help-28

[sleek apex]

so antiderivative of 1/x^2 = 1/-1*x

you divided it by the exponent before adding one

12+1=13

oh

-12+1=-11

divide it by -11

2/4*-11*x^11

[glossy valve]

BrotmitHonig

[sleek apex]

$\frac{2}{-44x^{11}}$

[glossy valve]

Arctrices

[sleek apex]

its all just n+1

$\frac{2x^{n+1}}{4*(n+1)}$ where n=-12

[glossy valve]

Arctrices

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

[sleek apex]

yes

$\frac{32}{3x^{32}}$ would be $\frac{32}{-93x^{31}}$

[glossy valve]

Arctrices

[sleek apex]

yes

you cant use power rule for that

well

1 to the power of anything is 1

no

thank you lol

[full forum]

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[silk mirage]

Uranium weighs 238 g per mol (1 mol is 6.02 • 10^23 particles)

a. How much does 3.01 • 10^23 uranium atoms weigh?

b. how much does 6.02 • 10^22 uranium atoms weigh?

c. How much does 6.02 • 10^25 uranium atoms weigh?

d. How much do 4.8 billion uranium atoms weigh?

[silk mirage]

need someone to give me step by step instructions on how to do task a and b then i should hopefully be able to do the rest myself but im not entirely understanding what i need to do in order to get the answer to these tasks

<@&286206848099549185>

[lusty vector]

dm

@silk mirage

[silk mirage]

hey

whats up

[lusty vector]

good wbu

[silk mirage]

good if we look around this task

[lusty vector]

yeah its pretty simple

first a atom contains 6.023^10^23

[silk mirage]

isnt it •10^23?

[lusty vector]

it is

sry my mistake

[silk mirage]

alright no worries

so far im in

[lusty vector]

so for the task a

they are asking for 3.01

[silk mirage]

right

[lusty vector]

can u come to dms..

i can explain it easier or vc

[silk mirage]

i cant talk

[lusty vector]

i cant too'

[silk mirage]

im outside

[lusty vector]

oh then

6.023*10^23 gives 238

3.01*10^23 gives x

so do unitary method

and ull get somth about

[silk mirage]

should i be getting 238 on my calculator when putting in this?

[lusty vector]

like multiply

these

4,314.75674

u will get this

answer

[silk mirage]

right yeah

thats what im getting

nvm im not getting that anymore

not sure what i ddi

did

[full forum]

@silk mirage Has your question been resolved?

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[barren iris]

I'm pretty sure I have my bounds correct. I'm not sure what's wrong with my definite integral

[barren iris]

(uploading the picture, one sec)

[full forum]

@barren iris Has your question been resolved?

[barren iris]

Not yet

[gritty rose]

that inner radius is 3/10 * x^2, but looks like you wrote 13/10. where's your work to evaluate this?

[barren iris]

Ignore that. I don't why that little mark is there.

I haven't evaluated the definite integral yet!

[gritty rose]

then how'd you get

[barren iris]

oh that

I did but I got the answer wrong so I erased everything...

so I'm starting at the beggining again

[gritty rose]

???????

[barren iris]

thinking it was an issue with where I started

not my computation

I can just tell you what I did.

I dealt with the exponents and eventually combined thw two fractions after taking the difference

[gritty rose]

just show the calculation

[barren iris]

I can do it again sure

I just wanted to know if it was with the definite integral

if it looks correct, then it was just my computation

[barren iris]

Took me some time but here it is

[barren iris]

^

[barren iris]

.close

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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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[zenith remnant]

Can someone help me to understand the steps pls

[jolly terrace]

damn that's hard to read

what are you trying to show?

[zenith remnant]

I need to linearize cos^3(x)sinx

That’s what our teacher showed us

Btw I translated the word linearize from french idk if it’s right in English @jolly terrace

[jolly terrace]

linearize, as in you don't want any exponents?

[zenith remnant]

Ye

There is the rest here

I get lost from there

[jolly terrace]

try to use sin(2x)

from the beginning

[zenith remnant]

Wdym

[jolly terrace]

sin(2x) = 2 sinx cosx, right?

you can use that from the very beginning

[zenith remnant]

You want to linearize cos^3x using this ?

[jolly terrace]

no

i want to linearize the WHOLE thing

[zenith remnant]

Damn you’re too smart for me

[jolly terrace]

so i need the sinx as well

[zenith remnant]

I wanted to linearize both

Then add them

Like our teacher showed us

I mean that’s what he wrote

[jolly terrace]

group it like this

$\cos^3 x \sin x = \cos^2 x \cos x \sin x$

[glossy valve]

TooManyCooks

[zenith remnant]

I want a way that I can use in any case tbh

Cause I also have cos^2(x)sin^2(x) to linearize for example

And tomorrow I have an exam maybe others cases

[jolly terrace]

that's even easier

like i said sin 2x = 2 sinx cos x

so $\sin^2 (2x) = 4 \sin^2 x\cos^2x$

[glossy valve]

TooManyCooks

[jolly terrace]

sin^2 (2x) is easy to linearize

[zenith remnant]

So i could solve any by using that sin 2x thingy ?

[jolly terrace]

It's a very nifty trick to be honest

So it would be nice to have it in your bag of tricks

[zenith remnant]

Im not smart enough for all those tricks tbh

It’s so boring

[jolly terrace]

Do you know the angle sum formula for sine and cosine?

sin (a+b) that sort of stuff

[zenith remnant]

Yeah

I do

[jolly terrace]

ok

that's all you need

same with cosine

[zenith remnant]

Cosacosb-sinasinb

For cos(a+b)

[jolly terrace]

sin 2x = sin (x+x) = sinx cosx + cosx sinx = 2 sinx cosx

[zenith remnant]

Etc

[jolly terrace]

it's just that trick

over and over

if you know the angle sum formula you're good to go

you can always derive it if you're in a tough spot

[zenith remnant]

Ok lets start again from 0

For cos3(x)sinx

[jolly terrace]

Go on

I'm listening

[zenith remnant]

Idk where to start tbh

How can i use the sin2x thingy

[jolly terrace]

Well what does sin2x equal to?

[zenith remnant]

Sin (x+x)

[jolly terrace]

and what is that equal to

[zenith remnant]

Sinxcosx+cosxsinx

[jolly terrace]

okay good. try to simplify next time

anyway

how can you get cos x sin x in your cos^3 x sin x?

[zenith remnant]

Cosx(coxcosx)sinx

[jolly terrace]

good

so use that cos x sin x to get a sin2x in your expression

[zenith remnant]

But what is cosxsinx equal to

[jolly terrace]

You answered that

what is sin 2x

[zenith remnant]

Sin x+x

[jolly terrace]

use the angle sum and simplify

sin 2x = ?

you already answered it correctly earlier. I just want you to simplify your answer

[zenith remnant]

Im so bad at manipulating those cos and sin

It’s frustrating

[jolly terrace]

just take it slow

what's sin (x+x) if you use the angle sum formula for sine?

[zenith remnant]

Sinxcosx+sinxcosx

[jolly terrace]

okay good. Can you simplify that further?

[zenith remnant]

Sin(2x)+cos(2x)

[jolly terrace]

no that's not how addition works

let me ask this

what's z+z

[zenith remnant]

2z?

[jolly terrace]

good

now what's sinxcosx + sinxcosx

[zenith remnant]

But idk since it’s multiplied

How do I simplify them

[jolly terrace]

okay how about this

(stuff) + (stuff) = ?

This is not a trick question. I'm trying to make you understand something

Don't overthink it

[zenith remnant]

2(stuff)

[jolly terrace]

good

so what if that (stuff) is sinxcosx

does that change things?

[zenith remnant]

I think I got it now

[jolly terrace]

ok so what is sin 2x

[zenith remnant]

Thats 2(cosxsinx)

[jolly terrace]

perfect

so earlier you had $\cos^2 x * \cos x \sin x$

[glossy valve]

TooManyCooks

[jolly terrace]

just now you told me $\sin 2x = 2 \sin x \cos x$

[glossy valve]

TooManyCooks

[jolly terrace]

how can you use that information ?

[zenith remnant]

Im back in 5 minutes

Im back sorry @jolly terrace

Si

So

I can replace that ?

@jolly terrace

[jolly terrace]

yes, exactly!

you have the formula up there

[jolly terrace]

this one

[zenith remnant]

,rotate

[jolly terrace]

perfect

now you have a cos^2 x to deal with

[zenith remnant]

Tbh i figured that and knew I should divide by 2 cause I’ve seen it on the teacher work before

[jolly terrace]

you remember the cos (a+ b) formula?

[zenith remnant]

Yeah

[jolly terrace]

Let's do cos (x+x)

[zenith remnant]

Cos^2-sin^2?

[jolly terrace]

not quite

that's cos (x-x)

[zenith remnant]

My bad

[jolly terrace]

Alright good

[zenith remnant]

And that’s=1 yeah?

[jolly terrace]

which one?

[zenith remnant]

Oh yeah it’s the + one

My bad

[jolly terrace]

Oh ok

Anyway, what's cos(2x)?

[zenith remnant]

Cos^2-sin^2?

[jolly terrace]

don't forget the argument

that means nothing without the argument

[zenith remnant]

Yeah that’s cause I’m on my phone writing tbh

Sorry ahah

[jolly terrace]

Ok

Well let's look at what we have

you have a cos2x

which is linear. Great!

We also have a cos^2 x

Perfect for the current expression we have

but there's a problem

there's that pesky sin^2 x as well

What do you think we should do?

[zenith remnant]

Wait wait

Where are we now

Whats on my line

[jolly terrace]

You need to write this down

[zenith remnant]

Yeah

[jolly terrace]

Not just look at the screen

[zenith remnant]

That’s why I’m asking

I got lost

[jolly terrace]

lmao

[jolly terrace]

this

[zenith remnant]

I should replace cosxcosx by cos^2-sin^2?

[jolly terrace]

Not yet

Like I said, there's that sin^2 x

[zenith remnant]

Where

I only have sin(2x)

[jolly terrace]

Dude this is why you need to write this down

[zenith remnant]

Or you mean that ?

Im trying to write

[jolly terrace]

What's cos 2x

[zenith remnant]

This ?

[jolly terrace]

Great

Like I said, that sin^2 x isn't helpful

wait

no that's not right

[zenith remnant]

Ah

They are not equal ?

[jolly terrace]

how did you get from the first to the second?

[zenith remnant]

Cos(x)cos(x)=cos(x+x) yeah?

[jolly terrace]

No

[zenith remnant]

ah omg

[jolly terrace]

$\cos x \cos x = \cos^2x$

[glossy valve]

TooManyCooks

[jolly terrace]

which isn't cos(2x)

[zenith remnant]

Yeah wtf

My bad

That’s why I got lost

[jolly terrace]

Don't substitute yet

Anyway we have $\cos(2x) = \cos^2 x - \sin^2 x$

[glossy valve]

TooManyCooks

[zenith remnant]

But I would I know I need to calculate that

From seeing my cosxcosxsin(2x)/2

[jolly terrace]

Yes.

[zenith remnant]

Ok i guess I will try to figure that out when I have a look at it on different exercises

Aswell

[jolly terrace]

At any rate. you need to eliminate the sin^2 x

[zenith remnant]

I divide cos(2)/sin^2x?

[jolly terrace]

cos(2x) is already linearized, and cos^2 x is in your expression

[zenith remnant]

Idk

[jolly terrace]

Is there a relationship between sin^2 x and cos^2 x?

[jolly terrace]

no

Do you remember the pythagorean theorem?

[zenith remnant]

On a triangle yeah

[zenith remnant]

Yeah

[jolly terrace]

Does that help you eliminate sin^2 x?

[zenith remnant]

Cos2(x)=-sin2(x)

?

[jolly terrace]

no

[zenith remnant]

+1

Cos2(x)=-sin2(x)+1

[jolly terrace]

i was asking for sin^2 x, not cos^2 x

[zenith remnant]

I don’t get the relationship tbh

[jolly terrace]

what do you mean?

[zenith remnant]

Between those two

Like u asked

[jolly terrace]

It's already up there

You just need to give me an expression for sin^2 x

[zenith remnant]

You mean the Sinxcosx+sinxcosx thingy ??

[jolly terrace]

no

i meant this

$\sin^2 x = ?$

[glossy valve]

TooManyCooks

[zenith remnant]

It’s equal to -cos2(x)

+1

[jolly terrace]

ok

how can we use that in your expression for cos(2x)

[zenith remnant]

Im so lost beacause we are just finding tricks on one side and some on another side

And idk how I would find that alone

[jolly terrace]

What do you think you'd be doing when you said you need to "linearize" an expression?

I don't expect you to be an expert on your first try

That's why we're doing this slow

I need you to understand how these tricks work so you can use them in the future

[zenith remnant]

Alfifht

Alright

[jolly terrace]

So we established that $\cos(2x) = \cos^2 x - \sin^2 x$

[glossy valve]

TooManyCooks

[jolly terrace]

how can we use that stuff you just saw

[zenith remnant]

Can i switch of side the cos2(x)?

[jolly terrace]

no

well,

why do you want to do that

You can

but i wanna know why you want to

[zenith remnant]

I want to make appear the relation idk

[jolly terrace]

Sure go ahead. If you think it will help

Make sure you get rid of $\sin^2 x$ though

[glossy valve]

TooManyCooks

[zenith remnant]

Nah actually I don’t want to do weird stuff

☠️

I prefer to understand ur point

[jolly terrace]

Just eliminate sin^2 x

Yo're gonna rearrange things either way

But the priority is eliminating sin^2 x

you'll see why in a moment

[zenith remnant]

How can get rid of it tho

[jolly terrace]

use the pythagorean theorem stuff from earlier

I asked you what sin^2 x is

[zenith remnant]

Sin^2(x)=-cos^2(x)+1

U want to do -cos^2(x)-cos^2(x)??

[jolly terrace]

Almost

But yeah, the idea is to get a relationship that involves cos(2x) and cos^2 (x)

You missed the 1 I think

[zenith remnant]

My brain is fcking dead

How do I get rid of that fcking sin2

😭😭😭

Im sorry for you this must be painful to read

☠️

[jolly terrace]

$\cos (2x) = \cos^2 x - \sin^2 x = \cos^2 x - (1 - \cos^2 x) = 2\cos^2 x - 1$

[glossy valve]

TooManyCooks

[jolly terrace]

Where I used the fact that $\sin^2 x + \cos^2 x = 1$

[glossy valve]

TooManyCooks

[zenith remnant]

I don’t understand the 2nd equal

[jolly terrace]

what's confusing

[zenith remnant]

I Guess u used that fact right there

But i dont understznd how

[jolly terrace]

What do you mean

I can't help you if you don't tell me what you don't understand

[zenith remnant]

That

[jolly terrace]

I plugged in the formula for sin^2

the one you wrote earlier

$\sin^2 x = 1 - \cos^2 x$

[glossy valve]

TooManyCooks

[zenith remnant]

Ohhhhh

[jolly terrace]

I just replaced it

[zenith remnant]

You replaced Who le thing

In general just so i know i will have to replace all the sin^n in first ?

Then cos^n?

[jolly terrace]

No

It's just something you learn from doing these problems over and over

There's no one trick that fits all problems

That's why you need as many tricks as you can get

So you can try them out when you do get stuck

[zenith remnant]

Alright

[jolly terrace]

Anyway. Your expression is still $\cos^2 x \frac{\sin 2x}{2}$

[glossy valve]

TooManyCooks

[jolly terrace]

You need to eliminate the cos^2 x because you want to linearize

so you need to use this new formula we just derived

[zenith remnant]

How to i deal with the 0.5

-1

-0,5

[jolly terrace]

I want you to isolate cos^2 x

that's what we want to replace

Also it's bad habit to use decimals

stick to fractions if you can

[zenith remnant]

Cos(2x)+1/2

[jolly terrace]

good

So put it all together

[zenith remnant]

Now im lost in my original thing

[jolly terrace]

$\cos^2 x \frac{\sin 2x}{2}$

[zenith remnant]

Its that ?

[glossy valve]

TooManyCooks

[jolly terrace]

no not quite

[zenith remnant]

We dont replace cos2(x) by cos(2x)+1/2?

[jolly terrace]

We do

but you did it wrong

[zenith remnant]

I know what

[jolly terrace]

Almost

Be careful with the substitution

It's a product

So there should be a parenthesis

[jolly terrace]

💪

You're done

No more power terms

actually

You could go further

But I don't know if you want to

[zenith remnant]

Our teacher wanted to yeah

Make it an addition

[jolly terrace]

Okay let's keep going then

so you have $\frac{1}{4}\sin(2x) + \frac{1}{4} \cos(2x)\sin(2x)$

[glossy valve]

TooManyCooks

[jolly terrace]

Notice a pattern?

There's something here that's very familiar

[zenith remnant]

Almost sin(a+b)

?

[jolly terrace]

Good!

You're getting good at this

I like that

[zenith remnant]

😂

[jolly terrace]

So where does that apply here?

[zenith remnant]

CosSin?

[jolly terrace]

Ye!

Ok now go simplify that

You know the formula

[zenith remnant]

Here it becomes sin(4x)/2?

[jolly terrace]

Great! So what's your final answer? Don't forget the 1/4 you had in front

[jolly terrace]

https://tenor.com/view/applauding-yes-clap-clapping-leonardo-di-caprio-gif-17849163

[zenith remnant]

I SWEAR I WOULD NOT EVEN BE ABLE TO DO THIS ONE AGAIN

😭😭😭😭😭

[jolly terrace]

It's all about practice

Gotta build that muscle memory equivalent for trig functions

But that's it. You got it!

[zenith remnant]

Our teacher introduced the cos(a+b) things

Then for him we were able to do that easily

😂

He literally did those 2 exercices and he’s putting it in an exam tomorrow

I’ll try to do this one again from zero

[jolly terrace]

Yeah that's a good idea

don't look at your notes

[zenith remnant]

Yeah I won’t

[jolly terrace]

just remember the sin and cosine angle addition formulas

and the pythagorean theorem

and you're good

[zenith remnant]

Basically tomorrow I have an exam on all this expect few

We must justify everything with the good mathematical writing for the derivative to show we can dérivate etc

Same for all basically

We’ve seen this in one week 😂

[jolly terrace]

[zenith remnant]

I guess that’s how it will look the whole year when u have 11h/week of maths ☠️

I guess I will get used to it

And then 1h of oral in maths aswell in +

Omg i did all of it without looking at my notes @jolly terrace

I got used to the fact that when I see cosxsinx I should instantly replace it

Same with cosxcosx

[jolly terrace]

Great job!

[zenith remnant]

Thanks a lot for your time

It took you

Forever

To make me understand that

I’ll try cos2sin2 now

[jolly terrace]

All that matters is that you know it now

[full forum]

@zenith remnant Has your question been resolved?

[zenith remnant]

Did I do something wrong or am what am I missing ? @jolly terrace

[jolly terrace]

almost

Good job getting there tho

[zenith remnant]

What’s wrong

[jolly terrace]

You forgot to square them

it was supposed to be cos^2 x sin^2 x

You only did cos x sin x

oh wait

gimme a sec

no nvm you did that part right

You didn't simplify the cos^2 further at the end

You also forgot a minus sign

[zenith remnant]

Yeah that’s what I was thinking about

Where did I miss it

[zenith remnant]

That’s good yeah ? @jolly terrace

[jolly terrace]

perfect!

[zenith remnant]

Thanks a lot and have a good night

/day idk

[jolly terrace]

[zenith remnant]

.close

[full forum]

Channel closed

Closed by @zenith remnant

Use .reopen if this was a mistake.

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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.

[full forum]

Please don't occupy multiple help channels.

[short sentinel]

this is what i have so far
is my graph correct and am i on the right direction

[full forum]

@short sentinel Has your question been resolved?

[full forum]

Channel closed

Closed due to timeout

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Send your question here to claim the channel.

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• 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.

[worn matrix]

, rotate

[worn matrix]

this is what i did, i can make my answer match, or is it that my answer is wrong?

[rapid rain]

Are you always allowed to simplify by cos x ?

[worn matrix]

it says to find the general sol of x I don't know what are you saying, i didnt understand

[rapid rain]

The first step of your equation

where you cross out cos x on both sides

are you always allowed to do that?

[worn matrix]

maybe yeah?

cant we do that?

[rapid rain]

I'll let you think about it

Is it always true that if ac = bc, then a=b?

for ANY value of c?

[worn matrix]

i mean if c=0?

[rapid rain]

yes it doesn't work if c = 0

[worn matrix]

lets go

[rapid rain]

So apply it to your equation

either cos(x) = 0 or not

[worn matrix]

uhm do you mean that we need to do this in 2 case, one with cos x = 0 and another with not

?

[rapid rain]

yes

[worn matrix]

okay let me try

aye bro @rapid rain
i got the same answer 😭

[rapid rain]

Again you forgot to distinguish the cases when cos x = 0 and when it's not

[worn matrix]

😭😭could you help me

what should i do

[rapid rain]

$cos(x)(2cos(2x) - 1) = 0 \Longleftrightarrow cos(x) = 0$ OR $cos(2x) = \frac{1}{2}$

[glossy valve]

rafilou2003

[worn matrix]

yeah ik

[rapid rain]

What is x if cos(x) = 0?

[worn matrix]

x=pi/2

[rapid rain]

+...

[worn matrix]

what?

[rapid rain]

pi/2 + npi

[worn matrix]

and what about second case?

[rapid rain]

well it's what you wrote

pi/6 + npi

[worn matrix]

also should there be plus minus?

[rapid rain]

you just forgot the other case

[worn matrix]

thats not on any option, like its simplified more

[rapid rain]

if n is a relative integer not necessarily

[worn matrix]

ohk

[rapid rain]

I should write k instead, where $k\in \bZ$

[glossy valve]

rafilou2003

[rapid rain]

Your solutions are : $\pm \frac{\pi}{6}+k\pi$ and $\frac{\pi}{2}+k\pi$

[worn matrix]

c option?

[rapid rain]

?

[worn matrix]

here

which option

yes sir?

[rapid rain]

Oh I see

[worn matrix]

yeahh

?

?

[glossy valve]

rafilou2003

[rapid rain]

so writing it under the same denominator :

Your solutions are : $\frac{\pi}{6}(6k\pm 1)$ and $\frac{\pi}{6}(6k+3)$

[glossy valve]

rafilou2003

[rapid rain]

So if every solution is an integer of the form 6k-1, 6k+1 or 6k+3 (times pi/6)

Then it's just an odd integer times pi/6

so (2n+1)pi/6

[worn matrix]

alright

thankyou so much

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[limber ermine]

i hoped to get a negative final ans but didn't work

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@limber ermine Has your question been resolved?

[limber ermine]

also is this a valid way to proof

my prof used a method involving approximating p/q to sqrt(2) as worse case

and saying this is true for this worse case

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[gleaming frigate]

Can someone help me with the domain restriction part, idk what to do next

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[gleaming frigate]

<@&286206848099549185>

[split swift]

[-4,infinity) is the image of the function, not the domain

you want to restrict the domain (which inputs you allow) such that the function is injective (or bijective on its image)

so the original function, 3x^2-4 isn't injective because say, x=1 and x=-1 both get mapped to f(x) = -1

visually, the parabola graph doesn't pass the "horizontal line test"

we want to find a cutoff point for the graph such that it does pass this test

[gleaming frigate]

Could I do [0, infinity) for it to pass the horizontal line test

@split swift

[split swift]

yes

[gleaming frigate]

oh so that’s the restricted domain?

[split swift]

yes

[gleaming frigate]

Ok ty

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[simple dove]

Looking for help on this question, I don't understand how to write out the formula for this one, thanks

[glacial pasture]

do you the equation for a general term of an arithmetic sequence, and an equation for the sum of terms of an arithmetic sequence?

[simple dove]

yea i know the equation but idk how to turn the sentence into an qeuation

equation

Sn = n/2(first term + last term) or Sn = n/2(2a + (n-1)d)

[glacial pasture]

the sentence provides two equations that you can then solve simultaneously

one is the sixth term A_6, the other is the sum of 17 terms S_17

the sixth term for example can be written as A_6=a+5d=21

[simple dove]

what ab the one for s_17

is it like

0 = 17/2(2a + (17-1)d)

thank uu

[simple dove]

wait but then for this

it becomes 0 = 17/2(2a+17d-17)

so do i just take out 2a and 10d from that

and substitute it for 42

this doesnt make sense can somebody pls help :(

[glacial pasture]

it doesnt become 0=17/2(2a+17d-17) but rather 0=17/2(2a+16d)

its (n-1)d not n(d-1)

[simple dove]

how come?

OH

SORRY

my mistake sorry

[glacial pasture]

no worries, at that point you can divide both sides by 17/2 with no consequence to leave a simpler 2a+16d=0

or a+8d=0

[simple dove]

😭 thank u

[simple dove]

wait so does it become

0 = 17/2(2a+16d)

and then u divide bth sides by 17/2

so u have 0=2a+16d

and then u have 0 = 42+6d

right

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[topaz urchin]

Please translate this to English

[torn jolt]

yes, this is what I was doing

9. The three types of ants that are in a nest are shown. Take into account the real measurement of the worker and solve.

a. What is the actual measurement of the queen ant that is 1.25 times as long as the worker, if the measurement of the worker ant in the photo is 20 mm? What is the real size of the soldier ant if it measures 3/5 of the photo size of the queen?

b. What is the scale used in the representation of the ants?

[spice orchid]

stop

[royal rover]

#help-15

?

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[torn jolt]

<@&286206848099549185>

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@torn jolt Has your question been resolved?

[primal urchin]

Is the answer mentioned? I think the integral diverges

[royal rover]

I get 8 sq units

is it right?

[primal urchin]

how did you get it?

[primal urchin]

did you assume x = 3 as it is not mentioned in the question

[royal rover]

it is mentioned

[royal rover]

this like yah its not in here

the 18th q

[primal urchin]

the correct answer is 16

[royal rover]

how?

pls explain

[primal urchin]

after sketching the graphs, area bounded is equal to integral from -3 to 3 of |x+1| +1. First split it into two integrals (one with |x+1| and other with 1) . Then to solve the one with absolute value, substitute x+1 = u and change upper and lower bounds accordingly

[royal rover]

like I just copied from google idk how to actually plot the graph pls explain but I do know the integral part and all pls

[primal urchin]

do you know graphs for x = 3, x= -3 and y = 0?

[royal rover]

yah

i do know to plot

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[primal urchin]

.

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[modest rain]

isnt this wrong? you need to divide by the highest power of x but they divided by x

[narrow helm]

highest effective power in the denominator is 1

due to the sqrt

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[upper nimbus]

If a region in the first quadrant revolves around the x-axis, would the shells method to find the volume require us to use integration with respect to x or y?

same for if its rotating about the y-axis, would it require integrating with respect to x or y?

[atomic blade]

With y

[upper nimbus]

when revolving around x or y?

[atomic blade]

Around x axis

[upper nimbus]

alr cool cool

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[bronze sigil]

Hello, I am just wondering my my proof makes any sense

[bronze sigil]

I mean a^k+1 on the last part of the "we must prove part"

[stark forge]

Can you send the entire page of the original question @bronze sigil

[bronze sigil]

Kind of long sorry.

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[modest rain]

how can something be defined yet be discontinous?

[full forum]

Please don't occupy multiple help channels.

[ocean cedar]

We can see an example of definition in terms of a weird definition set

[modest rain]

do you want the problem?

[ocean cedar]

For example, We can write [0;2] = [0;1) union {1} union (1;2]

[modest rain]

???

[ocean cedar]

So there can be a piecewise function, defined in all [0;2]

But

At 1, it has a unique value which is distinct from

The limit at the right and the limit at the left

For instance, a function which is -1 for all x<0, 0 at x=0 and 1 at x>0

[modest rain]

is it better to draw it?

[ocean cedar]

Sure let he mave a min for that

Not a minimum

A minute

That's the function I've described

It's defined for all real number

Yet it's discontinuous

You give me any x value, I can give you the value this function outputs

Which means it's defined everywhere

Yet there is a point of discontinuity at x=0

Now about your problem, they say "g is continuous except at a point a"

It can very much be a function like I showed you

But it can also simply be a function like f(x) = 1/(x-a)

BUT

The distinction is that f is not defined here in x=a

But you know your g function is a function defined in all R

But

You can also have a function like this ...

g(x) =
1/x for all x<0
0 for x>=0

[modest rain]

not at a and thats why im confused about the statement

[ocean cedar]

It is

They say their domain is in all R

Listen, can we have a chat in vc ?

It will be easier to explain vocally for me

You can keep your mic muted if you feel like it, I wont mind

[modest rain]

tea

yea

i will add you hold up

[ocean cedar]

Hell ye !

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[soft abyss]

just want to check if my answer is right

[soft abyss]

x,y can be any real number such that (x,y) does not equal (3,1)?

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[glossy valve]

AKG

[jolly terrace]

What's the question

[glossy valve]

AKG

[jolly terrace]

Ok

So you need to make them have the same denominator

You see that lonely sqrt a on the right?

You want to include that in the fraction

I just did all of it. I got the expression you want

There's no need for rationalizing here

Yeah what did you get

That's the right step

Hahaha you may want to rewrite it then

Ok good

Here's the trick

choose any two pairs with both either a or sqrt a

I want you to factor either a or sqrt(a) from that pair

Great!

So I want you to group up the remaining ones as well

the other two you didn't pair

put them inside a parenthesis

Also you did your factoring wrong

There's a sign error

$\frac{\sqrt{a}(1-a) + (1-a)}{1-\sqrt{a}}$

[glossy valve]

TooManyCooks

[jolly terrace]

I just wanted you to add the parenthesis

Oh

Ok, yeah, just group them up is my point

What do you have now

Have you factored the numerator?

[glossy valve]

AKG

[jolly terrace]

Great

you see that a? The one without the square root?

You can still factor that 1-a

No don't do that

You have the 1-a

Focus on that

Everything in your problem has a sqrt a

The a is the only one that's odd

Can you think of a way to factor 1-a that involves sqrt(a)

[glossy valve]

AKG

[jolly terrace]

Okay. YOu haven't factored it yet

[glossy valve]

AKG

[jolly terrace]

No, that's not what I'm getting at

How about this

How would you factor $x^2 -9$

[glossy valve]

TooManyCooks

[jolly terrace]

Which gives you what

Great! Now use that same line of thinking here

Except you don't have 9

you have a

[glossy valve]

AKG

[jolly terrace]

Why are they squared?

Did you do that for 9?

[glossy valve]

AKG

[jolly terrace]

Great!

So given that, what does your expression look like now

YES!

👍

💀

You forgor

Feel free to close the channel if you no have no more questions

.

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[modern swift]

i only need -f(x)

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[modern swift]

<@&286206848099549185>

[void nova]

!status

[full forum]

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

[polar valve]

1. do you know what an "odd function" and an "even function" is?
2. if yes, write f(x), f(-x) and -f(x) for the given f. see you the answer?
   3 .if not, try x = 1, x = 2, x = 3 in the terms of point 2 ... and so on until you see the answer.

[modern swift]

I have everything

I just need to know what -f(x) is

Idk how to find it

[polar valve]

-f(x) is the short form for $(-1) \cdot f(x)$.

[glossy valve]

ThM

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[modern swift]

Wait so -x^3/x^2 + one?

Is that right

[modern swift]

^^^

[rocky vale]

do you mean -x^3/(x^2+1)?

yes

-f(x) is just slapping a negative sign in front of f(x)

[modern swift]

R thank you

So what is f(-x)?

Like how would that be explained

[rocky vale]

f(-x) means you're plugging in -x in place of x

for example if g(x) = x^2, then g(-x) = (-x)^2

[modern swift]

So this would be (-x^4+4)/(-x^2+1)?

[rocky vale]

you need brackets

-x^4 is not the same as (-x)^4

but other than that, yes

-x^4 means -(x^4), but you want (-x)^4

[modern swift]

Alr tysm

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[slate ivy]

how do i start with this

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[slate ivy]

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[icy tinsel]

How would I find the range of y= x+ sqrt(4-x^2)? The domain I calculated is [-2, 2], but according to mathway the range is [-2, 2sqrt2). I know that a number like x = 1.5, will be greater than x=0 through trial and error, but I’m not sure how I would get 2sqrt2

[white geyser]

what level math

[icy tinsel]

Honestly ap calc 💀 this is just review though

[hollow sable]

19.3893

[white geyser]

you can find maxima and minima through derivatives and the first and second derivative tests.

[icy tinsel]

Is there a simpler way?

[white geyser]

lol, yeah, graphing calculator and manually scrolling through a table of values.

[icy tinsel]

Ok lol, thank you

[white geyser]

mind you, it wont be exact.

answers in most calc classes need to be exact.

[icy tinsel]

I see

[white geyser]

exact answers would be by hand in most cases.

[icy tinsel]

What do you mean by hand?

[white geyser]

first and second derivative tests.

[icy tinsel]

Oh

[white geyser]

most times you only need first.

[icy tinsel]

I didn’t learn derivatives yet so I can’t use that, but thank you

[white geyser]

o_O

derivatives are first thing you learn in calculus.

[icy tinsel]

I live in NY, so we are only in school for 2 days so far

My teacher just gave a review sheet to help us review some algebra II and pre calc stuff

[white geyser]

using precalc techniques you would find the inverse function and find the new domain.

[icy tinsel]

Lemme try that

[white geyser]

the new domain would be the range of the original function.

[icy tinsel]

The domain I got is [-2sqrt2, 2sqrt2]

The latter is now correct

But not the former

Unless I only include the latter, and manually solve for former?

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[plain kite]

uhhh

[plain kite]

just to confirm im not missing anything cause of my sleepiness, f(-5) is clearly defined here right

https://prnt.sc/PsLI3QCQYjZn

i mean undefined*

[hot herald]

based on what can be seen in that ss yes, f(-5) seems to be undefined
is there something saying otherwise?

[plain kite]

nope, all we have is that graph

prob a mistake from the teacher then

ty for the confirmation

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[hot herald]

what's the teacher saying

[plain kite]

its an online homework, and apparently me saying its undefined isnt correct

[hot herald]

can you ss the whole thing

[plain kite]

sure, its in french tho

https://prnt.sc/4sGHjwOi_hmh

[hot herald]

.reopen

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✅

[hot herald]

mmk, yeh, probs an error in the system

[plain kite]

yea, thanks 🙂

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[green trail]

How do you simplify this ?

[silent quest]

Simplify what

[green trail]

Its coming

Soon

Its out

[silent quest]

using cross method

ig

or no...

Can't factorize

[green trail]

But they say you cann

What are the ways I can factor this ?

[hot herald]

do you know how to simplify radicals

consider
sqrt(ab) =sqrt(a) * sqrt(b)
and
identify perfect square factors of 45

[green trail]

Uhhh

There is one ?

The closest am getting is 6.71

[hot herald]

what are the factors of 45

[green trail]

Ok I got it!

3sqrt5

Is this a unique ability of i?

It was originally inside the radical

But you could also take it out

But how is that possible

You can take a number out of the numerator and multiply yes

But when its in a radical?

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[stuck skiff]

I assume finding the population in 20 years involves taking the matrix L to the power of ten and applying it to the initial population, but we're supposed to do this by hand somehow. I did this on python just to see and I get numbers which I have zero chance of computing by hand, and I dont see an easy way to diagonalise it either. Am I wrong to take the matrix power? Or are there other ways to compute the result that would be possible by hand? I'm really stuck

[stuck skiff]

i posted this on the help forum already but im urgent so i'm putting it here as well

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[proven jay]

I know this is incorrect, how do i show the middle add up to 90?

[mighty crescent]

Middle what?

[proven jay]

Those vectors are supposed to be at 90 degrees apart

This is what i want to show

It has to come something like 90-thetha+ theta =90

@mighty crescent

[desert steppe]

How can you show something that is incorrect?

It adds up to 180-2theta

[proven jay]

I mean 90-theta+90-thetha is not 90

[desert steppe]

Yeah sure it's not (for all values of theta)

[proven jay]

Can I show they are at 90?

suppose take them as vectors <x,y> and <-y,x>

how do i show they are orthogonal using geometry

I can take dot product, <x,y>.<-y,x>=0