help-27

[pseudo basin]

if you just naïvely divide the volume of the room by that of one cup, you get 62,500 (ish) cups fitting in the room.

[gusty merlin]

so what units is volume measured in?

coz all i need is volume for one cup and them im done

[pseudo basin]

cm^3, a.k.a. ml, in my last calculation.

[gusty merlin]

so the explanation -previously was wrong?

[pseudo basin]

no...

[gusty merlin]

im so confused

what is 62,500 for?

[pseudo basin]

i was going to demonstrate what would happen if we took the naïve approach of dividing the volume of the room by the volume of the cup.

[gusty merlin]

oh

I just need the volume for one cup

[pseudo basin]

also uh

[gusty merlin]

thats it

[pseudo basin]

ok wow

yikes.

[gusty merlin]

and how i caluclate it

[pseudo basin]

big yikes.

[gusty merlin]

is that correct>

[pseudo basin]

are you really just taking what i said without thinking and pasting it into your work???????

[gusty merlin]

for how many would fit in

[pseudo basin]

please don't do that!

[gusty merlin]

i reworded it

Alr I won't ill re do it then

[pseudo basin]

i mean like

the fact that you said

"putting them in widthwise will give 2% more cups than vertically, so we will do it vertically"

to me that shows blatant disregard for what was said

[gusty merlin]

we did it vertically didn't we?

[pseudo basin]

wasn't your goal to fit in as many cups as possible?

[gusty merlin]

yes]

[pseudo basin]

you did not let me show you the calculations for widthwise stacking

you dismissed me

[gusty merlin]

oh...

[pseudo basin]

as if you would not care about a higher number

it's kind of shitty on your part to do this...

[gusty merlin]

im confused man

[pseudo basin]

you took my words, regurgitated them, and vomited their mangled remains onto the page.

[gusty merlin]

ima just try to do it on my own - honestly i got nothing out of this besides from the answer

[pseudo basin]

..............

[gusty merlin]

obviously ill reword them and add grammar i was asking if that was correct

[pseudo basin]

and why is it only now that you are admitting to not getting what i said

[gusty merlin]

because i'm still confused bro

[pseudo basin]

please don't call me bro

...shall we start over?

[gusty merlin]

well ima stick with that I had before honestly

theres no luck - ill still be confused

[pseudo basin]

maybe you won't if we actually walk through this step by step

[gusty merlin]

I need the answer in a non-complicated way

[pseudo basin]

maybe i can draw some pictures too

[gusty merlin]

look if u think theres luck im more than happy to start again

i need this before an hour tho

yk what

ima try and solving it on my own

ill keep this ticket open - try it with a different cup and check with u as i follow ur steps

[pseudo basin]

okay

[gusty merlin]

I wanna try with that cup now.

So the volume...

@pseudo basin

[pseudo basin]

well as i said before, volume does not matter much if we are stacking cups inside each other

[gusty merlin]

im just going to see how many we can fit inside randomly

[pseudo basin]

as you wish. i take this as meaning you don't want to go through with the stacking thing.

[gusty merlin]

yea sure.

its a bit harder like that

how do i get 0.0445 to get to 1 cm

[pseudo basin]

i have drawn up an illustration (with the smaller cup size) to hopefully demonstrate what idea i was trying to suggest.

[pseudo basin]

no

you are grossly misusing units right now.

[gusty merlin]

OMG

WAIT THAT PICTURE KIND OF MAKES SENSE NOW

[pseudo basin]

hopefully my handwriting is legible, by the way.

[gusty merlin]

i love it

now im on the same page as u

how do we find out the answer now

@pseudo basin I read and understood it now im on the same page as u

at the end u wrote count the number of stacks - how do we do that

u still there....?

[pseudo basin]

sorry, had to answer a phone call.

first decide which axis you want to orient the stacks along.

for completeness we'll want to do all three options anyway

[gusty merlin]

oh okay dw i thought u left me

[pseudo basin]

just to see which one gives more cups and by how much

[gusty merlin]

i just need one way

i don't have time and i dont wanna waste urs

[pseudo basin]

so you have three choices: lengthwise (along the 3m length), widthwise (along the 4m width) or heightwise (along the 2.5m height, so vertical)

[gusty merlin]

so stick to one and we'll see how many cups that gives u

[pseudo basin]

ok let's just go with height again

[gusty merlin]

perfect

[pseudo basin]

so that means the cross-sections of our cups (89mm diameter circles) are facing the floor

[gusty merlin]

so basically in a line

can we do lengthwise?

[pseudo basin]

lengthwise, ok.

[gusty merlin]

so theyre in a line facing the right or left

[pseudo basin]

well, no, lengthwise they'll be facing forward or backward.

[gusty merlin]

oh

[pseudo basin]

sticking here with your naming of the dimensions where length = 3m and width = 4m

if you want them to face along the longest axis that'll be widthwise lmao

[gusty merlin]

lets just do the one that gets the cups to face right '

like theyre in a line

[pseudo basin]

okay

that'll be widthwise

[gusty merlin]

oh

lets go widthwise then

[pseudo basin]

and each stack will be 4 meters long and face into the 2.5m × 3m wall

the area of the wall is of course 2500 * 3000 = 7,500,000 square millimeters

[gusty merlin]

Correct

[pseudo basin]

and the area of the cross-section of each stack is something we've calculated before

since the diameter is still 89mm

,calc 89^2 * pi/4

[woven radish]

Result:

6221.1388522712

[pseudo basin]

6221 square millimeters

now as i said, packing circles like i drew only covers 91% of the available area

so we need to take that into account

[gusty merlin]

listening

[pseudo basin]

the area covered by the stacks is thus 7,500,000 * 0.91 square millimeters

,calc 7500000 * 0.91

[woven radish]

Result:

6.825e+6

[pseudo basin]

6,825,000 mm^2

so to get the number of stacks we divide this by 6221 mm^2

do you follow thus far

[gusty merlin]

so to get the number of stacks we divide 6221 by square so like half it?

[pseudo basin]

no.....

did you read what i just said

[gusty merlin]

what is "this"

[pseudo basin]

6,825,000 mm^2

wall area adjusted for packing density = total area of stacks

[gusty merlin]

oh okay

im following now

so whats the next step

@pseudo basin

[pseudo basin]

,calc 6825000/6221

[woven radish]

Result:

1097.0904999196

[pseudo basin]

let's just get the number before proceeding

1097 stacks

[gusty merlin]

sure

[pseudo basin]

so now, if you refer to the picture i sent, we find the number of cups in each stack.

[gusty merlin]

yes

just need to know how

[pseudo basin]

well that is what we are about to find

can you show me the dimensions of the bigger cup again

looking for vertical ones specifically

[pseudo basin]

right

ok

so this one has a thinner lip, only 2mm

and the height without the lip is 128mm

[gusty merlin]

yes

[pseudo basin]

so that means n of these cups stacked will have a height of 128+2n millimeters

and our attack will be 4000mm tall

[gusty merlin]

the stack will be 400mm tall?

@pseudo basin next?

4000x1097 then convert it into cm?

@pseudo basin did i lose u?

[pseudo basin]

no you didn't, but also no it's not correct...

apologies for being a little harsh, but it sounds as if you want to avoid doing any thinking of your own and just want me to spoonfeed you all this stuff

[gusty merlin]

im just confused

maths isnt my thing

im an english person

[pseudo basin]

the height of a stack of n cups is 128+2n millimeters
the height of our stack is 4000 millimeters
128 + 2n = 4000, what is n?

[gusty merlin]

how do we find n?

[pseudo basin]

i just gave you an equation which you can solve to find n

[gusty merlin]

im not that advanced man

im only 15

[pseudo basin]

it's not advanced

this is something a 15 year old is definitely capable of solving

especially one who is doing comparably more advanced stuff like volume calculations

[gusty merlin]

back to this

no more ditractions

[pseudo basin]

yes

[gusty merlin]

distractions*

[pseudo basin]

2n + 128 = 4000

[gusty merlin]

im just confused

[pseudo basin]

confused how exactly?

let me try to summarize the ways you could be confused as i see it.

[gusty merlin]

how to solve for n

[pseudo basin]

what if the letter was x instead, would that make it easier for you?

[gusty merlin]

like i was good

Ann — Today at 23:00
the height of a stack of n cups is 128+2n millimeters
the height of our stack is 4000 millimeters
128 + 2n = 4000, what is n?

in this

all i need to know how to solve for n

[pseudo basin]

subtract 128 from both sides, then divide by 2 on both sides.

[gusty merlin]

OH MY GOD

HOW DID I FORGET

2n = 3872

no now we need to take away 2 from both sides?

[pseudo basin]

no

we need to divide by 2.

as i said before!

[gusty merlin]

thats what i meant

mb

so

3872/2

1936

[pseudo basin]

yes, so that will be the number of cups in a single stack.

to tie this back to our problem and not make it look like a simple play-around-with-numbers affair.

[gusty merlin]

yup

so what now?

1936 x 4000?

because there are 4000 stacks

[pseudo basin]

no

there are not 4000 stacks

[gusty merlin]

oh

thats 4000 mm tall

[pseudo basin]

you have not been paying enough attention to our convo

[gusty merlin]

mb mb

i have

[pseudo basin]

you've just been parroting back the various numbers that came up without regard for their meaning in the problem

[gusty merlin]

let me look at ur book again

[pseudo basin]

.

[gusty merlin]

1097X1936

?

no?

[pseudo basin]

please do not use the letter x for multiplication.

[gusty merlin]

oh

[pseudo basin]

also, please do not take a 20-second silence as a no.

[gusty merlin]

sorry

[pseudo basin]

but yes, the total number of cups in the room will be 1097 * 1936.

keep in mind, by the way, that these numbers aren't exact and aren't to be treated as such!

,w 1097 * 1936

[woven radish]

Results provided by WolframAlpha

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

Requested by Ann#0413

[gusty merlin]

so 1097*1936=2,123,792

[pseudo basin]

yes

i would report that as 2.1 million

[gusty merlin]

and thats my answer?

[pseudo basin]

well

[gusty merlin]

oh okay!

[pseudo basin]

that's the final number we get yes

i was just going to comment on how it would be silly to plan for EXACTLY that many cups and no more

in a real world scenario

[gusty merlin]

OMG THAT ACTUALLY MADE SENSE

THANK YOU SO MUCH

[gusty merlin]

U don’t have to dwww

I’m probs not gonna have time do read it - if u wanna do it feel free to dm me

But thank you so muchhhhh

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[limber socket]

i need help with finding the values of x° and y°

[cosmic trail]

ntoice the right angle

that consits of 28 and 2x

so 28 + 2x = what

[limber socket]

28+2x=90?

[cosmic trail]

very good

do you know how to find x from here?

[limber socket]

hmm

let's see

ohh yes i know now

it's like this right?

2x=90-28

[cosmic trail]

yeah,

so 2x = 62

x ?

[limber socket]

x = 62÷2

=31

[cosmic trail]

ye

ok now for y, all the angles make a straight line

angles on a straight line equal?

[limber socket]

180°

so it's gonna be like-

31°+23°+y = 180°

right?

[cosmic trail]

not quite

y + 28 + 2x + 23 = 180

[limber socket]

ohh

[cosmic trail]

but you already know x, so substitute it in

[limber socket]

alright

so then

it will be

y + 28 + 2×31 + 23 = 180

right?

[cosmic trail]

yeah

now simplify it

[limber socket]

the answer i got is 67°

[cosmic trail]

yeah that's what I got too

[limber socket]

ohh ok then

thanks for the help

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[tiny rain]

hi can someone help me with this

[devout snow]

@tiny rain Has your question been resolved?

[tiny rain]

.close

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[celest hatch]

B right? but how exactly

anyone?

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[teal star]

Would it be better if u solve it like
2/3 > |x-4|

[teal star]

And then
-2/3 < x-4 < 2/3

10/3 < x < 14/3

Is this okay

[bright maple]

Perfectly fine

[restive river]

You forgot the x is not 4 but yeah

[bright maple]

Idk why he is making it more complex

[teal star]

Thank u

[teal star]

👍

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[thorn sage]

I think it's true, but im not sure how to prove it?

We learned about proof by case analysis today, but we also learned about direct proof yesterday?

[fathom rivet]

if we let the first integer be x

the next 4 have to be

x+1, x+2, x+3 and x+4

[thorn sage]

x+1 x+2 yes

I thought about this too

[fathom rivet]

when you add them together its 5x+10

which is divisibke by 5

[thorn sage]

But like then I got stuck on what to do

OMG

HAHA that is soo nice

[devout snow]

@thorn sage Has your question been resolved?

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[spice island]

hello, how can I solve this?

[spice island]

my work so far

[prime egret]

So what are you stuck on?

How to simplify this?

[spice island]

I need to get the volume of the sphere

but don't know how

[prime egret]

Well that’s the volume of the sphere

[spice island]

khan academy says this is wrong

[prime egret]

What do you mean you don’t font know how

What did you put in as your answer

[prime egret]

Simplify it

[spice island]

but how can I take 4/3 of pi

[prime egret]

What is $\frac{4 \times 216}{3}$

[woven radish]

Pure

[prime egret]

Leave pi alone

Just simplify the number

[spice island]

how do I simplify?

[prime egret]

$\frac{4 \times 6 \times 6 \times 6}{3}$

[woven radish]

Pure

[spice island]

<@&286206848099549185> help please

[toxic swift]

288pi?

just multiply 216 by 4/3

[spice island]

thank you

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[prime egret]

That’s exactly what I told you to do…

[spice island]

.reopen

[devout snow]

✅

[spice island]

where did you tell me?

you never explained to me

[prime egret]

Just simplify the number

[prime egret]

This is not enough?

[spice island]

yes and that doesn't explain how to simplify it

[prime egret]

kk

[spice island]

anyways thank you for the help @toxic swift much appreciated

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[devout snow]

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[worldly shore]

ok

[worldly shore]

so

(a-1)²-a(3-a)

i need help factorising this

[onyx wind]

The answer is x+1

[worldly shore]

wait how

my teacher did it infront of me

and she got 2a²-5a+1

[onyx wind]

What

how

[worldly shore]

idk

[onyx wind]

So

[worldly shore]

i didnt learn it properly

i forgot it after 1 hour'

[prime egret]

How did you even get that

[onyx wind]

Idk I just plugged it into math way, I’ll show the work tho

[worldly shore]

how did u get the x?

[onyx wind]

x is a

I just used x

so

(a-b)^2 is equal to

a^2 - 2ab + b^2

So let’s use that for this equation

[worldly shore]

idk what to do after this

[onyx wind]

a^2 - 2(a)(-1)

Now

a^2 + 2a + 1

Best

Next

[worldly shore]

shouldnt u multiply

each one

[onyx wind]

I did

wait mb

There

-a(3-a)

Distribute

-3a + a^2

[worldly shore]

no u gotta do aa a-1 then -1* a -1*-1

[onyx wind]

2a^2 - a + 1

[onyx wind]

For what

[worldly shore]

my bad

i meant

simplify the expression

[onyx wind]

Mb my phone keeps on

Let me get a piece of paper

[worldly shore]

ok

[onyx wind]

K

What was the equation

[onyx wind]

Okay

There u to

Go

2a^2 - 5a + 1

[worldly shore]

tysn

tysm

[onyx wind]

Yeah no problem i was getting rusty on algebra haha 😅

[worldly shore]

i got test on this on friday

u think i still got it?

[onyx wind]

Uh yeah just practice your weak points

Always ask questions to your teacher

If you are wondering about something’s

[worldly shore]

3 hours a day with practice?

imma try that

3 hours a day in school days from now on

[devout snow]

@worldly shore Has your question been resolved?

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[tawdry depot]

.open

How does this work

[tawdry depot]

Can someone help with this

<@&286206848099549185>

[topaz beacon]

!15m

[devout snow]

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.

[tawdry depot]

oh sorry

[young fossil]

Do you know how to turn "a fraction with a whole number bit" into a simpler fraction (without a whole number bit)?

[tawdry depot]

No because i forgot how to do fractions

[young fossil]

hmmm

okay

if you have a number divided by the same number (say x/x, 1/1, 2/2 or 3/3 for example) what would you get?

what would 5/5 equal?

[tawdry depot]

Is it 25

[young fossil]

no

[tawdry depot]

Does it stay the same

So 5

[young fossil]

a number divided by itself always equals 1 (unless you're dividing by 0)

[tawdry depot]

oh

[young fossil]

when we make fractions, we're essentially just dividing

[tawdry depot]

ohh

So its 1

[young fossil]

yes!

[worldly shore]

its pretty simple

think it this way

[tawdry depot]

But it says Times in my question

[young fossil]

we'll get to that

[worldly shore]

4x5+1

thats how u can start

[tawdry depot]

Is that 21

[worldly shore]

yea

[young fossil]

yes, you'll need that but ignore it for the moment

you have to do it with the fraction

[tawdry depot]

Alright

[worldly shore]

sorry for interrupting

[young fossil]

So, remember that 5/5 = 1?

[worldly shore]

imma leave you guys for now

[tawdry depot]

Yes

[young fossil]

s'ok bud, just trying not to confuse him :v

so, the number 4 can essentially be written as:
5/5
+
5/5
+
5/5
+
5/5

do you agree that that would equal 4?

[tawdry depot]

I don’t get it

[young fossil]

you know how brackets work?

with brackets you just do the stuff inside the brackets first in an equation then do whatever left

so....

[tawdry depot]

yes i think

[young fossil]

(5/5)+(5/5)+(5/5)+(5/5)
Is the same as:
1 + 1 + 1 + 1
Since we know (and we've already established that) 5/5=1

make sense?

[tawdry depot]

Oh yea

[young fossil]

So, the number "4" component of that fraction can be written like that instead

you also have to add the 1/5 bit aswell

but theres a neat "trick" that you can do with fractions that have the same denominator....
Since they are all being divided by "5" seperately, you can basically add up all the numbers and divide them together

[tawdry depot]

Oh

[young fossil]

So this is what the first part of your equation should look like:
4+(1/5) = (5/5)+(5/5)+(5/5)+(5/5)+(1/5)
=(5+5+5+5+1)/5

so, as a fraction, what do you think the first part of your equation (4+(1/5)) looks like when written as "just a fraction"?

[tawdry depot]

hmm

[young fossil]

Hint: its a number divided by 5

[tawdry depot]

Okay

Is it 4 5/5

Wait

Actually is it

20/5

[tawdry depot]

if my answer is right to i have to simplify it

[mental citrus]

bro stop making it hard for yourself

ok look

imma show u a much easier method

[tawdry depot]

Alright

[mental citrus]

so u can start off with 4 x 5 + 1

u understand so far what i did right?

[tawdry depot]

Yes

[mental citrus]

after that

u do 4x5+1

which is?

[tawdry depot]

21

[mental citrus]

yes

now u got 21/5 x 5/14

do u see any similar numbers here?

[tawdry depot]

There’s 5 in both fractions

[mental citrus]

yes

now u remove them

[tawdry depot]

So 21 x 14

[mental citrus]

and u will get ?

almost

21 x 1/14

what can u do to make 21 and 14 smaller?

[tawdry depot]

Simply

14 devided by 2

7

[mental citrus]

and 21

[tawdry depot]

21 devided by 3

7

[mental citrus]

and u get?

[tawdry depot]

7/5 and 7/14

Wait no

[mental citrus]

no

bro

u had it

cmon

how many times did u divide 21?

[tawdry depot]

3 times

[mental citrus]

3 right?

[tawdry depot]

Yes

[mental citrus]

yes then 21 turns into 3

and 14 into 2

and u will get

3x

1/2

[tawdry depot]

Oh

[mental citrus]

after that?

[tawdry depot]

Do you you turn it into a fraction

[mental citrus]

calculate

ok look

3/1 x 1/2

what is

3x1?

[tawdry depot]

3

[mental citrus]

right

1x2?

[tawdry depot]

2

[mental citrus]

there u have it

the answer is?

[tawdry depot]

3/2

[mental citrus]

yes

did u understand?

[tawdry depot]

Yea

[mental citrus]

what happened to the other dude

[tawdry depot]

Idk

[mental citrus]

anyways

was that all?

[tawdry depot]

I think he left

[tawdry depot]

Yes

[mental citrus]

feel free to ask me

[mental citrus]

alright

[tawdry depot]

Ty for helping

[mental citrus]

np

[devout snow]

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[devout snow]

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[edgy prairie]

help plz

<@&286206848099549185>

[devout snow]

@edgy prairie Has your question been resolved?

[edgy prairie]

no it hasnt

[devout snow]

@edgy prairie Has your question been resolved?

[devout snow]

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[night gust]

14/9 doesnt work

[winter patrol]

why do you have a quartic (4th degree) polynomial

[night gust]

the x^2(x^2 part

[winter patrol]

why are you multiplying the whole thing by x^2...

[night gust]

since isnt it the coefficient

[winter patrol]

huh

?

no

x^2 is not a coefficient

the wording is poor,
if the coefficient of x^2 is 9

[night gust]

oh sorry wrong one, same everything but the coeffcient

but wont that be the same sinxe 1 to whatever power thats posiive is 1?

[winter patrol]

wdym

[night gust]

so the x^2 wont matter bc its 1?

[winter patrol]

usually you'd have the scaling factor

in the previous question, that would be 9

[night gust]

?

[winter patrol]

here it's 1

[night gust]

im confused, someone else old me to plug stuff into he quadratic intercep form with the roots as p and q

[winter patrol]

note that using only
y = (x - p)(x - q)
gives a quadratic equation with a coefficient of 1 for x^2,
ideally you'd use /start with
y = a(x-p)(x-q)

[night gust]

whats a?

i just put x^2 htere

[winter patrol]

no

a will be the coefficient of x^2

if you are told the coefficient of x^2 is 1, your a will be 1

[night gust]

ohhh

sso can i just leave it out? since 1 doesnt do much

[winter patrol]

if a is 1, yes

[night gust]

so id end up with (x^2 + 2x^2/3 -1/9)?

?

and itss just be 1+ 2/3 -1/9?

14/9

[devout snow]

@night gust Has your question been resolved?

[night gust]

<@&286206848099549185>

[night gust]

it sasy this is wrong

[winter patrol]

you didn't expand properly, doing unnecessary stuff you shouldn't be doing, what exactly are you entering

[night gust]

14/9

[winter patrol]

14/9 is not an equation

why does it look like you substituted in x=1 for some reason (you were NOT being asked to do this)

so id end up with (x^2 + 2x^2/3 -1/9)?
also
the middle term should be 2x/3, you have an extra ^2 that doesn't belong there

[night gust]

oh yeah

wait so im jsut supposted to put x^2 + 2x/3 -1/9?

[night gust]

i think I did?

[winter patrol]

x^2 + 2x/3 -1/9
since they want an equation
put something like
y = x^2 + 2x/3 -1/9

[night gust]

ohh aalr

ill try that

says its wrong

did i mess up womwhere else?

does uadractic eqution mean its 0=?

[devout snow]

@night gust Has your question been resolved?

[night gust]

that didnt work

[winter patrol]

did you try
x^2 + 2x/3 -1/9 = 0

[devout snow]

@night gust Has your question been resolved?

[night gust]

Going to try that

Worked

So I just solve everything else the same way by putting the coefficient in front of the (x-p)(x-q) and writing it as an =0 equation?

but how would I do this? since the factors for -2 are -1x2, -2x1, and teh numbers that add up to -2 and -1-1,-2-0, etc but none are a factor of -2

[devout snow]

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[alpine pier]

Hi I just had a question, are the x-intercepts of a parabola just the zeroes??

[midnight bane]

yes

[alpine pier]

I have to find them somehow with this formula, y=-x2+18x

and Im not sure how

that's the equation*

y=-x2+18x

and I gotta find the x intercepts

I'm not sure how soooo

@midnight bane You able to help??

[midnight bane]

factor out an x

x(x+18)=0

x=0,-18

@alpine pier

also that's an equation not a formula

[alpine pier]

Yea mixed them up

whoops mixed it up one sec

y=-x^2+18x

thats what I mean

x^2

[devout snow]

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[devout snow]

@alpine pier Has your question been resolved?

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[sullen pond]

what is 2.31 years in exact years and months?

[devout snow]

@sullen pond Has your question been resolved?

[quaint citrus]

u solved it? nice

so 2 years

.31 years

0.31 * (12 months)

go from there

@sullen pond

[sullen pond]

yes I convert 0.31 years to months

thanks

.close

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[woven radish]

Couldn't find an attached image in the last 10 messages.

Oct 26, 2022, 5:23 AM

[bright maple]

,rotate

[devout snow]

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[bright maple]

.close

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[bright maple]

Question 5 please

[devout snow]

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[bright maple]

No. 5 please

[devout snow]

@bright maple Has your question been resolved?

[bright maple]

<@&286206848099549185>

[devout snow]

@bright maple Has your question been resolved?

[bright maple]

<@&286206848099549185>

[devout snow]

@bright maple Has your question been resolved?

[rich summit]

I think you should multiply both sides of the equation by A

And notice that X^-1 * Y^-1 = (Y * X)^-1

@bright maple

Not sure though

Where do you get all these determinant questions from?

[bright maple]

its in the module of a coaching institute where i go for jee

[bright maple]

It gives I + AB^-1 on RHS theb?

[devout snow]

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[teal spindle]

hello can someone help me memorise my timestable?

[devout snow]

@teal spindle Has your question been resolved?

[devout snow]

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[dawn rivet]

I don’t understand why a bijective function is necessarily one-to-one. If the function A->B has the conditions that every element of B is the image of at most one (injective) and at least one (surjective) element of A, I understand that every element of B has exactly one corresponding element in A, but I do not see why every element of A must correspond to an element in B. (Abstract algebra / algebraic structures)

[dawn rivet]

Sorry in advance if it’s painfully obvious

[pseudo basin]

but I do not see why every element of A must correspond to an element in B.
that's what makes it a function

[left robin]

the fact that every element in A has a corresponding element in B comes from the function being well defined

[dawn rivet]

how embarrasing

thanks for the help!!

.close

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[devout snow]

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[dreamy holly]

I feel stupid asking this but why is a^x * b^x = (ab)^x

[dreamy holly]

Btw the other help channel got yeeted because apparently I used a bad word 😐

[ripe arrow]

what's n?

[dreamy holly]

Oh I meant b

Not n

Like I have always just sort of accepted this fact but I’m wondering why it’s true

[pseudo basin]

if x is a positive integer then you can appeal to the commutative law of multiplication

to say that the product of x copies of a and x copies of b can be rearranged (in the literal sense) with the a's and b's grouped one by one to get the product of x copies of (ab)

[dreamy holly]

Oh because (ab)^x = (ab)(ab)… x times

I seeeee

[pseudo basin]

yes

[ripe arrow]

yeah

[dreamy holly]

Thanks a lot guys

.close

[devout snow]

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[restive river]

please help me with this. I was able to solve a), but I have no clue how to solve b)

1. Polynomials. The four polynomials are given

P1(x) = x³ + x²

P2(x) = x² - 2x - 4

P3(x)=3x+4

P4(x) = 2x+3

(a) Write the polynomial 2x3 +3x²-1 as a linera combination of the polynomials Pi, i = 1, 2, 3, 4.

(b) Calculate the product Sp (P1, P2, P3, P4).

[ripe arrow]

what don't you understand?

[devout snow]

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[dawn spruce]

Need help with binomial distribution in geogebra

[devout snow]

@dawn spruce Has your question been resolved?

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[flint snow]

What even is this someone help please 💀

Use proportions to calculate the length of the identical side of each triangle

[cursive jacinth]

If they’re identical then the left side should be 5/9 * 18 and the right 4/9*18 is what I think they mean

Unless they mean both sides are identical in which case it would be 1/2 * 18

[flint snow]

It's says to use proportions

I have a geometry test in 15 minutes and idk how to do it

[ripe arrow]

if two triangles are proportional, each corresponding side's ratio is the same

[devout snow]

@flint snow Has your question been resolved?

[devout snow]

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[random pendant]

Number 11

[random pendant]

How do i integrate numbers

Do I paste the same number and add ln e

[twin sapphire]

first you find the antiderivative

[random pendant]

Uhhhh

How

5^x len 5?

That is the derivative

[twin sapphire]

it's just what function'

's derivative would be that

[random pendant]

That is the derivative

Of a number

I only got 5^x

[twin sapphire]

idk integration

i just know the antiderivative part

[random pendant]

That

Is confusing

How about I multiply e

I will be able to turn the 5 to a constant

And outside the integrate I I have 1/e x 5

[oak harness]

$\int \frac{e^{3x} + 2e^{2x} + 4}{e^x} \dd x$

[woven radish]

Remavas

[random pendant]

Wha

Holy

I didn't take that

Or i did

That seems like pain solving

[oak harness]

Or, equivalently, realize that dividing by e^x is the same as multiplying by e^(-x)

You get the same thing.

[random pendant]

.

Is this correct

[oak harness]

what is happening

[random pendant]

I multiply e

Then divide outsides

So it became 5e^x

I take the 5 outside the integral

And there is 1/e outside

Removing the integral it becomes 1/e multiply 5e^x

[oak harness]

2 * 3^10 =/= 3 * 2^10

[random pendant]

Yea

What do u mean by that doe

[oak harness]

that 5^x multiplied by e is not equal to e^x multiplied by 5

[random pendant]

Oh

[oak harness]

no, he multiplied 5^x by e

[random pendant]

Okay let's

Start over

5^x

Multiple 1/e?

[oak harness]

why?

I have no clue.

I am just worried about all the crimes of mathematics that are being committed here.

[random pendant]

Uhhh

5^x is the base

Of the questjon

11

[oak harness]

$\int \frac{e^{3x} + 2e^{2x} + 4}{e^x} \dd x$

[woven radish]

Remavas

[oak harness]

how did you get to 5^x from here?

OH

[random pendant]

No no

Question part 1

[oak harness]

$\int 5^x \dd x$

[random pendant]

OHHHH

[woven radish]

Remavas

[random pendant]

Yes

[oak harness]

In any case, since this is given as an exercise, I guess you can't just look this up in a table.

[random pendant]

That is the integration?

Wow

That's it?

[oak harness]

Yes, but you can also derive this yourself

positive constant*

[random pendant]

My pen is dying writing tuis

This

Is there steps

To getting the ln a

[oak harness]

Yes.

[random pendant]

Or it is a constant rule

What are they

[oak harness]

Write $a^x = e^{x\ln a}$

[woven radish]

Remavas

[oak harness]

the perform a u-sub where $u = x\ln a$

[woven radish]

Remavas

[random pendant]

Huh

I'm confused

5^x =e^xln5

Ln5*

What do I do next

[oak harness]

lost the x

$\int 5^x \dd x = \int e^{x\ln 5} \dd x$

[woven radish]

Remavas

[random pendant]

What is next

Divide them?

How do i grt

Rid of integration

Divide 1/ln 5

Wait

It will be

1/ln5 e^xln5

[oak harness]

$\int e^{x\ln 5} \dd x = \frac{1}{\ln 5} \int e^{x\ln 5} \ln 5 \dd x = \frac{1}{\ln 5} \int e^{x\ln 5} \dd(x\ln 5) = \frac{e^{x\ln 5}}{\ln 5}+C = \frac{5^x}{\ln 5} + C$

if you want the full view

[woven radish]

Remavas

[random pendant]

So basically

5^x/ln5 is same as e^xln5 / ln 5

[oak harness]

yes

[random pendant]

Holy moly

That is such a confusing question

I think I know that abit

Can I ask about other questions if I get confused?

[oak harness]

[random pendant]

Let's say

As an application of what I learnt

Number 12 in part 1

Is it gonna be

[oak harness]

$\int 2^{-5x}\dd x$

[random pendant]

2^-5x /ln 2^-5x

/

[woven radish]

Remavas

[oak harness]

no

[random pendant]

Why

So it has a different rule

?

[oak harness]

$a^{-x} \neq a^{1/x}$???

[woven radish]

Remavas

[oak harness]

Or am I misunderstanding your statement

Ah, there we go.

[random pendant]

Hh

Well

Let's say

How about

The 5x

Basically

1/2^5x over ln1/2

I will wriite in

It

Idk

Wha

Isn't the question done at that point

Yes

Hm

It will be

1/ln1/2???

I don't know what is U

I did

But im bad at it sometimes

I have been screaming for a while

Can u tell me what is the point I'm wrong at exactly

I didn't do anything other than this

I will temple it

Do I flip the fraction and change the sign so it becomes -2/1

[devout snow]

@random pendant Has your question been resolved?

[random pendant]

But what is u

But what do o do after making the

I really don't get the question imma ask the teacher about it

Thanks for your help

[devout snow]

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[dim rapids]

Why do I multiply by e^-x when lim x-> infinity but I multiply by e^x when lim x-> - infinity?

[scarlet sequoia]

because then they give 0

if it comes to evaluating limit

[restive river]

it's simply a trick to manipulate the expression to get something that obviously converges

[dim rapids]

How do I know which one to pick? How can I tell the one I pick will make it "converge"

[devout snow]

@dim rapids Has your question been resolved?

[devout snow]

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[rich sage]

Today my professor was discussing lagrange mean theorem and he draw a function to illustrate (inserted) his point of the theorem which i get but he said that the slope in this function is not zero anywhere but that does not make sense because the function is going up and down which intuitively mean that there is a max or min points can someone explain to me what does he mean?

[supple knot]

yes the slope is 0 at two places here

[rich sage]

But my professor said that that is not the case

That this*

[supple knot]

you probably just misunderstood

or they mis spoke

just forget it and move on

[rich sage]

🤣🤣🤣😭😭😭😭😭

Well thanks 😊

.close

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[tiny shore]

▪️ The 1st pump alone takes three times longer than the three pumps together.
▪️ The 2nd pump alone takes 5 hours longer than the three pumps together.
▪️ The 3rd pump alone takes 12 hours longer than the three pumps together.
a. In how many hours can the cellar be emptied by each of the three pumps?
b. In how many hours can the cellar be emptied by all pumps combined
(Problem translated from French)

I am unsure on how to tackle this problem, I’ve already tried putting them together, but I always end up with multiple variables and I don’t know how to solve for them.

[devout snow]

@tiny shore Has your question been resolved?

[stuck cipher]

You can just use 3 variables to solve

Let's say I have a,b,c which are the first, second and third pumps respectively

Assume that the amount of water being pumped is 100

Then :

100/a=300/(a+b+c)

100/b=500/(a+b+c)

100/c=1200/(a+b+c)

Then just solve the system of equations

[tiny shore]

This system of equations does not give a solution, I think you forgot to consider that pump 2,3 take 5 and 12hours longer, not 5 and 12times longer

Checked it with wolframalpha

.close

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[brazen arrow]

-19 + 3x = 2(3x)

[brazen arrow]

how would I solve

[left robin]

can you simplify 2(3x)?

[brazen arrow]

6x?

[left robin]

yes

now put all x on one side and the rest on the otehr

[brazen arrow]

that actually works?

[left robin]

yes it does

because multiplication is in pretty much all cases commutative, meaning a(bc)=(ab)c

[brazen arrow]

subtract everything by 3x?

-19 = 3x?

[left robin]

correct

[brazen arrow]

divide by 3?

which leaves $-19/3 = x$

[woven radish]

justjustinjr

[left robin]

👍

we can double check if you want

,w -19+3x=2(3x)

[woven radish]

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Requested by ~Martin#3125

[left robin]

looks good

[brazen arrow]

ok so my homework says to see which equations are equavalent to that

$3x + 4 = 5 - (3x + 14)$

wait nvm i can figure it out

.close

[devout snow]

Channel closed

Closed by @brazen arrow

Use .reopen if this was a mistake.

[devout snow]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[spare zealot]

How do I find the intersection point of two parametric lines?

[spare zealot]

$\alpha_1(t) = (2t-1, -1+t, -4+2t)$ \ $\alpha_2(s) = (-2s, -4s+1, s)$

[woven radish]

lexitorius

[spare zealot]

I tried substitution to solve for t when they're equal and got some whack stuff

Not really sure what I'm doing

<@&286206848099549185>

[devout snow]

@spare zealot Has your question been resolved?