help-28

[inland sand]

but webworks doesnt want it

ive tried everything i know

[leaden ermine]

erm

[inland sand]

the same thing that i calculated

[leaden ermine]

i need to see how you figured out your max

[inland sand]

its right there on the board

[leaden ermine]

your min seems to be fine

[inland sand]

-1.16

on the right of the whiteboard

[leaden ermine]

so it's not reading it correctly

[inland sand]

which picture is this linking to

discord is glitching

[leaden ermine]

you miscalculated somewhere

[inland sand]

how tho we are taking about a graduated math bachelor degree with me

and chatgpt says the same

is there a simplification tho

[leaden ermine]

did you compute the solutions of this

[inland sand]

their was one of them out of the interval

so we didnt calculate it

[leaden ermine]

well there is actually one

[inland sand]

I dont understand what you are saying

[leaden ermine]

there is one solution within your interval

[inland sand]

let me send you my part a too

maybe that could help

[leaden ermine]

i hardly get what you calculated

i only can tell you rewrote sec and tan in terms of sine and cosine

and then suddenly numbers appeared

[inland sand]

the trig circle

thats where most of the values are from

[leaden ermine]

let me write it down

[leaden ermine]

you can turn that into a quadratic equation anyway

[inland sand]

I sent an email to my tutor ;) this was an extremely tough number

[leaden ermine]

no

[inland sand]

we got wack values because webworks assigns random numbers for everyone and we got wierd ones

[leaden ermine]

i see no what you did

(sqrt(2)/2,sqrt(2)/2) correpsonds to what angle

on the unit circle

[inland sand]

let me go get a circle

[grim skiff]

Why'd you just use the end points for the max and min?

[inland sand]

we used the pi 4

[leaden ermine]

you mean pi/4

?

[inland sand]

yes

[leaden ermine]

this is the solution you missed out

it's between 0 and pi/3

and at x = pi/4 your actual max value

[inland sand]

let me go look at my part b again

These are the pts i tested right

[leaden ermine]

ok, but havent tested x = pi/4

[inland sand]

,w pi/4

[glossy valve]

Results provided by WolframAlpha

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

Requested by mrb0808

[inland sand]

ok going to test it brb

[rough tundra]

writing pi out is crazy work

[leaden ermine]

you checked your end points and missed out the critical value at x = pi/4

[inland sand]

let me live this is tutoring channel lol

[leaden ermine]

i also write my numbers out, got a problem

[lime ether]

$\pi$

[glossy valve]

knief

[inland sand]

happy pi day

[rough tundra]

icl I thought it was e^i at first, had to do a double take but yeah I'll let you live lmao

[inland sand]

sec is 1/cos x right

0.247

[leaden ermine]

😦

[inland sand]

holdup il do it again

ITS CAUSE MY CALC IS IN DEG

NOT RAD

k

DRUMROLL PLEASE

-0.67

[leaden ermine]

looks good lets see

,w f(x) = sqrt(10)x-sqrt(5)sec(x) where x = pi/4

[glossy valve]

Results provided by WolframAlpha

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

Requested by adoniszgks

[inland sand]

WHAT THE HELL IS THAT

[leaden ermine]

a close form

,calc 1/2*sqrt(5/2)(pi-4)

[glossy valve]

Result:

-0.67863059371935

[inland sand]

AYO

SO YOU KNOW WHEN YOU WERE ROASTING ME

probs cause my calc was in deg not rad

[leaden ermine]

do you drink red bull by any chance

[inland sand]

i have adhd

leave me be

[leaden ermine]

i drink too

whats your fav taste

[inland sand]

redbullÉ

nah thats nasty

[leaden ermine]

redbully skull

[inland sand]

ive never had one

i only drink celsius

[leaden ermine]

you drink temperature?

[grim skiff]

Monster?

[inland sand]

never had it

mountain dew and celsius is all

and its like once every 2 weeks

ok so let me check my min max

[leaden ermine]

trust

your min seems to befine btw

[inland sand]

holdup i dont wanna give you more reasons to roast me

IM COOKING

this

is

my

max

[leaden ermine]

you cant cook if the solution is right infront of you

you can only mess it up parsing

[inland sand]

i was cooking while you wrote

stawp it

[leaden ermine]

[inland sand]

K

im trying it

NO NO NO

im about to loose hair

WHY

[leaden ermine]

welp

you remember what close form was

did it tell you to write it in decimals and round it

[inland sand]

i ummm

dont know

im not used to that form

[leaden ermine]

it's just plugging in pi/4 into f

[inland sand]

ya thats what i did no

[leaden ermine]

and simplifying the form (without decimals)

[inland sand]

OH you want me to write the whole thing

[leaden ermine]

nooo

[leaden ermine]

i dont want you lol they want you

[inland sand]

i never understand when you say it that way

ok

[leaden ermine]

i was right when i said it was here skull

[inland sand]

you will always be right

im the stupid one here

HAHAHHAA

[leaden ermine]

https://tenor.com/view/young-sheldon-sheldon-cooper-crying-in-my-pillow-is-not-an-option-question-iain-armitage-gif-14020278

[inland sand]

im so lost

I think i give up

this is my fourth hour of my today or smth

[leaden ermine]

so you cannot even type that down?

,calc 1/2*sqrt(5/2)(pi-4)

[glossy valve]

Result:

-0.67863059371935

[inland sand]

k last call i try it

[rough tundra]

what are you trying to do?

[leaden ermine]

like it's literally there

just write it

[inland sand]

aguys

GHSDYHFGAGIUFUSAI

IT WORKED

[leaden ermine]

[inland sand]

my work here is done

[leaden ermine]

you are supposed to always write out your solution like that

[inland sand]

ladies and gentleman

the monkey is hitting the sack

[leaden ermine]

when it didnt specifiy in decimals especially rounding

[inland sand]

or the hay

idk

[inland sand]

webworks is ummm

odd af

sometimes it doesnt mind sometimes it does

[leaden ermine]

sure

[inland sand]

stupid americans

[leaden ermine]

btw

[leaden ermine]

i also have a whiteboard

[inland sand]

omg twinssss

did i convert you

[leaden ermine]

i hope i convert you

[rough tundra]

problem 5 and 12 😭

[inland sand]

convert to what, looksing my hair

problem 5 is almost done

but im so dead

my eyes are burned

[leaden ermine]

parsing your solutions

[inland sand]

im trying to pars my joy

hey at least i got a bangar midterm grade

[flint hull]

AHHH WEBWORK

my greatest enemy

[inland sand]

krish

[leaden ermine]

i meant pasting and said parsing skull

[inland sand]

you and i

[leaden ermine]

you converted me indeed

[inland sand]

been through hell frl

[flint hull]

yk what pisses me off the most about it

it's not the math

[inland sand]

anti do you want to go bald and help me finish n5

[flint hull]

not the questions

[inland sand]

ITS THE ANSWERS

[flint hull]

why is it called "WeBWorK"

[inland sand]

it dont work

[flint hull]

WHY IS IT SPELLED LIKE THAT

[inland sand]

webwoke

[leaden ermine]

it only works with me

[flint hull]

i absolutely hate that website

same with pearson mathlab but that's a whole other story

[inland sand]

Anti

You wanna try this

Or are you dead inside

[leaden ermine]

rainbow keyboard

[inland sand]

Il put it yellow for curious george

Holdup

[leaden ermine]

thank god chartbit is here

[inland sand]

Just for you

YOU READY FOR OUR LAST PROBLEM OF THE WEEK TOGETHER ANTI

you hyped

Problem 5

[minor basin]

i have no clue what i'm looking at but my pocorn is ready

[leaden ermine]

i am just ready

[inland sand]

LETS DO IT

[leaden ermine]

do you happen to be merbs best friend

[minor basin]

doubt it

[leaden ermine]

two merbies

[inland sand]

You wish you were

[leaden ermine]

(You don't)

[inland sand]

Math is lit with me

[minor basin]

i dont

[inland sand]

well leaf me alone

[minor basin]

ok

[leaden ermine]

i will call 911

[inland sand]

ok so anti

i was googling the solution for this one

[leaden ermine]

not proud of that but sure

[inland sand]

and theres something that i dont understand why they were doing it

let me bring it up

its loading

so you see on my whiteboard i understood how the factoring worked

but what is the non highlighted

i wanna know

[leaden ermine]

you know i can't explain something that is of chatgpt because it might just be wrong

instead lets have a look at what you did

[inland sand]

ok

in my head id be a at critical numbers step

[leaden ermine]

it looks correct?

are you asking how to factor now?

[inland sand]

no cause this is factored i think

im just wondering why chatgpt isnt doing so

sometimes it does different techniques then me and i wanna know

[leaden ermine]

this aint factored yet

[leaden ermine]

it's literally ai

it's prone to do mistakes

[inland sand]

the 8x^8(1-x)^7 is not the factored

[leaden ermine]

like a selfdriving car might get you killed at any moment

[inland sand]

can you explain to me why its not factored

i explained my reasoning at the bottom

i dont get whats missing

[leaden ermine]

because you have a sum

let's just say it's not fully factored

[inland sand]

im listening

could you show me an example

as ive said because my precalc class was a total waste of a semester

[leaden ermine]

ab+bc

this can be factored

b(a+c)

[inland sand]

it doesnt matter if its a - or +?

[leaden ermine]

i mean you just have to compare the terms and find the greatest common term

[leaden ermine]

it doestn

[inland sand]

wouldnt this be lowkey me expanding

[leaden ermine]

what do 72x^8 and 64x^9 have in common

[leaden ermine]

exactly so you are trying to unexpand

[inland sand]

8x^8(1-x)^7

[leaden ermine]

ok.. so you knew it

[inland sand]

its on my white board

[leaden ermine]

i didnt find it

can you highlight

[inland sand]

do you see it now

ok

will do

now thats why i didnt understand what you going on about

yes its factored

[leaden ermine]

oh i am blind asl

now you can roast me all you wnat

[inland sand]

so now i do critical points right

nah i still appreciate you anti

[leaden ermine]

i thought you wanted to factor?

[inland sand]

but this is the factor

[leaden ermine]

this is the factor but thisis not y'

[inland sand]

HEY DONT GASLIT ME

[leaden ermine]

you found the keys to your car nice

[inland sand]

so i find the derivative to this

[leaden ermine]

noooooooooooooo

factor it

[inland sand]

IM SO LOST

stop this madness

[leaden ermine]

ok i will demonstrate what you did

y' = ab+bc

[inland sand]

yes

[leaden ermine]

anti i found the common factor, it's b

now i find critical points of b, so b = 0

you didnt write y' as factors which means

y' = ab+bc = b * (a+c)

b * (a+c)

this you didnt do

[inland sand]

wait so is this what chatgpt was doing

[leaden ermine]

idk and again

forget chatgpt

stop relying on that

[inland sand]

it helps me understand

im not joking

[leaden ermine]

i think it confuses you more

[inland sand]

you also confuse me so

hahahaha

[leaden ermine]

ok..

[inland sand]

ok im trying to understand what you said

let me highlight some shit and ask more

so i did the red pen

but you need me to do the yellow too

because thats the rule

[leaden ermine]

thats not a rule

it's a suggestion coming from the good of my heart

[inland sand]

❤️

[leaden ermine]

so you have an easier time finding the roots

applying the zero product theorem

[inland sand]

ok il do the highlight

WAIT

[leaden ermine]

doing the hightlight means factoring the expression

[inland sand]

NO

i need to do the red

[leaden ermine]

[inland sand]

i dont know where im going

i think its time

just not worth it anti

i did good for the rest

[leaden ermine]

maybe you just tell me the actual objection

you are like giving me mixed signals

[inland sand]

i dont understand what the next step is at all

[leaden ermine]

like i have to admit, very neat work

it's all correct but what are you supposed to do

just send the original task

[inland sand]

I dont know

i just want to do critical points

and set the thing i factoroed to zero

to find those pointd

[leaden ermine]

there you go

go ahead and do that

[inland sand]

but what were you on about

another strategy

?

[leaden ermine]

no

it's the same like last time

[inland sand]

ok let me try that

so just to be sure

8x^8(1-x)^7=0

[leaden ermine]

calculating the derivative -> factoring it nicely -> setting it to 0 -> zero product theorem and so on

[leaden ermine]

so you didnt understand the demonstration

[inland sand]

this is what ive been saying

[leaden ermine]

.

[inland sand]

this is what i dont understand

im lost

[leaden ermine]

i cant make a simpler example

[inland sand]

thats why i said it would be ok to just leave on that note for tonight ;)

we wont go anywhere like this unfortunately

im not trying to just waste your time

[leaden ermine]

what you highlighted is not your y' that's all i am gonna say for now

[inland sand]

il ask my tutor tuesday! this week we are starting concaves which is easy

[leaden ermine]

the thing in the other bracket is what happens when you take away the common factor

[inland sand]

this was my initial question

with the chatgpt

I wanted to know what it was

but alas

gn! george signing out

[leaden ermine]

i understand but i can't and won't try to explain chatgpt stuff

[inland sand]

ya thats ok

[leaden ermine]

most of the time it's just wrong and wastes time

[inland sand]

I respect your values anti

gn!

banana

[leaden ermine]

dont slip

[inland sand]

.close

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[modest yoke]

is the answer R = sqr (44.14^2 +- 215.84^2)
R = 220.31

[modest yoke]

and also how do i find the angle?

[full forum]

@modest yoke Has your question been resolved?

[modest yoke]

<@&286206848099549185>

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@modest yoke Has your question been resolved?

[warm summit]

Which angle are you looking for, and can you show your work that u have so far

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[dense turret]

Can anybody see what the code or cipher rule is?

It is zero index and there are as many secret numbers as letters in the encrypted message

However, there are less in the secret message

[summer fable]

I think it might be skip take

skip by the number, take the next letter

then continue from that position

[full forum]

@dense turret Has your question been resolved?

[dense turret]

Could you explain this? So how would they get h in the decoded message

[flint hull]

idk what the rule is but all i can say is its not getting any new letters its just rearranging some of them in some way

[summer fable]

for that one, skip 7 letters, take the next one (so 7+1 th)
then skip 23 letters, take the next one (7+1+1+23+1 th)
then skip 3 letters, take the next one (7+1+1+23+1+1+3+1 th)

[summer fable]

also, reply to the bot or the channel will close

[summer fable]

oh and it wraps
if it gets to the end, it continues from the beginning

[dense turret]

The 38th letter is _

So the third one should be _

[summer fable]

,calc 7+1+1+23+1+1+3+1

[glossy valve]

Result:

38

[summer fable]

hm

[full forum]

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[versed grove]

can some one explain part c

[versed grove]

i understand part b its just c

the answer to c i is 1260.429kJ

and if it helps answer to part a is 588.2

[umbral dome]

how many servings are there in 60 g of chips?

[versed grove]

2?

[umbral dome]

not exactly

[versed grove]

2.14

[umbral dome]

don't round, just give it as a fraction

[versed grove]

oh okay

15/7

[umbral dome]

ok

so if there is 588.2 kJ in one serving of chips, how many kJ are there in 15/7 servings?

[versed grove]

would we have to do 588.2/x = 15/7

and work it out like that?

[umbral dome]

no

[versed grove]

would it be 15/7 times 588.2

[umbral dome]

yes, if you were to eat 2 servings clearly it would be double the energy. so 15/7 servings is 15/7 times the energy

[versed grove]

oh yesyes

so for part d would you do the same thing

[umbral dome]

yes

[versed grove]

okay

thank u sm !

-close

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[slate meteor]

Assuming i did all my calculations correctly, is this solved in the correct way ?

[gritty flax]

Yes

[slate meteor]

thanks

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[gleaming solstice]

Guys is my solution for this question correct

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[gleaming solstice]

?

[cunning tartan]

bruh

[gleaming solstice]

.reopen

Hii

[cunning tartan]

haiii lol

i was reading and it just disappeared

[gleaming solstice]

I made some mistakes

[cunning tartan]

ahhh i see

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[golden shore]

"A" be 6 times higher than "B".

[gleaming solstice]

A=6b=> b=1/6A

[golden shore]

how can I express it with mathematical terms.

[onyx glen]

A = 6B.

[golden shore]

My tutor took a different interpretation.

[onyx glen]

ok, what did your tutor say?

[whole lily]

"Higher" could mean addition

[latent sonnet]

times means multiplication

[whole lily]

It's not correct linguistical usage though

[golden shore]

he said if you insist on using the word higher than, then it should be difference instead of multiplication.

He also added that I should have said A is 6 times as many as B.

[whole lily]

Lets say I'm 180 cms tall

Friend is "6 higher"

oh wait

I didn't see the times

[latent sonnet]

6 times higher

yeah

[whole lily]

6 times just means it's multiplied 6 times, or by a factor of 6

[golden shore]

Only until now that I realize it is incorrect.

[onyx glen]

so the supposed correct interpretation is that "6 times higher than" is bad phrasing?

[golden shore]

Yes. I'm astounded

I'm still in shock.

I did not notice it is incorrect the whole time

[onyx glen]

this is more about English than math

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[nova wraith]

\begin{align*}
f(x)&=\dfrac{x}{(x^2-1)^{\frac{1}{3}}} \ \
f'(x)&=\frac{(x^2-1)^{\frac{1}{3}}-x \cdot \frac{1}{3} \cdot \frac{1}{(x^2-1)^{\frac{2}{3}}}}{(x^2-1)^{\frac{2}{3}}} \ \
&=\frac{(x^2-1)^{\frac{1}{3}}}{(x^2-1)^{\frac{2}{3}}}-\frac{x}{3} \cdot \frac{1}{(x^2-1)^{\frac{4}{3}}} \ \
&= \frac{1}{(x^2-1)^{\frac{1}{3}}}-\frac{x}{3} \cdot \frac{1}{(x^2-1)^{\frac{4}{3}}} \ \
&= \frac{1}{(x^2-1)^{\frac{1}{3}}}\left(1-\frac{x}{3} \cdot \frac{1}{(x^2-1)}\right) \ \
&= \frac{1}{(x^2-1)^{\frac{1}{3}}}\left(1-\frac{x}{3} \cdot \frac{1}{(x^2-1)}\right) \ \
&= \frac{1}{(x^2-1)^{\frac{1}{3}}}\left(\frac{3x^2-3-x}{3(x^2-1)}\right)
\end{align*}

[glossy valve]

waffle

[nova wraith]

Are there any mistakes so far?

[hoary ember]

i dont see any

[nova wraith]

How do I simplify further?

[hoary ember]

prolly combine so the denom becomes (x^2-1)^4/3

,w differentiate (x)/((x^2-1)^(1/3))

[nova wraith]

$\frac{3x^2-x-3}{3(x^2-1)^{\frac{4}{3}}}$

[glossy valve]

waffle

Results provided by WolframAlpha

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

Requested by skill_issue7119

[hoary ember]

hm

[nova wraith]

What is wrong?

[hot herald]

first step,
didn't apply chain rule for v'

[nova wraith]

Oh yeah

So there would be a 2x which when multiplied with x becomes 2x^2

and that is subtracted from 3x^2 and we're left with x^2-3

Okay

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[analog oracle]

Could anyone explain how they got 3/2 and subsequently the rest of the answer?

[plain fox]

n * (n-1) isn't n²-1

[analog oracle]

Shit I didn't catch that, thanks

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[gilded matrix]

Hi everyone, I want help with sequence and series, mine is weak, how to become pro at it? please help

[hallow gulch]

Fello jee aspirant😭😭😭 i suggest u watch maths unpluggeds theory vid

[gilded matrix]

ok thx

[hallow gulch]

Its in his crash course playlist just watch theory vid

Its nice

[gilded matrix]

btw is it on advanced level or from basic

[hallow gulch]

For series watch his big lecture one

[hallow gulch]

Its just basics to get u started

Not extreamly basics

[gilded matrix]

ok

[hallow gulch]

Series ull have to figureout

Vn method and stuff

[gilded matrix]

thank you sir

[hallow gulch]

Real

[gilded matrix]

broo it's just name

[hallow gulch]

Just sleep and ull get answers

[gilded matrix]

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[whole lily]

It’ll come to you in a dream

Ramanujan core

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[torn jolt]

Can someone help me with this pls

[torn jolt]

#help-28

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

@torn jolt Has your question been resolved?

[torn jolt]

Idk where to begin

#help-28

[narrow path]

similar triangles ratio is same or something

808s

finally lol

[torn jolt]

Huh

🥲im even more confused

[narrow path]

i thought someone was about to get mad i was trolling then actually help

[torn jolt]

😂

#help-28

[narrow path]

10:2x = (x+7.5+5):(x+5)

[torn jolt]

Why.

[narrow path]

the corresponding sides in a similar triangle are always proportional

$\frac{10}{2x} = \frac{x+12.5}{x+5}$

[glossy valve]

Banana Steeler

[narrow path]

essentially you get the quadratic from expanding this out

by cross multiplying

[torn jolt]

Ohhh ok

I got it

Thank u

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[hot crypt]

i havent done math in so long i need help with basics

[hot crypt]

here is a closer image of the graph

[gritty flax]

If you want to find f(x) = 3 for x you need to draw a line y = 3

[hot crypt]

ok

[gritty flax]

Ok and now you see the intersect point.

[hot crypt]

yes

[gritty flax]

You draw a vertical line on it

[hot crypt]

i believe the point they intersect is (3,3)

[gritty flax]

Yes

So the x value is ?

[hot crypt]

3

[gritty flax]

Perfect

[hot crypt]

ok but im a bit confused

[gritty flax]

About what

[hot crypt]

its just where it crosses

?

[void nova]

What's "it"?

[gritty flax]

Its x value where f(x) and y = 3 cross yeah

[hot crypt]

the line

[void nova]

Which line?

You have drawn two lines 😅

[hot crypt]

the horizontal

[void nova]

Horizontal lines are:
y = some number

Vertical lines are:
x = some number

[hot crypt]

ohh ok

i understand

you have time for 1 more question?

[void nova]

So y = 3 is a horizontal line that passes through the number (0, 3) (which of course is on the y-axis)

[gritty flax]

Sure

[void nova]

Yeah sure

[hot crypt]

ive been stuckk

[gritty flax]

What have you tried ?

[hot crypt]

nothing

i dontknow where to start

[gritty flax]

For this just evaluate at bound

And you'll see what happen

[hot crypt]

ok

thanks both of you guys for the help

🫂

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[tired blade]

the values of f''(x) have opposite signs when passing through a root
can someeone explain this to me

[tired blade]

so this means x intercepts of f(x) are inflection points??

i dont think so

[fast peak]

can you give more context?

[full forum]

@tired blade Has your question been resolved?

[tired blade]

this is the original question. i was reading my book's solution and this part just stood out to me

[fast peak]

when you just consider f''(x) on its own, then the values of that have opposite signs on the left and on the right of its roots

cause f''(x) is a parabola

[tired blade]

oh kk i thought it was talking abt f(x)'s roots

thanx

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[dense turret]

Can anybody see the Sypher or code rule from this?

[full forum]

@dense turret Has your question been resolved?

[unique wagon]

have u tried shifting each letter by the index provided in the secret number?

ie m goes to position 7

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[wild sleet]

you get voha_#hmee_rlawGaYeT'shuaNi__
maybe you mean like sequentially, not at the same time

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[torn jolt]

how do I even get started with this

[sweet sky]

recall that a^3+b^3=(a+b)(a^2-ab+b^2)

[gilded matrix]

ya m doing with that only

[lunar veldt]

no way ramanujan is here

[torn jolt]

ok so 14(a^2 - ab + b^2)

[torn jolt]

sum of cubes?

[sweet sky]

yea

[torn jolt]

then a^2 - ab + b^2 = 58

[sweet sky]

yeah looks right

[rapid rain]

you can also use (a+b)^2 or (a-b)^2

[torn jolt]

a - 2ab + b^2 = 58 - ab

[rapid rain]

or that

[torn jolt]

the "that" is where im stuck

[gilded matrix]

it will neeed 2 qeuations

[torn jolt]

im repeating what i did on my work

[gilded matrix]

of a+b and a-b

[rapid rain]

well now that you wrote (a-b)^2 = 58-ab

oh no

you need (a+b)^2

[gilded matrix]

yes

[rapid rain]

because you don't know the value of a-b

so instead

[gilded matrix]

we have to find ab first

[rapid rain]

rewrite this

into (a+b)^2 = ...

[gilded matrix]

is ab =46?

[torn jolt]

a^2 + 2ab + b^2 = 196, or (a + b)^2 = 196??

[rapid rain]

sure

[torn jolt]

i dont know

[rapid rain]

so now use that a^2+2ab + b^2 = 196

[rapid rain]

and this

[torn jolt]

do i make a system?

[rapid rain]

sure, but just use both those equations

to extract the value of ab

[gilded matrix]

I got :- 1. 58=a^2+b^2-ab
2. 196 = a^2 + b^2 +2ab
subtract 1 from 2

[torn jolt]

ab = 138?

[gilded matrix]

?

[torn jolt]

yo im getting somwher

[gilded matrix]

3ab=138

[rapid rain]

2ab - (-ab)

not 2ab - ab

[torn jolt]

mb

oh so ab = 46

now im getting sowher

[rapid rain]

ok so now

either solve a polynomial

or find values for a-b

whichever

[torn jolt]

so now I do (a - b)^2 + 46 = 58?

and solve

[rapid rain]

sure

[gilded matrix]

why am I getting a-b = sqrt(12) ar - sqrt 12

[rapid rain]

because that's it

[gilded matrix]

then the answer is irrational

[rapid rain]

yes

[torn jolt]

2sqrt(3)

is that right

?

[rapid rain]

it's not the only value

[torn jolt]

yeah + o -

[gilded matrix]

yes

[rapid rain]

$a-b = \pm 2\sqrt 3$

[glossy valve]

rafilou is not not born in 2003

[rapid rain]

$a+b = 14$

[glossy valve]

rafilou is not not born in 2003

[gilded matrix]

a = plus minus 21sqrt(3)

[rapid rain]

uh

what

a = 7 pm sqrt(3)

[torn jolt]

I got a = +/- sqrt(3) + 7

[rapid rain]

b = 7 mp sqrt(3)

[gilded matrix]

final answwr is :- a = 7sqrt(12) and b = 7sqrt(12)

from my side

[rapid rain]

why did you multiply instead of adding

[gilded matrix]

what?

[rapid rain]

ok

what operation do you do

[rapid rain]

from here

[rapid rain]

(and here)

[rapid rain]

to here?

[gilded matrix]

added a+b and a-b

[rapid rain]

ok

so (a+b) + (a-b) = ?

[torn jolt]

wait im confused

[gilded matrix]

wait I got it wrong

[torn jolt]

how would I divide +/-sqrt(12) by -2

[rapid rain]

.

[rapid rain]

it becomes -/+

[gilded matrix]

a = 7+sqrt(3)

[torn jolt]

so its still +/-sqrt(3)?

[gilded matrix]

I am not taking minus as a^3 + b^3 is positive

[rapid rain]

nono, -/+ is different from +/-

it's the opposite sign of +/-

[torn jolt]

what

how

[rapid rain]

$$a = 7 \pm \sqrt 3$$
$$b = 7 \mp \sqrt 3$$

[glossy valve]

rafilou is not not born in 2003

[rapid rain]

meaning

if $a = 7 + \sqrt 3$

[glossy valve]

rafilou is not not born in 2003

[rapid rain]

then $b = 7 \mathbf{-} \sqrt 3$

[glossy valve]

rafilou is not not born in 2003

[torn jolt]

ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

very intersting

[gilded matrix]

ok now the answer is :- a = 7+ sqrt(3) and b = 7-sqrt(3)
that's final

[rapid rain]

that's the first possible solution

there are 2

[gilded matrix]

no

are you thinking of minus?

[rapid rain]

i'm thinking that swapping a and b remains a valid answer

[gilded matrix]

oh

[torn jolt]

wait why am I getting -/+sqrt(3) - 7 and not 7 - sqrt(3)

[gilded matrix]

can be

[rapid rain]

it is

[gilded matrix]

but according to question it can't be

IG

[rapid rain]

where is that stated

[gilded matrix]

so you just interchange a+b to b+a

then b-a

[rapid rain]

?

[rapid rain]

it's already explained in this step

[gilded matrix]

nvm

[rapid rain]

from (a-b)^2 = 12

either a-b is negative or positive

[gilded matrix]

a-b is positive

[rapid rain]

why?

[gilded matrix]

you see that a^3 + b^3 is positive

[torn jolt]

just to clarify a = +/-sqrt(3) + 7 and b = -/+sqrt(3) - 7

[rapid rain]

and?

[gilded matrix]

so a-b is positive

[rapid rain]

I still don't get why

[rapid rain]

no it should be + 7 for b

i'm assuming that to get b, you did (a+b) - (a-b)

so 2b = 14 -/+ 2sqrt(3)

or

[torn jolt]

oh

[rapid rain]

by (a-b) - (a+b)

you get -2b = -14 +/- 2sqrt(3)

[gilded matrix]

cubes of positives are positive and cubes of negatives are negative

[rapid rain]

ok, so?

I never said a or b was negative

[torn jolt]

ok I have 2 soltutions then

[rapid rain]

they could both be positive

and a-b < 0

[gilded matrix]

idk but one of the answer is which I gave

[rapid rain]

ok, and you lost marks

because you didn't find all solutions

[torn jolt]

[(sqrt(3) + 7), (-sqrt(3) + 7)] and [(-sqrt(3) + 7), (sqrt(3) + 7)]

I think thats how aops wants it written

[rapid rain]

which is unfortunate because you get the other solution by literally switching a and b

[rapid rain]

I don't know what syntax aops has

but the solution is good

[torn jolt]

ok

Im good for now but I will study this problem further thank you

do I close it now?

[rapid rain]

you can if you think it's resolved

[torn jolt]

.close

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[gilded matrix]

it wasn't written that we have to find all solutions

[shrewd falcon]

@gilded matrix do you need help

[gilded matrix]

nah

.close

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[shrewd falcon]

💀

beefing while not needing help is wild

[torn jolt]

it is lol

all real numbers

such that the system is true

[gilded matrix]

oh

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[worldly cairn]

any idea where i went wrong

i just used 2pi*y*sqrt(1+(dy/dx)^2)

[leaden ermine]

isnt that for x-axis

[shrewd falcon]

shouldn't it just be r(x)

instead of y

[worldly cairn]

oh yeah it is

[worldly cairn]

for this

[worldly cairn]

im not sure

what that means

[shrewd falcon]

try to graph the function

you are rotating it around y-axis

would your radius necessarily be 4+sin(x)?

[leaden ermine]

,, \int 2\pi x \sqrt{1+\left ( \d{y}{x}{1} \right)^2} , dx

[leaden ermine]

looks ugly

[worldly cairn]

ohhh

it makes sense

thanks

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[full forum]

@stoic salmon Has your question been resolved?

[shrewd falcon]

try to create an infinite product

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[torn jolt]

How do I calculate the surface area of this pyramid

[alpine pecan]

4 triangles + rectangle

[shrewd falcon]

surface area of each face

you know how to calculate slant height?

[torn jolt]

Area =1/2 b and h

Do I have to use pythagoras?

[shrewd falcon]

slant height

[shrewd falcon]

Yes

[torn jolt]

I tried to donthat

[alpine pecan]

thers a formula for slant height

[torn jolt]

Is it square root 5²+1.5²

[shrewd falcon]

good!

[ebon fulcrum]

For the longer side yes

[torn jolt]

The answer i got is 5.220

1/2 and b and h

1/2 × 3 × 5.220

=7.83

Now what do I have to do?

[shrewd falcon]

there will be 2 of those triangles

and 2 other triangles

[torn jolt]

Oh so for the other two triangle do i have to again seperately do pythagoras using 3 this time?

Like

Square rt 5²+3²

I got 3 from 6÷2

[shrewd falcon]

Yes

[alpine pecan]

isnt the formula this?

[shrewd falcon]

that is just intuitive from pythag

no need for a formula

[torn jolt]

Im still not getting the answer for some reason

[alpine pecan]

oh ye lol mbmb

[torn jolt]

Its supposed to be 66.8

But im not getting that

[alpine pecan]

ig u forgot abt the rectangl

[torn jolt]

Nope i added that

[shrewd falcon]

sus

ahhhh

hehe

[torn jolt]

Wait ill send the working

[shrewd falcon]

it should be 1/2*6, the base is 6 for this

[torn jolt]

Why 6?

In that the base is 3 noh

[shrewd falcon]

look at which slant we calculated

[torn jolt]

Ohh

Oki lemme try that

[ebon fulcrum]

And I think this would only work for a square base since the catheter is equal to half the base side length, allowing the 1/4*b^2

[shrewd falcon]

no

(clearly we have a rectangle in here and we can cut it in half)

[ebon fulcrum]

That’s true

But for other cases where the catheter is not equal to half the base side length

[shrewd falcon]

of course

you just went a tad bit specific so the argument is not 100% correct

[ebon fulcrum]

Indeed

[ebon fulcrum]

Just wanted to get the general idea across hh

[torn jolt]

Hopefully its clear

I didnt but any units cus i was in a rush ill put them when i get the answer

When i added all of them i got 66.6

It should be 66.8

I thought it was something wrong witb my rounding

But is my one correct ?

[ebon fulcrum]

This seems good to me

[ebon fulcrum]

Likely because you didn’t keep the exact square root values until the end

[torn jolt]

Then must be something with my rounding

[torn jolt]

Ohh

[ebon fulcrum]

And multiplying by values bigger than 1 should amplify the effect

[torn jolt]

Ohh ok

[ebon fulcrum]

But rounding aside what you did seems to be good

[torn jolt]

Oo oki thanks

[ebon fulcrum]

😄

[torn jolt]

Oki thank uuuuu so muchhh have a nice day

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[hidden bane]

Does the integral look right?

[hidden bane]

.close

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[flint hull]

yes its right

[hidden bane]

lol ty, stared at it for a while and I convinced myself it's right too

[flint hull]

lmao yeah dont doubt yourself, be confident in your answers

but also good to double check

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[stuck fiber]

I thought I got pretty far but maybe I was doing it all wrong

The derivative of ln(ax) is 1/x

We know that line l_a goes through (0, 4) and (x, 0)

And it is perpendicular to the tangent of f_a so the slope must be -x

Using the slope equation or whatever its called we can sub in all of these into (y1 - y2) = m(x1 - x2)

(0 - 4) = (-x)(x - 0)

-4 = -x^2

x = +-2

How come theres 2 values for x?

Ah wait

Cause -2 isnt a solution

So we have ln(2a)

Im not really sure what we do next though?

<@&286206848099549185>

WAIT

I think I just got it

y = ln(ax)

0 = ln(2a)

e^0 = 2a

a = 1/2

Right?

Yeye its right 😄

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[stone mortar]

Evaluate ∬S A ⋅ n dS, where
A = (x + y²) î - 2x ĵ + 2y² k̂
and S is the surface of the plane
2x + y + 2z = 6 in the first octant.

[stone mortar]

not urgent

take your time

<@&286206848099549185>

why helping everyone but me

its just basic integration

[spiral vigil]

ugh

find n

it's a vector normal to that plane

then find A . n

then integrate it

[stone mortar]

hmmm

yes i dont know double integration

but i'll do it somehow

how to find n

is the real question here, i guess

<@&286206848099549185>

not really

dont do this to me

[stone mortar]

[spiral vigil]

this is an example

it usually means that they've just explained it to you

or even that they're about to do it in front of you

[stone mortar]

thats not the answer to my question

[slow field]

It's an example, usually they'll give you the answer anyway.

[stone mortar]

no i have the answer but i dont know why is that the answer

thats why im asking for help, technically

[slow field]

So, they gave you the answer, and you weren't listening to how they got it. And now you're asking why it's the answer.

[stone mortar]

exactly

the answer to the question is 81

And when I see this:
Evaluate ∬S A ⋅ n dS, where
A = (x + y²) î - 2x ĵ + 2y² k̂
and S is the surface of the plane
2x + y + 2z = 6 in the first octant.

I dont see 81

<@&286206848099549185>

[slow field]

All I see when I see that is some vectors and a double integral. Can't help you, sorry...

Also.

!15m

[full forum]

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

[slow field]

!vol

[full forum]

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

[stone mortar]

!vol

[full forum]

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

[stone mortar]

!15m

[full forum]

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

[stone mortar]

!15m

[full forum]

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

[stone mortar]

!15m

[full forum]

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

[stone mortar]

!vol

[full forum]

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

[stone mortar]

wow

cool