math-help

[brave ledge]

so is it like dynamics particle? normal force stuff like that? or just like graph?

[left surge]

i didnt check using it

[fringe geyser]

you should read a bit more about a properties of exponents

[random flame]

You mean the laws of ln?

I got these

[fringe geyser]

no, logarithm properties is another thing

[random flame]

Hmm

[fringe geyser]

i mean these one

[random flame]

Ohhh

Yea I rmb those

[dapper sun]

oh i got that one alr ty

[brave ledge]

aight

[dapper sun]

can sb help ~~

[fringe geyser]

oh, wrong person

[random flame]

XDD

[fringe geyser]

@random flame

[random flame]

Q2 don’t have a part e-?

You meant Q9?

[fringe geyser]

yeah, messed up as always

what is wrong with me today

[random flame]

Mood 🤣

I’ve been there HAHA

[gentle heron]

don't pay attention to language pay attention to the formula

[random flame]

Wrong person, Lukious- WHEEZE

XDD

Q9e ans is 2ln2, ln5

@fringe geyser

[brave ledge]

chotto matte xD

[random flame]

Btw thanks @gentle heron ^^

[brave ledge]

u learn ln and e in school?

[random flame]

Add Maths, I’m in high school currently

[brave ledge]

my school didnt teach that :'v

[brave ledge]

only this

[cyan glacier]

I got pinged..?

[slate dune]

Im learning logarithms and exponentials in hs too

[random flame]

Yeah someone pinged the wrong person just now

[gentle heron]

this is the basic

[brave ledge]

ya i learn it in 10th grade

but i didnt get ln and e

[random flame]

I’m in Year 10 rn

[fringe geyser]

yeah, sorry, ping you by accident

[slate dune]

natrual log and e^x is pretty straight forward

[brave ledge]

ah i see

[fringe geyser]

@random flame

[zinc dagger]

e is just euler's number

it comes up in many areas

[random flame]

Thanks a lot man

I’ll let you know if I got any questions

[fringe geyser]

funny enough, im in 10th grade too

[random flame]

Holy shit XD

[brave ledge]

im in 12th xD

[slate dune]

you studying for finals as well?

[gentle heron]

I'm 12, too XD

[fringe geyser]

The education system is different everywhere

we have only 11 grades

[random flame]

Yo you’re a genius-

[random flame]

Sameee

[brave ledge]

oo i alredy accepted via snmptn(like,based on your academic transcript+achievement on competition)

12th grade im dying man :'v

[fringe geyser]

there is nothing hard in those imho

[brave ledge]

integral + trigon :'v

[random flame]

only smart ppl say that

Jkjk XDD

[fringe geyser]

i mean, we did similar tasks with my classmates

[random flame]

I can’t even understand a single shit tbh T^T

[dapper sun]

anyone knows cal vectors can help?

[fringe geyser]

ahh, physics

[random flame]

Oh and last one, Q9f if someone can help

[zinc dagger]

send it and maybe someone might be able to help

[random flame]

I got a surd for some reason

[zinc dagger]

that's just quadratics

in the form of e^x

[random flame]

I guess you can say that

Hmm

[zinc dagger]

replace e^x as a

and then go from there

[tight plover]

you'll get a surd lol

[random flame]

But there’s a e^-x

[tight plover]

Jesse is correct

[frozen karma]

man i can’t even do 9 times 12

[zinc dagger]

you need help on c?

[tight plover]

you will get a surd

it'll be two solutions bc plusminus

[random flame]

Yea but it’s not the answer in the book

ln don’t have negative value tho

[tight plover]

you right

its extraneous

so you eliminate it

[random flame]

This is what I got

Idk man

[fringe geyser]

@random flame ever heard of properties of exponents?

[tight plover]

oh

wait f?

[random flame]

Yea

[random flame]

Yeah, but idk how to apply it in here

[tight plover]

i read 10c

lmfao

[random flame]

XDD

[fringe geyser]

as you can see

like e^-1 = 1/e

is these are correct answers?

[zinc dagger]

it's been a while but i got ln(80/(1+2/e))

so 3.83

[random flame]

Yeah I rmb that rule

[fringe geyser]

ln(2), ln(3)

[zinc dagger]

oh i was looking at 10 lol

bruh

[tight plover]

same hahaha

[zinc dagger]

they had 9 crossed out

so i looked at 10

[random flame]

Btw I don’t get your third and fourth line, how did you solve it?

[random flame]

HAHA sry sry I do that to know which Qs to do

[zinc dagger]

is this f

or c

[random flame]

Q9f

[fringe geyser]

oh, so you change e^x to variable "t" so it will be easier to solve

and then solve for t

[random flame]

But how did you solve a fraction?

[fringe geyser]

multiplied everythin by t

and got squared equation

[random flame]

So it becomes t^2+6t-5=0?

[random flame]

+5?

[fringe geyser]

wait

t^2 + 6 - 5t = 0

[zinc dagger]

yea you havei t right

[random flame]

Ohhh okie

[fringe geyser]

so yeah, the reason why i got here, can anybody help me with this?

[random flame]

I feel bad that I can’t help cuz I have no idea-

[fringe geyser]

yeah, this one is hard

[zinc dagger]

same

no idea what computational graph is

[brave ledge]

me either

[left knoll]

what is the question?

[fringe geyser]

It is neural network thing

I need to find the derivative of c2

[left knoll]

derivative of ?

[fringe geyser]

Variable c2

At the bottom of the graph

[brave ledge]

so d/dx tanh?

i dunno im just guessin

[limpid oyster]

is it live pst fix problem

like*

[zinc dagger]

dz/d(c2) means you're taking the derivative of z with respect to c2

[fringe geyser]

something similar to this

need to find the derivative using backpropagation

[zinc dagger]

that's partial differentiation

[fringe geyser]

partial is at letter a

the second scheme is finding derivative using forward propagation

[left knoll]

this is what phd in maths looks like huh

[zinc dagger]

maybe try googling

[fringe geyser]

and the third one is finding the derivative using back propagation

[fringe geyser]

this picture is the best google result))

this is not the task

[zinc dagger]

i can try asking in a mathematics server

[fringe geyser]

It is not quite math problem

[zinc dagger]

it's computational graph

there's a channel for it

[fringe geyser]

It is used in machine learnig

Oh

Yeah, would be nice

[zinc dagger]

machine learning is founded more on linear algebra

[glacial reef]

My brain abt to explode rn looking at the pic

What grade will we learn that?

[left knoll]

A particle, P, of mass M is released from rest and moves along a horizontal straight line
through a point O. When P is at a displacement of x metres from O, moving with a speed
v ms–1, a force of magnitude 8Mx acts on the particle directed towards O. A resistive
force, of magnitude 4 Mv , also acts on P.
Initially P is held at rest at a displacement of 1 metre from O. Describe completely the
motion of P after it is released.
Fully justify your answer.

would anyone be able to help?

[fringe geyser]

We are currently doin this in 10th grade

[glacial reef]

Oooo

Oh no im gonna face it in 1 year

[fringe geyser]

Not really, this is not our math lessons, this is our additional education

[random flame]

Eyo umm I’m back, I just need help with solving for x -^-“

[glacial reef]

Ook nice to know

[fringe geyser]

@glacial reef This is what you'll be doin in 10th grade

[random flame]

I was thinking of factorising 3 out but idk if that helps

And I oop-

[fringe geyser]

what is the task?

[random flame]

Just solve x Ima deal with the rest of the question myself

[brave ledge]

lne^x=x

am i correct?

[random flame]

Hmm

I think so

But tbh I’m not even sure if I shld put ln there or not

I tried looking back at the exponent laws thingy

[brave ledge]

ya so basically ln6+ln3=-x, -ln18=x?

[glacial reef]

Ookk thx

[brave ledge]

oo my bad

[random flame]

That I’m not sure

[fringe geyser]

yeah, got the same answer, -ln(18)

oh, not the same

but yeah

[brave ledge]

typo xd

[random flame]

Sooo like this?

[fringe geyser]

yeah

[brave ledge]

ya

[random flame]

Aight thankieww

[opal bough]

Guys, I am stuck. Does it really have complex solutions?

[fringe geyser]

what is Mx?

[left knoll]

@random flame I'm confused, how come you haven't divided the -6 by 3 to get e^x on its own?

[fringe geyser]

and what is the speed?

[left knoll]

this is why i'm confused it is an 8 mark question. and it doesn't tell you the speed, everything you need is apparently already in th question

v is (v) ms-1

it's all in algebraic form so it isn't a specific example

[fringe geyser]

Im confused with condition, a few words, symbols i dont know

Is it some unit of measure?

I mean, i just cant translate the condition, the task seems to be not hard

[left knoll]

so the force is 8 times M (which is the mass) times x (which is displacement)

[random flame]

Yeah originally I thought of that

But then if I do that then I might get wrong and

*ans

[left knoll]

hmmm

[random flame]

Anyways Ima head to bed it’s 10:32pm, gn

[limpid oyster]

and here we put the speed up to the point 0 + ut + (1/2)at^2-(8Mx+4Mv)=1

maybe this

[reef lark]

Hi guys I'm facing difficulties to model a problem where I'm responsible of a plant and I have to meet the demand in a 10 week planning horizon. My production consists of 2 operations so I have bulk products in the middle , I don't know how to handle the variables . For example a product manufactured in the first operation can become 2 different products with the second processes. My final demand is in finished and not bulk products. Thanks for your help and sorry if I'm not in the right channel I could not find one which fits better

[left knoll]

there are no real solutions to 3e^x +6 = 0, you cannot log a negative number

[halcyon crystal]

hi 🙂 does anyone know how to integrate this with the method of substitution (i wrote the answer above the equation but i dont know how to do it) thanks!!!

[swift garnet]

@halcyon crystal Download photomath on your phone and it gives you all the steps, really helps for any future questions you may have!

[left knoll]

sure give me a few minutes to do it

[halcyon crystal]

yeah i downloaded photomaths but it isnt using method of substitutions but the question requires us to use it so yea...

[halcyon crystal]

thankyou!!

[cunning temple]

Consider z = 1+ y. You can do it easily after that

[gentle heron]

@opal bough X=4,y=100

[halcyon crystal]

wait let me tryy

but what do i do with 1-y?

[left knoll]

reaarange z= to get y on its own

[halcyon crystal]

oh is it make 1-y to y=z-1

[left knoll]

yep

turn everything you can into z's

[halcyon crystal]

omg why did i not think of it thankyou so much!!!!

[gentle heron]

@opal bough X=4;Y=100 and X=100; Y=4

[left knoll]

no prblem we're all here to learn!

[slate storm]

Hey guys a quick query I’m new here so if i have a quetion in any subject in maths could i ask for help here

[rain gazelle]

ask the question

[slate storm]

No i dont have one right now but

When i need help

[wintry violet]

can i do something like this?

[left knoll]

yes

[prisma matrix]

are they both part of the same question?

[wintry violet]

ofcourse

[prisma matrix]

yessir u can

[severe swallow]

Any1 know how to do Product Rule in Maths

[left knoll]

just you shouldn't write it like that (i do prefer you just state that u add them both)

[prisma matrix]

^ ye this or at least draw an arrow

[wintry violet]

this is the simplest one ⬆️

[left knoll]

which one ?

[wintry violet]

.

[prisma matrix]

theres a more complicated product rule?

[left knoll]

nop

if you have three functions it's the same you put three times the product as three term of a sum and derivate one function of the product and not the other for each term of the sum

replace three by n (natural) to have more

[west citrus]

this is chain rule,is'n it ?

[prisma matrix]

nop

chain rule is this

[west citrus]

yep

this is Derivative of function

[halcyon crystal]

chain rule is the one with index right?

[west citrus]

i am learning FFT(fast fourier trans)

[prisma matrix]

index?

[west citrus]

@prisma matrix u know this ? https://en.wikipedia.org/wiki/Schönhage–Strassen_algorithm#:~:text=The Schönhage–Strassen algorithm is,an 8th root of unity.

[prisma matrix]

thats a yikes 0.0

[fossil willow]

I always remember product rule as dy/dx= udv/dx x vdu/dx - if that helps anyone

[prisma matrix]

no i don't know it haha

[west citrus]

it quite hard

[halcyon crystal]

its the same as power...?

[west citrus]

i got in in https://codeforces.com/

it is about algorithm

compelexity

[prisma matrix]

i just remember it with words: dy/dx = differentiate first fuction x second fuction + differentiate second function x first function

[left knoll]

U derivative of v + v derivative of u.

With language

[prisma matrix]

oh are u refering to the first thingy i sent

[severe swallow]

is this simplified?

[prisma matrix]

yep

thats the power rule

[severe swallow]

cheers

[prisma matrix]

np

[left knoll]

nx^(n-1).

?

[prisma matrix]

dang that looks tough

[west citrus]

because my major is computer engineering.

[halcyon crystal]

like chain rule applies when theres powers right

[west citrus]

I got this problem in ICPC contest

[sweet mirage]

Shat is chain rule?

[west citrus]

it quite hard, i can not slove it in the pass

but now i can slove it

[sweet mirage]

We speaking derivatives”

[left knoll]

In derivative you dont need to remember any hard formulas ,intuition is everything.

[prisma matrix]

ahh yea you can

but usually when theres power involved i just use the product law

[sweet mirage]

You all enjoy, you guys have got this😂😂

[left knoll]

Don't think so, pretty usefull to know the formula, otherwise you have to demonstrate it every time with rate of increase..

[prisma matrix]

i think the only formula i need to memorise is IBP

integration by parts

the rest just flow naturally because it's been hammered into me

[fossil willow]

that would be the last method of integration to go for - for me ha

[left knoll]

Yeah pratice help a lot but you do "memorise them" not in your short memory but a stronger one with memory of exp

[prisma matrix]

i still don't really get it hahaha

[left knoll]

Hum in fact it's more easier than variable change that you have to intuite

[prisma matrix]

yup, pure maths gang

[prisma matrix]

whaaat

variable change is ez pz compared to ibp

[left knoll]

Lol if u are given then variable change yes but not if not given

[coarse rose]

https://youtu.be/HfACrKJ_Y2w help me a lot in calculus 1

[prisma matrix]

well if not given youll just need to do the individual components using the info

which i def prefer over ibp

hahah

[left knoll]

Hum don't get it

"to do the individual components "

[prisma matrix]

youre talking about chain rule right?

[reef lark]

Hi guys I'm facing difficulties to model a problem where I'm responsible of a plant and I have to meet the demand in a 10 week planning horizon. My production consists of 2 operations so I have bulk products in the middle , I don't know how to handle the variables . For example a product manufactured in the first operation can become 2 different products with the second processes. My final demand is in finished and not bulk products. Thanks for your help and sorry if I'm not in the right channel I could not find one which fits better

[halcyon crystal]

hey guys how do i do this

i wrote the answer down

[zinc dagger]

input 4 into the equaton

to find the upper bound

your lower bound would be y = 2

so the bounds would be lower bound = 2, upper bound = whatever your x is into that equation

then simply integrate with respect to y

using the disc or whatever method you're using

[still thistle]

some of yall need to calculate where the hoes at

[vague wave]

Does anyone know for a wepsite to learn uni level integrals?

[deft crane]

you could try this one: https://www.khanacademy.org/math/integral-calculus/ic-integration

else you can find everything you ever need in university on youtube

[wispy orchid]

hey guys sorry if my english is not very good or if this math question is very basic but I need help to check if I'm right on this exercise. I need to check the limits of this sucession 3+(-1)^n.1/n just so we are on the same page for example for the 2n-1/n the limits are 1<=2n-1/n<2

[zinc dagger]

could you send an image?

[wispy orchid]

yes give me a sec

its in portuguese though its the 11.4.

[odd mist]

É limitada porque ao calculares o limite para n->+inf = 3 e não é monotona porque esse -1 vai estar a "mudar entre negativo e positivo" o que vai causar uma perturbação no grafico

[wispy orchid]

@odd mist Ah alguém português xD Nice. E está correto mostrar que é limitada desta forma certo?

[shut jolt]

c1?

[thin marten]

they have a rule that english (see #723133783573921852 ) should be used everywhere with exception to #non-english-chat

[hoary root]

1/0?

[halcyon crystal]

ok thankyouu!!

[simple glacier]

What is the name of the topic? Im passed high school but we did not have such questions here😶

[halcyon crystal]

its simply called application of integration😂

in my region tho idk for others

[odd mist]

Do you know how to calculate limits? It is way simpler proving it that way. What you have done there isnt right afaik because you are saying that n = 1 or n = 2 however, n = all natural numbers (and change that Un to Xn before your teacher kills you xd)

[odd mist]

That was my bad

[shell grove]

can someone explain this ping if u can

[simple glacier]

Yeahhh, Area under the curve and volume of some standard things ik, but didnt have any revolving regions..

[halcyon crystal]

ohh

anyways im sleeping now gl y’all

[simple glacier]

And i am tempted to learn that, but i got exam to cram🙂

[sharp ferry]

0<a<6 I guess

[shell grove]

oh bruh

[sharp ferry]

coz the graph of sec(x) and cos(x) meet exactly at 1 point

ie 2pi intervals

at 0 then pi then 2pi

so on

so basically to bring the graph of secx down you need to scale it down so that it can meet the graph at more points

[shell grove]

got it thanks

[wispy orchid]

ahah first of all thanks for trying to help :P. Secondly I'm not saying n=1 or n=2 😛 im saying that 2<=Xn<=7/2 but on my book says that its 2<=Xn<7/2 has you can see on this print and I think its wrong

[odd mist]

Ah bruh, I read it wrong mb
Nah, your book is right

You can prove it that way, yes

[wispy orchid]

so Im also right saying Xn<=7/2 instead of Xn<7/2?

[odd mist]

I guess so

I was not understanding your problem at all lmao

[wispy orchid]

ahah ty

im just confused has to why they put (<) instead of (<=) since 7/2 is a term of the sucession

[gaunt cobalt]

trying to come up with a rotation matrix that transforms the normal vector (0,1,0) to (a,b,c) using euler angles... anyone know how?

[woven orchid]

find an expression for the area of ​​the figure using this formula (a+b) / 2 * h

[left knoll]

wouldnt it just be ((a+b)^2)/2

h=a+b

area of a trapezoid

[drowsy rose]

anyone know how to find the inverse of h(x)= sqrt(x^3-x-6)

[cedar niche]

I speak another languange so I dont know what inverse is, but a lot of times i dont like to use sqrt but instead do to the power of 1/2. Its the same and it is easier most of the times

[lyric goblet]

inverse is a number power -1

[hardy sky]

anyone here good with drawing activity networks?

[dusky notch]

to find inverse, plug in y for all x terms and x for all y terms, then solve for y. so for h(x), you would say x=sqrt(y^3-y-6). idk if that is what you needed but yeah 🙂

[drowsy rose]

thanks maia, bit tricky rearranging it for y with that one, luckily turned out that I didn't need the inverse to work out the gradient of the inverse in the end so its cool

[viral roost]

@hardy sky like a computer science type graph?

If so use draw.io it's fire

[hardy sky]

like this

[viral roost]

Yeah draw.io

[hardy sky]

yeah its for my maths mock exam, so i need to know how to backwards scan and forward scan

[viral roost]

Wdym by those terms

[hardy sky]

so the number on the right is the forward scan and i dont remember how or what it is. The number on the left is the backscan

[viral roost]

I haven't really seen it mapped out like this before but from what it seems to me the numbers on the left and the right is the "cost" to travel from one "node" (a letter) to another. As an example, if you look at the RIGHT side of E and G those numbers match the LEFT side of H. This is the same for every "node" in the graph. The number in the middle represents the value of the "node" and depending on whether or not your supposed to count it you add that to the cost of travel. I'm kind of guessing here but what I'd imagine your supposed to do with a forward scan is find the LOWEST cost for traveling from A to K, and a backscan would be K-A. So, looking at the value of the nodes will allow you to do this. As a quick example, A-B costs less than A-C because the value of B is higher. The only route from B forward is to D, so you don't need to worry about that one. From D you can pick E, F, and G, the lowest cost here would be either E or F as they both have the same "weight" (the middle number). And you can kind of keep doing this over and over again. So the lowest cost forwardscan is A-B-D-(E or F)-H-J-K

[hardy sky]

life saver! tysm

[frosty raft]

Quick question. if it asks for the average density (it's just an example), could I get the average mass, then the average volume, and get the density off of that?
would the answer be different if I found 3 different densities and then averaged them?

[viral roost]

Should be the same as long as you follow order of operations. (A1 + B1 + C1)/(A2 + B2 + C2) = A1/A2 + B1/B2 + C1/C2

[frosty raft]

thank you :D

[dusk forge]

is anybody here really good at solving related rates/optimization problems?

[teal nebula]

someone know how could be this matrix jacobian ? fog(x)

[wispy parcel]

Anybody understand bearings and how to work through these two problems?

[dusky oasis]

bearing is an angle measure from the north clockwise Maybe try to draw it ? with the angles

[austere vale]

Any know how to start this problem? I’m in math(20 bring grade 11 level) 20-1 and this is the radical exponents application unit right now

[plush jasper]

You can set up set up 2 equations:

x+y = 25
1/x + 1/y = 1/4

Then it’s just a system of equations

[severe garnet]

^^ For one of the equations, solve for y and then substitute it into the other equation.

x + y = 25 becomes:
y = 25 - x

Therefore:
¹/x + ¹/(25-x) = ¼

[loud steeple]

You gonna find the numbers is 5 and 20

[austere vale]

you guys are goated, thanks so much

[plush jasper]

Np

[modest sequoia]

Guys, 4+4?

[plush jasper]

I think 9

[modest sequoia]

big help, man! 😁

[left knoll]

Lmao

[native mason]

can someone explain this problem a bit to me, like the conceptuals

[mental dragon]

critical points are where the derivative is 0 or undefined (the function is vertical for example).
looking at f(x), this seems to be a function that goes down, then up, then down again within this interval.
do you know which of the answers you can eliminate?

[native mason]

I know i can eliminate A, because theres no saying that the function can't go below 0

it also can't be C, because it might equal zero between 10 and 11, thought im not sure about B and D

[mental dragon]

Right.
Edit: Since this is a function that goes down, then up, then down again, the two critical points that the problem mentions have to be where the function changes direction. if f'(12)= 0, then 12 is the critical point where the function changes direction, but that can't be true - you can try drawing the function and see.

Regarding B, it's possible that the point where the function changes direction is V-shaped, so in that case, f'(x) would not exist at that point.

[rare island]

for part b the integral of each given parametric eq (displacement) when graphed is always below the x axis, and goes in the same x direction. does that mean that i just take the absolute value of the vector to get total distance if the direction never changes in x or y?

[dull imp]

anyone know probability

[native mason]

that makes sense thanks

[dusty token]

ap calculus ab test tmr?

[native mason]

so basically for B it doesn't necessarily have to be true because there could be a vertical slope or a sharp point cusp

yea

[dusty token]

gl

[native mason]

you?

[dusty token]

yep

[native mason]

gl too man

[dusty token]

feeling kind of underprepared but im gonna just go to sleep now and hope that everything goes well

[silk quiver]

If you want a clarification just message me

[silk quiver]

I can try

[heavy raptor]

can someone help me w this?? ^^^

[heavy raptor]

thank you so much!!😌 💗 💗

u saved me!!!😭

can I ask u something? @grave geode

[gentle axle]

are these questions asking different things?

like is a and c the same sort of question just worded differently?

[mental dragon]

for a) and b) you should multiply to get a number
for c) and d) you should divide to get a percentage
hope that helps?

[grave geode]

Sure!

[heavy raptor]

honestly i dont even understand it 😩

[gentle axle]

(this is not coursework or homework this is just studying btw)
Answers i got are
a)408.408
b)156.25
c)84.84%
d)124%
seem correct?

[grave geode]

Well, the way I solved, I think is the easiest. Honestly I don’t know other way to solve v,: But if I find I will tell you on private chat.

[wicked turtle]

Factoring difference of squares in binomials.
I need to find the common binomial factor of "m^2 - 4m - 45" (1st polynomail) and "6m^2 -150" (2nd polynomial). I factored the 1st polynomial and got "(m+5) (m-9)". And Divided the second polynomial with 6 and got "6(m+5)(m-5)" . and the answer is (m+5). My question is can I divide the second polynomial with some other number but not 6(like 2,3. etc) and get a common factor?

[sharp ferry]

guys I had a really weird doubt
If f (x)=(x+3)^2/(x+3)
and g (x)=x+3
Then is g(x)=f(x) ?
Because at the input x=-3,
f(x) is not defined whereas g (x) is,
so that means in in general:
(x+3)^2/(x+3) ≠ x+3

And now the implication this has is that we cannot divide polynomials because it changes the original function?

[silk quiver]

g(x) = f(x), the only reason why it is not defined when x=3 is because the denominator will be 0 but just like in getting the limit of a function, you need to simplify the function first before trying any value . In that case simplifying f(x) will just be x+3 then try any value

[sharp ferry]

But doesn't simplifying the function change the function? Coz a function which is not supposed to be defined at an input is now defined?

Sure limit x tending to -3 f(x) is x+3=0 but f(-3) is not 0

[random flame]

Eyo can someone help me with Q11b? Pls ping if you do thanks!

[gentle axle]

How do i work this out? I was assuming that it was essentially just doing 2/7 but apparently that's wrong according to the calculator. I must've missed something in a lecture

Like it can also be written as 2^-1/7^-1 right?

maybe i just don't understand how ^-1 works

oh wait yeah i was doing it wrong 2^-1 is essentially 1/2

so i do that to num and den and then divide those

[sharp ferry]

Basically take the reciprocal of the entire thing

So it's essential 7/2

[silk quiver]

I think your prof wants this way

[flint sage]

có ai việt nam ko ạ

cho em hỏi tí

any Vietnamese here

[random flame]

Thks thks

[heavy raptor]

heyy how did u do thiss?? now im confused huhu

[random flame]

@left knoll Yo rmb this Q? Here’s the solution

[barren venture]

In general they are definitely not the same function for exactly the reason you mentioned: f has a singularity (undefined point) at x = -3, g does not. Graphically f is a straight line with a “hole” at (-3,0), g is a continuous straight line.

About dividing polynomials, it is fine to divide polynomials as long as the singular point is not included in the domain (input). So in your example, if I’m only dealing with positive x values, then you can treat f and g as “the same” without encountering any problems.

[valid comet]

can someone explain this.
3r^2-39r+90

---

r^2-3r-70

the line is divide

i need to simplify

[manic hull]

3 (x-3) (x-10)

---

(x+7)(x-10)

= 3x-9/x+7

is it clear?

[silk quiver]

wait i'm solving it now

[heavy raptor]

ohh okay no worries 😌

[sharp ferry]

So if the domain is not mentioned in a question then we cannot divide a given polynomial just like that? Hdhwjajauwoqkajajnsjs

I saw this question as a true or false statement
(x+3)^2/(x+3)=x+3

So the answer should be false right?

[barren venture]

Without anything else, yea false

If they wrote an additional x not equal -3, then it’s true

[sharp ferry]

Yep they didn't mention anything

I inputted this to wolfwram alpha and it gave the out put to be true without specifying any conditions

I initially thought it was false then after checking with wolfwram I got confused lol

[heavy raptor]

thank you so muchh😣😣 I think this way is what my prof wants us to do.

thank u again to @grave geode for helping me out too! I think ur way is much more advance and I need to keep up first😢😢

[silk quiver]

no worries, glad to be of help🙂

[barren venture]

@heavy raptor just note that the solution above has a small mistake, there should be a plus in the ln, not multiply.

(I left out the a^2 because you can always multiply it back in at the end)

[heavy raptor]

ohh thank you so much!!🤗💗💗

[random flame]

Eyo can someone help me with Q2b? Ping if you do and thank you!

[heady patrol]

Ln(0) —> - infinity and ln(1) = 0 so when x = 2 then 3x-6 = 0 so ln (3x-6) goes to - infinity. When x= 2.33333... = 7/3 then 3x - 6 = 1 so ln (3x -6) = 0 so u just want to draw the ln shape graph passing through 7/3 as the root and asymptotic to -inf at x=3

[random flame]

I’m not sure which shape to draw actually

That’s all

Then the rest I can handle

[heady patrol]

Sorry x=2

[random flame]

Cuz the b value here isn’t positive

[heady patrol]

Ah ok

[heady patrol]

All ln graphs have the same shape no matter what is inside their bracket

[random flame]

B value is negative tho, how did you know the shape?

[heady patrol]

Is the b value ur talking about the -6?

[random flame]

By shape I meant by this

I just learned it today

[random flame]

Yes

[heady patrol]

The b part just tells u where to start drawing the function

[gentle heron]

its rely on a

[random flame]

a as in the x?

[heady patrol]

For any function f(x) if u have the same function but f(x+b) then u draw the function to the left by b

[gentle heron]

a=3>0

[heady patrol]

If u have f(x-b) then draw it to the right

[random flame]

Hmm okay

Thanks guys! ^^

[frosty geyser]

Hello, I am an engineering student and I am willing to help people in need for help in Math, (Calculus, Trig, Geometry, Algebra,...) My prices are relatively low, and the results are incredible. My tutoring will be through zoom essentially.

[winged ingot]

Hello anyone can help me with differntial equation

[rapid mantle]

what do you need help with?

[maiden sigil]

I dont understand this, I got answers no solution and infinite solutions

[silk quiver]

x = -24, y = 47

[valid kite]

Don't worry, @maiden sigil , there are multiple methods to the answer. Which one did you use? 🙂

[maiden sigil]

my teacher said just to use desmos since im not supposed to know this

[valid kite]

Did you use Matrices, or...? I have never heard of desmos...

[left knoll]

desmos is a graphing tool

[valid kite]

If I understand the question correctly, they want you to find whether these two lines intersect, don't they?

[maiden sigil]

yeah

[valid kite]

Well, I know two methods not involving the drawing of graphs, and...the graph thingy. The first one is the boring one, and I feel almost the...worst one:

Solve for y, and insert the obtained y in the other function:
-25x-10y=130
-10y=130+25x
y=(130+25x)/-10
Now insert in the second graph:
-41x-18 * ((130+25x)/10)=138
-41x+1.8 * (130+25x)=138
(25*1.8-41)x + 130 * 1.8 = 138
x = (138-(130 * 1.8))/(25 * 1.8-41))
We now find that x = -96/4 = -24.
y therefore becomes
y = (130+25 * -24)/-10 = -470/-10 = 47. As such, the lines intersect at x=-24, and y=47
@maiden sigil

[silk quiver]

using desmos

[valid kite]

-41x - 18*((130+25x)/-10)=138.

[maiden sigil]

oh I see

[valid kite]

Oh, THAT tool, @silk quiver !

[silk quiver]

Just a tip, if you're allowed to use a calculator like 991es plus, you can just easily type the coefficients and the answer will be shown

[maiden sigil]

oh ok thank you

[random flame]

Eyo can someone help me with Q2e? Ping if you do and thanks!

[violet mist]

do you need help with when y becomes zero or the graph itself? Try Geogebra app, its quite useful in plotting graphs. as for y=0 is at x=2.5. the equation inside must be equated to 1.

[random flame]

Erm I need working tho, hold on ima send my working

[violet mist]

cool

[random flame]

I got stuck, idk what to do now tbh

When I went to e^0=(2x-4)^4

It felt wrong -^-"

[violet mist]

wait

[random flame]

Oh damn I thought the 4 cannot be brought to the left hand side to be divided

[violet mist]

it's a constant

[random flame]

Ah k thanks man

[violet mist]

np 😄

[random flame]

Appreciate it

[opal bough]

Does anyone have any idea how to solve this equation? The series is weird.

[random flame]

BRO MY JAW DROPPED WHEN I SAW THAT- damn good luck with that

[opal bough]

If the |log(sqrt(x))| < 1, the series should converge. It would make sense, but I do not know the exact way to solve this.

[violet mist]

I got the answer as x=10..

[opal bough]

How?

[violet mist]

let me know if I'm wrong

[opal bough]

Yeah I get that, but in the exponent is 2^(n-1), so if n = 1, 2, 3, 4, 5, ..., the exponent of the log should be 1, 2, 4, 8 , 16, etc.

So the rule you used does not apply I think.

[violet mist]

Ah my bad, thought it was 2*n -1

[opal bough]

Maybe some substitution?

[wicked turtle]

can anyone clarify that simplifying 3x^2 + 30x + 75 is equal to (x+5)(3x+15) cuz in khan acadamy it said 3(x+5)^2 . am i wrong or both is correct?

[valid kite]

Let x be any real number, something about a sum of all log (root of x) to the power of 2(n-1)^, with n ranging from 1 to infinity. How hard is that to understand? 😉 (I don't know what the : symbol means in this question. nor do I have any freaking clue to attempt an answer.)

[valid kite]

3x^2+30x+75 = 3(x^2+10x+25) = 3((x+5)^2).

(x+5) * (3x+15) = (x+5) * 3(x+5) = 3 (x+5)^2. So they're equally correct.

[wicked turtle]

thanks mate

have a nice day

[valid kite]

No worries! Likewise! Algebra should be spelled Algebruh sometimes....

[wicked turtle]

ikr lol. i literally got 5 practice questions wrong because of this

[valid kite]

Try to break everything down in even smaller parts. That's why they tell you it's wrong.

Because, by breaking the equation into as fundamental pieces as possible, manipulation becomes easier.

For instance, it is hard to say what shape (x+5) * (3x+15) would be. It's a line multiplied with an even bigger line! Scary stuff. By simplifying, you make it 'obvious' what's going on here. 3(x+5)^2 is definitely easier to understand. It's a parabola. And oh, the 3 is saying the parabola is stretched over the y-axis! Now that's easy to understand. @wicked turtle

[wicked turtle]

correct me if im wrong, a parabola is if a graph is in the shape of U or something like that right?

[valid kite]

It is indeed! It is either an U shape, or an inverseU shape.

[wicked turtle]

Playing minecraft while in maths classes are hitting me back rn

[valid kite]

However, they can be stretched over two dimensions (assuming we're talking x,y only). So, the parabola won't always be that pretty to look at. But, they're usually symmetrically built. 🙂

(I say usually, because you can apply conditions in such a way which might mess up the parabola). Any function with powers can be written as a(x+b)^e. In this case, e=2, and the rest speaks for itself. 😉

But parabola's are very, VERY interesting, because you can use them to find out whether an area can be divided in whole parts! 😄

Alright, alright, I'll stop. 😛 Good luck, @wicked turtle !

[wicked turtle]

lol thanks mate

[valid kite]

Look up 'Lockdown maths 3blue1brown abc-formula' you'll be in for a treat!

[wicked turtle]

so the same things applies for this too?

[valid kite]

All polynomials can be written as n(x+b)^e. 🙂 So yes.

[wicked turtle]

cool, ik im just so dumb sometimes.

[valid kite]

I....don't think I know what binomials are... But that's probably because in our language, it has a different word for it. 😛

I remember one philosopher saying: 'Asking a question will make you look like a fool for one minute. Not asking the question will make you a fool for life.'

Well then, gotta continue now. Need to eat something. :p

[dense atlas]

Binomials are basically the coefficients that appear when you expand the expression.
Suppose (x+y)^2 = 1x^2 + 1y2 + 2xy
Here, 1,2 are the binomial coefficients.
In general, any expression that has 2 unknowns, viz. x and y here, is known as a binomial.

[wicked turtle]

not really

binomial is just a polynomial with 2 terms

[valid kite]

I leave this discussion to you both. I do have a book on algebra, which might say something about binomiality.

[wicked turtle]

this might show you better

[dense atlas]

I thought he's asking about binomial coefficients.
My bad!

[wicked turtle]

lol

[valid kite]

Oh, I see. Well, Raghs, it's then not true what I said!

Wait, huh?

Oh right, n, I get it now.

[wicked turtle]

👀

[wintry violet]

step bro im stuck

[wicked turtle]

imma pretend i didnt see that

[valid kite]

Well, see here: for n(x+b)^e, with e>2, assuming b is positive... won't give you a binomial system, I guess, after expansion...

[opal bough]

give me sec, i already encountered a thing like this

[valid kite]

Jesus, my eyes. Eeeeeh, I forgot how to do these. I recommend you have a look at the Calculus LIfe-saver, where they have a chapter devoted to working with logarithms (the only chapter you need from that book).

[wintry violet]

i'm not that im generally understand what i should to do in such cases

[left knoll]

i hope these r college questions cuz even though i finished high school i dont understand non of them

[wintry violet]

its look like this but the first one is easy

[wicked turtle]

@valid kite you mentioned you are not english, so whats your language lol?

[valid kite]

I'm Russian, but born in The Netherlands to a Russian/Jewish mother and an Iraki/Kurdish father.

[valid kite]

Wtf is that thing? Is crying an option?

[opal bough]

Yes, just find the solution for each one of them. I think it will be a range (an interval) of numbers.

And then find an overlap of those solutions (dunno the english words for the operations)

[dense atlas]

Is there any restriction on a? Does the question say anything about a?

[wicked turtle]

nice

[wintry violet]

yes

i need to solve this system of equations in terms of a

[opal bough]

a musnt be 1

then the log would break

[wintry violet]

with different a there will be different x

[dense atlas]

Yup, the range will be in terms of a.
If a>1 then we will proceed differently and if a<1 then the procedure will be different.

[wintry violet]

so i need to find correlation between them

[opal bough]

Just solve them separately, and then combine the solutions, cause the first one is easy.

[dense atlas]

See, if the question says that a>1 or a<1, something like that, then you can solve it using the single case.
If there is no restriction on a then you will have to consider two cases. One where a>1 and one where a<1. This would be procedure ig.

[opal bough]

And the second one needs to be solved for two cases depending on the base of the log.

Cause the inequality symbol changes if the a/x < 1.

I really don´t wanna do this rn, cause it seems like a lot of work.

I will send you what I got to dms.

[wintry violet]

but the base of log is always positive

so a/2>0 and a/2 /= 1

[ionic nebula]

help I'm stuck

[opal bough]

oh fu

i misread the problem

[timid delta]

in general If base is greater than one , then inequality holds , if less than one it just reverses

[opal bough]

yes, thank you

[timid delta]

Uh a>0 and not equal to 1

[ionic nebula]

help

[wintry violet]

also (x-a+2) should be positive as well

[timid delta]

Yes

[wintry violet]

and (a-1)

[timid delta]

Yep

Log of 0 and negatives are not defined

[opal bough]

but if the a<0 the sign changes
(edit: i meant a/2 < 1, but said complete stupidity, forget me lol)

[timid delta]

No a<0 then question is wrong cuz log of negative is not defined

[dense atlas]

w=-15 or -4/3

[timid delta]

a>0 and not equal to 1 if it's base

Cuz log of x base a Is = logx/loga

If a=1 then log a =0

[wintry violet]

so if

then

am i right?

[ionic nebula]

HOW

[timid delta]

No

a-1)^2

[dense atlas]

Complete the square or use quadratic formula.

[opal bough]

i am stupid

[timid delta]

Wait wait lemme write in detail to avoid confusion

[opal bough]

holy fuck

sorry

i am out

[wintry violet]

i got some very weird roots

so x∈ (-∞; a-1-√a^2-2a] U [a-1+√a^2-2a; +∞)

[timid delta]

Aah one more condition

a is not equal to 2

And greater than 0

[ionic nebula]

ok tq I was using cross

[timid delta]

You did wrong at the second step

Lemme check again

[wintry violet]

i seee

Fuuuuuuuu

[timid delta]

Should I solve?

Sorry for bad Eng tho

[wintry violet]

there should be 4x

[timid delta]

Yep

[wintry violet]

i was trying to solve this for 2 hours

☹️ 🔫

[timid delta]

Happens with everyone

[wintry violet]

thanks

for your help

[timid delta]

Yeah np

[tired crypt]

Hey ! How do you prove that 0,1 = 0,10 ? rigorously

[sharp ferry]

0,1=0,10 what?

[tired crypt]

Why 0,1 is equal to 0,10, why are they the exact same quantity ?

[sharp ferry]

What is 0,1 is it a coordinate, vector, matrix wym?

In what sense is 0,1=0,10

[tired crypt]

i mean 0.1 like 1/10

and 0.10

decimals

[sharp ferry]

Ahhhhhhhhhhh

[indigo sinew]

lol

[sharp ferry]

Ohhhh ohh why did you use , then

Lmao

[tired crypt]

sorry, in france we use "," for "."

^^"

[timid delta]

Hmmmm 1/10 = 100/1000 = 10/100

[sharp ferry]

Ah I see I got confused

[timid delta]

0.1= 0.100=0.10

[valid kite]

Where did the 2 go?

[tired crypt]

i agree with you, but why ? We learnt it that way, how do you prove it ?

[valid kite]

0.1 is NOT the same as 0.10.

[timid delta]

Atleast in maths it's same

Not in physical quantities

[indigo sinew]

It’s the same in maths and we learnt is that way tbh

[valid kite]

Decimals have to do with approximating an answer. The number 1 for instance, scale-wise in mathematics, means 0.5<1<1.5.

[ripe flint]

what

[valid kite]

Saying 1.0 for instance is the range of 0.95<1.0<1.05, which is VERY accurate.

[timid delta]

But it's not exactly equal

[sharp ferry]

I mean isn't this used in physics

[timid delta]

0.999999999999 is not equal to 1 but tending to 1 if repeated

[sharp ferry]

Then what is 1-0.999999999999999repeated

[ripe flint]

what am i reading

[indigo sinew]

Isnt it 1 if accurate to one dp?

[valid kite]

Mmmmm, I don't know. 0.9999999....*10 = 9.9999999.... and, if we take 1/3 of that, we get 3.3333333..... But 1/3 * 3 = 1, so 0.999......=1.

[valid kite]

It is 0.000000........

[valid kite]

Oh right. My brains are fried at the moment lmao

[tired crypt]

still a mystery why 0.1=0,10 in base 10 as decimals shits 😦

[timid delta]

Tending to 0

Not equal to 0

[tired crypt]

Thx ! it looks nice

[sharp ferry]

Why in the sense if you have a big cake and you divide it into 10 parts and take 1 part of it
It is as good as dividing it into 100 equal parts and taking 10 parts

[tired crypt]

yeah but in your exampl you postul that it's the same. It dos'nt prove it.

[ripe flint]

why does it say 2012

[timid delta]

Cuz I use old diary for rough work ;-;

[ripe flint]

what grade is this

of section or whatever

[sharp ferry]

Yea I mean you asked why are we taught that way so it was just an intuition

[tired crypt]

my problem is what to answer to a child who asks "why is it aqual wheras it's not the same". Like a 9 years old pupil

[sharp ferry]

What does it equal then ?

[timid delta]

Well science is studying universe not creating things so at the basic level something which cannot be explained is either it's common sense or it just happens as we don't know why universe behaves that way ( maybe we will find in future ) I guess

[timid delta]

?

[sharp ferry]

You said 1-0.99999999repeated does not exactly equal 0

[timid delta]

Yep

[unreal swan]

Anyone here have any knowledge in laplace transforms?

[valid kite]

It honestly depends on the accuracy you want. By adding decimals, you simply make the distinction between numbers sharper. But whether that truly helps the cause, depends. If we were to take a map, and divide it into equal square areas, we might find an area of 1010 to be divided by one square, 10 * 10. Now, let's say that this square represents the amount of women living on this dimension. Well, having a resolution of 1010 on a 10 * 10 map is...not very useful. But, if we take 100 squares, all of which have an area of 1 (1*1 length and width), we immediately see that in some areas, women live more than elsewhere. This is of course, a practical application of this distinction of decimals. The more decimals, the more accurate you'll see the area. But, if there's a lot of information, then the problem becomes something else; called uncertainty. If you were to increase the amount of squares per area, we see that there are more 'edges', which don't contain very accurate data.
TL:DR; increasing decimals gives more accuracy, at the cost of simplicity.

[wintry vessel]

hello, can you help me?

[valid kite]

https://tenor.com/view/nervous-sign-of-the-cross-praying-hoping-nico-santos-gif-10946409

I'm sorry, my mathematics isn't that good. :c

[sharp ferry]

I don't even understand that language sorry 😔

[valid kite]

HOLY SHIT I THINK I UNDERSTAND THE QUESTION.

[wintry vessel]

area between f and g

[sharp ferry]

What omg I think I can translate

Without help

[valid kite]

Consider the following: bla bla bla, f(x) = -3x^2 + 7x and g(x) = 4/x. Find the area of the region, if we enter the following values for x in both graphs. They probably want you to find the area of f(x), g(x) and the x-axis?

[sharp ferry]

And the integral is a hint?

Remember that log(t)= integral from 1 to t 1/X dx???

Gshsheheksk

[wintry vessel]

yes

[valid kite]

Yeah, I remember doing this crazy stuff two years ago. Screw linear algebra....

[valid kite]

Find the area of the integral from 1 to 1/x of the function log(t), with t ranging from 1 to 1/x. Crazy stuff.

[sharp ferry]

Alright I have to learn all about integration this year :')

I have just been introduced to integration through physics

And all I have done is simple integration :')

[valid kite]

Question about 2a: Is 7/2-4 log(2) = x?

[valid kite]

We had this terrible book, I still HATE it. It's by Boas or someone else...

@wintry vessel Gimme a second, I might have a book here which helps me out on this one.

[wintry vessel]

thanks, i have a calculus book

the exercise is a bit confusing

[valid kite]

No worries, we'll get there. 🙂

[wintry vessel]

The exercise is in Spanish, I live in Uruguay

[valid kite]

I'm sorry, @wintry vessel I thought I could help, but I don't know how to integrate a domain of all positive real numbers. :C

https://tutorial.math.lamar.edu/classes/calci/areabetweencurves.aspx Maybe this can help, but I don't know for sure.

[wintry vessel]

Thank you so much

[valid kite]

I can only hope it helped a bit. I have NO clue. Sorry. 😭

[wintry vessel]

thanks for your time!!

[timid delta]

Yeah, then?

[primal grail]

hi. what would you guys suggest me to do in order to improve my arithmetic skills? I have a big exam coming up in like 80 days. the exam is based on organic chem and there are a lot of calculations to be done. they allow calculators into the exam, but i am afraid that i will use it too much and waste too much time on it doing easy calculations. the exam is notorious for its short time frame. in organic chem there are mostly multiplications/subtraction, unit conversion, some logs. Thanks in advance...

[trail grove]

Since you speak Spanish, this may help you with any problems in the future. When I did scientific mathematics, well, all Spanish mathematics students in general loved this man, I hope he serves you, I think there are videos of absolutely everything

https://youtu.be/Rp94H7KG-oQ

it's not about your exercise but is this man

[wintry violet]

FINALLY I DONE IT!

[sharp ferry]

Yea then I meant
Is this statement wrong then
0.0000000000.......=0

[timid delta]

Uh no

[wintry violet]

but i have one more question

[timid delta]

Problem is where you did 9x= 9

[sharp ferry]

I didn't preset that proof

[timid delta]

Ohhhh

[sharp ferry]

I just asked one question what is 1-0.999999999....

[timid delta]

Tending to 0

[sharp ferry]

What can it exactly equal

It just becomes indeterminate then

[timid delta]

Never?

[sharp ferry]

But isn't this argument kinda trivial XD

[timid delta]

0.999999999.... is very very close to 0 but it's not equal to one exactly , we just take it as one cuz it's more significant

0.000000000000000 is 0 but we 1-0.9999999999999999999.... is tending to 0 , it can be 0.000(millions of millions of 0s ) and then 1

[sharp ferry]

Well consider this then the famous sum
1/2 + 1/4 +1/8....=1

[sharp ferry]

So will you say it does not exactly equal 1

This sum

[timid delta]

We get it's limiting value to be one I can say

Take an example

Add that series upto 100th term with calc

We get the answer close to 1

Increase more

Answer starts to tend to 1

[sharp ferry]

Yep it's limiting to 1 but if we have infinitely many it does indeed equal one

I mean start with a square of area one
Then divide it into 2 portions and then take one half and divide it into more halves

[timid delta]

Take an example

[sharp ferry]

Do this infinitely many times you still have the square

Well the thing is you cannot possibly divide it infinitely many times

[barren venture]

0.9... is precisely 1. There's a few different kinds of arguments that you could provide to show this. I'll provide 2 possible arguments below.

1. The real numbers have the property that if 2 numbers x < y are different, then there exist another real number z that is not x and y that's between them, i.e. x < z < y. We can easily construct this by having z = 1/2 (x+y). There is no such number between 0.9... and 1, so they must be the same number.

2. We can argue algebraically. We learn about the geometric progression, and in particular 1 + r + r^2 + ... = 1/(1-r), given that |r| < 1. In the case of 0.9..., we can rewrite it as 9 * (0.1...) = 9 * (1/10 + 1/100 + ... ) = 9 * 1/9 = 1.

[sharp ferry]

^ as well

[timid delta]

Hmm

[barren venture]

What you are referring to, @timid delta , is a partial sum, that is, you're taking a finite number of terms and summing them together.

However, 0.9... is an infinite sum, which is not the same

[sharp ferry]

Infinite sum must exactly equal to one

Yea

[barren venture]

https://en.wikipedia.org/wiki/0.999...

There are a lot of good arguments on this wiki page, feel free to have a look 🙂

[timid delta]

Ohk

I will thnx

[barren venture]

I tried my best to understand what the question is saying. Hope I interpreted it right, hope this helps.

[north geode]

guys u are AMAZING

[wintry vessel]

Thank you so much

[final island]

has someone a documentation (like a book or a pdf) to get started with combinatorics and probability calculation?

the one from my university is really bad

[pastel girder]

Anyone can help me with this problem?
An arithmetic sequence has 100 articles in it, the sum of second 50 is equal to 3 times the sum of first 50, if the first number is 3 (a1), what is the spacing between each number (d)?

[pastel girder]

I just have some 20 problems in combinatorics, but they are in Serbian and don't think they are of any help

[final island]

just give them to me. i speak bosnian actually haha

[sharp ferry]

(S100-S50)=3S50
50(2(3)+99d) -(25(2(3)+49d)) = 3(25(2(3)+49d))
I think it should be like this

Then you can solve for d from here

[dense wadi]

Please could someone explain to me how to find "nth term"

[sharp ferry]

4+2n+1 I think not too sure

[timid delta]

4+( (n-1)/2 ×( 6+(n-2)2))

[sharp ferry]

Wait no lmao

[pastel girder]

Yea that's what i tried, thanks, but when you try to solve it you end up with 99d=49d which is not true, you can see that cus S50 goes to the other side and with the other 3S50 you get 4S50 which is almost the same as S100 but you end up with that 99d=49d

[timid delta]

@dense wadi

If anything is incorrect then pls notify

[timid delta]

Ignore upper part , just second half ( from S1 part)

[sharp ferry]

50((2)(3)+99d)=4(25((2)(3)+49d))
(50)((2)(3))+(50)(99d)=4900d+600
300+4950d=4900d+600
4950d+300=4900d+600
50d=300
d=6 ????

What's wrong

[timid delta]

Aah I did a calc error

d=6

[sharp ferry]

I got d=6

Ye

[dense wadi]

@timid delta is what you wrote 4+n-1(6+(n-2)6*2)?

imma ask my teacher tomorrow, but thanks for trying, I appreciate you

[uneven zodiac]

whats 9 + 10?

[stark karma]

can someone help me set this up? i must be doing it wrong

[raven snow]

afaik they ask you to take the derivate for x=0, calculate the function value at x=0 and use these 2 to construct a linear function to approximate the function at value 0.5

[barren venture]

@stark karma You're trying to first find the equation of the tangent line passing through x=0. You should hence be evaluating the derivative at x=0, which will give you the slope of the tangent line.

[stark karma]

oh, one sec let me try it

[stark karma]

i took the derivative, plug in .5, i get .382 -> but how do i construct the linear function? i know the formula (y-y1) = m(x-x1)

[barren venture]

You need to plug in x=0, not 0.5

[stark karma]

what do i do after that exactly

[barren venture]

The number you get out of f'(0) is the gradient of the tangent line passing through x=0.

[stark karma]

got 1/4 from plugging in 0

[raven snow]

a linear function is f(x) = a + m*x. You know m when you take the derivative. Now you need to figure out a

[barren venture]

Ok, so now we have a line with gradient 1/4 passing through (0 , f(0)=2)

What's the equation of this line?

[stark karma]

never heard anyone call it gradient before

but uh

[barren venture]

Gradient, slope, whichever you were taught

[stark karma]

(y-2) = 1/4(x-0)

[barren venture]

Yes, so this line is now your approximation for the function f(x)

[stark karma]

o

[barren venture]

So we approximate f(x) as 1/4 * x + 2

And now using this approximation, what can you approximate f(0.5) to be

[stark karma]

using approximation?

like (fa)-(fb) / a - b

[barren venture]

Use your line to approximate the value of f(0.5).

[stark karma]

or you saying to just plug in0.5

[barren venture]

So 1/4 * 0.5 + 2

Yes

[stark karma]

but then you have an empty x

[timid delta]

4+(( n-1/2 )(6+(n-2)×2)

[stark karma]

(y-2) = 1/4(0.5-0)

oh

i dumb

makes sense

[barren venture]

This is what you're doing graphically

[timid delta]

That's not six , that was just I was cutting next to (n-2)

[barren venture]

Blue is f(x), purple is your tangent line @ x=0

So you can see your tangent line "splits" apart from the curve f(x), but we're saying that we can just use the line as a rough approximation

[stark karma]

i see

okay i got it. thanks for the help!

[barren venture]

There's a very easy way if you are able to spot it. You'll notice that if you take every term and subtract 3, you'll get the sequence 1,4,9,16,...,n^2. So the nth term is just n^2 + 3.

Spotting it without doing anything is kinda based on luck though, so below is a way you can show this properly.

[dense wadi]

probably luck, but i kinda saw it like it was right there

[dense wadi]

ayt, imma try it

[inland rain]

Can u help me with math

[charred marsh]

Can anyone help me,Josefa’s phone case costs 1.5 times more than Mia’s holster, Julia pays 1.80 more than Mia’s, and the three cases cost a total of 25.95.

[weary arrow]

@charred marsh

[charred marsh]

@weary arrow thank you my sister

[distant walrus]

check the role 👀

[stark karma]

is this b? i thought the inverse of -8 was 1/8 not -1/8

[frail geode]

@stark karma it is -1/8, since (-8)^-1 is equal to - 1/8

[stark karma]

woa genius dint think aobut it like that

[fiery widget]

How would you do this?

[frail geode]

wait ill write it down on ipad

[fiery widget]

tysm 🙏

[paper cypress]

what just (6+7)/2

?

[frail geode]

6.5

something to the power of 1/2 is equal to taking the root

[fiery widget]

oohhh

got it now

[frail geode]

nice

[fiery widget]

thank you so muchh

got a math test tmr so doing last minute revision :p

[frail geode]

ah you'll be fine

math is always the same concepts with different numbers

so as long as you understand the core concepts you'll do fine

[fiery widget]

just quickly

would i be able to combine the a^7 and the a^3 to a^10??

[frail geode]

yep

i just wanted to point out the root thing, youre correct

[fiery widget]

ah ok thank youu

hope you have a good day or night and thanks for the help 🙂

[frail geode]

ill be here for another 30 min i think, then ill go to bed

so if you have any questions just ask i guess

oh yes

to use l'hospitals theorem?

[native mason]

cause dividing by the reciprocal is the same as multiplying

[frail geode]

if you have 0/0 you can just derivate both parts and the limit doesnt change

obv you see, that lim x->inf of 1/x goes to 0 as well as sin(0) is also 0, so you can derivate both parts separately

so its the same as cos(1/x)*(-1/x^2)/(-1/x^2)

wait let me write it down

but the condition for l'hospital is, that as the limit there should be 0/0

hope thats clear enough xD

@left knoll are you a math undergrad?

oh lol

so this is an advanced math class then?

ah okay got it

if you need any help, you can shoot me a dm, ill try to answer it if im awake lol

[fiery widget]

How abt this one?

[frail geode]

^3 both sides and then transform for x

[fiery widget]

so 1/3 is the same as ^3?

[frail geode]

nah power 1/3 is equal to the 3rd root

[fiery widget]

ohhh but you ^3 both sides so the 1/3 gets cancelled out right?

[frail geode]

yeah

[steep jacinth]

what school do you go to

[fiery widget]

can you run through the last step of this?

im abit lost

[frail geode]

4^3 = 64, so 64 = 8x so divide both sides by 8 and voila

[frail geode]

i go to uni in germany

[fiery widget]

ooooh ok thank you

[fiery widget]

less go europe gang

[frail geode]

yeaaah

[steep jacinth]

Jimbo how old are u

[fiery widget]

15

im going exams for my gcses

but cause they got cancelled

were doing small tests here and there

[stark karma]

Can someone explain how to do this problem?

I feel like its parallel so same slope, then it gives you the points, so you can make a point slope formula for it

but im not sure how to get k from that

[stark karma]

wft i lookin at

[frail geode]

you take the derivative of h

then you put in -2

[pastel girder]

Oh, sorry dude, now i found the mistake 😂 i just forgot to divide with 2, thanks!

[frail geode]

the you calculate the gradiant of the tangent

and then they are equal and you solve for k

[stark karma]

ohh, ok lemme try

[noble jacinth]

Hey can someone help me with vectors?

I'm just stuck on b)

How do you find the value when parallel?

[frail geode]

its been a long time since i had vectors

but this should be fine

or maybe there is more p's

[noble jacinth]

hmm

[icy quiver]

Looks like functional analysis 🧐

[frail geode]

not really, i think they are parallel as soon as they have the same direction so i first find an a so that they literally are the same right?

and then solve for p

[icy quiver]

Should be unique

[noble jacinth]

I'm not fully understanding how you got the 2/3?

[frail geode]

oh you look at the other two equations

-2 = a*-3

and 4 = a*6

and when you solve for a, a is 2/3

[noble jacinth]

Ah I see

[icy quiver]

Two lines described by directional vectors u and v are parallel if and only if one directional vector is a multiple of the other

[frail geode]

yeah, thats why you have to find the multiple so they are pointing in the same direction

[icy quiver]

Yeah, theoretically you're solving the linear equation, but in this case p isn't in every component and you can see directly the 'a' you're looking for

[frail geode]

yeah okay, so p is unique

i was just thinking about way too much xD

oh fuck i made a huge mistake

[noble jacinth]

Yeah lol

I saw the answer

[icy quiver]

Haha, i get that every time you return to school math

[noble jacinth]

But still want to know how lol

[gray cipher]

Can someone help me out with probability what do I even do

[frail geode]

in the first you dont divide by 4!

[gray cipher]

how comr

come

[frail geode]

because the order matters in this case

so you dont divide by the amount of ways you can play it

[icy quiver]

Depends if you understand the exercise to imply that the order of the games matter

[noble jacinth]

Thank you I get it now

[frail geode]

great!

[gray cipher]

so if im not dividing by 4! what would i do>

?

[sullen locust]

i think you would just do 15x14x13x12

[frail geode]

simply 151413*12

[gray cipher]

what would the problem look like if the order didn't matter?