math-help

[blissful ridge]

i use chatgpt or talk with the other students

[proper venture]

Hey, I need help. Can someone tell me all the chapters of the IB Math curriculum. Grace 7.

[terse meadow]

I think you can find this online

[proper venture]

I tried but no

[terse meadow]

It's this ?

[proper venture]

Can I know the site? I tried but I got very scattered and less content

[novel harness]

Do you guys have any tips on how to memorize? I know to do worksheets or flashcards . But, is there any other way

[vale wyvern]

I usually write the stuff down to remember and if it's a formula, just do as many questions using the formula, eventually I just remember it by heart

[winter depot]

Can someone please help with these two problems??

[candid rivet]

you calculate as usual (knowing that every inversible matrix M, then by definition M×M^-1 = M^-1×M=I_n) with the only difference being that the matrix product is not commutative ( which means AB is different than BA most of the time)

[candid rivet]

Q.5. first we want the expression of the tangent in a certain point a, then we want this tangent to be parrallel to y=2x+1, which is equivalent to say they have the same slope

[candid rivet]

Q.6. I'm probably not right sorry i've never studied this, but i guess we want to express t(x) to then have y(x), yet i have to do the assumption that t is always positive

[novel harness]

Thanks 🙏

[left knoll]

Anyone?

[graceful crag]

sorry but does anyone know how to solve this?

[candid rivet]

@left knoll It is not the most beautiful math exercice that exist haha but at least the system of equations is pretty easy to solve

[graceful crag]

thank you!

[candid rivet]

you're welcome (:

[left knoll]

could u have saved your steps by using Cayley Hamilton Theorem?

[ebon sail]

Just my opinion. Please use pen and paper more, write down whenever you solve a problem. Think and write down anything, if in 30-45mins and you cant solve it, you should look up for hints.
Make sure you know the theory quite well
About linear algebra, I only know 3Blue1Brown (and found it really useful)

[candid rivet]

huum maybe idk i haven't studied this theorem yet. But from what i've seen on wikipedia this theorem does not use the inverse matrix so i don't think it is enough to solve the exercice. but i might be wrong

[left knoll]

well if u multiple by 3 both sides..then u get a equation and then multiply by A both sides...these will be the characteristic equation

[candid rivet]

does it work then ?

[left knoll]

i have a solution can you check?

[left knoll]

Professor Leonard on YouTube, saved me calculus in uni

he has full classes recorded of everything

[cinder locust]

gilbert strang on YouTube for linear algebra

[candid rivet]

yeah go on but i think you're better than me haha

[left knoll]

Lmao

[candid rivet]

Looks really good to me ! good use of Vieta's formulas 👍

[vestal peak]

why is the RAA θ - π in Q3? shouldn't it be 3π/2 - θ? Like in Q2 we do the next quadrant's starting point (1π) minus the principal angle, same thing with Q4, next quadrant's starting point is 2π and we would subtract the principal angle by it. i'm sure its simple but man i cant figure out why this is the case someone pls explain.

makes sense in degrees but not in radians

[fair pecan]

the theta is in Q3 and when you subtract pi, you are really just subtracting Q1 + Q2 (Q1+Q2 = pi), then you get the angle starting from Q3

RAA is the angle with the x-axis, the theta in Q3 is more than pi. so what do you think should be the angle theta (in Q3) with the x-axis(horizontal line)?

[sonic pulsar]

i take so much time on each exercice . i can take 1or 2 hours per exercices is it good for me

or must i do simple exercices who take me 10mn instead of difficult exercices

[gloomy fiber]

Any clue how to reverse this function?

[candid rivet]

I'd say it is good to sometime spend like an hour on 1 exercice, and then when reading the solution you will remember it
yet most of the time it is better to spend less time on one exercice
the most important thing is to read the solution and one or two day later try to do the exercice again without looking at the solution to see if you now know/remember how to do it

[candid rivet]

if you're not paying too much attention to the intervals of definition of x and y, then :
y=arcsin(log_2(x)) , sin(y)= log_2(x) , 2^(sin(y)) =x

[candid rivet]

and yes always start with pretty easy exercices to make sure you understand how to properly use a property/theorem, and then you can search harder exercices

[sonic pulsar]

thanks

[still briar]

can someone help me with d)? the sketching part

[terse meadow]

You can draw th two point (y, 0) and (0, x) , after you make a line between this two point and you get the sketch.
Have a good day

[vale wyvern]

<@&942391219206647828>

[still briar]

ohh okay thank u

[magic gull]

The fule for a machine is a mixture of 8 parts petrol to one part oil. How much oil is needed to make 1 litre of fule??

how can i find the answer??

[fast heath]

I'd divide the 1 litre by 9 parts to get how many ml there are in a single part so 1000ml / 9 = 111.11...ml of oil

[magic gull]

ohh

omg

i m so dumb

[fast heath]

You're not dumb you're just learning I forget even the most basic physics all the time and have to remind myself : D

Until you start to use these things on an atleast weekly or monthly basis you'll forget stuff so just find a way to store this information somewhere where you're able to check once it's needed.

[magic gull]

oh o k

is IGCSE hard?

[random bolt]

Can someone help with the general solution for theta

[left knoll]

I posted the solution. Let me know if it helps.

[random bolt]

Thanks really helpfull👍

[left knoll]

😄

[tacit pollen]

how did this determine sin = u/sqrt(u^2 +1)

[quasi bridge]

theta = arctan(u), so tan(theta) = u
draw a right angled triangle whose height and base are u and 1 accordingly and from that they've found the value of sin(arctan(u))

[steady zephyr]

Hello, how to solve the limit pointed in red please 🙂

[weak lotus]

just plug in f(x) and calculate

tip: draw fx

should be easy after that

and if you mean $cos(\frac(1/x)) -1$

just draw the graph of it and rest is trivial

good luck

[quasi bridge]

isn't it possible to find the value of the limit without the help of graph?

[weak lotus]

of course but its analysis probably

everything is so much easier with a graph

you can draw, so you can use it

[quasi bridge]

idts drawing the graph manually is easy. ive tried attempting the problem but wasn't able to do it just properties. drawing the graph felt like an difficult choice cause of how the function looked.

[weak lotus]

i think its personal

we really trained on sketching graphs and that

so when i can use it, i use it

math is like a journey, you have different ways of walking it, but at the end you will have the position

[quasi bridge]

can you help me out with sketching the graph? i find it easier to solve limits question using graph but most of time i can't sketch the graph properly

[quasi bridge]

ig so the problem can be solved in the following way via analysis,

f(x) = -x + sqrt(x² - x), x < 0
find the value of limit x tends to -infinity of f(x) via rationalization, you'll get it to be 0.5

now, as f(x) tends to 0.5 when x tends to -infinity. put f(x) = 0.5 in the limit, you'll see that it's 0/0 form.

use l'hopital rule, you'll get a term f'(x).
when you differentiate f(x), you'll get -1 + [(2x - 1)/(2 * sqrt(x² - x))].
if x is extremely large, then it could be approximated and written as -1 + x/|x| which would tend to -1 as x approaches -infinity. now use the fact that f'(x) tends to -2 in the limit (the one which you get after applying l'hopital rule)

at the end, you'd get the answer to be -infinity

limit x tends to -infinity [cos(πf(x)) * πf'(x) - 2f'(x)]/[sin(1/x) * (1/x²)] (the limit after l'hopital)

@steady zephyr

[quasi bridge]

@weak lotus lmk if it's correct

[steady zephyr]

Thank youu, I really appreciate your help 🫡 <333

[hasty oxide]

I would really appreciate someone's help with this stats question

I'm pretty sure you use this formula

I havent been in class all week, so I'm behind and my prof doesnt record the lecture /:

[fair pecan]

do you know what is null hypothesis?

[hasty oxide]

yes, I might have figured it out. Is the null hyp. rejected?

[fair pecan]

what did you get for z

[hasty oxide]

calculated z= -3.83

[fair pecan]

ok this is correct

what did you get the probability

[hasty oxide]

the number I compared it to? 1.645?

[fair pecan]

no, on the z table

anyways, what did you write your null hypothesis

@hasty oxide

[hasty oxide]

my friend just sent me the answer, THANK YOU SM

https://tenor.com/view/thank-you-thanks-hey-bro-fist-bumb-gif-16262296206650437916

[fair pecan]

oh nice, no problem

[quasi bridge]

you're welcome!

[fiery surge]

Would appreciate some help on this question

[sage cobalt]

Could someone help solve this question for me please?

[quasi bridge]

i) if there aren't any restrictions then it'd be 8!/(3! * 2!)
in total there 8 letters in the word INFINITY and out of which 3 are I's and 2 are N's

ii) if I is at the end (fixed), you've more 7 letters which must be arranged out which 2 are I's (as one of I is fixed at the end) and 2 are N's
so it'd be 7!/(2! * 2!)

iii) if no two I's are adjacent then there must another letter between them. refer to the image. the "/" indicates a possible position where an I can be placed. there are 5 such places but we've only 3 I's
so first select which 3 position are the I's are going to be placed = 5C3
then you can arrange NFTY internally in 4! ways
so it'd be 5C3 * 4!

lmk if you're confused in the last one

[undone ledge]

Could someone please help me out with this question

[fair pecan]

they will have no solution when the discriminant(D) < 0. You should equate both the equations and then solve for m in the discriminant formula, i.e., D = b^2 - 4ac.

[undone ledge]

thank youuu

[stuck bane]

Please help me with this

[tacit pollen]

how would I solve the square root in this (trig)

[quasi bridge]

sec²(x/7) = 1/2
the range of sec(x) is (-inf, -1] U [1, inf)
so it isn't possible for sec²(x/7) to be 1/2. it can be verified by plotting y = sec²(x/7) and y = 1/2, they both never intersect

[ornate coral]

Can anyone help me with this question?

[left knoll]

How do I solve the limit

[vale wyvern]

do you want a hint? it's easy after that

[left knoll]

Yeah tell me . I have been stuck for so long

[vale wyvern]

cosx + i sinx = e^(x.i)

you recognise this formula?

[left knoll]

Tried it then what??

[vale wyvern]

put it in the limit z1.z2.z3... thingy,
you will get all the powers of 'e' adding up in telescopic form
you just solve it and the you get the answer

[left knoll]

How do I solve the sum of powers

[vale wyvern]

What are you getting exactly in the power?

[left knoll]

After this

[vale wyvern]

so it's comes to be 1/6

[left knoll]

Thanks a lot

[vale wyvern]

your welcome

[hushed flax]

can somoene answer 1,5,6 please thank you !

[candid rivet]

1. x² always definie so f is define on R
2. you just need 3-t to be different than 0 so f is define on R{3} = ]-inf,3[U]3,+inf[
3. you want t²-16=(t-4)(t+4) different than 0 so t different than -4 and +4 so G is defined on R{-4,4}

[lean crane]

hi,can anyone help me with these questions pleaseeee? the 2nd picture is the options available for all of them

[amber vapor]

Can someone pls give me a HINT with this problem, thank you!

[fair pecan]

split the integral and use Trigonometric substitution in one part and u-substitution in another part

[lavish copper]

can someone help me with this idk what to do

[cyan pine]

|| is failing grade 11 math okay? (cuz i failed it and now im scared) ||

also, please share any worksheets or problems related to straight lines, derivatives and intro to 3D geometry so that I can prepare for the upcoming exams

[magic gull]

x - 2x/7 = 10

can't we just

move the 7

to the 10 side

and

multiply it?

[quick wraith]

is it (x-2x)/7=10 or x-(2x/7)=10

[magic gull]

is just x - 2x divided by 7 = 10

x is not divided by 7

only 2x

[quick wraith]

yeah then we cannot do that we first have to make denominator of x also 7 (i.e. 7x/7)

[magic gull]

so you multiply everything with like 7

and you get

[quick wraith]

7x/7-2x/7=10
5x/7=10
x=14

[magic gull]

7x - 2x = 70

oh ok

[quick wraith]

yes

[left knoll]

Of course its okay for rn if you dont really care, but if you are continuing with maths in your next 2 years then its definitely a big issue caused the foundation is really important to the following years

[lavish copper]

@everyone help

[hushed flax]

thanksss

[candid rivet]

The idea is to show that if f injective then f surjective, and if f surjective then f injective. Hence f is bijective and you take the inverse function on both sides of the equation f•f=f which gives f = Id.

If f injective,
let's take y in E. we know f(y)=f( f(y) ) so x=f(y) works (since f(x)=f( f(y) )=f(y)=y, last equality true because f is injective) thus f is surjective

If f surjective,
then let's take a and b two elements of E such that f(a)=f(b). Since f is surjective there exist x and y in E such that f(x)=a and f(y)=b. Hence a=f(x)=f(f(x))=f(a)=f(b)=f(f(y))=f(y)=b so f is injective

[lavish copper]

thanks

[crimson finch]

How to solve this questions? It’s an assignment of sines and cosines

[quick wraith]

you can do this question by the similarity of triangles

[crimson finch]

Yes I thought the same but don’t we have to prove similar triangle for that?

[quick wraith]

yeah if we know that x and 4m are parallel we can

[crimson finch]

Yess but it is what is given in question…so should I go with similar triangles?

And it’s an assignment of law of sines and cosines but I am not able to apply it? Do you think we can apply that?

[quick wraith]

wait ill try to do this by trig

[crimson finch]

Okk thanks

[quick wraith]

have you been taught law of sine of triangles?
that is the only other approach I could think of

[crimson finch]

Yess

But I am confused how to apply it as I have no angle given

[crimson finch]

You are a saviour man!!!!!! Thanku so much! You are a genius!

[little gazelle]

I dont trust anyone who write x like )(

[gentle trellis]

😔 surry

[vale wyvern]

I dont trust anyone who writes x (in maths) like its a multiplication symbol

[little gazelle]

I write multiplication symbol as •, for example 4 • 2 = 8

[left knoll]

yea thats much better idea but some of my teacher hate me for doing so

[vale wyvern]

then what about decimal??

4.2 = 8

when you actually writing from hand, its still confusing

[little gazelle]

I use comma instead of dot when writing decimal number

and most of the time I dont use decimal notation

[blissful ridge]

what does this weird sign mean that is in the red thing?

i dont mean the waves that circle with the line

i've never seen that before

[candid rivet]

i think you're talking about the greek letter "phi". In maths it just is the notation for the "golden number/golden ration" constant

[blissful ridge]

oo oke thank you

[opal crystal]

e

[sage cobalt]

Could someone help me with this question please?

[sage cobalt]

especially part c

[echo quest]

hey, i'm kind of bad at maths, but want to start learning the basics again (don't need it for studies, just a personal want), any place i can start to learn theory, and then practice with exercises ? thanks in advance !

[left knoll]

save my exam, the chemistry teacher, etc, there is several platform. You can use photomath to assist you if you struggle

[echo quest]

thanks a lot!! i'll check these all out !

[left knoll]

a) if a number is greater than 40,000 then it's ten-thousandth place will be 4 and we'll arrange the remaining places.

4 _ _ _ _ 

there 4 remaining places and 5 digits (1, 2, 3, 7, 9)
first choose 4 digits out of 5 (5C4) then arrange them (5C4 * 4!)

b) in the second one, the last two digits can be either 2 4 or 4 2

_ _ _ 2 4 

there are 3 remaining places and 4 remaining digits (1, 3, 7, 9)
so number of possible ways to arrange = 4C3 * 3!
and as the number of possible ways for "4 2" case is also the same, the total number of cases would be 2 * 4C3 * 3!

c) find numbers which can greater than 40,000 and are even.

4 _ _ _ 2 

the reason why only 2 is present in the units place is cause no repeation is allowed.
now using the method which we've used above find number of numbers which greater than 40,000 and are even. subtract that from total (i.e. answer of a part) to find the numbers which are greater than 40,000 and are odd

[sage cobalt]

Hi notamy! thanks for the response, but just some clarifications

1. for part a, can't the number in the ten thousand be 4, 7, and 9? So I don't know if it is right to assume that it can only be 4, since 71,234 is also greater than 40,000

2. for part c, same as part a, the number in the ten thousand place can be 4,7 and 9 no?

[left knoll]

erm yes, i'm sorry. i've made a huge mistake. it went top off my head while typing

[sage cobalt]

ahhh I see, no problem!

[left knoll]

so it'd be 5C4 * 4! * 3

[sage cobalt]

Ahh, ok! how about part c?

[left knoll]

it'd be 4C3 * 3! * 3

[naive dew]

Can someone explain when we factorize the above expression, where does the HIGHLIGHTED negative sign came from? I'm confused on this step

[cinder ibex]

It is because x tens to minus infinity

I believe this video explains it https://www.youtube.com/watch?v=UBP1GxYxHLY

around minute 7.20

[fallow lark]

does anybody know a good video on First Order Logic? i can't find a good one

[keen walrus]

how do you solve this?

[fair pecan]

general equation of a circle is (x-a)^2 + (y-b)^2 = r^2. The center of the circle is given by (a, b), and radius is given by r.

[keen walrus]

so radius is 3

[fair pecan]

exactly

[keen walrus]

and center is 3, 1

[fair pecan]

yes

[keen walrus]

how would I find the second point on the circle?

I got this but it says it's wrong

[fair pecan]

you are inputing the radius wrong

the circle should be smaller

[keen walrus]

still says it's wrong

[fair pecan]

radius is 3, that does not change

[keen walrus]

?

[keen walrus]

^

[fair pecan]

ah, i though you have to drag the circle in the graph to the radius's length

should be like this

[keen walrus]

where do I put the second x?

[fair pecan]

put it at y = 1

[keen walrus]

nvm

got it

[fair pecan]

awesome

[tacit pollen]

how would I go about solving this?

[polar glade]

guys can u evaluate this equation plz

[vale wyvern]

do you just need the answer or you need the solution?

[polar glade]

both

[vale wyvern]

answer is 3/2

for the solution,

[vale wyvern]

I will write it and send the solution in sometime
is it ok?

[polar glade]

can u send it today?

[polar glade]

I need the math equations steps

[vale wyvern]

yes in half an hour or so

[polar glade]

thanks

[vale wyvern]

@polar glade sorry got a little busy

I made a little mistake before
Forgot to add 1/2
Sorry

But here's the solution, if you don't get anything please message me

[polar glade]

thanks for solution

[still condor]

can anyone tell me why there are two formulae for variance in statistics

like show me how one can be manipulated/converted to the other

[amber vapor]

compute the determinant of matrix of order 2022 below:
D=abs(a_ij)_2022x2022; a_ij= x if i= j. a_ij= y if i + j= 2023 and a_ij = a for other cases
Note that: D= (x+y+ma)(x+y-2a)^n^h. Compute m+n+h= ?

Yo I am strugling with this problem, do anybody have any idea how to solve this, pls help me.

[still condor]

take a big determinat and substract one row from another, you will get alot of zeroes, find a pattern and repeat, you will get a value

h would be 2022

n zero ig

wtf is this question

[abstract wagon]

someone help me with this please

[deep robin]

WHO KNOW HOW TO GET GPT4 FOR FREE?

[solar raven]

What does "interleaved retrieval" mean?

[left knoll]

x^(4x)^3 = 256, how can i find x

[vale wyvern]

did you try converting sec and tan into sin and cos and then solving?
or the second way to make
(sin x)^2 - (cos x -1)^2 in the numerator

[vale wyvern]

try taking log on both sides and solving

[worldly copper]

Hello guys, is the determinate -(4)^n ?

[candid rivet]

i might be totally wrong but i think every time you switch two colums you multiply by (-1), and we want to get the matrix where the diagonal has all the 4, so there are E(n/2) switches of columns which gives us (-1)^(E(n/2)) 4^n

[worldly copper]

I think you are right thank you, I forgot this trick

[abstract wagon]

thanks

[left knoll]

why do me use sin and not cos, im confused

[warm crypt]

If you are going to find the silding force that cause by the gravity, it will be sin if the theta represents the slope angle.

And the cos would be the normal force, it's mostly used to determine friction.

[left knoll]

gotcha , thanks

[undone ledge]

Hii could I get some help with this question? Like how you get to it

[warm crypt]

If you replace x directly in to the function, it will be zero over zero

[vale wyvern]

hmm one method is this,
another method is too factorise the numerator
here use formula,
a^3 - b^3 = (a-b)(a^2 + b^2 + ab)

then you can divide it by denominator and just put in x = 3 for your answer

[warm crypt]

Then use l'Hospital's law, take derivitive.

[karmic spoke]

idk if anyone will see this, but for my calculus class we are going to need to recursively call a function for newtons method. I dont remember how to plug in x values to the Y funtions on my calculator, anyone know how to do it? i remember it being so simple during class i didnt write it down.

[naive dew]

What to do if value inside trigonometric functions approaches infinity?

It's a question on limits and continuity

Nvm I got it (squeeze theorem if anyone's curios)

[left knoll]

anyone know fourier series?

[nocturne zodiac]

is this right

[gentle trellis]

its continous right?

[left knoll]

in 7/d why dont we accept t=1 as an answer?

[gritty smelt]

Can you help me find the extreme value of the function and at what point it is? tysm!

[left knoll]

if you mean local minima and local maxima by "extreme value" then you'll get one at x = 0. differentiate y wrt to x and equate it to 0

y = (1 - x^2)^(-1/3)

dy/dx = (-1/3) * (1 - x^2)^(-4/3) * (-2x) = (2x(1 - x^2)^(-4/3))/3

[wet lark]

lim x-->45 sinx-cosx/x-45 Can you solve this without l hopital? 🥺

[quick wraith]

yeah but dont put x=1 (in derivative to get dy/dx=0 as x=1 is not in domain of function) and you'll have local minima at x=0

[quick wraith]

multiply and divide by 1/rt(2) ==> cos45sinx-sin45cosx in numerator = sin (x-45)
now you have lim x--->45 rt(2)* sin(x-45)/(x-45)
and answer will be rt(2)

[quick wraith]

In the numerator make it sinxcos45-cosxsin45. Rest is fine.

[wet lark]

oh sorry

I am sleepy sorry for that

[quick wraith]

its alright

happens to the best of us

[gritty smelt]

hey again! can anybody help me with this? I translated the question. b)Find the points where f(x) is not differentiable and explain why. TYSM!

[polar glade]

can u evaluate?

[vale wyvern]

is the answer 2/5?

you can use this formula to calculate it

integral by parts
you take 't' as u and 'e^(-5t)' as v

I might have made a mistake so just try it by yourself once

[polar glade]

thanks i’m going to try

[gritty smelt]

thank you so much Buse for your reply. that helped a lot!

[naive dew]

Yes

[quick wraith]

btw this is a very repeated kind of question and there is a trick for these kinds of question
if the power of x >1 then f(x) is cont and differentiable
and if power of 1>/= x >0 then f(x) is cont but not differentiable

[magic gull]

is n = 2 or 1/2

[noble falcon]

def 2, just plug in and try

[naive dew]

2

[coarse spear]

Can anybody explain why the lines of best fit have to touch (0,0)?

[left knoll]

The graph you've showed plots Kinetic Friction against Normal Force for various surfaces like sandpaper, rough table, and highly polished table. Each of these surfaces has a different coefficient of kinetic friction, which is evident from the different values of frictional force at a given normal force.

The reason why the lines of best fit for these data points must pass through (0,0) relates to the fundamental nature of friction. The formula for kinetic friction (( F_k )) is given by ( F_k = \mu_k N ), where ( \mu_k ) is the coefficient of kinetic friction and ( N ) is the normal force. According to this formula:

1. Proportionality to Normal Force: Kinetic friction is directly proportional to the normal force. If there is no normal force (i.e., ( N = 0 )), there can't be any friction because nothing is pressing the surfaces together.

2. Zero Normal Force, Zero Friction: When the normal force is zero, kinetic friction must also be zero, irrespective of the coefficient of kinetic friction. This is why the line must pass through the (0,0) point, as it represents the scenario where there's no normal force and hence no friction.

3. Linear Relationship: The graph's linearity also comes from this formula. As the normal force increases, the kinetic friction increases linearly, assuming a constant coefficient of kinetic friction for a given surface.

TLDR:
So basically the necessity for the line of best fit to pass through (0,0) is a direct consequence of the basic principles of friction, where the absence of a normal force means there's no force available to cause friction, regardless of the surface characteristics.

[left knoll]

.

[coarse spear]

thanks man
its been buggin me since my teacher didn't really explain it and just showed the graph to me

[left knoll]

Of course friend ^^
In your next class, I hope you two can go into more detail

[cinder ibex]

Wow such a nice offer doesnt look like a scam at all lol

ye i guessed lol

but still people who are trying to hack are kinda clueless does anyone actually fall for that?

[fast heath]

Hi, can someone help me solve this I know the answer is 1 but I'm not sure I'm getting it correctly.

[signal gorge]

is anybody here skilled with financial mathematics? I need something to be cleared up

[fair pecan]

write tan(a) and cot(a) in terms of sin(a) and cos(a). The terms will cancel out, leaving you with sin^2(a) + cos^2(a), which is just 1.

[left knoll]

trying to equate i hat vectors yields ti = 2.4 and tj=2.3333 but the given answer is t=2.2

i dont understand what im doing wrong

[left knoll]

what is 1+1

[timid delta]

11

[steel acorn]

hi! can someone help me with this pls, it says : Draw the vectors AB, -AB, AB+BC, AC-AB, AB+AC. I understand how to draw the first 3 but i don't get the "AB+AC"

here is the correction but why is it like that ?

[left knoll]

how do i calculate the distace between 24 and 26

[naive dew]

Try making the traingle cyclic. The tail of one vector should touch the head of the other

[naive dew]

Subtract the distance at 26s and 24seconds

[polar glade]

could u evaluate it?i need a solution with answer

[weak lotus]

let me write it down real quick

its just using that formula no?

lim for k --> infinity of \frac{a_{n+1}}/{a_{n}

@polar glade

[polar glade]

thanks i will check it in 10 minutes

[weak lotus]

Let me know!

Also seeing this material

[steel acorn]

oooh ok i see why, thank you for clearing that up

[ionic plover]

just asking. 2/k does converge as a sequence. But thats a series right? since your result was a harmonic sequence in the series, doesnt that mean its actually not converging?

[weak lotus]

isnt harmonic 1/n?

@ionic plover

[ionic plover]

yeah it is, but if thats your result in a series, its not converging or is it?

[weak lotus]

its pretty funny because we made this one is class today, could be wrong in my solution

let me recheck

[ionic plover]

it converges to 0 if its a sequence but the question was if its converging as a series

1/n is not converfging as a series but 1/(n^2) is

[weak lotus]

true

[potent radish]

Plz someone help w 1st question 🙏😭

[candid rivet]

the general term of the series is positive and is ~ 1/2n² which converges

[candid rivet]

pour le premier terme, pose u=x+1 ca te donne (u-1)(u)^1/3 = u^4/3 - u^1/3 qu'on sait primitiver, pour le second membre dans le cas 1/(polynome de degre 2) on cherche a se ramener à du 1/u^2+a^2 et eventuellement un terme en plus etant un polynome de degre 1 sur un polynome degré 2(avec a une constante) qui admet pour primitive arctan(u/a) et pour cela tu complète le carré x²+2x+x =(x+1)^2 +1 et t'es bien de la forme 1/(u²+a²)

[worldly dome]

could someone explain the rule that allows for the limit to be written as an exponent

[candid rivet]

if you don't know what is ~, you can also show that it is smaller than K/n² where n is a constant

[candid rivet]

if f is continuous on a, then lim f(x) where x->a = f(a)

[candid rivet]

here exponential is continuous on R so is in particular coninuous on lim(ln y)

[potent radish]

@candid rivet Ya thnx
I'll see it
What u said

[zealous swan]

hi guys

i need help with math

i have an exam tmr

highschool math

[minor sand]

Write the topic or ask questions, i am not sure i can solve them but let me try 😅

[naive dew]

The graph of e^x is always continuous and it will be continuous on lnY too so, we can write it as lim(e^lnY)

[sick edge]

What grade math is that?

[naive dew]

I guess it’s college level calculus in the us

[left knoll]

can someone solve this question im stuck at it

[sonic karma]

If anyone is good in aptitude please dm me I needed some help!

[undone ledge]

Could someone help me differentiate this? Could you please send step by step? :))

[candid rivet]

you are right on everything except for v' (use the chain rule !)
the derivative of (3x-5)^4 is 4×(3x-5)^3 × (derivative of 3x-5) = 12(3x-5)^3

cute cat by the way haha

[undone ledge]

ohhhhh omggg i forgot about the chain rule thank you so much!!!!!

[undone ledge]

thank you soooo muchhh!!!

[undone ledge]

heheheeh cats>>>>

[undone ledge]

is the last line 3x^2(3x-5) is the (3x-5) supposed to have a power of 4?

[fair pecan]

oh yes it does, good job on noticing that

[ebon relic]

hello does anybdy know how to find
the set of values ​​of the function?

[bold atlas]

hi can someone help me draw the graph of this function, i tried taking cases and drawing individual grAPhs and superimposing but mine was complete different than the answer.

[bold atlas]

u can find increasing decreasing, and find you will find a point where from its left side its decreasing and on its right it will be increasiing, that wud give u the minimum value, try it and it see if it helps

[ebon relic]

well it decreases till -3 right ? and then increases from -3 to infinity

but what are the values?

[fair pecan]

are you trying to find the roots of the equation?

[ebon relic]

the set of value , like ( x ; +inf)

or (-Inf ; x )

[fair pecan]

i think its the range of the function, do you have the answer perhaps

[ebon relic]

it can be i translated it so it can sound weird

gimme a min

[fair pecan]

ok

[fair pecan]

A.)

[ebon relic]

how did u find it?

[fair pecan]

wait lemme send u the solution

[ebon relic]

ok

[fair pecan]

you need to memorize the formula to find the vertex point of a parabola

i forgot how to find the vertex so i had to google it💀. we better memorize it

[ebon relic]

Thanks a lot!

[ebon relic]

yea 💀

[left knoll]

can use derivatives to find the minima
y = ax² + bx + c
dy/dx = 2ax + b
at minima/maxima, dy/dx = 0
so x = -b/2a

[quick wraith]

Cross-check it once i think this should be the graph ( i have highlighted the actual line of the graph you will notice if you see closely )

[bold atlas]

i got a similiar graph as well, i guess the solution was wrong, Thanks buddy!!!!!!!!!!

[carmine cosmos]

some 1 help with this integral please

[polar kestrel]

@carmine cosmos grade??

[carmine cosmos]

lolo ignore this now

it isn't solvable for where i am in math

im in grade 11 taking calc bc

[polar kestrel]

oh that's great mee too in 11th

[smoky topaz]

Tips to pass real analysis ( math) exam

[fair pecan]

i need those as well

[left knoll]

How do you prove ex 6

This is the formula the exercise uses the way we write it is different but same formulas

How do you prove something like this pls help

[surreal valley]

hi

Let 𝛼 and 𝛽 be real numbers such that −𝜋 4 <𝛽<0<𝛼<𝜋 4 . If sin(𝛼+𝛽)=1 3 and cos(𝛼−𝛽)=2 3 , then the greatest integer less than or equal to ( sin𝛼 cos𝛽+cos𝛽 sin𝛼+cos𝛼 sin𝛽+sin𝛽 cos𝛼 ) 2 is _____________.

i need help in this question

[candid rivet]

maybe try using the formulas sin(x+y)=sin(x)cos(y)+cos(x)sin(y) and cos(x-y)=cos(x)cos(y)+sin(x)sin(y)
and if needed we also know that :
-1 < cos(alpha) < 1
0 < sin(alpha) < 1
cos(-pi/4)=sqrt(2)/2 < cos(beta) < 1
sin(-pi/4)=-sqrt(2)/2 < sin(beta) < 0

[candid rivet]

from what i've seen on the internet the expression of the solution uses the polygarithm function, i can't tell you more as i don't know it sorry

[candid rivet]

the easiest solution is by understanding what these numbers are counting.

left: number of ways to choose k people among a group of M+N, by definition of the combination number

right : also the number of ways to choose k among M+N, but this time instead of immediately choose those k people, you count them by choosing r people in a group of M, and then k-r people in the other group of N. So if r is fixed, this makes C_r^M × C_(k-r)^N. And to count every possibilties you want to sum this for every value of r possible (and r can be an integer between 0 and k) which gives you the formula.

ps: it is known as the Vandermonde formula

ps : ps : it is common when combination numbers are implied in a formula to try to prove it with combinatorial (which is counting the number of possibilities of something in 2 different ways)

an other solution by calculation would be to calculate (1+X)^(m+n) and (1+X)^m × (1+X)^n by using Newton's binomial formula and sum properties, and then compare the term of degree k

[rugged portal]

i understand that K is postive but im comprehending that a can be vector set from (+0, infit) to (-0 and infit) is that true

any help appreciated

[steady zephyr]

hello, how to find the reciproque (inverse function) of this function pls ((x-1)/(sqrt((x-1)^(2)+1)))

[rugged portal]

swap x and y

and algebra

it

[left knoll]

Can you provide a written answer like full solve I'm dumb I just understood what you wrote but can't prove it with calculations

[left knoll]

is anyone here really good at math i have some questions to ask if someone could help me out

[left knoll]

Thx a lot

[candid rivet]

here's the second method

[candid rivet]

you're welcome, and feel free to ask me if you don't understand something in my solutions !

[left knoll]

Sure will thx

[candid rivet]

i'm not sur what (-R+²) means, but if it means R_² (like negative numbers) then i think ka is always in W unless k is zero
and question 2, W can not be a subspace of R² since 0 is not in W (0 must always be in a subspace since if x is in W, x-x should also be in W)

[candid rivet]

just share your problems/questions so people can see it and eventually give an answer

[vital shard]

Is 7,3x10^(-5) the same as 73x10^(-6)?

[vale wyvern]

Yes

[timber thistle]

Anyone knows Lagrange mechanic

[keen walrus]

how would I find the x coordinates for this trig function graph?

[quick wraith]

draw the graph for y=2cot x which is nothing but basically graph of cot x but more steeper ( slope of 2cotx is[-2(cosecx)^2] twice that of cotx [-(cosecx)^2].
Now shift the graph pi/4 in right direction. Basically meaning that all the values you used to get at y=2cotx will now be delayed by a difference of pi/4 in x (you will lag behind by pi/4 in x)
hope this helps

[modest pagoda]

A lamp is suspended above the center of a horizontal circular table. Its height is 90 cm from the ground and its radius is 20 cm. The lamp moves vertically downwards towards the table at a speed of 6. Find the rate of change of the area of ​​the table’s shadow when the lamp is 60 cm above the table.

can someone please help me

Its to hard for me ☹️

[rocky moth]

which grade

[modest pagoda]

12 grade

it came in my exam

[rocky moth]

bro i am in 10 hopin to solve this

[modest pagoda]

i was crying because i didnt fot the full mark

if you want i can tomorow send my exam in arabic

[rocky moth]

HMM send me two years later

but it will also work

[modest pagoda]

ah your still young

i thought that you are a collage student

dont worry i dont think in west country its hard like that

[naive dew]

I'm not very sure about it

[modest pagoda]

how you got the dx

[naive dew]

Lamp is going downwards and that is the same rate at which the radius is changing

[modest pagoda]

i dont understand that

[naive dew]

Well I'll try this problem again

[modest pagoda]

I think it will look like that

Dy will be - because it downword

i think we need to use the similar triangle

guys i need help

[rocky moth]

ayo pld help me in science cornon

[modest pagoda]

Thanks guys my teacher send me this

I think he solve it wrong 💀

[quick wraith]

phi + arctan(-cot(phi/2)) = phi + 3pi/2 + phi/2 = 3/2( phi + pi)

<@&942391219206647828>

[keen walrus]

How do you do vector calculus?

[naive dew]

You got the right solution bro?

[modest pagoda]

it maybe like my teacher said but still not convinced

[modest pagoda]

.

[naive dew]

Well he gave Dr/dt

[modest pagoda]

yeah

[naive dew]

Which should help us calculate da/dt

[modest pagoda]

wait

[naive dew]

Da/dt=2πr•dr/dt

[modest pagoda]

i konw

i mean you can got it from similar triangle

whats your grade?

r equal 50

from the rule that we got in photo

y equal 60

[modest pagoda]

so

[naive dew]

I try to approach it by rate measuring by derivates

Not by similarity

[left knoll]

i didn't understand

[candid rivet]

once you have the arctan(...) you need to use trig identity, there are many so use one you know (maybe not the trig identity i did)

[candid rivet]

also if you define the argumeny as the unique real number between 0 and 2pi then the answer is -pi/2 + 3phi/2 since phi is between pi/2, 3pi/2

[gentle trellis]

can someone help me with problem

[sour sky]

This is how my exam paper looks like

[dire onyx]

ig you'll require logarithms too.

https://www.youtube.com/watch?v=EOhU6EkXf6E

[dire onyx]

.

[winged spindle]

some help with question 2 plz ?!

[naive dew]

Can someone provide the solution?

[gentle trellis]

can someone , send solution for this problem

thank u in advance

[keen walrus]

Does anyone know how to do this?

[sonic cloud]

https://tenor.com/view/request-to-chat-gpt-request-apply-to-chat-gpt-ia-gif-7947862683229666925

[sonic cloud]

https://tenor.com/view/request-to-chat-gpt-request-apply-to-chat-gpt-ia-gif-7947862683229666925

[sonic cloud]

https://tenor.com/view/request-to-chat-gpt-request-apply-to-chat-gpt-ia-gif-7947862683229666925

[candid rivet]

if c(t) is the cost of the phone calling in function of the time t, then we know it is linear, so c(t)=at+b with a and b constanst. Now you also have c(47)=47a+b =12.84 and c(78)=78a+b=16.38
From these two equations you can deduce the value of a and b, so you know the expression of c(t). Now juste put t=74 in this expression of c(t)

[spice halo]

ncert?

[naive dew]

Exemplar

I got it tho

No need to solve

[sonic cloud]

https://tenor.com/view/request-to-chat-gpt-request-apply-to-chat-gpt-ia-gif-7947862683229666925

[ember notch]

chatgpt sucks at math lmao

every time i've used chatgpt to walk me through a math problem, it messed up on it's lower level calculations

[candid rivet]

id took f: R -> R but taking f:N->N is enough, we just need to have zero in the domain of definition of the function.
And if f : R-> R is solution then f restricted to N* is solution too (that's why i can suppose f defined on every real numbers)

[unique sinew]

can anyone solve this for me please:
given the region below the line y=1 and above the curve y=x^2/4 in the first quadrant, set up the integral in polar form

[plucky mango]

To set up the integral in polar form for the given region, we need to express the equations of the lines and curves in polar coordinates.

First, let's express the line y=1 in polar form. Recall that in polar coordinates, x = rcosθ and y = rsinθ. Since the line y=1 is a horizontal line, its equation in polar form will be y = rsinθ = 1. Solving for r, we have r = 1/sinθ.

Next, let's express the curve y=x^2/4 in polar form. Substituting x = rcosθ and y = rsinθ into the equation, we have rsinθ = (rcosθ)^2/4. Simplifying, we get rsinθ = r^2cos^2θ/4. Dividing both sides by r, we have sinθ = rcos^2θ/4. Rearranging, we get r = 4sinθ/cos^2θ.

Now, let's determine the limits of integration for the angle θ. Since the region is in the first quadrant, θ will range from 0 to the angle at which the line y=1 intersects the curve y=x^2/4. Setting the two equations equal to each other, we have 1 = 4sinθ/cos^2θ. Simplifying, we get cos^2θ = 4sinθ. Dividing both sides by cos^2θ, we have 1 = 4tanθ. Solving for θ, we get θ = arctan(1/4).

Finally, we can set up the integral in polar form. The integral will be evaluated over the range of θ from 0 to arctan(1/4), and the integrand will be multiplied by r:

∫[0, arctan(1/4)] ∫[r=1/sinθ, r=4sinθ/cos^2θ] r dr dθ

I can write down the solution if you want!

[unique sinew]

hi thank you so much for your time but shouldn't we split the integral into two bc the radius will hit 2 different functions as we move from the x axis?

i actually have the final answer but i couldn't understand how we got the bounds of theta

[frosty reef]

Hello I’m cs student and we have math as primary subject and I’m naturally bad at it can y’all plz give me the blueprint on how to study math I always study but with no results I’m commit a lot of mistakes when trying to find solutions and can’t understand concepts fully any advice?

[round pivot]

guys, help me understand this

what's wrong with my working

[humble needle]

Hi I need statistics help

[left knoll]

ive got a question

when founding out hte primitive of a function

if its liek this

shouldnt there be a value

where the primitive is equal to a constant only

because the function has the value 0

then what are these values

like is it just - 5

and the other one cant have 1 since its always greater than 0

[naive dew]

The lower one?

[left knoll]

yeah

its always greater than 0

so it cant be 0

[naive dew]

I guess the function is zero only at x=(-5)

[left knoll]

yeah

so there

the primitive

is a constant right

i mean all the constants

[naive dew]

Idk about primitives

[left knoll]

oh ok then

[naive dew]

Any other term for it?

[left knoll]

integral

[naive dew]

Yes

You mean the integral of x+5?

[left knoll]

yeah

its x squared over 2 + 5x

• C

[naive dew]

Yes

[left knoll]

thats when x is less than -1

[naive dew]

Yep

[left knoll]

so when i write it out how will it look

this or what ?

[naive dew]

Nope

[left knoll]

THEN HOW ??

i have them in my hw

but havent studied this yet

just how to calculate the integral of a stnad alone function

[naive dew]

I’m not sure about integrals either

Let’s just wait

[left knoll]

🙂

nice

https://tenor.com/view/maniac-laughing-laughing-hysterically-maniac-laugh-gif-20538400

[naive dew]

😶

[left knoll]

then can you verifiy smth for me

im not sure

if e to the power 2x is equal to 2

[naive dew]

Ya?

[left knoll]

is x = ln 2 over 2

[left knoll]

thanx

[round pivot]

Thanks a lot bro

[candid rivet]

I think you need to understand fully every property and theorem of the chapter your studying, maybe write them down on a sheet of paper, but most importantly spend some time to learn the examples and exercises done in class. You don't need to know them by heart, but you have to remember the tricks or techniques to use and how to use them. Also if needed, train your calculation skills since thats what we are constantly using. Always start with easy exercices when learning new notions, and try to like maths, from my experience it has always been easier when i think that this chapter is fun and easy

[left knoll]

Hi guys,
Not sure there was already asked or not, but
Do you know program on laptop where it is possible to write different problems (limits, derivatives, integrals and others) with ability to visualise it on 2D/3D plane?

I am bad in abstraction and maybe computed tasks with visualisation might help me((

[frosty reef]

I Will live by this advice never looked at it in this way thank you so much will update if it got better

[candid rivet]

I'll be happy to hear from you ! take care

[candid rivet]

i know sometimes wolframalpha can graph functions in 3D but it is not the best, or desmos can be good for 2D things. Again there are probably better websites/programs

[lusty moon]

Demos and Symbolab are great for graphs. They work on every device as well.

[undone ledge]

Could I get some help on question 8?

8b

[left knoll]

after you've found the value of k (by equating f'(x) at x = 2 to 0), integrate the equation on both sides and to find the value of c, use the information that at x = 2 the value of f(x) is 1

[undone ledge]

Ohhh and then put x=7 and find f(x)?

[left knoll]

yep

[undone ledge]

I understand now thank you so much!!

[left knoll]

you're welcome

[silk quail]

I have , a doubt in simple mensuration

5 the 5 th one some one please help

[pseudo basalt]

Can someone help me with this

I solve it with De L' hospital

I am wrong somewhere for some reason , wrong answer

[left knoll]

share your working

[pseudo basalt]

π is the 3,14... Number

Π/2 = 90⁰

[left knoll]

the answer would be limit doesn't exist cause the left hand limit would be -infinity and right hand limit would be +infinity

after you've applied l'hopital, the limit would be tanx (which is basically sinx/cosx)

see the sign of sinx/cosx when you approach it from the left of π/2

sinx is nearly 1 and cosx is nearly 0 (but it is +ve)

so it'll be +infinity

when you approach it from the right

sinx is nearly 1 and cosx is nearly 0 (but it is -ve)

so it'll be -infinity

[pseudo basalt]

Oh fk so is it right?

Because is nearly + infinity

[left knoll]

the answer is undefined cause left hand limit ≠ right hand limit

[left knoll]

^^

what's the given answer tho?

[pseudo basalt]

Ohhh you take two different limits

[left knoll]

yep

[pseudo basalt]

I dont know but i did think that i was right that is why i asked for help

Ty bro

[left knoll]

you're welcome

is there the texit bot in this server?

[pseudo basalt]

I dont know

[left knoll]

oh okay

mhm it's correct

[quiet sable]

hello!
can anyone tell me why is it that when we want to calculate the probability of an outcome we divide the favourable outcomes by the total outcomes?
I'm supposed to write some kind of essay on it and I don't know how to explain it so that it would be acceptable and not sound like some random examples
I'd be really thankful if anyone could help ^^

[fair pecan]

Probability is a percentage, and the maximum percentage is 100%. Or you can think of it as a fraction, then the probability is less than or equal to 1. For example, 0.63 means 63% and 0.04 means 4% and so on. Now, Total number of outcomes will always be bigger than the number of favourable outcomes, and when you divide a smaller number (favourable outcomes) by a bigger number (total outcomes), your answer is in [0,1] such as 0.04, which is the same as 4% when 0.04 is multiplied by 100. We cannot divide the Total number of outcomes by the number of favourable outcomes because then our answer would exceed 1, which implies that our percentage is greater than 100% which is logically incorrect.

[quiet sable]

oh I see,
so basically the reason why we divide these is to see just how many of our favourable outcomes exist in the total outcomes?
(it seems obvious but I was wondering if there's a better way to put it)
which will always be a number less than or equal to 1 for the reasons you mentioned.

[fair pecan]

yes, you're correct.

[quiet sable]

thanks a lot for the help!

[undone ledge]

Hey guys I have been doing integration, and I did this one but my answer is wrong I’m not sure what happened any help will be appreciated. The textbook might be wrong but idk

[fair pecan]

you cannot do that when there is a linear equation with a power (3x+6)^1/2. You need to use the u-substitution method to simplify the equation and then apply integration

[slender temple]

can someone let me know the process of how the equation to find x was formed?

[left knoll]

Can someone help me with this

[left knoll]

consider the number of hours mark has worked in bob's bakery to be x and in ciara's cafe to be y

x + y = 16
11x + 9y = 152

solve the two simultaneous equations and you'll get the answer

[left knoll]

Isn't x and y technically 20

[left knoll]

huh? no

why do you think it's 20

11 hours plus 9 hours

[left knoll]

x and y aren't 11 and 9

they're the number of hours he has worked

mark is getting paid €11 in the bakery and €9 in the cafe. he has worked a total of 16 hrs

so how'd you express 16 in terms of x and y

where x is number of hours he has worked in the bakery

Oh

and y is the number of hours he has worked in cafe

[left knoll]

So y is 3.8 according to this, right?

[left knoll]

uh nah, you'll get x = 4 and y = 12

That's how I tried it

you've done mistake in the 4th step on the right side

it'll be -11y + 9y = 152 - 176

so, -2y = -24

y = 12

[left knoll]

you've written 11y + 9y instead of -11y + 9y

[left knoll]

Oh

That makes x 4

[left knoll]

yep

Thank you

you're welcome

Greedy crocodile eats the bigger number

when you multiply or divide by a negative number, the inequalities switches

Im confused again

-x < - 10
dividing by -1 on both sides
x > 10 (notice that the sign became the opposite)

It irritates me so much that you can't find a definitive awnser in inequalities

[left knoll]

what are the possible pairs of integers whose sum is 7 and product is 12?

6 and 1

idts

what's the product of 6 and 1?

isn't it 6

[left knoll]

"product is 12"

go through the factors of 12

3 and 4

yep

so you split the middle term as 3x + 4x

x² + 3x + 4x + 12 = 0

now, x(x + 3) + 4(x + 3) = 0

you can factorise ahead and find the values of x

did they teach you this method in school?

So it ends up being (x+3) (x+4)

yep

(x + 3)(x + 4) = 0

so, x + 3 = 0 or x + 4 = 0

x = -3 or -4

[left knoll]

Yes, but I'm dyscalculic and really didn't learn much

[left knoll]

ah alright, no worries

the constant term is the product of pair of integers

the "x" term is the sum of pair of integer

That's used for factorisation

yep yep

after you've factorisated the quadratic equation, you find the values of x

[left knoll]

^^

Tell me why my tutor sends 5 page homework and hour before we meet 🎶🙄

💀 oh oof

The knows it takes me a good few hours

It surprises me that u can solve a rubiks cube but not do maths

if you've anymore questions post them over here, i'll check them later on. i'll have to study now ;-;

[left knoll]

Thak you so much

[earnest wharf]

There is an integer in each square of an 8 × 8 chessboard. In one move, you may
choose any 4 × 4 or 3 × 3 square and add 1 to each integer of the chosen square.
Can you always get a table with each entry divisible by (a) 2, (b) 3?

I have the solution but can't seem to understand it

A diff solution or just help in understanding the solution would be good

[earnest wharf]

Ooh an Indian

[left knoll]

I'm not Indian

[earnest wharf]

Btw try using the quadratic formula

It's not an excuse for not being able to factorize but if u need it then it helps

[left knoll]

do the squares contain any arbitrary integer?

or else they're consecutive?

[earnest wharf]

All are random

[left knoll]

mhm

[earnest wharf]

Oo then the explanation is universal , mb .

We learnt it that way too

[left knoll]

I don't understand why you'd think not being Indian is an excuse?

[earnest wharf]

I was talking about ur problem with the quadratic question....

X^2 +7x +12 I think it was

[left knoll]

wdym by "always get a table"? the entries in 4x4 or 3x3 are divisible by 2 or 3?

interesting question ngl

[left knoll]

I said multiple times that I don't understand. And clearly stated I'm dyscalculic and have trouble learning these concepts. Not that it's any of your business.

[earnest wharf]

Nah , basically out of the 8x8 , u can pick a 4x4 of which u can add one to each square

[earnest wharf]

I didn't mean any offense ;-;

[left knoll]

i've understood that part but what do they mean by "table"?

[earnest wharf]

Was just saying that u could try the quadratic formula if u needed the solution specifically

Cuz factorising gets hard sometimes

[earnest wharf]

The chess board

Table means the chess board itself

[left knoll]

huh?

[left knoll]

I am taking offense, because I don't understand why you'd say anything about excuses. Excuses implies I can but I don't want to.

gimme a second

oh

[earnest wharf]

I was saying that ,
The quadratic formula would diminish ur need to learn factorization

But that doesn't mean that just learning the quadratic formula

And neglecting learning factorization is a good idea

[left knoll]

'It's not an excuse for not being able to factorize but if u need it then it helps'. This is what you said

[earnest wharf]

Jesus

What i meant was

Again

Actually lemme rephrase

Maybe ull get what I meant by excuse

"using the quadratic formula is not a valid reason for neglecting learning factorization"

Aight? Thass it

Mb

[earnest wharf]

Any? ideas

[left knoll]

damn, im not able to get any idea how to even start the problem

[earnest wharf]

Lmfao

It's a problem set of a book

[left knoll]

which chapter is it related to

[left knoll]

Ah okay. I misunderstood.

[earnest wharf]

Arthur engel problem solving strategies

[left knoll]

or is it some olympaid question

[earnest wharf]

Invariance

[earnest wharf]

Nah its way too easy for that

[left knoll]

mhm

[earnest wharf]

Wanna see the soln?

[left knoll]

idk wait

[earnest wharf]

Okay

Btw the Principle of the chapter is

[left knoll]

im pretty sure those kinda stuff aren't there in jee T-T

[earnest wharf]

"when something changes , try finding what stays the same"

Night help idk

[left knoll]

ooh

[earnest wharf]

Well yes but I love math so what can I say

I study in the mornings , and spend maybe an hour on this as my pastime

Better than watching YouTube and stuff

[earnest wharf]

I didn't read the part u said before that either plus phrased it weirdly mb ;-;

@left knoll ping me if u want the soln ig , I gtg in a bit

[left knoll]

uh, share it ;-;
i'm not getting any idea on how to even begin lmao. i'll try to understand the solution

[earnest wharf]

I don't get why they skipped the third and sixth rows

[left knoll]

T-T what's this sorcery

[earnest wharf]

Yeah modulus isn't in jee syllabus either

Lmfao DM

If ur giving jee which I'm guessing u are

Then this is way beyond what u need

[left knoll]

i'm giving it

jee'24

[earnest wharf]

Me 25

[earnest wharf]

Ah Jesus

[left knoll]

lmao, understood it earlier itself :P

[earnest wharf]

U solve problems here for practice?

Not in a posn to give advice but

P sure that's a bad idea

[left knoll]

;-; uh, i don't have the enough knowledge about the topic's domain so probably might have to wait for someone else to solve it

repost the question over here again

[earnest wharf]

Yeah I'll post it and wait

[left knoll]

it got flooded cause all the convo

[earnest wharf]

Yep

[left knoll]

wdym?

[earnest wharf]

.

[left knoll]

i'm just there in this server so i just check the math and science help during breaks

[earnest wharf]

Ah well that's good

Goodluck lmfao

[left knoll]

ty ig so ;-;

[earnest wharf]

Wait didya guess I was jn 11th cuz

I was doing external stuff?

[left knoll]

yep

[earnest wharf]

;-;

Well it's kinda fair ig

[left knoll]

alot of 11th class aspirants just do them

[earnest wharf]

Yeah ik what u mean

[left knoll]

ive noticed that alot so yea

[earnest wharf]

They're really enthusiastic in the beginning

[left knoll]

in 12th, they just focus on jee stuff

[earnest wharf]

Ik what u mean

Im in allen so

We see all types

There is an integer in each square of an 8 × 8 chessboard. In one move, you may
choose any 4 × 4 or 3 × 3 square and add 1 to each integer of the chosen square.
Can you always get a table with each entry divisible by (a) 2, (b) 3?

[earnest wharf]

A soln or an explanation of the solution (which I have) would help

[left knoll]

oh, i was typing something then deleted it lol

was pinging a person whom i think can solve it but thought it was weird

[earnest wharf]

Every nice person* appreciates a nice math problem

[left knoll]

mhm

[left knoll]

@candid rivet heya! pinging you cause i've seen you help others over here quite a few (probably alot) and ig you can help him out as well? i'm sorry to disturb you btw ;-;

[earnest wharf]

🛐

[candid rivet]

yooo that looks super hard 😂😂

[candid rivet]

no problem i'm happy if i can help

maybe you can send me the solution i don't think i'm able to solve it lol

[candid rivet]

have you ever heard of invariant ?

[earnest wharf]

Yeah that's the chapter im studying

[candid rivet]

well for (a) it makes sense is S is an invariant, yet we have to prove it is an invariant

[earnest wharf]

My solution was that if u consider only the edges , the square can cause a change only in 4 or 3 of them at a time ,
As each changes it's parity , there will always be a non zero number of odd integer containing squares

Which kinda works but idk if it's satisfactory , and doesn't work for the second part

[earnest wharf]

Yeah

Oh wait

I think I got why the solution works

[candid rivet]

yeah but in a corner you're gonna change more than 4 tiles ?

[earnest wharf]

Yeah but still , if u start with n odd and 7-n even

Then u just end up with 7-n odd and n even

U can't get all evens unless u start with all evens

[earnest wharf]

If all squares are divisible by n , then their sum is also divisible by n

[candid rivet]

i think it makes sense for their solution with S, like if you take a 3×3 square, then you're adding +6 to S, and with a 4×4 square you're adding +12 so it never changes the parity of S

[earnest wharf]

But the solution proves the opposite of that right ? Idt it applies backward , if the sum is divisible by n that doesn't really mean that all the integers are same

[earnest wharf]

Ur adding 9 with a 3x3

And 16 witha 4x4

[candid rivet]

no because they remove the 3rd and 6th column

or row

[earnest wharf]

I don't understand

OHHH

ahhhhhhh

I seeeeeeeee

Got it

[earnest wharf]

Yeah my bad im stupid

Uk

[candid rivet]

OK so for (a) we're good xD

[earnest wharf]

Whoever wrote that solution

Must've been really really smart

[earnest wharf]

I'll get the second part myself

I couldn't see why they were removing the 3rd and 6th row

[candid rivet]

well taking the sum of everything is pretty usual for an invariant but yeah removing the 3rd and 6th row is genius

[earnest wharf]

Ikrrr

[candid rivet]

fun problem though

[earnest wharf]

Ikik

It's from Arthur engel

Problem solving strategies

[candid rivet]

you do it in class or by yourself ?

[earnest wharf]

Any tips on how to get better on making functions for finding invariants

[earnest wharf]

Myself

My class teaches sufficiently high level for being able to understand with some effort so

I think I'll slowly manage

[earnest wharf]

I should've worded better ,
Finding "invariant proving functions" better

[candid rivet]

well i think you (or we since i'm really bad a this) just have to solve many problems and i think a lot of time the invariant is pretty usual, with maybe some more details (such as removing a row or two)

[candid rivet]

that's really good !

[earnest wharf]

Well sounds good on paper but I'm still not that great myself

Got a long way

[earnest wharf]

Yep

There's 10 examples and 60 problems , and that's the whole chapter so

[candid rivet]

and yeah always try to think about the examples you've already seen (sum of every numbers, parity...)

[earnest wharf]

I think the author has the same message

[earnest wharf]

Yep I'll note down the keys to each problem

[candid rivet]

well understanding the solution is already pretty good 🙂

[earnest wharf]

And try plugging it in to the new ones

[earnest wharf]

Ye but it's more fun making ur own

[candid rivet]

exactly

[earnest wharf]

Okay well thanks a lot

Would've been hard to notice why removing the rows was absolutely fantastic

[candid rivet]

You're welcome that was fun !

[earnest wharf]

Or why it even worked

[candid rivet]

yes and (b) is the same technique yoi can try to find it if you havent read the solution yet

[earnest wharf]

Well I have but i forgot so I'll figure it out slowly

Gotta sleep rn

[candid rivet]

Also I notice better when someone is asking for help on a problem if he/she sends a pictures

[candid rivet]

Alright good night then haha

[earnest wharf]

I'll do that next time then

There's tons of more problems in that book

[left knoll]

ah, coolio! it has be solved

lemme take a look

;-; most prolly i won't understand it lol

[earnest wharf]

Basically used the divisibility by 2 before and after the change (step of adding 1)

In a very very smart way

(removing the rows(

Such that even if u do the change , it proves that unless the conditions u want aren't already there , they haven't come yet

[amber inlet]

okay so im a bit stuck
i have the option to either take multivariable calc or linear algebra
i have to take both at some point/

i just dont knwo which one to take first

[left knoll]

can sombady help with this question

[lusty hare]

Hello, I hope you are all doing very well! I need help in mathematics on an exercise that is not obvious, here is the instruction: study the existence and possible value of a limit in (0,0) for the function defined by f(x,y) = (x^2 * y^3)/(x^4 + y^6)

[echo birch]

can anyone help with this statstics problem

i dont know why it would be a

[worldly dome]

hi i dont know what to do for the inductive step

[elfin hill]

how do i find mid value of 5-8

is there any sort of formula for it ?

okay got it

[left knoll]

(5+8)/2?

[hollow hearth]

7.5

[distant basalt]

you need help still?

[candid rivet]

there you go

[worldly dome]

thank you

[regal nova]

anyone good with stats

[silver pier]

can someone explain to me why R is Rcos15-4g

[left knoll]

normal reaction always acts perpendicular to the surface. in vertical direction, there is a component of the normal reaction present (Rcos15°)

[silver pier]

why don't we use 4gcos(15)? is it because we dont know the y-component of F?

[left knoll]

you can solve the question via taking axis along the incline and perpendicular to it. you'd need to write an additional equation (along the incline and perpendicular to incline)

the y-component of F will be Fsin15° (vertically opposite angles)
R = Fsin(15°) + 4gcos(15°) (perpendicular to the incline)
4gsin(15°) = Fcos(15°) (along the incline)

you'd get the answer via solving those two equations as well

taking vertical and horizontal as the axis just simplifies the equation solving part

[silver pier]

yeah fair enough

thanks

you can explain things well

[fair pecan]

not sure about the a.) part but for the b.) part you can use the density of rational numbers in real numbers to prove that it is True

im also taking real analysis this semester so im not the best, so you better fact check everything regardless

c.) part seems False. you can take, for example, g(x) = 2-x. then x = 1 belongs to R gives g(x) > 0. But then for every x ≥ 2, g(x) ≤ 0

[elfin hill]

if u do that sum is 9, what u r trying to say is first do the adding then divide but u r not following the rules so its still breaking maths. i found a better way to find the mid value, if you take the "digit gap" eg. 5-8 = "3 digit gap between" then divide that with 2 => 3/2 = 1.5 add this number to lower value "5" then u get the mid value 5+1.5 = 6.5, thats the mid value between 5-8

[fair pecan]

interesting

can you, if possible, share the explanations?

[elfin hill]

question no 6 any idea what to do ?

statistics btw

[fair pecan]

this seems fun, i'll look at this with you till it makes sense, or is straight up wrong

[fair pecan]

@daring plover does this make sense for you tho?

are you talking about the online solution or the one I gave which was a counter example

i cant understand the online either

[raw relic]

Sorry to interject randomly but, @daring plover

Your proof relies on the fact that the cardinality of the real numbers is uncountable and that g is continuous

you can do a proof by contradiction here and assume that it is countable, meaning that there is a finite number of points 'n' if you will such that g(x_i) >0

[fair pecan]

you mean g(n) > 0?

[raw relic]

well here lemme ask you this

in your class did your professor cover the uncountability of R?

As in the uncountability of an arbitrary interval of R i.e. (a,b) where a,b are real numbers

Okay if you did then that's good

you can use that fact

there is an interval already on the real line

and it's an open interval between (0,g(x_0))

you can use that fact and the continuity of g

If you let g(y) = 0 and g(x_0) > 0

The epsilon proof is a great way of doing this

You have g(x_0) being fixed so then

you have that there for all epsilon there is a delta such that for all y in the delta neighborhood around x_0

g(y) > 0

then you have an interval (x_0 - delta, x_0 + delta) then boom your done via

uncountability of an interval on the real line

[fair pecan]

Inspired by this but with a little more explanation. I think the key is that we can control epsilon to be as less than G(X_o) such that every x between (X_o - delta, X_o + delta) gives us G(x) between (G(X_o) - epsilon, G(X_o) + epsilon) which will always be greater than zero since G(X_o) > epsilon.

[fair pecan]

look up how to calculate weighted means

[silver pier]

can anyone explain to me how the moments are acting on this object

[fickle oriole]

can someone explain what the input parameters for viewsolid in matlab is ?

[fast heath]

hi, can someone help me with this?

[left knoll]

forces along DA and AB won't apply moment as they pass through the point A. DC will produce an clockwise sense moment. place your right hand fingers in the direction of force i.e towards right and curl them in the direction towards A, the direction in which your fingers curl is the sense of moment caused due to that force and your thumb would be pointing towards the direction of the torque/moment vector

[left knoll]

f(2x - 1) = x + 5
to get value of f(1 - 2x), you'll need to replace x with something in f(2x - 1)

2t - 1 = 1 - 2x
2t = 2 - 2x
t = 1 - x

f(1 - 2x) = f(2(1 - x) - 1) = 1 - x + 5 = 6 - x
f(2x - 1) + f(1 - 2x) = 6 - x + x + 5 = 11

[left knoll]

Hmm, ok you might be right
I said how I learnt it from middle school, soo :))

[worn rune]

I need a book for Topology, any recommendation?

[silver pier]

gotcha, thanks!

can someone explain the the workings of these two statements

[left knoll]

Any math tips I generally get burned out when I can't solve math qsn

And I tend to just give up

[left knoll]

ig the question meant to consider that the book doesn't topple after shifting the bracket. so basically it means there is no imbalance of torque and equilibrium is still maintained. when bracket B is shifted it's torque reduces (torque = F * r) so to keep it constant the magnitude of force increases

[left knoll]

even i've faced the same issue rather than focusing on getting the answer correct, focus on "learning something new". with that mindset, you won't feel burned out when you don't get a question or get a question wrong.

if you're spending too much time on a problem, see the solution and try it yourself again

[left knoll]

Thanks will give it a shot!

[silver pier]

How tf , someone is supposed to know that without reading the answers 💀

[undone ledge]

Could I get some help on question 2

[left knoll]

true true :/

[fair pecan]

you need to calculate the weighted mean

[undone ledge]

Thankkkqqq

I’m a bit confused on question 8 O.o could I please get some help ?