help-41

[azure goblet]

Yup

[split sail]

Nice

Let’s continue from here

We have the area function with us

However it is in terms of two variables

To maximise the function, we must get the function in terms of ONE variable only….either x or y

[grizzled pagoda]

Edmund Cloudsley

[split sail]

We can substitute this value of y into the area function

$$A(x) = (\frac{485}{x} - 4)(x-6)$$

[grizzled pagoda]

Edmund Cloudsley

[split sail]

Now that we have an expression for the area function in terms of x only

We can use calculus to find its maximum

But first let’s expand the area function

,w expand (\frac{485}{x} - 4)(x-6)

[grizzled pagoda]

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[split sail]

The expansion is

$$A(x) = -4x - \frac{2910}{x} + 509$$

[grizzled pagoda]

Edmund Cloudsley

[split sail]

Did you understand till here @azure goblet

[azure goblet]

Yeah so we multiply the them to avoid a product rule

[split sail]

Yes exactly

Product rule is a bit tedious given that we can expand it quite easily

Let’s differentiate it now

$$\frac{d}{dx} ( -4x - \frac{2910}{x} + 509 )$$

[grizzled pagoda]

Edmund Cloudsley

[split sail]

Do you know how to differentiate?

This should be

$$A^\prime (x) = -4 + \frac{2910}{x^2}$$

[grizzled pagoda]

Edmund Cloudsley

[split sail]

Now we can set this to 0 to find then maximum of the function

,w solve -4 + 2910/x^2 = 0

[grizzled pagoda]

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Requested by alison_burg3r5

[split sail]

We KNOW that length can not be negative therefore we only take the positive root

And plug that into our area function

,w solve -4 * \sqrt{1455/2}- \frac{2910}{\sqrt{1455/2}} + 509

[grizzled pagoda]

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Requested by alison_burg3r5

[split sail]

This should be the maximum area

293.22

[azure goblet]

That was similar to what I originally got, but I'm not sure if my rounding was off, I actually converted the square root to a rough decimal number

[split sail]

Or $509 -4 \sqrt{2910}$

[grizzled pagoda]

Edmund Cloudsley

[split sail]

What is the final answer given in the book

Or whatever it is u are using?

[azure goblet]

I don't have access to any answers, I can get examples that are similar and check the answers for that

[split sail]

Gotcha

Well then I suppose 293.22 should be the right answer

Atleast according to my calculations

However I am not entirely sure as the question doesn’t explicitly specify if the total area 485 is taking into account the margins or not

[azure goblet]

That might be the problem then, because everything you calculated was exactly what I had

[split sail]

If you want to be doubly sure, just wait for an undergrad or a postgrad helper to come along

And verify our working

[azure goblet]

What would change if we didn't take the margins into account?

[split sail]

I’m not particularly sure myself

Wait I’ll call someone smarter

Just gimme a sec

[azure goblet]

For sure

[split sail]

This is where the working starts @split sail (do help if you are free obviously) ❤️

It’s a simple optimization problem

But the phrasing is a bit perplexing

..... i have skipped everything that has optimization in it

im sorry

...

😭

Oh lol np

if u can give me equations i can do stuff

[split sail]

That’s the challenging part😅

Forming the equation in the first place

@azure goblet you could close the channel if you are satisfied with 293.22 (which I think is the right answer) or wait for someone else to come and verify it

Your call

Anyways I’ll go now

Have a good day

[azure goblet]

This everything I have so far

[split sail]

,w solve 26.972 * 17.982

[grizzled pagoda]

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Requested by alison_burg3r5

[split sail]

Hmmm

Weird

[azure goblet]

That would just be the original 485 that the problem gave at the beginning

[split sail]

Exactly!

They are definitely NOT taking the margins into account

,w maximum of y = 509 - 4x - 2910/x

[grizzled pagoda]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by alison_burg3r5

[split sail]

,w y = 509-4x-2910/x find y if x = sqrt(1455/2)

[grizzled pagoda]

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Requested by alison_burg3r5

[split sail]

,w solve 509-4*sqrt(2910)

[grizzled pagoda]

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Requested by alison_burg3r5

[split sail]

wtf 😭

It shud be 293.22

[azure goblet]

Same 😭

[split sail]

If the area function is f(x)

Then this SHOULD be the answer

[split sail]

Also if we take this answer into account

485.010504

1. it is exceeding the maximum possible area

2. if we use this area, the printable area would have NO top, bottom or side margins

Anyways I tried @azure goblet

[azure goblet]

...

[split sail]

Just wait for someone smarter to come along ig 😭

[azure goblet]

It was wrong because I didn't add in extra 2 in the decimal

293.222

[split sail]

OMG 🥲🥲🥲🥲🥲🥲🥲🥲🥲🥲

Bruv

[azure goblet]

Thank you @split sail 😭

[split sail]

lol no problem

Made me question my knowledge of calculus lol

All cause of a stupid decimal place

Have a good day! Bye

[azure goblet]

.close

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[split sail]

Can someone please explain why h(3) is undefined?

[split sail]

I got 1.5 as my answer

[elder harbor]

...

the denominator is zero

[molten shale]

h(3) should be undefined

[split sail]

Can someone please explain why h(3) is undefined?

[tender pilot]

9/0 isn't real

Well it's underined

You can't divide by 0!

[split sail]

i got the wrong answer

i got 1.5

[molten shale]

how

[tender pilot]

1/0 will be the same as 29495950/0!

[tender pilot]

Well can you show me your working?

[split sail]

3+ 3 = 6 3-3 = 0. so the denominator is 6 9/6

[tender pilot]

I can help then find where you went wrong

[split sail]

oh wait

then u multiply

so its 0

[tender pilot]

Yeah!

[split sail]

ok thanks

[tender pilot]

Np! Anything else?

[split sail]

i guess i Had to say it outloud

i will probabaly be back

got mid terms tmr

[tender pilot]

Yeah lol, I have that too!

[split sail]

.close

[amber wasp]

Channel closed

Closed by @misty flame

Use .reopen if this was a mistake.

[tender pilot]

Well best of luck on that!

[split sail]

.reopen

[amber wasp]

✅

[split sail]

same problem

why is it both -3 & 3

[molten shale]

Because x being -3 will make x+3 0

And x being 3 will make x-3 0

[split sail]

thanks

.close

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Channel closed

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[amber wasp]

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Remember:
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• Be polite and have a nice day!

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[pulsar oxide]

I need help with problem 2 a and c

For question a, i got 2 different value for A and B, for question c i have no clue on how to solve it

[amber wasp]

@pulsar oxide Has your question been resolved?

[pulsar oxide]

Not yet

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@pulsar oxide Has your question been resolved?

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[fallow anchor]

Help

[fallow anchor]

Idk know what to do to even start solving this problem

[split sail]

what have you tried

something worthy is:

this 2 things

$a\sqrt{b} = \sqrt{b\cdot a^{2}}$

[grizzled pagoda]

Bellax24

[split sail]

an

d

[fallow anchor]

I tried tat

[split sail]

wait i neeed to draw it

[fallow anchor]

But I just got stuck so I thought maybe not?

Okk

[split sail]

then theres also 2 more alws

laws

i will write 1 s

[fallow anchor]

Okk

This is what I got

[split sail]

this should be enough

to solve everything you need there

[split sail]

this is what

A B C D

numerotate it

[fallow anchor]

I got this from doing that

[split sail]

sorry cant ghelp if you dont numerotate it

[fallow anchor]

What is numerating ?

[fallow anchor]

I did this

I figured it out, thank you !

.close

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[fallow anchor]

Help

[fallow anchor]

Give some hints please!

For problem one I did this

But don't know what to do next

[amber wasp]

@fallow anchor Has your question been resolved?

[fallow anchor]

<@&286206848099549185>

Please help

[brisk leaf]

Hello

[fallow anchor]

Hiii

[brisk leaf]

The problem is quite simple

And honestly quite elegant

[fallow anchor]

Oh

[brisk leaf]

It's very pretty question

I prefer writing solution down

Can you please wait 2 minutes for me

[fallow anchor]

Okk

Take your time

[brisk leaf]

Check it out

Proceed in similar fashion for the remainder of the problem

We getting somewhere

?

We made a perfect square

To get it out of the root

Since you have stopped responding

I am just going to send the rest of the solution

Hope it's enough to help

And answer is just (3+(2)^1/2)

Hope this was enough

Have a great day

[fallow anchor]

Oh thanks sorry was working on another problem and didn't c

Really appreciate your help, thank you again!

.close

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[coral lance]

Can someone help me, I'm stuck in this %deviation, please help me

[weak zinc]

,rccw

[coral lance]

How to solve this?

= |11,74 / 76×10^-3| ×100%
Is this right?

Hmm wait I think I post in wrong server

[amber wasp]

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[sand fractal]

I am wondering if there is a way to solve this algebraically without writing out the graphs

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[slender blaze]

tan(4a) + tan (2a) = 0 for 0 <= a <= 360

[violet raven]

we have to prove that

??

[slender blaze]

equation

after simplifying everything I got

[limpid sun]

hey marito, how is going?

[slender blaze]

sen(6x) = 0

[slender blaze]

hi

[violet raven]

well let 2a=x

[slender blaze]

on the num

[violet raven]

then the equation becomes

tan(x)+tan(2x) =0

tan(2x) = 2 tan(x)/1-tan^2(x)

[slender blaze]

yea

this was on an exam I just finished

I transformed everything to sines and cosines then combined gravitons

fractions

i think it’s the same thing right

[limpid sun]

$sin (4a)cos(2a)+sin(2a)cos(4a)=sin(6a)$

[grizzled pagoda]

everg

[slender blaze]

yes

I had that on the num

so sin(6x) = 0

6x = 0

x = 0?

[limpid sun]

$6x=k\pi$

[grizzled pagoda]

everg

[slender blaze]

for 0 <= x <= 360

[limpid sun]

$x=k \pi/6$

[grizzled pagoda]

everg

[slender blaze]

that’s the general solution

?

[violet raven]

yes

prety much

[limpid sun]

so k=0,1,2,...,6,...,12

[slender blaze]

oh sorry

degrees

[limpid sun]

in your case, since x<=360

[slender blaze]

i just can’t find the degrees symbol on my phone

[limpid sun]

is it your dog the one in your pic?

[slender blaze]

oh I get it

[slender blaze]

no I wish

thank you guys

[limpid sun]

it is very cute

[slender blaze]

.close

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[runic kraken]

i'm lost trying to solve this

i did the following but its not correct

i'm having issues getting the value of (|1+z|)^2

[crisp stratus]

try saying $z=e^{i\theta}$

[runic kraken]

i asked chat gpt for the answer of that and it gave me sqrt(2+2a)

[grizzled pagoda]

artemetra

[crisp stratus]

that satisfies |z|=1

[grizzled plume]

!nogpt

[amber wasp]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[strange spear]

dont use gpt shlawg

[runic kraken]

at the time that we did that exercise we didn't know that so i want to try and do it without

bruh

[crisp stratus]

also recall that $|w|^2 = w\cdot w^*$

[grizzled pagoda]

artemetra

[crisp stratus]

use that with the denominator

[runic kraken]

so |1+z| = (1+z)(1+z)?

[crisp stratus]

|1+z|^2 = (1+z)(1+z*)

[runic kraken]

ah yes

the star is the conjugate form?

[crisp stratus]

yes

[runic kraken]

okok i'll try again

thank you

[crisp stratus]

good luck

[runic kraken]

i got this far but i can already see that i would end up with the same thing

@crisp stratus

sorry for the ping

<@&286206848099549185>

.close

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[crisp stratus]

.reopen

[amber wasp]

✅

[crisp stratus]

try z=e^(i theta) as i said

.close

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Channel closed

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[runic kraken]

oh

oops

[amber wasp]

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[nocturne plaza]

the other problem I had to do here, 145, was pretty easy and came out to be -5. I just equalled the two equations together. But I'm not sure about 148? the (kx) exponent scares me and Idk what to do xD

[amber wasp]

@nocturne plaza Has your question been resolved?

[brisk leaf]

Hello

What part of the question do you need help with

I believe what we must analyze is that the exponential function is continous in it's interval

And x+3 is also continous in its interval

So we must make the function continous at the point where the function changes it's definition

That point is x=4

So the value of definition 1 and 2 at x=4 should be same

So e^4k = 4+ 3

e^4k = 7

Taking log on both sides

4k = ln7

k= (ln 7)/4

That's the answer

Hope this helps

[nocturne plaza]

ah hello, sorry lemme read up

oooh that's pretty simple, thank you! :D

.close

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[nocturne plaza]

what went wrong with the equation?

listed answer

:<

[brisk leaf]

Hello

Can you pls tell me what is eq 3.4

[nocturne plaza]

oh yeah 1 sec

[brisk leaf]

The answer written out in the solution is correct though

The slope is -4

And tangent to a line

Is the line itself

For any point

Got it @nocturne plaza

[nocturne plaza]

sorry was grabbing a ss

but this one doesn't behave the same? D:

I know a was right, but something went wrong in b :<

for 11 I mean

[brisk leaf]

Could you post the question pls

For 15

[nocturne plaza]

yeh

[brisk leaf]

Their is no way for any tangent of line to exist

Than the line itself

[brisk leaf]

Their is the problem

15 isn't a line

[nocturne plaza]

.... o h

[brisk leaf]

It's a rectangular hyperbola

[nocturne plaza]

is that where I use the point slope formula? Our teacher has mentioned it a lot, but it didn't work w 11

this thing

point slope form*

[brisk leaf]

For 11 i think you applied it wrong

Give me 2 mins

[nocturne plaza]

drat

oki ty

[brisk leaf]

I will write this out

To make this easy

[nocturne plaza]

<33

[brisk leaf]

See if this works

[nocturne plaza]

OHHHHHHHHHH

I'm an idiot, thank you xD I see now

[nocturne plaza]

no problemo if not, I can make a new chat, but do you think you could help me with the slope of 15? I'm normally good at DQ, but I somehow ended up with a 1

[brisk leaf]

It's ok

Everybody makes mistakes

[nocturne plaza]

true true 🥹

[brisk leaf]

Sure!

[nocturne plaza]

thank you :D

I'll send my work on my phone, 1 sec

[brisk leaf]

Just send it here

You can send more than 1 question

This help chat is yours till you close it

Or it gets times out

[nocturne plaza]

I knoww, but I don't wanna like- trap you and I thought I'd be fine after working out what I did wrong formula-wise :')

I was not, in fact, fine 😭

[brisk leaf]

Interesting wording

Trap you

Lol

[nocturne plaza]

xDD IDK

[brisk leaf]

I am not the most active guy around

[nocturne plaza]

what if you were done with math today :')

[brisk leaf]

This is the first time I have been active in months

Not the best pick for trapping

[nocturne plaza]

oh dang, welcome back then :D

I didn't even process the new player symbol, haha

[brisk leaf]

Skill that matters 😎

[nocturne plaza]

very true B)

ok so this is really bad, and there's some erased stuff cause I was just so lost 😭

[brisk leaf]

7× 3 is 21

Not 49

[nocturne plaza]

I'ma be totally honest, I was going for 7*7 😅

I am very tired

[brisk leaf]

Really sorry for that

But for the lcm

3 will be multiplied

Not 7

[nocturne plaza]

This?

[brisk leaf]

This

[nocturne plaza]

... a h

[brisk leaf]

So

solve further by yourself

And tell me what you get

[nocturne plaza]

this is a subtraction symbol, right?

[brisk leaf]

Mhm

[nocturne plaza]

oki kewl, ty

[brisk leaf]

Sorry for the handwriting

I am writing with a marker

[nocturne plaza]

nono you're totally fine

oh yeah markers are a pain :')

gonna grab water so I'll be an extra sec

[brisk leaf]

It's fine

[nocturne plaza]

little unsure what to do at (-7h)/(9+3h) 🤔

I want to say remove the h on top and bottom, but that simply isn't right xD

[brisk leaf]

Welcome back

[nocturne plaza]

thank you :D

[brisk leaf]

Their is another h in the denominator

[nocturne plaza]

true but like

[brisk leaf]

Forgot about it?

[nocturne plaza]

nah, I'm just lazy and don't write it in till I have to xDD

BUT

caps

[brisk leaf]

So they cancel out, right

?

[nocturne plaza]

true, but would that just be the top top h?

or

no sorry wait

ugh ;-;

[brisk leaf]

I' ll help

Just wait

[nocturne plaza]

thank you :')

my math abilities plummet when I'm tired xD

[brisk leaf]

I think that is true for everyone

Does this make sense?

[nocturne plaza]

ack sorry lemme read it

ooooh

ok I see

[brisk leaf]

And that's it

That's your answer

[nocturne plaza]

but where does the other h go D:

[brisk leaf]

I suppose I am done here

.-.

[nocturne plaza]

oop

[brisk leaf]

What is h

?

[nocturne plaza]

... 0?

[brisk leaf]

Something that is infinitely greater then 0

Not exactly 0

Something that tends to 0

So 3+ h is simply 3

[nocturne plaza]

I see 🤔

[brisk leaf]

If it were 0

[nocturne plaza]

makes sense, thank you :D

[brisk leaf]

How could you divide by it

[nocturne plaza]

fair point xD

[brisk leaf]

Anything else

[nocturne plaza]

nope, have a great day :>

[brisk leaf]

I am like genuinely invested

Lol

[nocturne plaza]

xDDD fair

tutoring seems fun :D

[brisk leaf]

Today I came online after several months

And joined this math server for the first time

[brisk leaf]

I am just bored

This is my way of untangling

Sort of

That I just found today

[nocturne plaza]

oooh well I'm glad it's working out!

[brisk leaf]

Lol

I will probably disappear again for months

[nocturne plaza]

😭 fair enough

[brisk leaf]

But all is good while it lasts

[nocturne plaza]

true! There's also science help servers if that also fancies your interest

[brisk leaf]

Anyways had a great time

[nocturne plaza]

I am in a lot of homework servers :')

[brisk leaf]

Hope you did too

[nocturne plaza]

I did, much appreciated :D

[brisk leaf]

I will now go get trapped somewhere else

And you should get some sleep

I guess

Lol

[nocturne plaza]

XDD

I wish, got two more units to do after this :')

I pop in and out of the server for hours and then appear in a week when I'm confused again, lmao

good luck and have a good day :D

[brisk leaf]

You too

[nocturne plaza]

.close

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[torn wigeon]

is this rihgt?

[light kelp]

walk me through ur thinking

[torn wigeon]

its not mine its my friends 😭

we both dk tho

[light kelp]

okay

have you been taught the complementary angle theorem?

wait no

ugh its been so long i forgot all the names of the theorems

have you been taught the vertical angles theorem

[torn wigeon]

alittle bit yeah, we just started the unit

shes a few lessons in ahead of me tho

[light kelp]

okay basically it states that angles opposite of each other are congruent

so u can just say 7x-15=5x+31

which allows you to solve for x

then plug x back in

sorry for the rushed explanation im a bit busy rn

[torn wigeon]

oh its no problem

thank you

so 31x?

[light kelp]

um im not sure how you got that

[torn wigeon]

the equation you gave

OH

wait it needs to be solved

my bad

23X

[brisk leaf]

Hello

How can I help?

@torn wigeon I Suppose it's your question

[torn wigeon]

HI

oops

[brisk leaf]

Could you please state the question

[torn wigeon]

its this

is 23x right

[brisk leaf]

Ok let's start

Ready to follow through?

[brisk leaf]

Make a horizontal line like this

This line is parallel to the x axis

Would you agree

[torn wigeon]

yeah

[brisk leaf]

Ok

Now let's obeserve

The slope of both of these lines are given

And the slope is the tan theta of the angle the line makes with the x axis

Where theta is the angle that the line make

So

[brisk leaf]

Let assume these as their angle with x axis

And since we know their slope

Tan alpha is just 5

Tan beta is just 7

Angle BEC is beta - alpha

So let's try to get it

[verbal tiger]

I’m confused

I think m means “measurement of” in this question, not slope 🥲 @brisk leaf

[brisk leaf]

Tan (beta - alpha) = (tan beta- tan alpha)/(1+tan alpha . Tan beta)

[brisk leaf]

I am taking about

Slope of lines given

[brisk leaf]

Tan (beta- alpha) = 7-5/(1+7*5)
= 2/36
=1/18

Beta - alpha is just arc tan 1/ 18

[brisk leaf]

Observation

[brisk leaf]

I think we can safely say that

[torn wigeon]

yeah

[brisk leaf]

So theta = 180 ° - (beta-alpha)

And theta is what we needed

[brisk leaf]

Which is 3.08609414834

In radians

Which is 176.820169507 in degrees

Hope this helped

@torn wigeon am I right?

Any query?

[verbal tiger]

I have never learned this at school tbh😭 I wish I also learned this tho

I did the simple way and I got a different answer somehow

[amber wasp]

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[formal elk]

heyo

[formal elk]

so im trying to simplify a root

but goggle is doing a poor job at explaning how

[elder harbor]

try

[formal elk]

ik you go by prime factors, but i dont quite get how to do that

[elder harbor]

Factoring it

[celest cove]

well if i have a number and we get its prime factors to be, for example
2^4 * 3^2 * 7

that is (2^2 * 3)^2 * 7
so we pull out the ^2 bit

sqrt(2^4 * 3^2 * 7 * 9) = sqrt((2^2 * 3)^2 ) * sqrt (7 * 9)= (2^2 * 3) sqrt ( 7 )

[formal elk]

uh

[celest cove]

oops

[formal elk]

this is very hard to read sorry

[celest cove]

9 is not a prime number haha

ill rewrite it, one moment

[formal elk]

kk

[celest cove]

if i have a number and its prime factors were:
$2^4 \cdot 3^2 \cdot 7$ then this is equivalent to $(2^2\cdot3)^2 \cdot7$
so if i had $$\sqrt{2^4 \cdot 3^2 \cdot 7}$$ then that is equal to
$$\sqrt{(2^2\cdot3)^2)} \cdot \sqrt{7} = (2^2 \cdot 3) \sqrt{7}$$

[formal elk]

@-@

[grizzled pagoda]

AℤØ

[celest cove]

ie sqrt(1008) =12sqrt(7)

[formal elk]

ok so

the question gives multiple options on what the answer could be

" 4 √2 √3 √5"

is one of them

[celest cove]

bit dodgy

[formal elk]

and i think its correct becouse those are all the primes of 480

but

480 also has 7 as a prime

and NONE of the sujestions have 7

what am i missing here?

[celest cove]

uh

[celest cove]

does it?

[formal elk]

as far as im aware?

[celest cove]

sadly not

[formal elk]

35/5=7

[celest cove]

?

[formal elk]

i went down the prime tree

[celest cove]

how did you get to 35

[formal elk]

480/2=240 , 240/2 = 120 60/2=30 ,30/2=15 ,15/3 = 5

nvm i and dumb and did something wrong

[celest cove]

tut tut

[formal elk]

u-u

[celest cove]

you didnt write the 120/2 also

[formal elk]

oh

well 120/2 is 60

guess i just mentaly skipped it lol

[celest cove]

anywho, what do we end up with

[formal elk]

2,3,5

[celest cove]

thats not a prime factorisation its a list

[formal elk]

um

then i dont know what i am ment to be getting from it

[celest cove]

remember how i wrote it like this

do that

[formal elk]

wait so

ohh

i see

2^5 , 3 , 5

?

[celest cove]

shouldnt be a list, its a product

but the spirit is there

[formal elk]

i am seriously lost

what do you mean

[celest cove]

you are listing numbers

a,b,c

its meant to be a product
abc

[formal elk]

so its product is 2^5 x 3x 5

./..

[celest cove]

yeah

[formal elk]

ok

so with the answers it also puts a number before the product

origonal number

but it for the answers gives

" 4 √2 √3 √5"

" 3 √2 √3 √5"

" 2 √2 √3 √5"

[celest cove]

the issue being?

[formal elk]

i assume the last one would be correct

[celest cove]

it isnt

[formal elk]

but i dont get what its trying to sujest

[celest cove]

its not suggesting anything, its just a simplification, albeit theyve written it weirdly

[celest cove]

just follow the same process

[celest cove]

whats your largest square factor

[formal elk]

5

[celest cove]

5 isnt a square factor

[formal elk]

,n,

[celest cove]

5^2 or 5^4 or 5^26 would be

but you just have 5

[formal elk]

ok why does square factor matter here at all

[celest cove]

because we're simplifying a square root

[formal elk]

ok

[celest cove]

if it was a cube root id be asking for the largest cube factor

[formal elk]

so in that case, 2^5?

[celest cove]

thats not square

[formal elk]

then we dont have one?

[celest cove]

you do

[formal elk]

cus 3 isnt square

[celest cove]

what is 2^5

how many 2's are there being multiplied

[formal elk]

32

[celest cove]

what is a square number

[formal elk]

a number that can be cleanly rooted

[celest cove]

meaning it can be written in what form

[formal elk]

no idea

[celest cove]

k^2 for some integer k

2^5=2^4 * 2

2^4 is square

[formal elk]

ok

so now we have 2(2^4) 3 5

?

[celest cove]

true

[formal elk]

ok... what next

[celest cove]

what did i do on the last line

you have sqrt( [2^2]^2 * 2 * 3 * 5 )

[formal elk]

ok i can read a picture, but i dont understand why your doing any of that

[celest cove]

because when we split the root into the largest square factor and the rest of the factors
ie sqrt(k^2) * sqrt(a) where a is not square
then we end up with k sqrt(a), because the square root of a square number simplifies

[formal elk]

this isnt helping at all

im just gona use the actual numbers becouse the hypathetical example is just missleading here

2^5 x 3 x 5

this is the product

[celest cove]

misleading how?

[celest cove]

sure

[formal elk]

i dont understand what the hell we are doing to it or why, so im just gona follow what you said so far

so 2(2^4) x 3 x 5

so now we have a square number

what is the next step to do

[celest cove]

in very plain words we're splitting the stuff inside the square root into a square factor and a non square factor
the square factor roots to an integer, the non square factor stays irrational

[celest cove]

split the root into the square factor and the non square factor

[formal elk]

how

[celest cove]

sqrt(ab)=sqrt(a)sqrt(b)

[formal elk]

i dont see what ab is in this senario

its not 2 and 4 is it

[celest cove]

its just two numbers, i could have wrote any number of things

im just telling you that the square root of a product can be rewritten as a product of square roots

eg sqrt(6)=sqrt(3)sqrt(2)

[formal elk]

ok? we cant do anything with that tho?

[celest cove]

you literally have a square root of a product

i did it in my example

last line

[formal elk]

so sqrt 32

[celest cove]

no

32 is not square

[formal elk]

thats 2^4???

[celest cove]

2^4 is 16

[formal elk]

ffs thats 16

ok so sqrt 16

[celest cove]

sqrt(16) * sqrt( 2 * 3 * 5 )

[formal elk]

ok 2 sqrt 16 x sqrt (2 3 5)

[celest cove]

where did the 2 come from

[celest cove]

that 2 is there

the 2 outside came from nowhere

[formal elk]

BUT YOU SAID TO LOWER THE POWER WE MOVE THE 2 OUTSIDE?

[celest cove]

where on earth did i say that

everything you wrote was fine, except that 2 at the front

sqrt 16 x sqrt (2 3 5) it would just be this

[formal elk]

here>

?

[celest cove]

yeah?
in the first square root you have the 2^4=16
in the second square root you have the other 2, youve written that fine

but the 2 at the front came from nowhere

[formal elk]

but we HAD 2^5 from working out

how did we drop a power then

[celest cove]

how have we dropped a power??????
you have written sqrt( 2^4 ) * sqrt( 2 * 3 * 5)

if we recombined that you would have sqrt( 2^5 * 3 * 5)

because 2^4 * 2 = 2^5

the other 2 never existed

[formal elk]

your number manipulation is making me MORE confused

we started with 2^5, 3 ,5

we got them from the prime of 480

[celest cove]

sure

[formal elk]

we want to simply

so you are sujestion doing (2^4) x (2 x 3 x 5)

[celest cove]

yes

[formal elk]

ok

what is next

from that step

[celest cove]

sqrt [(2^4) x (2 x 3 x 5) ]

split the root

[formal elk]

show how

i do not know how to split a root

[celest cove]

sqrt(a * b) =sqrt(a) * sqrt(b)

ive literally shown you

[celest cove]

^

ie sqrt( 2^4 ) * sqrt( 2 * 3 * 5 )

[formal elk]

so?

if i knew what to do with this i wouldnt be in here asking for help

[celest cove]

all you have to do is simplify the root

what is sqrt( 2^4)

[formal elk]

16

[celest cove]

2^4 is 16

[formal elk]

yes

[warm burrow]

,tex .exp rules

[celest cove]

what is sqrt( 2^4)

[grizzled pagoda]

Steel

[formal elk]

sqrt 16

right?

or is it 2^3

[formal elk]

wait... sqrt 2^4... is 4

,n,

i dont... see how it is

[celest cove]

Yes sqrt(4^4) is 4

Therefore we are left with 4 sqrt(2 3 5)

[formal elk]

and thus you can just write 4 sqrt (2 3 5)

ye

well we got there in the end i suppose

[celest cove]

Indeed

[formal elk]

thank you for helping

[celest cove]

Sorry if i started getting a tad snappy

[formal elk]

pff, i snapped first

your fine

.close

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[fast nova]

im trying to see if i can use integration to find the perimeter of a function

[fast nova]

anything along the lines of either defining a function, say, for y(x) i define a y(x+h) such that the difference of:
∫y(x+h)-y(x) gives me an expression that involves h in a way, that when i take the limit h->0, i end up with the perimeter

my reasoning is something along the lines of;
a rubber band is basically the perimeter of a disc...In going to a rubber band from a disc, requires you to cut a very large portion of the disc such that the width is minimal

is there a way i can, atleast approximate to a practical extent, the perimeter of a function using such a way?

i tried using binomial expansion for negligible terms, or trying limits and such, but it doesn;t really go anywhere

[pallid canopy]

this just seems like a line integral

[fast nova]

ehhhh kind of

like the area of a line is defined to be zero, yeahh im jus trying to get a veryyy little bit of area

so that it gives me an approximation of the perimeter

i do think it has something to do with the derivative too, but i can't really make any meaningful progress

[fast nova]

ngl i can;t say i understand any bit of that-

[pallid canopy]

derivation https://math.libretexts.org/Bookshelves/Calculus/Calculus_(OpenStax)/16%3A_Vector_Calculus/16.02%3A_Line_Integrals

it really depends on the dimensions of your function y and its argument x

[fast nova]

I see

i dont really get tho, does it say something about the perimeter of the function

I haven't really studied this in detail, so pardon me

isnt this quantity still giving me, the area under the function?

[pallid canopy]

your notion of "perimeter" is not defined enough to answer you

do you have a shape you want the perimeter of? like an ellipse or something more complicated

[fast nova]

actually i was looking for something more general

given any function, how would you examine it's perimeter under a limit

[pallid canopy]

again, perimeter isn't defined enough

[fast nova]

ah

i can only explain what i'm visualizing

if i use a string and lay it in the shape of a function, and i know the function, then what can i do to calculate the length of the string to an appreciable extent

[pallid canopy]

this gives you the length of the string

[fast nova]

ooooh

ah alright, I'll look more into it, thanks a ton!

.close

[amber wasp]

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[pallid canopy]

another resource with some shapes you should learn https://tutorial.math.lamar.edu/Classes/CalcIII/LineIntegralsPtI.aspx

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[sharp dock]

Can anyone help me solve this using long division?

[sharp dock]

<@&286206848099549185>

My teacher did it but I'm not sure how

I'm only used to dividing by 2 terms like 2x + 1 or something not 4 terms

[fresh gust]

It's the same principle

[sharp dock]

How

[fresh gust]

OK. So, first, what do you multiply the divisor by so that the degree becomes 4?

[sharp dock]

x

x³ • x

Is x⁴

Right?

[frank zealot]

u can try solving this by identification

basically setting:
(x⁴ + 6x² - 8x + 12) = (ax + b)(x³ - x² - x + 1) where a and b are real numbers

and u can identify the coefficients a and b by foiling up the expression on the right

and so after finding them, (ax + b) would be the answer

[sharp dock]

I'm confused

Do you think u could write that part down

I'm just lost rn lol

[frank zealot]

ok so

(x⁴ + 6x² - 8x + 12) = (ax + b)(x³ - x² - x + 1)

now were trying to find a and b yes?

[sharp dock]

So x⁴ + 6x² - 8x + 12 is ax+b?

[sharp dock]

Yea

Shouldn't it be x⁴ + 0x³ + 6x² - 8x + 12

[frank zealot]

no, its (ax+b)(x³-x²-x+1)

i set it up that way

[frank zealot]

sure if u want to

[sharp dock]

So what's a x and b?

[frank zealot]

(x⁴ + 6x² +0x³ - 8x + 12) = (ax + b)(x³ - x² - x + 1)

[frank zealot]

some real numbers

that we are trying to find

[sharp dock]

alr

How do we find them

[frank zealot]

foil up the expression on the right

(ax + b)(x³ - x² - x + 1)

can u simplify it?

[sharp dock]

Like factor something out?

I'm confused

[frank zealot]

like multiplying it

[sharp dock]

ax³

[frank zealot]

opposite of factoring out

[sharp dock]

ax²

Idk

This doesn't make sense

[frank zealot]

alr ill try to go from the start again

[sharp dock]

Alr

[frank zealot]

so lets say that when we divide them, we will be left with (ax+b)

right?

when we divide the top by bottom, we are left with some expression in the form ax+b

[sharp dock]

How 😭

Where do u get ax+b

[frank zealot]

so

when u divide a polynomial by another polynomial that has a lower degree than it by 1

u will be left with a polynomial with degree 1

[sharp dock]

Yea like x⁴ ÷ by x³

[frank zealot]

exactly

[sharp dock]

What about the 6x² ÷ x²?

[frank zealot]

thats why i said ax + b

[sharp dock]

Same degree

[frank zealot]

i am not too certain but that would depend whether u want integers in ur answer only or irrational numbers

[sharp dock]

Lemme check the final answer

[frank zealot]

tell me whether the final answer is in the form of ax + b or not

[sharp dock]

Final answer is 8x²-8x+11

[frank zealot]

.

[sharp dock]

That's how my teacher did it

Im not sure how tho

[frank zealot]

how is that right

if u multiply 8x² by x³ u get 8x⁵

smt is off

[sharp dock]

Yea idk

[frank zealot]

tho did u understand my way

like how it came up

[sharp dock]

not really 😭

I'll talk to my teacher about it

Could u explain another question instead?

Something easier

Thank u for trying to help me out I just wanna know how the teacher did it

[frank zealot]

ur teacher used synthetic division

[frank zealot]

which i have no knowledge about

[sharp dock]

He used long division

[frank zealot]

whatever theyre called, i dont use them, i use identification

[sharp dock]

It's all good

[frank zealot]

i would literally use it here too lmao

[sharp dock]

Oh

Yk anyone else here who could help with long division?

[frank zealot]

ping helpers

[pallid canopy]

,tex \polylongdiv{x^4+6x^2-8x+12}{x^3-x^2-x+1}

[grizzled pagoda]

riemann

[sharp dock]

What is that 😭

[pallid canopy]

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

[sharp dock]

Ik how to do this

I just don't know how to divide it by 3 terms or more

[sharp dock]

Like this

[sharp dock]

And this

[pallid canopy]

why not

what makes 3 terms harder

[sharp dock]

Cuz there's a term in the middle

And idk what to do with that term

for example if we divide by x² + 7

x² + 0^x + 7

Like how

[pallid canopy]

0 = 0 * x

0 * anything = 0

[sharp dock]

So it's x² + 0 + 7

So how would u solve this

[sharp dock]

.

[pallid canopy]

,tex \polylongdiv{x^4+3x^3 -2x^2 + 5x-1}{x^2 + 7}

[grizzled pagoda]

riemann

[pallid canopy]

do you know where x^2 came from?

the one at the top

[sharp dock]

yea bc x² • x² is x⁴

Right?

And then we subtract

But we don't add the 0 in there?

We just bring the 3 down?

And then x² • 3x is 3x³

And then x² × 7 is 7x² which we then subtract it from -2

Then we grt -9x²

And then x² • -9 is -9x² which is why it's at the top

Then we bring the 5 down

What happens to the -1?

@pallid canopy

Shouldn't we bring the -1 down to the 5 as well?

So 3x³ - 9x² + 5x - 1

[pallid canopy]

,w expand (x^2 + 3x - 9)*(x^2 + 7)

[grizzled pagoda]

Results provided by WolframAlpha

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

Requested by rie.mann

[pallid canopy]

there's a remainder

the remainder has degree less than the degree of x^2 + 7

[sharp dock]

.

That's what my teacher did

I think I understand it now

[pallid canopy]

the -1 is brought down in the full solution

i was just highlighting one at a time

[sharp dock]

Oh that makes sense

Thanks for ur help

Take care

.close

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[amber wasp]

@ornate crane Has your question been resolved?

[fading hinge]

Are you matching them based on derivatives?

If so, yes

[amber wasp]

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[lethal raft]

Im on my last attempt 😭

[lethal raft]

Ive been watching yt tutourials

[uneven seal]

What are you trying to solve??