math-help

[boreal bridge]

In the manufacturing of a product, the cost, in reais, to produce q units is given by:

𝐶(𝑞)=0,1𝑞^3−3𝑞^2+36𝑞+100

(a) Obtain the marginal cost function

Answer:
Cmg = 0.3q2 - 6q + 36

I just want to know how can I get to this answer exactly

[frosty fog]

divide numerator denominator by e^y
1/1+e^y becomes e^-y/e^-y + 1

[past sand]

You could get the marginal cost by differentiating the cost function.
d = 0.1q^3 -3q^2 +36q +100
Hence d/dq = 0.3q^2 -6q +36

[left knoll]

https://media.discordapp.net/attachments/1042878117343154206/1042878117569634364/image.png

can someone help me out with this please?

[honest canyon]

Negative degree x^-y means 1/x^y so you can inverse the fraction and get this one (2x^3y^5)^3/(4x^2y^4)^4. After expanding the brackets it becomes 8x^9y^15/256x^8y^16. After simplifying the fraction we'll get x/32y so p = 32 and q = 1.

[vapid ocean]

Can someone show me how to enjoy doing mathematics? I always dislike them because of how they're written.

[glacial dust]

can someone explain to me how to union a natural numbers to a set that does not have ay specified elements in it?

please HELP

am desperate lol

[orchid osprey]

im not sure what you exactly mean but,
basically its asking to create a union of set of natural numbers and a set containing a single element '0'.
so this union will give you the set of whole numbers.
also not sure how we can specify the cardinality of the set of whole numbers cuz it has infinite numbers.

[orchid osprey]

I've always found that if I understand it, then I can enjoy it, no matter how ridiculous the symbols used are😆

[sour matrix]

@left knoll

[glacial dust]

its finite

theres a limit to the set but I don't what it is though

can someone help please

this is taking me days to figure out lamao

anyone whos expert on sets n relation

[nimble juniper]

can someone help me? How do I prove the following statement: A_0 is a subset of A. The statement is: A_0 ⊆ f^−1(f(A_0))

[late root]

hello

can someone please help me out with this one

at first i thought it was something with sin cuz of the inverse rules but apparently it isnt

[exotic cobalt]

= square root of (1-x^2)

[sour matrix]

@late root

[exotic cobalt]

@sour matrix Dont Forget Plus C

[sour matrix]

OOHHHHSSSSHHTT

Bro i was studying trigonometry

i never forget again

[late root]

wait but why is that 1-x^2 = u^2?

[sour matrix]

For square root

Just for same degree to make easier operation

[celest berry]

hello

[median grotto]

Matrices question

Any ideas?

[median grotto]

but we dont calculate detA*A^T

we need to proof that det A = 1 or -1

[ember garnet]

if you take the determinant of both sides and apply the properties, in the end you will get (detA)^2 = 1 therefore detA = +-1

[glacial dust]

#math-help message

help..

[glacial dust]

#math-help message

help

[sour matrix]

I tried a lot things but didnt work...

[ember garnet]

did you try https://www.integral-calculator.com/ ? :P

[sour matrix]

oh first time i see this👍🏻 Thank you so much😍♥️

[lusty hare]

I need some help in math but if someone can teach me in French please, thanks for the order

[fiery pecan]

Hi can someone help to, determine the value of the constant a so that:

[wanton river]

"a" can't be a real constant . But dropping the constant constraint we can get a function that works .
a = 5^(-x) works and it does give 4 as outcome.

[soft lintel]

How can I proof that this series converges

[dreamy oasis]

How many different (x,y,z ) integer triples are there that satisfy the equation
|x|+|y|+|z|=9 ?

Can someone help?

[wanton river]

First find solution when x , y , z all are strictly positive . Then notice that if (x,y,z) is a solution then all possible other 7 combination where atleast one of x,y,z is negative is also a solution. So multiplying the answer with 8 gives you number of total solutions when all three of the variables are
Non zero

Now set x to zero and find the number of solutions when y and z both are non-zero. multiply the number with 4. Then notice there are three variables so we need to add the number of solutions when we set y=0 , z=0 separately as well.

Then set z=0 and y=0 then find number of solutions(here x is non zero). Do this for all three possible combinations of variables. Find the individual answers.

Now add everything that you found in the previous three steps to find the final answer.

@dreamy oasis I hope this helps

[halcyon monolith]

I need some urgent help guys

Anyone there?

[rotund vessel]

if the limit is zero, then the series converges

[ember garnet]

That's not true because, as a counter example, the harmonic series diverges

[rotund vessel]

exactly, that is, a series is called convergent if there is a finite limit to the sequence of its partial sums

[ember garnet]

That's true, yes. But your previous picture means that the limit of the sequence is zero.

[rotund vessel]

I just can't change the picture, so I'll delete it and send this

[soft lintel]

Is someone familiar with the equation(1+w+w^2) that this guy used in order to factor this polynomial ?

[ember garnet]

you must use a convergence test to prove it. Use the ratio test, it works out.

[soft lintel]

Yeah that's what I did and it was less than a convergent geometric ty

[solemn vessel]

what is your question exactly?

i dont understand

[soft lintel]

what is w is it i ? and how did he know that 1+w+w^2=0 ? @solemn vessel

[solemn vessel]

honestly just looking at the screenshot you sent Im not sure if I can tell what they are solving

are you trying to find the roots of x^2 + x + 1?

[soft lintel]

yeah that's what hes doing in the video

[solemn vessel]

if thats the case, why not just use the quadratic formula?

here w is -1

[soft lintel]

well it doesn't give me a neat factorisation like

[solemn vessel]

if you complete the square

im confused

as to why they are adding it

that w

[soft lintel]

w^2=-1 so w=i right ?

well if that is not the usual way to go then I'll pass on that video thank you anyway @solemn vessel

[solemn vessel]

I think you should use quadratic formula

if you are solving for x

it wont yield real solutions, they will be complex

(-1 +/- sqrt(-3))/2

[soft lintel]

thank you

[solemn vessel]

Right?

Unless you are not just soliving for x

can you link me t hat video? I am curious

[soft lintel]

yeah sure

https://youtu.be/A8y6VAzMepU

[wanton river]

He is using complex number field to do the factorisation.

That equation is strictly positive in real number line.

That omega is a complex number.

[soft lintel]

thanks I think I get it now

[left knoll]

Can someone please help me simplify this in terms of n?

[steep citrus]

Idk what I’m doing wrong

[hallow vault]

Sorry for interruption. But I badly in need of some info. I guess, there are many people here who took online courses for Calculus and aced Calculus after. So, is there anybody who can suggest me the best Calculus-1 & 2 free courses online?

[dreamy oasis]

Hey @wanton river thanks for explanation but ı didn't get the point why we have to multiplying with 8?

[wanton river]

@dreamy oasis well you can add as well. Multiplication is addition in natural numbers right.

So I did it in shortcut.

[dreamy oasis]

But why with the 8?

[wanton river]

Well there are 8 total cases

Let me explain ☺️

(+x,+y,+z);(-x,-y,-z);(-x,+y,+z);

(+x,-y,-z);(+x,-y,+z);(-x,-y,+z);

(+x,+y,-z);(-x,+y,-z);

Now do you see why 8 ?

[dreamy oasis]

Ohhh now ı got ittt so we find the 3 numbers to put x,y,z and multiply 8 bcuz of - nd + right??

[wanton river]

Yes exactly

[dreamy oasis]

Thank you so much for explanation 😊

[wanton river]

Btw where did you get this question

This type of questions come in Olympiads mainly.

[dreamy oasis]

Well, ı am prepearing a hardcore exam that's why ı want to learn how to solve these hard questıons. Probably this question isn't hard for u but for me it is hard really.

[wanton river]

Well math is hard . That is why I like to do it. This problems was infact beyond my reach once but not at the moment. The bottom line is just try and you will get it. Best of luck for your hardcore exam.

[dark tendon]

why 1 + 1 = 2

someone help me

[wanton river]

it is a "sign" nothing else.

[rotund vessel]

https://youtu.be/5cQF_gx0Ftk

[wanton river]

Reasoning is circular in nature. So video is a bs.

[proper venture]

I need help in these questions

[fast otter]

someone pls help

[pure crescent]

Did you get it right?....if not lemme know

[cedar pecan]

anyone know how to solve this

[dark tendon]

thank you so much

[rotund vessel]

the most important thing is to simplify correctly

[wet minnow]

ı just see sin2/c=1/c2

[north pecan]

here is what i could see

[unborn igloo]

anyone know a good way i can study for calc, plan on skipping ab next year and just going to bc

[pulsar turret]

For this limit, why didn’t I just substitute x for 2 to get 8 as the limiting value? Why did I construct tables and calculate different values as the function gets closer and closer to 2?

[north pecan]

i think they're trying to head you know about the graph because the graph play an important role on the limit, i guess so. you are not wrong buddy

if you give me some more detail on your note maybe i could know what are they meaning to .

[solemn vessel]

they are likely trying to give you a feel for what is happening as the graph of x^3 approaches 2 instead of just telling you the answer. indeed since x^3 is continuous we may plug in 2 and get the answer, but since you are just learning about limits, it is helpful to test other values to aid your understanding of the concept of limits

[solemn vessel]

you can probably find a full course for free on youtube. if you prefer books there are tons of beginner texts that you can use to self study

[unborn igloo]

Aight that’s what my teacher recommended, is there any websites like leetcode(it’s a cs website) where you can practice at like any skill level?

[solemn vessel]

hmm.. not that I am aware of

[sage cobalt]

Hi! I really need help in understand this problem

particularly part b

[left knoll]

Hello everyone ! I find that there is no solution for this question. Is this true or is there one? Thanks a lot !

[ember garnet]

you can prove it by induction

[ember garnet]

you can solve the diff. eq. in (a) with the condition that u=1 when x=1

[left knoll]

But I’m not sure how to show it in the right way

[frozen hare]

think anyone could hop into a break time call and help me with exponential functions at some point tonight?

[unborn igloo]

what do u not get?

[frozen hare]

nevermind im good now my friends gonna help thank you tho!

[left knoll]

But isn’t the basis step wrong ?

[ember garnet]

it's true for n=1

1^2 + 2^2 = 5
1*(2+1)*(4+1)/3 = 5

[left knoll]

Ho yeah thanks a lot but how can we do the inductive step for the left hand side ?

[ember garnet]

left hand side will be 1^2 + 2^2 + 3^2 + ... + (2n)^2 + (2n+1)^2 + (2n+2)^2

[left knoll]

Oh yes now is see, thanks a lot 😄

[ember garnet]

yw:)

[ember garnet]

if your roots are r1, r2, etc. then right it in the form (x-r1)*(x-r2)*(x-r3) and then just expand and simplify.
if a root has multiplicity of 2, then right (x-r)^2 for that root only and then expand again.

yes

yeah just write (x+2+i)(x-2-√2)(x-2+√2) and expand

just expand the two parentheses first using this rule: (a+b+c)(e+f+g) = ae + af + ag + be + bf + bg + ce + cf + cg

some terms will cancel out

this is the final solution

you're welcome

[smoky knoll]

I need to find the derivative

Help pls

[ember garnet]

set the function in the parenthesis equal to u and apply the chain rule

[hushed wadi]

4[(1-5x+x^(3))^3][-5+2x^(2)] is this the answer?

[exotic dagger]

Anybody here familiar with linear algebra?

Specifically the spectral theorem

[charred mountain]

Guys can you give me some tips to improve my arithmetic... it's not good at all...i mean I'm a non maths student preparing for exam where 1/3 questions of maths come

[mild plank]

Just start with the basics, do some exercices

and it will come from alone

[exotic dagger]

Just spectral decomposing a symmetric matrix

Like given symmetric matrix A, find Q, M, such that A=Q•M•transpose(Q)

[still panther]

prove that t[X → Y ][Y → X] = t

t is a Boolean term

I have to use Structural induction

[vocal ruin]

Now Playing

Horror Girl Screaming - Sound Effect

Added by Mahin#1149

[left knoll]

:>

[small python]

wtf

💀

[left knoll]

Salam

[dusty hill]

Salam brother

[sour rapids]

(x-360)=3/5 (y+360)=4560

im stuck on this

[solemn vessel]

what dfo you want to do with it?

@sour rapids

[sour rapids]

i need to know x and y

[gaunt niche]

X= 4560 + 360

X = 4920

(4920*(5/3))-360 = y
7840 = y if I’m correct

[rotund vessel]

you had in mind such a task, if I understood correctly?

[grizzled lotus]

How to do number 2

[next plover]

let the number of floors after the first be X
this means that the total cost of cleaning X floors will be 100 + 50X
then just use that formula for the two situations

[heady vault]

does anyone know on what basis I'm supposed to select the coefficients

This is my Numerical Analysis hw btw

[short rover]

plis help how?

ping when replying

[smoky knoll]

Someone help

[hushed wadi]

can you send the first part of the question too?

[sacred gull]

Soo this looks like an AP to me (arithmetic progression)
STEP 1: make it look like an AP
Let first floor cost be X. Let the number of floors be n
Cost = x, x+ 50, x + 2(50), x + 3(50)…x + (n-1)(50)
STEP 2: APPLY THE AP FORMULA
Cost of floor 50:
Formula: xn = x + (n − 1) × d
xn (floor 50) = 100 + 49(50)
Solve.

STEP 3: SUM OF ALL TERMS
Apply formula: Sn = n/2[2x + (n − 1) × d]
S50 = 50/2(2(100) + 49(50))
Solve.

[sacred gull]

.

[glass swallow]

Anyone??

[ember garnet]

can you use complex numbers?

[glass swallow]

no

[ember garnet]

you sure? it's pretty tedious without them

[glass swallow]

110% bro
nd it is of high school level

[ember garnet]

so what other tools do you have?

differentiation? trigonometric identities?

you need to solve for K and find its range

[glass swallow]

trigonometric identities

[ember garnet]

ok then these are the trig identities you need

[glass swallow]

oh okiee

[mild pier]

Can anyone help with this

The answer should be 11

[solemn vessel]

what’s the question?

if it’s division, are you allowed a calculator?

[left knoll]

Translation:

give the recursion as a sum using a summation factor and use this sum to calculate the value for x2. you do not have to break down the summation display any further

Maybe someone can help me ??

[left knoll]

Got it thank you

[cedar storm]

Hey, anyone know how to calculate the expected value, that looks like this?

[digital galleon]

Can anyone help me with this ?

[lethal hill]

why is this mans multiplying both the top and the bottom by 1/x

[dreamy oasis]

sorry for bad english

[ember garnet]

The probability that the 1st person is a girl in red costume is (3/6)*(3/6) = 1/4 (it's 3/6 for the prob. to be a girl and 3/6 for the prob. to wear a red costume).
Now, for the 2nd person, since the 1st one has to already be a girl in red, there are 2 girls out of 5 people left and 2 red costumes out of 5 total costumes, so the prob. that the 2nd person is a girl in red is (2/5)*(2/5) = 4/25.
Finally, you multiply the two probabilities to find the prob. that both the 1st and 2nd people are girls in red. (1/4)*(4/25) = 1/25

[dreamy oasis]

Your solution is very nice and explanatory, thank you very much.

[ember garnet]

you're welcome :)

[left knoll]

If f is continuous, is its inverse also continuous

?

[warm axle]

if f is continuous, it also needs to be one-to-one (injective) for an inverse to occur. so yes, if the inverse exists (if f is injective) and f is continuous, then the inverse is continuous

for a function to be one-to-one, google the horizontal line test

[left knoll]

Τhanks

[left knoll]

yo so as we know anything divided by infinity tends to zero so basically he is dividing by 1/x so that numerator 8-5/x remains and here as x tends to infinity 5/x will tend to zero similarly in the denominator also hence we will be left by 8/2 or 4 as our final answer

[left knoll]

um no it will be 22

[mild pier]

That’s what the book says

[left knoll]

cause ur left with two √ 2 and multiplying we get 2 and 11

[left knoll]

make 242 factors u will get (2*121)^1/2

121 is square of 11

u can take 11 out of the root

u will be left with √ 2

multiply with other√ 2

u will get 2

[vale trench]

Can anyone solve questions of partial derivative?

[woven orchid]

ok how di solv this
This entire exercise must be solved in CAS. Finn von Flugenbinder funds part of his hobby by tying fishing flies which he sells online. The weekly sales of the number of flies f(x) varies throughout the first year (52 weeks), and after x weeks is given by
f(x) = 0.006x^4 - 0.07x^3 + 2,2x^2 - 8.2x+22
b) Use CAS to find in which week the increase in sales was greatest? How many flies
he then sold per week?
and last question is: use CAS to find how many flies he sold that whole year?
i dont get how i am supposed to solve these?

[woven orchid]

anyone pls?

[ember garnet]

It's divided, not multiplied

[left knoll]

oh didnt saw that it may be misprint then

[woven orchid]

anyone can help?

Finn von Flugenbinder funds part of his hobby by tying fishing flies which he sells online. The weekly sales of the number of flies f(x) varies throughout the first year (52 weeks), and after x weeks is given by:
f(x) = 0.0006x^4 - 0.07x^3 + 2,2x^2 - 8.2x+22

a) find how many flies he sold that whole year?
b) find in which week the increase in sales was greatest? How many flies
he then sold per week?

quick help

[ember garnet]

a) it's the integral of f(x) from 0 to 52
b) find the x for which f''(x)=0 and f'(x)>0

[woven orchid]

THANK YOU!

[left knoll]

think of it as factoring out x from denominator and numerator

[random moat]

can anyone help me with this?

[woven orchid]

When i did the integral of 0 to 52 of f(x) i got 10841

[clever talon]

Can anyone help me with no. 7 plsss

[ember garnet]

both sin and cos are bounded by 1, so for the sum of their squares to be 2, each of them must be 1. So a+b = 90 deg and a-b = 0 deg

[clever talon]

Bounded by one as in?

[ember garnet]

the sine or cosine of any angle can't be larger than 1. 1 is the max value of both the sin and cos functions.

[clever talon]

Why r we taking max value

[ember garnet]

because it's the only way that the sum can equal 2

if A and B can take any value between 0 and 1, A+B=2 is true only if A=1 and B=1

[tropic smelt]

any math websites to help out with IGCSE Edexcel furthermaths

[worldly copper]

Hey guys can someone help me with this one

[fierce light]

Anyone knows why lim x->oo log(xsin(1/x)) = 0? If i put the limit in shouldnt it be log(0 x oo) which is undefined? Tks in advance

[winged trellis]

what is difference between dot product of 2 vectors and scalar resolute?

[rustic shuttle]

Do you know that lim x->0 of sin(x)/x is 1?

[brazen wagon]

hey

phisics questions are here?

[carmine basin]

how do i do this?

No carrots are red fruits.
Some fruits are carrots.
Therefore, some fruits are not red fruits.```

[fierce light]

OH RIGHTTT thank youu

[cerulean elbow]

can anyone help me solve polynomial equations?

(3x^4 - 12x + 15) ÷ (x + 1) using long division

[stark onyx]

hope it helps

[pliant agate]

I can translate this can someone help

2

[normal finch]

valid

[carmine basin]

thanks

[flat charm]

I am in yr 9, any ideas on what math progression I should be doing?

[sweet karma]

Hope this would be helpful

Excuse my hand writing

[scenic silo]

Help pls I dont get it

[runic garden]

@here Come we need help

come chill room

[drifting saddle]

,tex ?

%tex something %?

a study server wo textit

meh im out

[worn lava]

i get how to get the cartesian eqn but does anyone know how to solve for domain

[stone hemlock]

how

[grizzled gorge]

rip quality

It's basically applying the addition property of the log function, the rest is just changing variables

[stone hemlock]

thank you for your help

it must have went over my head in class but i didnt know you could do that lmao

[grizzled gorge]

no prob

the general rule is log(a . b) = log(a) + log(b)

and if you are curious this is the full list

[autumn glacier]

Quick question when I’m doing the quadratic equation between roots of m.l can I put brackets between the numbers in the addition? Or is it not allowed? Cause I asked a few people some said I’m only allowed to write it during the multiplication and others are saying we can’t

[sand night]

could i have some help with this question? i struggle with order of operations stuff

[winter grail]

you can but you dont need to because + is associative

[next plover]

im not sure if it is order of operations but in what step do you exactly need help in?

[sand night]

like i get you have to make it equal y and then sub into the second then solve for x… im just having trouble simplifying it

[next plover]

ahh

if you dont mind showing your current solution?

[sand night]

ok gimme a sec i gotta get my book right out

this is the one solving for x

i hope my handwriting is somewhat legible lol

that’s what i got up to

i just need help like simplifying it in the right order

[next plover]

hahahaah it took a while for me to get p and b HAHAHAHA

umm okok

so from that step isolate x once more

[sand night]

sorry i’m australian lol

[next plover]

ok no offense but idt that is related but its fine hahaahha i have horrible handwriting too

[sand night]

oh oop i thought it was like the connected p and b thing

cos i don’t connect mine

[next plover]

ahhh okok

anyways from the last line of your solution

isolate x

[sand night]

ok

[next plover]

so if i distribute the coefficient a i will get
=tex bx - \frac{ap}{b} - \frac{a^2x}{b}

=tex bx - \frac{ap}{b} - \frac{a^2x}{b}

wut the math bot doesnt work oh no

[rotund crypt]

Hey, can someone help me with this problem? "Being t(x) continuous and lim x->5 t(x) = 3; analize the continuity of h(x) = (sen(3-t(x)) / (tg(t(x)-3) in x=5 "

[raw hollow]

I suppose sen is sin right?

[raw hollow]

if it's really sin then u have

I accidentally inversed the stuff inside the sin and tan but it's fine you get the idea!
So I guess you can conclude by yourself after that!

[wraith lodge]

can someone help me with this?

[misty hatch]

from each point draw a straight vertical line and if any of the lines intersect it isn’t a function i think

[coral mountain]

https://youtu.be/wZ9QIeWKStQ

[coral mountain]

https://youtu.be/PqqcwSUoQmA

[surreal flint]

<@&942391219206647828> spam ^

[pale meteor]

ayo who's out here studying for AP Stats?

i made a basic notes that covers all that important formulas and points

DM me if any of yall is interested

[subtle sluice]

Can anyone help me find the sequence formula for

I got this but it doesnt work for n=1 or n=0

[misty hatch]

what about n/(n+1) for the second part

[subtle sluice]

i got the answer

[hazy seal]

how did you get it

[normal iris]

Can someone help me with this?

[lapis pecan]

do you have the final answer for a? then maybe i can figure out the steps

[ember garnet]

is the answer a≈28.97 ?

[topaz geyser]

plz can anyone solve it?

[lapis pecan]

thats what i got too

[subtle sluice]

Trial and error

[hazy seal]

can you show the answer

[potent moth]

b

cosecA is 1/sinA and 1 - sin^2 A is cos^2 A . Put these formulas you will find your answer

[left knoll]

it would be A option then

[potent moth]

Yes yes exactly my mistake 😅😅

[distant vault]

Hi everyone, im new here, i just want to know how i can understand math questions, i know how to do math but i cant understand the question

[raw hollow]

Hey do u mind giving an example?

[distant vault]

Im not good to interpretate the question, even easy ones

I just cant give an example because its in portuguese

But my problem is with interpretation

I know all the formulas but i dont know when i need to use it

[potent moth]

So, have you any language issue?

or the technical terms used in the problems?

[potent moth]

I mean do you want your mathematics problems in english, is that you want to say?

[distant vault]

no no, i speak portuguese

[distant vault]

this

[potent moth]

Ok in which chapter are you facing these types of problems

???

[distant vault]

''A company rented a sports court to a group of co-workers for a fixed price. If the rent is divided equally among 20 people, each will pay n reais. However, if the division is between 16 people, each one will pay n + 6.50 reais. The value, in reais, of the rent of this block is equal to:''

i used translate

questions like this

its easy, but my brain doesnt know how to solve it

when i see the solution after trying i feel useless bcs its so easy

[left knoll]

try and visualise this types of questions, sentence by sentence, rather then just trying it mathematically

[remote linden]

I do the opposite, I rewrite the question to mathematical equations, meaning first line: rent = 20 * n, second line: rent = 16 * (n + 6.5), and then after that it's clear that I just need equate both rent expressions to find out the solution.

[left knoll]

oh, everyone owns different method tho, visualisation of word problems helps me out

[remote linden]

yeah I know, could definitely see yours be more beneficial, just sharing mine in case it helps

[distant vault]

Yeah i started doing this

I think i understand a little better now

I doing math questions everyday to understand how the questions works

I only have 2 months to learn

[raw hollow]

I used to draw the problem simply in order to better understand it before doing anything serious, i still do it now but in my brain, maybe you can try that??

[potent moth]

Ok do you watch movies or any reality show or any normal films?

If you do so you can imagine it

For eg forget that this question is saying you to pay n reais. Let's say it's saying something familiar to 20 and 16. Let's say 80. Now imagine,

If 80 reais is to be divided among 20 people each people have to pay a rent of 80/20 i.e 4 reais.
Similarly, if 80 reais is to be divided among 16 people then each people have to pay 80/16 i.e. 5 reais.
It means if there will be less amount of people then the amount will be more for each people and if no. of people will be more, it means amount that has to be paid by each one is less.
Now after you understand this concept now you can feel the variables too.

I know this is a large paragraph to explain but I tried my best to use simple words.😅

Now, like this, you should firstly feel the question in your real life then you can easily solve every ques. And don't rush into it. Take small steps, you will grow everyday.
A long jump can't always needed to be successful.

So firstly take small steps

And solve questions by feeling it.

I hope it will help you 😅😅😅 @distant vault

[potent moth]

And yes most important thing don't look at the solution until you tried atleast once it with confidence.

[glossy sparrow]

bade?!?!

[timber night]

🤫

[glossy sparrow]

ogae

[solid falcon]

can someone help me with the integral in the last row? i can't solve it
don't mind the steps above, i checked with the textbook and they are right

[left knoll]

you didnt notice me😔

[glossy sparrow]

tera naam search kiya maine but nai aayi tu

[left knoll]

oh😔

[undone helm]

x=e⁻ᵗ
y=t³ given by the parametric equation y = f(x) for fonction yᵗ = fᵗ(x) ?

A)3t^2/e^+t
b)-3t^2/e^+t
c)-3t^2/e^-t
d)-e^-t/3t^2
e)3t^2/e^-t

[sick cave]

yo what is a kernel and image for in linear algebra

[gentle creek]

do you still need help with that?

[undone helm]

yes

[limber pagoda]

The kernel (also known as the null space) of a linear transformation is the set of all vectors that are mapped to the zero vector by the transformation. It is the set of all vectors x such that A(x) = 0, where A is the linear transformation.

The image (also known as the range) of a linear transformation is the set of all vectors that can be obtained by applying the transformation to some vector in the domain of the transformation.It is the set of all vectors y such that y = A(x) for some vector x in the domain of A.

||https://math.libretexts.org/Bookshelves/Linear_Algebra/A_First_Course_in_Linear_Algebra_(Kuttler)/09%3A_Vector_Spaces/9.08%3A_The_Kernel_and_Image_of_a_Linear_Map||

[limber pagoda]

So I am assuming you know calculus as you need to use derivatives to solve this.
(1) Take the chain rule
y = f(u) and u = g(t) and dy/dt = dy/du * du/dt
(2) Plug in with respect to the chain rule
y = t^3 and u = e^-t
(3) Take the derivative and solve
dy/dt = 3t^2 * (-e^-t) = -3t^2 * e^-t

Are you sure that's what the question is asking because I got something close but not one of the choices

[sick cave]

thank you, you beatiful Lettuce!!

[gentle creek]

dm me

wait nvm

acctually yeah sure dm me, its easier to do it trough voice

oh nvm i just saw the other guy's explanation

[ashen lagoon]

So I'm a complete beginner at math. I never really got taught it at school, but I want to learn. Should I start with the basics? Like multiplication and division?

[indigo ruin]

Yes, and building a good foundation in math, from the most basic subjects to the most difficult: addition, subtraction, multiplication, fraction and division is the beginning, start practicing these simple subjects and solve difficult subjects later, use videos and websites that have good content, if you have a private teacher it is of great help

[ashen lagoon]

Thank you!

[ashen lagoon]

Would someone be willing to help me with math sometime?

I'm having trouble multiplying two digits

[ashen lagoon]

What formula should i use for this?

[vestal spoke]

Do u perhaps know the associative law of addition?

[ashen lagoon]

I don't

[vestal spoke]

its not a multiplication.it's an addition.where we can change the parenthesis but not the numbers. here, 15+58= (13 +2 )+ 58 which is equals to 13+(2+58)

both them are basically the same

the general formula of this looks a bit like this (a+b)+c=a+(b+c)

i dont know if im able to make u understand tho sorry. I didnt study maths in english T-T

[ashen lagoon]

You did help me! Thank you ❤️

[ashen lagoon]

Does anyone have any good resources on learning fractions?

by that i mean

adding and dividing them

[ashen lagoon]

I DON'T GET fractions at all...

[maiden wasp]

i think duolingo math is pretty good

[ashen lagoon]

Is it?

[maiden wasp]

yeah

[ashen lagoon]

Cheers! I'll check it out!

[maiden wasp]

no problem and best of luck to you!

[ashen lagoon]

I downloaded duolingo but I can't see the "math" one anywhere

[maiden wasp]

ohh darn
i wonder if they’re testing it in the us first https://apps.apple.com/us/app/duolingo-math-learn-practice/id1598161822

[ashen lagoon]

It doesn't appear to be on android

[limber pagoda]

https://www.wikihow.com/Divide-and-Multiply-Fractions

Any google search ending with 'easy' or 'in depth' after any beginner math question will provided really good results

[ashen lagoon]

Thank you! ❤️

[wheat oriole]

why is x+y a liner expression? as x and y are different variables, don’t you have to add the twos’ exponents up?

sorry i’m learning this in a different language

ok so this technically did explain my question but if x^3+y^2’s degree is 5, how come x+y isn’t 2?

[ember garnet]

the degree of x^3+y^2 is 3 and the degree of x+y is 1. You add the exponents only when they are in the same term.
https://www.mathsisfun.com/algebra/degree-expression.html#:~:text=Degree of a Polynomial with More Than One Variable

[wheat oriole]

tysm!!!!!!!!!!

[limber pagoda]

To put it in perspective I got an A in clalc3 and studied about 4 hours a week for it. I got a C in linear algebra with a 40% curve and only 20% of the class passing. Studying 20 hours a week. They are both very different types of math. But if your good with proofs and difficult terminology then go for it.

[limber pagoda]

While I am familiar with this, the syntax is different then how I learned it. About to go to bed will let you know if I figure it out tomorrow morning. Where did you get the screen shot from I might need more context and I am confused are we assuming R = R^n or is R a vectorspace.

[gritty karma]

Hello, I need help in Lagrange Polynomial Interpolation with error bound (Numerical Analysis). If anyone can help, please DM me and I will send the solution of the question. I just want an explanation on one value which I don't understand how it appears in the solution.

[left knoll]

can anyone please recommend me a good youtube channel to study 10th grade mathematics from

[candid moth]

You are missing the following permissions required to run the command: manage_messages.

Runtime error in iterm_1
On line 1 at position 6

sin (\pi)
     ^
Attempted to extract tail of non-list

0

[eager sun]

@formal forge Thats quadratic equation

Solve it with formula easily

Can someone tell me how to learn all high school math? I need it for university admission.

Maybe some tips and strategies will be helpful

[forest tapir]

why didn't you just put it in the formula?

[ember garnet]

easy
a. group the real and imaginary terms separately
b. apply distributive property of multiplication and then do the same as in a.
c. multiply both numerator and denominator with the conjugate of the denominator, and then do the same as in b.
d. remember that sqrt(-1) = i, substitute that, and then do the same as in b.

[rancid sleet]

represent 2^x as a variable u. then you have u + 64/u = 20. solve for u with u^2-20u + 64, factor into (u-4)(u-16). 4, 16 = 2^x yielding 2 and 4 as solutions for x

you can also just test numbers and arrive at the answer very quickly

[sleek rain]

Can someone help with this ? The teacher asks to calculate the area, I tried to find the area of the first triangle (60 000m^2) and then by using the pythagorean theorem I tried to calculate AC.. but I'm sure I'm missing something important :((

[mystic thunder]

I think first u find the area of the triangle ABC (using 1/2×base×height)then by Pythagoras theorem u find AC. after that find the area of triangle AED using herons formula

damn that's in french

WAIT OK SO we know that AC= 50 (using Pythagorean theorem) and AC=AD+CD (where CD=10 m) so 50= AD+10
=> AD=40 m
now use herons

formula

[sleek rain]

I found the area (ABC triangle) : 600m^2 but I don't know how to found the area of AED triangle, I never used heron formula :/

[mystic thunder]

have u solved such type of questions before?

because I think herons can be used we can't use the formula of area of quarilaterals too

[sleek rain]

Nope it's my first time with this kind of qst

[mystic thunder]

hm well its kinda dumb to give such hw if students dont know rhe concept

[sleek rain]

So it's (30+15+40)/2 and then I add area n°1 to area n°2 ?

[mystic thunder]

30+15+40/2 will only be the semi perimeter

in herons u find the semi perimeter then take sides as a, b and c and put in values in formula "√s(s-a)(s-b)(s-c)"

[sleek rain]

I've found 191.11m^2 for the second area, is that correct ?

[mystic thunder]

using herons formula u get 191.11106064276 m^2

hahaha yeah correct

[sleek rain]

Thank youuu😭💕

[mystic thunder]

of course<3

what grade are you in?

[sleek rain]

First year in biomedical sciences

[mystic thunder]

that means university?

right?

[sleek rain]

Yes it's uni😅

[mystic thunder]

damn im in 9th 💀

[sleek rain]

And you saw Heron formula ?? I bearly heard of it in high school 😭😭

Where do you study?

[mystic thunder]

hahah I see 😭

i study in india

[sleek rain]

You guys are genius in everything 😆

[grave elbow]

can somebody help me please

idk how to solve for x

[grave elbow]

okay tysm

[mystic thunder]

haha I guess so 😁

[left knoll]

ik its a dumb question but i am hving problem in taking common out from this 💀

[sharp night]

Try rewriting it into a form like this and then simplify it

[left knoll]

okeyyy thanksss a lot!!!

[tame dome]

can anyone please explain 2nd part

[rustic shuttle]

Do you use normal distribution tables?

[tame dome]

this the answer but idk how they got that

[left knoll]

Idk where to start

have whole book to do

[restive thunder]

Could somebody help me with this question? How does the answer get n+1 as an exponent on the first number?

[ember garnet]

try to apply this formula for the geometric series part

[restive thunder]

I think I get it; would this be the proper work? The equation you sent is a little different that what my class shows it as ( x(1-x^n)/1-x) so i used that instead. So basically is the +1 getting added to the n exponent because of the x getting distributed? @ember garnet

[ember garnet]

Yeah if that's what your class shows it should be correct. You could also transform the second sum as SUM[2^i] = 2 x SUM[2^(i-1)] and then use the formula I sent

but it's the same either way

[restive thunder]

Gotcha. Thanks!

[ember garnet]

no problem

[wheat oriole]

why is 3a and 2/3a not a like term????

as the degree and the variable are the same

aren't they like terms?

okay chatgpt is confusing me even more

hehhhhhhhhh

[raw lintel]

iirc because they have different exponents. You can rewrite the fraction to (2/3)(1/a) = (2/3)a^(-1)

[wheat oriole]

heh? why is the exponent -1?

i tried googling it up and the result is very different...

i think i wrote the question wrong

it's 2/(3a) not 2/3a

but i still dont get why this isn't a like term with 3a

[raw lintel]

x^(-1) is the multiplicative inverse of a non zero number so x*x^(-1) = 1 with this we can come to the following conclusion

[raw lintel]

it is irrelevant if there are parentheses

[wheat oriole]

there arent

the denominator in the fraction

is 3a

[raw lintel]

like i wrote in my first comment you can split the fraction into two fractions to visualise it better and then rewrite it into the fomulation with a negative exponent

[wheat oriole]

wait i think i'm getting it

tysm

got it 👍

[shadow yoke]

Hello guys, need help for this derivation pleaseeeeeeeee

[left knoll]

if u didnt understand use wolfram alpha or something like that

[shadow yoke]

ty so much <33

[honest ravine]

Please can someone help, idk what to do, cus u can never get rid of T?

[left knoll]

I am having some difficulty in 10thgrafe maths

Can someone please teach me on call

It's about polygons

[left knoll]

whats the difference between equal to (=) and strictly equivalent (≣)?

[dire aurora]

Can someone please explain whats wrong with this?

[dire aurora]

I think this is the correct explanation

[shadow rapids]

for example you can do x=y <-> x-y=0 but strictly equivalent means they cant be compared since they are the exact same thing not just equal values, like a different name for the same thing

[shadow rapids]

rotate them my neck hurts

[dire aurora]

ok

[shadow rapids]

|u| is not +-u

|u| is always >0

sqrt(u^2)=|+-u|=|u|>0

[dire aurora]

give me one second please ill so u what I'm trying to ask about

So u agree this is true

I guess im asking why is this incorrect

Its been a long night can’t think straight

[shadow rapids]

how did u go from step 3 to step 4

[shadow rapids]

thats it you dont need all that

[shadow rapids]

*x=+-2 on the last part

[shadow rapids]

yeah its better to write each case separately

but you dont have to write all that

x=+-2 is enough

[dire aurora]

so this is correct?

root 4 is not +-2 tho its just 2

can u see why im confused

for root x to be +- 2 there must be an absolute value involved

because my impression is that the absolute value ( or modulus) is what gives the positive and negative case

my curiousity and frustration is about why absolute values are an identity for the sq.root of an expression to the power of 2 only

and not any old expression

like x^1

as shown in the second picture i drew

second picture should be incorrect if im not mistaken

[shadow rapids]

yeah

[dire aurora]

x = 4 tho

[shadow rapids]

ops i mean +-sqrt of 2

[dire aurora]

isnt that worse

[shadow rapids]

no wait

yeah my bad youre right

just remember a sqrt is always a positive number and the thing under the root has to be positive too

(or 0)

and you can think of the |x| as the the distance of x from the center of the axis (0,0) so that's always positive

you cant be -2m away from something

if u know what i mean

[dire aurora]

i know

Is this identity true or just rubbish?

[ember garnet]

In this picture it would be correct if you wrote u = +-sqrt(u^2) = +-abs(u)

[shadow rapids]

its true

+a if a>0
-a if a<0

or 0

[dire aurora]

the core of my question is: why absolute values are an identity for the sq.root of an expression to the power of 2 only but not any old expression.

[shadow rapids]

the power of two and the root cancel each other out but since the thing under the root has to be positive you have to use its absolute value which makes it automatically positive

hope that helped

[dire aurora]

thats not the meaning of the identity

[shadow rapids]

wdym

[dire aurora]

maybe the identity is wrong

fucks sake

Can u explain why this is wrong?

[shadow rapids]

x is postive so |x|=x

[dire aurora]

if this is correct why is the picture above it wrong

[ember garnet]

Square root of 4 is not +-2, it's just 2

[shadow rapids]

yeah you use +- if you dont know the value of x

[dire aurora]

yes. but i am applying the same logic from the x^2 = 4 process to get x = +-2

[ember garnet]

No, in that case the +- comes from the absolute value

[shadow rapids]

if you already know that x is positive you dont use +- you use + since 4>0

[dire aurora]

i appreciate this. i cant show it algebraically at this hour but my question is: if the abs value comes if i square root a square number as shown, why cant there be an abs value if i square a number like x? x can also be thought of as a square number

[ember garnet]

Because x^2 is positive but x is not necessarily positive. If you take the square root of just x, you have to assume that x is already positive, otherwise you wouldn't be able to take the square root.

[shadow rapids]

@ember garnet geia sou

[dire aurora]

im am really just puzzle about where absolute values can be utilised and why they are exclusive to sq roots of expressions to the power of 2 (or even) when any expression can be thought of as a square

[dire aurora]

ohhhh

[shadow rapids]

i think you should sleep on it and tomorrow it will be clear

[dire aurora]

jesus i think its making sense

for me

[shadow rapids]

haha good to hear

[dire aurora]

if i use complex numbers will i be able to apply the identity where an absolute value comes from square rooting an expression to any power?

is this abs((x-1)^2)?

and is abs((x-1)^2) = +-((x-1)^2)

[shadow rapids]

square root cancels out only with the power of two

[shadow rapids]

no square just |x-1|

[dire aurora]

ok let me retry

is this abs(x-1)

and is abs(x-1) = +-(x-1)

[shadow rapids]

yeah +x-1 if x-1>0

otherwise -(x-1)

[dire aurora]

will i lose marks in an exam if i wrote +(x-1) instead?

[ember garnet]

I don't think so, because the absolute value is always a real number but a complex number is not necessarily real, even if some power of it is real

[dire aurora]

im hoping that i have to include +-

other my understanding of abs value is incomplete

[shadow rapids]

you have to check all cases

so yeah ig youll lose marks

[dire aurora]

ok

ive done 8 hours of maths today but i think you guys answered all my queries

was trying to play devils advocate to see why that identity is true

thanks a lot

[shadow rapids]

np

[ember garnet]

np

[shadow rapids]

@ember garnet fusikos?

[ember garnet]

yes :P

[shadow rapids]

same 🤠 🔫

[dire aurora]

can u simplify +-abs(u) please?

[ember garnet]

wdym?

[dire aurora]

can it be simplified?

abs(u) is +-u right? so my next thought is +-+-u but that doesnt make sense

[ember garnet]

Yeah but in the end you would basically write something like u = +-u which is kinda silly

[dire aurora]

yeah

I can’t figure out how to continue correctly

There must be a proof by contradiction that yields insight just too stupid to do it

[ember garnet]

is there something in particular that you wanna show? what do you want to contradict?

[dire aurora]

Algebraically that taking the square root of a number cannot bring about absolute values

Since u is technically a^2 idk what substituting u into the identity will look like

Will it work? Or not

Is it impossible to keep writing?

[silver rover]

Where to study arithmetics

[dire aurora]

At school?

[ember garnet]

the absolute value may come only when you try to get rid of the square root

[ember garnet]

idk if this helps you

this just says that the sq. root of a (positive) number is just the sq. root of that number :P kinda obvious
The absolute value only comes when you have the square of number represented as a variable of which you don't know the sign

[dire aurora]

The algebra is useful to me because couldnt work out a = by myself

Just verifying abs(+-rootu)

[silver rover]

No, like are there online courses or YouTube videos kinda like that

[dire aurora]

My very initial logic is basically if 5 is -root5 x -root5 then how is the number 5 different to a^2

[dire aurora]

What do u mean by arithmetic? Theres stuff online for any specific topic u want to learn about. Each topic in maths will assume ur knowledge of more fundamental topics and cumulate

[silver rover]

I think the basics of arithmetic i guess

[dire aurora]

Thanks for the algebra and explanation. I just wonder about what the flaw in my logic is and how to articulate it or show it

Theres what u taught me

[ember garnet]

yeah that is correct

[ember garnet]

yeah 5 is a^2 and a can be either sqrt(5) or -sqrt(5)

[dire aurora]

Oh

Gosh

So root of 5 is always positive root 5

And hence why i was unfortunately baffled

But if u equate 5 to a^2

U can get both positive and negative root 5

How that works is still slightly weird to me

And thats me so ill take a closer look

I think i know what the problem has been for me

My intuition wants root 5 to equal +-root 5

Due to both directed numbers squared equating to the same number

But u can’t write it like that

Because root 5 is positive

So u equate 5 to an expression that contains 5 with a sign that is ambiguous i.e a

And then my intuition can follow correctly

I think im very satisfied 🙂

As satisfied as one can be regarding the concept of square rooting

[ember garnet]

there is a confusion with notation and conventions. You can say that -3 is a square root of 9 (just like with 3) because its square is 9. But when you say the square root of 9 you mean the positive square root which is 3 (also called the principal square root). When you write the symbol √ you always mean the positive square root. So the square root as a function always "returns" a positive number.

[dire aurora]

Thanks a bunch man. I think ive learnt overall that my grasp with the mechanics of maths is letting my intuition and conceptualisation down

[ember garnet]

no problem, you can also watch this video if you want, it explains what I said just above https://www.youtube.com/watch?v=90Kwt9U6L-s

[dire aurora]

Yeah seems that was completely overlooked in my mind. If i had a better awareness of the convention then using a in root a^2 as a tool wouldve made my intuition clear to me much sooner

I will watch it

[dire aurora]

This has been really helpful for me actually

Never had a clue the radical sign had such a caveat i.e the principal root is different to all the square roots

To find both roots u can’t just use the radical sign but u have to use a pronumeral to make it so that its not just the positive result

[ember garnet]

yes, it's the same thing when you have an equation of the form x^2 = a > 0, x has two solutions which are the positive and negative sqrt(a)

[dire aurora]

Yep

In my mind there was such a disconnect

I was never taught about the radical sign convention

Its an important little technicality because not knowing about it left a gap in my intuition and im not smart enough to figure these things out naturally haha so thank you

Good to have an actual person to ask for guidance

So i relied on algebra to try and articulate my intuition but im terrible at that too lol

Learnt a lot of things in the midst of it

[ember garnet]

Glad to help. Like one of my professors said, when you're not sure about something always start from the definition.

[dire aurora]

Will remember that

[ember garnet]

he called it the desperation method :P

[dire aurora]

Feel so much better to have the assurance of knowing something exhaustively and exactly every which way its used

I can probably hobble along just fine without such an assurance but its a big difference having spent what seems like more than necessary energy to get it

[ember garnet]

doing that work is an important part of learning

[alpine quartz]

hi can anyone help me on point b

translation to english is down below

[left knoll]

Someone help me with this partial fraction

[dusty saffron]

I got the values of A B C I assume that's the question

[ember garnet]

Did you try calculating the integral?

[left knoll]

I found A but later got confused with value should I assume with x

[alpine quartz]

Already Solved it ahah

Thank you anyways

[dusty saffron]

My A is 1 B is 0 and C is -1

I compared RHS and LHS didn't assume anything

[left knoll]

huh

share what you did it's about decomposing equation

Well i am dumb only first bit is question

[dusty saffron]

Huh

[left knoll]

wait

it was this i don't get how they put x=0

@dusty saffron

[dusty saffron]

I got the same answer wait lemme see theirs

[dusty saffron]

By doing that the Bx becomes zero so we get equation in A and C

What I did was compare the coefficients of x² x and constant on both sides

[left knoll]

oh i see ty

[cyan lodge]

Statistics help needed. I've performed a T-test on two populations and refuted the null hypothesis. The thing is, my p-value is extremely low (6.04e-7). Is it common to refute a null hypothesis with this enormous amount of evidence?

[grim shell]

variable acceleration help please :)

[shadow rapids]

integrate a

[dire aurora]

Is there any difference in finding the domain of solutions for x across these two questions due to the use of the use of the word "and" in one question compared to the use of "or" in the other?

i.e how would the answer to each question differ if their usage of the word "and" and "or" respectively were to swap?

if someone could kindly give me the 4 such correct answers that would be lovely

my answers are:
q31 using the word:

• "and"... -2<x<-1
• "or"... all real x except x=4

q32 using the word:

• "and"... -4<x=<-2
  _ "or"... x=>1 or x<-1

[rotund vessel]

the only difference is that in the answer with 'and' specify the intersection of the intervals, and with 'or' specify the union of the half-interval with the interval....

[solemn vessel]

@rotund vessel answer is correct. Here is another way of wording it without the use of “intersection” and “union” if you’re unfamiliar with those terms.

and = must simultaneously satisfy BOTH inequalities

or = can satisfy one or both of the inequalities

[near ocean]

i hate myself

[timid delta]

ouch

[cosmic elm]

what is a monomial

[hallow glacier]

a monomial is an variable expression with one term (such as 2x), as opposed to a binomial (2x + 4y) or a trinomial (3x^2 + 5y - 4z)

[cosmic elm]

oh okay thanks

[tiny sphinx]

stuck at this for like half an hour, help would be greatly appreciated

[hasty girder]

do you understand the notation?

[tiny sphinx]

Yes I do, I need help with simplifying it

[hasty girder]

simplifying what?

[tiny sphinx]

like this

[sharp night]

you can rewrite the fraction like this

and then continue from there i guess

[tiny sphinx]

thank you so much, I was making a silly mistake in between, this definitely helped!!

[dire aurora]

Were my answers correct?

[ember garnet]

Yes

[dire aurora]

Thanks 🙂

Can someone explain how the simplification could go from the 2nd line to the 3rd line (and 3rd to 4th)? I can get to the solution domain in the last line if i take each of the two cases separately but i want to know how to take both cases at the same time as they seem to have done. I don’t seem to be very good at these kind of inequalities and i don’t know how to get around having to square root a negative number without ending up with a surd

[jaunty holly]

Well just add one to all for the 2nd line and for the 3rd line x squared is always positive so we put 0 instead of -2

Just out of curiosity o
How old are u

[wintry olive]

anyone familiar with calc 3 parametric equations?

this problem has me stumped

idk how to even approach it

[wintry olive]

nvm i figured it out im stupid lol

[left knoll]

what is intercepted angle

can someone pls explain this in more simplest words

[restive thunder]

So how exactly is 4-2^n incorrect but the less simplified version is correct?

[solemn vessel]

still confused?

[restive thunder]

Yes

It still says wrong

[solemn vessel]

let me try to do it then

4-4\2^n

@restive thunder

[restive thunder]

nope :^\

[solemn vessel]

the rigjt side is correct?

[restive thunder]

Yes

Honestly I think it's the program being stubborn, not us being wrong but idk

[rotund vessel]

express y using the second equation (y = 2x+3) and substitute it into the first one. Find x then find y.

[lone heart]

I used the Microsoft Edge Math Calculator and I got this answer:

[sharp night]

I won't lie and say I used symbolab to get the sum of (1/2)^i to equal that

but the rest is simplifying it. You can also rewrite that to equal 4 - 2^(2-n), but not 4 - 2^n

[weary arrow]

Because the two terms are not equal.
If you test out with f.ex. n=4, the answer to the left equation is -12, while the answer to the right equation is 3 3/4

[sharp veldt]

Because those are different expressions. If you open brackets in the answer on the right you will get: 4 - 2^(2-n)

[gleaming monolith]

sorry, maybe this is a stupid question but, how do you solve (a-b)-(-a-b)?

[rotund vessel]

(a-b)+(-1)((-1)a+(-1)b)=(a-b)+(-1)(-1)a+(-1)(-1)b=a-b+1a+1b=a+a-b+b=2a+0=2a

we also need to prove that -a = (-1)a

[gleaming monolith]

nice, thnaks!!

thanks*

but um is any trouble if I ask for more explanation? sorry, and thanks again

[sturdy harbor]

how to solve this question?

[left knoll]

Can I only learn from textbook alone if Idk anything about chapter

Yt slowly sucks me in

[wheat oriole]

well i’m learning maths from textbooks and the internet rn

also for the reason i’m here if a=b, ac=bc but not the other way round? why?

oh wait nvm there’s an answer in my textbook

[gleaming monolith]

@rotund vessel ohh nvm I understand now, thanks!

[thick lance]

bro i need math help

how do you find the integral of log(x)?????

[thick lance]

ooooo so you have apply uv rule and take v=1

Thanks

[dire aurora]

what was the explanation?

[wheat oriole]

basically if c=0, ac and bc would both equal 0 but a and be could basically be any number

@dire aurora

sorry i wrote the question wrong as well

[obtuse crater]

If any help is available, I would greatly appreciate it

[brazen vector]

how to solve this?

[left knoll]

Question: Write the rule of an affine function passing through the following points

(These are the answers to the question, I just want to know how to get them)

[left knoll]

il me semble (!) que tu trouves le vertex, de ou tu as l’equation. utilisant x=0, tu finis par trouver y… pas de garantie mais ça devrait être ça

[ebon sage]

you have to subtract five to the argument "x" @left knoll

to translate vertically --> + to y and move up

viceversa

[left knoll]

yes but my problem is that the solution says x2 + 6x +4 and i dont understand why 4x became 6x

[left knoll]

sorry, -6x

[ebon sage]

which is the equation that the problem gives you? @left knoll

I cannot see it anymore

[left knoll]

x2 + 4x - 1 becomes x2 -6x +4

5 units to the right

[ebon sage]

it's right

(x-5)^2 + 4(x-5) - 1

[left knoll]

ooooh okay tysm!!!

[ebon sage]

np

it's not like vertical translation, you have to deal with the argument in this case. it's very important to understand this

[left knoll]

yes, your explanation makes that much clearer, thanks again (:

[left knoll]

Oh, I don’t think we’ve learned about vertexes, but I somewhat understand now, thanks 🙏

Oh nvm we did, it’s just called smt different in French

[left knoll]

I want to relearn math from scratch, can someone recommend me a book or lectures i shoud start with?

[untold flare]

Khan Academy, offers everything you need from arithmetic, up to college level calculus

https://www.khanacademy.org/

[ebon sage]

send the exercise so we can help you

[cerulean elbow]

Is there any websites that I can use to practice math problems?

[ebon sage]

expand (...)^2

where do you have problem?

[scarlet vale]

Anyone knows a good video explaining a 3x3 matrix's eigenvalue that's not using the sarrus rule? Sarrus rule is a no go since it would take too long to calculate in an exam situation

But I cannot find a video using the determines of a matrix to get the eigenvalue

[left knoll]

Okay i'll check them up, thanks! 😄

[dire aurora]

what can +ve and -ve mean in math?

[cerulean elbow]

Can someone help me find the degree with radius (46cm) and arc length (64cm)?

[dire aurora]

length = radius x theta (radian measure)

theta = length/radius

theta (in radians) x 180/pi = theta in degrees

79'43' (nearest minute)

[cerulean elbow]

So 64/45=1.391
1.391 x 180/pi=0.442

Is the process correct?

[dire aurora]

no

64/46 x 180/pi = 79.72 degrees (nearest 2 d.p)

if u want the answer in radians then 64/46 = 1.39... and then express that in terms of pi i.e. 1.39.../3.14... x pi = 0.44 pi (nearest 3 d.p)

[cerulean elbow]

So radians and is different from degrees

I see I got those two confused. Thank you

[dire aurora]

there are the same angle expressed in two different units of measure

[cerulean elbow]

Oooh

[dire aurora]

like km vs miles except miles is arbitrary whereas degrees and radians are not

radians are a confusing concept but somewhat easy to use if you know how to change from degrees to radians and vice versa

[cerulean elbow]

I will learn that too, it was really helpful

[dire aurora]

i.e 2pi units (called radian measure) is 360 degrees

pi units is 180 degrees

and so on

2pi units x 180/pi = 2 x 180 = 360 units or 360 degrees

[cerulean elbow]

Mhm

[dire aurora]

hence k x pi units x 180/pi = k x 180 units or k x 180 degrees

to go in the reverse direction: 360 units x pi/180 = 2 x pi units (called radian measure)

its worth noting that radians are not a unit of measure

[cerulean elbow]

Quick question what is k?

[dire aurora]

any number

[cerulean elbow]

Thx

[dire aurora]

if you want to know exactly what a radian means, then someone else may be able to explain further

if ur maths teacher is very good or on youtube

otherwise its not important to know how a radian is defined if u are just interested in how to use them, which ive shown above

[cerulean elbow]

I’m interested in circles so ya

[dire aurora]

@cerulean elbow check dm for videos

what can +ve and -ve mean in math?

[gritty palm]

anyone good at calculus?

i dont quite understand how to graph the 2nd and 3rd derivative in exercise 1A.

the example above doesnt quite help me understand either ;-;

[dire aurora]

the derivative will be a continuous set of numbers which are the gradients of y over x instead of just y over x as it were originally

so for each point x, you find the gradient of y and plot that on the vertical component of point x and you have a point for the derivative function

since the turning point x of the original function y is where the gradient changes from negative to positive or vice versa, THAT point x is where the derivative function curve on the graph will cross the horizontal axis as dy/dx IS the gradient of y at any point x.

So in 1a) where theres a max turning point at x=2, the gradient of y changes from >0 (positive gradient) to <0 (negative gradient). That is where the derivative dy/dx will cross the horizontal axis from above

gradient means slope in non-american

continue this while using this pattern and u will sketch the 1st derivative. do it again on that sketch and you will draw the 2nd derivative

if you look carefully, you should notice patterns about the concavities of each overlapping graph and those patterns are important in understanding the significance of the second derivative function of any function y

[errant totem]

did you solve this?

if not

finding the inverse function of f(x) is out of the question

so you'll have to find f^-1(e) instead which will probably have an obvious solution

if you set f(x) = e then you can easily see that x=1 is a solution

and that's f^-1(e)

so the answer is g(1) = 1

[grave elbow]

can someone explain this to me? ik im supposed to differentiate but idk what to do with the A and B

[muted zodiac]

Could anyone help me out with the order of operations here? As I understand it since they have the same base they would be multiplied? I'm still getting the answer wrong though so I'm assuming I'm messing up with 6 ln(x^2 +2) somewhere

[silk patio]

Can anyone help me with this ?

[gritty palm]

THANK YOU SO MUCH

omg

[dire aurora]

no worries. did you notice why the points where f''(x) = 0 is significant?

[gritty palm]

yeh thx

wait could u help me with some other calc questions tho pls ?

i have calc test tmmr ;-;

it’s fine if no lmfao, i get ur busy haha

[dire aurora]

differentiate and sub the x and y coord of the given point into the first derivative and solve the equation for a and b

[dire aurora]

i can help

[gritty palm]

thanks 😭❤️

these 2

for question 1 this is what i have done so far:

i don’t think i’m supposed to get x=0 😭

[dire aurora]

i think x = 0 for the second derivative is correct

but its irrelevant

to the question

[gritty palm]

oh damn ok...

so how do i solve it

[dire aurora]

remember I asked you why the second derivative where f''(x) = 0 is important? it is where the concavity of the original function changes

ull notice that in the graphs u drew yesterday

but we dont care about concavity

here

[gritty palm]

right ok

[dire aurora]

do you understand cubic functions? how this one is a positive cubic function?

and the shape of it?

[gritty palm]

i don’t understand the shape

i don’t think i need to graph it tho

[dire aurora]

ok 1 sec

u dont

[gritty palm]

so i don’t think the shape is too important?

[dire aurora]

but its helpful to know what the graph should look like

[gritty palm]

ok, thx :)

[dire aurora]

because then u can understand what the question is asking for

here are notes on the shape of a cubic function in general

[gritty palm]

oh ok thanks

[dire aurora]

the cubic function in ur question looks like this:

[gritty palm]

huhhhh ok

thanks

[dire aurora]

if u read the question now it says

[gritty palm]

ok so its asking for its minimum

so the point at x=20

[dire aurora]

that C(x) is the cost of making the goods where x is the size of the batch made

exactly

[gritty palm]

but like i need to solve that algebraicly somehow

[dire aurora]

the only way you can do that is by finding the first derivative

[gritty palm]

i did

i got 0.03x^2-10

[dire aurora]

since x = 20 C'(x)=0

[gritty palm]

wait but i need to find 20 algebraicly tho?

cause this seems like a non calculator question

[dire aurora]

so far u want to find the min turning point where x>0 because the size of the batch cant be negative

[gritty palm]

right ok

[dire aurora]

by definition, the gradient of C(x) is 0 at a turning point

[gritty palm]

yeh

[dire aurora]

so u want to find where the gradient of C(x) is 0 in terms of x

thats why u find the first derivative

and then

[gritty palm]

btw the answer in the textbook says x=18 ....

[dire aurora]

u equate the first derivative to zero

and then solve that quadratic for x

[gritty palm]

okkk

[dire aurora]

u will get two solutions

a postive one and negative one

the postive one should be...

18.257

[gritty palm]

i did that and used the quadratic equation but i got a negative under the square root so i thought i was doing the wrong thing and scribbled it all

idk if u can see it cause i scribbled it

[dire aurora]

Im just trying to explain it so you know how to figure out what to do according to the question by using the tools at ur disposal

[gritty palm]

yeh ik

[dire aurora]

in this case the tools at ur disposable are ur knowledge of cubic functions and the first derivative

and alegrebra

[gritty palm]

yeh

OH WAIT IM SO DUMB