math-help

[trim saddle]

Two posts with 5m of height are separated by 5m. There is a cable conecting both posts on their tops. The cable is 10m long. Whats the minimum height betwen the cable and the ground??

[trim saddle]

PLS explain this to me

[weak lotus]

This is a really fun one actually

Let me show you

Have seen hyperbolic functions

You could graph it and use hyperbolic functions

X-axis should be -2.5 and 2.5 my bad

Hope this gets you on the right path, good luck

[trim saddle]

i dont know how to continue. should find the minimum of the function by derivating it? whats the function? or should i go by a triangle and find the angles/sides?

[weak lotus]

As i said, hyperbolic functions

If you the function you derive it to find a min or max

[trim saddle]

<@&942391219206647828>

[trim saddle]

ah i get it now. I didn't learn those functions yet i look it up. Thanks g

[weak lotus]

Oh you havent seen those functions yet?

[trim saddle]

ye, that problem i saw on the internet somewhere and i tought it was simple but i couln't get it right, so I asked you

[weak lotus]

Oooo

Yeah then its to do with hyperbolic functions

Idk if you have the solution? You can check if you want

[gray veldt]

@trim saddle is the answer is 0.88 or 1 ?

[trim saddle]

i dont know ┐(´･c_･｀ ;)┌

[gray veldt]

thats sad it took a while for me though

Soo, when will you get the key? @trim saddle

[weak lotus]

im sure there are different ways on how to approach the problem

i just thought hyperbolic functions were the best approach (imo) but sure you can solve differently

maybe even trig functions

[gray veldt]

trig aint useful here

[weak lotus]

how come

[trim saddle]

chatgpt solved with a simple Pitágoras theorem, but i think its wrong

[gray veldt]

curves and all

[weak lotus]

you could rescale everything so they are part of the domain

[trim saddle]

but yeah gpt said close to .88 too

[weak lotus]

transformations

[gray veldt]

[gray veldt]

damn

[gray veldt]

I did use hyperbolic functions though

[weak lotus]

😉

we got it so thats the most important part!

[gray veldt]

YEah!!

[trim saddle]

guys, off topic question, will james stream again?

its been a while

[gray veldt]

dunno man :(

[weak lotus]

i dont know if you are seeing derivatives etc but i can give you a tip: if you are asked to find a min or max of like a volume or surface,...
you can (always) like most of the time, solve those kind of problems with graphing it with x and y coordinates

[trim saddle]

yeah i use that

[gray veldt]

Well one of this type was asked during the interviews conducted by amazon

[weak lotus]

o for real?

[trim saddle]

for what role?

[weak lotus]

thats sick yo

[trim saddle]

cs stuff?

[gray veldt]

yeah cs stuff

it wasnt this hard, but a logical question which can be answered in seconds if you really use your brain

[weak lotus]

and dont overthink the question xp

[trim saddle]

ye they do that

[weak lotus]

cuz stress can do mad stuff

[gray veldt]

@trim saddle ayo le me know if you get the real answer(key)

[trim saddle]

i cant get it. that problem was an image from 4years ago. idk the user

[gray veldt]

damn, you do have good memory though

[trim saddle]

man i did memorized it. i was searching and found it. sorry i dont have the answer

[gray veldt]

Well I was appreciating your memory power nvm

[trim saddle]

i shared with you bc i didnt have the answer too ehehe

[lusty hare]

Hi guys

How would you have solved this system with four unknowns and what parameters would you have chosen to change the variables?

thanks for the help

[left knoll]

This is how I would have done it, which is very similar to your solution.

[lusty hare]

Thank u so much

[fiery widget]

Hi how would you do b)?

I dont think my answer is correct, as for fg(x) i got (x+3)^2+2

[gray veldt]

Does the range belongs to (2,infinity)?

[fiery widget]

yea it does

[solar drift]

can anyone please solve this? ig i am doing calculation mistake

[gray veldt]

option C ?

[weak lotus]

<@&942391219206647828>

[frank igloo]

Hi, does anyone know what formula to use to solve the cross product of two vectors that both have two points in a 3d space? All I can find is how to calculate for vectors which have one point. Or do I somehow choose which one of those points to input in the formula?

[fiery widget]

okay thats what I got, thanks alot

[meager kite]

two points?

cross products are normally just done with the vector components

[frank igloo]

well i'm asking because i'm doing a thing for programming, and the task we're given has you create a vector "with two points" so each vector has such coordinates stored in an array - x1, y1, z1, x2, y2 and z2. One of the functions i need to implement is a crossproduct of two vectors. I think I understand how to do it normally, but this "two points" part is messing with my understanding

[frank igloo]

Anyway, I think I'm on the right path, i think the description our prof gave us "vector with 2 points" is instead meant to be a line segment. And then I would need to get the vector from that, and then calculate the cross product. Does that make sense or am I still doing something wrong? If it does, then I've solved the mystery, otherwise someone tell me I'm tripping

[compact needle]

hey guys, can't figure out how to form the equations for this problem, i get decimals with mine 😭

[gray veldt]

boys = 11
girls = 16

[compact needle]

i didn't get how to make the equations though

[compact needle]

and the answers say 11 and 27 ┐⁠(⁠´⁠ー⁠｀⁠)⁠┌

[gray veldt]

yep

[compact needle]

tysm!

[compact needle]

OH MB, didn't pay attention

[obtuse lagoon]

can someone help with this co-ord geometry question pls🙏

[maiden epoch]

Why we’re taking [1/2;inf) as an answer?

@weak lotus sorry for disturbing you, but maybe you can explain?

[weak lotus]

2 says x has to be larger then 0,5

or equal to 0,5

everything larger then and equal to 0,5 = 0,51,0,52,...n

with n = infinity

@maiden epoch

[maiden epoch]

but we also have 0>-1 in 3

so why we wont include -1?

[weak lotus]

because zero is always larger then -1

and

you need all solutions

i think you can have nr 4 to

-x >= x +1

[maiden epoch]

3 numbers giving the answer tho

[weak lotus]

number 1 is false as you did above
number 2 is x being larger and equal to 1/2 so till positive infinity

BUT

0 is always bigger then -1 and 0 isnt a variable its a constant

you need to know the values of x which is a variable and thats for (1/2; + infinity(

[maiden epoch]

got it now, but got confused here again

interval ends on -5/6 because it must be bigger then x? or?

[weak lotus]

do not include -5/6

[gray veldt]

well this can be simply solved by symmetry and all

Well its the real method, If you want it

[dense wigeon]

How do i solve this

I'm stuck here

I tried various things, like substitution

[naive dagger]

I don't understand this formula:< can someone help me with it

[left knoll]

hii, can someone explain this to me? im watching a class video on how to solve it but i just don't get it

[naive dagger]

A)

[unborn creek]

for b

[gray veldt]

wait,,, can we write x+1 like that??

[fringe trellis]

hi does anyone know how to solve this?

[night kindle]

Can someone help me! My teacher teach me Dijkstra's algorithm, and this is a example about it. I just don't know how my teacher write this table and how it work?

[tacit vine]

Use pemdas

[cunning oasis]

Hello can someone help me in the last equation why the right hand side is one?

[cunning oasis]

book= fundamentals of wave phenomena, akira hiroshi page 149

[obtuse lagoon]

tysm !!!🙏

[cosmic kestrel]

I don't see any zeros here

[fringe trellis]

tyy

[cunning oasis]

sorry i meant 1

[cunning oasis]

but i already figured it out tho

[left knoll]

Anybody studies math in french?

[warped panther]

I do

[slim prawn]

Anyone can solve this question?

[gray veldt]

pi/2?

[obtuse lagoon]

can someone help w this differentiation and integration q pls 😭

[gray veldt]

q no?

[obtuse lagoon]

both if u could 🙏

[gray veldt]

4 and 5?

[obtuse lagoon]

yes ! much appreciated

this is the answer

[obtuse lagoon]

THANK YOU SO MUCHH !!🙏

[unique coral]

help

the last

[gray veldt]

does the 3rd term really has power 3? or it is a printing mistake?

if it is a square then the answer would be around 44.5

use Cos(90-theta) = Sin(theta), you will get 44 pairs of(sin^2(theta)+cos^2(theta)) and a lone term sin^2(45)

[slim prawn]

can you please explain the working?

[gray veldt]

Well do you know the formula for Sin^-1 (X) + sin^-1y ?

Tbh, you can take any point on the circle in the given equation and substitute in arc sinx and siny

pick (1,0) xD

[fiery dome]

Probability calculations:
P(B|¬A) = 1 - P(¬B|¬A)
Is this correct?

[slim prawn]

Thank you so much!

[quartz epoch]

guys

i need quick help

[sharp ferry]

think about the maximum and min values of arcsin(4x-1)

the max value of arcsin corresponds to max value of y and min to min value of y then u have the range

[timid delta]

damn , nice way to help, rather than giving answer, u are making him think. I like that

[vale wyvern]

we all should do it that way only
I have seen many people asking for fully exam like written answers
even though I have sent them the explaination

[sharp ferry]

yeah i mean straight up answers dont help much methods do :>

as they say.Give a man a fish, and you feed him for a day. Teach a man to fish, and you feed him for a lifetime

[trim saddle]

yes

[fiery widget]

Hi can someone help with me part a)?

I use u = 3+2x

but the worked solution gives me this as the method on how to complete

I understand the concept of where the u-3 and the 2dx being replaced by du

but I dont understand why it becomes over 4

any help would be appreciated 🙂

[sharp ferry]

x=u-3/2 and dx=du/2

the 2s get multiplied

[fiery widget]

im so stupid thank you so much

I got so confused by the mark scheme saying 2dx = du

[fiery widget]

thank you so much

[sharp ferry]

nahh it happens to everyone

[fiery widget]

What about this one?

[spare ice]

help please 😭

NVM guys I solved it 👍

[sharp ferry]

put x=sinu then dx=cosudu then it will be sin^2u * cos^2u du = (sin2u)^2 du then you can just turn it into cos4u

[still radish]

Hey everyone hope you're doing good. I'm studying Statistics and Probability in Maths if someone can help me with resumes or courses about Probabilty. Thanks 😁

[weak lotus]

Whach u need ma man

[still radish]

The basics how to calculate a probability and random probability

[weak lotus]

Let me share you a link because my native language is dutch

https://youtu.be/4VcSIy9JIUE

Khanacademy is really good to

[cedar badger]

Please help

[gray veldt]

Language?

[neon shuttle]

How should i become fast

in math

i was called im slow at math

[gray veldt]

It takes time+ do more problems

[weak lotus]

Practice makes perfect. Start from the bottom. Make sure your fundamentals are ON POINT. make A LOT of practice problems. The more you do, the more you learn, the goal here is to connect neurons and the more neurons arz connected, the faster you think!

[left knoll]

Anyone explain it plz

Check for injectivity part ..

[still condor]

all the points that can be represented on a graph denote a real number, right?

[gray veldt]

well there is a plane called argand plane, where imaginary numbers are plotted

[still condor]

Do you graph functions on the argand plane? 💀

[gray veldt]

well, if its complex numbers then yes

[atomic dagger]

Hi, I'd like help with a very simple problem...

A DVD production cost is 25 euros. When the factory sells one unit to a store, it makes a profit of 40%. What must be the selling price of the DVD so that the store makes a profit of 30% ?

i completely forgot how to do something like this

[atomic dagger]

Thank you!

[empty pelican]

yre welcome

[dusk cedar]

can anyone help me with this differential equation

[left knoll]

I am a three-digit number,
The sum of my digits is 7.
Multiply me by 5,
And you'll reach a number that's alive.
Add 200 to that number,
And the result you shall uncover.

The number you get after solving this puzzle is smaller than the main number (Guess the number)

Riddle number < The correct number*

2nd Hint for stage 1(Gues the number) :-

(500 + 200) - (400 / 2) + (150 * 2)

The number you get after solving this puzzle is Greater than the main number (Guess the number)*

Therefore if you get the solution to 1st and 2nd riddle

1st Riddle number < The correct number < 2nd Riddle number

[weary arrow]

Is this all of it?

I get two answers

It's worded so oddly but I'm assuming that
1st Riddle number = 'x' (sum of digits = 7)
Correct number = 5x + 200
2nd riddle number = (500+200) -(400/2) + (150*2) = 800

That gives x<120, which gives x=106 or x=115
And then the correct number would be 730 or 775

[left knoll]

hi

i need some help with indefinite integration

[gray veldt]

use substitution method

x^2 = t

[left knoll]

Thanks mate.. i also got the same ans

[weak lotus]

1 + x^2 as u

will make things wayyy easier

@left knoll

[gray veldt]

yeah we can do in that way too

[surreal cypress]

f is injective
is equivalent to
there don't exist pair of different values x,y such that
f(x)=f(y)

f(x)=f(y) is equivalent to
(x-y)(x²+xy+y²-1)=0
so
there don't exist pair of different values x,y such that
(x-y)(x²+xy+y²-1)=0

which is equivalent to
there don't exist pair of different values x,y such that
(x-y) = 0 or
(x²+xy+y²-1)=0

which is false
because x²+xy+y²-1 can be 0 when x≠y

[left knoll]

Hello can someone help me with math problems?

[left knoll]

Post it here@left knoll

[cunning oasis]

Find the temperature distribution in a semi-infinite plane with a width of 20 cm if the temperature at the bottom is 𝑇 = 𝑓(𝑥) = 𝑥, and the temperature at the other edges is maintained at 0 degrees.

can someone help me with this problem? thanks

[clever talon]

Can someone tell me the meaning of this

[pale agate]

as far as i know there's some psychology scientists invitend laws like that

there's :the subjective sensation is proportional to the logarithm of the stimulus intensity.

i don't know about this one tho lol

[odd pivot]

Since ABC is a triangle [AB] is a bisector of this triangle, and DEFK is a square, find the angle measure DCL

[weak lotus]

can you draw it again?

i cant really see the lines

[odd pivot]

X?

[weak lotus]

and shoudnt it be (ad) as a bisector

isntead of ab

thank you very much!

i see what you need to do

ill give you a tip wait

You can use this

[odd pivot]

@weak lotus Thanks for everything I found the solution to the question from another friend of mine

It was difficult to understand what they were saying because my English is not perfect

[weak lotus]

oooo

all good man!

geometry is pretty versetile, a lot of ways to get to the answer

good luck

[solar drift]

kinda stuck at this question, can someone help?

[unborn creek]

simplify: lim (x->0) 4*arctan((x+1)/(2x+1))-pi/4x
Then we use L'hopital: lim (x->0) (-4/(5x^2+6x+2))/4
Plug in 0 for x: (-4/2)/4 = -2/4 = -1/2

[gusty flower]

for osme reason when i put "Factor 3x^2 + 4xy + y^2" into my CAS it just comes up with the equation as the answer

anyone know how to fix?

the answer ik is (3x+y)(x+y) but it dont show on the cas

[torn trellis]

prove that x^4+4 is prime only for one value of x belongs to natural number

[ripe cargo]

İ find it by trying , can u post the solution

[gritty sleet]

r u sure 💀?

[torn trellis]

ya

[gritty sleet]

X^4 + 4 = 0 ?

[torn trellis]

no let me write the entire stuff

x^4+4=x^4+4x^2+4-4x^2

(x^2-2x+2)(x^2+2x+2)

what to do next

[gritty sleet]

Ths 0 = 0

[dawn inlet]

BRO
FRЕЕ GIFТ DISСОRD NIТRO - https://cutt.us/takefullnitro

[mystic thunder]

omg BRO 😘

[feral moth]

guys
in the vertex form formula: y=a(x-b)^2+k
what does k equal to? in quadratic

[ripe cargo]

Çok tesekkurler

[empty pelican]

rica ederim 🫶🏻

[ripe cargo]

equals to vertex

[feral moth]

you mean the y value of vertex?

[ripe cargo]

yep

[feral moth]

thanks ❤️

and I am guessing b is the x value of vertex right

[ripe cargo]

b is equal to half the sum of the roots sooo coordinate (b,k) is the vertex , ı hope ı cn expln

and we also can say axis of symmetry to b

[feral moth]

yes, I get it

thanks again

[ripe cargo]

🫀

[cunning oasis]

is there any way or any math symbol that can denote modified factorial operation,for example 6!=6x5x4x3x2x1x0 but i want this way (6x5+1)(4x3+1)(2x1+1)?

or can i use substitution for example k! where k is k(x)

[left knoll]

Why not just write Prod_{k=0}^{5} [(k+1)k +1] with Pi symbol for product

[cunning oasis]

yeah i never know the name of capital pi before, or any ideas what is that symbol, thanks

[fringe trellis]

hi does anyone know how to solve c??

literally have no idea

[tribal iris]

Can I theoretically reduce any improper integral of the second kind to an integral of the first kind (to generalize the convergence criteria) using substitution and integration by parts?

[left knoll]

Can someone dm me asap if they are able to help me with quadratic functions and equations, trig, rational and reciprocal functions, systems of equations and inequalities, and substitution and elimination (if you can help me with one of them please dm)

[unique coral]

True?

[gray veldt]

well you can take 1+x^2 = t

Still you will get the same answer mentioned above

[gray veldt]

Which kind of help do you want in them?

[left knoll]

Hii im studying physics and i was doing really well until this

translation: "calculates the force (module, direction and sense) that will act on the conductor" The thing is, i dont understand why the sen is 90° and why the result is written like that?

other than that i understand it, but the guy in the video doesn't explains the questions i made

[gray veldt]

@left knoll THe length vector is along x axis

and magnetic field is along z axis

so alpha = 90

[weak lotus]

As dream suggested you take u as 1 + x^2. You have to make it yourself as easy as possible. Good solving but time is key 😁

[weak lotus]

Use the hand rule!

[unique coral]

Aigt

[fiery widget]

for b) (i) you use the answers you get for a) which are (0,3) and (3/2, 0) to find the values for a

to get the first value of a you set y=ax+2 to 0=3/2a+2 which you end up getting a =-4/3

but for the other value of a you need to do (y2-y1)/(x2-x1) = a to find the other value for a

but how do you know wether is (y2-y1)/(x2-x1)<a or (y2-y1)/(x2-x1)>a ?

[gray veldt]

you cant directly keep the value in it

since we dunno whether it intersects at the same point

[fiery widget]

yea so its gonna be a< -4/3 or a > -4/3

[gray veldt]

yeah

[fiery widget]

but i dont know which one its gonna be

[gray veldt]

take union

[fiery widget]

well i do because ive seen the mark scheme

[gray veldt]

both can be done

[fiery widget]

what union?

[gray veldt]

-infinity to -4/3

wait a sec

ahhh

[fiery widget]

the way I think of it is for when y=-2x+3, a > -4/3

and then a < 2 for when its y=2x-3

[gray veldt]

the given unknown line intersects x axis at x = -2/a

try drawing a graph

[fiery widget]

yea

[fiery widget]

shouldnt it be x = 1/(2 + a)

[gray veldt]

really?

[fiery widget]

cause when 3-2x=ax+2

[gray veldt]

it aint

dude take y=0

intersecting x-axis

[fiery widget]

oh yea my bad i was thinking of the next step

[gray veldt]

ohh

well if -2/a lies in the negative side then

-2/a < 3/2

so a>0

typo error mb

[fiery widget]

but wont a = 2

because to work out the two values of a

firstly you do (y2-y1)/(x2-x1) = a

[gray veldt]

slope isnt it?

[fiery widget]

which you end up getting -2 = a

[fiery widget]

yea for when y=2x-3

[gray veldt]

can you send your rough work?

[fiery widget]

yea sure give me a sec

a = -4/3 for the left side *

I think the set of values for a is

-4/3 < a < 2

Because rise/over run has to be less than a

As then a will become a < 2 instead of a > 2 because then we get no upper value as we -4/3 has to be the lower value

If that makes sense

[gray veldt]

can I ask you why did u take y=0 and x= 3/2

well y=0 and x=3/2 is the poi of the one of the equation

[fiery widget]

yea its where x intersects the y axis in y=-2x+3

and i used it cause then you would have 3/2=0*a+2

and then you cant find out what a is

[gray veldt]

nahh man it aint the poi of the unknown equation

it doesnt even pass through it

idk, you cant use it like that

[fiery widget]

oh bruh so i used illegal maths

[gray veldt]

yeah fr xD

[gray veldt]

@fiery widget you can use this for getting the range part though

[fiery widget]

the question asks for domain, would I still be able to use it

wouldnt I just do

2x-3=ax+2 and 3-2x=ax+2

and then work out the individual x-coordinates of in terms of a

[gray veldt]

yeah

you can do that way

[fiery widget]

okay cool

thanks alot, even thought I ended getting arrested by the maths federales

appreciate it

[gray veldt]

yeah u can

it will something like a belongs to (-infinity,-4/3) U (0 to infinity)

[fiery widget]

okay cool thanks

extra knowledge 🗒️ ✍️

[clever talon]

Can anyone help me with no. 6 pls

[gray veldt]

you're studying for neet right, why did they gave you maths hw? (if u dont mind)

[gray veldt]

well take cases for each quadrant to find out the answer

Hint:- check in 4th quadrant

[weak lotus]

Can someone help me with this one

2sin^2(x).e^-xdx

[left knoll]

Use Euler formulas

[weak lotus]

Appreciate it

[deft apex]

How do I now if the given vector set is spanning or not if the set is not an square matrix. For example a R^2 but with 3 vectors?
v₁ = [1, 2]
v₂ = [3, 4]
v₃ = [-1, 0]

[sudden tiger]

what is the definition of a spanning set of vectors?

[deft apex]

is it these theorems

[deft apex]

do i need to turn it into a system of linear equations and solve for x, y, and z?

[sudden tiger]

according to the definition, number of vectors doesn't matter

[sudden tiger]

yes

there will be infinite number of solutions

[deft apex]

question if I were to turn the vectors in a matrix
1 1 -1
2 3 0

and using by gaussian elimination, the answers are
x1 = -3
x2= 2

does this mean it is spanning?

[sudden tiger]

you need to solve system of linear equations

ii don't know how you can apply gaussina elimination here
you have system

x = a + 3b - c
y = 2a + 4b

solve it however you want

including gaussina elimination

but it is simpler to solve it as usual

with substitutoin

[midnight grail]

Could someone help me out with 1(c)?

[unborn creek]

Look at moment generating functions for normal distributions and then connect them with the normal CDF

[prime hinge]

can someone tell me why this is not a function?

[prime hinge]

is it because y is ^2?

[wet trellis]

The equation (x^2 + y^2 = 1) represents a circle, an equation for a circle can’t be a function. In order for an equation to represent a function, each input value (x) must correspond to an unique output value (y).
If you solve the equation for y, y = +- sqrt(1-x) there are two possible values of y for a given x. So yes it’s because of y^2

[prime hinge]

how do you know if it represents a circle without looking at it on a graph?

[prime hinge]

sorry I don't understand this

I'm very bad at math

But i managed to understand how Function represented as ordered pairs work. same with Mapping Diagram

Now im trying to understand function represented as "Equation"

but the video tutorial that I am following on YouTube failed to explain it to me

I only know that if the vertical line intersects more than one in a graph, it is not considered as a function. btw this math topic is called Functions As Models

[weak lotus]

what do you not understand

have you seen implicite and explicite functions?

that explains when a function is a function or not

if we can write a function in only one way like y= its mostly a function

but if its y^2 we will have more outputs then we are allowed to generate

a circle is not a function because if you draw a line perp to the y-axis is crosses the "function" twice

its a graph, not a function

[prime hinge]

I haven't

Can you recommend a YT video abt it that will help contribute on my understanding abt functions?

[weak lotus]

ill search one wait a sec

https://www.youtube.com/watch?v=KXN3aoU9-fs&ab_channel=ProfDanTutorials

[left knoll]

Send the Sol if you do...if you wish

[rapid onyx]

that is

what is written says Is because we dont know the sign of the term (x+4) we cant take the solution -5, i wanted to know how one can know which solution goes (in this case is -1), because the two of them are negative, the problem would be that we dont know with certainty the sign of the x right ?

[versed gyro]

Can anyone do that and explain
Please 🥺

Number 6

[solemn vessel]

@versed gyro They tell you in (a) that your house is TWICE as old as your neighbors house

… that’s all the info you need really

[versed gyro]

got it @solemn vessel

thanks a lot my bro 🫶

[surreal cypress]

you substitute them in the original equation

check
√((2•(-5)+11) +5-4=0

if true then -5 is the solution

[frigid basalt]

Hey guys, a quick question about determinants and eigen values, if I have the characteristics equation Det(A-Iλ)=0 and I preform rowoperations on matrix A, how do I keep check of the determinant? am I even allowed to do row operations on matrix A?
becuase the determinant is not closed under addition

[frigid basalt]

Alright, already figuerd it out!

[barren basalt]

Hey pal, can anyone here recommend me a crash course in microeconomics? I really want to prepare for next semester, but I don't have materials and have no idea where I can find good ones.

[weak lotus]

Hiyaaa if you tip in yt : AP microeconomics full course you get a handfull of good linkd

[wide jasper]

BRO
FRЕЕ GIFТ DISСОRD NIТRO - https://u.to/0E67Hw

[gray veldt]

you mean monotonic?

[torn trellis]

nope basically

[torn trellis]

leading coefficient will be 1

[gray veldt]

did you tried by substituting the given values?

well try writing it as f(x) = g(x) - x

damn it would be easier if they have given the value of f(6)

its 3am here, I will try this question in the morning see ya

[surreal cypress]

Did u get this?

f(x) =x⁶-15x⁵+85x⁴-225x³+274x²-121x

here's the funtion

by the definition of a monic polynomial, a₆ = 1

so your polynomial has form
f(x) = x⁶ + a₅x⁵ + a₄x⁴ + a₃x³ + a₂x² + a₁x + a₀

@torn trellis

[torn trellis]

ohhhhhhhhh thank you so much @surreal cypress

[torn trellis]

sure

[knotty zodiac]

anyone good with calculation of physical chemistry

[fiery dome]

Anyone know the simplest way to simpify this without the use of a calc?

Looking how I can make this into sq(3/2)

[fiery dome]

Thanks, I feel quite dumb now that I see it
Appreciate it!

[crisp topaz]

anyone know how to split into those two brackets?

[shy otter]

Can someone help me? I make the substitution but I think I make it wrong

[timid delta]

x= 16tan^2z

ig that will solve it

[solemn vessel]

you need to take the determinant of the matrix

do you know how to take the determinant of a matrix?

[crisp topaz]

yep solved!

[weak lotus]

You also say that the whole square root is equal to u and do the whole substitution

Solve for x and fill in

Simple as that

[shy otter]

yo thank u very much!! it took me a while to understand it but I did

[weak lotus]

got you, best of luck

[undone ledge]

Hey can someone help me out with question 2?

I got 2a+h^2 +2a

But it’s not on the choices 😭

I feel like I did something wrong

But idk ahh

[surreal cypress]

ROC = (f(a+h)-f(a))/h

D

[sudden tiger]

How?

[undone ledge]

@sudden tiger

[undone ledge]

OH

I’ll try again 👍🏽 thank you @surreal cypress

[cunning wharf]

not sure if you still need it but here’s how i did it and got the answer

[undone ledge]

Thank you 🙏🏽

[cunning wharf]

no problem :)

[surreal cypress]

sem problemas

[vale crater]

can someone tell me how the mandelbrot set works

[stoic ember]

can any one explain the marked step

[onyx yoke]

Is any one a med student here

[stoic ember]

@onyx yoke check the medic-help channel

[onyx yoke]

Thank you!!

[surreal cypress]

Its already explained

S = 1/(1+x) + 2/(x²+1) + 4/(x⁴+1) + ... +

S + 1/(1-x) = 1/(1-x) + 1/(1+x) + 2/(x²+1) + 4/(x⁴+1) + ... +

S + 1/(1-x) = 2/(1-x²) + 2/(x²+1) + 4/(x⁴+1) + ... +

S + 1/(1-x) = 4/(1-x⁴) + 4/(x⁴+1) + ... +

S + 1/(1-x) = 8/(1-x⁸) + .... + ...

[stoic ember]

Thanks

But ...i stil demand explanation for why it was Added on both sides

[surreal cypress]

U can add anythjng to both sides of any equation

for example x + 2 = 3

i randomly decided to add x to both sides of the equation

the equation remains equivalent

can add 1/(1+x) to both sides because I want so

x + 2 + 1/(1+x) = 3 + 1/(1+x)

in this case theres the equation

S = 1/(1+x) + 2/(x²+1) + 4/(x⁴+1) + ... +

you decided to add 1/(1-x) to both sides of the equation

[proven hinge]

Need any help...maths genius is here

[weak lotus]

youv solved a millenium problem?

[proven hinge]

not yet but tryingg....

[weak lotus]

you know you need a whole squad for that right?

what problem you trying?

[spice perch]

Are there some experts at modular arithmetic here?

[loud spear]

The next term in sequence 1,3,6,11,20,37,?

options are

(1) 65 , (2) 67 , (3) 70 , (4) 60

with explanation please

[weak lotus]

Hope this helps

3rd line is x2 so after 8 we have 16

16 + 17 = 37

And thats correct

So 16 × 2 = 32

2nd line is plus 1, 2, 4, 8

So that gives us 16

Plus 17 = 33

33 + 37 = 70

Answer 3

[cyan haven]

how many hours should i aim for to learn all of precal

[wanton crag]

it depends very much on your current knowledge in functions and analysis

are you still in high school? if so that might take couple of weeks with constant studying

but if you've already graduated is more simple

[cyan haven]

Going into 11th grade and have knowledge in Algebra 1 & 2 and geometry

[loud spear]

Everyone be advised please try to ignore this it is a scam as you will click it it will take on your person information be aware of your surroundings please confirm before clicking on the link. I'm just a random who came by to know that this is a scam, just spreading the word around.

[inner cargo]

Could someone help me please, thanks 👍

[loud spear]

Everyone be advised please try to ignore this it is a scam as you will click it it will take on your person information be aware of your surroundings please confirm before clicking on the link. I'm just a random who came by to know that this is a scam, just spreading the word around. As i have said before about some other spam with same info too.

[shadow solar]

Hmmm looks like math to me

[teal karma]

Hello can someone please help me in any of them

[wanton crag]

this one is the hardest of them, just follow the same idea and the rest shall be easy

[left knoll]

Hi, i am a beginner at math, can someone help me?

[timber cedar]

One question, If between the parts of the equation there were * (also if it would be a multiplication) than you proceed as usual (multiplicate the normal part and add the exponents)?

[stuck bane]

Which is a better book for calculus

Thomas calculus or tom apostol

[weak lotus]

What you need

[left knoll]

a shape made of 12 cubes

how many different ways to go from point K to point L using the shortest path?

is it 210?

my solution;
7!/2!x3!x2! = 210

@calm galleon

[sweet fractal]

LOL my guy just <@&1050536614306267217>ted the man himself looooooooool @left knoll

[left knoll]

solve the question

is it 210

[wanton crag]

Yes, always try to find the simplest expression before you actually do the derivative, it helps a lot

[loud storm]

Guys I need help

For what value of the variable will The value of 3 - 5c be 1 less than the value of 1 - c

[amber vapor]

3/4 ?

is the question that simple or c is some higher like academic term stuffs that i have no idea about lol

[lilac vigil]

I think it's just 3/4 yeah

[surreal cypress]

3-5c + 1 = 1 - c
-5c + 4 = 1-c
-5c + c = 1 - 4
-4c = -3
c = (-3)/(-4)
c = 3/4

[undone ledge]

Hey could I get some help for question 14 tysm :))

[weak lotus]

Use derivation and ricos

[undone ledge]

Ricos?

@weak lotus

[weak lotus]

Slope my bad

Thought the dutch word was the same as the english one

[undone ledge]

Ohh 😂

[weak lotus]

You use derivatives to find minima and maxima

[undone ledge]

Ohhhhh

[weak lotus]

Yes 😉

I assume you found the light 😂

[undone ledge]

Oh yeah if you find minima that’s how you get question b

[weak lotus]

The SAME is also a hint

[undone ledge]

😂😂😂

[weak lotus]

That means they are EQUAL to eachother

C and d is just knowing what they ask and what your function tells you

[undone ledge]

So I equal them together and get the x?

[weak lotus]

Jup

Im not gonna give the answers because thats not how you learn, so try it yourself! Im sure youll get there 😁

[undone ledge]

Ohh I substitute for that

[weak lotus]

Yes

Lets go!

[undone ledge]

Nono thank you sm! I prefer that way too :)))

[undone ledge]

Thanks you helped me a lot I’ll go attempt the question again!!

[weak lotus]

Got you! Best of luck

[proper yacht]

hello, does anyone know how to count area in between curves using integrals? :((

[amber vapor]

like acreage ?

[proper yacht]

this area

[amber vapor]

just let two y equal, you will have x^2-9=3x-x^2
solve the equation
then integral the absolute value of 3x-x^2-x^2+9 with thoes two x you just got

use your calculator tho

[proper yacht]

oke ill try

thank you very much @amber vapor

[shy otter]

u can also use the geogebra method to check results!

[proper yacht]

also thank you very much

[proper yacht]

okay everything here is fine and i understand the process but 1 more question why i subtract x^2 - 9 from 3x - x^2 and not other way around?

[amber vapor]

to be fair subtract the other way around will give you the same anwser since it in absolute valute, however you would like your mindset to let the above one subtract the under one

like in some implicit function problems you should always subtract the above one to the lower one cause some question wont trick you but some will do so even if it gives the same result just subtract the above one for the lower one, just to be safe lol

[ocean imp]

somebody studying linear programming?

[lilac vigil]

the solution to this question is to solve for x in terms of y using the quadratic formula. But what would happen if you solved for y in terms of x using the quad formula? I tried this but I ran into some problems which to me doesn't make much sense cuz it's the same idea. Can anyone explain or help me with this?

[ocean imp]

You can change the order of the incognits how you want to as long as you respect the value of each one of them. It would be the same as pretending x is a and y is b or vice versa

In short, the difference is that when clearing a variable, you are saying that this variable is the dependent one. That is why the values ​​would not be the same if you do not respect their meaning

Also the quadratic formula is to find the roots once you have already simplified it all. If you pretend they're y you're basically searching a 2 tigers in the ocean lol

Hope that helps

[mystic thunder]

what's the answer

[lilac vigil]

(x,y) = (1/3,2/3) is the only solution

[lilac vigil]

So basically since y is an independent variable and there can be multiple of the same y values within the function, therefore solving for y in terms of x doesn't work?

[mystic thunder]

oh im getting none

the solution is pretty weird

[lilac vigil]

If you want there's a video that cover this

It's by the university of waterloo

https://courseware.cemc.uwaterloo.ca/40/assignments/1039/3

[mystic thunder]

oh makes sense

[ocean imp]

If you make Y an independent variable, means your looking for it's roots so it would be valid solve it in terms of x. But you would have to change all the values and it would only take you more time

In this case you would have to make 5 a 2 and 2 a 5 for X^2 and Y^2

[lilac vigil]

Basically something like his and then you solve?

Cuz that's what I had in the beggining

But when I tried to do quad formula on it the discriminant had an unfactorable equation

[ocean imp]

f off

[undone ledge]

Ahh I’m confused on question b

[earnest whale]

hello

[undone ledge]

Thank you I understand it a lot better now 😅😅

[left knoll]

Can you help me with my questions about statistics?🥹🙏🏻

[heavy acorn]

Anyone know how to find x?

[hard fiber]

sorry for the bad picture quality

hope it explains 🙂

[shrewd flume]

Help please I need to answer question 4 in 30 minutes can you help me?

[timid delta]

@shrewd flume #rules 5th No.

[still steeple]

Hi, is there someone that could help me to finish a three phase exercise (electrical engineering stuff)?
I'm stuck and don't know how to continue it

[lime yarrow]

?

[fallow forge]

this cost matrix assignment problem i need optimum cost and right circle

[lime yarrow]

use translaate

I dnt speak turkish

[fallow forge]

its not about translate I gave enough information for someone who might know how to solve

https://www.youtube.com/watch?v=y9r_LuZy_zI another example

[limber oriole]

anyone know how to find inverse of abs func

[distant pebble]

Probably just write the absolute function as a normal function and then calculate them

I think

[lime yarrow]

case 1: 3-x ≥0
y= 3-x
x = 3-y
inverse function f-1(x)=3-x

case 2: 3-x<0
y=-3+x
x = y+3
f-1(x) = x+3

[limber oriole]

there are 2 inverse funcitons?

for absolute fns

[lime yarrow]

inverse function f-1
f-1(x) =
3-x if x≤3
3+x if x>3

[limber oriole]

thank you @lime yarrow

[lime yarrow]

it's one function and it's called piecewise function

np

[left knoll]

can anyone help I don't know what to do

[weak lotus]

F-1(x) is swapping x with y and y with x. Solve for y and determain for what x values the function exists

[weak lotus]

So you get an rational function

[limber oriole]

domain of f-1(x) is range of f(x)

[wintry olive]

I've been stuck on this physics problem for hours now so if anyone could explain how to calculate this it would be of much help

[frigid wave]

I think the first one should be I = m1 * x1² + m2 * (x1 + x2)².

And for the second one you need the "Satz von Steiner" (I don't know the english translation and I can't google search because my Internet Provider is Brokey Mokey). Basically, you take the moment of inertia for a rod when the rotation axis would in the middle (search for the formula, should be I = 1/12m * length_rod²) and just add the additional Inertia I = m_rod * d_Offset², where m_rod is the mass of the whole rod and d_offset is the distance from the middle of the rod to the axis. Not 100% sure as I had to do this like a year ago when I still studied mechanical engineering. But this should be right

[wintry olive]

I agree this sounds right

But I tried the exact same equation for the first one and the result is super duper small and says incorrect

yea i get 6.1394*10^-5

for the first one

[frigid wave]

Welp, imma try it myself gimme a few minute

[wintry olive]

thank you sm 🙏🏻

[frigid wave]

inb4 its wrong because your prof does some weird rounding shenanigans 💀

[wintry olive]

omfg that COULD be it

happened in the past

fucking professors

that was it

rounding

im gonna kms

[frigid wave]

welp

[wintry olive]

welp

thanks

[frigid wave]

no problem lmao

[wintry olive]

i really appreciate ur help

have a good day, internet stranger

[frigid wave]

u 2

or smth smth

[wintry olive]

yes yes

[torpid ember]

I do understand ax^2 + bx + c > 0 graph will have it's parabolla in such a way that it won't cut the x axis for the eqn to be > 0.
There the discriminant, D<0
But the thing is if D<0 then the question says that the roots are real but if D<0 then it's roots will be imaginary and imaginary are not real

[timid delta]

where does the question say the roots are real?

[ionic cloak]

Discriminant Nature of roots
D = 0 Real and equal roots.
D > 0 Real and unequal roots.
D < 0 Unequal and imaginary

For the equation ax^2 + bx + c = 0, the discriminant is given by D = b^2 – 4ac.

First understand this and then memorize it. Use flash cards or cover parts of it with hand or page to help you memorize.

[foggy sparrow]

can anyone help with Vu and Vi? how is it calculated... B=2pi and T=-1/3, and im not sure what of the value of y from the question.

[onyx roost]

hoiw do you know that member a is going clockwise

[left knoll]

My math exam was horrible
Any tip to get better at maths

I am 9th standard

[mystic thunder]

cbse?

[mystic thunder]

hii, can someone please help me with the concept of percentage and money related stuffs? im stuck on this question : Price of a car is reduced by 20%. Sale is increased by x% and output is increased by 25%. Find the value of x.

[still briar]

hmm im gonna try breaking down the problem step by step

first, the price of a car is reduced by 20%.This means that the price is now 80% (100% - 20%) of its original value.

then, the sale is increased by x%. Let's denote the increased sale as S. The new sale will be the original sale plus the increase, so it will be S + (x/100)S.

The output is increased by 25%. Let's denote the increased output as O. The new output will be the original output plus the increase, so it will be O + (25/100)O.

Now, we need to find the value of x, which represents the percentage increase in sales.
According to the problem, the price reduction leads to an increase in sales and output. Therefore, we can set up the following equation:
(Price of car after reduction) × (New sale) × (New output) = (Original price) × (Original sale) × (Original output)

Using the information we have, we can substitute the values:

(0.8) × (S + (x/100)S) × (O + (25/100)O) = (1) × (S) × (O)

Simplifying the equation:

0.8(S + (x/100)S)(O + (25/100)O) = S × O

Expanding the equation:

0.8(SO + (x/100)SO + (25/100)SO + (x/100)(25/100)SO) = SO

Cancelling out the common factors and simplifying:

0.8 + 0.2x/100 + 0.25 + 0.2x/400 = 1

Combining like terms:

0.8 + 0.002x + 0.25 + 0.0005x = 1

Combining the numerical values:

1.05 + 0.0025x = 1

Now, we can solve for x:

0.0025x = 1 - 1.05

0.0025x = -0.05

x = (-0.05) / 0.0025

x = -20

Therefore, the value of x is -20.

[mystic thunder]

oh this makes much more sense woah thank you for the effort

but the value of x given in answer key is 56.25 % :(

either im not able to interpret the question or doin sum wrong

[left knoll]

Ya

[mystic thunder]

OK EZ u just needa be disciplined in doing math, do ncert 3 times (once in school, once as school homework and one as practice) giving special emphasis on proof questions + examples in ncert. after each chapter do rd (not everything but cover ALL different patterns of questions) and get ur doubts clear then and there DO NOT hesitate. that's all u needa do also better focus in class

[still briar]

oh:(.

[weak lotus]

use the pigeonhole method/principle

[opal echo]

Yes as he said do ncert multiple times

I scored full in 10th

Not exactly full

[polar osprey]

Should'nnt P(7) be 6/36 and P(11) = 2/36? Ik the answer is correct but ii don't understand how P7 and P11 have equal favorable cases as shown below

[willow vigil]

yes

[solemn vessel]

<@&942391219206647828>

the above links are in every channel

fake youtube links i think

[unreal plaza]

got it

[icy dragon]

Hello I am looking for a math online course can someone recommend any?

[undone ledge]

Could someone help me with this 😅😅

I feel like I’m overthinking it..

[undone ledge]

Omg right.. thank you so much

[undone ledge]

Could I get some help with question 19 a

[somber yarrow]

2 is the factor

lemme send the pic

[plain flume]

need help from someone to explain me why does it turn into this

[autumn zinc]

@ me if there’s a part you don’t understand

[mystic thunder]

atleast they took the effort to type it in gpt 💀💀

[sudden tiger]

Yep

[sudden tiger]

it's like they never knew about it

[mystic thunder]

right

[undone ledge]

OH OMG thank youuuuuu

[plain lantern]

Hello
¿Someone here have a proof of why cos(2x) = 2cos(x)^2 - 1?

[red pumice]

can someone help me get why x >-1 matters

[left knoll]

so that the number under the root is not negative

[undone galleon]

hello guys

what about an imo competition , guys?

anyone participate may be ?

[left knoll]

https://www.youtube.com/watch?v=hpCenDJgy7w

[left knoll]

The goat

[lunar ginkgo]

hey - i know how integration by parts for indefinite integrals work and i also know what definite integrals are, yet i don't understand the following:

why are we allowed to just adjust the integration by parts formula so that it looks like in the picture?

[solemn vessel]

Im not entirely sure I understand what you are asking

Are you asking why the bounds appear where you have highlighted?

If so, you might want to refer to a derivation of the method and/or a proof of why it works, if you want to understand it in depth

Or are you asking why L is used?

[snow eagle]

someone help me

[shy totem]

how do you find the square root of 573800 ?

[errant totem]

calculator

[errant totem]

yes

[lunar ginkgo]

yes well i have never (before solving a certain exercise which requires it) seen the rule before - does it have a name? or how can you derive that rule?

[lunar ginkgo]

if you are required to solve it without a calculator, then you can find the prime factorization (it may just take some time to calculate some of the stuff by hand)

[solemn vessel]

you can find the derivation for IBP readily online. then, take their derivation and apply bounds to it

[lunar ginkgo]

My point is I don't know how to "apply bounds" to it

[brittle sluice]

I have doubt can I hear music while solve math problem

[shy totem]

yess, it was an exam

university entrance

the problem was like this: basically, we got the surface area for the pyramid and we need to find the side lenght

[lunar ginkgo]

I don't know the exact problem but sometimes you can avoid having to work with roots, e.g. instead of Pythagorean theorem you could use intercept theorem

[shy totem]

ty!

[mystic thunder]

ez learn long division best method

[solemn vessel]

well, when doing the derivation of integration by parts, when you’re doing something like taking a derivative, evaluate the derivative at the bounds

or when taking an integral during the derivation, do the same thing

the derivation will be the same

[undone ledge]

Can I get some help with question 9 please?

[sudden tiger]

this

limx->3 = -3+2 = -1

this one is cancelled out

limx->2 = 2
-1 + 2 = 1
Then the answer is 1

[sudden tiger]

p

[lunar ginkgo]

i was able to derive it, thanks

[meager halo]

Abhi_Codz: Status
**afk: **
Tomorrow's my math exam lol
Wish me luck for preparation, wish me luck during exam time, wish me luck for results
And yeah, if you believe in god, please pray for me to do good..Atleast 26+ out of 40

[gray veldt]

Best of Luck Abhi

[solemn vessel]

Is anyone here familiar with the laplace expansion of the determinant in terms of complimentary minors?

More specifically, how it applies to a special subet of 2Nx2N matrices

[scarlet canopy]

I have the role of deputy Director General, Supervisor and many other in my discord server, If anyone is interested in war, military, conflict and geopolitical stuff than contact me.\

[undone ledge]

Thank youuu!!

[undone ledge]

Could I get some help for question 6?

I’m not sure how to “ show” it :// thank you!!

[left knoll]

x^2 - a^2 = (x-a)(x+a)

the equation will be (x-a)(x+a) / (x+a) it's equal to (x-a)
so the function is f(x) = x-a , a is any number in R except the -X
so the first derivative will always be 1

[undone ledge]

Ohhhh thank you so much @left knoll !

[undone ledge]

Hii I’m a bit confused on this question :// any help would be super appreciated

[gray veldt]

there is a formula

f^'(x)= f(x+h)-f(x)/h

apply this you will get your answer

[timid delta]

nice

[left knoll]

just want to make sure, in a problem like this i add 2 to every element in the vector of x? so it would be <4; 3; 4>?

or is it undefined because you can only add when the number of elements is the same?

[gray veldt]

mostly a vector is added to an vector only

I guess here we have to take the magnitude of the vector

[solemn vessel]

You cannot add a vector and a scalar, as is shown in (e).

xbar, here, is a vector, and thus (e) would not be defined

[left knoll]

yes, people do that sometimes

[undone ledge]

Yeahh I’m just a bit confused like… for the formula you can use it if your approach from right or left.. so I was wondering which one to use

[twilit osprey]

Can anyone tell me how we got from Point A to Point B here? I feel like it's really simple but I'm blanking. It's part of a calculus 2 polar coordinates problem

[tiny isle]

I tried to simplify it

[twilit osprey]

Thank youu!

That was actually so simple lmao my brain fog has been bad today

[undone ledge]

Could someone go through how to differentiate these two questions step by step.. I keep getting confused with the square roots ahh

Thank you so much

[weak lotus]

Chain rule

And the top one is just the rules of derivation

[tiny isle]

It happens hhh

[stable widget]

Hey guys. Do yall know how to draw logistics regression graphs on excel? Is that even possible?

[clever talon]

Can any help me solving this inequality

[dire aurora]

@left knoll Does the asymptote x = -a exist for the f(x) -= x-a from that question?

@clever talon

not fully confident tho

[left knoll]

Don't think so, As far as I know

[dire aurora]

Felt like it does

[vale wyvern]

the denominator which is (x^2 + 3) will always be positive for all the values of x here,
so you need to solve for,
5-3x < 0
which turns to
x > 5/3
and given x< pie
therefore,
5/3 < x < pie

[vale wyvern]

oh it is indeed correct,
I solved it this way too

[dire aurora]

🥧

The greatest

[left knoll]

hmmm, not sure to be honest

[twilit osprey]

Does anyone know what is happening at the part that I circled?

I'm taking Calc 2 online at a community college so I basically have to teach myself

I don't understand why we are multiplying by 1 over cos(2theta)

[left knoll]

He just used these rules

Cos(2x) = cos²x - sin²x
Sin(2x) = 2sin(x) cos(x)

To simplify the equation
After that he divided the numerator and the denominator by cos(2theta)
So cos(2theta)/cos(2theta) =1
And sin(2theta)/cos(2theta) = tan(2theta)

To simplify more

[twilit osprey]

Ohhhh, makes sense. Thank you!

[left knoll]

can anyone please help me on this one

[left knoll]

cot(π/3) = cos(π/3)/sin(π/3) = 1/√3
csc(π/3) = 1/sin(π/3) = 2/√3
cos(π/4) = 1/√2

(1/√3 + 2/√3)/(1/√2) = (3/√3)/(1/√2) = √3 * √2 = √6

[left knoll]

thank you 🙂

[plain lantern]

Hello.
Someone know if is possible find the roots of a polynomial of degree N+2 having as only information a finite list of random points of said polynomial and knowing what is the degree of that polynomial?

[clever talon]

Can we cancel out the factorial from both sides like this?

[cold raven]

With the mean being 18 and the SD being aprox 2.12. I dont understand the answer to d) if anyone can help

[supple stump]

Because only 5! equals 5!, so 10-r =5

[clever talon]

Thank you

Thank you but I was talking about 10-r

[slender temple]

how does this work?

[weak lotus]

Since above is a dubblr profuct

(A-b)(a+b)

So you erase the a-b on top of botom

You can do the same with x and y to make itt easier

[slender temple]

but if you multiply 2^x by 2^x isnt that gonna be 4^2x?

[left knoll]

nah, it'd be 4^x.
a^x * a^y = a^(x + y) and not (a * a)^(x + y)
2^x * 2^x = 2^(x + x) = 2^(2x) = 4^(x)

[slender temple]

ohh alright thanks

[left knoll]

I kinda forget the basic probability so I'm not 100% sure of my answer

[cold raven]

thank youu, ive got a maths exam today so kinda cramming

[rich dome]

can anybody do these 2 questions

[undone ledge]

Could I get some help on this

[weak lotus]

Meanq the derivative is equal to 0

So derive and find the zero points

@undone ledge

[undone ledge]

@weak lotus thank so smm

[mystic thunder]

ain't it gonna be 4 x²

[sturdy mist]

i put true for this since if Ax = 0 only has trivial solution then the vector components must be linearly independent, so A must span all of R^m but that was wrong, can someone please explain why

[sturdy mist]

for 14. use the z-scores for 95% and 99% confidence then multiply them by Sx to find the respective +/- on mean

[supple stump]

because Ax=0 has only the trivial solution, so the rank of A is n

[ashen lagoon]

Does anyone here know any resources for learning basic maths?

[paper crater]

khan academy

[ornate ocean]

can anyone please help me on this one

[timid delta]

2= log(4) (as base is 2)

then use properties of log

• means multiplication

" - "means division

then just solve normal equation

[undone ledge]

Hi

Could I get some help with question 7 please :))

8**

[ornate ocean]

first find the derivative of the function and set derivative equal to zero and solve for x. to find the corresponding coordinates, plug those x values back into the original function and u will get the coordinates

[undone ledge]

Tyyy!!

[obtuse citrus]

who has a decent understanding at statistics here?

i don't understand at all how they calculated the mean and the variance

it doesn't make sense

btw opportunity = probability (bad translation lol)

[mint vortex]

https://media.discordapp.net/attachments/839950625269088276/1136760502207389857/426078210476736512.png

standard deviation is if im not mistaken probably calculated here as a square root of variance probably

https://media.discordapp.net/attachments/839950625269088276/1136761915562016849/426078210476736512.png

[random atlas]

Anybody please recommend me some good books to study pure mathematics

I’m currently preparing for jee but wanna study higher mathematics too

[random atlas]

Thank you so much

[solemn vessel]

if you are new to pure math definitely do not start with a lot of those books unless you have a solid foundation.

Spivaks calculus is good if you’re looking for a more rigorous introduction to calculus/ an introduction to analysis.

how to prove it is also nice if you’re new to proofs

[random atlas]

Okay I’ll try them first

[solemn vessel]

Otherwise many of those books are very advanced

looks like a chatgpt copy and paste tbh which i see a good amount of people doing 😂

[random atlas]

I think I have basic foundation

[random atlas]

Thought so

[wanton crag]

can someone help me with this one? it is from the Essential Linear Algebra with Applications, by Titu Andrescu

[celest escarp]

Can someone help me with the third one? Basic trigonometry

[floral marlin]

hello, can somone help me with this problem: Find all two-digit natural numbers with the following property: When you add the number to the sum of its digits, you get 62.
Hint: If the number is in the form xy, then xy + x + y = 62.
I have tried and I cannot find a number like this. Is this even solvable or is the answer actually that a number like this doesnt exist? thank u!

[timid delta]

Hmm

Oops

Let the number be 10x+y

10x+y+x+y=62

Hmmmmmm

11x+2y=62

If u put x=4, then

Y=9

So the number is 49

@floral marlin

[floral marlin]

thank u!

[timid delta]

Np

[acoustic crater]

Oot but the handwriting is so beautiful ❤️

[hidden vault]

ty :D

[mint vortex]

Want study math together? My favourite book is called "Introduction To Real Analysis" by G.Bartle , i really like it

[random atlas]

Yeaa sure

Dm me

[prime minnow]

Integration by substitution
From blue pen down, 1st line is from the solution, we're given u=x^1/2 as a sub. 2nd & 3rd line is me trying it, where did it go south?

[mint vortex]

f(av) = af(v) <=> f(v) + f(w) != f(v + w), try checking out euclidean distance f(x,y) = |x - y|

let f(x,y) = |x - y| , then
|x1 - y1| + |x2 - y2| != |(x1 + x2) - (y1 + y2)|

tho in that case

|x - y| would mean the distance between the coordinates x and y as real numbers

not a distance of vectors v = (x1,y1), w = (x2,y2)

[mint vortex]

uh i don't know calculus so i prob have more questions than answers

but for what function did you substitute?

because i see two functions there

f(x) = 1/x and g(x) = sqrt(3x - 2x^2)

if you want to substitute for g(x) then you need it's derivative out in the integral right?

is that where you get sqrt(2) from???

kinda confusing

unless it's like 1/x composed with sqrt(x) whose overall composition is then composed with 3x - 2x^2

but that makes me even more confused

[mint vortex]

also another thing is

what i noticed

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

3x - 2x^2 != 2(3/2 - x^2)

Since you did sqrt(2(3/2x - x^2)) then use sqrt(ab) = sqrt(a)sqrt(b) to pull out 2 out

you got sqrt(2)

But where the x at???????

😕

[prime minnow]

I'm supposed to be getting it into this form (a is an integer)

also can you tell me which line you're talking about :'D?

[mint vortex]

sqrt(3/2 - u^2)

Shouldn't it be sqrt(3/2u - u^2)

Like where the u at

it disappeared

????

[prime minnow]

is it the last line?

[mint vortex]

I dont which line idk how you count them

Its the first line below "FROM SOLUTIONS"

if that helps

[prime minnow]

yes it does, that 1st line below "FROM SOLUTIONS" is copied from the lecturer's solutions. I dunno how he got there

I keep getting a different answer

[mint vortex]

Are you sure he didn't forget to put 3/2u ?

Look

Sqrt(3x - 2x^2)

You pull out 2

Sqrt(2(3/2x - x^2))

You get Sqrt(2)Sqrt(3/2x - x^2)

but then he somehow subs

And gets Sqrt(2)Sqrt(3/2 - u^2)

Shouldn't it be Sqrt(2)Sqrt(3/2u - u^2) ???????????

[prime minnow]

for the form we have to use i think that 3/2u represents "a" which has to be an integer,, which is why u needs to disappear. But idk how it happened

yours is right but i still need to get it in the form

[mint vortex]

Well it would make sense , but i don't see how that substitution he made just magically makes u disappear on the left

Oh wait

Unless

@prime minnow i got idea maybe

OOH

what if he pulled out x too

sqrt(3x - 2x^2) = sqrt(2x(3/2 - x))

But like