help-10

[signal dagger]

I could take away that root

reverse of this

right?

[timid silo]

yup yup

good

and?

there is one more you have to use here

[signal dagger]

this?

[timid silo]

wonderful!

that's correct

[signal dagger]

wow

its really fantastic those notes i will take it

[timid silo]

so using the laws: 2, 6, and 3 you should be able to solve this problem

try to apply them and tell us if you can get the answer

[signal dagger]

Fantastic

I will let you know, thank you both for the quick answer

[timid silo]

bonne chance

[signal dagger]

It gave me
x^1/2 * y^2 *z^9

I can transform the x^1/2 into a root, that would mean that im simplifying ?

[timid silo]

yeah

or you could leav your answer in terms of x^1/2 as well

I don't think the examiner would mind

according to me, that is simplified enough

[signal dagger]

great great

[obtuse pebble]

@signal dagger Has your question been resolved?

Channel closed

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[obtuse pebble]

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[south night]

A particle moves along a straight line with its position at time t given by s(t) = sin(t) - t^2/4 for 0 <= t <= 2*pi. Determine the time when the particle is farthest from the origin

[obtuse pebble]

@south night Has your question been resolved?

[timid silo]

!status

[obtuse pebble]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[timid silo]

@south night

[south night]

1

[timid silo]

okay

np

[south night]

i really don't know that to do beside integration

what*

[timid silo]

at the local maxima and minima of a function, the derivative at the point is 0 correct?

[south night]

correct

[timid silo]

okay so we have the function $$s(t) = \sin(t) - t^\frac{2}{4}$$

[warm shale]

Edmund Cloudsley

[timid silo]

wait is it t^2 divided by 4

or is it t to the power 2/4

@south night

[south night]

t squared divided by 4

[timid silo]

oh okay okay

we have the function $$s(t) = \sin(t) - \frac{t^2}{4}$$

[warm shale]

Edmund Cloudsley

[timid silo]

the derivative of this displacement function would give us

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[timid silo]

.reopen

[south night]

$\cos(t)-\frac{t}{2}$

[warm shale]

ZiXO

[south night]

sorry xD

[obtuse pebble]

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[vapid path]

Pleasw help me answwr 24

[obtuse pebble]

Show your work, and if possible, explain where you are stuck.

[vapid path]

no work started

[stone holly]

hint: start by taking LCM

[vapid path]

lcm of $3x - \frac{2}{1 + \frac{2}{x}}$

yeah?

[warm shale]

aeth

[vapid path]

lcm of that?

[timid silo]

Yes yes

[vapid path]

bro im still not done with these questions lmfao

still need to answer 26

questions

[timid silo]

Actually

$$\text{LCM}(1, 1 + \frac{2}{x})$$

[warm shale]

Edmund Cloudsley

[vapid path]

wait what what happened there

[timid silo]

Metrobank math challenge no?

[timid silo]

Ok let’s have a look

[vapid path]

yeahhhh

practice for nationals (im cooked)

[timid silo]

We need to turn this into a fraction of the form

$$\frac{P(x)}{Q(x)}$$

[warm shale]

Edmund Cloudsley

[vapid path]

yea yea

[timid silo]

So let’s say we have the fraction

$$\frac{1}{3} + \frac{1}{2}$$

how would u turn this into 1 fraction?

[warm shale]

Edmund Cloudsley

[vapid path]

you make them the same base then add?

[timid silo]

Show me how

[vapid path]

2/6 + 3/6 = 5/6

[timid silo]

Yup good

Let’s apply the same concept here

$$3x - \frac{2}{1 + \frac{2}{x}}$$

Is essentially
$$\frac{3x}{1} - \frac{2}{\frac{1}{1} + \frac{2}{x}}$$

[vapid path]

yeahhh yaeh

[warm shale]

Edmund Cloudsley

[vapid path]

yeah

[timid silo]

Let’s turn this part into 1 fraction by making the base same

Can you do that for me?

[vapid path]

wait lowkey how u make them the same base

[timid silo]

Ok np I’ll teach ya

So if I have the numbers 2 and 3 in the denominator, the common base we made was 6 correct?

[vapid path]

yes

[timid silo]

In our example of 1/2 + 1/3

Okay

So if I have 1 and x in the denominator

The common base would be?

$$1 \times x = x$$

[warm shale]

Edmund Cloudsley

[vapid path]

ohhhhhhh

OHHH

$\frac{x}{x} + \frac{2}{x}$

[warm shale]

aeth

[vapid path]

yeah?

[timid silo]

The term $\frac{2}{x}$ ALREADY has this x in the base therefore it requires no more changes but $\frac{1}{1} \times \frac{x}{x}$

[warm shale]

Edmund Cloudsley

[timid silo]

Yup yup good!

So now we have the base being the same we can just add the numerator

What would be the single fraction?

[vapid path]

$\frac{x + 2}{x}$

[warm shale]

aeth

[vapid path]

right?

[timid silo]

Great job! Let’s put this where the original circle was

$$\frac{3x}{1} - \frac{2}{\frac{x + 2}{x}}$$

[warm shale]

Edmund Cloudsley

[vapid path]

yeahhh so now we need the same denominator again?

[timid silo]

Let’s make this base same

Can you find the common base for me?

[vapid path]

4x/x? yeah?

[timid silo]

Not exactly :)

[vapid path]

ohhh wait

you multiply

the denominator

of the 2nd to the 1st?

[timid silo]

Yup yup!

[vapid path]

oh wait wait

[timid silo]

You’ve got it

Tell me the common base

[vapid path]

common base is
$\frac{x + 2}{x}$

[warm shale]

aeth

[timid silo]

Awesome!

[vapid path]

you multiply that to the numerator too?

[timid silo]

So we see that the term $\frac{2}{\frac{x + 2}{x}}$ already has this base but $\frac{3x}{1}$ doesn’t

[warm shale]

Edmund Cloudsley

[timid silo]

So we multiply the common base only with 3x

[vapid path]

yeah so $\frac{3x^2 + 6x}{x}$

[warm shale]

aeth

[vapid path]

multiply common base with 3x?

[timid silo]

Yup good job!

$\frac{\frac{3x^2 + 6x}{x} - 2}{\frac{x + 2}{x}}$

[warm shale]

Edmund Cloudsley

[timid silo]

Correct?

[vapid path]

yeah yeahhh

we put same denominator on 2 again?

-2x/x?

[timid silo]

Let’s turn this into a single fraction now

Can you do it for me please?

[vapid path]

is this right

[timid silo]

Yes good job

Now turn this into a single fraction

$\frac{\frac{3x^2 + 6x}{x} - \frac{2x}{x}}{\frac{x + 2}{x}}$

[vapid path]

oh wait not 2x just two?

[warm shale]

Edmund Cloudsley

[timid silo]

Yeah sorry mistyped it

[vapid path]

$\frac{3x^2 + 4x}{x}$

[timid silo]

Gg good job

[warm shale]

aeth

[timid silo]

$\frac{\frac{3x^2 + 4x}{x}}{\frac{x + 2}{x}}$

[warm shale]

Edmund Cloudsley

[timid silo]

Yeah?

[vapid path]

yeahhh yeahhh

now reciprocal? that thing?

[timid silo]

If we are diving something, we are multiplying by the reciprocal

[vapid path]

yeah yaeh wait

$\frac{3x^2 + 5x}{2x + 2}$

yeah?

[warm shale]

aeth

[vapid path]

is this good?

[timid silo]

Not exactly no

[vapid path]

where did i go wrongg

[timid silo]

$\frac{3x^2 + 4x}{x} \times \frac{x}{x + 2}$

[warm shale]

Edmund Cloudsley

[timid silo]

$\frac{3x^2 + 4x}{\cancel{x}} \times \frac{\cancel{x}}{x + 2}$ = $\frac{3x^2 + 4x}{x + 2}$

[warm shale]

Edmund Cloudsley

[timid silo]

Are you with me @vapid path

[vapid path]

OHHhh cancel

yeah yeah yeah

[timid silo]

Noice

[vapid path]

thats the answer now right?

you just add it now

[timid silo]

Now we have this in the form of P(x)/Q(x)

[timid silo]

Yup

[vapid path]

$3x^2 + 5x + 2$

[warm shale]

aeth

[vapid path]

righttt? WOAH

[timid silo]

You’ve got it mate

That’s correct

[vapid path]

THANK YOU SOOO MUCHHHHH

22 more 😭

[timid silo]

Happy to help

[timid silo]

Haha you’ve got it don’t worry

https://tenor.com/view/fastest-lap-max-verstappen-gif-888747356393781215

[vapid path]

can you help me more im sorry 😭🙏 number 37

Im think of mod but like idk how to use it here

[timid silo]

Okay last question

Cause I’ve gotta do my econ hw after this 😅

[vapid path]

Oh alright thank you so much and goodluck with that

[timid silo]

Okay so

$4x + 10 = 2(2x + 5)$

[warm shale]

Edmund Cloudsley

[timid silo]

Does that give you a hint? 😉

[vapid path]

OHHHHHHH

wait lowkey im getting more of the idea i just dont know how to excecute it

24 first glance coz x 2 but idk tho

[timid silo]

Hmm not exactly :)

But we’re getting somewhere

Have you studied the remained theorem before?

[vapid path]

Yeahhh like where its 0? Then its a root? Is that it?

Should i get the x value

[timid silo]

That’s the factor theorem

Let’s revisit the remainer theorem for a bit

[vapid path]

ohh factor theorem wait whats the remainder theorem again

[timid silo]

Yeah just a sec….

[vapid path]

i know i know that i just forgot

[warm shale]

Edmund Cloudsley

[vapid path]

ohhh yeah yeahhhh

[timid silo]

So according to the remained theorem, if we input

$$P(\frac{-5}{2}) = 12$$

[warm shale]

Edmund Cloudsley

[vapid path]

uhuhh

[timid silo]

So in the case of 4x + 10 our input for the polynomial would be?

$$P(\frac{-10}{4})$$

[warm shale]

Edmund Cloudsley

[vapid path]

yesss yesss

[timid silo]

And this simplifies to P(\frac{-5}{2})

[vapid path]

OHHHHHH

SO ITS STILL 12

[timid silo]

Which is 12!

Yes

[vapid path]

LMFAOOOOO THANK YOU SOOOO MUCHH goodluck with your hw

[timid silo]

Good luck to you to cheers mate

[vapid path]

.close

[obtuse pebble]

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[old lily]

what's the state space

[bitter gust]

What do you mean?

[teal turret]

the set of possible states

[old lily]

{x in R such that P(X_n = x) != 0}

the possible values of the markov chain

it's basically 2 possible states (on a given day he eats meat or he doesn't) - we can label these with 1 and 0 respectively

so the transition matrix is 2x2

[bitter gust]

hmm ok

So either he eats meat or does not but doesn't the die first decide if he eats meat or not?

[old lily]

yeah that's for deciding X_0

[bitter gust]

How can we just say that the probability of him having meat is either 1 or 0 before mentioning the dice role tho?

[old lily]

so let's say he eats meat today (X_n = 1). what's the probability he will eat meat tomorrow?

[bitter gust]

0

[old lily]

i mean the question doesn't mention what happens on the first day

[bitter gust]

That is why I am really confused 😭

[old lily]

you could assume anything ig

[bitter gust]

Because won't how we set up the matrix change the answer?

[old lily]

no it won't

what happens tomorrow only depends on what happened today

(markov property)

so the first day doesn't matter

anyway the transition matrix is conditional probabilities

[old lily]

yeah so this is the (1,1) entry

so if he eats meat today what's the probability he will not eat tomorrow

[bitter gust]

Okay so let's say he ate meat today, the probability of that is 1/6 and what happens tomorrow depends on what happened today, so tomorrow the probability of eating meant is 0.

So would (1,1) not be 1/6 and (2,1) be 0?

[old lily]

ok wait i'm labelling it like 0 then 1

so top right is (0,1)

the (1,1) entry is P(X_(n+1) = 1 | X_n = 1)

[bitter gust]

hmmm

So the first column is if he has meat today

and the second column is if he has meat tomorrow?

So is this the matrix?

or would it be this:

[obtuse pebble]

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[stiff mortar]

Lhugo no

[timid silo]

why?

oh sorry

didnt see

[timid silo]

?

?

[stiff mortar]

You know what you can have this channel

Im out✌️

[timid silo]

didn't understand sorry

[stiff mortar]

No cause i wanted to type here a question but then i saw you typing and i wrote no but then i found the answer to my question and i dont need the channel anymore

[timid silo]

ok

[stiff mortar]

.close

[obtuse pebble]

Channel closed

Closed by @stiff mortar

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[obtuse pebble]

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[weak terrace]

im not sure which one is suppose to be used as a u sub

[upper shuttle]

probably 1-cos^3

its derivative would be that thing outside

[weak terrace]

ok from that point how do i go about

[upper shuttle]

find du/d theta

then change the d theta to du

[weak terrace]

is my du/d going to be 2costheta

[stone holly]

cos theta = t

[weak terrace]

what? is cos theta =t

[upper shuttle]

dont do that

[stone holly]

I mean cos theta = u

[upper shuttle]

no its

-3 cos^2 sin

[stone holly]

oh yeah

that works

[stone holly]

this would work too but will need to do 2 substitutions

[upper shuttle]

so the cos and sin cancels with the stuff outside the bracket

[weak terrace]

ok how do i set this up can i show u what i have

[wary badger]

no you cant!

[weak terrace]

does theta turn into a u

im so scared y are so many ppl in here

[upper shuttle]

oh no

[wary badger]

we all love to help

[upper shuttle]

no idea

[stone holly]

lmao

[wary badger]

you must love when i intrude

😹😹

i’ll let you help

🤝🏻

[upper shuttle]

only when its u

[upper shuttle]

was something wrong?

[wary badger]

nah

just trolling

because they asked if they can show

of course they can

[upper shuttle]

do u=1-cos^3 theta

[weak terrace]

IM GOING

I WORK SLOW IM GONNA SEND IT RN SRYYYY

[upper shuttle]

its ok im slower

[weak terrace]

Is that right so far or no

And if it is I’m stuck from that point

[upper shuttle]

,rccw

[weak terrace]

also next to sin i forgot but du

[upper shuttle]

its

theres a sin

so u should cancel the sin theta as well

pretty nice u use up the whole line lol

but please do put = before each equation to denote equality

[weak terrace]

im sorry

so im left with the same answer but with out sin

what happens to the 1/3? do i distrubute it back in when i pull the anti?

[wary badger]

are these u’s?

add a little tail

[weak terrace]

let me rewrite it so we can all understand

[upper shuttle]

i believe theres no - as well
theres a - and another - as cos derivative is -sin. they cancel out

[upper shuttle]

we all yep

[dire rain]

the first term is the derivative of whats inside the bracket

[weak terrace]

im so lost

[dire rain]

you cancel it after multiplying by 3 and then 1/3 outside the integration

[dire rain]

so u treat the bracket^10 like its x so u add power and divide power all multiplied by 1/3

loss

very sad

[upper shuttle]

oh sorry

lost not loss

[dire rain]

mb

imma die now

[weak terrace]

ok dont die

u made most sense

out of 100 million helpers

ty

[upper shuttle]

i didn't

rip

u good now?

[weak terrace]

u did but scary

wen that dude joined

[dire rain]

thank

[weak terrace]

yeah ty

[upper shuttle]

:((

[weak terrace]

appreciate u all

sry queen

[upper shuttle]

why i scaryD:

[weak terrace]

ur math is so advanced

be brave go learn more

bye

[dire rain]

have fun

[upper shuttle]

what xd

[weak terrace]

my u were not good enouigh

i use whole line

[upper shuttle]

no using the whole line is fine

its pretty cool to haha

[weak terrace]

im never doing it again

[upper shuttle]

why lol

[weak terrace]

bc u dont

i wanna become u

[upper shuttle]

no i do

it just depends on the Q

some ill have to use a few lines for each equation

👉 👈

[wary badger]

damn

[upper shuttle]

those are painful

[weak terrace]

ok if u wanna talk we can play valorant i need 2 finish hw u need 2 help ppl

[upper shuttle]

u scary

🔪

[weak terrace]

bye every1 forever

[wary badger]

very

[upper shuttle]

yikes forever

.close

[obtuse pebble]

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[upper shuttle]

could someone explain this to me

[gilded needle]

well if you want to find all x,y such that x+y = z, then x can be anything as long as y = z-x, right?

[upper shuttle]

isnt it more like, Z is defined as X+Y

[gilded needle]

i am distinguishing here between Z and z

Z is a random variable

z is one particular value that Z can take on

the underlined formula is computing the probability that Z = z

[upper shuttle]

could i try to understand

so could it be like the number of times z appears at x=17 for instance?

[gilded needle]

i don't see multiple trials happening here

you have two random variables X and Y

and their sum is Z

the formula is computing the probability that Z = z

i.e. the probability that X+Y=z

you have a joint probability distribution function for X and Y

namely p

so you just find all the combinations X=x and Y=y that sum to z, and add their probabilities together

[upper shuttle]

what does p_Z(z) mean

[gilded needle]

no, what they're calling p(x,y), the p without a subscript, that's the joint distribution function

[gilded needle]

that's the probability distribution for Z

p_Z(z) is by definition the probability that Z=z

and p(x,y) is the probability that X=x and Y=y

[upper shuttle]

the probability of x and z-x occuring?

[gilded needle]

poor notation but standard

[gilded needle]

that would be p(x, z-x)

the probability that X=x and Y = z-x

[upper shuttle]

isnt p(x, z-x)=p(x, y)?

nvm i shall go back to the start of this chapter

thanks bungo

.close

[obtuse pebble]

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[obtuse pebble]

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[vast cape]

I am mad lost, i have no idea where to start, forget work to show

i know it has something to do with the derivative, which is 12x^2 - 80x +125

but no idea what to do with it

[velvet spoke]

Hello

I can help

[vast cape]

hi

[vast cape]

ty

[velvet spoke]

give me some time to write down the full solution

[vast cape]

alr

[velvet spoke]

@vast cape

[vast cape]

wait what is ur y-k step?

[velvet spoke]

j k step

i assumed a point (j, k) on the curve

so (j, k) satisfies the given equation

and i can take the tangent at point (j, k)

now that tangent passes through the point (1, 5)

@vast cape

[vast cape]

ohhhh

ok

oh ok alr

yea i get it now

ty

[velvet spoke]

after solving for the various values of j, you can have various values of k as well (from the equation)

and you already know the tangent eqn in terms of j, k

so yeah there you go

[vast cape]

so i just solve for possible j values to get the different slopes of tan right?

then solve for equation of lines?

[velvet spoke]

solve j to get k

then you have this eqn

just put the various (j, k) in it

get k from here

i hope it's making sense

[vast cape]

mostly yea

i understand why you get to those last equations, but im not sure where id get my tangent slopes from

(j,k) is on the curve right?

so then would u plug j into the derivative for slope?

then use the point 1,5 for equation of the line?

[velvet spoke]

yep

[velvet spoke]

oh you can use that approach as well

there's no problem in that

you can plug j into the derivative yes

[vast cape]

u mind if i try solving and double check my asnwers with you?

[velvet spoke]

your slope then would be (6j - 25)(2j - 5)

[velvet spoke]

You can use Wolfram Alpha to solve this cubic, it will take a whole lot less time

[vast cape]

yea but i wont have it on my tests so tryna get hand written practice lol

[velvet spoke]

sure, ping me when you're done

@vast cape Your j is here

[vast cape]

oh ty

[velvet spoke]

get k, get eqns

[vast cape]

were the 3 k values

-120,-4,5

@velvet spoke

meaning the three equations are

y=-120x+125

y=-4x+9

y=5x

[velvet spoke]

let me see

yep yep yep

did your answer match ?

[vast cape]

yea

ty

[velvet spoke]

yw

you understood the method, right? @vast cape

[vast cape]

yea

[vast cape]

tysm

.close

[obtuse pebble]

Channel closed

Closed by @vast cape

Use .reopen if this was a mistake.

[obtuse pebble]

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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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[obtuse pebble]

Channel closed

Channel closed due to the original message being deleted.
If you did not intend to do this, please open a new help channel,
as this action is irreversible, and this channel may abruptly lock.

[ionic flame]

,rotate

[ionic flame]

Do mind the shadow, trying to use the quadratic formula, but not sure whether or not i have done it wrong.

[tardy epoch]

,w roots x^2 + 2x + 5

[warm shale]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by rie.mann

[tardy epoch]

looks right after you simplify

[ionic flame]

whats i?

[tardy epoch]

-2/2 = -1, sqrt(16) = 4, etc.

$i = \sqrt{-1}$

[warm shale]

riemann

[ionic flame]

Imaginary number?

[tardy epoch]

yes

[ionic flame]

is this bot able to plot graphs using this equation?

,help

[warm shale]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[velvet spoke]

yes

use https://desmos.com/calculator

by the way you can plot the graph yourself, it's super simple

[tardy epoch]

,w plot x^2 + 2x + 5

[warm shale]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by rie.mann

[ionic flame]

I have never come across this type of quadratic formula before

[velvet spoke]

do you know about √-1

[tardy epoch]

open a new channel if you want to keep asking since this one will close unpredictably

[velvet spoke]

complex numbers?

[ionic flame]

no...

[velvet spoke]

okay well we defined √-1 to be i

[ionic flame]

is there theory behind it, or just becuase?

[velvet spoke]

just because

and it lead to the world of complex numbers

well all you need to know right now is that when you solve the eqn using the quadratic formula

[ionic flame]

Oh, so is it safe to assume that any value within the surd if negative results in the line not intersecting the x axis?

[velvet spoke]

you got this, right?

[ionic flame]

yes,

[velvet spoke]

we solve such roots like this

where i is the imaginary unit

Obviously this equation has no roots in the real world

[ionic flame]

should i state my final answer with the imaginary unit included? or present it with a surd?

[velvet spoke]

since square root of a negative number has no meaning in the real world

[velvet spoke]

You should present it with i included

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• 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!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[velvet spoke]

your teacher would know what it is

[ionic flame]

ah ok

[velvet spoke]

damn this channel's broken

[wary badger]

^

[velvet spoke]

well we're done so

¯_(ツ)_/¯

[ionic flame]

My teacher has us to write all our answers using word...

microsoft word isnt the best for maths

it takes ages to type them up

[wary badger]

latex

[velvet spoke]

you can use alt =

open the equation editor

use latex in that

[ionic flame]

i love that!

tysm

may i ask, whats latex and how can it benefit

[velvet spoke]

it's a language

used to write math

[ionic flame]

i never knew of this, just tried it and it was instant

[velvet spoke]

basics are simple, ask #latex-help

[ionic flame]

is it already included in word? or would i have to install something else

[velvet spoke]

no i think it is already included

Word eqn editor has latex support, right

[wary badger]

$\int e^x dx$

[warm shale]

knief

[wary badger]

it’s nice

[velvet spoke]

mine does

[wary badger]

this uses latex

go to overleaf

it’s free

they have articles

that are easy to read

[ionic flame]

so this form is latex?

[wary badger]

and you can use youtube videos as a supplement

it takes less than a day to learn

[wary badger]

yea

[ionic flame]

$\int e^x dx$

[wary badger]

use a space

after int

[velvet spoke]

formatting, use space

[warm shale]

Lenmou

[ionic flame]

thats beautiful

[wary badger]

$e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!}$

[warm shale]

knief

[ionic flame]

when i saw all of you guys using it i thought it was pretty hard

[wary badger]

nah it’s easy

[ionic flame]

so the $ is to open prompt within the bot here?

[velvet spoke]

Refer https://www.overleaf.com/learn

[wary badger]

just looks scary

[velvet spoke]

@ionic flame

[wary badger]

yes

[ionic flame]

exactly what i thought

[wary badger]

you can also use $$\sinx$$

[warm shale]

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

[velvet spoke]

[wary badger]

bruh

[velvet spoke]

$\sinx$

[warm shale]

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

[wary badger]

interesting

[velvet spoke]

very interesting

[wary badger]

$$\int e^x dx$$

[ionic flame]

i clicked on the link

[warm shale]

knief

[wary badger]

you can use

(\int e^x dx)

[warm shale]

knief

[wary badger]

or

[\int e^x dx ]

[warm shale]

knief

[wary badger]

hmm the slash doesn’t show but it’s

back slash

[velvet spoke]

this is just a latex testing ground now lmao

[ionic flame]

hey fluxion, which section should i go under to learn the latex codes?

[wary badger]

just read the overleaf articles

they have a good amount

https://www.overleaf.com/learn/latex/Learn_LaTeX_in_30_minutes

i read that one first

then for more specific things they have other articles

[velvet spoke]

check sidebar

[wary badger]

read this^

[velvet spoke]

yeah read that

[ionic flame]

Ah thank you both!

[wary badger]

you’re welcome

[ionic flame]

ill probably have to read this when i am a bit less tired, so tomorrow.

ya both really smart too, congrats to learning something that looks scary

do either of you program?

[wary badger]

not much

you don’t need to know how to code

[ionic flame]

if i may ask, where arer you from?

[wary badger]

america

[ionic flame]

pretty nice

anywho, thanks again. 🙂

[wary badger]

you’re welcome

[ionic flame]

.close

[wary badger]

this isn’t your channel

[ionic flame]

oh yh

[wary badger]

it’s fluxions

i’ll close it though

.close

[obtuse pebble]

Channel closed

Closed by @wary badger

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[velvet spoke]

india

[velvet spoke]

fkcing okay i see how these work

[velvet spoke]

no

[latent walrus]

these arent social channels

.close

[velvet spoke]

.close

[obtuse pebble]

Channel closed

Closed by @latent walrus

Use .reopen if this was a mistake.

Channel closed

Closed by @velvet spoke

Use .reopen if this was a mistake.

[ionic flame]

Something like this

Should i have to write the -2+ or - on numerator line?

i do alt =
then write my equation but it doesnt ever put the -2 + or - inside the fraction

it always leaves it outside the fraction...

i have to manually put it back in

(word)

[tardy epoch]

$\sqrt{-16} = \sqrt{16 (-1)} = \sqrt{16}\sqrt{-1} = 4i$

[warm shale]

riemann

[velvet spoke]

type / then press space then do whatever you do

i s'pose it worked

[ionic flame]

YES

you are very smart

[velvet spoke]

im not

stop with the flattery omg

[ionic flame]

with this

when we factor out the negative

can we immediately put the i inside

[velvet spoke]

idk wym

[ionic flame]

do we have to take it through all those steps before putting it into 4i

[velvet spoke]

not really

just whenever you see smth √-x just do i√x

[ionic flame]

so if we see a negative within a surd we can write it as "i surd"?

[velvet spoke]

when you get to complex numbers you'll see why

[ionic flame]

ah ok

[velvet spoke]

for now this should satisfy your needs

[ionic flame]

sorry no idea what they are called

surds or radicals

[velvet spoke]

Both

[ionic flame]

preferred name?

[velvet spoke]

i like radicals

[ionic flame]

√-16
√16 -1
4i

or should we write it as √16 √-1

[velvet spoke]

both statements are equivalent

For neatness

use 4i

and it's just better

[ionic flame]

hmm

[velvet spoke]

why leave it as √16 √-1

[ionic flame]

to show steps?

idk really, just because i thought it looked right

[velvet spoke]

no need

[ionic flame]

ok

[velvet spoke]

if your teacher asks you to you can show steps to him

but it's not required

[velvet spoke]

ayo why u using this asterisk

type \cdot then press space

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ionic flame]

huh

[ionic flame]

\cdot

[alpine bison]

it is no a big deal

[ionic flame]

ill try it out gimme a min

[velvet spoke]

it's just so so neater

[alpine bison]

this is even better than who sends some hand written exercise

[velvet spoke]

are u calling me out

[ionic flame]

one on left is without, one on right is with

should i capitalise algebra?

[velvet spoke]

bro it's variables, do whatever

no one rlly cares

[ionic flame]

ill keep them like that then ig

my teacher is quite strict when it comes to presentation

[velvet spoke]

this is wrong

Like so

[alpine bison]

haha no no, I m not referring to some of yours previous posts

[ionic flame]

oh, because of the + or -

[velvet spoke]

no, your statement is mathematically incorrect

just the √-16 is equal to 4i

[ionic flame]

doesnt the -2 and 2 cancel eachother out?

[velvet spoke]

the rest of the stuff remains the same

yeah they do

leaving with -1

[ionic flame]

oh....

[velvet spoke]

@ionic flame try solving this eqn

[ionic flame]

hmm, i see where i messed up

[ionic flame]

ok sir haha

ill do it right now

may i write what i do here along the way?

[velvet spoke]

sure dude i dont mind

[ionic flame]

x^2 +x +1 = 0

a=1 b=1 c=1

x= -1+√-3 / 2

x= -1-√-3 / 2

so far so good?

[velvet spoke]

yeah

@ionic flame are u stuck

[ionic flame]

No i went to word

[velvet spoke]

oh

[ionic flame]

?

thats as far as i got

off topic, but i love the way word looks with maths

[velvet spoke]

aw no

[ionic flame]

aw no good or bad

[velvet spoke]

Cross check where you went wrong

[ionic flame]

i forgot to divide the entire thing 😦

[velvet spoke]

and you didn't solve the root correctly

you should stick to solving roots step by step @ionic flame

[ionic flame]

which step

[velvet spoke]

step 3

sorry typing err

[ionic flame]

could you give me another please?

[velvet spoke]

=0 @ionic flame

x^2 + 3x +5 = 0

[ionic flame]

may have messed up

[velvet spoke]

dont put the i in the root

i suppose that's just a typing error

[ionic flame]

i before the root?

like so?

[velvet spoke]

yeah, perfect

you got the hang of it

[ionic flame]

if you have root 11 (i)

is there a way to simplify it further?

it dont look nice to my eyes

[velvet spoke]

,w √11

[warm shale]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by _nofluxgiven

[velvet spoke]

@ionic flame

if you wanna

now what looks better to ur eyes?

[ionic flame]

oh wow

erhm

the first one

[velvet spoke]

indeed

[obtuse pebble]

@ionic flame Has your question been resolved?

Channel closed

Closed by @ionic flame

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tropic mirage]

Need help understanding the math

[deft magnet]

,rotate

[tropic mirage]

I don't understand why it's b(1-gamma) / gamma

[obtuse pebble]

@tropic mirage Has your question been resolved?

[unreal musk]

The “it” you’re referring to being? u’(w)?

[tropic mirage]

Yes

Oh mv

Mb

I thought it was wrt gamma

[unreal musk]

Fairs do you see it now, at least?

[tropic mirage]

Yep

[unreal musk]

Cool

[tropic mirage]

I have another question

Applying l'hopitals rule

Where does In(W) come from

[unreal musk]

,rccw

[unreal musk]

Derivative of $a^x$ wrt $x$ is $a^x \ln(a)$

[warm shale]

@unreal musk

[unreal musk]

In your case, you're differentiating wrt gamma

[tropic mirage]

Got it thanks

[obtuse pebble]

@tropic mirage Has your question been resolved?

Channel closed

Closed by @tropic mirage

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[timid silo]

.open

Hello

[timid silo]

The SHS officers are planning for a SHS Prom. The allocated budget for decorations, sounds, and other miscellaneous expenses is ₱100,000.00 and an additional ₱1500.00 for meal expenses for each guest. The organization received an amount of ₱200,000.00 from its external
stakeholders.
a. Write the total allocated budget as a function of the number of guests.
b. Find the inverse of the function.
c. State the domain and range for this situation.
d. Find the possible number of guest for a budget of ₱200,000.00

(a) 100,000 + 1500x

(b)

(c)

(d)

<@&286206848099549185>

Pin please

[rocky pelican]

for b u make 100,000 + 1500y = x

and you make y the subject

for c, doman of original function = range of inverse, and range of original function = domain of inverse function

for d u just solve for x of the original equation

[timid silo]

Sooo...

x = 100,000 + 1500y

What do I do now?

Divide?

[rocky pelican]

you make y the subject

first u isolate all terms with y

so move 100,000 to the left by subtracting both sides with 100,000

[timid silo]

Okay

-1000,000 + x = 1500y

[rocky pelican]

just write it as x - 100,000

[timid silo]

Okay

[rocky pelican]

easier to read

[timid silo]

x - 100,000 = 1500y

[rocky pelican]

yes

[timid silo]

x - 100,000/100,000 = 1500y/100,000

[rocky pelican]

ur trying to make y the subject

[timid silo]

Huh?

x - 100,000/100,000 = 1500 + y

[rocky pelican]

wait

stop

lets go back to x - 100,000 = 1500y

[timid silo]

Okay

[rocky pelican]

you're trying to make y the subject

and y is currently multiplied by 1500

so what should u do to make y not multiply by 1500

[timid silo]

1500 + y?

1500/y??

[rocky pelican]

not quite

divide by 1500

so (x + 100,000)/1500 = 1500y/1500

[timid silo]

OHHH

(x + 100,000)/1500 = 1500y/1500
1500x + 0.015 = y

[rocky pelican]

ur supposed to divide x + 100,000

by 1500

x/1500 and 100,000/1500

[timid silo]

That's what I did??

Divide x + 100,000

so its 1500x + 0.015

[rocky pelican]

bruh

u multiplied x by 1500, and idk how u got 0.015, by dividing 100,000 with 1500

[timid silo]

THEN ITS SUPPOSE TO BE x/1500?? That is??? Just a fraction??

[rocky pelican]

ur supposed to divide 100,000 by 1500

[rocky pelican]

yes

[rocky pelican]

yes

[timid silo]

So

x/1500 + 66.6666666667 = y

[scenic vapor]

Don't use that value, keep it as a fraction

But you can simplify the fraction

[timid silo]

Idk how to make a Decimals into a fraction

x/1500 + 66.70 = y

[rocky pelican]

don't use decimals

just use fracion

100,000/1500

[timid silo]

Oh okay

Sooo x/1500 + 100,000/1500 = y

Is that the answer??

[scenic vapor]

Yeah, for simplicity we could write $f^{-1}(x) = \frac{x+100,000}{1500}$

[warm shale]

Catgod

[timid silo]

Ohhh okay

[scenic vapor]

(a) f(x) = 100,000 + 1500x

(b) f^-1 (x) = (x+100,000)/1500

(c)

(d)

[timid silo]

(a) 100,000 + 1500x

(b) f(x) = 100,000 + 1500x
y = 100,000 + 1500x
x = 100,000 + 1500y
x - 100,000 = 1,500y
(x + 100,000)/1500 = 1500y/1500
x/1500 + 100,000/1500 = y
y = x/1500 + 100,000/1500
F-1 (x) = x + 100,000/1500

(c)

(d)

[scenic vapor]

For c, we want to find the domain and range of f(x) = 100,000 + 150x

Do you remember the definition of domain and range?

[timid silo]

IS IT THAT TABLE??

GRAPH THINGY

THE
x
y

SOMETHING

AND THEN GRAPH??

[scenic vapor]

The domain is the set of all possible values of the input

The range is the set of all possible values f(x) gives (the output)

[timid silo]

WAIT WAIT

Lemme give you another example

[scenic vapor]

Sure

[timid silo]

Is it that one??

The graph and it has boxes

For (c)

[scenic vapor]

Not really

The domain is a set, I see no set in your image

[timid silo]

That's really how were taught..

So..

Idk what you mean

[scenic vapor]

Oh...

[timid silo]

So.. next step??

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

<@&286206848099549185>

Please do not close this

Pin me if your there

<@&286206848099549185>

[tawny mauve]

Yeah

[timid silo]

PLEASE HELP ME

The SHS officers are planning for a SHS Prom. The allocated budget for decorations, sounds, and other miscellaneous expenses is ₱100,000.00 and an additional ₱1500.00 for meal expenses for each guest. The organization received an amount of ₱200,000.00 from its external
stakeholders.
a. Write the total allocated budget as a function of the number of guests.
b. Find the inverse of the function.
c. State the domain and range for this situation.
d. Find the possible number of guest for a budget of ₱200,000.00

(a) 100,000 + 1500x

(b) f(x) = 100,000 + 1500x
y = 100,000 + 1500x
x = 100,000 + 1500y
x - 100,000 = 1,500y
(x + 100,000)/1500 = 1500y/1500
x/1500 + 100,000/1500 = y
y = x/1500 + 100,000/1500
F-1 (x) = x + 100,000/1500

(c)

(d)

I'm in letter C

[timid silo]

Here's a sample of what my teacher taught me

[tawny mauve]

I'm not good at that thing
I can solve calculus, graphs, and etc

[timid silo]

Oh

<@&286206848099549185>

[tawny mauve]

If you have calculus problems then let me know

[rocky pelican]

i guess u just make a table

and write the values for x and y

[timid silo]

That's it??

Hm okay..

[rocky pelican]

isn't that what u did in the sample

[timid silo]

(D) then

[rocky pelican]

just solve the equation for 200,000 = 100,000 + 1500x

[timid silo]

Oh

200,000 = 100,000 + 1500x
200,000 - 100,000 = 1500x
100,000 = 1500x
100,000/1500 = 1500x/1500
100,000/1500 = x

Done

(a) 100,000 + 1500x

(b) f(x) = 100,000 + 1500x
y = 100,000 + 1500x
x = 100,000 + 1500y
x - 100,000 = 1,500y
(x + 100,000)/1500 = 1500y/1500
x/1500 + 100,000/1500 = y
y = x/1500 + 100,000/1500
F-1 (x) = x + 100,000/1500

(c)

(d) 200,000 = 100,000 + 1500x
200,000 - 100,000 = 1500x
100,000 = 1500x
100,000/1500 = 1500x/1500
100,000/1500 = x

[timid silo]

Is this correct @rocky pelican

[rocky pelican]

yeah

but u need to make a a whole number

the budget has to be less than 200,000

[timid silo]

How do I do that?-

[rocky pelican]

100,000/1500 = 66.66...

just make it 66

[timid silo]

Can I round it up?

66.70??

(a) 100,000 + 1500x

(b) f(x) = 100,000 + 1500x
y = 100,000 + 1500x
x = 100,000 + 1500y
x - 100,000 = 1,500y
(x + 100,000)/1500 = 1500y/1500
x/1500 + 100,000/1500 = y
y = x/1500 + 100,000/1500
F-1 (x) = x + 100,000/1500

(c)

(d) 200,000 = 100,000 + 1500x
200,000 - 100,000 = 1500x
100,000 = 1500x
100,000/1500 = 1500x/1500
100,000/1500 = x
66 = x

[rocky pelican]

it has to be a whole number

there can't be 0.7 of a guest lol

[timid silo]

Oh

So really 66.66??

[rocky pelican]

whole number doesn't have decimal

66

[timid silo]

Just 66??

[rocky pelican]

yes

round down because the budget is 200,000

if u round up it will go over the budget

[timid silo]

Oh okay

NEXT QUESTION

YESSS

ALMOST THERE

3. A Spotify Music allows member to download songs for ₱205.40 pesos each
   after paying a monthly service charge of ₱782.75. The total monthly cost C(x) of the service in peso is C(x) = 782.75 + 205.40x, where x is the number of songs downloaded.
   (a) Find the inverse function
   (b) What do 𝑥 and 𝐶^−1(𝑥) represent in the context of the inverse function?
   (c) How many songs were downloaded if a member’s monthly bill is ₱3843.75?

a is quite easy

C(x) = 782.75 + 205.40x
y = 782.75 + 205.40x
x = 782.75 + 205.40y
x - 782.75 = 205.40y
(x - 782.75)/205.40 = 205.40y/205.40
x/205.40 - 782.75/205.40 = y
y = x/205.40 - 782.75/205.40
F-1 (x) = x/205.40 - 782.75/205.40

@rocky pelican ??

[rocky pelican]

yes

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

So that's the answer??

Okay then soo

b?

How do I do b??

[rocky pelican]

c^-1(x) represents the nubmer of songs downloaded

x represents the money

[timid silo]

So..

I don't get it

@rocky pelican

[rocky pelican]

so in the original function x represents number of songs downloaded

c(x) is the money

c^-1(x) is inverse of original function

so x and y axis are switched

[timid silo]

OHHH

C(x) = 782.75 + 205.40x
y = 782.75 + 205.40x
x = 782.75 + 205.40y
x - 782.75 = 205.40y
(x - 782.75)/205.40 = 205.40y/205.40
x/205.40 - 782.75/205.40 = y
y = x/205.40 - 782.75/205.40
C(x) = x/205.40 - 782.75/205.40???

[rocky pelican]

isnt' this a

[timid silo]

Oh

Then how??

[rocky pelican]

b is asking u the relationship between x and y in the inverse function

so just say what each axis is

[timid silo]

...

How do I..

Do that..??

Like.. graph it??

NO WAIT ACTUALLY GRAPH IT??

[rocky pelican]

no

u just say

x is the money spent