help-26

[weak needle]

just want to confirm

does (a/b)^(x/y) = x(a/b)^(1/y)?

my algebra is kinda rusty

[whole geode]

No

[weak needle]

can you explain how we arrive h then ;_;

[whole geode]

The reason why the last transformation is true is because 2*(2)^(-1/3) = 2^(2/3)

\begin{align*}
\frac{V_0}{\pi} {\qty(\frac{2\pi}{V_0})}^{2/3} &= \frac{V_0^{3/3}}{\pi^{3/3}} \qty(\frac{2^{2/3} \pi^{2/3}}{V_0^{2/3}}) \
&= \frac{V_0^{3/3}2^{2/3} \pi^{2/3}}{\pi^{3/3}V_0^{2/3}} \
&= \frac{V_0^{1/3}2^{2/3}}{\pi^{1/3}} \
&= \frac{V_0^{1/3}2^{3/3}}{2^{1/3}\pi^{1/3}} \
&= 2 \frac{V_0^{1/3}}{2^{1/3}\pi^{1/3}} \
&=2 \sqrt[3]{\frac{V_0}{2\pi}} \
\end{align*}

[thorny flame]

OmnipotentEntity

[whole geode]

@weak needle this is as explicit as I can make it

[weak needle]

thank you man

im kinda slow so let me think about it for a sec

appreciate it 😄

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[unique dew]

How do i do problem #17?

My work

The answer should be 10root2 pi over 3

[fickle kiln]

whered you get 1/sqrt2

[unique dew]

Setting y^2=to 1-y^2

[fickle kiln]

is that your drawing of the graph?

[unique dew]

Yeah

[fickle kiln]

oooh ok

let me see

did you get 2-y^2 from 3-(1-y^2)

2pi ∫0-1/sqrt2 (3-y^2)^2 - (3-(1-y^2))^2 dy

[fickle kiln]

did you combine the 2? it looks like you did

[unique dew]

Yes

[fickle kiln]

i would keep it seperate though?

are you cmobining the squares?

[unique dew]

A1-A2

[unique dew]

Ooo

I see

I think thats where it went wrong

[fickle kiln]

you also did erorr for sum

yeah

i personally would keep it like this

[unique dew]

Yeah

[fickle kiln]

with the pi outside of integral

[fickle kiln]

wait but did you teacher say you can combine the squares?

[unique dew]

Wym?

[fickle kiln]

like the 5-2y^2

where did that come from

[unique dew]

Yeah i combined the squares

[unique dew]

I’m doing self study right now so i got it from khan academy

[fickle kiln]

prettty sure you cant do that

[unique dew]

Really?

[fickle kiln]

wait idk

oh wait maybe you can

sorry i was just never taught that way

are you taking calc rn

?

[unique dew]

Yeah

[fickle kiln]

ap test?

[unique dew]

Calc ab

[unique dew]

Yeah

[fickle kiln]

i mean, ap test , you usualyl get to use calc

but ig this is good practice

did you get the correct answer

[unique dew]

Havent tried yet

[fickle kiln]

ok

[unique dew]

Lemme try it rn

[fickle kiln]

sorry if this is wrong, i havent done this in some time, but when you do A1-A2, aren't they different bases with the same exponent, so you cant directly subtract them?

[unique dew]

Wdym different bases with the same exponent?

A1 is the area of the outer disc and A2 inner disc

[fickle kiln]

did you get (3-y^2)^2 and (1+y^2)^2 ?

[unique dew]

I thought washer method is the outer disc subtracting inner?

[unique dew]

For my areas?

[fickle kiln]

yeah

[fickle kiln]

yeah

but it looks like, from your work, you are directly subtracting the bases

[unique dew]

From how i got 5-y^2?

[fickle kiln]

yeah how did you get that?

[unique dew]

(3-y^2)^2= 9-6y^2+y^4

(2-y^2)^2=4-4y^2+y^4

[fickle kiln]

oh i see

mb

[unique dew]

Ye

[fickle kiln]

i didn't see any work and i just assumed you just subtracted

[unique dew]

Yeah i did most of the work on another sheet of paper

But when i asked my friend for help they couldn’t understand anything

So i just moved it to a new sheet

[fickle kiln]

lol mb, i think you just haad the sum error. you should get correct answer now

[fickle kiln]

ye

[unique dew]

Ty

[fickle kiln]

yw

watch out during the test though

[unique dew]

Good eye on spotting the error

[unique dew]

Gotcha

[fickle kiln]

thats the worst mistake

like double check is what i would do

[unique dew]

Ye thanks for the advice

[unique dew]

Wait

For the square

Even when i keep it separated

Ooo

Nvm

Got it

[fickle kiln]

nice

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[shut violet]

Hey guys, just really unsure how to add vectors could someone help me out?

[shut violet]

For example, when drawing the horizontal and vertical components do I start with the horizontal or vertical?

Take for example the resultant vector:

[sonic dawn]

same thing, doesn’t matter

[shut violet]

Would the horizontal and vertical components be represented like the drawing on the left, or the drawing on the right?

[shut violet]

Really?

[sonic dawn]

if you overlap the “base” of two vectors and they exactly overlap they’re the same vector

[shut violet]

So for this problem, how would I draw the components of P?

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[noble laurel]

I've proven this is a homomorphism from G to G already

and that it is surjective

but, I'm caught up on the injectivity part

if f(a^i)=f(a^j)
then
b^i=b^j
b^(i-j)=e
=> i-j congruent to 0 mod |b|
... ?

Not sure how this can imply anything about a^i=a^j

[pseudo jetty]

what is the order of a

[noble laurel]

oh right |a|=|b|
so i-j congruent to mod |a| aswell
so
a^(i-j)=e
a^i=a^j

[pseudo jetty]

yeah

[noble laurel]

brain poop

thanks

[pseudo jetty]

boop

[noble laurel]

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[noble laurel]

.reopen

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✅

[noble laurel]

Actually, wanted to ask if this checks out then

the rest I think is fine

[pseudo jetty]

uh yeah that's all correct

[noble laurel]

Okay, thanks for looking it over I appreciate it

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[wraith night]

can someone tell me if im doing this right?

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Please don't occupy multiple help channels.

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@wraith night Has your question been resolved?

[restive inlet]

missing du in the first line

$\eval_{5x}^{7x}$ shouldn't be there in the second

[thorny flame]

ℝαμΩℕωⅤ

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[gusty cobalt]

how do i answer this?

im not to sure where to start

for the intial velocity would i make the u1 and u2?

the the final for one of them being v1?

[lost goblet]

1-(8/u^2+4) is simplified version of the func inside integral

[gusty cobalt]

? is that for this question

wrong channel

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[lusty cedar]

wait nvm thats definitely a mark scheme error

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[atomic wadi]

marking scheme is coorrect tho

[lusty cedar]

how did the three indicie become a negative?

oh shit

fuckkkkkk

jiewifewhiofhehuwosf

[atomic wadi]

its at the bottom

[lusty cedar]

yeah

thanks

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[drowsy oasis]

,rotate

[drowsy oasis]

part b of question 3

[mellow arrow]

Chig Bicken

[drowsy oasis]

yh

[worthy storm]

what is your doubt?

[drowsy oasis]

no clue what to do

do i try to find cdf or?

[worthy storm]

try finding the mean in terms of k, a and b

[drowsy oasis]

do i do definite intergral or indefinite integral

[worthy storm]

mean (expected value) is a definite integral

[drowsy oasis]

ok

i get two answers for b tho

nvm

what about for part c

[worthy storm]

what did you get for (b)

[drowsy oasis]

0

idk waht to do for a

god i hate stats

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[plush raptor]

Does anyone have a good, concise definition for a function and a relation?

[hollow oracle]

in two sets X,Y a function maps X to exactly on value in Y
set X defines the domain, set Y defines the codomain

[plush raptor]

Hmmm, maybe a bit more simpler for Year 12 High School level

<@&286206848099549185>

[normal tapir]

functions are a specific type of relation. a relation maps elements from set A to set B is just any subset of the cartesian product A x B

a function is a relation with the additional property that if a is in relation with b, then a is not in relation with any other element in B

this is the generalization of the vertical line test that is usually taught in algebra

[plush raptor]

do you think I could use this when doing an investigation of designing a motor sports race track using a graphing application using functions and relations?

[normal tapir]

use this
use what

[plush raptor]

your defintions

do you think it would be applicable or appropriate to use in that context

[normal tapir]

i mena

it depends on alot

but im sure there exists an application

[plush raptor]

Im not sure if talking about set a and set b is applicable to talking about graphs and derivatives etc...

[normal tapir]

if that were the case the the foundation of almost every branch of math would be gone

idk what you're trying to do exactly but your approach just seems naive

[plush raptor]

yeah cos your definitions like a uni level or smth

like it seems a bit excessive

never mind Ill figure it out

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[cyan talon]

Any shortcut for this

<@&286206848099549185>

[ivory sorrel]

yes, use a u-sub

[jade thunder]

You can fiddle with the top

But that’s probably not a shortcut

[cyan talon]

I got it with the lengthy method

the Ax+B one

[cyan talon]

nope substitution didn't work

[ebon flume]

maybe completing the square might work?

in the denominator

[cyan talon]

let me try

thanks

[misty pollen]

Hey there can I be of any help here? Ping me if I can!

[cyan talon]

sure.. @misty pollen

[misty pollen]

Alright, how can I help

[cyan talon]

Any shortcut for this question other than Ax+B method

[ebon flume]

did it not work

[unborn kiln]

Use u sub after completing the square lol

[ebon flume]

completing the square

[misty pollen]

Use completing the squares of qf in denominator

Or*

[cyan talon]

Yeah I'm trying to to that

[cyan talon]

didn't work

[unborn kiln]

Show work?

[cyan talon]

wait a sec

2(x+3/2)^2 +1/2 is what u get after completing square

What u gonna substitute here

[ebon flume]

you want smth in the form x^2 + a^2 in the denominator

cuz that way you can use the arctan formula

so to get that you wanna take x + 3/2 to be u

[unborn kiln]

You can let u = x + 3/2

[ebon flume]

and then factoring a 2 out in the denominator gives this form

[cyan talon]

I got 2(u-1/2)/4u²+1 after that

[ebon flume]

uh you don't want a coefficient on u^2

[cyan talon]

yeah I'll simplify it

if someone gets this as the answer by any shortcut pls send the solution

[ebon flume]

did you simplify

[cyan talon]

yes but I don't see anything working

[ebon flume]

what did you get

after factoring a 4 out

[cyan talon]

one sec I'll send u where I've got to

u-1/2/2u(u+1/4u)

[ebon flume]

wait no no no

I meant

in the denominator

factor a 4 out

so that you have a coefficient of 1 on u^2

[cyan talon]

ok

4(u²+1/4)

in denominator

[ebon flume]

wait

in the numerator

shouldn't it be u + 1/2

[cyan talon]

2(u-1/2)

[ebon flume]

cuz you took u = x + 3/2

and the numerator was x + 2

so u + 1/2 is x + 2

[cyan talon]

so dx=du

[ebon flume]

yep

that's the convenient part

after the substitution you should have this

not 1/4 mb 1/2

[cyan talon]

yes

I got that

[ebon flume]

wait huh

no I just copied what you wrote lol

lemme complete the square

kk its right

[cyan talon]

yeah

[ebon flume]

so from here

you have the correct form in the denominator

all I did was factor out a 2 in the denominator and take it outside the integral

[cyan talon]

yeah now I'll use the form and see what I get

Thanks

[ebon flume]

split the fraction

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[neon iron]

Any mistake?

[cursive mango]

Looks good

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[summer crown]

help

[ivory sorrel]

find the sum and product ot the roots

[summer crown]

yea i just need verification

[prisma mesa]

The way the question is phrased is strange though. "are of the form a-b, a+b". Any 2 real numbers can be written in this form

[fair thorn]

^^

i think what they mean

like

how do i explain this

*thinks*

[prisma mesa]

I wouldn't overthnink this. Just find the solution using any way it's comfortable for you

[prisma mesa]

do you already have the solutions?

if so, i can verify them

[summer crown]

kinda

[restive inlet]

think they mean a+bi, a-bi

where a,b are real

[summer crown]

a = 1 , b =root -5/3

[prisma mesa]

that would make far more sense

[cursive patrol]

either way it's a redundant comment

so w/e

[prisma mesa]

thats correct, id write b as $b = \sqrt{\frac{5}{3}} i$ tho if you were already taught complex numbers

[thorny flame]

MethIsAlwaysRight

[summer crown]

so what is the answer?

[viscid mulch]

uttam darje kii guchchii kalaaii lapeṭ keval achchhe vaaibs ke saath chudaaii oh nitin mujhe tumhaaraa cheharaa dekhanaa chaahie oh nitin mujhe tumhaaraa cheharaa dekhanaa chaahie

[summer crown]

okok

thanks

.close

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[prisma mesa]

the answer would be the 2 solutions corresponding to a+b and a-b

as they are asking for the zeroes

[strong oyster]

I'm a farmer and im looking to purchase germinating mix to fill 200 seed trays and would like to know how many bags of mix i should buy. Each of the trays have 50 holes that are 2inchx2inch. The bags are 55lbs. Is there any way that you could help to give me a close estimate?

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[inland flax]

Hello, I have a probability-related problem

[neon iron]

Has the first one closed the channel?

[strong oyster]

Im in my channel bro

you can go in there

[neon iron]

Where is yours?

[strong oyster]

help 7

[neon iron]

Okay.

[inland flax]

My concern is the probability that needs to be calculated. From what I understand, i need to calc the Pr that exactly 2 accidents occur from july until November, however, my friends suggest that I need to compute for the Pr that 2 accidents occur for each month. What is the correct approach?

<@&286206848099549185>

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@inland flax Has your question been resolved?

[inland flax]

<@&286206848099549185>

[unborn kiln]

You can divide into 2 parts

July-August with mean 1 each and september-november with 0.5 mean each

[inland flax]

do i add them or multiply?

[unborn kiln]

Well both are involved

For each way to get 2 accidents within the 2 diff ranges you multiply them then sum for total prob

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[zenith gate]

How can I show that if U is a harmonic function and V and W are both harmonic conjugates of U, then V and W differ only by a constant?

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[zenith gate]

.close

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[crude merlin]

Could anyone help me with inequalities? and some test tips?

[neon iron]

do you have any specific problems

or example problems

[crude merlin]

for inequalities its mainly the part where u place it into those number line things. for example 6x+ 5>6 i can do that until i have to figure out which number line thing

[neon iron]

well solve it for x

[crude merlin]

yes i can do that part! i struggle trying to place it on number lines. with open and closed circles and which way it shouuld go

[keen venture]

In this case, there's no such step

Are you struggling with quadratic inequalities?

[crude merlin]

uhh whats the difference?

just searched it up- i can do the equation i just dont get the < > and the other ones with lines on it. especially when it comes to marking it on lines or word problems

[keen venture]

6x + 5 > 6

6x > 1

x > 1/6

Do those steps make sense?

[crude merlin]

yeah but how would u graph it on a number line????

[keen venture]

Oh. You'd put an open dot at 1/6, then an arrow on everything to the right.

Open, because 1/6 is not included in x > 1/6

[crude merlin]

ohh wait so if it was > with a line uhh greater then or equal to i think its called. would that be the closed dot?

[neon iron]

sorry i was busy

[crude merlin]

its fine!!

[neon iron]

if its ___ or equal to, its closed

cuz it can be that spot as well

but if its js ___

it cant be that number where the dot is at

itd be an open dot

= and <= is closed, < and > is open

[crude merlin]

oh. in word context < this would be greater then, >this is less then. and >=is lesser or equal and <= iis greater or equal? just checking- i kept getting the word problems wrong due to this

[neon iron]

yeah so

u got them mixed

remember

where it open to

like i learned it as an alligator

its always gonna go for the bigger food

so 9 is greater than 7

9>7

9 is less than 7

9<7

and u js add the equal to if there is =

[neon iron]

but the alligator is gonna eat the bigger number, see

[crude merlin]

yeah! i think im getting it!

[neon iron]

correction

9 is NOT less than 7

5 is less than 9

5<7

[crude merlin]

thanks for the help! would u have any test taking strats? i have a big test coming up so im trying to rush and reveiw everything-

[neon iron]

hmmm

js solve the problem for x

if its equal to, closed dot

that means its including that number

and the arrow goes in the direction of the great than sign

so if its x>9

that means x can equal 10, 11, 12, 13, etc

so itd go in that direction

[neon iron]

but that means x cannot equal 9

so no closed dot

and js rememer the alligator for the signs

[crude merlin]

yeah! ill def try

[neon iron]

yep, if u wanna try a few example problems, up to you, otherwise, thats my main tips

[crude merlin]

would u have any math test strats for the whole of math? the big test is going over every seventh grade standard and a little of eighth grade (im in math honors)

[neon iron]

hmmmm

well its been about 7-8 yrs since i took that math

ik it all but

idk whats in that specific section

[crude merlin]

its mainly the start of algebra i feel like i get it. but i have a huge problem with overthinking. my teachers say i dissect the problem too much to the point it doesnt make sense lol

[neon iron]

i like to visualize it, helps me

but always remember to stick to the basic formulas and stuff

understanding the problem is good but can lead to too many questions, that you will understand like 5 yrs later the answer to, but doesnt matter in that grade

just read the question, and do exactly what it says

[crude merlin]

ok ill try- ohh quick question how in the world do u do percentages? like 15% markup or decreased by 5% tax rate percents. im bad at percents-

[neon iron]

ohhh

just remember

its affecting the orginal number by that much

theres 2 ways u can go about it

so like for example 15 percent markup

that means it goes up by 15% of the original price

so the original price + 15% of the original price

making 115% correct?

[crude merlin]

and u got 100 from percentages usually going to 100 right?

[neon iron]

well the original price would be 100%

and 15% of it is 15%

you add the 2 together

to get hte original price, plus, how much its marked up by

[crude merlin]

so if u had the original price of 78 dollars marked up by 15 u would add 15 to 100- 115% and then times it by original price?

[neon iron]

you would do

78 + 78*0.15

or 78*1.15

making 1.15x the original price

115%

[crude merlin]

why would u add 78 with itself?

[neon iron]

cuz its going up by 15% of the original

so its adding 15% of it to itself

[crude merlin]

uh so wouldnt it be easier to times it with 15% then add it to 78?

[neon iron]

thats

what i did

[neon iron]

pemdas

78+(78*0.15)

[crude merlin]

ohhh

that makes sense!! if u were to do taxs would it be similar? like ur taxed 6 percent

[neon iron]

yep

exact same

and if it was a discont or markdown or sm

js subtract instead of add

or u could of it as like

if its a 5% mark down

theres 95% left

so multiply by 0.95

[neon iron]

like 6% tax, js do 78+(78*0.06)

[crude merlin]

so whatever the markdown/discount is subtract the opposite? 12% is the mark down then subtract 88%?

[neon iron]

no

if u dont wanna subtract

like 5% markdown on 78

then either do

78-(78*0.05)

or js

78*0.95

either one

cuz if u had 100

taking away 5%

would leave u with 95%

so u either subtract 5%

or u js find the leftover

[crude merlin]

oohhh thanks for the help!!

[neon iron]

yep

anything else?

[crude merlin]

uhh i think thats it!!

thank u very much!!!

[neon iron]

could u rate my help from 0-10 rq

[crude merlin]

full 10!

[neon iron]

tyty

much appreciated

[crude merlin]

u would make an awesome teacher! ur welcome

wait how did i close this again?

[neon iron]

.close

[crude merlin]

thanks.
.close

[neon iron]

..

[crude merlin]

did it work?

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[rotund ingot]

Gentlemen, this is important to me, so please give me REAL information:
are the numbers 1- "1" and any number prime numbers Decoupled BETWEEN THEM?
2- is the number "1" and the number "1" the prime number Decoupled BETWEEN THEM?
3- Can prime numbers be negative?
4- Can the numbers with Decals BETWEEN them be negative?

[odd pagoda]

prime numbers are usually defined to be positive

I dont know what you mean by your other three questions

[rotund ingot]

what? did i miss translate

i was talking about "coprime numbers" "relatively prime numbers" "decoupled between prime numbers"

[smoky sinew]

What is decoupled

[rotund ingot]

isnt that three goes to same?

[smoky sinew]

First 2 are the same

Decoupuled isnt

Idk what that is

[rotund ingot]

sorry its miss translate then

[smoky sinew]

Anyways 1 isnt prime

[rotund ingot]

well what about the coprime numbers? i was trying to talk about it with that 3 question

[rotund ingot]

it doesnt matter is the number prime or not when it comes to coprime numbers

[smoky sinew]

So you are saying “are any numbers coprime with 1”

[rotund ingot]

yeah

[smoky sinew]

All of them are

Since gcf(1,n)=1

Mistyped sry

[rotund ingot]

so what about 1 and 1? are they coprime in each other 2?

[smoky sinew]

Yea 1 is coprime with 2

Since gcf(1,2)=1

[rotund ingot]

no i used 2 as "too"

1 and 1

i ask

[smoky sinew]

Oh

Yeah

[rotund ingot]

gcf(1,1)

[smoky sinew]

=1

So they are coprime

[rotund ingot]

hm oky oky

what about negative numbers in being coprime?

-2 and 3?

i know there is a limit in being prime of being positive numbers

is coprime too

[smoky sinew]

Negative numbers dont have a well defined concept of greatest factor really

So negatives cant be coprime

[rotund ingot]

oky dude thanks a lot have a nice day

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[left torrent]

I'm not really sure what this is asking me for

[rigid nimbus]

It is asking you to find the coefficient of du in that equation

If you know that du = 3x² dx, then what is x² dx?

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[thorny flame]

Ransik

[gritty birch]

looks good

[thorny flame]

Ransik

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[nimble vault]

did I mess up here

my other friend got 728/15

but im pretty sure i just did the formula

i see my mistake

[snow timber]

I dont think it should be 3t^3 there @nimble vault

[nimble vault]

sorry!

yup

that is correct

[snow timber]

Yep happens

[nimble vault]

thanks

so much

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[snow timber]

Np

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[heady pike]

Hey y’all , I was just wanting to check my answer for 1, I got pi/2 but I’m not sure if it’s correct or not, I got 0 for An and Bn

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@heady pike Has your question been resolved?

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@heady pike Has your question been resolved?

[radiant marlin]

the sine coefficients shouldn't be zero

[heady pike]

hmm, I tried a second time and got 2/n but that seems also wrong for Bn

[radiant marlin]

2/n is right

er it is for half of the n's

you get like sin(npi/2)^2 with something in front

and that sin^2 goes between 0 and 1

[heady pike]

I thought that the sin term would just be summation of Bn times sin((n pi t)/L?

[radiant marlin]

I mean for the coefficient Bn

it should've integrated to 2/n*sin(npi/2)^2 which is 2/n for odd n

[heady pike]

I didn’t get the exact thing but just overall still got 2/n

Ohhh ok I think I see what to do

I think I forgot to specify for odd values of n in that case

So then this looks like it matches on the graph to the conditions

[radiant marlin]

👍 ok good

[radiant marlin]

repost this in an unnamed channel above like #help-33

[stoic yacht]

Mb

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[lusty quest]

Help please

[keen venture]

Round your answer to 4 decimal places

But how did you get that answer?

[lusty quest]

Maybe I did it wrong

[empty niche]

-0.2084

remember the property: log(a/b)=loga-logb if all have the same base

[lusty quest]

This is correct

How did you get this number?

[empty niche]

check the next mesage

[empty niche]

this one

so if you let a=2 and b=3

you only have to substract the values that the problem gives you

log2-log3

(base b)

you got it?

[lusty quest]

A little

[empty niche]

check this

this is the logaritm property you have to use in this problem

[lusty quest]

So log(2):0.30120 : log(3): 0.47712?

[empty niche]

and the information already gives you the value of both logaritms you have to substract

exactly

[lusty quest]

I got -0.1761

[empty niche]

wait

the othe logaritm

logb(3) is 0.5646

the problem gives you the values

chek it again

[lusty quest]

Ah okay

Thank you

I got it

[empty niche]

yep

you have been calculating the logaritm base 10 in the calculator

but the base in this problem is b

[lusty quest]

Ok

[empty niche]

and they already gives you the result

[lusty quest]

👍

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[radiant marlin]

try writing out the inequality a+b+c+d+e<? adjusted so that each variable is greater than or equal to 0, then you can apply stars and bars

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[raw nacelle]

hello

[earnest pine]

wassup??

[raw nacelle]

can you help me

on a math question

[earnest pine]

yeah, sure. but close your other channel first

[earnest pine]

just type .close in the other channel above this one

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[raw nacelle]

no

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[thorn niche]

is this 1/1/(1-1(x+y)) or 1/((1-1/(x+y)))/1

[restive inlet]

the latter

[thorn niche]

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[deep crow]

How do i integrate this?

[slate valve]

trig sub

in this form you should substitute with tangent

[deep crow]

i thought trig sub only worked with sqrt on the bottom

[slate valve]

take the 2 out, and substitute

[slate valve]

nope,

try sub x=(sqrt3)tanθ

[deep crow]

Is this the case for all of them?

or is this more circumstantial

[slate valve]

if you see x^2+a^2 then you should substitute with tangent

a^2-x^2 then sine

x^2-a^2 then secant

a is a constant

[deep crow]

Thanks

[slate valve]

👍

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[maiden elk]

on that second last line, the first term is $\frac{(10-x_1)!}{x_2!(10-x_1-x_2)!}$. im failing to understand how we got there from the line before though, what am i missing?

[thorny flame]

hhhapz

[maiden elk]

oh, it just goes there from the denominator, duh

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[neon iron]

I don't understand why I keep getting these problems wrong

the answer I'm getting is incorrect

even though the procedure seems alright

[blazing siren]

angle QPR = 142 means that P over there is 142

[neon iron]

how come?

[restive inlet]

notation

<QPR refers to the smaller angle formed between the segments

[half edge]

trace the path of ur hand as you go from point Q to point P to point R

[restive inlet]

QP and PR

[neon iron]

so the middle thing is the letter that posesses the angle?

[half edge]

the angle it makes is the angle u want

[neon iron]

ok I'll try that

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[mild badge]

May i know how to solve this?

[normal tapir]

solve for C in the equation ACA^-1 = B

[mild badge]

yea but how do I go around this with the matrices?

<@&286206848099549185>

[radiant tapir]

Use inverse matrix rules:

Just remember that matrix multiplication is not commutative. So $AB \neq BA$

[thorny flame]

MellowDramaLlama

[radiant tapir]

aka, keep track of which side you're multiplying stuff

[mild badge]

alright

I'll try it out

[radiant tapir]

any luck?

[mild badge]

Nope

How do i go about this?

[radiant tapir]

Ok so do you know what A^-1 is?

can you figure that out and let me know what you get?

[mild badge]

Okay

[radiant tapir]

ok very good

So the first step is that we need to isolate C by itself, and we can do so like this

[mild badge]

alright

[radiant tapir]

$ACA^{-1} = B\\$
$ACA^{-1}A = BA\\$
$ACI = BA\\$
$AC = BA$

[thorny flame]

MellowDramaLlama

[radiant tapir]

Note I just used the rules here

[mild badge]

Ohhh thanks

[radiant tapir]

So can you do the A in front of the C? 🙂

same logic applies

[mild badge]

Thank you very much, i,ll try it out

[radiant tapir]

soudns good. I'm here if you need help or get stuck

[mild badge]

Thank you

Is this how i go about?

[radiant tapir]

Yep bingo!

oh wait

it's supposed to be A^{-1}BA not A^{-1}BC

we're trying to solve for C 🙂

So just multiply out A^{-1}BA and that's C !

[mild badge]

oh wait

Thank you

[radiant tapir]

yep np!

[mild badge]

Is this how it is solved?

[radiant tapir]

sorry I got distracted

one moment

[mild badge]

Alright

[radiant tapir]

I gotta head out but check your math again. Start off by doing (A^{-1}B)A then do the rest

good luck!

[mild badge]

Alright thank you!!

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[toxic stirrup]

i need to find the remainder of the third taylor polynomial, but for that i need to find the max value of xln(x)

[toxic stirrup]

but im not sure how to find it

[outer portal]

youre finding the max value of x ln x when 1 ≤ x ≤ 2

have youtaken the derivative of x ln x yet

[toxic stirrup]

yes

its ln(x)+1

[outer portal]

yep

when is the derivative 0

[toxic stirrup]

never

[outer portal]

the derivative is 0 when x = 1/e, which is outside of 1 ≤ x ≤ 2

"never" is a misleading answer

so since the derivative is never 0 in the interval [1, 2], what do you do next

it has to do with endpoints

[toxic stirrup]

oh

we find their values

[outer portal]

yep

[toxic stirrup]

into the original function right?

[outer portal]

yep

whichever one is bigger will be the max youre looking for

[toxic stirrup]

2 is bigger

2ln(2)>ln(1)

[outer portal]

yep

so 2 ln 2 is your max

[toxic stirrup]

oh

but why specifically from 1 to 2?

[outer portal]

review your class material

your taylor series is at x = 1, and youre approximating f(2)

[toxic stirrup]

right

thank you for your help!

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[rose bough]

can someone please explain to me why you're not supposed to multiply 5 by 3 but later you do multiply it by 12?

[rose bough]

here's the full image

[tawny crescent]

lemme read rq

[blazing siren]

you get the x on one side first

[tawny crescent]

^^

[rose bough]

what makes more sense to me is to first do x/3 = (5-(7-2x))/4

and then multiply the left side by 4 and the right by 3

why is that wrong

I just don't really get how it makes sense to ignore the 5 and only multiply the fraction

but later suddenly not ignoring the 5 and multiplying the whole thing by 12

???

[topaz sinew]

@rose bough Has your question been resolved?

[rose bough]

<@&286206848099549185>

[honest ember]

what exactly is your question?

[next nimbus]

yeah true

[next nimbus]

you cant do that. you have to multiply both sides by the same thing. otherwise its not an equation anymore

[honest ember]

see to solve this or any equation
we need to simplify it
instead of complicating it

so if it is linear equation

take x one same side

take lcm if needed

[next nimbus]

i dont think he understands that

[honest ember]

I think the problem is when people look for solution for such questions
it just confuses them

just try to solve it

[next nimbus]

yeah

[honest ember]

it eventually gets solved

hey @rose bough

if you wanna ask something go on

don't hesitate

[next nimbus]

yeah true

[rose bough]

I'm gonna try to explain my confusion more concisely 1 sec

[honest ember]

sorry for being rude

[rose bough]

no no it's okay, I didn't take it as rudeness

[next nimbus]

when were you rude lol

[honest ember]

Idk
I felt like I was

[rose bough]

I'm probably being dumb and missing something glaringly obvious that I've already learned

[rose bough]

I hope you get what I mean from this screenshot @honest ember @next nimbus

[next nimbus]

no you cant really do that. in the first case you are multiplying both sides by 12 . in the 2nd one you are multiplying one side by 4 and the other by 3 which isnt possible

[next nimbus]

we are not

we are also multiplying the 5 by 12

[honest ember]

okay
so how does it help

aren't you just doing the same thing

[rose bough]

yeah, why not by 3 too?

[honest ember]

it would have been same
if you would've just taken an LCM

[next nimbus]

why by 3?

[honest ember]

there is not point

[next nimbus]

he ll understand through his questions give me a sec

[rose bough]

because we multiply the right side by 3 from the denominator of the left side

[next nimbus]

you are multiplying (7-2x)/4 by 3/3 right?

[rose bough]

right

[next nimbus]

3/3 is 1 so its like you multiplied it by 1

[rose bough]

and why not like this for example?

oh

[rose bough]

ohh

[next nimbus]

yep like this its okay

[rose bough]

ahhhh

[next nimbus]

but you dont wanna multiply 5 by 3/3 cause there is no point

[rose bough]

I see now

so technically I am multiplying the whole side by 3/3

it simply was not written because 5/1 * 3/3 is 15/3 which is 5/1

got it

thanks

[next nimbus]

yep

[next nimbus]

yeah

[rose bough]

I appreciate you taking time to help, I hope you have a good day

Ginny too

[next nimbus]

be careful tho, you cant multiply one side by a number and the other side by another number

they have to be the same

[rose bough]

wym?

[next nimbus]

well you cant multiply one side by 3 and the other by 4

[honest ember]

actually

he did the correctly

[rose bough]

that is done to get the same denominator for both sides

[honest ember]

he multiplied and divided it

[next nimbus]

no i aint saying about that, i am talking generally

[honest ember]

I think you are getting confused for no reason
solve it the way you want to
you must get an answer

also

[next nimbus]

not in this example, generally. for example if you had x/4= (x-1)/3 how would you solve it can you show me?

[honest ember]

true mathematics is when

you can solve it faster

and effectively

[rose bough]

multiply the left side by 4 and the right by 3

[next nimbus]

nope you cant do that

[honest ember]

actually he can

[rose bough]

I mean 4/4 and 3/3

[honest ember]

I image in he took LCM

[next nimbus]

oh well thats not 4 lol

[honest ember]

result would be same

[rose bough]

yeah mb

[next nimbus]

alr

[rose bough]

I get how solving such equations work, I just had a little confusion over the 5 and thought that it was simply being ignored which confused me

but it's okay I got it now

[next nimbus]

alr good job

[next nimbus]

anything else you want help with?

[rose bough]

I have more equations to solve for later, if I'll get confused on something I'll post again in one of the help channels, thanks though

[next nimbus]

alr you can ping me if you want so i can help

[rose bough]

np I appreciate it

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[karmic fox]

At the end my last term is negative when it should be postive but idk how

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[sharp spindle]

i dont get

how this region lies in 2pi/3 to pi region

isnt this supposed to be 2pi/3 and pi region which is empty graph?

[sharp spindle]

and shouldnt this be betwen 5pi/3 and 0?

can someone please explain

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[rose flame]

the question: f(x)=sinx+x+3 D, [0,5]

The body of revolution we get when we rotate the graph of / about the x axis forms the outside of a large concrete urn for flowers. The unit along the axes is decimetres.

The urn must be filled with soil, so that the top of the urn is 1 dm higher than the top of the soil.

How large a volume of soil is needed when the wall is 0.5 dm and the bottom 1 dm thick?

i am stuck on this part, how do find the volum of the empty space or the insind part, V of urn is 514.74 Vsol = Vurn -Vinner

[rose flame]

<@&286206848099549185>

[fathom grotto]

tofind the volume of the soil needed:
calc the volume of the entire urn by revolving ( f(x) = \sin(x) + x + 3 ) about the x-axis from ( x = 0 ) to ( x = 5 ) using the disk method.
Secondly calc the volume of the inside part of the urn by revolving the region between ( f(x) ) and the x-axisAnd Subtract the volume of the inside part from the volume of the entire urn to find the volume of the empty space inside This volume represents the volume of soil needed. Adjust for the thickness of the walls and the bottom of the urn when finding the volume of the inside part

[thorny flame]

ويسالوني بعشقء مين؟🫨

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[rose flame]

i got that part how do i find the volum of the inner part first?

i have struggling with that part

how do i find the volum of inner?

the rest of the question is easy

like even a formula or hint will help

<@&286206848099549185>

can someone help_

<@&286206848099549185>

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[topaz sinew]

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<@&286206848099549185>

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[rose flame]

the question: f(x)=sinx+x+3 D, [0,5]

The body of revolution we get when we rotate the graph of / about the x axis forms the outside of a large concrete urn for flowers. The unit along the axes is decimetres.

The urn must be filled with soil, so that the top of the urn is 1 dm higher than the top of the soil.

How large a volume of soil is needed when the wall is 0.5 dm and the bottom 1 dm thick?

i am stuck on this part, how do find the volum of the empty space or the insind part, V of urn is 514.74 Vsol = Vurn -Vinner

[scenic flare]

You can do it with one integral if I read right, first we want 1dm of free space, so we'll shorten the interval to [0,4]

after that note that the bottom is 1dm thick, so we shorten again:

[1,4]

and then note that the walls have thickness 0.5

so we can subtract 0.5 from the given function

Vsoil = Integral[1->4] f(x)-0.5 dx

which gives us the volume of the soil

[scenic flare]

hope that made the process a bit clearer :]

[rose flame]

i could check if i get right answer but thank you for helping me

[scenic flare]

np

[rose flame]

its showingg us 206 not 276 which is the correct answer

man i hate calculus

[scenic flare]

oh does the thickness 0.5dm mean it's always 0.5 thick wrt to y or wrt to the min thickness at any point?

if it's the second then I'm not sure how to solve it

[rose flame]

the walls are alllways 0.5 thick and the bottom is 1 dm thick

[scenic flare]

Hm how can one calculate the volume of a body with a set thickness?

didn't learn it yet, perhaps you have a formula for it from your course?

[rose flame]

no its normal high school ap calcus

the only thing we learnerd is how find the volum of figurs

[scenic flare]

I did attempt calculating distance based functions and integrals before but it was some time ago and they probably refer to thickness wrt y

then my above approach should yield the right number

The urn has height 5 right

Oh oops I miswrote a 4 to 3

in my explanation

should be right now 🙂

[rose flame]

so intergrate from 1 to 4?

[scenic flare]

yup

[rose flame]

its showing 326

iam doing this stupid question for 2 days

[scenic flare]

hm 1 to 4 for bottom and free space

Then -0.5 for walls

don't see the issue rn

[rose flame]

what do u get?

is it 276?

[scenic flare]

Am not calculating it aorn

[rose flame]

iam getting 326 isntead of 276

[scenic flare]

I get 276

🐛

Same formula

[rose flame]

can u take screanshot pls?