help-17

[fiery oriole]

If x is 0 then its a lower triangular though

is that what you mean? @crimson jetty

[vocal sleet]

@fiery oriole Has your question been resolved?

[vocal sleet]

@fiery oriole Has your question been resolved?

[vocal sleet]

@fiery oriole Has your question been resolved?

[vast shale]

still having problems?

[vast shale]

its an upper triangular, even if x =0

[vocal sleet]

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[waxen hawk]

Throw two coins, what are the probability that there’s a head and a tail

[waxen hawk]

Can someone tell me the number of outcomes

[sly sierra]

imagine that the coins have different colors or are somehow distinguishable

work out the four possible outcomes

and their probabilities

[waxen hawk]

Why?

[sly sierra]

it's easier if you can somehow apply a label to the coins

[waxen hawk]

Let say they are two identical coins

[sly sierra]

even if it's just coin1 and coin2

[waxen hawk]

I can’t accept it, it changed the circumstances

[sly sierra]

it doesn't change the probability, it just makes thinking about it easier

[waxen hawk]

What if they are identical

[waxen hawk]

I wonder how it works?

[sly sierra]

even if they are identical, you can throw one to the left and the other one to the right

and still distinguish them

"left coin" "right coin"

and you have four outcomes:

   left   right
     H      H
     H      T
     T      H
     T      T

each of those outcomes has the same probability

and the event you want consists of the 2nd and 3rd outcomes

[waxen hawk]

Is it because each of those outcomes has the same probability, so them two identical coins are being distinguished as the left one and right one

[sly sierra]

it's because the left coin is independent of the right one

the left one is H or T with probability 1/2 each

same for the right one

so the four outcomes in the table above each have probability 1/2 times 1/2 = 1/4

[waxen hawk]

That sounds legit

[sly sierra]

so now your desired event "there's a head and a tail" consists of the 2nd and 3rd outcomes

so the probability of that is 1/4 + 1/4 = 1/2

the probabilities of the individiual outcomes add because they are mutually exclusive

[waxen hawk]

What if I treat these coins as identical, what would the probability be then?

[sly sierra]

same

it makes no difference if they are distinguishable or not

we just pretended they were distinguishable to explain the calculation

the coins don't care what we call them

btw the answer would be exactly the same if you just had one coin and tossed it twice

[waxen hawk]

How do I get a head and a tail simultaneously by just one coin?

[sly sierra]

no it's two successive tosses instead of two simultaneous

the timing is irrelevant

the probabilities work the same way

[waxen hawk]

Why do we assume timing is irrelevant

[sly sierra]

it's implicit in the assumption that the outcomes of the two coin tosses are independent

if tossing them simultaneously somehow makes them not independent then our assumption is invalid

but there's no reason to assume that's the case

[waxen hawk]

Invalid, why?

Why would it be invalid if they are not independent

[sly sierra]

the probabilities of HH, HT, TH, TT are all 1/4 if and only if the two coin tosses are independent

so if they are not independent, then the probabilities will be something else

you'd have to model exactly what the dependence is in order to assign the correct probabilities

[waxen hawk]

I couldn’t see it, what will those probability will be then if we treat these coins independently

[sly sierra]

independently? what i said above

1/4 1/4 1/4 1/4

for HH, HT, TH, TT

[waxen hawk]

Emmm

[karmic imp]

Btw it's independent because flipping one coin does not affect the outcome of the other

[waxen hawk]

I mean Not independent I’m sorry

[sly sierra]

then like i said, you'd have to characterize in what way they are dependent, if you want to assign probabilities

one way to do that would be to simply toss them many many many times and count how many of each outcome you get

[waxen hawk]

That seems illegal in my point of view

[sly sierra]

illegal why?

[waxen hawk]

It seems I have no reason to do it

And why I cannot treat these as dependent event

[sly sierra]

you are completely welcome to do so

i shall not stop you

but i won't be able to tell you what the probabilities are in that case

[waxen hawk]

I’m so confused

[waxen hawk]

Why it is impossible to tell the probability when throwing two coins and each of them dependent

[waxen hawk]

What does it even means?

Is it exists in real life?

[sly sierra]

it's not impossible to tell

i just can't tell you ahead of time

you'd have to perform experiments or analysis of some kind to work out the probabilities

because while there's only one set of probabilities that work if they're independent

pretty much anything can happen if they're dependent

you have to specify how they're dependent

[waxen hawk]

It seem to me that (H,T), (T,H) represent the same thing, in other words those two represent one outcome as them two coins are identical

[sly sierra]

and so, according to you, what should the probability of that one outcome be?

[karmic imp]

I think you should review what dependent and independent outcomes means

[waxen hawk]

I know what they mean

[sly sierra]

^

[waxen hawk]

It seems that I’m not able to tell the probability without treating those two coins as two different items

[sly sierra]

they are two different items

it doesn't matter if you can distinguish them, there are two of them, right?

[karmic imp]

Even if the coins are identical, each coin flip is independent from each other. One coin does not affect the outcome of another

[waxen hawk]

Is that sort of proof by contradiction

[sly sierra]

what contradiction?

[waxen hawk]

Since we are not able to calculate the probability when these coins are “identical”

So these coins are different

[sly sierra]

we can calculate the probability, i just did it above

what is your definition of "different"

they are two coins

not one coin

thus one coin is not the same as the other coin

when you throw them you are throwing two of them

you can hold one in your left hand and the other in your right hand, and throw them in such a way that you keep track of which is which

the one on your left i'll call coin 1

the one on your right i'll call coin 2

then do the analysis as above

[waxen hawk]

So it is because the positions of each coins making them different items

[sly sierra]

it is because of them consisting of different atoms that they are different items, if you prefer to think of it that way

AA <-- here i have typed two A's. They are identical A's, but there are two of them right?

[waxen hawk]

Yes

[sly sierra]

if i took those A's and tossed them (assuming they could land as head or tail) I would get the same probabilities as above

[waxen hawk]

I suppose these two A are two different items once you took it to the real life

Emmm

[waxen hawk]

Ignore it

In conclusion, there are no identical items in real life

Even they have same formation(atoms), they are still different, as the positions of them are different

If a question asks what is the probability of getting a head and a tail when throwing two coins simultaneously

Then we have to do the experiment and record those results, therefore we can create the simple space of throwing two coins simultaneously

Only then we will be able to calculate the probability

[vocal sleet]

@waxen hawk Has your question been resolved?

[vocal sleet]

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[lilac plaza]

!status

[vocal sleet]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[boreal vigil]

2

I'm trying to figure out how to get the domain and range

I believe the domain is 0 ≤ 𝑃 ≤ 40

and the range is 0 ≤ 𝑄𝐷 ≤ 2000

but I'm not sure

honestly if I could just watch a video on this topic I'd be good but I can't find anything on this sort of question

@grizzled halo do you mind guiding me in the right direction?

guess I'll wait

[grizzled halo]

damn i'm getting personal requests already

[boreal vigil]

saw you helping someone out so thought I'd ask

[grizzled halo]

for the domain, you do have one part of Q for [0,40], but there's another part there

[boreal vigil]

honestly I saw someone's answer on this and so I'm trying to understand what they wrote

https://www.studocu.com/en-ca/messages/question/3472636/question-3-you-decided-to-produce-and-sell-homemade-gelato-your-fixed-costs

[grizzled halo]

so yeah they've said the domain is all values of P

[boreal vigil]

their answer to question a is: domain is 0 ≤ 𝑃 ≤ 40 and the range is 0 ≤ 𝑄𝐷 ≤ 2000.

[grizzled halo]

huh

[boreal vigil]

and I'm kinda lost

[grizzled halo]

I don't think the domain they've given is correct. The function Q(P) has two parts, one over [0,40], and another for P>40. Altogether, that should make P>=0.

[boreal vigil]

I see..

so their answer is wrong

[grizzled halo]

And then for the range, you can plug in the extremities P=0 and P=40 to see that it's [0,2000].

[boreal vigil]

what do you mean plug in the extremitites?

[grizzled halo]

because 2000-50P is predictably a straight line, you can check where it starts and ends to find the range

[boreal vigil]

okay so

[grizzled halo]

which is P=0 and P=40

[boreal vigil]

when looking at this

the domain is

P is between 0 and 40

but also bigger than 40

[grizzled halo]

it means that it does one thing between 0 and 40, and another thing after 40

[boreal vigil]

or does it mean when Qd(P) is 2000 - 50P than P is between 0 and 40

[grizzled halo]

yes

[boreal vigil]

or when Qd (P) = 0 than P is greater than 40

[grizzled halo]

also yes

[boreal vigil]

so how would I express that as a domain

[grizzled halo]

domain is just the acceptable values for P

[boreal vigil]

so I can just write P > 0

[grizzled halo]

P>=0

[boreal vigil]

or do I have to say that when Qd(P) is x than P is y

[grizzled halo]

just state that the domain is $P\geq0$

[twin meteor]

chlamydia

[boreal vigil]

okay

and what about range now

range is Qd(P) right

[grizzled halo]

yes

[boreal vigil]

but this doesn't list it does it

[grizzled halo]

no you'll have to put in work to figure it out

so do you know how to find range?

[boreal vigil]

not exactly sure??

[grizzled halo]

we'll look at 2000-50P first: it's just a line right?

[boreal vigil]

a line?

ah a linear?

[grizzled halo]

yeah

[boreal vigil]

follows the y= mx + b formula

yes

[grizzled halo]

so when it has a domain of [0,40], we can easily predict what the range will be

[boreal vigil]

2000 - 50P?

[boreal vigil]

ah is it between 0 and 2000?

i have 50 minutes before I have to submit this assignment oh no

[grizzled halo]

i was making a shoddy diagram, but yeah

right

so are we clear for a)?

[boreal vigil]

yes

thank yuo

[grizzled halo]

onto b)?

[boreal vigil]

for the next question he lists:

but he doesn't quite complete his thought

he's basically saying that the inverse is whatever P can be right?

[grizzled halo]

so do you know how to find an inverse function

[boreal vigil]

you reverse the 2 variables no?

[grizzled halo]

yeah

so for P:[0,40], you reverse it to get another linear, but for P>40, what happens?

it's a horizontal line a 0, which turns into a vertical line at 0

[boreal vigil]

okayy

so

[grizzled halo]

this can't happen

[boreal vigil]

oh

[grizzled halo]

do you understand why?

[boreal vigil]

vertical line test?

[grizzled halo]

yeah

so it's not a function

[boreal vigil]

yeah

[grizzled halo]

which means we can only count [0,40]

[boreal vigil]

ah okay

[grizzled halo]

so that's the maximum possible domain for b)

[boreal vigil]

but he says

[grizzled halo]

and then finding the inverse

yeah

[boreal vigil]

he rearranges

but it's a werid rearrangement

[grizzled halo]

we start with $Q=2000-50P$

[twin meteor]

chlamydia

[boreal vigil]

oaky

[grizzled halo]

$\Rightarrow 50P=2000-Q$

[twin meteor]

chlamydia

[grizzled halo]

$P=\frac{2000-Q}{50}$

[twin meteor]

chlamydia

[boreal vigil]

so isolate for P

[grizzled halo]

yeah to find inverse function

[boreal vigil]

oh yup

understood

[grizzled halo]

which gives $P=40-\frac Q{50}$

[boreal vigil]

now that we've reversed the variables thats the inverse function

[twin meteor]

chlamydia

[boreal vigil]

okay and so this tells us the domain?

or the range of the original function

[grizzled halo]

huh

[boreal vigil]

we've isolated for P

[grizzled halo]

the domain and range swap between the original and the inverse, after you swap the variables

[boreal vigil]

oh

we've just found the inverse function of P(Qd)

which the question asks

[grizzled halo]

yeah

[boreal vigil]

okay

but we still have to find the domain no?

of the inverse

[grizzled halo]

it doesn't ask that?

[boreal vigil]

or is the maximum possible domain

0 < P < 40

[grizzled halo]

maximum possible domain of the original, such that it has an inverse

[boreal vigil]

that's the maximum possible domain of the inverse

ah okay

so the max possible domain is 0 ≤ 𝑃 ≤ 40.

[grizzled halo]

yeah

[boreal vigil]

and the inverse function is P = 40 - Q/50

[grizzled halo]

part c)?

or is there anything confusing you

[boreal vigil]

ah one second

[grizzled halo]

i'm just trying to move quickly because of your time constraint

[boreal vigil]

yes I was writing it down

okay

yes

qeuestion c

this is what he says

[grizzled halo]

yeah

revenue - costs

revenue comes from selling your gelato for price P per quantity Qd

[boreal vigil]

I see

but we don't konw

how many i'm selling

or is that the domain

[grizzled halo]

that's left as a variable in the profit function

[boreal vigil]

so what does the equation he write mean

that's the total profit function?

[grizzled halo]

yeah

the price function we found in b) times the quantity minus costs

[boreal vigil]

ah

oh

[grizzled halo]

.

[boreal vigil]

so profit (q) means total profit

So do I write it all out?

[grizzled halo]

yeah profit as a function of quanitty

[boreal vigil]

Profit (q) = 40 - Qd/50 * Q - C(Qp)

[grizzled halo]

the answer says we assume we sell all the gelato we make, so all the Qs are the same

[boreal vigil]

ah I got you

so we aren't actually inputting anything of our own

right

[grizzled halo]

$Profit=\frac{2000-Q}{50}\times Q-(1000+10Q)$

[boreal vigil]

we're just assuming that Q is between 0 and 2000

[twin meteor]

chlamydia

[boreal vigil]

why 2000

oh wait nvm

it would work if I just wrote 40 - Qd/50 as well right?

[grizzled halo]

yeah

$P=-\frac1{50}Q^2+30Q-1000$

[twin meteor]

chlamydia

[grizzled halo]

is what it should simplify to for the next question

[boreal vigil]

should I simplify it

oh

you mean the dervative?

[grizzled halo]

you can if you want

yeah

[boreal vigil]

also is the Q

multipling the 40 - Qd/50

like a bracket so

P = (40 - Qd/50 ) Q - (1000 + 10Q)

for c

[grizzled halo]

yeah

remember the assumption we sell everything we make

so Qd=Q

[boreal vigil]

oh so Qd becomes Q

anyways

so for d

we get the dervative of this equation?

[grizzled halo]

yup

[boreal vigil]

that's sorta difficult isn't it

[grizzled halo]

do you know how to differentiate?

power rule?

[boreal vigil]

sorta

let me see

firsy you would get the dervative of the brackets?

so 40 is removed

[grizzled halo]

oh expand it first

[grizzled halo]

to get this

[boreal vigil]

expand it

so Q multpied by 40

Q x Q/50 is just Q^2 /50?

[grizzled halo]

yes

[boreal vigil]

okay so then it's 40Q - Q^2/50 - (1000 + 10Q)

and then dervative

so

what's the dervative of Q^2/50?

how would you get that

[grizzled halo]

do you know how to differentiate x^2?

[boreal vigil]

2x

[grizzled halo]

so what about Q^2

[boreal vigil]

2Q/50?

[grizzled halo]

yeah

[boreal vigil]

so the derivative is

40 - 2Q/50 - 10

or is it not

[grizzled halo]

yeah

simplify it to get -Q/25+30

[boreal vigil]

why do you have 1000

there

[grizzled halo]

it's the same as this

[boreal vigil]

so that isn't fully differentiated?

[grizzled halo]

that isn't the derivative, that's the profit function

[boreal vigil]

I thought the profit function was P = (40 - Q/50) Q - (1000 + 10Q)

and we get the derivative of that

[grizzled halo]

yeah but you can expand it to get what i sent

[boreal vigil]

ah

anyways

so the answer to d

is

P = -Q/25 + 30

and solve for Q?

[grizzled halo]

do you know how to find maximum of a function?

[boreal vigil]

not exactly

[grizzled halo]

so maximum implies that your profits stop increasing

which means that the gradient is going to be 0 at some point

yeah?

[boreal vigil]

yeah

it has to be 0

[grizzled halo]

so how can we find when the gradient is 0

[boreal vigil]

set P to 0?

or Q to 0

[grizzled halo]

yeah the derivative

[boreal vigil]

okay so 0 = -Q/25 + 30

[grizzled halo]

and this gives Q=750

[boreal vigil]

yes

Q = 750

and finally e

[grizzled halo]

so our profiti function is

[boreal vigil]

yep

[grizzled halo]

and we want the range for Q:[0,2000]

we can see that it's a parabola right?

with maximum at Q=750

[boreal vigil]

quick question that's the same as P = 40 - Q/50 Q - 1000 + 10Q right?

[grizzled halo]

yes

[boreal vigil]

okay

[boreal vigil]

okay so at max Q 750 we want the range?

oh no

we sub

it says we sub the "these values" into the profit function and find min and max

[grizzled halo]

yeah soon

[boreal vigil]

what are "these values"

[grizzled halo]

0 and 2000

[boreal vigil]

okay so 0 and 2000 are the 2 values we sub into for Q into the profit function

and that should give me the min and max

[grizzled halo]

because the profit function looks like this, with the peak at Q=750

no

[boreal vigil]

okay

so

[boreal vigil]

why is it going all the way to 10000

[grizzled halo]

because the profits reach past 10000

[boreal vigil]

ah

[grizzled halo]

when you sub into the formula at max

[boreal vigil]

makes sense

[grizzled halo]

so that's at Q=750

[boreal vigil]

so we sub Q into the profit function

and get max?

[grizzled halo]

yeah

[boreal vigil]

and for min?

[grizzled halo]

and then for the ends of the domain, 0 and 2000, because the parabola only goes down from Q=750, we'll test both of them for min

i worded that badly

[boreal vigil]

7 minutes left rip

[grizzled halo]

the parabola will keep going down until the profit curve ends, so we want to see where it ends

[boreal vigil]

I gotta make a pdf as well

so the max is 10250

right

[grizzled halo]

yup

[boreal vigil]

and the mix is

when Q is 0?

[grizzled halo]

check both 0 and 2000

[boreal vigil]

so plug 0 and 2000 into profit function?

[grizzled halo]

it's going to be 2000

[boreal vigil]

and whichever one is lower is min?

[grizzled halo]

yeah

at -21000 profit

so your range is [-21000, 10250]

[boreal vigil]

just submitted in time

with like 2 minutes remaining

jesus christ

thank you so much

gonna make sure to do my assignments earlier next time

phew

[grizzled halo]

lol any time

[boreal vigil]

can I ask you a quesiton if you don't mind

[boreal vigil]

howcome you're a helper on this discord server?

do you just like doing math?

and helping people?

[grizzled halo]

i guess

[boreal vigil]

this is your free time right?

[grizzled halo]

i did it a bit in the past and enjoyed it

[boreal vigil]

but you're not being paid either?

shouldn't you pursue a tutor job or something

[grizzled halo]

i'm going to 🤫

[boreal vigil]

oooh

nice

are you in university?

[grizzled halo]

yeah

[boreal vigil]

majoring in math I'm assuming?

I'm in finance, a lousy major...

first year

this was actually my first assignment lol

[grizzled halo]

hopefully the next ones are more fun?

[boreal vigil]

hopefully 😭

sad thing is that last question, I've never seeen

It's not even in my textbook

I was so lost

[grizzled halo]

really

i would think that that's like high school applications of differentiation kind of stuff

[boreal vigil]

yeah idk

perhaps I've forgotten everything after highschool

the differentiation was pretty easy in hindsight, I just haven't used it in a while

but the qeustion format

never seen it

I can't even find videos on it

usually there's videos explaining questions similar but nothin

[boreal vigil]

anyhow, thanks again

have a goodnight!

[grizzled halo]

cya man

https://www.youtube.com/watch?v=jqPvsGQHupM i guess there's stuff like this

[boreal vigil]

I feel like I've done this before in highschool

just looking at the thumbnail

ig it's because they were using Qd and unfamiliar variables?

idk

.close

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[vocal sleet]

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[little folio]

Find a real value of x from the equation!

[little folio]

😑😭

Ig I'll just close this...

.close

[vocal sleet]

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• Show your work, and if possible, explain where you are stuck.
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[cinder oyster]

what is the name of this formula

[cinder oyster]

i have it memorized but dont know the name

(x-h)^2+(y-k)^2=r^2

liike the circle formula?

[woeful hull]

gives the equation of a circle

i mean thats like a quick google search

[tiny trench]

Put the picture of the question you need

[vocal sleet]

@cinder oyster Has your question been resolved?

[vocal sleet]

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Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[frigid parrot]

Where did the 2x come from?

[regal slate]

chain rule

[vast shale]

derivative of x^2+1

[vocal sleet]

@frigid parrot Has your question been resolved?

[sharp anchor]

@reef grove

Are my answers for questions 2 correct?

[frigid parrot]

Why is that added as a multiple to the rest of the equation, though?

[vast shale]

chain rule

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

[frigid parrot]

Do you need to use the chain rule to solve that problem?

[vast shale]

yes

[frigid parrot]

thanks

.close

[vocal sleet]

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[vast shale]

np

[vocal sleet]

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[velvet cove]

Evaluate $\frac{\log_{16.25π} 125}{\log_{16.25π} 5}$

[timber cypress]

Hi

[twin meteor]

Jash

[timber cypress]

What's the matter

[velvet cove]

hi

how to evaluate

[timber cypress]

Do you know the properties of log?

[velvet cove]

which one

how do i deal with the 16.25pi

[timber cypress]

Loga^m=mloga

[velvet cove]

since it’s a no calculater question

[timber cypress]

This one

[velvet cove]

how do i use that

[timber cypress]

Say I have log4

Log 4=log2²

Log2²=2log2

[velvet cove]

ye

[timber cypress]

What's 5³

[velvet cove]

5•5•5

25•5

125

[timber cypress]

Now solve it yourself

Using the property

[velvet cove]

does the 16.25pi not matter

[timber cypress]

Yes

It doesn't matter

[velvet cove]

is the answer 3

[timber cypress]

Yessir

[velvet cove]

ohhhhh it’s a change of base form

log_5(125)

[vocal sleet]

@velvet cove Has your question been resolved?

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[vocal sleet]

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[vast shale]

Hey

[vast shale]

I need help with exercise 2)

I need to find the verticale and horizontal asymptot

I learned to first grab the denominator and find x

But in this case x^4+1 its not possible without imaginary i we don’t use that here not allowed from teacher

[loud pivot]

So what does that tell you

[vast shale]

Idk

Is it still possible? No?

Cause i know its y= 25

I am supposed to get an answer out of this that not (its not possible)

<@&286206848099549185>

[loud pivot]

What

To find vertical asymptotes, you equate the denominator to 0 and solve for x

In this case, you get $x^4 = -1$

[twin meteor]

USS-Enterprise

[loud pivot]

Which is not solvable when x€R

Therefore there are no vertical asymptotes

[vocal sleet]

@vast shale Has your question been resolved?

[vast shale]

Hey

I know there is not verticale

But am tryna find the horizontal whoch is 25

How do u get 25?

<@&286206848099549185>

[grizzled halo]

find limit as x--> infinity

$lim_{x\rightarrow\infty}\frac{(5x^2-7)^2}{x^4+1}$

[twin meteor]

chlamydia

[vocal sleet]

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[vast shale]

I dont get it? U didnt anwer ?

[grizzled halo]

do you not know how to do that

[vast shale]

U only gave me the function

I dont know how to get horizontal asynptopt

[grizzled halo]

it's not on me to give you the answer

[vast shale]

Its 25 but how

[grizzled halo]

if you don't know how to do it?

[vast shale]

I know the answer

I need to onow how to do it

[grizzled halo]

so do you know how to take the limit of that function?

[vast shale]

No

[grizzled halo]

we can start with expanding it

$\frac{25x^4-70x^2+49}{x^4+1}$

[twin meteor]

chlamydia

[vast shale]

But thats a harder method wasnt there an easier one?

[grizzled halo]

this is the easiest method i can think of

[vast shale]

Alright continue

[grizzled halo]

an important thing to keep in mind is

$lim_{x\rightarrow\infty}\frac1x=0$

[twin meteor]

chlamydia

[vast shale]

Yes ik that

[grizzled halo]

so we want as many terms to turn into 0

$\frac{25-\frac{70}{x^2}+\frac{49}{x^4}}{1+\frac1{x^4}}$

[twin meteor]

chlamydia

[grizzled halo]

can you see where this comes from

[vast shale]

Not rly

[grizzled halo]

i took this and divided both top and bottom by x^4

[vast shale]

Oh ye

[grizzled halo]

so now, $lim_{x\rightarrow\infty}\frac{25-\frac{70}{x^2}+\frac{49}{x^4}}{1+\frac1{x^4}}$

[twin meteor]

chlamydia

[grizzled halo]

where a lot of the terms just cancel to 0

[vast shale]

How do they cancel to 0?

[grizzled halo]

.

[vast shale]

What?

Oh ye

[grizzled halo]

alright

good?

[vast shale]

But not 25

Oh nvm

[grizzled halo]

why isn't it

ok

[vast shale]

So

With other exercises

I gotta get as many number devided by x?

[grizzled halo]

this can be useful

but sometimes it might not work

[vast shale]

Ik ask help again if i encounter such thing thnx

.close

[vocal sleet]

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[plucky sparrow]

Hello

[plucky sparrow]

I need help

with

Soo i just have a doubt

I have three equations

x+y=4
y+z=6
z+x=6

can anyone solve these please?

i cant understand how these works

<@&286206848099549185>

[sage wind]

!15min

[vocal sleet]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[merry python]

Hint:||Add all the three equations||

[sage wind]

we dont solve problems we help you to solve them

[dim rain]

Yo dm me

[plucky sparrow]

yes i did that

[dim rain]

im gonna help you

[plucky sparrow]

,

[plucky sparrow]

i need specific values of x y z

[merry python]

Yes you will

What do you get after adding them

[plucky sparrow]

x+y+z=8

[merry python]

yes

now, do you see any further step?

[plucky sparrow]

nope

actuallu its a question from straight lines

[merry python]

like you have x+y=4
and x+y+z=8

[plucky sparrow]

omg im dumb

tyyy

.close

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[dim rain]

The equation x + y = 4 represents a linear equation in two variables, x and y. To find the values of x and y that satisfy this equation, you can use various methods, such as substitution or elimination. Here, I'll demonstrate both methods.

Method 1: Substitution

Solve one of the equations for one variable in terms of the other. Let's solve for x in terms of y:

x = 4 - y

Substitute this expression for x into the original equation:

(4 - y) + y = 4

Simplify and solve for y:

4 - y + y = 4

4 = 4

Since the equation simplifies to 4 = 4, it means that y can be any real number. There are infinitely many solutions for y.

To find the corresponding values of x, use the expression for x:

x = 4 - y

So, for any value of y, you can find x by subtracting y from 4.

[dim rain]

why u close the dm bro?

[merry python]

Late bud

also ChatGPT answer

[dim rain]

bruh i did a joke with him and he blocked me

[dim rain]

be quite dude

[vocal sleet]

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[vast shale]

I am full stuck in the solution, can someone tell if i am going in the right way or the wrong one ?

[merry python]

@elfin moon

[vast shale]

yes

dude

[stuck obsidian]

vectors :/

[vast shale]

😩

pls

[cursive tusk]

I think you should use properties of determinants.

It will be easy, rather breaking it out

[elfin moon]

Ha bhai

Kya hua

[hard atlas]

you need to use in some way that they are coplanar. how can you do that

[vocal sleet]

@vast shale Has your question been resolved?

[vocal sleet]

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• Be polite and have a nice day!

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[stark lichen]

hello, can i get help on a question?

"Show that for any whole numbers a,b,c,d theres 2 whole numbers x and y with the condition (a^2 + b^2)(c^2 + d^2) = x^2 + y^2"

[sage burrow]

!status

[vocal sleet]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[stark lichen]

1

[sage burrow]

with the condition you're working with, you can see a common idea being that both sides consist of sums of squares

(a^2+b^2), (x^2+y^2), etc

these have certain properties which can come in handy with proofs involving them

what theorems do you know involving sums of squares?

[stark lichen]

uh

idk

none..?

[sage burrow]

have you ever heard of the Sum of two squares theorem?

[stark lichen]

nope

[sage burrow]

if you don't mind me asking, what area of math were you working on when you were set/came across this question?

[stark lichen]

algebra

[hard atlas]

do you know complex numbers maybe?

[stark lichen]

the ones with 'i'?

[hard atlas]

yes

[sage burrow]

i presumed whole numbers just meant ∈Z

[stark lichen]

no we didnt do that

[stark lichen]

well yea

[hard atlas]

there is a nice trick to do this question by jumping into complex numbers for a bit

but ok lets ignore that

[stark lichen]

we do complex numbers next year so i doubt it

[sage burrow]

my first thought was number theory 😓

just having a go at an aglebraic approach this 'sec

[hard atlas]

you have to be smart about adding a zero

[vocal sleet]

@stark lichen Has your question been resolved?

[tawdry grove]

What were you studying in class to motivate this problem? What textbook is your course using and how far along are you in it?

You can use the complex number approach Denascite mentioned to find the answer and manually check it works but you won't learn anything from that if you don't understand complex numbers.

[stark lichen]

idk some 9th grade problem book

[tawdry grove]

Which one?

[stark lichen]

the teacher sent us pictures of the pages

[stark lichen]

idk which one💀

• its in romanian

[tawdry grove]

Were you learning anything in class related to this?

[stark lichen]

nope

[tawdry grove]

I would just look up complex numbers then. Try figuring out how you can express $a^2 + b^2)$ as the product of a number times its conjugate. Your problem immediately follows from that. Even if your teacher does not allow you to use complex numbers, you can use it to find $x$ and $y$ and then check the values you find are correct.

I recall there are methods to prove what you want without complex numbers, but it's decently complicated and certainly more difficult than simply learning a bit about complex multiplication.

[stark lichen]

theres no way we have to do it with complex numbers because we learn complex numbers in 10th or 11th grade and im only in 9th

[twin meteor]

chencking

[hard atlas]

you just need to add a zero

it's a bit harder than with complex numbers but really not that bad

x and y will be of the form m+n where m and n depend in some way on a,b,c,d

multiply out the LHS

compare with stuff that could look like (m+n)^2 or (m-n)^2

[vocal sleet]

@stark lichen Has your question been resolved?

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[copper pebble]

Hi

[copper pebble]

How do I solve this by hand using calculator for the decimal numbers?

I need to get the value of a

[grizzled halo]

the angle of the number?

you use arctan(Im/Re)

[vocal sleet]

@copper pebble Has your question been resolved?

[copper pebble]

yeah

i dont know how to get the angle

confused as fuck

[dark kiln]

the calculator has the button

they told you the button

[copper pebble]

which calculator?

[dark kiln]

any one

i don;t understand the problem though

maybe they solved it wrong

[copper pebble]

I just have to find the value of a

[dark kiln]

ok yeah, angle from coords

they solved it right

[vast shale]

Yes but I am unable to solve it

[vocal sleet]

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[olive sequoia]

Can anyone help me with this question.

Not sure on where to start from.

[timber cypress]

Find da and ab

[olive sequoia]

DA and BA are equal to AG.

I think so.

[timber cypress]

Yeah

Find ag

[olive sequoia]

how can I find ag?

[solar saffron]

Trigonometry. Notice that triangle EAF is an isosceles triangle. Angle EAF is 45, and if you cut that triangle in half (line AG), you also cut angle EAF in half.

Diagram is poorly annotated perhaps, realize that 3cm belongs to line EC.

[olive sequoia]

We haven't learn trigonometry.

[solar saffron]

sin(x), cos(x), tan(x)?

[olive sequoia]

nope

just congruence criteria

and corresponding parts of congruent triangles.

[solar saffron]

If I can ask, what grade do you go to?

[olive sequoia]

I am 9th. CBSE board.

it's a type of system in India

[solar saffron]

Ah I see. ok

does this say 90 degrees?

If that angle C says 90 degrees, that's a very good hint.

[olive sequoia]

yes

[solar saffron]

Because what do you know about squares/rectangles? What angle does each corner have?

[olive sequoia]

it's 90°

[solar saffron]

Easy.

[olive sequoia]

90°

[solar saffron]

And what angle would angle DAB be?

[olive sequoia]

90*

[solar saffron]

tada!! That triangle was a distraction.

[olive sequoia]

oh I see..

but in the chapter that we are studying. There is no relevance of squares/rectangles.

Kinda weird that they would add such a thing. Since rest of the questions are based on triangles only.

[solar saffron]

yeah, it's a weird question, but it's good practice.
Complicated ideas and methods can blind us from seeing the obvious. This was a small practice to see if you can detect the trap in this question.

And the trap: looking too deeply into triangles.

[olive sequoia]

Yup, thanks for helping. I have understood it now. 🙃

[solar saffron]

No problem! Wish you well onwards ❤️

[olive sequoia]

Thank you!

.close

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[azure zinc]

Hi

[grizzled halo]

go on

[azure zinc]

my assesment for tmr

no idea how to do it

[loud pivot]

,rccw

[azure zinc]

the assesment also stated i need steps. thank you

[loud pivot]

Which question are you having problems with

[azure zinc]

All of them... i dont understand it since i just came out of the hospital and returned to school

sorry...

[loud pivot]

No need to apologize. We are here to help 🙃

[azure zinc]

thank you so much i just don't want to disappoint my parents

since my math grades arent the best.

[loud pivot]

Do you mind typing out Q1 for me because I can't read that 😅

[azure zinc]

oh sure

Draw another different shape of the 4 joined square beds which causes the maximum possible perimeter with 4 beds

btw i got the questions from a friend so sorry for the handwriting

[loud pivot]

So, if I understand correctly, you have 4 square flower beds, each with a side length of 1 and you are trying to find the shape which gives the longest perimeter?

[azure zinc]

i think so, but im not sure where you got the each side with length of 1, but other than that i think its correct

[loud pivot]

Well the example in Q1 has the 4 squares in a bigger square shape and each side is made of 2 smaller squares and is of length 2

So then each square has a side length of 1

I mean, the length is irrelevant here anyway

But I am just wondering

[azure zinc]

Ah okay thanks

So am i suppose to draw a diagram tommorow?

or smthin like that?

[loud pivot]

The problem with having them arranged in a square like that is each square shares 2 sides with other squares

Which takes away from the perimeter

[azure zinc]

Oh alright, so i have to replace the squares and make them in other shapes like a rectangle?

[loud pivot]

It will be a rectangle, yes.

Try to minimize the amount of sides each square shares with another

[azure zinc]

so would it be smthing like this?

[loud pivot]

This is another square made of 4 squares though

[azure zinc]

how about like this?

like 2 rectangles stacked on top of each other

[loud pivot]

See how this bottom left square shares sides with two squares when it could share a side with just one

[azure zinc]

oh yeah.

[loud pivot]

So you can move it somewhere else, for example to the right of the bottom right square

Which will make it share only one side with other squares

And thus increase perimeter

The easiest way to do this is to arrange the squares in a line

[azure zinc]

hm ok is it possible you show me it like in a diagram so i can note in down?

[loud pivot]

See, on the left, you have 4 squares sharing 2 sides with other squares while on the right you only have 2 squares sharing 2 sides with other squares while 2 are sharing just 1 side

[azure zinc]

yeah.

[loud pivot]

This means 2 less shared sides and 2 more sides revealed

Increasing the perimeter

And that's the maximum perimeter you can have here

10a

[azure zinc]

oh ok so thats the maximum okay thank you!

[loud pivot]

No problem 🙂

[azure zinc]

ok q2

[loud pivot]

What does it say

[azure zinc]

Draw one arrangement of sioined square beds with MPP

no idea what is sionied

[loud pivot]

6 joined?

[azure zinc]

not sure but the drawings might help

would you have any ideas?

[loud pivot]

Hm

I don't...

[azure zinc]

hm let me try to rephase it

would sioned = joined?

sorry for my friends bad handwriting

[loud pivot]

It might

I thought they had to be joined in the last one already

[azure zinc]

hmm

[loud pivot]

My interpretation of "joined" is they need to share at least one side together: a composite shape

If that isn't required in Q1, you can just have each square seperately

And the maximum perimeter is 16a

[azure zinc]

Yeah, should we skip question 2 and head on over towards question 3?

[loud pivot]

And then you do the same in Q2 as we did in Q1

Just make them in a line

And max. perimeter is 14a

[azure zinc]

Ok

question 3: Draw one arrangement of 6 joined square beds which shows a MPP

[loud pivot]

What do you mean shows

[azure zinc]

not sure, but i think it means to show the MPP of the 6 joined square beds

[loud pivot]

I mean

Isn't that the same thing as Q2

[azure zinc]

yeah i guess so

so i just do the same and make a line?

[loud pivot]

I'd say so

[azure zinc]

but it says i need to show the mpp

which im not too sure how to do

[loud pivot]

Me neither

[azure zinc]

What does MPP stand for?

[loud pivot]

I am guessing Maximum Possible Perimeter

[azure zinc]

oh ok ill just write it down as well i guess

question 4:

oh i dont have the table...

so question 4 says "complete the table and predict the MPP

is it possible u make a table and show me as a example

so i can maybe try to convert the numbers?

[loud pivot]

What table?

[azure zinc]

but

this is from question 8

im assuming

its smthin like this

[loud pivot]

I have no clue

[azure zinc]

oh

q5 then

explain each time sfb increased by 1

do u knwow?

[loud pivot]

What's sfb

[azure zinc]

dont know

but

do you know why it increases?

[loud pivot]

Truth be told, I don't know anything about this anymore 😂

[azure zinc]

oh

[loud pivot]

Yeah, sorry 😦

[azure zinc]

its ok

thank you for you're support 😄

but should i be finding someone esle/

[loud pivot]

Yeah, maybe wait for a bit and see if someone understands this

[azure zinc]

oh okay but i cant rly wait lol i have to wake up at 6 tmr and its 12 rn

[loud pivot]

Oh damn

I'd help you but I have no idea

It's been 15 minutes, you can mention @ Helpers 😄

[azure zinc]

oh okay

thank you

<@&286206848099549185> please help.

sry for ping

<@&286206848099549185> i need help with this assesment i have finished till q4 but i need help with others

[slim lily]

how much money will i earn

[azure zinc]

i only have 7.80 USd with paypal

[oak turret]

wait, is this legal in this server? >.>

[azure zinc]

if you could help me out ill be willing to transfer it all to u

wait its illegal?

[slim lily]

how old are you

[azure zinc]

14

[slim lily]

i was joking man. Don't fall for this

[azure zinc]

oh.

[slim lily]

you should not pay someone if he helpls you with something

[azure zinc]

but i really need help, since i just got out of the hospital and my school is already in the assesment phase

oh okay

[slim lily]

ok send me the picture again

and the questions

[azure zinc]

sure

i finished up till q4

but others im not done

also this picture is taken by my friend who has terrible hand writing so sorry for that

[obtuse radish]

wowz

[obtuse radish]

,rotate

[obtuse radish]

which one?

[azure zinc]

the first photo

[slim lily]

how can you rotate

[azure zinc]

i need to do question 4

[obtuse radish]

question no?

[azure zinc]

until the ned

end

[slim lily]

,rotate

[obtuse radish]

k

[slim lily]

,rotate

[slim lily]

,rotate

[slim lily]

,rotate

[obtuse radish]

bro

stop messing

[azure zinc]

thats the second photo.

[obtuse radish]

go to #bots

[azure zinc]

this is the first one

[slim lily]

i want to rotate the first picture wtf

[obtuse radish]

umm so i cant read q 4

can u type it out for me

[slim lily]

shah please rotate the picture

[azure zinc]

sure

[karmic imp]

Assessment as in it's a test?

[obtuse radish]

i mean u've been here 10min u "joked" abt being paid and now disturbing; go to bots is all i can say rn

[azure zinc]

Complete the table and predict the MPP, so i dont have the table but i was wondering if it possible u guys make like a example

so i can like convert it

[slim lily]

oh ok, is it against the rules to not joke in this server, did not know that at all

[obtuse radish]

idk what MPP is sorry; could help u if u explain a bit

[slim lily]

same. My first language is not english so MPP is vague

[azure zinc]

i think its maximum perimeter possibility

[obtuse radish]

joking isnt the problem the channel is for helping not wasting others time; they wanna learn; they wouldnt be here if they wanted to hear a joke

[slim lily]

oh ok

[slim lily]

damn, must be fun at parties huh. Wasted all this young man time

[azure zinc]

Please help me with these questions i have no clue on how to do it

[karmic imp]

Then ask your teacher for help tbh

[obtuse radish]

well i feel like i get it sorta.. but there are some rules right? do i need to join sides or like the vertex of two squares can join

[azure zinc]

there is a assesment soon, and ive been in the hospital for like the past month and that month the class was practicing this subject

so i missed out on alot of things

[obtuse radish]

idk from ur coming from; ur new to the server too it seems; plz go and read the rules; this is a purely academic place and no one's meaning to be any fun here

[karmic imp]

That doesn't mean you don't have to not ask your teacher. You can still ask your teacher for help, on things you missed

[slim lily]

lol 3 hours ago we were talking about weed and everything. Maybe you should check the server more often

[azure zinc]

The assesment is tmr, i asked if i could have extra time but for some reason the teacher said it would deduct my score

so im staying up all night

im suppose to wake up at 6 and for me its 12

[obtuse radish]

<@&268886789983436800> is this channel for talking abt "weed and everything"

[blissful sentinel]

Everyone who is talking about stuff other than helping this person with math, please leave

[slim lily]

go check the discussion place then

[azure zinc]

please i really dont want to flunk this test

[blissful sentinel]

You can talk about non-academic stuff in #discussion and #chill, not here

[karmic imp]

Then honestly, take the penalty, so that way you can not stress yourself out, and you are able to ask questions on the assignment you are working on

[azure zinc]

for this past term i worked so hard for my grades to get into my dream school

i dont want 1 test to ruin it