins lol

[patent rain]

sin(45)/(5*sqrt(2)) = sin(30)/x

x = 5

[hardy hare]

ohhhh okok never heard of that law in my life LOL thanks

[patent rain]

learn law of sines and law of cosines

[hardy hare]

okkk

[sharp ferry]

india

this was the first time i encountered such a question as well

[cinder yacht]

the solution seems elegant XD

[torn torrent]

how do we solve this using the first and second derivative test?

[sharp ferry]

i was studying distance between curves and this question was in there thats why i knew something like that had to be used and i still had to take some helpp

[cinder yacht]

ohhh

[sharp ferry]

if i saw such a question out of context in a test i certainly would never have thought of that ahhahah

[cinder yacht]

hmm I should've thought abt it when it's the square root of a sum of squares

but ive gotten bad at geometry stuff :(

[sharp ferry]

i dont remember coordinate stuff as well :( parabola hyperbola circles st lines and stuff man why are high school students pressured so much here jhfsdwke

anyways imma keep this chat clean xd

[sharp ferry]

i sent the steps

along with an example i think it would help

[coarse cypress]

please help

[inland sigil]

Each figure is made out of equal sized squares, you need to count how many squares are in each

[inland sigil]

Draw the boundary lines for edges in that cube and see the 3 faces

[idle remnant]

Can someone please explain to me what a prisoner and escape set is in fractal geometry, I'm having trouble understanding it.

[obsidian talon]

okeh im rdy

[rustic sapphire]

here it is @obsidian talon

[obsidian talon]

ah okay, im looking at it now

[obsidian talon]

Trycky one. I assume you are familiar with partial integration?

[rustic sapphire]

lemme check

yes i am

[obsidian talon]

If you apply partial and differeniate with respect to g(x) = x^2

you will need to solve ln( expression ) with partial too, but that only is fairly simple integrate ln(x) = x * ln(x) - x right

[rustic sapphire]

you mean like this?

[obsidian talon]

altho the inner derivitive for the logairthm is messy, Its definitel gonna fill the paper 😮

[ember kernel]

ln(a/b) = ln a - ln b

[obsidian talon]

thats a rly good one!

[ember kernel]

That'll help

[rustic sapphire]

ooh okok almost forgot that thanks @ember kernel

[obsidian talon]

use that logarithimn rule

[rustic sapphire]

yeah dude i am so dumb!

[obsidian talon]

and solve for the sum of two partial integrations i assume

[rustic sapphire]

it gets pretty messy as you do the maath

i mean

it isnt terminating for me

[obsidian talon]

Ye chain rule is abit messy for that expression right?

Maybe we can find some substitution?

I will try to write it on paper, sex

[rustic sapphire]

yeah sure

[obsidian talon]

wooh, i totally feel you on that one. I would put that into wolfram step by step solution

life is too short to loop around with partial integrations

[rustic sapphire]

dude this is too hard...

[obsidian talon]

yeep

i was trying to reform the expression in ln

with its conjugate, might work

[rustic sapphire]

it might work

[obsidian talon]

do a taylor expansion on it 😄

cause that integral is gnarly man

[rustic sapphire]

dude.. i evaluated the partial integration, i got the same term upon completely evaluating it

i am gonna die!!

[obsidian talon]

The professor wants you to solve this integral analytically?

[rustic sapphire]

there is no professor, i was giving a 20 minute prep test, with 10 questions and this was the first one in it hence, the test expects us to solve it in 2 minutes

[obsidian talon]

to me since the integral is indefinite and u have the boundaries -1 and 1, it feels like you are supposed to solve the integral with taylor series at x = 0

even to expand the ln function is fairly annoying with that expression

[red spruce]

why does this look like a fittjee mocktest

[rustic sapphire]

it is

[red spruce]

nice

[obsidian talon]

xD

[rustic sapphire]

here i tried evalutaing by simplifying the term inside ln[], and the result was the question :< @obsidian talon

[obsidian talon]

ye. I dont know what to do with this one man :/ It looks rly damn complicated to actually solve it without approximations

just plot the graph, its terrible looking 😄

[obsidian talon]

between -1 and 1 ye

[rustic sapphire]

do you think we could go with option D?

[obsidian talon]

2 x^3 + x^5/3 + x^7/12 + O(x^8)

lets see if that one gives the result

integrate that function between 1 and - 1

[rustic sapphire]

what is the last term

[obsidian talon]

Ordo

dont mind it

[rustic sapphire]

what does it mean

[obsidian talon]

its the 'error' term if i remember correct

when you approximate functions with taylor expansions you get an error. The higher the degree, the less error you get

but its better if you reach out to a mathematician

engineers are bad at math 😉

[rustic sapphire]

ok

[obsidian talon]

I was expecting a really nice integral when u said it was definite haha

[rustic sapphire]

upon integrating the expression you gave, we get a complex term while evaluating with limits

so ig it we wont get answer by that

[obsidian talon]

how do you get a complex term ?

[rustic sapphire]

well try substituting '-1' to the integral of the second-last term

[obsidian talon]

integrate the expression: (2/4) x^4 + (3/8) * x^8/3 + (12/19) * x^19/12 + C

all degrees > 1/2

you wont get a compelx term by the argument -1

this is a complete real expression

oh soz

u are correct

[rustic sapphire]

yep

[cinder yacht]

hmm

I think u got baited as f*ck

that function is odd and the interval of integration is symmetrical to 0, so the integral is 0

ahahq

ahaha*

the x<0 part cancels out the x>0 part of the integral

[cinder yacht]

Taylor series at x=0?why would it have helped to approximate the function around x=0

[rustic sapphire]

well it was hell for me i hadn't studied that part yet

https://tenor.com/view/anime-cry-crying-inosenpai-sad-gif-16477983

[cinder yacht]

well

if u studied integration by substituion

substitution

then u could prove it that way to

too*

by splitting the integral on ]-1,1[ to two integrals : the first on ]-1,0] and the second on [0,1[
then on the first one, you do a substitution : y = -x, and u find that the two integrals compensate each other :p

[obsidian talon]

lol ye haha, if you look at the graph u see its symmetrical. Man, I shall go back to multiplicaiton table

[cyan night]

yes

[elfin folio]

hello, can someone help me find the all the parts of the parabola?im on number 5 im stuck on this equation. thank u for the answer

[cinder yacht]

take the 8y to the other side (it becomes -8y), then divide everything by (-8), u get the equation of the parabola

[elfin folio]

oki thank u:>

[tropic bear]

does anyone know the answer for this ??:(

[cinder yacht]

1. draw every forbidden region on the (x, y) graph. so u can only find the (x, y) that maximize 5x+2y on the remaining allowed region
   2)z=5x+2y means y = - 2.5x + 0.5z
   so draw the line D : y=-2.5x
2. now draw the line Dmax that is:

• parallel to D
• crosses at least 1 point of the allowed region
• as high as possible

4. that line Dmax's equation is y=-2.5x + 0.4 Zmax
   find Zmax.
5. now draw the line Dmin that is:

• parallel to D
• crosses at least 1 point of the allowed region
• as low as possible
  6)that line Dmin's equation is : y=-2.5x+0.5 Zmin
  find Emin.

Zmin*

I guess this would work

idk if there's a better way or not

[halcyon crystal]

hi does anyone know how to do part b thanks :///

[cinder yacht]

prove by (easy) induction that [x(n+1) x(n)] = M^n * [x(1) x(0)]

then u just compute x(n) from that

(u don't have to compute x(n+1), but it's fine if u do as well)

@halcyon crystal

[halcyon crystal]

ohhh i know now

thanksss :))

[ruby tinsel]

Can someone please help me with this Q,,,? tyyy!

[cinder yacht]

1/(x * x * (x+2)) = a/x + b/(x^2) + c/(x+2)
so
b=1/2
c = 1/4
a=-1/4
(check if my mental math is correct)

so u can split the integral into 3 integrals that are easier to compute

@ruby tinsel

[cyan night]

i need math help

given triangle abc, p is any arbitrary point inside the triangle. d,e,f are the respective intersections of AP with BC, BP with AC, CP with AB. prove that pd/pa+pe/pb+pf/pc >= 3/2

[main plume]

ive a differential equation question, can someone help me?

[left knoll]

u can put up your eq. here!

[frosty heath]

is anyone here familiar with laplace transformation?

[frosty tide]

Does anyone know some good sites which teach integration?

I dont know anything about it but wanna know

[jovial dew]

http://exo7.emath.fr/un.html

[ember kernel]

So you have :

[ember kernel]

^

[ember kernel]

Error in first line, it should be sin²x instead of sin^x

[last echo]

yea buts not there in the options given 😕

[left knoll]

do m+n
m-n

[supple island]

well if mn=sin^2tan^2 and m^2-n^2=4 * sintan

[last echo]

got it! thx

[supple island]

isn't 4sin* tan=4sqrt(sin^2*tan^2)?

[left knoll]

@last echo

is the ans

4 tanx sinx ?

use basic id

(m+n)(m-n) = m^2 -n^2

[fierce jewel]

Can anyone provide me an example for absorption law , in. TOC ( theory of computation) i have seminar tmrw pls help . 🥲

If possible also for involution and De Morgans law .

[dense wadi]

please could someone help me with a, attempted but couldnt get anywhere, ps: no diagram

[cinder yacht]

let's call x and y the lengths of the rectangular base. (x is also the length of the side of the square vertical face)

the total surface covered is :
S = surface of the base + 2 * surface of a square vertical face + 2 * surface of a rectangular vertical face
= xy + 2 * x^2 + 2 * y * x
= 3xy + 2 *x^2
so y = S/(3x) - 2 x/3
we know that S = 54 m^2
so y = 18/x - 2x/3
and the volume is :
V = x * y * x
= x^2 * (18/x - 2x/3)
= 18x - 2 /3 * x^3

[junior blaze]

Hi guys..Going to have a big test in two days, have been almost failing almost all this year..
Does anyone know how to find these limits?

[fierce bone]

Dita will create an Instagram account. For this purpose, it requires a password consisting of eight characters. Passwords are said to be good if they combine letters and numbers. Dita will use her name on the first or last four characters in a row, then add four numbers that can repeat from 0, 1, 2, 3, 9 between 3000 and 5000 for example DITA3556, 3277DITA, and others. The number of passwords that Dita can use are

anyone can solve this?

i got 10080

is it true?

[dense wadi]

Thanks, understood and worked it out with yours ✊🏽

[cyan night]

for 4. use L hopitals, and since b is a constant its derivative is 0

and for 5. im assuming its saying t -> 0?

if so then you use L hopitals too then sub t = 0 in

[cinder yacht]

another way is to say that :
x^10 - b^10 = (x^5)^2 - (b^5)^2 = (x^5 - b^5)(x^5 + b^5)

but yeah hospital works faster if he knows it

[cinder yacht]

and if he doesnt wanna use hospital here : he can multiply numerator and denominator by : ( sqrt(t+2) + sqrt(2) ) and use (a-b)(a+b) = a²-b² which will simplify the denominator's "t"

[cyan night]

yes

but ur way is very creative ngl

[rough eagle]

hiii can someone pls help me with this sets qs 😪

[cinder yacht]

empty set

PxQ is the set of couples (p,q) where p is in P and q is in Q

but there is no p in P, so there is no couple (p,q) in PxQ

so PxQ is empty

its like if u have 0 straight man, 3 straight women, what are the possible married couples that you can think of? None ahaha

[cyan night]

thats a brilliant analogy

[cinder yacht]

well that's just how i was taught math in school, im not sure why but they never taught us l'hopital rule in france/morocco, they taught us techniques like these ones instead

wait ur in middle school

lol i learnt limits in 2nd year of high school

[cyan night]

im in middle school

i learn stuff above my grade

[cinder yacht]

oh gj for the dedication

it'll all pay out

[left knoll]

can you guys help me in maths

[rough eagle]

ayeee thank u sm !!

[rough eagle]

loved the way you explained it tho 😭

[left knoll]

oh

[cinder yacht]

ahaha

[steady charm]

pls help

[wise hazel]

multiply 1000 times x ray wavelength for the task1 a

check that with two numbers given in task 1b and find where does it fit

[wise hazel]

2^20 *x where x is number of bits per byte

for task 2 a

2^30/2^10 = 2^10 so 1024 Mega bytes

for task 2b

[wise hazel]

idk if this is helpful at all

[steady charm]

Thank youu, I appreciate your help so much.

[twilit wasp]

can someone help me with this sum

[warm nexus]

hii can u guys help me on question number 5? the answer is supposed to be 16x^4 - 64x^2 + 96

i tried to do it by myself but i think im kind of lost

[cyan night]

do u know the pascal triangle trick

you may have made a mistake when using the combination function

[twilit wasp]

afaik u can only find one part of the distance using the speed and time but its not enough information i think im missing something

[cinder yacht]

just so u know, 10 choose 8 = 10 choose 2
= (10 * 9) / (2!)
= 45

[warm nexus]

hii omg tysm i figure it out already

[cinder yacht]

yeh I didn't rly help, just u can compute combination numbers more easily

[warm nexus]

yepp got it

[cyan night]

you should also learn the pasal trick just in case

[cinder yacht]

XY = 0.75 * 60 = 45 m
u should work with the angles between the declining lines and the VERTICAL wall (so one is 90°-50° =40°, the other is 90°-30° = 60°
call A the point at the top of the wall and B the point at the bottom left of the figure
in triangle ABX : tan(BAX) =tan(40) = BX/H
so BX = H * tan(40)
in triangle ABY : tan(BAY) = tan(60) = BY/H
so BY = H * tan(60)
but we know that XY = 45 = BY - BX
so 45 = H * tqn(60) - H * tan(40)
so 45m = H * [tan(60)-tan(40)]
so H = 45 / [tan(60)-tan(40)]

[steady charm]

pls help

[cyan night]

construct an equation

an increase of 7% = 107% of the original = the original * 1.07

and its a cumulative exponential growth every year

so let n be the number of years chessville exceed checkersville

50000*(1.07)^n

do the same process with checkersville

a decrease of 4% = 96% of the original = the original * 0.96

70000 * (0.96)^n

you would want to find the minimum value of n such that it satisfies the condition that 50000*(1.07)^n > 70000 * (0.96)^n

if you are allowed to use a calculator then you could try values of n

the essence here is when you see percentage, you would know that the problem alludes to exponential growth/decay

[steady charm]

ohh I get it now, thank you so much for your help<3 I really appreciate it ^ ^

[cyan night]

np!

[pulsar turret]

Is there a way to solve the quadratic equation in the bracket without using the quadratic formula?

[steady charm]

apply exponent rules

[pulsar turret]

But don’t I first have to solve the quadratic equation?

[cyan night]

x^2 - 4x + 6 = 3

x^2 - 4x +6 -3 =0

x^2 - 4x - 3= 0

split middle terrm

you dont need to use quadratic formula

you can split the middle term

@pulsar turret

-4x = -3x-x

[steady charm]

the answer are x=3, x=1 right?

[cyan night]

x^2 - x - 3x -3 =0

[pulsar turret]

Yes

[cyan night]

really?

oh wait ye

[cyan night]

thiss should be + 3 lol mb

[steady charm]

(x-1)(x-3)

[cyan night]

yes

[steady charm]

u can solve it by factoring

[cyan night]

yes i know

i got it wrong because i thought +6 - 3 = -3 LOL

my brain malfunctioned 😭

[pulsar turret]

Can I know where the 3 came from?

[cyan night]

because 2^ that = 8

and 2^3 = 8

so that = 3

so lets say x^2 - 4x + 6 = A

2^A = 8

so A = 3

hence x^2 - 4x + 6 = 3

[pulsar turret]

Ohh I understand now thank you both

[cyan night]

👍 np!

you dont have to use the quadratic formula at all actually

there are problems that even if splitting the middle term wont work then there are other methods

like completing the square

or vieta's theorem i think

[steady charm]

the quadratic formula is the thing that I always use, factoring is harder for me lol

[cyan night]

some are not factorizable unless you split the constant

like

x^2 + 2x + 3

this has 2 imaginary roots

but

yeah

[fluid summit]

derive and equal to 0

[left knoll]

hi guys! I am struggling with calculus and have to prepare for a midterm! Could anybody help me?

[vague temple]

👍

[left knoll]

Hey, can someone help me please?

[dusky kindle]

I am confused on how to find neighbourhood of vertex in graph theory. Because according to its definition neighbourhood of vertex is : The set of all adjacent vertices of a vertex is called neighbourhood of that vertex. And the definition of adjacent vertices is : two vertices are said to be adjacent, if there is an edge between the two vertices.

in this example they have shown how we can identify the adjacent of vertices

so we we have to make a set of the vertices of those adjacent vertex it should be {a,b,c,d,e,f} right?

but here in this example they have shown that the set of adjacent vertices is just {b, f }

now if we refer to its definition shouldnt the answer be {a,b,c,d,e,f} except g since it has no adjacent?

[cinder yacht]

what is

"the set of adjacent vertices"

adjacent to what? i'm confused

if they said {b,f}, i guess that the quesiton was "set of A's adjacent vertices". But what you understood from the question seems to be "the set of vertices that are adjacent to at least one other vertex"

[ripe hamlet]

helppp

[cinder yacht]

solutions are -1 and 8 so

"two distinct rational solutions"

another way to justify is "the discriminant is (-7)² - 4 * (-8) * 1 = 81 = 9² : the discriminant is the square of a rational number and the polynomial coefficients are rational so the solution(s) is/are rational. But the discriminant is positive so there are 2 distinct (rational) solutions.

[last echo]

C part

s²-7s-8=0
s²-8s+s-8=0
s(s-8)+1(s-8)=0
(s+1)(s-8)=0

Therefore, s = -1 or 8

[dull plover]

Wrong.
you forgot about the differential in the third column. Therefore s= 2 or -8

[last echo]

Nope, it's correct

[dull plover]

Photomath is cheating

But you scanned it incorrectly anyways

[last echo]

What, i literally checked it ri8 now

It's 2.12am ri8 now, I sent ir at 2.07

[dull plover]

Look, thats not an excuse for making such a fatal mistake

[dull plover]

People need to learn to use they're brain and don't rely on some app on they're smartphone

[last echo]

Plz show me the steps, lets see who's correct

[last echo]

Bruh, who needs one for such a simple q? And i can't even use calculators for my exams, so mental calculations r my only option

[dull plover]

You know the book "das ist Alpha" ?

[last echo]

Nope.

[dull plover]

A pity. Good luck with your exams

[last echo]

Yea I'm not german lmao, not sure bout the lang

And srly how is that relevant right now?

[last echo]

@dull plover

[dull plover]

Let me finish up my 3:1 protein shake real quick

[dull plover]

Then I'll help you

[last echo]

Yea i dont hv that much of time

Ping me when u send the sol

[dull plover]

I will my friend

[real bobcat]

Can anyone help me here for maths

How would anyone do this

No.6

[dull plover]

First of all you need to know the definition of value

[real bobcat]

Ok

[cinder ibex]

@real bobcat

Here you go, let me know if u need help understanding what i wrote

[real bobcat]

Thanks this was very helpful

[cinder ibex]

Np : )

[dull plover]

Could you explain it to me. I have the same results but an entire different way of calculating.

[last echo]

V hv to substitute the values of y cuz it's interesting the y axis ri8?

[cinder ibex]

Well basically they gave us two points/dots? (excuse my english i dnt know very well the correct names for math language) so what i mean is they gave us (-2,6) and (1,9) and both belong to the function so if u go to the expression given f(x)=ax²+bx+4 and we put there the values for each point/dot then we get two different expressions that have a and b. If we resolve in order to b for instance then we get an expression for b and if we go to the second expression for the function we had then we can substitute b by the expression we got. Im sorry if i didnt explain very well gets kinda hard cause its not my main language. How did u do it tho?

[dull plover]

I did it by equating the coefficients of a and b. And then insert it for y.

[dull plover]

Thanks helped a lot

[last echo]

In the rhs part and take the abscissa coordinates to be the zeroes

[cinder ibex]

I think i understood what u did but that sounds kinda harder idk never done that

[cinder ibex]

Np : )

[dull plover]

Yeah, it was more complicated than yours. It was just dumb, I didn't knew how to do it easier.

[cinder ibex]

Oh dnt worry, u know now ^-^

[last echo]

Lmao u done with the other problem? @dull plover

[dull plover]

Ill look at it now

[cinder ibex]

Oh how sad u changed ur username

With practice u can get pretty good at it

[dull plover]

x^2-7x-8=0
c=-8 b=-7 a=1
-7^2-41(-8)=81

@last echo here you go

[last echo]

Did u consider both the possibilities?

[dull plover]

if I rest on excuses, I will never reach the alpha version of myself.

[last echo]

Either way, the answer is the same, -1 and 8

[dull plover]

Not really

Kinda

[last echo]

It'll be [-(-7) + or - root(-7²-4(1×-8)]/2×1

Ur signs were wrong

[dull plover]

That's the midnight formula, right ?

[last echo]

Quadratic formula
x = -b ± root(b²-4ac)/2a

[cinder ibex]

But dnt think u are bad, u just need a lot of practice to get good at it, last year i never clarofied my doubts in class and i basically only studied before the tests like the weekend before nowadays i always ask for clarification when i have doubts and i study on almost a daily base, also i do more work that the teacher asks so that that way i can get confident in what im learning and be prepared in advance for tests if u implement this strategies or others that u might prefer im sure u can get good at maths, make an effort to understand and dnt forget that practice is very required

[dull plover]

I know, but I don't have time to study, so I only study 2 hours for an exam. If I had more time life would be so easy

[last echo]

Oof and I thought I was wrong lmao

[dull plover]

That's the abc formula

[wise hazel]

is every one in your class bad at maths ?

[cinder ibex]

Well i understand that the reason i have been studying more is cause i have less classes, just do ur best to manage ur time im sure u will get good at it

[cinder ibex]

For me it is called quadratic as well

[wise hazel]

don't take this wrongly because time is not an excuse for being better since everyone in your class have 24 hrs so it depends on priorities

[ember kernel]

It's usually called quadratic formula as @cinder ibex mentioned

[last echo]

Dude wt do u do all day?

[dull plover]

Yes but everyone has different priorities

[wise hazel]

make maths priority

[last echo]

Midnight formula and Quad formula r the same thing

[dull plover]

Training

[wise hazel]

for which skill

[last echo]

For wt?

[dull plover]

Bodybuilding

[cinder ibex]

Thats a good advice but it depends on whether maths is important for his future or not, u need to know what u want if u want to pursue arts then maybe u dnt need much maths but if u need it u should make it a priority, it is totally up to u what u want to do tho

[wise hazel]

yes

[cinder yacht]

u guys aren't realizing he's trolling?

ahahaha

[dull plover]

I am at a gym that's far away so I have to take the train for 2 hours

[ember kernel]

https://tenor.com/view/typing-several-people-are-typing-gif-15407184

[wise hazel]

my bad im bad at reading trollers

[cinder yacht]

it's an internet troll

just don't mind him

[dull plover]

?

[last echo]

Well, it does make sense

[wise hazel]

idk bro it just seems that you can study while on train

or just make some time

[last echo]

Exactly

[dull plover]

Not really

[last echo]

And also, wt is ur career choice?

[wise hazel]

its tough i know but it will be worth it if you complete the tasks

[dull plover]

You never took the train in germany

[wise hazel]

yes

that is correct

[cinder ibex]

Yeah u will feel great when u understand maths very well

[cinder ibex]

I think i have ahah

[last echo]

Oh plz, it's nothing compared to the Delhi metro xd

[dull plover]

Professional deadlifting but I know I can't do this as a full-time job

[wise hazel]

write down your priorities and your risks and your backup plans and decide if you want to get better at maths

[cinder yacht]

someone un ironically says "reach the alpha version of myself", "first of all you need to know the definition of value", "look that's not an excuse for making such a fatal mistake" and some other bullshit

that's impossible

he's just trolling

[last echo]

Exactly, u need a safety and math is used literally in every subject

[wise hazel]

math is everywhere math make man life easy even while in uni

[dull plover]

You don't know me...

[cinder yacht]

that's true

[wise hazel]

chill

im just curious

[last echo]

@dull plover which grade r u in?

[dull plover]

Im not the one talking shit about smbdy else

[wise hazel]

are you in college?

[dull plover]

13

[cinder yacht]

math is good for developping ur logic skills, good for getting a secure good career

[cinder yacht]

if ur not a troll im sorry, u just seem like one

[last echo]

Oh right, Germany has an extra yr
Basically hs senior ri8?

[cinder ibex]

How many grades yall have? Here it only goes up to 12 and then uni

[wise hazel]

you have time bro take time and learn

[dull plover]

In Germany there are some schools stretching it to 13 years so you don't have to learn as much as 12 year schools

[cinder ibex]

Ah alright never heard about it

[last echo]

I would rly suggest that u pause (spend less time) on ur body building thing and focus on getting a degree

From college ofc

Cuz even if u dont wanna pursue that career u will hv another option

For sure

[wise hazel]

If you get into good uni you don't need to use train and waste two hrs

[dull plover]

If I pause, I'll be never able to be a professional

[cinder yacht]

ur also in Germany?

[last echo]

Did u read wt I wrote in the braket? Plus u'll hv plenty of time after college

[cinder ibex]

No

[dull plover]

Waste? I really love working out

[last echo]

U dont hv to think bout studying then

[wise hazel]

Train travel bruh

[dull plover]

If I have a job I wouldn't be able to go 100% on deadlifting

[cinder ibex]

Well we were tryinh to help but in the end it is ur life and u should make ur own decisions and live ur life the way u want, just try to do the best of it

[dull plover]

Thanks, I will

[wise hazel]

Check out Khan academy

[last echo]

Nobody said anything bout a job, getting a degree is rly vital in this world ri8 now and u dont wanna end up with just 1 option for ur whole life

[wise hazel]

Tuee

Trueee

[dull plover]

When I'm finished with school i need a job

How could I survive then ?

[ember kernel]

Hey ! I've been silently reading for 15+ minutes now, and it looks like the discussion got a bit off track. It's just a suggestion, but would you mind carrying it on in a thread ? 🐨

[dull plover]

I'll sleep now anyway

[last echo]

Uhhhh, wts the legal age for earning there? And also, I'm pretty sure ur parents might help ya

[wise hazel]

ohh i didn't know threads for that

[last echo]

Yupp

[dull plover]

My mom isn't really supportive when it comes to a sports career

[ember kernel]

Thanks ! :D

[last echo]

Then they'll definitely support ur decision for going to college
Anyways its 3.40am here, it shud sleep now but on a serious note, think bout wt v said

[dull plover]

Ill think about it. Good luck with school and anything.

[cinder ibex]

Well i had already left the convo but just wanted to add that i hope u find something that you are passionate about (maybe u already found maybe u will in the future) and that u can make a job out of it and most important that u are happy regardless of what u choose for ur life : ) @dull plover

And we were just trying to show that maths is important but everyone is different and has different interests so in the end it is up to you whether u want to do something related to maths or not also its never to late to learn in case u decide u dnt want maths but u change ur mind in the future

[dull plover]

Thanks. Best luck for you too. We really did disgress far from maths :)

[cinder ibex]

Yeah, thanks : )

[junior blaze]

I got it, thanks!

[cyan night]

wait did you see my message?

[junior blaze]

she*
but yeah, I am not too familiar with it, I shall review it tonight, thank you for your help!

[cyan night]

yes when its intermediate form after you plug in you shall L hopitals

be careful with constants

[junior blaze]

okee, gotta go watch some khan vids, don't wanna bomb ap calc test again, thank you

[junior blaze]

would you per possibly be able to check one more problem for me?👀

[cyan night]

yes sure

[cyan night]

sure

[junior blaze]

Number 5, ill send my answer in a sec

[cyan night]

find the points?

i think we are ought to find the intervals where they are continuous right

its discontinous at x = 2; x = 5; x = 7

[junior blaze]

Yeah, here is what I said, I think I'm wrong tho

[cyan night]

0 should be inclusive

[0,2)

because it is defined at 0

same with others

[junior blaze]

But there is no left limit that exists for 0

Or it doesn't matter?

[cyan night]

hm wait

i think that

your answer is correct

just visualize continuation as if you were to draw the grpah without lifting your pen

it should just be inclusive 0

and then exclusive for the other intervals

do you think so?

[junior blaze]

sounds good, but I still am not sure, does 0 have a left limit or it doesn't?

[cyan night]

you mean an asymptote?

i dont see any asymptote here

and if it actually exists at x=0 then theres definitely no asymptote

[junior blaze]

no as x approaches 0 from the left, it doesn't approach it at all thus it doesn't equal to the right limit

which doesn't match the definition of continuity

[cyan night]

🤔

im actually confused let me seek help

[junior blaze]

lolol, it's ok, I'll just ask a teacher tomorrow if she has time for me

thanks tho

for taking your time on this

[cyan night]

👍

[desert glacier]

can anybody help me with this?

[patent rain]

this is correct

[cyan night]

no

there was no approach from the elft

since the function isnt defined for x < 0

mb

[patent rain]

search up continuity at endpoints

[cyan night]

im still confused 🤔

[patent rain]

the point exists

and

from the left or right side its not approaching any other point

[cyan night]

@junior blaze

[patent rain]

there is no left so u dont have to worry about that and on the right its approaching the point meaning it’s continuous

[junior blaze]

oh no

[cyan night]

but doesnt that contradict the definition of continuity?

as overdose said

[junior blaze]

this is getting even more serious

[cyan night]

no its not

its just discussing

[junior blaze]

why don't you have to worry about the left?

[patent rain]

bc it doesn’t exist in the function

[junior blaze]

wouldn't that tho?

[junior blaze]

for the limit to exist, both, left and right should approach the same number

it would fail step 2

[cyan night]

it contradicts the 2nd one

yes

[patent rain]

it dorsnt

bc there is no left

[cyan night]

lim f(x) exists if and only if it approach from both sides

but because there is no left it means it doesnt exist right

[patent rain]

where else is it approaching

the point is there

[cyan night]

only from the right

[patent rain]

this isnt the definition

[cyan night]

but doesnt mean the limit diverges if theres no left side

[patent rain]

thats only for twi sided limits

There are three different types of limits: left-hand limits, right-hand limits, and two-sided limits.

[cyan night]

hm i didnt know that

[junior blaze]

so it's just a right hand limit then?

[patent rain]

yes bc theres nothing on the left

so (7,8] is continuous as well

otherwise ud have to label 0 and 8 as discontinuties which

makes even less sense

[junior blaze]

ok, now that makes sense, I also didn't know that there is right-handed limits

thanks

[patent rain]

yeah np

[tropic bear]

what is a Symmetric Relation and Transitive Relation?

[flat lava]

Is this what you looking for?

[pulsar turret]

Can someone help me understand how to reach to this answer? Specially the 61/4 part — I don’t get how that’s there

The way I did it — I added (5/2)^2 with the 9 and got 11/4

[last echo]

can someone send me the working of this question

[vague temple]

r = diagonal/2
Area = pir²/4 - area of triangle with sides r,r and 42
so the answer is 2.Area

[last echo]

ohkk i was going in the right path, thx!

[left knoll]

If x cos A = 8 and 15 cosec A = 8 sec A, then the value of x is

anyone who can help me with this problem

[solemn sphinx]

@left knoll

Not much methodical, but I hope you get the gist

[ember kernel]

(Don't pay attention to the expressions at the bottom of the screenshots)

Area of 4 flower beds = Area of the green square [of radius 21*sqrt(2)] - Area of blue square [of side length 42]

Area of 2 flower beds = Area of 4 flower beds / 2

Hope this helps

[last echo]

oh i figured it out, thx though!

[dreamy leaf]

Hello, I'm a 9th grader and I'm very stupid at math, Scholz has given me great motivation to learn math, but since I lost my roots for a long time, I don't know where to start, anyone can show me the way

[glacial dust]

guys can anyone help me find the gradient at 2s and 4s

[cinder ibex]

Hi, well idk but maybe u should focus on what u are learning in school and study the basics of that, what are u learning rn? Also if u have doubts feel free to ask me i should be able to help

[ember kernel]

The gradient (also called derivative) of a * e^(bx) is ab * e^(bx)

Consider using the formula with b = -1/tô (tô is the greek T-looking letter)

[glacial dust]

yes ik that but its asking for a gradient isn't that the slope or m?

i know c but i dont understand b somehow

[cinder yacht]

yeah u have to measure the slope I guess

by drawing the tangent

[glacial dust]

like drawing a diagonal line?

for each point?

like this?

[ember kernel]

Well, gradient is a function such that, if you plug in a specific value for x (or t in this case), you get the slope (or m) of the tangent line to the function associated with that point

For a linear graph (a straight line, like a tangent line eg.), we have the gradient = f'(x) = m = a constant. But take a different function, like f(x) = x² (not a straight line) ; its gradient is f(x) = 2x (not a constant m)

We don't need to draw every tangent line to x^2 at any point if we have the generic expression f'(x) = 2x

That's the same here

Why would you want to draw the tangent for some specific points on the graph, when you could just calculate the generic expression f'(x) (the gradient) that works for any point (you just need to plug in a value for x)

[main plume]

Can someone help me solving these circled exact differential equations?

[ember kernel]

So yeah, the gradient is always a function.
Even in the particular case where f(x) is a linear function (like a tangent eg.), its gradient is still a function (a constant function to be precise : f(x) = m)

[ember kernel]

Have you gotten to the point where you simplified the differential equation to :

[main plume]

Yes but I couldn’t integrate

[cinder yacht]

yep like that and measuring the slope

[cinder yacht]

because the next question (c) asked to compute the gradient, so the question (b) probably meant the slope

[soft stag]

Hey guys, is it possible to simplify one of those 3 terms (black color)?

Would love to get help. I study taxation but this prof is going nuts with mathematics 😅

Like can I get rid of the ln or if the 1/Q thing?

[safe ember]

I mean, you could write the last one as sqrt(2/Qh) I believe

[cinder ibex]

Yeah he can do that

[soft stag]

Like this?

Sorry guys my last math lesson was 6 years ago I’m trying to catch up

[cinder ibex]

Yes

Np, u got this !

Because u had 2Q/Q² and that is equal to 2/Q

[soft stag]

Thanks man! That helps me so much!

[left knoll]

@everyone can anybody help me with this

[left knoll]

@ember kernel

Some said 8ft and 2ft

I tried to use pythagoreon theorem but couldn't find the answer in the choices

[pliant wave]

Hi, nice 2 meet Does anyone know about statistics? I need help getting an exercise and I don't know how to solve it

[still briar]

math help, anyone

[safe ember]

K, first think about the probability of getting an even number in this unfair die. Next consider the two ways of having a number add up to an even: Even+Even, Odd+Odd. Calculate the probability of these outcomes and you'll be done

[safe ember]

First consider the triangle. Hypothenuse is 10, and the sides are X+2 (height) and x (base). Just solve for X then.

[safe ember]

You just got to choose the path which adds up to less distance

[still briar]

got it thank u

[pliant wave]

A doctor wants to know the frequency of Cirrhosis in the population in which he provides his service. To do this, he chose 625 individuals by unrestricted random sampling, out of a total of 3,520. He gave them a complete medical history, physical examination as well as liver function tests. One of the variables of greatest interest to the researcher was the consumption of canned foods.

Some of the results showed that there were 328 subjects who had a strong consumption of canned products (this was considered when they consumed 3 or more canned products daily), of which 218 had a clinical picture compatible with Cirrhosis. Among those who had a mild consumption of canned products (2 or less a day) there were 168 people without Cirrhosis.

Is it possible to say that the consumption of canned products is associated with the development of Liver Cyrrhosis?

[cyan night]

the triangle isnt valid according to the triangle inequality tho

[last echo]

B->A->D

[queen sphinx]

HI GUYS HOW DO I DO THIS:(((((

[ember kernel]

Formula to use :
P(A|B) = P(A inter B) / P(B)

To get P(A inter B), you need to use the formula :

P(A union B) = P(A) + P(B) - P(A inter B)

Hope this helps

[queen sphinx]

ahh that helped a lot. thank you!

i forgot about the formula part of this bc i'm doing revisions

[weary arrow]

I have forgotten everything from statistics but it sounds like the exercise is about significance testing and p-values, I'd look into that in your book or notes.

[glacial dust]

guys how do i diffirentiate 12(1-e to the power of -1/2)

i need help ive spent hours trying to figure this one out

i only know b in number 4

[ember kernel]

It's a constant, so its derivative is 0

[glacial dust]

which number

[ember kernel]

OOh you forgot to mention that the exponent depends on t

[glacial dust]

ye after i diff it i sub the 2 and 4

to the equation

[ember kernel]

But ... you asked 10mins ago how to differentiate v(t), so how were you able to sub 2 and 4 in an expression you couldn't compute 🤔

[glacial dust]

becuase t is apart of the equation

youe see its in the e power -y/2

-t/2

i meant

[ember kernel]

Yes, but that means you subbed 2 in v(t), not dv(t)/dt

[glacial dust]

i just need to know the derivative of 12(1-e to the power of -t/2)

[ember kernel]

Yeah, because otherwise you can't plug in 2 and 4 in it

Thus you'll need to redo b

[glacial dust]

what??

i cant change the question 😅

that is the question

[ember kernel]

No that's not what I mean

Listen

And think

You haven't computed dv/dt yet (question a), so how were you able to plug 2 and 4 (question b) in it, since you don't have its expression

You plugged them in v(t), right, not in dv/dt (they're different)

So, you'll need to change your answer for (b), since the first one you came up with is wrong (because you can't plug values in an expression you don't have)

So leave (b) aside for now, and focus on (a)

[glacial dust]

but it says there clearly find dvby dt so thats the derivative of 12(1-epoer-t/2)

[ember kernel]

You need to differentiate 12(1-e^(-t/2))

[glacial dust]

yah

that is what am asking 😅

[ember kernel]

Yeah

OK

[glacial dust]

so what is the derivative of that

[ember kernel]

First step

[glacial dust]

do imultiply the exponent to 12?

[ember kernel]

Multiply both terms in the brackets by 12

[glacial dust]

ohh ok

[ember kernel]

that gives you (12 - 12 e^(-t/2))

Now, the derivative of a sum is the sum of the derivatives

So Derivative(12 - 12e^(-t/2)) = Derivative(12) + Derivative(-12 e^(-t/2))

BUT 12 is constant, so Derivative(12) = 0

Therefore, you get 0 + Derivative(-12 e^(-t/2)) = -12 * Derivative(e^(-t/2))

[glacial dust]

wowww thankssssss i get it now

so we ditributed 12 inside the parenthisis?

[ember kernel]

Yeah

[glacial dust]

so the 12 outside the parenthesis is out

so i have 12-12epower-t/2

[ember kernel]

No, not the 12 outside the brackets

The real constant is the 1 inside the brackets, but you multiply it by the 12 that's outside

[ember kernel]

No

Because 0*(anything) = 0

What I just did is :
12(a + b(t)) = 12a + 12b(t)

And since 12a is not a function of t (its constant), its derivative is 0

But 12*b(t) is a function of t, so its derivative is not 0

[glacial dust]

so the final ans is-12 to the power of -t/2?

[ember kernel]

Therefore, Derivative(12a + 12b(t)) = 0 + Derivative(12b(t))

[glacial dust]

12e

[ember kernel]

Not really, the final answer is -12 * Derivative(e^(-t/2))

As we calculated it before

You still need to differentiate the exponential

[glacial dust]

is there a possible way for u to write it?

i cant understand it by text

[ember kernel]

Sure

@glacial dust does it help ?

[glacial dust]

bro switch my prof

why cant he make it dis simple

thank you so muchhh

[ember kernel]

Np man, sorry I made it difficult to understand in the first place

[glacial dust]

this 6 e power -t/2

is just the frist derivv right?

[ember kernel]

It is the first derivative

[glacial dust]

okok

[ember kernel]

You need to differentiate this expression to get the second derivative of v(t)

[median pendant]

hey I got a question: Can we perform matrix on oxyz coordinate plane?

[glacial dust]

yes ik that

[ember kernel]

Depends on what you mean by "perform matrix" (I haven't learnt linear algebra with English vocabulary), but I'd guess yes, since that's the space in which we use matrices the most (in mechanical engineering at least)

[glacial dust]

so therefore the second derivative will be -3epower -t/2 right? cuz i multiplied -t/2 to 6 giving be -3

[cinder yacht]

he used the slope on the graph I think

[ember kernel]

You need to multiply by -1/2, not -t/2 but you got the spirit. The second derivative is indeed -3 e^(-t/2)

[glacial dust]

ye

[cinder yacht]

that's nice of u to detail it so much and spend that much time explaining :o

[glacial dust]

type t cuz i assumed u know that t=-1/2

thank u so much btw

[median pendant]

And my teacher ask for the Geometrical meaning of AP (I don't know if it's correct, I translate it word by word)

[glacial dust]

quentin if u dont mind what course are you taking?

[ember kernel]

From April to July that's how I used to answer, with a picture right away. I just got lazy with time 😅

And started answering in the bus as well, which made it difficult to solve on paper

[cinder yacht]

where do u study in France?

la fac ?

[ember kernel]

I'm Belgian, 2nd year of civil engineering

[cinder yacht]

ohh ok

[glacial dust]

am a freshman engineering thats why 😅

[cinder yacht]

im 4th year ""engineering""

[median pendant]

And she gave us a hint: "To understand the geometrical meaning of AP, consider P as the coordinate of a point in 3D space. AP is also the coordinates of a point. Thus, multiplying matrix A by P turns point P into another point. That is, this is a type of transformation. If you apply matrix A multiplication on a set of points, for example a line, triangle, or rectangle, what will result in a new set of points? It is possible to consider a few specific cases (eg when the theta angle is 0, or 45 degrees, 90 degrees, ...) to see clearly, and then draw general conclusions." but i still can't see how to solve it

[glacial dust]

wow u guys are my seniors i guess

[ember kernel]

First one is a "stretch" of each of the input vector components by a different coefficient. You could get any output vector from it, depending on the values of the greek letters

Second one is a rotation of an angle theta around the x-axis (clockwise when you look in the direction of the x-axis)

Third one is a rotation of an angle theta around the y-axis (same process)

I highly recommend you watch 3brown1blue's playlist on linear algebra, it helped me a ton understand and visualise these kinds of problems

[cinder yacht]

I see one rotation around x axis, one rotation around y axis, and one "expansion"? idk how to say it

[ember kernel]

Like, really, GO watch the playlist

Lifesaver

[median pendant]

Thank you so much 🥰❤️

[ember kernel]

Np

[lilac flint]

anyone fancy some stats

This question is about arrangements of all nine letters in the word ADDRESSEE.

Find the number of different arrangements that can be made where the E’s are not together, S’s
are not together and the D’s are not together.

[glacial dust]

@ember kernel u have any vid recomendations on differential calculus?

[oblique siren]

It's in French sorry. We need to find the probability of the event: "the bakery will sell at least 100kg of bread tomorrow", knowing that our aleatory variable is the quantity of bread sold and we have the density function (I don't know if I'm using the correct words in English). Could someone explain to me how to find the answer? I'm sure it's not difficult, it's just me who sucks at maths 😦

[fringe violet]

Hello.. can anyone help me solve these equations please? 😭 i have to hand in it as soon as possible and I haven’t found any solutions yet ( ･᷄ὢ･᷅ ) I’m at sea now.. plz helpp 🙏🙏✨😭 thanks

[ember kernel]

No, you'll have to look up for a ~20 min that sums up all the basics. You seem to have some struggle with the matter

[cinder yacht]

cette proba = P(X>=1)
= 1-P(X<1)
= 1-P(X<=1) (because X has a density, so P(X=1) = 0)
= 1-F(1)

[broken stratus]

ok so the question is 1/sin2a + 1/1+cosec2A = 1 , just have to prove the 1

its Pythagoras

[delicate cave]

this is not true for all values of A
are you looking for solutions of the given equation ?

[broken stratus]

yes

i have to prove how its 1

[delicate cave]

it is not equal to 1

in fact there is no value of A for which it is equal to 1

this is your question right ?

[broken stratus]

this

[frigid narwhal]

how do I partially integrate lnx + 1 / x

[safe ember]

Start off by multiplying the second fraction's numerator and denominator by sin^2(X). You probably will see the answer straight away after that

[frigid narwhal]

Yo how do i continue from here

I am confusion

[safe ember]

Isn't the integral of f(X)f'(X) just f(X)^2/2?

[frigid narwhal]

Idk

Wait i think i know jow

how

[cinder yacht]

you need to pay more attention to parentheses

(lnx+1)/x is one thing, lnx + 1/x is another thing

[frigid narwhal]

Oh yeah

Sorry

[cinder yacht]

anyway (lnx+1)/x = lnx / x + 1/x, you can integrate each one separately

the first one is : ln(x) * ln'(x) so a primitive of it is ln²(x) / 2

the second is 1/x so a primitive of it is ln(x)

[frigid narwhal]

But what happened to the +1? Wait so it's considered as lnx + 1/x and not as (ln(x) + 1 ) * 1/x ?

Oh right

I made that wrong what confused me

Thank you

[safe ember]

You can also just do ((ln(X)+1)^2)/2

[cinder yacht]

yep true

[frigid narwhal]

how are people so intelligent

.-.

[cinder yacht]

we're just more used to it

[frigid narwhal]

this is just so confusing to me, that topic

guess I'll do more of it tomorrow so maybe I'll get it

still have 3 days till exam

the 2 topics I still don't understand 100% are partial integration and full induction so that will be on my to do list for tomorrow and on saturday. on sunday I'll focus on some more excercises and then hopefully it'll be gud.

[oblique siren]

maybe it's a dumb question, but how did you know that the probability was P(X>=1)?

[cinder yacht]

"probabilité que la boulangerie vendra demain au moins 100kg de pain"
= "probabilité que la quantité vendue soit supérieure ou égale à 1 centaine de kg de pain"
= "probabilité que X>=1"
= P(X>=1)

[oblique siren]

ahh j'ai compris, merci!!

[cinder yacht]

you're welcome

[left knoll]

hi ! i was doing algebra for my test exams and while looking through an equation, i got a little confused on how the first line turned into the 2nd one 😭😭 i feel so dumb

[vestal plaza]

Are you asking how the first line turned into the second line? They just pulled a 24 out (divided by 24).

I'm curious how you go from line 3 to line 4. Isn't (a^3 + b^3) = (a+b)(a^2 - a*b + b^2)

[left knoll]

yes, but i don't get how 9 was divided into 216 (though i saw that when you multiply 9 with 24 its 216) why wasn't it applied the same way as they took out 24 from 24x

[left knoll]

its the rule of cubes as far as i understand (idk the actual name for it cause i do maths in my own language)

[vestal plaza]

when you pulled the 24 out, you can think of it as 1/24. So for the term that is 1/9x^3, pulling a 24 out from that means that 1/9x^3 * 1/24

Is this the solution?

[left knoll]

ahhh i get it i think

[vestal plaza]

so its 1/9 * 1/24

9*24 = 216

[left knoll]

ah i got it now

thank you!

[vestal plaza]

no problem

out of curiosity, what does the question say?

[cinder yacht]

i'm guessing they gave him x+1/(6x) = 1 and they asked to compute 24x^3+1/(9x^3)

or actually that was an intermediary step nvm

[vestal plaza]

Ahh I see, but still line 3 to line 4 still doesn't seem to look right

[cinder yacht]

its correct : a^3 + b^3 + 3ab(a+b) = (a+b)^3
so a^3 + b^3 = (a+b)^3 - 3ab(a+b)

they didn't factor a^3+b^3, they only rewrote it in terms of (a+b)^3

[vestal plaza]

a^3 + b^3 =/= (a + b)^3

they aren't the same though

[cinder yacht]

look at what i wrote though

XD

that's the binomial expansion formula of (a+b)^3, not the factoring of a^3+b^3

[vestal plaza]

Ah I misread. Yes you're right, sorry

[left knoll]

yeah they asked for the answer to 24x^3 + 1/9x^3

[fiery haven]

do u guys know what math level they teach this in??

[fervent tide]

We did integrals like those in calculus 3, and some simpler ones in calc 1

[cyan night]

hi

i got this one correct using trigonometry, but not calculus as desired

when solving using trig, i just knew the minimum and maximum values of cos(x) are -1 and 1, and then i just substituted and solved

but from what i heard, we can take the derivative and set it = 0 to find the minimum or maximum point, but does that work as this requires us to find both the minimum and maximum point?

when i took the derivative, (via chain rule), i got -sin(2pi(t-12))/365*2pi/365 = 0

resululting in t = 12

which gives me the minimum value (aka 24) only

[green flicker]

can someone help me with this?

this too

[echo temple]

does anyone have an idea any way i could proof this?

[loud kiln]

Is there some rule for the use of certain trigonometric identities? I couldn't get the correct answer earlier and well...😭

[loud kiln]

Oh, the constants can be included into + C, but what about definite integrals? EDIT: nvm they cancel out hahah

[cyan night]

it isnt in english..

[cinder yacht]

help with what LOL

[soft stag]

Hey guys i need some help with my math answers before i send them to my professor. Its basic math but i did my last tasks like 6 years ago and he is disappointed very quickly.

[cyan night]

sure

[soft stag]

Can i simplify any of my solution (black text on white background with green lines)?

Like im looking for some rookie mistakes

[cyan night]

u can simplify 1/q^2

sqrt of 1/q^2 is 1/q

wait thats a t

[soft stag]

No its no t sorry 😄

So the first one top right is right but you mean the second on on the right side?

[cyan night]

second one n the right

[soft stag]

So i write 1/q sqrt 2qh?

[cyan night]

yes if thats 1/q^2 then you put 1/q outside of the sqrt

[soft stag]

Thank you so much! If i have so many variables(?) under a sqrt can i just write them like qrt or do i need to make multiply signs? Normally i wouldnt but it distracts me as soon as i have so many

[cyan night]

wdym by qrt

[soft stag]

Do i need to write q x r x t under a sqrt or can i also like normally write qrt?

Like without multiply signs

[soft stag]

Is it possible to simplify the last 2 ones on each sight? Can i short them because i have the same ones on both + sides?

[cyan night]

you can write qrt yeah

is q' the derivative of q?

[soft stag]

Yes i think it is

[cyan night]

the last equation on the left is basically 1/2 (x+1/x) with x as Q'/(sqrt2QlnQ/h)

idk if you might wanna simplify that

same with the last equation on the right

[soft stag]

Im going to try it without simplify it and see what he says

I really need to learn this kind of stuff. Never had math again since school and now in my master degree its coming back

This is so embarrassing 😄

[cyan night]

ahh i see

i think its fine to put it like that

fyi, x+1/x = x^2 + 1

so Q'/(sqrt2QlnQ/h) + 1/Q'/(sqrt2QlnQ/h) = ((Q')^2/(2Qln(Q)/h)) + 1/Q'/(sqrt2QlnQ/h)

ok this text looks suck

[soft stag]

Hahahah no its okay i understand it

Thank you so much!

[cyan night]

but i think its fine to put it like that

np

good luck with your degree sir

[patent rain]

isnt this only true if x=1

[fair canopy]

You forgot a case ( hope it’s readable )

[cinder yacht]

more like = (x^2+1)/x

[cinder yacht]

or x=i or x=-i if we're in complex numbers hehe

[mellow cradle]

Idk if anyone else speaks bengali tbh

[cyan night]

yeah the line below i wrote th final answer as that form but mb

[tough elk]

I am very confused can I have some one quickly help me on this big thx

[cyan night]

when you differentiate implicitly the change in y wrt x, whever you differentiate that has a "y", you additionally multiply by dy/dx, or y'.

rewrite sqrt xy as (xy)^1/2

so x^1/2*y^1/2

you use the product rule, but whenever differentiating that involves taking the derivative of variable "y", multiply by y'

[terse swan]

can someone help me with this? 😆

[soft stag]

Is 1 the same as 2?