math-help

[robust oak]

can anyone help me with this?

[robust oak]

can someone help me with this question

[ember kernel]

2 = log3(9)

Therefore the initial equation is
log3(x+4) - log3(9) = log3(x-4)

Which is equivalent to
log3((x+4)/9) = log3(x-4)

Since the logarithm function is injective
log_a(x) = log_a(y) implies that x=y

Therefore
(x+4)/9 = x-4

I leave the rest for you to solve

[weary arrow]

<@&717391911132069929> I think this is a scam link? It's weird at least

[trail swift]

its the real deal, just gonna delete it anyways because we dont need this kind of trolling

[tawdry girder]

it isnt its just discord guidelines link

[ember kernel]

Yeah but what's the spam for ? 🤨

[quaint imp]

guys i need help

[barren wadi]

Add the number of parts 6+1=7 parts.

Those 7 parts will equal 637mL
To find out how much one part is, do 637/7=91 ml for one part.

Ratio of water:lemon juice is 6:1. So do 6 x91=546 ml of Water

[quaint imp]

ohhhh

ok

thank u

[shadow kestrel]

PROBLEM SOLVED I was forgetting the first x on the RHS was also beneath the square root hehe.

[wary bison]

i know its easy

my brain is stuck

[left knoll]

Q 10b pls srry for image rotation

[ember kernel]

Is d(x, 2) defined as |x-2| ?

Because if not we need more details about the function d

[atomic dagger]

could anyone please explain to me why this R^3 -> R^2 associated matrix is surjective, but not injective ?

[ember kernel]

Because of the two identical columns

Because the matrix applied to (0, 1, 0) and (0, 0, 1) would return the same output vector (1, -1) , even though the input vectors are different

Reminder :
The matrix M is said to be injective if and only if :
Mu = Mv implies u = v

[ember kernel]

Start off by identifying what kind of quadruples could be the constant coefficients of the fraction, then move on to the powers of x and y

[quaint imp]

mmm

like 2 and 4 cud be a constant coefficient

@ember kernel

[ember kernel]

Think deeper

The quadruple 1 2 3 6 could work because you could create 2/1 and 6/3 with them, which are equal

You're looking for equal fractions

[quaint imp]

yeah so wouldn't 2/4 wrk?

[ember kernel]

2, 4 is a pair, not a quadruple

[quaint imp]

okkk

OHHH

i get it

so for example 2/4 and 6/12

[ember kernel]

Yeah

Once you've made a list of all possible quadruples for the constant coefficients, move on to all the sets of 3 numbers that could go as powers of x

(They'll be the same for y)

[quaint imp]

y 3 numbers

[ember kernel]

Because there are 3 powers of x involved in the equation

You're looking for these powers so you need 3 values

Once you've listed all valid combinations for the constant coefficients, the x's and the y's (which are the same as the x's) just pick a combination of one quadruple and two 3-digit-long sets so that you end up with 10 different numbers in your final set

[quaint imp]

ohh

okk

[ember kernel]

Any question ?

While I'm still here

[quaint imp]

yeah imma answer the question then if u r free u can see if correct

@ember kernel

these r all the possible coefficients
i found

1/2, 3/6
.
2/4, 4/8
.
1/2, 2/4

[left knoll]

@ember kernel if ur availiable sir could you please explain q10 b to me

[ember kernel]

All pairs equal to 2 :
2/1
4/2
6/3
8/4
10/5

All pairs equal to 3 :
3/1
6/2
9/3

Quadruples can be made from combining pairs

Regarding x, you have all the triples : m, n, (m-n)
(same goes for the y's but with different values)

[atomic dagger]

okayy thank you so much!

[ember kernel]

P(X <= x) is defined as the area under the density curve from -inf to x

[left knoll]

ty ty !!!!!!!

sir you are a godsend

[ember kernel]

np :D

[quaint imp]

damn thats ur choice...but i think u shud do them urself...but thats just my opinion

[left knoll]

bro ur not gonna learn anything lmao

[tawdry dust]

Sorry for disturbing, how to solve cosh x -3 sinh y = 0 and 2 sinh x + 6 cosh y = 5 ?

[ember kernel]

Rule #5 of this server #welcome-verification

[atomic dagger]

hi, i have this reduced matrix and I'm asked to find (x,y,z) such as T(x,y,z) = (0,0,0).. What exactly am I supposed to do ?

considering this is the answer:

[supple island]

you have to find a vector that if multiplied to the matrix T the product=0

[atomic dagger]

but how does the result give us 0 ?

[supple island]

wdym

matrix product is different from product between scalars

two matrixes multiplied by each other can give 0 as a result even if one is not 0

[atomic dagger]

yes, but i don't see how we found this result

like what steps did we take, it's confusing me

sorry if i'm being confusing

[supple island]

can you do the product between a matrix and a vector?

[atomic dagger]

yes

[supple island]

ok so

[atomic dagger]

when i put the multiplication into a system, i obtain: x = -14/5 z and y = 8/5 z

and i don't know how we go from here

[supple island]

z can be whatever we want

so we just say 5 for covenience

[atomic dagger]

ohh okay then what about the "s" in front of the vector that's any real number ?

[supple island]

yes because whatever s is the result doesn't change since s is a scalar

[atomic dagger]

if z was a fixed number, and not any number we choose, "s" wouldn't exist right ?

[supple island]

no, s would still be there

since s is a scalar, it's commutative for multiplication, so we can imagine we put it before the matrix

and the product between the matrix and the vector is 0

so no matter what s is

if we multiply a scalar by 0, the result is always gonna be 0

[atomic dagger]

okayy i get it now!! thank you ^^' you always explain things really weel

[supple island]

np

[tardy tinsel]

Hello

Can someone helpme solve the first one in q1 b)

[sullen verge]

pour la premiere limite (celle en 2-) ca représente le taux de variation en 2- et donc la pente de la demi-tangente en ce point. si tu fais le calcul tu devrai avoir -2 je crois

[sullen verge]

la demi tangente est déjà representee sur le graphique dc ta juste a calculer sa pente

[tardy tinsel]

Pour qu’elle soit la pente de la demi tangente il faut que f(4-x) soit f(x) non ?

[sullen verge]

oui mais ici ca revient au meme

[tardy tinsel]

Comment je trouve f(x) à partir de f(4-x)

[sullen verge]

puisque f(4-x)=f(4-2)=f(2)

[sullen verge]

tu n'as pas besoin de lexpression de f(x)

[tardy tinsel]

Ahh j’ai compris

Et la deuxième limite ?

h—> 0+

[sullen verge]

honnêtement g tjrs pas trouver

[tardy tinsel]

Ahh merci en tout cas

[sullen verge]

je crois que tu peux remplacer f(2-h) par f(-1) pour trouver la pente en -1 mais je suis pas sure que ce soit ca

[sullen verge]

de rienn

[sullen verge]

tu pourrais m'envoyer tt la donnee de cette fiche s'il te plait ? ca pourrai etre un bon entraînement pour moi 😅

[tardy tinsel]

Tous les exercices ?

[sullen verge]

merci beaucoup !

[tardy tinsel]

Derien

[cinder yacht]

x=-14/5z and y=8/5z
<=> there exists s€R such that : z=s and x=-14/5 s and y=8/5 s

basically we have total freedom in our choice of z so we say that z can be any scalar s, and we express x and y en fonction de ce scalaire

[atomic dagger]

thank you!

[orchid orbit]

ah jm

anh cambodia

[hasty quartz]

hey i rlly need some help with this can anyone help me?

[quaint imp]

guys i need help

[shell comet]

I might be able to help what do you nee to know?

I’m assuming on the left side of the chart you write the name of the expense (ex. Spotify) and on the right side of the chart you write the amount it costs (ex. $10) then you sum all of the numbers (add them together) for the total amount

Since there is only one source of income the total will be the same as the one income

Sorry I’m not sure if this is helpful I understood why you’re confused. What does her having to save for a car have to do with it?

[wraith void]

In terms of x and y only?

[wraith void]

Is there another part to this question?

[glacial dust]

any physics or eng ppl that can help

this was a lil bit spicy compared to the problems I solved already

[left knoll]

Where did I go wrong with my integral ( in the red) the answer is meant to be 25/3

[wraith void]

can anyone explain me strain on the rope? (ik it's physics)

[left knoll]

tension force (clue use horizontal and vertical components)

[wraith void]

no like the definition

I understood the other parts

but the strain part I don't know

[left knoll]

ok hold on ill explain once i help the user with part d

[wraith void]

ok sure

Making the angle lower will increase frictional force right?

[left knoll]

oh lmao nvm i understood my mistake smh

[left knoll]

yep!

[wraith void]

normal reaction is mgcosθ

so the frictional force 375×2×(rt(3)/2) right?

[wraith void]

This one can you send me the question or the question is there in the pic itself

[left knoll]

no i figured it out

forgot to change bounds in u sub

so dumb lmao

[wraith void]

No like I want to try

that question

[left knoll]

is a continuous probability question

so application of integral

[wraith void]

probability?

[left knoll]

yep

[wraith void]

I didn't touch probability yet but I know a bit of integration

[left knoll]

i can send u some hard integrals lol

[wraith void]

Send one just for fun

Idk if I can solve it

[left knoll]

can u integrate trig functions

ill just send on

dm

one sec though

[wraith void]

ah ok

[left knoll]

Easy one

[glacial dust]

Isn't it the other way around

if a car would go up a hill frictional force increases as the angle of inclination also increases

they are not inversely proportional to each other

[wraith void]

No
You know that a car slips when it goes on a steep incline right

Also on a flat road friction is maximum

[glacial dust]

oh yeah ur right

[left knoll]

bro we talked about this

im kidding its a confusing topic

want me to explain again?

[atomic dagger]

can someone tell me how can I calculate the determinant here T.T the determinant is 1 * 3 * 5 * 7 i'm pretty sure but then...?

[solar ruin]

You probably have to solve it the long way ,but I can't see why any book would ask this.

[atomic dagger]

you mean by calculating minor matrixes ?

[solar ruin]

yes

[atomic dagger]

ah i see, i thought there might be a shortcut

thank you!

[quaint imp]

nothing its just a story

[quaint imp]

yes

[wraith void]

Send that

[quaint imp]

ok

@wraith void

[wraith void]

variable expenses?

[quaint imp]

idk

[wraith void]

I mean it seems simple
Fill in the details

[quaint imp]

whats variable expenses

[wraith void]

Idk too

[quaint imp]

wud that be like spotify

since its like how much u use it?

cuz its like a monthly subscription...the variable wud be a month

[wraith void]

I guess it's more like when you don't know how much you are gonna spend on something every month or like when you suddenly have something extra you need to spend on

[glacial dust]

would appreciate if someone could correct my work

[wraith void]

metal removed while machining one hole will be just the volume of one cylinder hole

the total volume after machining 4 holes will be vol(cuboid)-4(vol(cylinder hole))

[glacial dust]

so for b it would only be the volume of the cylinder?

[wraith void]

yeah

The metal which is removed

[glacial dust]

ok thanks

[pseudo estuary]

for the 1st three years it is simple interest

so use PxRXT/100

and take that amount as the new principle for the next 5 years and apply the compound interest formula

[quaint imp]

u mean p x r x t

why devide by 100

@pseudo estuary

[pseudo estuary]

thats...kinda the formula for simple interest

since r is a %age

[quaint imp]

yeah ik

so wouldn't it be 3000 x 4.5 x 3

[pseudo estuary]

also, add the original principle rate to the simple interest rate

[quaint imp]

?

3000?

[pseudo estuary]

its 4.5 per CENT

per cent means divide by 100

[quaint imp]

ohh

so it wud be 3000 x 4.5 x 3/100

[pseudo estuary]

add that to the new found prt/100 value

[quaint imp]

oh yeah ofc

[pseudo estuary]

yea that alone is the interest, so now add the original 3k

[quaint imp]

so after i calcualte the interest i need to add the og 3000 with it

ye got it

[pseudo estuary]

yep

and that new amount is your input for the next 5 yrs of compound interst

[quaint imp]

wuts the formula for compund interest

WAIT

ik

@pseudo estuary

[pseudo estuary]

bruh

[pseudo estuary]

okay we still have hope

[quaint imp]

?

dw ik it

[pseudo estuary]

cool lmao

[quaint imp]

A = P(1 + \frac{r}{n})^{nt}

that

teacher told us

[pseudo estuary]

i cant understant computer language but it looks correct

so yes

[quaint imp]

lol

wait but can u clarify that

like cuz thats what the teacher gave us

[pseudo estuary]

that is p+( 1+r/n)^nt right

[quaint imp]

idk thats what the teacher gave us

[pseudo estuary]

yeah its 100% correct

dw

[quaint imp]

how wud u write it

[pseudo estuary]

the answer you got after 3 years

that is your new "p"

[quaint imp]

yes

this is the formula aunty google is giving me

[pseudo estuary]

yeah thats correct

A will be your final answer

p is yoour amount that u got after 3 yrs

r is interest rate

t is 5 yrs

n is the number of times you apply the interest rate, in this case its 5 (cuz 5 yrs)

[quaint imp]

wudnt it be 8 including the previous 3 yrs

[pseudo estuary]

i will be included

[quaint imp]

so its 8?

[pseudo estuary]

no since the comp interest only for 5yrs

[quaint imp]

ohhhhhhhhhhh

ok

i get it now

k thanks

wait

[pseudo estuary]

yeah right here

[quaint imp]

but n and t are powers at the end

what does that mean

and since compund interest is also a percent wudnt we devide by 100

[pseudo estuary]

take n=1

since it is compounded only 1 time in each year

if they say "compounded half a year annually" or something like that you will have a diff n value

[quaint imp]

so

for my case

what wud the compund interest formula be

[pseudo estuary]

1 sec

what is your p value?

[quaint imp]

p?

3000

[pseudo stump]

when studying about derivatives i got these two formulas, i don't understand what 'a' stands for, if it's just the name of a variable then both formulas apply to the same thing?
(x^n)′ = nx^(n−1)
(a^x)′ = (a^x) ln a

[pseudo estuary]

in the first case you are diferentiating (x itself) with respekt to (x)

[pseudo stump]

i don't understand

[pseudo estuary]

d/dx (x^n) is nx^n-1

[pseudo estuary]

d/dx (a^x) isnt the same as this

here (a^x) is being differentiated WRT x

[pseudo estuary]

here (x^n) is being differentaited WRT x

[pseudo stump]

i see

did the 'a' suggest this or the equation?

[pseudo estuary]

the "a"

i mean you are differentiating x wrt x in the first case

albeit that "x" has a power/exponent

in the 2nd case, "a" is differentiated with x, just that a has the power/exponent "x"

[pseudo stump]

i still see no difference

i'll look some more online

[pseudo estuary]

okay

sorry i couldnt help

[pseudo stump]

haha thanks for the attempt anyways, i bet that makes sense, just not for me (yet)

[pseudo estuary]

lmao no, prolly my bad since i dont study math....i know this stuff from physics so thats prolly why i cant explain it clearly

[pseudo stump]

wait so does this mean a is a constant?

ok nevermind

[pseudo estuary]

yeah i guess,

constant raised to some power

[pseudo estuary]

cuz differentiation of only a constant ist 1

[left knoll]

does anyone know continuous probability

5 c pls

where ami going wrong

my work

[floral jungle]

Does someone need help with your math problems? I am using Gauthmath, it has LIVE tutors who will give answers and step-by-step explanations 24/7 for FREE. Here's my invitation code: KCGGJY.
https://s.mathme.xyz/lp/invite?code=KCGGJY

[fervent tide]

did you forget to square expected value in task c) ?

[wraith void]

Ok so for first one

d(f(x))/d(x)=x^n
Now look at the base of the term
It's x right?

Now consider this
d(f(x))/dx=a^x
Now the exponent is x right?
Here a is another constant which doesn't depend on x

Now let's take this
d(x^2)/dx= 2x right?

What will d(2^x)/dx be?
It's not going to be 2x

ok now let's take y=f(x)=2^x
that means y=2^x (note it's not x^2)
now log(y) = xlog(2)
d(logy)/dx= log(2)
1/y(dy/dx)= log(2) (diff of y w.r.t x)
dy/dx= ylog2
now what is y? It's 2^x
therefore
dy/dx= (2^x)log(2)
now we know that in place of 2 any valid number can come so..
d(a^x)/dx= (a^x)log(a)

(Here all logs are to the base e)

Now you might have heard about the derivative of e^x which is simply e^x again right?

now watch this

d(e^x)/dx = (e^x)log(e)

now we know that log is to the base e
so now what is log(e) to the base e?
It's 1
so it becomes e^x

[left knoll]

i dont think so

[fervent tide]

been a long time since i studied statistics, but i was referring to this

should the answer be (c^2)/12 ?

[scenic oyster]

How I should do this equation? I can't use the calculator to resolve it.(teachers dont let use calculators on the exam)

I already demonstrated that only have one real solution between 0 and 1

I could use bolzano to make that interval even smaller, but I don't think that would be correct

[left knoll]

u fking genius, u did it

tysmmmmm

[safe ember]

Most you can do is use Lambert W function, that way: X=W(ln(2))/ln(2)

[scenic oyster]

ohh thanks!

[safe ember]

np, you're welcome

[pseudo stump]

thank you kind sir with Rick Astley pfp

[wraith void]

no problem

[glacial dust]

can anyone help me out 😀

[supple island]

can you do a and b?

[glacial dust]

yes

b idk

am not confident but yeah I can

can u just walk me through

then I'll solve it myself

[wraith void]

B seems easy right?

it's just rt(2gh)

[glacial dust]

rt?

[wraith void]

root

Square root

[glacial dust]

are u pertaining to the v^2=u^2+2as?

[wraith void]

yeah

[glacial dust]

cuz that will not work bcuz the hammer was not at rest

its was being lifted

[wraith void]

It was not?

[glacial dust]

yep

[wraith void]

so what initial velocity was given

[glacial dust]

nothing

thats why I need help xd

[wraith void]

then we can assume it's dropped right?

[glacial dust]

yes

[wraith void]

And what does dropping mean

[glacial dust]

free falling?

[wraith void]

yeah

[glacial dust]

potential to kinetic

[wraith void]

in free fall initial velocity is 0

right?

[glacial dust]

uhm yes

[wraith void]

so u is 0
v²=2gh

v=root(2gh)

[glacial dust]

ah ok then for a its just potential enrgy asking which is mgh?

[wraith void]

yeah

mg(change in h) since they asked change in potential energy but anyways its 3.2m so m(9.8)(3.2)

[glacial dust]

yep ik that

[wraith void]

now m

[glacial dust]

but for c will I use momentum principle

[wraith void]

Is this question a continuation of the previous question you sent?

[glacial dust]

no it was the same

[wraith void]

ok

[glacial dust]

cuz I was struggling

[wraith void]

now we know velocity of hammer and pile since inelastic collision
and we know it goes 0.22m in the ground

so find the retardation and multiply by the total mass to get the resistive force ig?

[glacial dust]

velocity of the pile was 0 right?

[wraith void]

after collison

it's not 0

[quaint imp]

guys

im so confused

[pseudo estuary]

b bruh

[wraith void]

This?

bro

It's 7x+6

[pseudo estuary]

9x-2x and 5+1

[sullen verge]

its equal to - 0.5
because you factorise by sin and tan then you get
sin/tan which is 1 (cz x=0) then you just calculate the rest

[wraith void]

I thought we can use sinx/x

[quaint imp]

yeah i got it....srry for disturbance

[wraith void]

np

[sullen verge]

?

[vocal dock]

ok. thanks. lim (sin u)/u =1 when u -> 0

[wraith void]

like how lim(x->0) sinx/x=1 but nevermind

[sullen verge]

ohhh i dont think you can use that here since all of the variables are in the form of trigonometric functions

[vocal dock]

hopital too hard

[wraith void]

Yeah hopital is too long

[vocal dock]

L 'hospital

[wraith void]

what is it exactly anyways l hospital or hopital?

[ember kernel]

L'Hospital's rule is that, if the limit of f(x) := p(x)/q(x) at x = a is an undefined form (= 0/0) then the limit of f(x) at x = a can also be expressed as p'(a)/q'(a) to avoid the 0/0 thing

Example :

[wraith void]

No no

I know the rule

I was asking the spelling lol

[ember kernel]

Ohhh ok

[wraith void]

sorry to bother

[ember kernel]

It depends on your language

[wraith void]

well my sir uses both interchangeably

[ember kernel]

In some language they translated it by removing the s I think

[wraith void]

mhm

[ember kernel]

But the spelling doesn't matter, as long as you understand/are understood when speaking about maths

[wraith void]

Yeah

[red spruce]

tan theta = y2-y1/x2-x1

answer is 2

[quaint imp]

anyone that can help me?

[red spruce]

are u makinus solve ur assignments?

[quaint imp]

lol what

its homework

but since covid its online

im just new to this

like she didnt even explain

can u explain?

its cuz i skipped the questions i didnt understand

and came back to them

theres 25 quesions im done all except 3

[red spruce]

answer is 4 number

[quaint imp]

is that for me?

[red spruce]

yes

[quaint imp]

so the fourth option?

[red spruce]

ye

[quaint imp]

but can u explain how

[red spruce]

now go ready theory ill not answer more

[quaint imp]

ill try

[fervent tide]

0. Assume x = a + bi and y = c + di
1. Use the first equation to derive a formula for either x or y
2. Combine the equations so you only have one unknown
3. Then substitute that unknown with the expression from 0.
4. Continue to find the other unknown

[left knoll]

idk if im allowed to help @quaint imp

[wraith void]

ok so first you find out the slope of the given equation.
Then since the other line mentioned is parallel it must have the same slope

Now use the point-slope equation for a line
y-y1=m(x-x1)
where x1 and y1 are the coordinates of the given point
And now just put in the values and you are done

[somber reef]

helpp~

[left knoll]

all of it? @somber reef

[left knoll]

Does anyone have any good calc 2 worksheets, specifically integration by substitution, and with answers.

like hard q

[somber reef]

yeaa teach mee aaa :')

[wraith void]

The question c is straightforward
P and Q are the roots of the equation and so p+q=-(-8) which is 8/a
And pq is c/a so answer is 8/c

the first part I guess the answer is [p,q]

second part you can maybe do a=c/pq?

[stoic zinc]

VECTORS A, B, C DIFFERENTS FROM ORIGIN ANGLE BETWEEN A and C = angle B and C, find "t" to C⊥D = ||B| | A+tB

anyone can help me? 😦

[solar ruin]

I can't understand much from the language, but here is what I can tell you:-
As D is ||B| | A+tB, thus D lies in the plane of A and B, and as C⊥D, that means C is perpendicular to the plane of A and B, thus it is perpendicular to A and B.

The angle between A and c= angle between B and C and as angle between A and C is 90, thus angle between B and C is also 90., which we already know.
So, C⊥A and B and D.
I don't know what to do after this, some detail which I can't read in that.(I don't know Spanish)

If the question is asking for the value of t, then any value of t is possible.

...

Here's in Spanish(using google translate):-
No puedo entender mucho del idioma, pero esto es lo que puedo decirte:
como D es ||B| | A+tB, por lo tanto, D se encuentra en el plano de A y B, y como C⊥D, eso significa que C es perpendicular al plano de A y B, por lo tanto, es perpendicular a A y B.

El ángulo entre A y c= ángulo entre B y C y como ángulo entre A y C es 90, entonces el ángulo entre B y C también es 90., que ya sabemos.
Entonces, C⊥A y B y D.
No sé qué hacer después de esto, algún detalle que no puedo leer en eso. (No sé español)

[main plume]

i have a matrix determinant evaluation question can someone help me

[left knoll]

for improper integral what do i do when i evaluate teh limit subbing in infinty on top

cause ik if its in the denomenator then its zero

[cosmic mountain]

Anyone knows how to do this?

[left knoll]

@cosmic mountain

You can simplify the denominators

If anyone sees an arithmetic mistake please point it out though i think it should be fine.

can someone please help me with this?

[left knoll]

f(5)-f(1)

I think

[lofty arch]

Yeah that’s right

[floral jungle]

Whoever needs a math help, come Dm me or ask here

[cosmic mountain]

Thank youu!

[arctic crater]

hi there
can u help?

[frosty flare]

so <DAE= <ADE = 75
Angles in a quadrilateral = 360

360- 75-75=210

<ABE+ <BCD = 210

<ABE= <BCD therefore <ABE + <BCD = 2x

therefore 2x= 210

x= 105

i think thats right and i hope that makes sense : )

[frosty flare]

: )

[arctic crater]

omg. 10q~~

[frosty flare]

np anytime

[pseudo estuary]

there is no angle ADE??

where is angle ADE?

[ember kernel]

She meant DAE

[pseudo estuary]

ahh

but can you please explain how theyre equal? sry havent done math in a while

[ember kernel]

Symmetry

That's how you can tell they're equal

[pseudo estuary]

abe isnt an angle too right

[pseudo estuary]

but is that given? or is there some postulate?

[frosty flare]

ADF even sorry

[frosty flare]

ABC for that one

[pseudo estuary]

ah

[frosty flare]

i think there is a thing in regards to circle theorem but i havent done math in a couple months, cant remember

[wraith void]

is the theorem anywhere related to the two chords being parallel?
If so then the angle can be 105

[pseudo estuary]

i havent done math in 2 years 💀💀

[pseudo estuary]

bruh if the cords are parallel then we can just find the corresponding angle and subtract 180 (angles of a line) and direct we get 105

so maybe thats it

[wraith void]

Yeah
But thing is I wanted to know whether such arrangement of circles and lines would result in parallel chords

[pseudo estuary]

exactly, we cant assume AD||BC....there must be something to prove that

[wraith void]

Yeah

If we join FE then that creates 2 cyclic quadrilaterals
Now we know opposite angles add up to 180
So that means <FEA is 105° and FEB is a supplementary angle to angle FEA therefore <FEB is 75°
Now we apply that property that opposite angles in a cyclic quadrilateral adds up to 180° and we get angle FCB as 180-75 which is 105° hence proven

[wraith void]

we just can't assume that the angle ADF is 75°

[frosty flare]

i mean

fair enough

[pseudo estuary]

oof lmao

[pseudo estuary]

where is angle fae?

[wraith void]

We join F and E

Cause we can

Wait

sorry

[pseudo estuary]

that still doesnt make fae

[wraith void]

FEA

[pseudo estuary]

yeah

[wraith void]

my bad sorry

[pseudo estuary]

yeah nvm

[wraith void]

Edited it

[pseudo estuary]

yeah, hopefully its less confusing to the OP now

lol

[wraith void]

lol

this is undergraduate level stuff?

[pseudo estuary]

lmao itso

idtso

[wraith void]

We learnt it in 9th grade

[pseudo estuary]

lmao yeah, cyclic quads and stuff

[wraith void]

yeah

[pseudo estuary]

if i were in 9th/10th, id be able to solve this easily.....i havent touched math in 2 years 😭😭

[wraith void]

I haven't touched this type of geometry in 2 years

we currently learning 2d and 3d coordinate geometry

[exotic dust]

does anyone know how to do transformations in alg 2?

i need help lol

[cyan night]

sure where do u need help

[pulsar turret]

Can someone help me find the volume of a cube with a surface area of 24a^2?

[exotic dust]

Thanks, i have trouble identifying the translations, scale factors, etc between 2 different functions

[pseudo estuary]

find the value of one side

and the volume of a cube is = (side^3)

was that a joke question?

[cyan night]

do u have concerns about a specific question or just those concepts

[exotic dust]

Here i'll send a picture of the problem in a bit

[atomic dagger]

Anyone knows what this symbol means ?

[ember kernel]

Need context. I'm pretty sure it's an unconventional ln

[ember kernel]

judgemental

[pulsar turret]

No lol it’s from a SAT practice test

[pulsar turret]

But how exactly do I find the value?

[pseudo estuary]

so surface area of a cube is given by the formula 6a^2 where "a" is a side

[pseudo estuary]

ah i see, thank you for telling this....sorry if i came off as rude

[pseudo estuary]

so basically, if 24a^2 =6(side)^2 then "side" will be equal to sqrt(24/6)------> is basically 2a. Since "side" is 2a, the volume is (side)^3 and hence it will be 2^3 = 8 a^3

[outer pond]

In the question, surface area should be 24 only but he/she has written 24a^2 and this makes it confusing

[pseudo estuary]

yeah, thats why i didnt write the units

regardless, the answer becomes 8a^3 if the area is indeed 24a^2

[outer pond]

Yup

[pseudo estuary]

lmao i didnt use the "a" in my initial answer as i gave them the formulas as 6a^2 and a^3 for surface area and volume respectively

so if i used the same "a" for the formula and what is given, the op might have gotten confused looking at how is 6a^2=24a^2.....thanks

[outer pond]

Yup this will confuse anyone cuz you can clearly see that a^2 can be cancelled out in this equation

[pseudo estuary]

yep

[left knoll]

hi, i got some trouble in normalize the vector. In picture you can see that second table is aggregate of first table but the third table idk how they normalize the vector
Anyone can help me ty

[ember kernel]

Divide each cell of the vector by the total sum of all of its cells

Thats gives :
total = 18 + 12 + 2 + 16 + 10 = 58

normalised cell #1 = cell #1 / total = 18/58 = 0.31

normalised cell #2 = cell #2 / total = 12/58 = 0.21

normalised cell #3 = cell #3 / total = 2/58 = 0.03

...

That's how you normalise the vector

[azure lion]

help pls

[left knoll]

I see. Ty for your explain

[left knoll]

why does P(Z<-a) = 1- P(Z≤a) explaining through symmetry of standard normal graph

[ember kernel]

A standard normal graph is pair. Therefore we get formula [1] : P(Z >= b) = P(Z <= -b)
That works for any b. Here's we'll use b = -a

Using one of the probabilty-related identities, you calculate :
P(Z < -a) = 1 - P(Z >= -a)
And using formula [1], you can prove it is equal to 1 - P(Z <= a)

[left knoll]

tyyyyyy

[left knoll]

How do i do q 8 h

nvm im an idiot

[proud portal]

hey lads, can anyone help me with this

[left knoll]

first for its position put the value of t=1, second for velocity find its dx/dt or derivative and then put the t=1

[left knoll]

answer position= 5units velocity=-1 units

[ember kernel]

Chain rule

dg/dv = dg/df * (df/dx * dx/dv + df/dy * dy/dv + df/dz * dz/dv)

Evaluates all expressions (x, y, v, dx/dv, ...) at (u,v) = (-1, 2)

All the necessary values are given

Correct me if I made a mistake pls

[proud portal]

U right, thx!!

[left knoll]

hi guys, how are you? I'm Giorgio, 15 yo and attend the second year of high school in italy. I don't understand analytic geometry, we are doing the first things, could someone help me. Thanks

[left knoll]

does anyone know how to solve this?

[clear fern]

i am not sure if i am right but
sin 2theta = 2 sin theta cos theta
therefore if you expand the equation, 3x2sin(theta)cos(theta)+cos(theta)=0
6sin(t)cos(t)+cos(t)=0
factor out cos(t), cos(t) x (6sin(t)+1)=0

you will have 2 equations, cos(t)=0 , 6 sin(t)+1=0

[half coyote]

guys, can anyone help me about solving that? I couldn't solve it

[left knoll]

x=5 y=6

[left knoll]

thank you

[clear fern]

how tho kinda stuck at the equation when i sub y=31-x^2 , y^2?

[half coyote]

thanks but if u can, explain how pls

[half coyote]

ya same

[left knoll]

i just did trial and error

like i guessed that x squared would be like 25

and then 31-25 is 6

and then that would mean that y squared is 36

if that explains it lol

i just guessed

because for 31 the lowest square you can have is 25 without going over 31

[pseudo estuary]

substitute y = 31-x^2

[clear fern]

lets say that (-x^2+31)^2 and we expand it
(-x^2+31)(-x^2+31).....

[pseudo estuary]

yep

[half coyote]

it becomes x^4 - 62x^2 + x + 961 = 41

[clear fern]

nope im tripping my bad

[half coyote]

there is 3 different degree xs, so I think there must be another technique. Solving with matrice maybe?

[supple island]

was this a question or a problem lead you to this?

[pseudo estuary]

nah its a=b x a-b

[pseudo estuary]

noo you wont have any x^2 term

[half coyote]

No, this is a plain question.

[pseudo estuary]

i mean no 62x^2

[supple island]

?

[clear fern]

i agree tho

[half coyote]

check again buddy

[supple island]

how

it's y^2

[pseudo estuary]

MY BAD

[half coyote]

yup

[clear fern]

a^2+2(a)(b)+b^2=(a+b)^2

[clear fern]

haha we got different method but ultimately i got this too

[supple island]

you are confused, you seem to say that (a-b)²=(a+b)(a-b)

which isn't true

[clear fern]

yea i just realised

thats when a^2-b^2

[pseudo estuary]

oh frick

my bad

[clear fern]

from here what to do?
factor out??

[pseudo estuary]

sry my bad

[clear fern]

its fine amigo

[half coyote]

no idea

[clear fern]

oh well, cant help ya much

[half coyote]

it's okay tho

thanks for effort

[supple island]

idk if this helps but you can think it as the intersection of 2 parabolas

"The intersection points of a vertical and horizontal parabola lie on a circle whose centre's distance from the directrices is the sum of distances of the foci from the directrices (in both the x and y directions."

rn i don't know why this works but it should

[sullen verge]

any of you can plz help me with that?
i have to find the points M with an affix z that verify this equation:
|3iz + 6| = 3|z - 1 + i|

ive been trying to find it but im finding something weird i dont think it's correct

[supple island]

wdym poitns M with an affix z? also what's z? is it a complex number?

also M points of what

[sullen verge]

M(z) with z=x+iy

[supple island]

ok, what did you do so far?

[sullen verge]

i tried to develop it i got
(y+3)²=3(x²+x+8)

that doesnt seem right tho

[supple island]

you can start by saying |iz+2|=|z-1+i| so you have |ix-y+2|=|(x-1)+i(y+1)| , right?

[sullen verge]

can i do that? i mean the symbol "||" signifies a module

[supple island]

i mean you just divided by a scalar

3|z|=|3z|

[sullen verge]

ahhh right omg idk why i got confused

[sullen verge]

then u just develop?

ull get x²+y²+4-4y = x²+1-2x+y²+1+2y

oh lol that's so simple

[supple island]

yep then try to isolate y

or x

[sullen verge]

thanks! got it. i just thought i couldn't simplify by 3

[cinder yacht]

ehm

[sullen verge]

je pense que c'est bon j'ai eu ma reponse. merci !

[cinder yacht]

<=> |3i| * | (3iz+6) / (3i) | = 3 |z-1+i|
<=> |z + 6/(3i)| = |z-1+i|
<=> |z + 2i/(i^2)| = |z-(1-i)|
<=> |z-(2i) | =| z-(1-i)|
<=> AM = BM with A : (0,2) and B: (1,-1)
<=> M is in the médiatrice de [AB]

okay

j'aurais dû lire le dernier message oups

[sullen verge]

ah non j'ai une question en fait

comment ta trouver la mediatrice si tu as le zi

[cinder yacht]

j'ai fail un truc

fixed

[cinder yacht]

hm?

|z(M) - z(A) | = AM

et |z(M) - z(B)| = BM
et en géométrie (pour A différent de B) AM=BM <=> M appartient à la médiatrice de [AB]

[sullen verge]

ouii mais puisque z est multiplié par i, ca n'inverse pas laffixe des point ?

[cinder yacht]

my bad

un autre fail

fixed

comment ça ?

[sullen verge]

j'y comprend rien a cet exo 😭

[cinder yacht]

c'est quelle étape exactement que t'as pas compris

dans ce que j'ai fait

quelle ligne

[sullen verge]

pourquoi ta factoriser par 3i et pas par 3 ?

[cinder yacht]

1ere ligne : j'ai multiplié et divisé par |3i|

ensuite le |3i| au numérateur vaut 3, ce qui s'est simplifié avec le 3 que j'avais au côté droit de l'équation

[sullen verge]

ahhh

ok ok c bon

[cinder yacht]

la raison pour laquelle j'ai choisi |3i|, c'était d'avoir rien à côté du z de gauche

[sullen verge]

ouii justement c'est sur ca que je bloquais

je pourrais te poser d'autres question sur le même exercice pour vérifié mes calculs ?

[cinder yacht]

oui ?

[sullen verge]

|-2iz(barre) +4| = |2z +4i|

jai trouver y=1

donc M(x+iy)

et puis ya
|z(barre) + 4 + i| = |3+4i|
j'ai trouver
(x+4)² + (y-1)² = 25
donc M appartient au cercle de centre A(-4;1) de rayon 5

[cinder yacht]

j'aurais dit y=0

notamment si tu remplaces z par i dans l'équation, ca donne 2=6
par contre si tu remplaces z par 0 (ce qui vérifie y=0) ça marche bien : 4=4

donc j'en déduis que "y=1" est faux, et que "y=0" pourrait être juste

(d'ailleurs je suis sûr de y=0, mais je voulais te dire que c'est un bon réflexe de vérifier avec des cas particuliers quand on trouve une solution)

ensuite pour la dernière equation
c'est correct

[sullen verge]

ahh oui mercii je reverifierais mes calculs

[sullen verge]

merci !

[cinder yacht]

t'inquiète ^^

t'es français?

[sullen verge]

non jsuis libanaise mais francophone

[cinder yacht]

ohh

j'ai des potes libanais avec moi dans mon école, ils ont fait prépa au liban

[sullen verge]

ah bon ? ils l'ont probablement faite là ou je pense moi même la faire

t'es en polytechnique ?

[cinder yacht]

oui comment t'as su

[sullen verge]

pacque les libanais font pratiquement tous prepa pr finir en polytechnique 😂

[cinder yacht]

ahh

mais jcrois vous avez une arnaque, je pense que vous faites prépa mais que vous passez les concours en filière universitaire (et non prépa), sales arnaqueurs :(

[sullen verge]

oui c'est ca je crois mais le nombre de personnes prises est largement inférieur a celui qu'ils prennent chez vous

[cinder yacht]

yes c'est vrai, après d'expérience les gens les plus forts sont le plus souvent en prépa (et surtout en MP, moi j'étais PSI), jcrois c'est un bon plan

en tout cas c'est des sucres les libanais que je connais

[sullen verge]

PSI n'est pas plus ouverte ?

[sullen verge]

ah ba ils nous rendent fiers alors

tu as fais ta prepa ou ?

[cinder yacht]

ouverte?
sinon PSI y a moins de places à l'X donc c'est pas un bon plan, le mieux c'est PC car y a bcp de places ET tu esquives les génies de MP

sorry for the French spam

[left knoll]

Pls help

[clear fern]

how do you integrate question 6? Am I right to put u= In^3t? If yes, du/dx how do I differentiate that

[supple island]

integrate by parts

[left knoll]

<@&717391911132069929>

[supple island]

write sin(2x)=2sinxcosx and cos^4(x)=(1-sin^2(x))^2 (since it's square you could also write sin^2-1), then u=sinx, with du/dx cosx cancels out

[left knoll]

Consider log t = a

[ebon spire]

Guys how is ln(an) converging to 2 here?

The power is n in the pic

[supple island]

can you post the whole question?

[ebon spire]

I tried through 1 raised to infinity form but the question is asking me to specifically take l hospital after taking ln of an

[weak mortar]

so the first thing they use is that if your series converges then its ln will converge as well and the other way around

so by taking the ln of an we get ln(a_n):=nln(n+1/n-1)=(ln(n+1/n-1)/(1/n)

now you can use that ln(a/b)=lna-ln b so we get

ln(a_n) = (ln(n+1)-ln(n-1))/(1/n))

wait

nevermind

taking the logarithm gives you infinity* constant

so it would diverge

[clear fern]

Thanks tho , I solve it using U= In t

[ebon spire]

Exactly but apparently it should converge to 2 ..

[weak mortar]

ill see how the graph looks

okay it does indeed converge

okay i see my mistake

as n goes to infinity ln(n+1)=ln(n-1)

[weak mortar]

so this is 0 over 0

and then i think you can use l'hopital right?

sorry for the confusion

[tardy bone]

derivative is the opposite of integral right?

[ebon spire]

Ohhh ok I got it now ! Basically take n in the denominator as 1 by n and then apply l' hopital rule right.. thanks for the help!

[weak mortar]

draw it and remember pythagoras' theorem

you will see it pretty fast then

and one other important point is that in an equilateral triangle the perpendicular line splits the opposing side in two equally long parts

[regal oxide]

hello

[left knoll]

Express the information on the graph in the form of a single equation

For this, do I just extend the line to meet the y-intercept and take any 2 coordinates to find the gradient?

[left knoll]

a) 5.2

b) 4.62

c) 35.72

[clear fern]

hi i am not sure how do u integrate (sin 1/3x + cos4x)dx

[barren nacelle]

yes

[clear fern]

got it.

[atomic dagger]

<@&717391911132069929>

When changing the basis of a matrix. When is using this formula necessary? Isn't it enough to simply multiply said matrix with the changing basis matrix ?

For example if we have the matrix T expressed in the canonical base, let's say [T]_e, and I want it expressed as [T]_b as in the B basis. M the matrix changing basis from e to B. i've done an exercice where all we do is M*[T]_e = [T]_b, and another like this one, where we need to do [T]_b = M^(-1) * [T]_e * M

[worn mist]

!purge user AbhiNoe#0857 50

[ripe bay]

Member "AbhiNoe#0857" not found

[worn mist]

its only per channel aaaaaaaaaa

[honest oxide]

You can also use the fundamental theorem of calculus for this exercice [F(t)= \int f(t) dt]. It’s easier and less time consuming! As you know F’(t)=f(t). For the exercice 6, you have to find the function F that gives you f(t)=ln^3t/t when it’s differentiated. So you know that F(t)=\int ln^3t/t dt and F’(t)=ln^3t/t. Therefore, F(t)=(ln^4 t)/4. And it is the same for the exercice 3. You need to find the function F that gives you exp(x) (1+exp(x))^2 when it’s differentiated. So F(x)=(1+exp(x))^3 / 3.

Don’t hesitate to use the thm when you have to integrate something where its derivative is in it. Here you know that the derivative of ln t is 1/t and the derivative of exp(x) is exp(x).

[honest oxide]

You need to use the SOH CAH TOA rule. Here you always use the TOA part of the rule which is: The tangent of your angle equals the lettered side divided by the given side.

[glacial musk]

Hi people

I need help with maths. function optimization. Can someone help me pls?

[cinder yacht]

u=ln(t) much cooler, u deduce t = e^u so dt = e^u * du
and it becomes the integral of u^3 / (e^u) * (e^u du)
= the integral of u^3 du
so u^4/4 would be a correct primitive
which is ln(t)^4 / 4

oh ppl alrdy answered that

[ember kernel]

Send the question here. Someone will answer

[supple island]

well yes, but A/infinty=0 and 0/A=0 with A a real number

so 0/infinity obviously=0

[buoyant wedge]

hey, would anyone be willing to help me with these 3 problems?

[frozen onyx]

Just need a hint on how to approach, please help

My solution:-

[frozen onyx]

Just need a hint on how to approach

Please help

[left knoll]

CAN ANYONE HELP ME

[ember kernel]

Send the question. Someone will answer

[left knoll]

Find the surface area of this

[left knoll]

I will when I will get my test 💀

[ember kernel]

What do you mean ?

[left knoll]

0.2 × (8+3x) = 0.4 × (3+2x)

[idle bone]

A trader buys 30 kg of type A oranges for Rp. 360,000.00 and 20 kg of oranges of type B for Rp. 210,000.00. The two types of oranges are mixed and sold retail per kg. If the trader wants to make a profit of 25%, then the selling price of oranges per kg is ..............

A.IDR 14.250.00
B.IDR. 14,500, 00
C.IDR 15,425.00
D.IDR 15,450,00

[weary arrow]

Check rule 5 in #rules

[left knoll]

anyone? 😭

[left knoll]

I dont have a test dw

Smh

[ember kernel]

That's what your message suggested

Don't just "smh" her

[left knoll]

My bad but I always say smh but dont mean it so dont come at me [and everyone else -_-]

[clear fern]

thanks a lot for the explanation !

[valid idol]

Formalize in N the following statement:
"If a and b are relatively prime, then there are infinite prime numbers congruent to a mod b”
using the language L = { 1, <, + , . }. anyone ?

[dusty sequoia]

does anyone know what epsilon and " | " mean in this pictures?

[ember kernel]

It's not epsilon, it's a special mathematical symbol that means "belongs to"

And the | is also a maths symbol that means "such that"

Knowing them is a plus, since they are formal symbols

So you could read the last screen as :
"A(x) is defined as the set of all values y such that, for any given x that belongs to the set L, y belongs to the interval between hl(x) and hu(x) included"

The first one is
"L is defined as the set of all values x that belong to [0,l]"

I leave the translation of the second screen to you

[dusty sequoia]

Thanks for the answers

[ember kernel]

I don't know, so I can't know that
I read smh, so I interpret it as smh ¯_(ツ)_/¯

[dusty sequoia]

for the second screen, does the flipped A hold any special meaning?

[ember kernel]

Yep

It's the formal math symbol of "for all"

Wanna give it a try ?

[dusty sequoia]

Then,based on what I know,the second screen has this meaning: l is greater than h(x) for any given x that belongs to L.

[valid idol]

anyone into this stuff?

[atomic dagger]

Hi! I have this matrix and the eigenvalues are (4,1,1). I'm really confused as to how to find the eigen vectors. I always find something different than the actual answer.

For example, this is the correct answer:

When I replace lambda with 4, I obtain
2x+3y =0
y+z = 0
<=>
x = -3/2 y
y = -z

[ember kernel]

Yep ! Also ">>" doesn't only mean "greater". It means "significantly greater", which is to emphasize that one is much much much bigger than the other

[valid idol]

hey quentin could you please look at my problem, if you know anything of that stuff 😇

[left knoll]

anyone? 😭

[ember kernel]

Sure. Could you reply to the message you sent so I can see where it is pls ?

[valid idol]

@ember kernel

[ember kernel]

Oh yeah that one thanks

I saw it, but I've never been introduced to congruence I'm sorry

[valid idol]

no problem, thx anyways

[left knoll]

would u somehow know mine?

it’s maths but not maths 🙂

[atomic dagger]

okay nevermind I found the answer, if for some reason someone else is struggling with how to find eigenvectors i can explain

<@&717391911132069929>

[ember kernel]

If the pentagon is regular then some basic geometry might be sufficient I think. But I'll be honest with you, geometry (just like congruence lol) is one of my weak points regarding maths

[supple island]

when you replace lambda=4 you obtain
000
230
203
so you have x=-3/2y, x=-3/2z, we could write (1.-3/2,-3/2) which is the same thing as (-3,2,2)

[left knoll]

thanks, but not that one. i solved it already

[left knoll]

^ this one

[supple island]

wdym "a mod b"

[ember kernel]

modulo

[supple island]

oh ok

[ember kernel]

The rest of the division of a by b

[atomic dagger]

thank you! but i was wondering, how come the two other eigen values are 1 and 1, yet we are given two different eigen vectors ?

[supple island]

it's 1 eigenvalue that produces 2 eigenvectors

because when you substitute lambda=1 all you get is x=0

so you have freedom with y and z

so you just need to write 2 vectors that are lineary indipendent from each other and the first one and that have x=0

the easiest ones are (0,1,0), (0,0,1)

[supple island]

<@&717391911132069929>

[valid idol]

do you have an idea on how formalize that with the given language?

[supple island]

honestly i'm not really understanding the statement

[dusk harbor]

Knowing that p(1) = 2 and p'(1) = 1 and p(2) = -1 how do i write the polynomial on Newton's polynomial (Interpolation)?

[dark sorrel]

Have you seen hermite interpolation, it is newton interpolation in the limit where two interpolation points fall together, then you can use the derivative in that point

[vast gyro]

does anybody know any resources for vector calculus?

[brave garnet]

hi guys , need some help here, thanks

[real zenith]

hello

can anyone help me with statistics?

[torn flower]

Guys help me please

[left knoll]

<@&717391911132069929>

[quaint imp]

im so confused

[glacial dust]

guys I have a concern my prof said that I have to convert it to SI units so there was one question to find the area my ans was right but I wrote it as 10^-7

should have I wrote it as nano or micro?

plz someone respond thank you in advance

the reason why am confuse bcuz its an area but with a diff unit yeah np but hearing me say nanometer squared kinda sounds wrong

[supple island]

100 nano or 0,1 micro

whatever you like

[glacial dust]

nanometer squared sounds weird tho

[supple island]

wait, squared?

[glacial dust]

yeah cuz its area

[supple island]

so 10^-7 meters?

squared

[glacial dust]

yah i typed it in the calcu they gave me that

I times it with 10^6

to make it m2

the result was 1.25x10^-7

I multiplied it with 10^6

[supple island]

sorry, it's 0,1mm²

[glacial dust]

SI units

[supple island]

yes

mm is millimeters

it's not nano nor micro

[glacial dust]

how do u know mm or cm tho?

its 10^-7

[supple island]

because in squared units 1m²=100dm²

so 10^-6m²=1mm²

[glacial dust]

oh so 10^-7 is the same as -6?

[supple island]

no?

10^-7m²=0,1mm²

[glacial dust]

then how do i convert this to 1.25x10^-7

how should I write it

[supple island]

if you multiply the left hand side of this by 1.25 you'll get what you want to convert right?

multiply the right hand side too

[glacial dust]

but what happens if i multiplied it with 10^6

is it still considered as m2?

am getting 0.125

[supple island]

yes

[glacial dust]

oh ok thxx

[willow basin]

hey can anyone help?

i did x^1/2 * x^7/2 = x^4 and x^1/2 * x^1/2 = x^1. therefore x^4-x^1 = x^3, which differentiates to 3x^2. got it wrong tho idk why.

also there's this other question that idek what it means.

i thought it meant the grad = 1. so i do 9-x^3 = 1. solve and it gives -2. but i also got this wrong and idk why.

thanks in advance to whoever helps.

[left knoll]

use product rule

dy/dx= uv'-vu'

<@&717391911132069929>

[willow basin]

I tried using it and still got it wrong.

[left knoll]

you need product and chain rule. think of it as y = x^.5 * f(x)

[left knoll]

ye thats what i meant my b

[left knoll]

it should simplify to x^3-x = f(x) and also try to keep things on the same side of the equatily sign. you missed that there was a dy/dx on that left side when moving it. As for the second question its giving you the derivative. The rate of change of y with respect to x can be read as dy/dx, so dy/dx = 1 = 9-x^3, and you solve for x.

[ember kernel]

x^4 - x is definitely NOT x^3

Differentiate x^4 - x and you get 4x³-1

Do not use chain rule here, it's a waste of time

because it's easier to just calculate that the initial expression is equal to x^4 - x rather than multiplying several terms by many square roots, which is very error-prone

[left knoll]

mb yea, thats def easier ^ and yea i was wrong, it should be y = x^4-x

[tough elk]

quick help why is it not 0

[left knoll]

(ok i hope im right this time lol) the derivative of e^t = e^t and d/dx (a* f(x)) = a* d/dx f(x). so the derivative should be the same as your first answer

@tough elk

[gritty cloud]

Guys

How to prove triangle inequality?

[ember kernel]

https://www.cuemath.com/geometry/triangle-inequality/

[supple island]

?

[pulsar turret]

Can someone help me solve this question? Answer: (2,3) and (4,1)

[cyan night]

i can help u

do u know how a distance between two points are calculated?

use the distance formula

let the coordinates of the point(s) you want to find (x,y)

by the distance formula, sqrt ((x-1)^2 + (y-0)^2)) = sqrt 10
and sqrt ((x-5)^2 + (y-4)^2) = sqrt 10

this is the crucial part

and then you just solve for x and y

two variable equation

[left knoll]

Hello can someone answer me the question why there is suddenly a -3? And not a -2?

[cyan night]

i think it may be a typo

[left knoll]

So it is a mistake by the teacher right?

[cyan night]

yep

[left knoll]

Thank you

I seriously was like am I silly or the prof?

[cyan night]

😅

[pulsar turret]

Thank you!!

[hoary bloom]

I think it's -17/2

[left knoll]

Hello there is this -3 again. Shouldn’t it be -2?

My prof is a genius. But he is confused from all his knowledge

You know people who has a high IQ have some struggle with thinking clean?

His classes are a mess. You sit there and he explains and makes many mistakes and suddenly he says things over your knowledge 😂

Can be. But he got professor without learning

You are German?

Exactly. I have to study it by my own

[slow cobalt]

this is parametrics

do you have to do anything before eiliminating t

can u make x = 90 and y = 7.5

[left knoll]

Which is the correct answer now?

[slow cobalt]

man the numbers are not nice to solve it

ill try it

[left knoll]

Feel you bro

[slow cobalt]

this doesnt seem right

what if u find the time

by doing 90/35

and then sub in that for t for x and y

t was 2.97

if u put that in y

u get 7.87

huh

ahaha

i guess so lol

imma have to check that agane with my tutor

its a stupid question

thnx for the help

[left knoll]

Can someone explain me how do I get the result 1/6 ln(x^2+2)+c

I do not get the way there

How the heck can be 2/2 there

[slow cobalt]

is the right side the working out for the asnwer

or is it part of the question

[left knoll]

No left side is the function and right side the answer

[slow cobalt]

oh okay

[left knoll]

I need an explanation

I do not understand where the heck this 2/2 come from and then 1/6

WTF?

Yes pls

But if you do 2/2*1/3

It is 1/3

How do you suddenly get 1/6

[cyan night]

zanza r u middle school

[left knoll]

Uhm

[cyan night]

o okay thought ur role