help-33

[fair gate]

I'll just ask my teacher tmrw

I understand it more when he's explaining it on the board

[proud ice]

Yeah. Sorry, Discord isn't a great place to draw stuff 😦

[vital oracle]

you mind if I try drawing this?

[fair gate]

It's totally fine

[fair gate]

Sure

[vital oracle]

for this, what I usually do is begin one condition at a time

lets say you only need a rational function with a vertical asymptote of x = 1

what would be the easiest rational function you can find

[fair gate]

idk..

3x-1

[vital oracle]

do you remember any rational functions?

[fair gate]

3x-1/3x-1??

[vital oracle]

try not to guess

Im just asking for a rational function with an asymptote right now

[fair gate]

(3x-1)/(3x-1)(x-1)

That

[vital oracle]

it looks like youre not paying attention to what Im asking

lets go with what youre doing then

[vital oracle]

do you know where the hole is for (3x-1)/((3x-1)(x-1))

[fair gate]

nope

[vital oracle]

you know why you went for dividing by (x-1) right?

[fair gate]

Yea cuz in the question it says x=1

It's a vertical asymptote

Right?

[vital oracle]

yep

and what about the (3x-1)/(3x-1)?

[fair gate]

Yea idk about that

They cross out

[vital oracle]

they do cross out for almost every value of x

except for x = 1/3

do you see why

[fair gate]

no

Is it cuz it's in the question?

1/3

[vital oracle]

do you know what the question means by "hole"?

[fair gate]

And that's where the hole is

[fair gate]

Not really

I'd appreciate if u could explain

[vital oracle]

lets say you had the function x/x

what would its value be if x = 2

[fair gate]

x-2

[vital oracle]

if x is 2,

what would x/x be

[fair gate]

2/2

[vital oracle]

you didnt say 1

[fair gate]

Oh

💀

[vital oracle]

2/2 is 1

[fair gate]

Yea 1

Yea mb

[vital oracle]

now if x is -2

what would x/x be

[fair gate]

-1

[vital oracle]

-2/-2 is -1?

[fair gate]

Nah its 1

Cuz 2 negatives is a positive

[vital oracle]

so if x is a negative number,

what would x/x be

[fair gate]

Wym?

[vital oracle]

if x is a negative number, would x/x always be 1?

think about what happens when you divide a number by itself

[fair gate]

If only 1 x is a negative number and the other x is a positive then it'd be a -1

[vital oracle]

???
presumably if I use the same letter on the top and bottom, they would have to be the same value

if the xes were different, I would instead be using different letters

[fair gate]

No idea what ur saying

As I said I'll just ask my teacher tmrw

Thank u for tryna help tho

[vital oracle]

bruh

[fair gate]

I'm just not feeling it today

[vital oracle]

yea I can tell

do you want to still see the picture anyways?

[fair gate]

I've been sick for the past week

[fair gate]

Sure

[vital oracle]

that doesnt mean giving up

[fair gate]

yea ur right I just want the break to start already lmao

[vital oracle]

you know you bothered to ask on the server

you might as well stay to see how its done

we can start with this picture

[fair gate]

Alr fine 😭

[vital oracle]

yea

[vital oracle]

this is the graph of x/x

when x is positive, x/x is always 1

[fair gate]

Hm alr

Yep

[vital oracle]

when x is negative, x/x is always 1

[fair gate]

Yea I understand that

[vital oracle]

then you cant make up a reason for saying it cant be 1

[vital oracle]

now take a look at what happens when x is 0

you would get 0/0

now you cant divide by 0, so 0/0 cant mean anything useful for us

[fair gate]

Which is 0

Yea ik that

[vital oracle]

0/0 is not 0

dont guess on 0/0

0/0 is "indeterminate"

[fair gate]

Huh

[vital oracle]

you know youre already tryna guess when Im still teaching you what is even up with x/x

0/0 is too different from most numbers to count as a number

[fair gate]

Alr

[vital oracle]

the problem here is that 0/0 can be reasoned to be any number

if you had 0/0 = a number

then 0 = 0 * a number (multiply both sides by 0)

any number can fit there

so 0/0 can be any number

[fair gate]

I see

[vital oracle]

for this reason 0/0 is called an "indeterminate form"

it is one of seven

wait afk

[fair gate]

Yea I saw

[fair gate]

I gtg in a bit

My phones about to die

[vital oracle]

yea you can charge for now, you lmk if you want to go back to this

[fair gate]

Alr thanks for ur help tho

Take care

.close

[marsh citrus]

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[vital oracle]

cya later

[marsh citrus]

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[jolly shell]

Am i missing something? are the intercepts not -2 and 3?

[sinful pier]

How do I do this? I missed this lesson in class and I have zero clue

🧍🏻

Well nvm

[marsh citrus]

@jolly shell Has your question been resolved?

[jolly shell]

<@&286206848099549185>

[marsh citrus]

@jolly shell Has your question been resolved?

[marsh citrus]

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[undone tangle]

Algebra 2 Honors

[half shell]

.ccw

[half shell]

thanks

open a separate help channel.

Don't interrupt someone else's question.

[undone tangle]

This sector is occupied.

[odd orchid]

#❓how-to-get-help

[undone tangle]

I have to go

.close

[marsh citrus]

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[sinful hare]

why are there 3 inflection points and not 2?

I can only see the concavity change 2 times

[fervent rampart]

it's a graph of the first derivative

[lofty otter]

There are 3, the first from negative to positive, then from positive to negative and finally from negative to positive

[sinful hare]

oh youre right

for some reason I thought it was just f(x)

thanks

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[marsh citrus]

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[marsh citrus]

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[grand smelt]

how do i prove A = B = C

[main idol]

Use definition of complementary

[grand smelt]

its 2 angles that add up to 90

[main idol]

And the sum of the angles in a triangle equals ?

[grand smelt]

180

[main idol]

Write that in an equation

[grand smelt]

ok

but wouldnt A + B + C = 180 be supplementary

[main idol]

I don't see how that relates to anything here

[main idol]

Sorry I led you astray

That was a bad hint, I misread the problem

[grand smelt]

is this good

[main idol]

135 not 145. You can do 135 - (B+C) = 135 - 90 and you're done with A

[grand smelt]

oh yea i miscalculated

thanks for ur time

.close

[marsh citrus]

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[sand wind]

Help

[sand wind]

Idk how my friend got this question

And also

How do i solve this

<@&286206848099549185>

[cedar stone]

notice 2y+50 = ?

[sand wind]

No?

But i understand you

[cedar stone]

ok

the angle opposite to the 50* is also 50*

[sand wind]

Correct

[cedar stone]

so y*+50*+y* = 180, right

[sand wind]

Ye

The star means x right?

Nvm nvm

Continue

[cedar stone]

it means degrees

so

2y* + 50* = 180*

2y* = 130*

[sand wind]

Do we divide the 130 by 2?

[cedar stone]

yes

[sand wind]

65

Aight thanks man

Can you help me with the next one?

[cedar stone]

hm

[sand wind]

P and q one

With the circles

Why is the answer 2?

Is it because the circle is just smaller???

@cedar stone

[odd valley]

The radius of the big circle is the diameter of the small circle

[sand wind]

So we just divide the 4 by 2 then?

Since it's a half of the big circle?

Maaaaan

How 2 do question?

Both

[north socket]

B

[sand wind]

Ok

I know why

I just don't know the process

[north socket]

The price in Feb is 120 + (120x10%)= 132

[sand wind]

Yeah i get that

I'm struggling like

132 - (0.1)

Mentally

I cannot use a calc

[north socket]

why can't you use calc??

where are you from??

[sand wind]

Indonesia

[sand wind]

This is a practice book for a entrance exam for a uni i wanna go to

I am not allowed a calc

[north socket]

how old are you??

[sand wind]

Why???

[north socket]

I am from Vietnam and my country allows to use calc

[sand wind]

Well that's vietnam

[north socket]

i am just 16 years old

[sand wind]

I see that's interesting man

Ok i found out how to do question 8

How do i do the next one?

Rstu

[north socket]

what do you struggle with??

[sand wind]

Idk it's asking for the measure of st?

Idk what that means

[north socket]

ydk how to solve 132 - (0.1)??

[sand wind]

No i already know now

What I didn't know is that 132 + 10% = 13.2

13.2 - 132 = 118.8

[north socket]

It is not 132 + 10%= 13.2, it is 132x10/100

[sand wind]

I see, thank you Vietnamese boy

[north socket]

can you share me your practice book

because i am going to do a exam entrance for uni

[sand wind]

Diff uni diff exam

I can't show you this one cuz it's customed to my uni

Just go to khan academy SAT

Most unis are really similar to that one

[north socket]

thks bro

[marsh citrus]

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[small stream]

Why is this incorrect?

[small stream]

The answer is

[modern sedge]

Your answer looks correct.
Idk why they have (2x+y) instead of (x^2+y)

[small stream]

Ok maybe they missed smth...thx

.close

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[frank lintel]

Let $f:[0, \infty ) \rightarrow \mathbb{R}$ be a continous funciton such that $L=\lim_{x \to \infty} f(x)$ exists and is finite

Prove that if $f(0) \leq L$ then the function f has an absolute minimum in ray $[0, \infty)$

[elfin berry]

prograce

[frank lintel]

Can someone explain why this is even correct ?

[devout mauve]

try drawing a few graphs

you'll see that they will always have some minimum point

[proud ice]

what is f(0)?

[frank lintel]

Let's say this converges to 5 but it f(0) is -infinity

[proud ice]

f(0) makes no sense as infinity

f maps to R

[frank lintel]

Minus infinity?

[proud ice]

Is this a real number?

[frank lintel]

No

[proud ice]

https://tenor.com/view/well-there's-your-problem-mythbusters-adam-savage-jamie-hyneman-broken-gif-17934071823679545476

[frank lintel]

😭 why is this a problem

[proud ice]

Because f maps to R

and minus infinity is not a real number

so mapping f(0) to minus infinity is contradictory to how f was defined

[frank lintel]

Y=x^2 maps to R ?

[proud ice]

yes

[frank lintel]

It has infinity

[proud ice]

where?

Which number maps to infinity?

[frank lintel]

When x goes to infinity

[proud ice]

But when does f(infinity) happen?

[frank lintel]

Never

[brave knoll]

(Since f maps from [0, infty), your function must have an image in 0. i.e. f(0) exist and is a real number
It is like g : R \ {0} -> R defined by g(x) = 1/x
we dont have an image in 0
but it is false to write
g : R -> R defined by
g(x) = 1/x
since g(0) is not defined)

[proud ice]

precisely

[frank lintel]

I understand

Thx

.close

[marsh citrus]

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[marsh citrus]

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[terse basin]

for recursive form questions, what do i do when it says n is larger than or equal to any value other than 1?

[terse basin]

like in this case question 2

says for n larger than or equal to 2

how many n values must i prove then?

[desert dirge]

your base case would just be 2, then everything else is as normal

though you can check 1 (its given to be 7)

[terse basin]

so do i check n=2, n=1, or both?

[desert dirge]

id start with 2

since u_2 requires u_1 anyway

theres no way to use that formula with 1

[terse basin]

so the equation next to U1 is the one i plug n=2 into to get a value for n=2?

[desert dirge]

yeah

[terse basin]

ohhh okay

[desert dirge]

n_1=7 which fits the thing youre proving anyway so you dont really need to mind it

though a small note of it would probably be worth it

n=2 is your real base case though

[terse basin]

so for example if it was n is larger than or equal to 4

am i meant to test 1 up to 4?

i.e. 1,2,3,4?

[desert dirge]

if it said 'all positive integers'

then it would be worth a note before you begin induction

[terse basin]

what does that mean

[desert dirge]

dont lose anything from it

i mean just saying they fit the induction

like here U_1 is given to be 7

the thing we are proving is un=3*2^{n}+1 , u1=6+1=7

thats the most id write for 1

then begin induction with 2

[terse basin]

then in this example i test for n=1 then begin the induction with n=4?

[desert dirge]

youd check for 1,2,3

then begin induction with 4

though i doubt that would happen

[terse basin]

do i write out the working for 1,2,3?

or just straight up start with S1 n=4

[desert dirge]

just a simple whack in the formula being proved would be enough

if its telling you 'for all positive integers' then you can likely assume its true for those its not asking you to prove anyway

but you may as well look yourself for completeness

[terse basin]

then for this specific question i just start step 1 with n=2

yes?

[desert dirge]

yeah

[terse basin]

okay

thanks

do u mind checking my working after i finish it

[desert dirge]

sure

[terse basin]

thanks

where did i go wrong

[marsh citrus]

@terse basin Has your question been resolved?

[terse basin]

.close

[marsh citrus]

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[raven sky]

a physics question , can someone help me with this one?

[raven sky]

cant seem to understand what formula to use or what to do D:

[still temple]

are you supposed to use maxwell equations ?

[raven sky]

dont think so

studying amperes law for now

[still temple]

with the integral stuff ?

[raven sky]

yeah i can solve those (somewhat xd)

i would like if its a normal equation but if all come to this integral , i can do smthing

(tho im not sure what that thingy in integral really means)

[still temple]

i forgot how to do this sry

[raven sky]

.close

[marsh citrus]

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[marsh citrus]

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[split vigil]

a deck of 52 cards will be given without replacement to 4 people, each will be having 13 cards, what is the chance that one person gets all 4 aces, does anyone know how to approach this question or what to do?

[daring cradle]

First calculate the denominator

[night mica]

$\binom{52}{13}\binom{39}{13}\binom{26}{13} \binom{13}{13}$

[elfin berry]

everg

[daring cradle]

I think there is multinomial notation for this

But it’s basically 52!/(13!)^4

[night mica]

right

in the numerator you start assuming that the 4 aces has been already distributed to (e.g.) the first person and you count another time how many distribution of the deck's cards (now it is of 52-4=48 cards) are possible

then you multiply by 4 what you get, as everyone of the four people can get the four aces

[rotund violet]

wait no?

it isn't

i think a constructive approach is better for this

so lets assume without loss of generality that Bob has the Ace of spades

[daring cradle]

That’s the denominator

[rotund violet]

oh

[daring cradle]

Everg already showed how to calc numerator

[night mica]

lucky bob

[daring cradle]

Sandwiched by green guys

[split vigil]

okay so

[split vigil]

wouldnt the denominator be 4^52 huh

[daring cradle]

no

[split vigil]

is the answer 1 in 106k

[rotund violet]

no thats not correct

here

so Bob got the ace of spades lets say right?

now assuming nothing other than the fact that Bob got the ace of spades, what is the chance that Bob got the aces of hearts?

well, he has 12 cards remaining

and there are 51 cards in total remaining

so its a 12/51 chance, that he will also get the ace of hearts right?

[marsh citrus]

@split vigil Has your question been resolved?

[split vigil]

Yeah

[rotund violet]

okay, now assuming that bob has both the ace of spades and ace of hearts, can you calculate the chance that bob has the ace of diamonds

[split vigil]

Wait im sorry ace of heart is a one in 51 chance and bob needs 12 more cards therefore its 1/51 x 12 right

[split vigil]

That chance would be 11/50

[rotund violet]

yes

now assume that bob has ace of spades, hearts and diamonds. what is chance bob also has ace of clubs

[split vigil]

In total the chance would be 13/52 * 12/51 * 11/50 * 10/49 that he has all 4

[marsh citrus]

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[rotund violet]

.reopen

[marsh citrus]

✅

[rotund violet]

well yes, but we don't multiply by 13/52. because we just need one person to have all 4 aces. it doesn't have to be Bob. we took the person who had a certain ace as "given" and calculated the probability that he recieved the other 3 aces. thus the answer is $12/5111/5010/49$ only

[elfin berry]

Arnavutköy

[marsh citrus]

@split vigil Has your question been resolved?

[split vigil]

Ohh that makes sense

Thank you, one last question, is it possible to do this with the hypergeometric distribution

X~Hypn(13, 3, 51)

[rotund violet]

wikipediaing the definition of this it seems yes

although i believe it would be Hypn(12,3,51) if i am reading it right?

[split vigil]

Oh yeah

Right

Eyvallah arnavut köy

[marsh citrus]

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[raven sky]

$$\int \frac{1}{a^2-x^2}dx$$

[elfin berry]

Mythicility

[raven sky]

im getting a answer of $$\frac{1}{a}(\ln \frac{\sqrt{a^2-x^2}}{a} + \frac{x}{\sqrt{a^2-x^2}})+c$$

[elfin berry]

Mythicility

[raven sky]

but wolfram alpha says its $$\frac{1}{2a}(\ln(\frac{x}{a}+1)-\ln(1-\frac{x}{a})$$

[elfin berry]

Mythicility

[raven sky]

i dont think these are same , i tried solving with trig sub

x=asintheta
dx = acostheta

int(acostheta / a^2cos^2theta) dtheta
1/a int(1/acostheta) dtheta
1/a int sec theta dtheta
1/a int ln|sectheta + tan theta| +c

and then it results in the answer im getting , where am im going wrong?

[still temple]

idk but simpler is to split into 2 fractions with no x^2 at denominator

[still temple]

split this i mean

[raven sky]

i dont wanna do partial fractions :C

[still temple]

ok

[raven sky]

tho whichever way i do , i should get same answer , no?

[still temple]

yes

[raven sky]

then why are my answers different D:

[still temple]

idk, my message was just about the simpler way

[raven sky]

<@&286206848099549185> D:

[marsh citrus]

@raven sky Has your question been resolved?

[raven sky]

<@&286206848099549185> D:

[narrow oak]

hm

I tried

[marsh citrus]

@raven sky Has your question been resolved?

[marsh citrus]

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[fossil osprey]

How to solve inequalities with complex variables?

[distant peak]

C isn't an ordered set

[fossil osprey]

Yeah C isn't ordered I agree with that

But can't we for example say that 1 > 0 ?

[distant peak]

in R ? yes

[fossil osprey]

what about in C

1 + 0i > 0 + 0i (?)

[distant peak]

we have imaginary numbers there
we cant say nothing

[distant peak]

this is just one case but it doesnt expand to the whole set

[fossil osprey]

Can I say that a + bi > c + di
is a verifiable statement whenever a, c are real numbers and b, d are zero?

[distant peak]

that would just mean you are working in a set like this :
A = {x = a+ib | a € R and b = 0}
and this set is R lmao

[fossil osprey]

Yes what I'm basically saying is that some complex numbers are real, and when they are we can do inequalities with them

[distant peak]

well yes, but again you are still restricting yourself in R

all your solutions will be in R

[ripe forge]

this actually makes no sense because complex numbers do not have a value that can be compared. A complex number is practically a vector or may be represented as a vector

and if your imaginary part is always 0 then it's just real numbers like herels has pointed out

[fossil osprey]

Well If I treat it as a vector then I can't do 1+0i = 1
(Because a vector and a singleton are different things)

[fossil osprey]

Let me give another example,
Does z = i satisfy
z² < 0 ?

[ripe forge]

have you tried solving it graphically?

from what i have learned about complex numbers, an inequality in terms of z only makes sense when you break it down into x+iy form and plot it on the argand plane

from the inequality you get your required region that satisfies it

i think it's about finding the locus that the complex number inequality represents rather than trying to figure out if a certain complex number is greater than the other

[marsh citrus]

@fossil osprey Has your question been resolved?

[fossil osprey]

So I tried this but without the plotting and what I got was this:

[ripe forge]

it still doesnt really make sense unless you take modulus of both sides of the inequality , you simplify z^2+z+1 into a complex number which you need to be greater than 0. That just doesnt make sense to me according to my knowledge of complex numbers

now if you want the modulus of the simplified complex number to be greater than zero then it signifies a distance being greater than zero which makes sense

otherwise a complex number i.e. a point on a plane being greater than another point on the plane is meaningless

the second line doesnt follow from the first line, honestly i dont even know what the first line even means. You should ask your teacher about this

a^2-b^2+a+1 + (2ab+b)i <----this is a complex number of the form x+iy. x+iy>0 does not carry any meaning

[marsh citrus]

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[marsh citrus]

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[shell ruin]

Help

[shell ruin]

Spring question

I’m stuck on in what energy considerations to use

[buoyant pond]

why dont you use the work energy theorem

[shell ruin]

What’s that

[buoyant pond]

change in kinetic energy = sigma work done

[shell ruin]

Oh yeah I know that

But I’m not really sure about the energies

[buoyant pond]

change in kinetic energy = 0 you agree?

[shell ruin]

I’m not a physicist and I’m forced to do mechanics as an option module which is why I struggle

[shell ruin]

Yeah

[buoyant pond]

same

[buoyant pond]

and the work will only be done by the fricitonal and spring force?

[shell ruin]

So no change in gpe which is what I thought?

[buoyant pond]

mg and N wont do any since they are perpendicular

[shell ruin]

Ok

[buoyant pond]

yeah

and i hope you know how to calculate the work done by fricttion and the spring

[shell ruin]

Nope

I know friction

[buoyant pond]

1/2kx^2

k is the spring constant

so till its relaxed the spring will do +1/2kl^2 after which it will do -ve work

[shell ruin]

I haven’t learnt that, we use T=(lambda x^2)/2l

For energy in spring

[buoyant pond]

whats lambda

[shell ruin]

Modulus of elasticity

[buoyant pond]

oh

yeah so modulus of elasticity/l = k

same thing

[shell ruin]

That’s just to find the tension force right

[buoyant pond]

No

spring force is kx

[shell ruin]

I’m only aware of tension=lambda x /l and the previous one

We don’t use the spring force I don’t think

[buoyant pond]

lambda / l is k

its just a constant dosent matter

[shell ruin]

Ok

[buoyant pond]

so what will be the +ve work by the spring you tell me

[shell ruin]

At what point in the motion?

[buoyant pond]

from when it is intially at rest to the point where the spring is in the natural length

[shell ruin]

Tension

[marsh citrus]

@shell ruin Has your question been resolved?

[marsh citrus]

@shell ruin Has your question been resolved?

[shell ruin]

<@&286206848099549185>

[plush gazelle]

what’s up

[shell ruin]

Mainly stuck on part c

Just lost what to do

Here’s answer

[plush gazelle]

it’s oscillating

[shell ruin]

No not part d I’m doing c

[plush gazelle]

yeah but every time it rests it’s only for an instant

same with the second

[shell ruin]

Ok

[plush gazelle]

what is the epe formula

sorry if i’m confusing my mechanics are very rusty

[shell ruin]

Lambda x^2 / 2l

Where lambda is modulus if elasticity x is extension and l is natural length

[plush gazelle]

what does that equal

[shell ruin]

EPE

[plush gazelle]

energy?

[shell ruin]

Elastic potential energy

[plush gazelle]

okay yeah

so you equate the potential to the initial kinetic and subtract off work done by friction

[shell ruin]

Oh nvm I’ve got it

Misread the q

Thanks for the help bro, have a good one!

.close

[marsh citrus]

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[marsh citrus]

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[fierce fulcrum]

how do i do question 6

[fierce fulcrum]

anyone

<@&286206848099549185>

[steel gull]

i think u just find two sols of x and find the differene (like subtract them)
so one root is like x^3=-2664+64
and the other is x^3=-2664-45
solve for each x

[fierce fulcrum]

o

ok

would this work thou

[steel gull]

but it looks to simple to be an answer what level is tjis

[fierce fulcrum]

like around grade 10 to 11

loom at the other qesations

[steel gull]

ok yeh i think thats how u do it lemme double check tho

[fierce fulcrum]

np

[steel gull]

ok no thats not the way

[fierce fulcrum]

ok

[steel gull]

x^6 - 19x^3 - 216 = 0

solve this

[fierce fulcrum]

can u factor this

[steel gull]

The real roots of this equation are x = -2 and x = 3

[fierce fulcrum]

$[x^6 - 19x^3 - 216 = 0]$

[steel gull]

this is what ai says

[elfin berry]

Slimy
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[fierce fulcrum]

which one

[steel gull]

im lost...

[fierce fulcrum]

ok

np

.close

[marsh citrus]

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[fierce fulcrum]

how do i do 6

[calm harbor]

Hint: Consider replacing x^3 with t.

[fierce fulcrum]

what t

[subtle pebble]

t is just a placeholder variable

[fierce fulcrum]

ok

[subtle pebble]

you can also just expand the equation

[fierce fulcrum]

yeah

[subtle pebble]

you will end up getting a quartic, and then you can just substitute another variable

then its just a quadratic

solve

[fierce fulcrum]

how

[subtle pebble]

try expanding first

[fierce fulcrum]

would it be ike x^6

[subtle pebble]

wait

is that a cubic

nvm

[fierce fulcrum]

yeah

[subtle pebble]

you can do the same thing i think

[fierce fulcrum]

ok

[subtle pebble]

yes

[fierce fulcrum]

how

[subtle pebble]

just multiply it out

FOIL

[fierce fulcrum]

ok

yeah

[subtle pebble]

you will get a power of 6, subtitute a variable so it becomes a quadratic so it's easier to solve

[fierce fulcrum]

you would get $[x^6 - 19x^3 - 216 ]$

[elfin berry]

Slimy
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[subtle pebble]

correct

[fierce fulcrum]

wdym

[subtle pebble]

you can subsitute another variable for x^3 and then solve for that variable

[fierce fulcrum]

so like $[x^6 - 19y - 216 ]$

[elfin berry]

Slimy

[subtle pebble]

wdym

[fierce fulcrum]

idk

i have to go eat sorry

[steel gull]

good idea

[subtle pebble]

if you substitute y for x^3, you will get: $y^2-19y-216=0$

[elfin berry]

抹茶
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[steel gull]

u can make x^3 = y

wait not

oh

hmmm

how did u do y2 then

both are x3

[subtle pebble]

now it is just a quadratic

$(x^3)^2=x^6$

[elfin berry]

抹茶

[steel gull]

ok ure solving the

x6 one

yeh right

[subtle pebble]

yep

[steel gull]

so two sols

cuz quadratic

[subtle pebble]

so now u can just plug in

[steel gull]

and then just plug back

[subtle pebble]

quadratic is not necessarily 2 sol

[steel gull]

or 1

or none

[subtle pebble]

yep

[steel gull]

but question told us its 2 roots

@fierce fulcrum

[subtle pebble]

right

[steel gull]

this is correct

[steel gull]

are u good in linear algebra

specifically vectore spaces and planes

[subtle pebble]

uh i'm not sure

do you have a problem

[steel gull]

yeh

hmmm

[marsh citrus]

@fierce fulcrum Has your question been resolved?

[fierce fulcrum]

Thanks

[marsh citrus]

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[still temple]

E

[still temple]

I should be splitting the function so that I can get rid of mod and step function

Am I right?

[proud arch]

Hmm

For the step function x^2 +2x is always increasing for positive intgers

[still temple]

by "spliting the function" i mean writing the piecewise function

[proud arch]

For bigger the x bigger the value

For |5x-7| for 5/4 to 5/7 it decreases then for 5/7 to 2 it increases

[still temple]

ah

substitutions

[proud arch]

Yup

Clearly at x =2

It's value is greater

So ofc max at x = 2

For min

Make the mod term 0

So at x= 7/5

Is min

That should do it I think

@still temple

[still temple]

could you give me some time

[proud arch]

Ofc

[still temple]

ty

[proud arch]

Is this for some competitive exam?

Cuz like the date at the side

[still temple]

yeah

JEE

[proud arch]

Cool

You in 11th or 12th

That's when most people prepare for this right?

[still temple]

hehe

im just helping someone else

passed JEE this year

[proud arch]

Let's gooo

Congrats man

What like rank

[still temple]

60k 😔

[proud arch]

Idk if that's good or not

[still temple]

not good

[proud arch]

Ohh

Is there a reattempt?

[still temple]

yeah but im not going for it

[proud arch]

So is that rank enough to get into iit?

[still temple]

no for IIT we need to write JEE advanced

my rank for that was 20 k

the closing rank is 14k ig

[proud arch]

So which will get with that rank?

[still temple]

nothing

[proud arch]

So you will go for something else

Like not an IIT

[still temple]

yeah

BITS

[proud arch]

Never heard of it

[still temple]

lol

[proud arch]

I definitely do find

Like a lot of questions online

That people say are like jee level

[still temple]

there are quite a lot of people in this server itself

[proud arch]

That's why I know about iit and stuff

Like this one

Someone said this jee level

[still temple]

JEE is a pain

they test your speed rather than your skills

[proud arch]

Hmm

[still temple]

or your understanding of the concept

btw

the answer is 15

[proud arch]

For this?

[still temple]

x=2 gives us 11 ?

no, the one i asked

[proud arch]

Oh

Forgot about that

Lol

[still temple]

e

[proud arch]

Ya

Um

Max at x= 2

Gives 11

And min at x =7/5

Gives 4

[still temple]

oh

mb

forgot we should be adding

[proud arch]

Is alright

[still temple]

thank you

nice talk

.close

[marsh citrus]

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[proud arch]

Welcome

[proud arch]

Sure was

[marsh citrus]

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[fierce fulcrum]

is this right

[fierce fulcrum]

ok
look
3 1/4 is 3.25 meters per sceond
x 60
is 195
then 2 3/4 is 2.75 x60 is 165
and in one lap they cross and 195/165 = 1.18
wait nvm
ok look
you do 195 x24 to find total distance ran
then divide by 180
to find laps ran
which is
26
and then (165 x24) / 180 = 22
then they passed 4 times

[marsh citrus]

@fierce fulcrum Has your question been resolved?

[fierce fulcrum]

.close

[marsh citrus]

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[buoyant jetty]

It is now 12:00:00 midnight, as read on a 12-hour digital clock. In 122 hours, 39 minutes and 44 seconds the time will be $A:B:C$. What is the value of $A + B + C$?

[elfin berry]

938c2cc0dcc05f2b68c4287040cfcf71

[marsh citrus]

@buoyant jetty Has your question been resolved?

[marsh citrus]

@buoyant jetty Has your question been resolved?

[rancid garnet]

After every 12 hours, time will be 12
122 = 2 (mod 12)
A:B:C = 2:39:44
2+39+44=85

[buoyant jetty]

ty

.solved

[marsh citrus]

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[digital hound]

why do we take a^-1 = q/p and not -p/q?

how do we know when to use additive and when to use multiplicative notation?

if we took a^-1 = -p/q then a^-1 < 0, so G wouldnt be a subgroup of H

[regal coral]

for all log(a) in H, show -log(a) is in H

since log(a) is in H we can assume a>0

[marsh citrus]

@digital hound Has your question been resolved?

[digital hound]

i just realized my question was stupid, so we implicitly use the multiplicative notation on Q because of the logarithm rules right?

[digital hound]

nvm i think i got it, thanks!

.close

[marsh citrus]

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[still temple]

yo

[still temple]

yes

i just dont get

the last bit

at the bottom

why is it 13^2?

i thought itd be 13^2 if only if we found variance

[dry prawn]

what do you mean "if we found variance"

[still temple]

i meant

standard

deviation

[dry prawn]

Var(aX) = a^2Var(X) in general

[still temple]

omdz

ffs

im sped

any clue

what ts means

[dry prawn]

indeed i do

what particularly is giving you issue?

[stark trail]

I have this same mentaility

[still temple]

the whole thing

what the hell does this mean mate

[stark trail]

Right matey @dry prawn explain ts

Tf

[still temple]

there is no way

ppl aiming for 100% s1

if ts is coming

absolute waffle

end it

[stark trail]

Theyyy cooked afff

Waffling

Fosho

[still temple]

😭

[lethal bridge]

No way is that austin

[stark trail]

watdup fam

[lethal bridge]

where have you been

[stark trail]

grinding

[lethal bridge]

grinding math

But you’re always mathing

[stark trail]

sir i dm u

[lethal bridge]

ok

[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

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[olive fog]

I need help with those equations

[pulsar pewter]

@olive fog Do you mind rotating that pic

[junior copper]

,rotate

[pulsar pewter]

a

ty

[pulsar pewter]

Oh dang it's in...Russian? Could you translate that for me, then I can help you

[tired oxide]

they’ve been banned. remember not to cheat on exams.

.close

[marsh citrus]

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[junior copper]

how do you know though

[floral rune]

Yeah

[tired oxide]

they said it was an exam in another chat.

[junior copper]

oh yeah i just checked the messages

[floral rune]

I see

[marsh citrus]

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[pliant quartz]

I think i did something wrong here

2233 - 2420 would equal -187

121 cannot go into -187 without a remainder, so i think i did something wrong, but i’m unsure what

No never mind. I see where i messed up now.

.close

[marsh citrus]

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[tranquil token]

Hello! May I ask for some help? I can’t seem to understand what to do with this question. I need to find the range of the function. I’m not sure where to start. (I apologize for the poor image quality, please let me know if you need a better photo.)

[vital oracle]

There’s a neat trick you can do here

[tranquil token]

[vital oracle]

Do + 1 - 1 to f(x)

[tranquil token]

Mhm ^^

[vital oracle]

Then choose one of the 1 to add/subtract into the fraction

[weak surge]

O damn

[vital oracle]

You are aiming to only have one x

[weak surge]

Nice

[vital oracle]

Now for another trick, which I did not know was possible until I saw it happen

You find the inverse, then its domain

(There are less flashy alternatives but I think you ought to check this one out)

[tranquil token]

Wait, convert f(x) into + 1 - 1?

[weak surge]

f(x) + 1 - 1

[vital oracle]

Continue from here, I gotta Z

cya later

[tranquil token]

So then I’d have f(x) + 1 - 1 = x^2 ?

[tranquil token]

Take care, thank you for the assistance ^^

I’m a bit confused, I’m not sure where we got + 1 - 1. Was it from 1 - x^2 ?

Wait, I think I might get it. So we’d replace f(x) with + 1 - 1 so we could get + 1 - 1 = x ?

[weak surge]

Dont think thats what he meant

I think he meant that x^2 / (1-x^2) + 1 = 1 / (1-x^2)

Then f(x) = 1/(x+1) multiplied by 1/(x-1) minus 1

Idk myself but think this is what he meant

[distant peak]

the range is R
why are yall doing all that

[weak surge]

Hmmm

[tranquil token]

I’m not sure either. But I started by replacing 1 - x^2 into (1 - x) (1 + x). So that I would get
f(x) = x^2 / (1 - x) (1 + x)

But wouldn’t that mean the denominators can’t be 0?

[distant peak]

you are looking for range or domain

[rain tangle]

Solve 3%[001€

Sowy

Wrong

[tranquil token]

Range

[rain tangle]

Question

I meant

3÷3×3±3

[distant peak]

rational fraction, it's R
now if you want to know why, you can study the function by doing a variation table or something like that

[rain tangle]

<@&286206848099549185> math.videos pls

[tranquil token]

I’m sorry, but I’m pretty lost on this.

I know what a rational fraction is, I just don’t know what you mean by a variation table

[distant peak]

this thing

[tranquil token]

What does the f(x) with the apostrophe mean?

The middle section

[distant peak]

you dont know derivative ?

🤔

[tranquil token]

I do know, sorry. It’s just my first time seeing this, and at first I wasn’t sure what it was

[distant peak]

it's ok

[tranquil token]

But I am still very lost. I have to find the range, so I was thinking maybe I should put 1 - x^2 on the opposite side of the function, with f(x)

[distant peak]

how ?

[tranquil token]

Multiply both sides with 1 - x^2

[distant peak]

you will just get (1-x²) f(x) = x²

what do you get from.that

[tranquil token]

Well I was thinking, since f(x) is y. Then we could multiply y with the numbers I multiplied both sides with. So
y ( 1 - x^2 )
Then I’d get y - yx^2 = x^2

Then I could add - yx^2 to the other side by turning it into a positive

To get y = x^2 + yx^2

[distant peak]

and ?

[tranquil token]

I’m not exactly sure. It was just an idea, but man, this is so frustratingly confusing to me, the function at hand, I mean.

[distant peak]

the range is an interval or a set, so i dont understand where this method is supposed to go

what I suggest is to do a whole study of the function by taking the derivative, studying the sign of that derivative, obtaining the variation of the function and calculate the limit of the function where it is not defined

[tranquil token]

Actually, I think I got the range. I tried a different method, I plotted the function onto a graph.

[distant peak]

not really rigorous but anyway

[tranquil token]

From there I noticed the y value of two of the quadratics always nears toward -1. And the lowest the function went was 0.

[distant peak]

yea, i got that with this method

,rotate

[distant peak]

the line x = -1 and x = 1 are asymptotes

[tranquil token]

That makes sense

I’ve never learned that method before, but now I really should. With the variation table and all

[distant peak]

the graph looks like this indeed

the range is obviously R

well kinda

[tranquil token]

I understand it now

[distant peak]

the function takes no value between -1 and 0 lmao

[tranquil token]

Range is ( -∞ , -1 ) U [ 0 , ∞ )

[distant peak]

yes

table of variation is truly powerful

[tranquil token]

Thank you, I can see where you got it from with the variation table

[distant peak]

No problem

[tranquil token]

How do I close this question?

[distant peak]

.close

[marsh citrus]

Channel closed

Closed by @distant peak

Use .reopen if this was a mistake.

[tranquil token]

.close

[marsh citrus]

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[slender comet]

a car with the length of 5 meters randomly parks on a street that has the length of 13 meters. What is the probability that another car of same length can fit in? Any help on how to handle this one?

[slender bobcat]

pardon but isnt this 100%

[knotty trellis]

nope

[slender comet]

no it depends how the first car parks

[knotty trellis]

but it nearly is

[slender bobcat]

oh the cars have to come from the same direction?

[slender comet]

I initially thought I could do 8/13 where I get approx 61% but the book says its 75% and im not sure how it got to that number

[slender bobcat]

ok ill just assume they have to come from the same direction

[slender comet]

direction is not mentioned

[knotty trellis]

i dont think it matter anyway

https://www.desmos.com/calculator/r5tauvbvny

[slender bobcat]

ok then whats stopping me from parking 1 car then parking the other car on the very open spot on the other side

[knotty trellis]

the problem is just whether another 5m car can fit here

[knotty trellis]

there is not always that spot

[slender bobcat]

oh im actually just so stupid

[knotty trellis]

But if you label the back of the first car t (as I did in the graph) then I would try determining for which t there is no spot for another car

[slender comet]

?

[knotty trellis]

Let the street start at x = 0 and end at x = 13 for simplicity

now the first car is between t and t+5

[slender comet]

whats t?

[knotty trellis]

just a chosen variable

its random

[slender comet]

ok

[knotty trellis]

e.g. here t is around 4.25

[slender comet]

t=meters?

[knotty trellis]

and t+5 (where the car ends) is around 9.25

[knotty trellis]

yeah, we could say its in meters

[slender comet]

ok

[knotty trellis]

so what's the maximal value of t?

what's the largest t could be?

[slender comet]

5

[knotty trellis]

why 5?

[slender comet]

thatsa the length of the car

oh i see what you mean

[knotty trellis]

i mean whats the largest possible t such that the first car even fits in the street

[slender comet]

whats left is 8 meters

[knotty trellis]

Yep

[knotty trellis]

8 is the largest T can get, otherwise the first car wouldnt even fit properly in the street

so T can be anywhere between 0 and 8

[slender comet]

yes

[knotty trellis]

alright, now for what T can there be another car parked?

[slender comet]

5

[knotty trellis]

If t = 5, then we can fit another car on the left side of it, right

what else?

[slender comet]

ah

[knotty trellis]

this is t = 5, it obviousyl works

because another car can be parked on the left

what other t works?

what intervals of t work?

[slender comet]

im confused

you mean 3=

?

[knotty trellis]

i meant 5

the blue rectangle is car 1 and the mark is T

so T = 5

[slender comet]

the possible t is 8 I get that part

[knotty trellis]

T = 8 also works

[slender comet]

as in the denominator