help-38

[viscid flower]

yea, dropped would be 0

[tardy ledge]

ok

ok

that makes sense

thank you

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[viscid flower]

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[vernal socket]

$Q+Q^T=0\implies v^T(Q+Q^T)v=0\implies v^T Qv+v^T Q^Tv=0$

[solid kiln]

Actformain

[vernal socket]

what is this man !>?

[wet lintel]

@vernal socket bro

[vernal socket]

hello ?

[wet lintel]

do you see your name or are you blind

[vernal socket]

I aint blind i have amploybia

[wet lintel]

anyways this most likely just follows from distributive property

[vernal socket]

what its a eye disorder

but not bad

[wet lintel]

its a figure of speech bro

[bright quarry]

tough

[vernal socket]

i have 20/20 vision on my right eye while my left is 20/50

i mean 20/40

[wet lintel]

bro i dont care 😭

[bright quarry]

lazy eye that bad?

[vernal socket]

kinda

[wet lintel]

to answer your question

[vernal socket]

sometimes it can make you blind forever

$Q+Q^T=0\implies v^T(Q+Q^T)v=0\implies v^T Qv+v^T Q^Tv=0$

[solid kiln]

Actformain

[vernal socket]

Hello?

[wet lintel]

i answered your question

[vernal socket]

Oh i answered it my self

[wet lintel]

unless there is more context

in that case !xy

!xy

[trim jolt]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[vernal socket]

$Q+Q^T=0\implies v^T(Q+Q^T)v=0\implies v^T Qv+v^T Q^Tv=0$3

[solid kiln]

Actformain

[wet lintel]

oh my god

exactly how much are you tweaking right now

[vernal socket]

I was just asking if it was correct kid

but i got another one

He he

might be hard to see

!xy

[trim jolt]

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[wet lintel]

ok what exactly do you need

?!

[vernal socket]

What it might be hard to look at

but just see if its correct

ill make it bigger

[wet lintel]

@bright quarry can you handle this

i gotta eat

[trim jolt]

@vernal socket Has your question been resolved?

[trim jolt]

@vernal socket Has your question been resolved?

[vernal socket]

hello?

[trim jolt]

@vernal socket Has your question been resolved?

[velvet gorge]

@bright quarry

[unique sonnet]

See if what is correct? There's no question here

[vernal socket]

yo

[velvet gorge]

@bright quarry wdym 👎

[vernal socket]

$Q+Q^T=0\implies v^T(Q+Q^T)v=0\implies v^T Qv+v^T Q^Tv=0$3

[solid kiln]

Actformain

[vernal socket]

is this correct

[unique sonnet]

Yes

[vernal socket]

i added the 3 by accident

$Q+Q^T=0\implies v^T(Q+Q^T)v=0\implies v^T Qv+v^T Q^Tv=0$

[solid kiln]

Actformain

[bright quarry]

not helping him

[velvet gorge]

Y?

[bright quarry]

^

[vernal socket]

what

bro dont talk about that

[wraith hinge]

!xy

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[ionic pendant]

it is matrix algebra

if you want more than that then i suggest you study a linear algebra textbook

[knotty oriole]

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[cinder lark]

hii

[cinder lark]

Would someone be so kind as to check my answers?

.help

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Page 3/4

[exotic pine]

pooks good, also the second one (a=2.02) should be rounded to im p sure, as it wants to round to 1 decimal place

[cinder lark]

Ah okay so like 2.0

[exotic pine]

yea

[cinder lark]

Alright thanks

Tysm

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[sullen cradle]

@frank rain you need help in that question ?

[trim jolt]

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2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
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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

[frank rain]

1. I don't know where to begin.

[sullen cradle]

just split the integral

first integral 1 to 4 2f(x) - integral 1 to 4 dx

you get this step ?

[frank rain]

yep

split two?

so it becomes 10 - (4-1)?

so is the answer 7

what if the bounds were different

[sullen cradle]

yep i guess

bounds were different ?

then we would have to use the periodic function property

[sullen cradle]

then we need more information to solve the problem i think

[frank rain]

oh ok

[sullen cradle]

they usually mention if the function is periodic over what limits

[frank rain]

idk what that means

[sullen cradle]

check this question for example

@frank rain

they have mentioned that f(x) is periodic with a period 3 so we can split the integral over periods of 3 and solve it

[frank rain]

what does the period mean

[sullen cradle]

i think they have not taught you that still , but if you want i can explain it in short

[frank rain]

nah no need

i have exam tmrw ill focus on whats being tested

thanks for helping and offering to help more

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[hollow nexus]

Here's my equation:
2x - 3(4-x) = 2x - 12 - 3x = 5x - 12
I don't get why we add 2x and 3x if there's a - sign in there. I thought the answer should be = -1x - 12 (because 2x - 3x = -1x)

A more interesting example is this one:
-9a - 2(a-2) - 3(3-a) = -8a - 5
What that means is that the first parentheses are consistent with what I said above (and we get -11a after subtracting), but then addition for some reason kicks is with the second parentheses and after -11a + 3a we get -8a.

How does this work?

[hollow nexus]

Not according to my book

[native shuttle]

I got it

Why

Cause you used your distributive property wrong

We are multiplying -3(4-x)

so how much is -3 * 4

And then it's -3 * -x

Hence it becomes positive

[trim lichen]

2x - 3(4-x) = 2x - 12 - 3x = 5x - 12
||intermediate thing is wrong, should be 2x - 12 + 3x||

[native shuttle]

Like you are multiplying -3 to both not 3

[hollow nexus]

So, let me redo it then

[native shuttle]

Got it?

[hollow nexus]

2x - 3(4-x) =
2x - 3 × 4 - 3 × -x =
2x - 12 + 3x =
5x - 12

Correct?

And the other one then

[native shuttle]

yes

[hollow nexus]

-9a - 2(a-2) - 3(3-a) =
-9a - 2 × a - 2 × (-2) - 3 × 3 - 3 × (-a) =
-9a - 2a + 4 - 9 + 3a =
-11a + (-5) + 3a =
-8a -5

[native shuttle]

Yea

[hollow nexus]

Thanks

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[worthy nest]

how do you do c) and d) ?
I have found how to do a) and b)

[supple copper]

Well what about cos 2pi/9 reminds you about w?

[worthy nest]

w is cis(2 * pi / 9) which means that w is a root of unity and so is cis(2pi/9)

[willow urchin]

theres a more direct relation

[worthy nest]

w = cis(2pi/9) ?

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[warm sedge]

How did my teacher get -10/3 and im getting -11/3 ??

[final kiln]

he messed up

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@warm sedge Has your question been resolved?

[warm sedge]

So its actually -11/3

[oak tartan]

I think it's -13/3

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[neat loom]

I need help with question 8 its note making any sense to me for some reason

[zinc ginkgo]

!ss

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[neat loom]

it's a Kinematics question I'm struggling on

hello?

[crisp kiln]

I'd recommend drawing this out on a piece of paper. the flight is heading NE, and there is a force pressing it from the north. The heading is the direction the plane will face, and the airspeed is going to be how quickly it needs to fly into the wind to make the 300km journey in 45 minutes

the key here is the plan will need to fly faster and indirectly to make the flight

[neat loom]

So would I figure out the displacement that the pressing wind makes to the plane first

[crisp kiln]

I'm not an expert at specifically kinematics but that would be the route I would take. Calculate over the east distance for 45 minutes how much displacement the 80kph wind would have, then adjust the plane to counteract it

[neat loom]

I know that the y and x displacements are 212.13km without the interference of the wind by SOHCAHTOA

the x displacement stays the same when the force is acted upon b/c its headed south at 80km/h

I think that the displacement with the wind will be 60 km south of the destination

how would I figure out how to find the heading to get there instead of where he ends up?

I figured out where the plane gets with 80km winds

what do I do next?

This is what I have so far

Sorry about my hand writing btw

hello?

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[twin yoke]

One message removed from a suspended account.

[simple panther]

I got 791.4 kmph with an angle of 59.6° with the east, is that correct?

[twin yoke]

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[simple panther]

How does M have x in it?

[twin yoke]

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[simple panther]

Shouldn't the limits be substituted?

[solid kiln]

Kenzo

[simple panther]

Oh, you mean it like that

[twin yoke]

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[solid kiln]

Kenzo

[twin yoke]

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[solid kiln]

Kenzo

[twin yoke]

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[solid kiln]

Kenzo

[twin yoke]

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[fluid bloom]

so I'm trying to redo these exercises from the beginning all over again

I understand I need to "Pick" an N now

but I don't quite understand how to go about it

[whole coral]

You want your N to be based on eps, for which that line that 1/N < eps, you can use to say where N must be

[fluid bloom]

so 1 < eps N

1/eps < N

[whole coral]

Yep, that’s it do they tell you that you have to explicitly state what N is? If they don’t, then you can just say that such an N exists

[fluid bloom]

they ask us to justify the limit

so we know eps > 0, 1/eps < N and n >= N

not sure if this is relevant

(note -> isn't a logical implication it's just my way of denoting my "line of thinking")

@whole coral sorry just read your profile

[whole coral]

Well, in that case, I guess you could say that “choose N such that N > 1/eps”, and you’d be done

Otherwise, if you needed to show what N actually is/could be, then you could e.g. choose N = ceil{1/eps} + 1

[fluid bloom]

i'm not sure I need to

the exercise states:

"Prove, through the formal definition of a limit, the following affirmations"

[whole coral]

Ah, I see, mind you sometimes people do want it, but I’m sure you should be fine if you just state that such an N must exist

[fluid bloom]

right but I wouldn't like

give a value for N right

i'd just say N needs to be greater than 1/eps

[whole coral]

You don’t have to, you could, e.g. Archimedes says that such an N must exist, but if you wanted to, you could find one

[fluid bloom]

right. i'm a bit confused though

when you say i can find one

you say N = ceil{1/eps} + 1

what have we found there

we don't know what eps is

we know it's > 0

so how can we say we found an N

[willow urchin]

we found N in terms of eps

[fluid bloom]

haven't I also found N when I say N > 1/eps

or am I just giving a range for N

[willow urchin]

any description of N based on eps is fine

[fluid bloom]

the "+1" is arbitrary, right?

could be +2

could be +100

[willow urchin]

as long as it gives the inequalities we need

[fluid bloom]

it just ensures N > 1/eps

[willow urchin]

mhm

[fluid bloom]

ok i think I get it

then

[whole coral]

The +1 is just in the case that 1/eps is an integer, to make sure you get the strict inequality

[fluid bloom]

is that it then

I've proven the limit?

is there some formality i might be missing?

[willow urchin]

N=ceil(..) not max

and this is considered scratchwork, finding N

you should reformat it as a formal proof

[fluid bloom]

hmm

ceil

is that uhh

[willow urchin]

ill clean it for you so u can see the language they expect

[fluid bloom]

supreme?

[willow urchin]

no

[fluid bloom]

sorry, I do my work in spanish

it's confusing at times

[willow urchin]

ceil(2.3)=3

ceil(pi)=4

[fluid bloom]

ohh

it's the rounding upwards function

[willow urchin]

mhm

so ceiling is a natural name

heres the clean proof

let $\ep>0$. pick $N=\ceil{1/\ep}+1$, so that $N>\frac1\ep$. then for all $n\ge N$,
$$\abs{\frac1n-0}=\frac1n\le\frac1N<\ep$$

[solid kiln]

ロケットジャンプ

[fluid bloom]

i'll ask my prof tomorrow. to make sure i've written |_1/eps + 0.5_|

oh wait im an idiot

that's floor not ceil

or whatever it's called

nevermind ignore all that

[fluid bloom]

that's it then, right?

alright cheers

i'll give another one a go

[willow urchin]

yes

[trim jolt]

@fluid bloom Has your question been resolved?

[fluid bloom]

headed down the right path, I think

[willow urchin]

yes

just put ceil on the whole thing

$\ceil{1/\ep}$

[solid kiln]

ロケットジャンプ

[fluid bloom]

fair enough

i think this is alright

[willow urchin]

for the reader's sake i would label the above scratchwork and the bottom the actual proof

[fluid bloom]

sure

also i think the equality holds between 1/N! and 1/N

if N = 0 or 1

[willow urchin]

yeah so put <= to be safe

[willow urchin]

ya

[fluid bloom]

alright perfect

thanks!

.close

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[willow urchin]

np

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[lilac dagger]

Hi, can I get some help on question d pls

[lilac dagger]

I've tried drawing a diagram, but my logic is flawed somehwere

[jaunty scarab]

show it

[lilac dagger]

and I've tried subtracting the combinations that dont work from 9!

also didnt work

lemme write it more clearly

one sec

[eager dawn]

Have you already done c?

[lilac dagger]

yes

[eager dawn]

Oke so d is c - when there only 1 woman between them

[lilac dagger]

ik this is wrong but my brain breaks when i try to figure out why

[jaunty scarab]

,rotate

[jaunty scarab]

where is the rest?

[lilac dagger]

the subtraction one?

i wasnt able to finish it that way so i scrapped it

[jaunty scarab]

a, b and c

[lilac dagger]

oh

a) 9!
b) 8!*2
c)7!*8C2*2

[jaunty scarab]

wait nvm, you did simplify it later, mb

yeah you combined it in the factorial, didnt rrealize

[lilac dagger]

alg

im j not sure how to approach d

theres a lot of exceptions and I cant keep track of them all

[jaunty scarab]

where does the 8c2 come from in c?

[lilac dagger]

after women have been seated

[jaunty scarab]

also, for d, you can enumerate the ways to be of the men

[lilac dagger]

there are 8 possible seats where men can sit

and theyll sit in 2 of them

8C2

[lilac dagger]

hm ok

ill try

[jaunty scarab]

that sounds weird

but for d

men can be in 14, 15, 16, 17, 18, 19, 25, 26....

and you will have 7 seats remaining for the women

[lilac dagger]

,rotate

[lilac dagger]

like this?

ohh and then for seats 2-7 theres 5 options for man 2

and 1 and 8 theres 6

This was my second attempt answer

Would this be the right answer

hmm

[trim jolt]

@lilac dagger Has your question been resolved?

[native shuttle]

which subquestion

[lilac dagger]

d

[native shuttle]

u got the answer?

[native shuttle]

.

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[frail heron]

.reopen

[trim jolt]

✅

[frail heron]

@native shuttle Has this question been resolved?

[native shuttle]

They didn'trespond

[frail heron]

Well

[native shuttle]

Did you solve it

I got an answer which I think is wrong but

[frail heron]

No, I wasn’t even here XD

[native shuttle]

Check pin

Try to solve if you can

Ping me once you get

[lilac dagger]

sorry I had to go do smth

Not sure if I got it right

[lilac dagger]

This was me attempt

[trim jolt]

@lilac dagger Has your question been resolved?

[lilac dagger]

It’s ok

Ty for helping guys

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[hollow nexus]

3(x-y) + 5(y-x) = 2(y-x)

I didn't get it at all. Why is 2 the common factor? And what happened to the stuff in parentheses?

[hollow nexus]

2 × y = 2y, not 3(x-y)

So we can't get the term back by multiplying

[ionic pendant]

x - y = -(y - x)

[hollow nexus]

Very well
3(-(y-x)) + 5(y-x) = 2(y-x)
Now what?
The common factor seems to be 1(y-x)

[ionic pendant]

3(-(y-x)) = -3(y-x)

[hollow nexus]

Because when you multiply, it doesn't matter which factor is negative and which is positive as long as one is negative and one is positive, right?

[ionic pendant]

when you put a - symbol in front of parentheses it is a shorthand for multiplying by -1

[hollow nexus]

So,
3(-(y-x)) = 3 × (-1) × (y-x) = -3 × (y-x)

[ionic pendant]

yes

[hollow nexus]

Is my explanation correct though?

[ionic pendant]

i'm not really sure what you mean by this

[hollow nexus]

-3(y-x) + 5(y-x) = 2(y-x)
What happens next?

[ionic pendant]

(y-x) is common

[hollow nexus]

I mean,

5 × (-1) = -5
(-5) × 1 = -5

[hollow nexus]

That's right

Wouldn't that give us
(y-x)×((-3)+5)?

[ionic pendant]

yes

[hollow nexus]

So we just simplify the last part?

Essentially getting 2

And then you just swap their places for fun?

Left goes to right, right goes to the left

Just for the kicks

[ionic pendant]

wdym "swap places for fun"?

[hollow nexus]

I mean that would be equal to
(y-x)×2

But the answer is 2(y-x)

So they kinda swapped them around for fun

[ionic pendant]

well the constants started out on the left, so you're the one who swapped them over to the right in the first place

[hollow nexus]

Which made it confusing, which made me think the common factor was somehow 2

[ionic pendant]

besides that it is conventional to place constants on the left

[hollow nexus]

Thanks, I think I got it

[trim jolt]

@hollow nexus Has your question been resolved?

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[shrewd stratus]

can someone

[shrewd stratus]

help me solve equations with an exponent of x

for e.g 1.25 to the power of x = 8.9

at an understandable level

[jaunty nebula]

1.25= 5/4

8.9=9-1/10

Maybe use this way

Or using logarithmic methods

U cant find the specific number using your brain ofc

[quiet timber]

1.25 ^ x = 8.9
log 1.25 ^x = log 8.9
x log 1.25 = log 8.9
x = log 8.9 / log 1.25

[trim jolt]

@shrewd stratus Has your question been resolved?

[quiet timber]

or you could think of it like this
a^b = c
log (base a) c = b
eg 10^2 = 100, log (base 10) 100 = 2
which means
x = log (base 1.25) 8.9, which is same as log 8.9 / log 1.25

When you don't specify the base of the log, that usually default to base of 10
You can have a think on why the following is true
log (base a) b = log b / log a

[shrewd stratus]

I havent been taught log yet

[quiet timber]

oof

[shrewd stratus]

so without log its quite impossible?

[quiet timber]

I think it could be possible. Gimmie a sec (unless other people wanna have a go)

[shrewd stratus]

ty

[trim jolt]

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[quiet timber]

If you are only required to estimate x, then two options that you could use is

1. Guess and check
2. Draw a graph and estimate x

Other method is to make the base equal. aka
a^b = a^c therefore b = c
one example is
4^b = 32
2^2b = 2^5
2b = 5
b = 5/2

For your case, it's kind of difficult to do the last method for a number of 8.9 though in my opinion 🫠

Other than these methods, I can't think of any other way, other then using log

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[naive socket]

i'm having trouble with polynomes. so i have a problem and the result, but when i do it it's not the same.

5z^3 - 7z + 2 - 3z^3 + 2z^2 - 4z + 1
5z^3 - 3z^3 - 7z - 4z + 2 + 1 + 2z^2
2z^3 - 3z + 3 + 2z^2
2z^3 + 2z^2 - 3z + 3

result should be

i don't know how did -11z came out

[tranquil merlin]

-7z - 4z = -11z

[naive socket]

do i have to put brackets?

[tranquil merlin]

not really

u just made a calculation mistake in 2nd step

-7z - 4z = -11z not -3z

[naive socket]

okay

thanks

[tranquil merlin]

np

[naive socket]

.close

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[fresh olive]

Okay I suck at math and I request assistance

[fresh olive]

Assuming one person at 2340 years old has one child every 30 years (that's 78 children) and each of those children has two children and each of those have two children, et cetera, how many descendants would that person have when they are 2340 years old?

[cosmic ferry]

you crafted that question didnt you?

[fresh olive]

Define crafted

[cosmic ferry]

made up

[fresh olive]

All questions are made up

[cosmic ferry]

i meant by yourself?

anyways

we will have to use geometric progression to solve it

im just tryna figure out how

this question is incomplete

how often do the children have children?

[fresh olive]

Once every 30 years

[cosmic ferry]

ok

[fresh olive]

So just once per generation

[cosmic ferry]

ok ok

ok so we see

at t= 30 yr
our guy (O) has a child (1)

so by end of first 30 yr he has 1 desendent

at t = 60 yr
our guy already had a child (1)
and (1) had a child (2)
he has another child (3)
and his child (2) has another child (4)

so by end of 60 yrs he has 3 descendent

at t = 90 yr
our guy already had a child (1)
and (1) had a child (2)
and (2) had a child (3)
and then (0) had a child (5)
then (1) had a child (6)
then (2) had a child (7)
then (3) had a child (8)
then (4) had a child (9)

so by end of yeaar 90 he has 6 descendent

hence equation formed is (n^2 + n)/2

[fresh olive]

4, I think
The first person also has a descendant every 30 years

[cosmic ferry]

yeah i know

i used it

[fresh olive]

Oh, right

[cosmic ferry]

yeah

[spring current]

Yeah idk why but something feels wrong with this
i dont see how the formula ties bakc to yout calculations + you have to show that the same rule keeps applying for all the generations to come you cant just show that it works for 2 times and assume it works for the rest

[cosmic ferry]

brother i did it for 4 generation and it works

• i showed it for 3 gen

and solved it for 4

[fresh olive]

Yeah but this is 78 generations

Genghis Khan levels of offspring

but with Genghis Khan still having children today

[spring current]

yeah plus right off the bat each generation a person has 2 children so his decendants double
so theres gonna be 2^n involved

prob not n²

correct me if im wrong tho

[fresh olive]

And of course for each generation it's +1 because the person themselves is still having children

[cosmic ferry]

wait what 2

isnt everyone having one

damn what

[spring current]

yeah
i think i have a solution now so let me demonstrate it rq

[fresh olive]

The original person is having one child every 30 years, their descendants are having 2 children every 30 years

[spring current]

so first consider a simpler case

just a single person who has 2 children every generation and the next people have 2 children etc..

if we dont count him himself the first gen will just be his 2 children

the second will be the 2 and each of their 2 = 2 + 2x2

[cosmic ferry]

so the genghis is having just one
but his ones are having twos

[spring current]

the third will be the previous ones plus the 2 of each of the previous 4 kids

[cosmic ferry]

point to be noted i didnt count him because he is not his decendent

[spring current]

so 2 + 2x2 + 2x2x2

the pattern is the nth generation is 2 + 2² + 2³... + 2 to the n descendants

as for our 2340 yesr olds case tho it isnt as simple as this

bc he will have 78 children

his first child lives for 78 generations

his second for 77 generations

his third for 76 generstions

etc... do you see why that mkaes sense?

[cosmic ferry]

i know bro

this question is a bluff

just to waste time

[spring current]

im talking to her

[cosmic ferry]

aight

my bad

[fresh olive]

i'm writing an immortal oc for a thing and i want to seek out how many children they would have

[spring current]

dude not all math is for achool you can do math for fun or in this case it seems to be for like a fiction novel

[fresh olive]

How many descendants would she have at the last 24 generations, actually?

I absolutely suck at math

[cosmic ferry]

alright apologies
im too academic

[spring current]

like how many decendants wpuld the last 24 gens themselves be?

[fresh olive]

Yeah

Or uh

How many descendants would be in the last 24 generations

Or the last 720 years of those 2340 years

[spring current]

well based on what i said
the 24th to last generation will live for 24 generations
the 23rd to last generation will live for 23 generations
etc...
so we have the n generation that doubles wvery generatuon thing applied to:
24+23+22+21...+1 generations

so for 24 generations its be 2+2²+...+2²⁴

for 23 itd be 2+2²...+2²³

etc

adding those all up and simplifying youd get
24x2 + 23x2² + 22+2³ etc... + 1x2²⁴

does what i said make sense?

[fresh olive]

Uhhhhh

I think so

[spring current]

btw if someone could double check my work thatd be great bc tbh there were alot of parts where i was too lazy to think about wether we start at the 0th or 1st generation and how it affects the calculations
so therell probably be some "off by one" error in the result

[fresh olive]

That's a little over 16 million people

That's certifiably a lot

In those last 24 generations or in total?

[spring current]

24 gens

[fresh olive]

Is that including the children from the original immortal?

[spring current]

total would be 2⁷⁸+ 2x2⁷⁷ ... + 78x2

[fresh olive]

Okay maybe I should tone down the children she has

[spring current]

no im pretty sure

to account for them youd add 24 for the last 24 gens and 78 for the last 78 gens

but remember theres probably an off by one error stuck somewhere inside there so theres a good chance the answer is half or double what i said

[fresh olive]

I need a fucking graph, man

[spring current]

look in maybe 20 mins or so ill be free to explain this better and ACTUALLY get the exact answer and make sure there aint any off by one errors

ill let you know when im back

[fresh olive]

Anyways I think I got a satisfactory number for my thing

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[grave dove]

hi so what is BF

[grave dove]

i gotta describe it using vector a, b and c

[frosty river]

whats your origin?

B?

[quick tusk]

think of a pythagorean triple using half of a and b

[frosty river]

if so it should just be (b+a)/2 no ?

since BF would just be half the distance of BD which is b+a

[grave dove]

yes but

im kinda confused like

why can u go left into the pyramid now

[frosty river]

look at the arrows which define the direction of a and b

a is the vector going left from b (BA)

again thats just how i've understood it

[grave dove]

shit yes makes sense

[frosty river]

FS is c right

just to double triple check

[grave dove]

yep

[frosty river]

also in a situation where the arrow is pointing opposite direction to what you want

you can use negative of it

[grave dove]

yeah

[frosty river]

so suppose a was actually AB then we just use -a

[grave dove]

AD is b right

[frosty river]

from what you've given me I woul say so

[grave dove]

then -b?

[frosty river]

opposite

BC = AD = b

CB = DA = -b

[grave dove]

so

i said this 😭

[frosty river]

yeah

idk if theres any information i'm missing or not that can change what i've said

[grave dove]

there isnt

[frosty river]

they may redefine it as something else, with what you've given me I would assume that BC = AD and therefore = b

[frosty river]

I understand now but better safe than sorry

i dont wanna tell u the wrong thing on accident

[grave dove]

hm okay

but on the side that we cant see

wheres the arrow pointing to

[frosty river]

looks like vector c is defining FS to me

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[wraith hinge]

Help me out

[quick tusk]

how much will there be after the first year?

[wraith hinge]

hi

can u help @quick tusk

[zinc dove]

Can you read

[trim lichen]

gonna close your other channel

[wraith hinge]

?

what i do ?

or atleast what did i do

[trim lichen]

you opened 2 channels with the same question, you're not supposed to do that

i closed your other channel so you can stay in this one

[wraith hinge]

oh i just started this serever my bad

• using

[trim lichen]

yeah i am just telling you how things work around here

don't take it personally

anyway i will repeat stitches' guiding question for you:

how much will there be after the 1st year?

[wraith hinge]

idk

[trim lichen]

do you know how percentages work generlaly

generally*

[wraith hinge]

nuh

i got a understanding for them

[trim lichen]

https://www.youtube.com/watch?v=WYWPuG-8U5Q&list=PL0o_zxa4K1BXWS3L0IqFwKk8Rr9dcVXPw

[wraith hinge]

a little

[trim lichen]

here's an entire playlist for you to watch

[wraith hinge]

ok

[trim lichen]

but once you're up to speed on that:

• in the first year, the account gains money equal to 2% of £5000
• in the second year, the account gains money equal to 2% of however much was in there after the first year

[wraith hinge]

Yes

gain 2 %

of initail amount

?

ohk

yeah

https://tenor.com/view/i-understand-it-now-ok-i-understand-it-now-i-understand-it-gurm-bear-gif-4859748791707698675

100 of 2 % then answer + 100

correct ?

IM SMART

Yesss

I have no idea

yes

50*x

x is varable

variable

nope

2.5

and 250

[native shuttle]

You can just use compound interest formula

[wraith hinge]

oh 2 tutors talking ?

[wraith hinge]

what is it

[native shuttle]

So that is

Idk how to derive it

Since it's two years you can find like 2 simple interests

and add it

[wraith hinge]

Im doing compound intrest

[native shuttle]

Yes

[wraith hinge]

ok

?

oh

[native shuttle]

So you want Beluga to just use the formula?

Oh I thought that was for me

[wraith hinge]

Oh i know the answer

what ever he said

man im losing BRAIN CELLS

[native shuttle]

So is derivation of compound interest using simple interest

[native shuttle]

what is 50%?

[wraith hinge]

1/2

3/10

ik

102/100

0.102

[native shuttle]

lol

[wraith hinge]

10.02

1.02

[native shuttle]

ok

[wraith hinge]

Sorry

mistype

YO PAUSE I HAVE MORE THAN 3 BRAIN CELLS

[native shuttle]

mq r u gonna derive compound interest?

nope

I think simple interest

[wraith hinge]

NOOOOOO

[native shuttle]

k

[wraith hinge]

yeah whatever she said

or he

[native shuttle]

I know what is compound interest

yea

yea

[wraith hinge]

I UNDERSTAND IT NOW

[native shuttle]

Lol

[wraith hinge]

Now dev needes help

im goo

[native shuttle]

yea

[solid kiln]

mq

mq

[native shuttle]

I know

1+2/100

OHH

but why raised to n

ok

oh so exponential

So it's like simple interest

PRT/100

p(R^t

PRT/100

[wraith hinge]

forget simple interest for now

[native shuttle]

@wraith hinge compound interest is multiple simple interests

We just need to memorize about 500+ formulas

No time for derivation

[wraith hinge]

if u see it from that angle , then okay

[native shuttle]

ok thanks

I learnt this like 4 years ago

lol

kk

I just solved a problem recently using that formula

ok then ig beluga can close

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[vocal hazel]

How would one approach part ii? I’ve tried plugging in the sequence for x in the a lipshcitz inequality and y = 0, however I only end up with the sequence converging

[vocal hazel]

I’m thinking maybe take the difference between two consecutive minima/maxima?

However I get a pretty messy inequality that I don’t really know how to analyze

[vocal hazel]

My approach has been assume that the hypothesis is true and then show a contradiction

[dense breach]

You want to make the y difference (relatively) large and the x difference small, right

[vocal hazel]

I.e. in this case the left hand side diverges

[vocal hazel]

Yes

[dense breach]

And the weird behavior this function exhibits is close to the origin

[vocal hazel]

Yeah

[dense breach]

So maybe let x be the origin, and let y be some point you know won't map to 0

[vocal hazel]

Yeah that’s what I tried I think

[dense breach]

Like choose some small y s.t. y^-M is a multiple of pi

[vocal hazel]

But I get that it converges to 0 when you manipulate the inequality

[vocal hazel]

Yes

[dense breach]

Hmm

And this isn't strong enough?

[vocal hazel]

But I don’t think that quite works, since what we ended up with is $(\pi n)^{-2/M + \alpha/M} \leq C$

[solid kiln]

LXDL

[vocal hazel]

Yeah

Since we only get $\alpha > 2$

[solid kiln]

LXDL

[vocal hazel]

Not the desired inequality

[dense breach]

I'm confused how you're getting something with alpha and M in it at the same time

Eh

Maybe I see

[vocal hazel]

Oh that’s after plugging in $x = (\pi n)^{-1/M}$

[solid kiln]

LXDL

[dense breach]

Right cause this should just match x^2 on that

Ok

[vocal hazel]

Ye

[dense breach]

So you probably want to choose two adjacent such x

Technically not maxima

[vocal hazel]

Yeah but then I end up with very bad inequality

[dense breach]

Your maxima will be really weird due to the x^2 part

[vocal hazel]

Oh why not maxima? Oh wait because then they would cancel to 0?

[dense breach]

Well there's that yeah

You want a high point and a low point

[vocal hazel]

Sorry I mean a maxima and a minima

[dense breach]

But also because of the x^2 part your extrema are slightly shifted off of where the cos function is exactly 1

But that's not important, the values where cos =1 are good enough

[vocal hazel]

Yeah hmm

So then I take ( pi * (n+1))^(-1/M) as well?

Still doesn’t really work tho I think

[vocal hazel]

Main problem is the inequality is not good

<@&286206848099549185>

[vocal hazel]

Sry my handwriting is pretty bad

[trim jolt]

@vocal hazel Has your question been resolved?

[vocal hazel]

hmm not sure really whats going on here

[tepid hamlet]

I don't think anyone is from that writing

[trim jolt]

@vocal hazel Has your question been resolved?

[unkempt oriole]

The hell is this

Is that some ancient chinese scriptures?

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[bleak oasis]

can someone please double check my work? i would appreciate it.

[bleak oasis]

.close

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[spring cradle]

how would I evaluate this? i cant think of any way to do it. i tried changing it from dx dy to dy dx to see if that'd be easier but im not seeing any way to do it.

[spring cradle]

<@&268886789983436800>

[gusty plank]

e^(x^2) doesnt have an elementary anti derivative

Are you sure you aren't missing something?

[spring cradle]

yeah this is the entire problem

maybe its just a typo or something then

[zinc ginkgo]

did you learn fubini's theorem

[spring cradle]

no

wait is that just what says you can switch the order of integration?

if thats all it is then yes we learned that. just wasn't told the name of the theorem

[spring cradle]

isnt that what i did above

i changed the order of integration in part b but still got stuck

also the region is a triangle in my problem i think

[zinc ginkgo]

your shaded region is sketched wrong

0 <= x <= y is the lower triangle, not upper

[spring cradle]

doesnt the lower triangle go from x = y to x = 3

[zinc ginkgo]

ah shoot my bad i had the limits switched in my head

this should be able to be solved with u sub

factor out exp(x^2) first

[spring cradle]

do you make u = x^2

im stuck here

[errant vortex]

I'm almost certain the value of the integral can't be expressed with elementary functions; are you sure there isn't a typo in the question or something?

[zinc ginkgo]

try u = 3-x first, then v= something else

[errant vortex]

since you can find the integral of -xe^(x^2) dx from 0 to 3(in fact, it's -(e^9-1)/2), and certainly cannot find the integral of 3e^(x^2) dx from 0 to 3(that's basically the error function, minus the negative exponent), I would doubt that you can express the sum of the two with elementary functions

[spring cradle]

okay i am guessing it probably is a typo then

thank you

.close

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[trim jolt]

@daring lichen Has your question been resolved?

[sacred jackal]

!showwork

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[crimson plank]

i’m js stuck entirely

i have no clue

[torpid ermine]

HI

[crimson plank]

hi

<@&286206848099549185>

i think it’s 4.5

given the chord length formula

[burnt panther]

hows it goin

did u do it or do you still need help @crimson plank

it is 4.5 but lemme know if you need help finding the answer

[trim jolt]

@crimson plank Has your question been resolved?

[crimson plank]

wait some i’m right to the answer of the question

or just for chord length

[crimson plank]

wait does the chord length answer the question

[burnt panther]

yes

[crimson plank]

oh thanks man

👍

[burnt panther]

How did you solve it?

you said a formula?

[crimson plank]

chord lenggth formula

[burnt panther]

you could make a right triangle

[crimson plank]

the simple one given we didn’t get a central angle

[crimson plank]

from the chord?

[burnt panther]

yes

[crimson plank]

i js put 2sqrt 2.6^2 - 1.3^2

[burnt panther]

one vertex is the center of the circle, another vertex is where the chord touches the circle, and the last vertex is directly below the center of the circle on the chord

[crimson plank]

ohhh

wait but how would you find those lengths given you turn it into a right triangle

hypo still radius

oh yeah

that makes sense

[burnt panther]

yeah

[crimson plank]

1.3 opp

[burnt panther]

you get hypotenuse and 3.9-2.6 for 1 leg

[crimson plank]

and pathag

[burnt panther]

exactly

[crimson plank]

then *2

ohhhh

thanks man!!!

[burnt panther]

I do whatever I can to not use formulas cuz if u forget it then ur done

in a test scenario

[crimson plank]

yeah

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[coarse kettle]

Can someone explain where I went wrong

Cause I know I do it right up till 4m+2n=-4 and 9m-3n=21

But I don't understand what I did wrong

[burnt panther]

m should be 1 and n should be -4

you just solved it wrong

[coarse kettle]

How would you solve it?

Nvm I'm dumb

Bro I'm actually selling my tests with these kind of mistakes

Thanks

.close

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[limber edge]

How and why do the terms in a polynomial affect its curvature? I ask because I was trying to understand Taylor series.

[pastel wren]

The degree of a polynomial describes the number of curves it will have.

Number of curves = degree - 1

X = 7 for example, it's just a straight line since the degree (highest power of X) is 1

Quadratic equations (polynomials with degree 2: containing x^2) have 1 curve

Try it out on desmos , it's pretty easy to understsnd that way. Come up with some random polynomials and graph them in it

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@limber edge Has your question been resolved?

[pastel wren]

Bro writing a book

[limber edge]

Ok. Yeah I was just confused when it came to approximating functions by using Taylor series. Sorry I am having some trouble typing this out as a question. Basically, why does the highest degree of a quadratic affect the slope of the parabola when graphed? I'm just lost in why or how that term which is squared is affecting the curvature of the parabola?

Lol

Does that make any sense?

Like where is the crossover here from equation to graph?

Sorry if that doesn't make sense? 😔

[wintry mulch]

can i get some help when yall are done

[pastel wren]

If you just graph the function

y = x^2

You will get a parabola. The smaller terms are kind of absorbed by this bigger value (x^2).

[wintry mulch]

im getting irritated

[pastel wren]

You need to post on a new help channel

[wintry mulch]

i did for like 2 days now

[limber edge]

Ok so like what would I do if I had to graph that equation myself, by hand? How would I conceive the slope of the graph to be, and how would I interpret more terms?

[pastel wren]

Now imagine an equation

y = x^2 + 1

Here x^2 draws the parabola, the +1 would simply shift the whole graph by 1 unit upwards

Similarly

If we have

y = x^2 + x + 1

We will have the parabola of exactly the same shape, but shifted upwards by "X + 1" units

The curvature of a parabola is affected by the coefficient of x^2

So

y = 2x^2

Has a steeper curve because 2 is being multiplied to x^2

y = x^2/2 will have a more flattened curve

I'd advise to out these equations in desmos and see the results

The curve is upside down if the coefficient of x^2 is negative

[limber edge]

Ok could you elaborate on those coefficients? Is that term, say 2x^2 essentially a slope?

[pastel wren]

Notice the difference, red green blue functions

[pastel wren]

The term 2x^2 represents a steeper parabola than x^2

[limber edge]

So does y equal the slope of the line at x=0?

In your examples...

[pastel wren]

My examples are simply showing different quadratic equations

y = 2x^2

It's a valid quadratic equation

I'm graphing specific terms to show you what they look like and how the curve is affected by the coefficients

[limber edge]

Ok, so yeah I am just confused as to how more terms affect the curvature.

Or more coefficients, rather

What's going on behind the scenes here?

Lol

When speaking from the perspective of graphing a polynomial

[pastel wren]

The other terms don't affect the curvature at all

In case of quadratic the curvature only depends upon x^2 and it's coefficient

When you multiply x^2 with a bigger value, the graph becomes steeper because you're basically multiplying every y point by that coefficient , it's the opposite for dividing x^2 by some value. You can better understand it by manually graphing 2-3 simple quadratics

[limber edge]

Ok

Thank you

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@limber edge Has your question been resolved?

[limber edge]

Yes

Yes

Yes

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[marsh forum]

so what I was thinking was

$\pdv{z}{x} = f'(x-y); \pdv{z}{y}= -f'(x-y)$
\
Adding them up
\
$\pdv{z}{x} + \pdv{z}{y} =0$

[solid kiln]

What a wonderful world !

[spring current]

I'm not here to help since i dont hve that much experience with calc 3, but i just wanna know is z is a single or multivariable function here? cuz its taking in a single input (x-y) but partial derivatives are being taken

[grim saffron]

I think it's supposed to be a multivariable function with argument x and y

[marsh forum]

Multi var

[ionic pendant]

z is a function of two variables, f is a function of one variable

[spring current]

ohh that makes sense ty i was thinking of f and z as the same thing

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[mystic robin]

i want to isolate for h dont know how

[frozen plover]

multiply both sides by h and use the quadratic formula

[mystic robin]

idk what quadratic formula is

[frozen plover]

[mystic robin]

lol

[solid kiln]

neon

[mystic robin]

ye

[frozen plover]

right so that's basically what you need to do

[mystic robin]

wait a sec

[solid kiln]

neon

[mystic robin]

so

[mystic robin]

huh😭

[frozen plover]

yeah keep going

i just multiplied by 2h instead

[mystic robin]

alr

so?

and then - by 20h?

[mystic robin]

right?

[frozen plover]

yes

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[dusty mist]

Need help for this question
"A ship, “Adventure Galley”, leaves the port at (8, 1) at 8 pm travelling at maximum speed of 17 km/hr
in the direction 61.93°T. At the same time a navy helicopter leaves (0, 5) travelling at 25 km/hr in the
direction 73.74°T. In order to evade the navy, at 8:30 pm the ship changes direction to 28.07°T. At 9:00 pm
the navy helicopter changes direction to 16.26°T. Does the helicopter meet the ship? If so, in what value of t (time in hours)?"

[split chasm]

what have you tried

[dusty mist]

can I send screenshots?

[split chasm]

yes

[dusty mist]

Its like a maths investigation

ignore where it says airplane

I meant helicopter