help-0

[trim herald]

<@&286206848099549185>

[undone tulip]

Yes?

....

[austere sluice]

which q?

[trim herald]

Question 4

.close

[lone heart]

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[unborn dock]

what would the equation to find the tension subjecting object Q be?

[unborn dock]

R(->) = 40+T-6=3*3 ?

[abstract hinge]

T-6=3a

[unborn dock]

what would happen to 40?

or its only affecting P?

[abstract hinge]

see u get two eqn

One will be what i said

and other will be T-40+10=-5a

considering left side +ve direction

if u solve both eqn simultaneosly u will get the value of acceleration

[unborn dock]

right

gotcha

thanks!

[abstract hinge]

no worries

[unborn dock]

.close

[lone heart]

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[lone heart]

@paper quiver Has your question been resolved?

[rocky flare]

hi

[rigid urchin]

Omg TYSM

[smoky lark]

help

.help

[lone heart]

Commands:
clopen: .close, .reopen, .solved, .unsolved
consensus: .poll
factoids: .tag
help: .help

Type .help <command name> for more info on a command.

[smoky lark]

.reopen

.reopen

[rocky flare]

hi

[smoky lark]

how do i add variables in algebra

like -3y+y to the power of 2 + 2y

[rocky flare]

well there's some rules

[smoky lark]

3hat

what

[rocky flare]

-3y+y^2+2y

[smoky lark]

yes

idk how to do -3y+y^2

what would y*y equal

2y?

[smoky lark]

what the hell is this

[rocky flare]

the rules

[smoky lark]

bro idk what half that means

im just starting algebra 1

[rocky flare]

remember those rules

[smoky lark]

dude

i wont remeber those

i dont have a use for those

those are all useless to me because i dont know how it works

show me how to solve it

thats all

-3y+y^2

[lone heart]

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[smoky lark]

.reopen

-3y+y^2

[rocky flare]

what are you looking to do with -3y+y^2+2y?

[smoky lark]

how would i do y^2

y*y?

2y?

[rocky flare]

just write it as y squared

that's it

[lone heart]

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[high mauve]

quick question

[high mauve]

if the weather report states that there's 25% chance of rain on saturday, and 35% chance on sunday, is it 60% probable that it will rain during the weekend?

i guess it's not 60 because maybe there's 5% chance of rain both days, but would it be less than 60? that seems wrong to me

[vale wigeon]

it's 25% + 35% - P(rain on both days)

i'm uncertain as to how kosher it is to claim whether on Sat and weather on Sun are independent

[high mauve]

yeah this is what the chapter was about

but it's more intuitive when the question's about only one time and not two points in time

[vale wigeon]

if we somehow know by divine interference that there will be at most one day of rain

then yeah the chance it'll rain on one of those days is 60%

[high mauve]

isn't it far less likely to rain the other day when it has rained the day before? at least in certain climates

but if i imagine a venn diagram i start to understand, two circles can be 35 and 25 but they must share some percent points

now there's another problem i wondered about

[shy wren]

wait isnt the probability of rain 1-0.75*0.65 if the events are mutually exclusive?

unless im missing sum

[high mauve]

"the next year ten of the students of class 1A chose chemistry and 20 chose maths, and five chose no subject. the probability that a random student has chosen both chemistry and maths is 25%. how many students are in the class?"

so with the fact that it is 25%, i can derive that the amount must be divisible by four, and there must be at least 20+5 and at most 20+9+5 students, so [25,34] students total

both 28 and 32 are divisible by four

but the book only lists 28 as the correct answer. what am i missing? why can't it be 32?

i suppose it's a typo

.close

[lone heart]

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[whole nebula]

how can I put 6/x^2 in the form nx^y

[high mauve]

hint: negative number

[lone heart]

@whole nebula Has your question been resolved?

[lone heart]

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[lone heart]

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[blazing charm]

why does f(x) = 3|x| and f(x) = |3x| result in the same function??

[blazing charm]

ping me if you can help 🙏

[vale wigeon]

$|ab| = |a| \cdot |b|$ for all real $a$, $b$

[ocean seal]

Ann

[blazing charm]

??

im confused @vale wigeon what's your point

[vale wigeon]

$|3x| = |3| \cdot |x|$

[ocean seal]

Ann

[blazing charm]

okay

OH

so

$3$ = 3

[ocean seal]

vert

[blazing charm]

wait

[pallid scarab]

|3| = 3 you meant

[blazing charm]

$|3| = 3

es

yes

and

3 * |x| is the same thing as |3| * |x| because |3| = 3

right

i think i get it

[pallid scarab]

Yes

[blazing charm]

ohhh okay

.close

[lone heart]

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[alpine sable]

Hello, I have some questions on Functions worksheet in maths anyone free to help out they’re quite a few questions but at least doing a few would be okay

[vale wigeon]

well post them

[alpine sable]

alright

[vale wigeon]

we gotta see the questions you want help with

[alpine sable]

alright

1 sec

They’re mixed but

[coral flower]

this server is for "helping" u understand the topic

[alpine sable]

u can tell from the number

[coral flower]

not for solving ur homework

[tardy tapir]

tf is this

[alpine sable]

bro

I need help with all of them

I skipped maths class

[coral flower]

bro , u need help with the entire topic go to ur teacher

[tardy tapir]

try some online source

[coral flower]

just pick 1 question and ask it , the helpers will help u with it

[alpine sable]

my teacher strict af and hates me bruh the guys gonna kill me tmr you know

[coral flower]

using that new knowledge , solve others

[alpine sable]

any websites u know that do functions?

[vale wigeon]

is your teacher actually planning to murder you?

[tardy tapir]

khanacademy

[alpine sable]

yes

[vale wigeon]

then you have bigger problems!

[alpine sable]

I can’t find the website he used for answers

[vale wigeon]

talk to your parents about your murderous teacher...

[alpine sable]

it’s saying British student but doesn’t show

[wary stream]

Tbh that's not our fault

[alpine sable]

I’m adopted

[vale wigeon]

he DEFINITELY shouldn't be teaching in any school or be near any kids if he really is so murderous.

[coral flower]

are u really just gonna copy paste the answer

[vale wigeon]

ok then go straight to your school's headmaster/superintendent/whoever else.

[alpine sable]

bro for now yes then later I’ll learn right now it’s 1 am I have school in a few hours

[alpine sable]

I’m joking…. But I’ll get punished

[coral flower]

tbh most of these questions are very simple to learn and simple to solve

[vale wigeon]

don't joke about murder.

it is too serious to be joked about.

[coral flower]

u can learn all those in like 30 mins ?

[vale wigeon]

you had the opportunity to say "no, my teacher isn't actually a maniac, he's just going to yell at me"

when i asked "is your teacher actually planning to murder you?"

[alpine sable]

I’m a slow learner

….

not a fast one

[coral flower]

u will learn , helpers here are very good

[alpine sable]

ahhhh I’m wasting time I’ll copy from my friend or just YouTube this

[wary stream]

Look up tons of resources on that topic

[alpine sable]

huh so the stress I’m having in school rn must feel like university stress

I hate my life

[wary stream]

Lmao university was chill tbh at least for me

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
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[whole otter]

I’m having a hard time understand hyperbolic trigonometric functions.

[whole otter]

I am trying to derive them along with that, and I can’t even think about it right now

Can someone please explain shortly and briefly about it

[vale wigeon]

do you mean the functions themselves or where they show up

[ember flume]

hey guys i got some problems can someone help me out?

[whole otter]

Different help channel please

[vale wigeon]

@ember flume please open your own channel. read #❓how-to-get-help for instructions.

[whole otter]

What do you mean by that

[ember flume]

which one?

[whole otter]

Any open one

[vale wigeon]

whichever one doesn't have a name on it.

[whole otter]

Such as #help-5

[vale wigeon]

"what even are cosh and sinh?" vs. "where did cosh and sinh come up that they deserve names?"

[whole otter]

Or #help-25

[ember flume]

ahh ookay thnks

[whole otter]

No I understand what cosh and sinh and cosh and sinh “origin” but the problem is like proving this and that

[vale wigeon]

what are you having trouble proving?

[whole otter]

Like “show the derivative of sinh x is cosh x

[vale wigeon]

you have their definitions $\cosh(x) = \frac{e^x + e^{-x}}{2}$ and $\sinh(x) = \frac{e^x - e^{-x}}{2}$ in front of you, yes?

[ocean seal]

Ann

[whole otter]

Or something like idk

Yes I have those definitions memorized

[vale wigeon]

do you know in general how to take derivatives

[whole otter]

But I don’t know how to “proof”

[whole otter]

Yes

[vale wigeon]

do you know how to take the derivative of e^x

[whole otter]

I have gone through 10 grueling chapters of derivatives

[whole otter]

Yes

[vale wigeon]

and of e^(-x)?

[whole otter]

e^x = e^x

e^-x = e^-x

[vale wigeon]

technically true, but you should not be using = as a "next step" symbol.

[whole otter]

Oh wait

[whole otter]

Wdym

[vale wigeon]

anyway the derivative of e^(-x) is not e^(-x)

[whole otter]

Ohhhhh

It’s negative

Negative e^-

-x

Cuz chain rule

[vale wigeon]

writing "x^2 = 2x" when you mean "the derivative of x^2 is 2x" is bad.

anyway!

[whole otter]

How so

[vale wigeon]

what's giving you trouble with differentiating sinh(x)?

[vale wigeon]

because that's not what the equals sign means.

[whole otter]

They want me to prove it

And prove other functions

[whole otter]

Oh I mean

d/dx e^x

= e^x

whoopsies

[vale wigeon]

then write the derivative symbol

[vale wigeon]

but again like

i dont understand what your problem is

sinh(x) = (e^x - e^(-x))/2

work out the derivative of (e^x - e^(-x))/2

right here right now in front of me

[whole otter]

Ok

So take out the 1/2

1/2 d/dx e^x - e^-x

And now

The derivative of e to the x is just itself

And the derivative of e to the -x is negative e to the -x

So then it changes it minus sign to positive

And then we have e^x + e^-x

Bring back the 1/2

We have e^x + e^-x / 2

And I think

[vale wigeon]

your notation is mildly shoddy, but yes, correct.

missing parentheses in a couple of places.

[whole otter]

I rather short Hand it

[whole otter]

But you get it

Hello?

@vale wigeon ?

[vale wigeon]

i was absent for LESS THAN A MINUTE

[whole otter]

I’m sorry

[vale wigeon]

and that only because i was typing in another channel

[whole otter]

I’m very impatient

Oh

Wait you work in multiple channels?

[vale wigeon]

do you REALLY BELIEVE YOURSELF SO FUCKING ENTITLED TO MY UNDIVIDED ATTENTION

THAT I CAN'T TAB AWAY FOR THIRTY GODDAMN SECONDS

[whole otter]

I’m sorry

[vale wigeon]

WITHOUT YOU PINGING ME A MILLION FUCKING TIMES

[whole otter]

I thought you just ghosted me

[vale wigeon]

30 SECONDS IS FAR TOO SHORT FOR A "GHOSTING".

you ticked me off with this

you really fucking did

[whole otter]

Ok I’m sorry

[vale wigeon]

anyway

there

you've proved that sinh' = cosh

you've done it

[whole otter]

But then we have this proof

Show that sinh-1x = ln(x - sqrt(x^2 + 1))

[vale wigeon]

yeah and?

do you know how to find inverse functions?

[whole otter]

Yes

[vale wigeon]

ok so then do it?

[whole otter]

sinh-1x = sinhy?

[vale wigeon]

$\frac{e^y - e^{-y}}{2} = x$, solve for $y$.

[ocean seal]

Ann

[vale wigeon]

it's all the same basic crap.

[whole otter]

Solve for y?

[vale wigeon]

yes solve for y.

you might have some success in temporarily substituting z := e^y and solving for z instead.

[whole otter]

2x = e^y - e^(-y)

[vale wigeon]

go do it on paper

[whole otter]

Ok

y = -ln(2x - e^y)

How do you solve thissss

[vale wigeon]

you might have some success in temporarily substituting z := e^y and solving for z instead.

[whole otter]

Ok

2x - z^-1 = z

[pale kestrel]

!volunteers

[lone heart]

Helpers are just people volunteering their time to help you. Be polite.

[pale kestrel]

no one is obliged to stick around and help u

[whole otter]

What

Did you fr read the conversation like 5 minutes ago

Yo are you actually against the name change?

You know it’s optional, right?

[vale wigeon]

ah yes because Five Minutes Ago is an inaccessibly distant period in the past obviously.

[whole otter]

Yes totally is

Oh I see it

I feel dumb

[vale wigeon]

if you couldn't tell, my last sentence was soaked through with sarcasm.

[whole otter]

I am aware

I felt dumb cuz the z strategy just turns it into a quadratic

z^2 + z - 2x

Wait

Multiply by z

z^2 - 2xz + 1?

From 2x - z^-1 = z

z^2 - 2xz + 1 = 0

Yeah that seems correct

[vale wigeon]

i told you to do it on paper

[high mauve]

if i were you i'd use symbolab.com as a tool

[whole otter]

Sorry

[vale wigeon]

you seem reluctant to do so and instead continue trying to do it in the discord message box

[whole otter]

But now it’s a quadratic equation

[whole otter]

I gotta write my thoughts

[vale wigeon]

yes, a quadratic equation is what you should end up with.

[vale wigeon]

then write them on paper.

[whole otter]

Ok

But waited

Don’t you just

Use the quadratic equation

Or is it like some stupid mysterious factoring thing that happens

x plus or minus the sqrt(+^2 + 1) = z

Wait

Do I use the plus or minus

Ima use the plus and see what happens

O

y = ln(x + sqrt[x^2 + 1])

FINALLY

I think

Idk

Is that the right answer

.

It’s been 5 minutes

Can that be counted as ghosting

,

I

[vale wigeon]

if you have to ask then no

but also again

!volunteers

[lone heart]

Helpers are just people volunteering their time to help you. Be polite.

[whole otter]

Oh

[vale wigeon]

shocked as you might be at this revelation, this also applies to me.

despite the fact that you in particular might consider me in particular to be your personal servant to always be at your beck and call.

but you might also not, so who knows.

you might understand why i am reluctant to keep hand-holding you through these problems.

[whole otter]

hmm

🤔

I’m kinda stupid

[real gazelle]

Please don't be impatient with helpers

[whole otter]

bro

[real gazelle]

5 minutes is much shorter than many people wait

[whole otter]

why do everyone keep scrolling up

[real gazelle]

people here have no obligation to help you

[whole otter]

I am aware

[real gazelle]

if they're helping you then they're doing so out of their own good will

then stop accusing people of ghosting you after five minutes

if you can't be respectful then you're not allowed here

[whole otter]

That message was not aimed at anyone

[real gazelle]

it was clearly referencing ann

[whole otter]

It was more of a “waiting move”

But anyway

If I wait 15 minutes can I ping helpers

Cuz

!helpers I think

[lone heart]

Please read #❓how-to-get-help

[whole otter]

Oh

[real gazelle]

Yes that's fine, but if you do so, please clearly repost what your question is and summarize what progress you've made on it

[whole otter]

[whole otter]

K

[real gazelle]

To ping them, type "@ Helpers" without the space but it hasn't been 15 minutes yet

[whole otter]

[real gazelle]

Also don't spam the channel

[whole otter]

Ok

[real gazelle]

That will make people less inclined to help you

[whole otter]

ok

<@&286206848099549185>

.close

[lone heart]

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• Be polite and have a nice day!

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[bright zodiac]

need help with the partial solutions, I can't seem to get the right result no matter how I try, for example I apply quotient rule to partial x and I always get sqrt(x^2+y^2) - x^2 / sqrt(x^2+y^2)^3

[bright zodiac]

.close

[lone heart]

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[quick peak]

Hi I was supposed to get a 2 as a coefficient instead of the x

Idk where I went wrong

[slim belfry]

What's the question? It's great that you're showing your work (far too few people do this) but this is really hard to read.

[quick peak]

For the bottom

When I plug it into wolfram

It says the a(n) is 2sin(nx)/n

But I got xsin(nx)/n

[alpine sable]

what does any of it mean

what are you trying to do

[quick peak]

Sorry

I’m finding the Fourier coefficients

And expanding it but im@not there yet

[lone heart]

@quick peak Has your question been resolved?

[lone heart]

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[viscid dock]

missing a rule or smt cant get the lhospital

[digital arch]

rationalise

[viscid dock]

how

[digital arch]

like how its done

[viscid dock]

.close

[lone heart]

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• Show your work, and if possible, explain where you are stuck.
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• Be polite and have a nice day!

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[brave moth]

ello

[brave moth]

I'm in electric engineering and where i'm from we have calculus subjects quite mixed up and i want to learn some of this stuff myself so ill post some problems from an exam of the subject and if anyone knows what i should search online please let me know

the question is "what does the equation represent in the complex plain"

where is the equation "reflected?" with the function w = i * z

Find the analytic function of variable z with real part being ^

[lime bobcat]

Bro bro, that's complex analysis

And that's it

Search for it, learn it

We can't solve all that questions

[brave moth]

find the Cauchy problem solution

[lime bobcat]

for you

[brave moth]

is it all complex analysis

[brave moth]

no i don't need them solved

i'm pretty sure the teacher has mixed different concepts of caluclus 1/2/3 and complex analysis in 1 subject

[brave moth]

for example this one is not a part of complex analysis as far as i understand

@lime bobcat you get my problem?

this is another exam of the same subject we have

<@&286206848099549185> can someone help me determine what should i search online and study to be able to solve the problems above?

[tacit arch]

Which one

Some look like ODEs

So find a book on ODEs

[brave moth]

yes ODEs are 6 and 7

aside from ODEs what else should i look for

Fourie and Laplace transform, what field to they belong to?

[tacit arch]

...

Those are part of ODEs

Maybe PDEs too

[brave moth]

number 5 says find the solution to the system using laplace

okay, first 2 are complex analysis

that's all i guess?

[tacit arch]

Yes

[brave moth]

also one more thing @tacit arch can laplace transformation help on solving integrals?

and would that integral still be part of the above mentioned fields?

or integral with starting point |z| = 3 that's another exercise i came by

[tacit arch]

Laplace transform is itself an integral

[orchid kestrel]

hey

[tacit arch]

You should just do problems or read

[brave moth]

i will it's just that i have no text book so i'll have to find the subjects online with what problems i have

thanks

[tacit arch]

#book-recommendations then and close this channel

[brave moth]

.close

[lone heart]

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[random snow]

Hi! I'm looking for help with this proof here
I'm coming back to uni and we have retakes in september but I can't figure out this proof from previous exam

[random snow]

I proved it for n = 1 but I need to prove it for natural numbers

and I'm stuck right here

proof by induction btw ^

[oak perch]

You break a_k into two terms

$\frac{1}{k(k+1)(k+2)}=(\frac{1}{2})(\frac{1}{k(k+1)}-\frac{1}{(k+1)(k+2)})$

[ocean seal]

Cogwheels of the mind

[oak perch]

Cancel each other, only two terms remained, beginning and last

[random snow]

I'm not sure if I understand, could you elaborate more on this topic

or guide me step by step on what's going on

[oak perch]

Your a_k now is of the form b_k-b_(k+1)

So when you sum a_k, b_k cancel each other

Like you add a(k)+a(k+1), it equals (b(k)-b(k+1))+(b(k+1)-b(k+2))=b(k)-b(k+2), b(k+1) canceled

You add all these a(k) for k from 1 to n, you will see that b(k) cancelled each other only b(1) and -b(n+1) remain

b_1-b_2 +b_2-b_3 +b_3-b_4… only b(1) and -b(n+1) remain

[random snow]

still unsure If I got the idea like I don't see where can I cancel it out

[oak perch]

Do it, ask afterwards

[random snow]

yeah I'm just unsure if I'm reading things correctly

since I'm not really american and the system is different, math stays the same but written differently

so it's hard to grasp

[oak perch]

Just read this, and do it yourself

[lone heart]

@random snow Has your question been resolved?

[random snow]

where is 1/k(k+1) coming from???

I understand how you get 1/2 - 1/((k+1)(k+2))

[lone heart]

@random snow Has your question been resolved?

[lone heart]

@random snow Has your question been resolved?

[lone heart]

@random snow Has your question been resolved?

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[torpid wharf]

My sister needs help

[junior iron]

You can add all the values of the numbers outside.

To get the perimeter.

[lone heart]

@torpid wharf Has your question been resolved?

[lone heart]

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[vital sun]

g - 6 = 2

[vital sun]

someone review one step equations for me

[last ether]

How would you isolate g

[stark scroll]

In equations, you can "do something" to both sides (like adding a number)

[midnight moss]

Uhh

[vital sun]

sorry

was doing something

like explain step by step

[midnight moss]

Idk if this is relevant to the topic but Play MONOPOLY GO! with me! Download it here: https://s.scope.ly/yb-_bwN6XVk

[vital sun]

hello?

[midnight moss]

This game kinda fun

To kill time

[stark scroll]

You want to isolate g

[vital sun]

so do that first

?

[stark scroll]

So you must cancel the -6

How would you cancel the -6?

[vital sun]

no idea

[stark scroll]

Well, the inverse operation of subtraction is addition

So what if you add 6 to both sides?

[vital sun]

what?

so +6 +?

[stark scroll]

Add 6 to both sides

[vital sun]

wheres the other side

[stark scroll]

g-6 is one side and 2 is this other

[vital sun]

could you use TeXit to demonstrate

the bot

[vital sun]

the 12?

[stark scroll]

we have $g-6=2$

[ocean seal]

Luke

[stark scroll]

$g-6$ is one side of the equation and $2$ is the other

[ocean seal]

Luke

[vital sun]

oh i wrote it wrong on my paper

alright

so g + 6 + 2

[stark scroll]

If we add 6 to both sides we have $g-6+6=2+6$

[ocean seal]

Luke

[stark scroll]

Do you see that?

[vital sun]

so add 6 to 6 again

and 2 + 6

?

[stark scroll]

Can you explain what you mean?

[vital sun]

theres 6 in the original equation

do we add it to 6 again

and 2 which was in the equation

plus 6 too?

[stark scroll]

Because we have -6, we want to add 6 to both sides

[vital sun]

what if it was a positive

[stark scroll]

Then we would want to subtract 6

[vital sun]

oh

[stark scroll]

We are trying to find $g$ so in this case we add 6 to both sides to isolate it

[ocean seal]

Luke

[vital sun]

you said we needed to isciolate it tho

[stark scroll]

Yes, we isolate $g$

[ocean seal]

Luke

[stark scroll]

If we have $g-6=2$, then when we add $6$ to both sides, we get $g=8$

[ocean seal]

Luke

[vital sun]

oh

alright

so -6 +6 would be 0

2 + 6 would be 8

[stark scroll]

Yes

[vital sun]

so its more simpler than said

[stark scroll]

Here's another example: If i have $2x=8$, then I can divide both sides by 2

[ocean seal]

Luke

[vital sun]

so then 2 / 2

and 8 / 2?

so thats 1 and 4

do we add them both then or let it be?

[stark scroll]

That is correct, because we have $x=4$ after we divide by $2$

[ocean seal]

Luke

[vital sun]

but do we add the 2 answers we got

?

hello?

[stark scroll]

What do yo umean?

[vital sun]

so we got 1 and 4

add them up?

from 2 / 2 and 8 / 2 from the example

[stark scroll]

No, we already have $x$

[ocean seal]

Luke

[stark scroll]

$x=4$

[ocean seal]

Luke

[stark scroll]

"x equals 4"

[vital sun]

so what do we do with the 1

[stark scroll]

Where did you get 1?

[vital sun]

from 2 / 2

since were dividing 2 from both sides

[stark scroll]

Well we divided 2x by 2

That only leaves x

[vital sun]

ohhh

wait so then

how do we format the equation

like how to solve and write it

well not the solving part

how do we show our work

[stark scroll]

I'm not sure for certain how you should, but I would like this

[vital sun]

alright

ty

wait but

nvm

peace

.close

[lone heart]

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[delicate sand]

Question 31

[smoky lark]

.reopen

[delicate sand]

.close

[lone heart]

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[deft swan]

Could someone explain to me how to solve this for p?
p^2 + 11p + 24 = 0

[deft swan]

I think it has something to do with factoring but I can't figure it out

[half mural]

either bhaskara or factor by sum and product

[deft swan]

Yes but I mean the steps

[half mural]

which way? bhaskara or sum and product?

bhaskara is simply plugging in the values

[wary stream]

Have you tried anything?

[deft swan]

I have with previous versions (the same problem with different numbers) but got them wrong. For this one I don't know where to begin with the factoring

[wary stream]

Well, you want to find the factor pairs of C that sum to B

[deft swan]

-3 and -8?

ehh wait

[delicate sand]

+8 +3

[deft swan]

yess

I mixed up with the orig version

Thank you i got it now

.close

[lone heart]

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[vital sun]

can someone confirm my answer

my answer is x 96

x = 96*

[vague coral]

-96

[vital sun]

oh

i think i did the same mistake with another one

but thanks

.close

[lone heart]

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[tight python]

How do I find the domain of the following function? f(d) = 2√d(20-d)

[tight python]

I thought of d(20-d) <= 0. Is that right?

[vague coral]

d(20-d) >= 0

square root doesnt take negative values

[tight python]

woops sorry I had a brainfart

yeah I meant >

[long axle]

[tight python]

heya steve

[long axle]

yoo

[tight python]

I'll dm you hold on lol

.close

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[vague coral]

[long axle]

Lol

[lone heart]

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[weary abyss]

idk what im looking at

[weary abyss]

<@&286206848099549185>

[alpine sable]

conditions

[weary abyss]

what

bruh

.close

[lone heart]

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[gilded cliff]

how can you find the domain algebraically of radical (1+x/x)?

[lunar ravine]

The denominator can't be equal to zero

So all values of x but the ones that make the denominator = zero

[gilded cliff]

and also the answer to radical (1+x/x) have to be greater than or equal to 0?

so i am solving for radical (1+x/x) > or equal to 0?

well ig x cant be 0, because then that would make the denominator equal to 0

so i am solving for radical (1+x/x) > 0?

[lunar ravine]

It can be less than zero generally unless it says something else in the question

[gilded cliff]

but the answer to a radical cant be negative right?

[lunar ravine]

No the denominator only can't be equal to zero cuz it will make the fraction undefined

[lunar ravine]

Yes

[gilded cliff]

so how would i set up the equation to solve for the domain

[gilded cliff]

yea thats why i put > 0 and not > or equal to 0

[remote heron]

you have two concerns right

1. the denominator is zero

2. the input is negative

[gilded cliff]

yea

how do i set up the equation for that

[remote heron]

you can ensure the input isnt negative by making sure the top and bottom have the same sign

so you want either x >= 0 and x+1 > 0

or x <= 0 and x+1 < 0

[gilded cliff]

wouldnt it just be:

radical (1+x/x) > 0

[remote heron]

no

try looking at this

[tame beacon]

X can be -2 think about it

[gilded cliff]

oh true

[remote heron]

,w graph x and x+1 and (1+x)/x

[ocean seal]

Results provided by WolframAlpha

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Requested by janniku

[remote heron]

idk how clear it is from the image

[gilded cliff]

its radical (1+x/x) btw

[remote heron]

its not important

[gilded cliff]

oh

[remote heron]

if (1+x)/x is negative, this is a problem

right-

taking the root of a negative number

[gilded cliff]

yup

[remote heron]

okay so (1+x)/x cant be negative

this will happen where the top and bottom have the same sign

[gilded cliff]

so i would have to set it up as:

(1+x)/x > = 0

[remote heron]

think about the sign

what is a negative number divided by a positive number

[gilded cliff]

negative

[remote heron]

right

how about negative divided by negative

[gilded cliff]

pos

[remote heron]

yea

,w graph x and x+1

[ocean seal]

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[remote heron]

so its gonna go like

from left to right

fine fine fine fine problem problem problem problem fine fine fine fine

right

the orange line crosses 0, but the blue line is still negative

so youll have a positive divided by a negative there

[gilded cliff]

hmm

[remote heron]

do you see what i mean?

[gilded cliff]

yea kinda

[remote heron]

at -1, the yellow line crosses

[gilded cliff]

im just confused on how i would set up the equation

[remote heron]

but the blue line lags behind

[gilded cliff]

to solve for the domain algebraically

[remote heron]

this is the hard part, but the easy way, i think

find where both the top and bottom have the same sign

so x < 0 and x+1 < 0

this is one equation

if you wanna call it that

then x > 0 and x+1 > 0

[gilded cliff]

🧍

[remote heron]

lets do this one

obviously x < 0 where x is negative

and x+1 < 0 means x < -1

so we need both x is negative

and x < -1

then this portion of the domain is x < -1

this matches what we see in the graph, at -1, and leftwards, both lines are below y=0, AKA they're negative

make sense?

[gilded cliff]

i did it a diff way:

(1/x) + 1 > = 0
x >= -1

radical (1+x/x) = radical ((1/x) + 1)

[remote heron]

okay\

but this is not the whole story, right

[gilded cliff]

and inside the radical has to be positive or equal to 0

[remote heron]

x > -1

[gilded cliff]

nah its not

but i got x > = -1

and we also know that x =/= 0

[remote heron]

for what. what does x >= -1 ensure

[gilded cliff]

that your taking the sqrt of a positive number

or 0

[remote heron]

but thats not true

for example x = -1/2 isnt defined

[gilded cliff]

then i messed up somewhere lol

im lost

🧍

[remote heron]

idk do you want to try the way im suggesting

[gilded cliff]

sure

but im trying to do it algebraically

[remote heron]

where is both x and x+1 negative

[gilded cliff]

can we use radical ((1/x) + 1) instead

[remote heron]

no

[gilded cliff]

isnt that the same as the original tho

[remote heron]

im talking about a different method

[gilded cliff]

nah im just asking if:

radical (1+x/x) = radical ((1/x) + 1)

if so, then can we find the domain of radical ((1/x) + 1)? because thats what the original problem was, i wanna see how that one works out

so we know that for radical ((1/x) + 1) the inside (1/x) + 1) has to be a non negative number

[remote heron]

youre going to end up doing similar reasoning either way

dealing with a reciprocal is less intuitive

just start here, where is 1/x positive

[gilded cliff]

x>0

[remote heron]

okay, so looking at 1/x + 1, will that still hold?

[gilded cliff]

yea

wait

[remote heron]

is that portion of the domain still positive

[gilded cliff]

for -1 it will

[remote heron]

this is not what im askin

[gilded cliff]

but for x = 0 it wont

[gilded cliff]

yes

[remote heron]

youre saying x > 0 ensures 1/x is positive

im asking does x>0 ensure 1/x + 1 is positive

[remote heron]

ok

any issue comes from x <= 0

is 1/x + 1 defined for x = 0

[gilded cliff]

yes

[remote heron]

look im sorry my sleeping pills are kicking in

we have to finish this more quickly

[gilded cliff]

alright

lol

sorry for taking up ur time

😵‍💫

[remote heron]

youre good i just didnt plan out this much time

its my fault

[remote heron]

.

[gilded cliff]

no

[remote heron]

okay so any problem comes from x < 0

for which x < 0 is 1/x + 1 > 0

you should notice that were specifying x < 0

this has implications for the inequality as you go manipulating things

i guess you already know what answer is gonna come out

[gilded cliff]

🤔

kinda confused on what ur asking

[remote heron]

we take x < 0

and solve 1/x + 1 > 0

[gilded cliff]

comes out to x < = -1

[remote heron]

okay

now join your domains

[gilded cliff]

x < = -1 U ?

[remote heron]

assuming youre convinced weve found all the problems

[remote heron]

see here

[remote heron]

.

[gilded cliff]

x < = -1 U x > 0

HMMM

[remote heron]

,w plot 1/x + 1

[ocean seal]

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[gilded cliff]

how can i find the range now

🤠

just solve for x?

[remote heron]

[gilded cliff]

solve the equation for x

and do the same thing

im assuming

[remote heron]

i have to go to bed

i cant even keep my eyes open

look at range of a radical

[gilded cliff]

lol all good

thanks for the help

[remote heron]

its a very easy problem

i can promise you

[gilded cliff]

aii

[remote heron]

its like this

so whats the range of sqrt x?

[gilded cliff]

[0, infinity)

[remote heron]

oh man this is not quite true

stupid sleeping pills

im gonna ask in the helper channel if someone can help you

im too tired to not make dumb mistake

good luck

[gilded cliff]

ty

[real gazelle]

yes

[\sqrt{\frac{1+x}{x}}]

[ocean seal]

propERICly_embedded

[real gazelle]

just to be clear you're asking about this?

[gilded cliff]

i mean i just answerd that cuz ik the graph of sqrt x

[gilded cliff]

yep

[real gazelle]

okay, as you already noted, x can't be 0

[gilded cliff]

ill just give u the entire problem:

[real gazelle]

okay

[gilded cliff]

a) write formulas for f o g and g o f
b) find the domain
c) find the range

f(x) = radical (x+1)
g(x) = 1/x

[real gazelle]

what is g?

oh

[gilded cliff]

mb

there u go

so for f o g i got:

radical (x+1) / (x+1)

[real gazelle]

how did you get that?

[gilded cliff]

f o g = f(g(x)

[real gazelle]

(f o g)(x) = f(g(x))

yes

[gilded cliff]

= f(1/x) = 1/radiacl (x+1)

[real gazelle]

f(1/x) is correct

but that's not equal to what you wrote

[gilded cliff]

= radical (x+1) / x+1

thats wrong?

🧍

[real gazelle]

yes, f(something) means that you replace x with (something) wherever you see x in the definition of f(x)

so for example f(2) = radical (2+1)

right?

[gilded cliff]

yea

hm

[real gazelle]

so f(1/x) should be what

[gilded cliff]

isnt it just:

f(1/x) = 1/ radical x+1

i substituted radical x+1 into f(1/x) for x

[real gazelle]

no

[real gazelle]

do you see how in this example I replaced the "x" in radical(x+1) with 2

similarly I could replace it with anything else

so f(whatever complicated thing) = radical ((whatever complicated thing)+1)

[gilded cliff]

OHHH

so its

radical (1/x) + 1

holy shit i feel sped rn

[real gazelle]

close, you're missing some parentheses

radical ((1/x) + 1)

[gilded cliff]

yea

😵‍💫

[real gazelle]

yessss

so we can summarize this by writing

[gilded cliff]

so i flipped my f o g and g o f

gotta erase this lol

[real gazelle]

[(f\circ g)(x) = \sqrt{\frac1x + 1}]

[ocean seal]

propERICly_embedded

[gilded cliff]

which equals radiacl ((1+x)/x)

[real gazelle]

yup

although it's probably simpler if you keep it like this

[gilded cliff]

really?

hm

[real gazelle]

now to find the domain of this

we have to think about what potential problems there might be

so the first potential problem is that we can't divide by zero

so x can't be zero

and the second potential problem is that the inside of a square root can't be negative

so 1/x + 1 must be ≥ 0

does that make sense?

[gilded cliff]

yea so we have two conditions

1. x =/= 0

2. ((1/x) + 1) ≥ 0

when solving for the 2nd one you get x <= -1

[real gazelle]

x ≤ -1 OR what?

[gilded cliff]

how do i solve for the other domain

[real gazelle]

so you can rearrange 2 to get the inequality
1/x ≥ -1

there's two possible ways x can satisfy this right?

the first possibility is that x is positive, so 1/x is positive and ≥ -1

the second possibility is that x is negative but large enough so that 1/x is a small negative number and ≥ -1

does that make sense?

[gilded cliff]

yea so we took care of if x is negative

so it would just be x > 0

how do ik theres no domain in the middle tho

[real gazelle]

what do you mean in the middle?

[gilded cliff]

in btwn -1 and 0

[real gazelle]

well because if it's in the middle, then 1/x will be a large negative number

so < -1

for example let's say x = -1/2

then 1/x = -2, and -2 < -1, so that doesn't work

[gilded cliff]

oh true

ok time to find the range 😼

i havent done algebra in a minute

this is for my calculus course

we're just doing pre-calc rn

[real gazelle]

you got this!

[gilded cliff]

algebra is sometimes the harder part in calculus lol

i have a question so lets say i use the other equation

1+x/ x

and set it equal to > 0

would i multiply x on both sides

no that wouldnt make sense

using the other equation is def easier

but i wanna see how it would be with this one

@real gazelle 🧍

[real gazelle]

you have two cases where that fraction is nonnegative: either the numerator is ≥ 0 and the denominator is > 0, or the numerator is ≤ 0 and the denominator is < 0

when is the numerator ≥ 0?

[gilded cliff]

when x >= -1

[real gazelle]

yup

and when is the denominator > 0?

[gilded cliff]

when x > 0?

[real gazelle]

yup!

so when are both of those true at the same time?

[gilded cliff]

OH

intersting way of solving it i see

[real gazelle]

when x > 0 right?

[gilded cliff]

it would just be x > 0

ye

[real gazelle]

yup

[gilded cliff]

hmm i lked the way u solved it

[real gazelle]

now can you work it out for the other case? when the numerator is ≤0 and the denominator is <0?

[gilded cliff]

x < = 1 U x > 0

how do i find the range now

🤔

do i just solve for x

[real gazelle]

well you said earlier that the range of sqrt(x) is [0, infinity)

is the same true here? is it possible to get 0?

[gilded cliff]

HMMM

so the range of the sqrt is always [0, infinity)

but lets say i didnt know that, how would u sovle it algebraically?

[real gazelle]

well

is it possible to get a negative number by square rooting?

[gilded cliff]

no

[real gazelle]

is it possible to get 0?

[gilded cliff]

yes

[real gazelle]

is it possible to get any positive number?

[gilded cliff]

yes

[real gazelle]

there you go lol, the range has to be [0, infinity) then

[gilded cliff]

so you just look at all possible outputs

[real gazelle]

yes

[gilded cliff]

aight

movign on 🏃‍♂️

[real gazelle]

I gotta go now but hopefully someone else can help

[gilded cliff]

wait isnt the range of f o g = (1, infinity)

becuase there is a horizontal asymptote at y = 1

[real gazelle]

well, is it possible to get 0 as an output?

[gilded cliff]

nope

wait yes