help-36

[south dirge]

it wasnt wrong, you just forgot to write the step while you did the differetiaton in ur head!

[hardy jackal]

wait so like what should i write

i just assume that would be the simplest way

[south dirge]

It should have just been 3 instead of 3t right?

[hardy jackal]

oh

ur right

[south dirge]

as you differentiated in that step,

[hardy jackal]

lmao

bruhhh so many silly mistakes

[south dirge]

lmao i havent heard this in so long

[hardy jackal]

LOLL

[south dirge]

One of my best friends used to say this

[hardy jackal]

im your best friend

[south dirge]

That would be really sweet of you but hes been dead for 4 years now🙂

[hardy jackal]

oh my gosh im so sorry

[south dirge]

Good job!

[south dirge]

Oh thats alrt lmao

This seems right now!

No other errors

[hardy jackal]

i redid b

is this look okay

[south dirge]

Yeah

Welp anymore?

[hardy jackal]

thats all for this assignment

everything look okay then?

[south dirge]

Yeah!!

Good job in not making any silly mistakes!

[hardy jackal]

bro

[south dirge]

?

[hardy jackal]

thank you so much for all the help you have been so helpful

[south dirge]

Anytime!

!done

[final saddle]

If you are done with this channel, please mark your problem as solved by typing .close

[south dirge]

Have a nice day!

[hardy jackal]

yes you too!! thank you again

.close

[final saddle]

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[shell plover]

How do I go about finding the max on lagrange bound error formula?

[shell plover]

from what i've heard you find the n+1 derivative then test both ends ( center and given x value) to see which makes that derivative the largest

then i use the largest ver as my M

ts for calc BC

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[winter dagger]

<@&268886789983436800>

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[keen vector]

Can someone pls tell me where I went wrong with part b

I get that the angle is 89 or something when it’s suppose to be 14

I’m doing part b btw

[night raft]

what does the first number read?

[analog kindle]

-2401

[keen vector]

Ohhh

It’s suppose to be -25 right

[night raft]

yeah, I don't think it's meant to be -2401

[keen vector]

Yeah oops thanks

Also

I get that tanx= 1/2 or -1/10

But the markscheme says 1/4

[night raft]

like 1/4 on its own?

[night raft]

,w 100tan(x) + 5 = 0

[soft zealot]

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Requested by mxrgd.

[keen vector]

Is this another method?

[night raft]

if you did 100tan(x) + 5, you'd get a negative angle

so that's why the mark scheme rejects it

[keen vector]

Where’d you get 100tanx+5?

[night raft]

here

i know it's meant to be alpha but I just replaced it with x

[keen vector]

Ah

Did I set up the quadratic wrong

.close

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[gritty flume]

The answer in the book is -45

But I’m getting positive

[woven ledge]

in the first one you got the sign of sin wrong, and in the second one you got the sign of cos wrong

[gritty flume]

How pls

[woven ledge]

well its better if you explain your thought process

[gritty flume]

Huh

[final tangle]

specifically what identities are you applying to get from
on the left side: cos(90°+t) to sin(t)
on the right side: -cos(-x - 360°) to -cos(x + 360°)

[final saddle]

@gritty flume Has your question been resolved?

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[lime crest]

Determine all functions $f: \mathbb{N} \to \mathbb{N}$ such that [f(2m+2n) = f(m)f(n) ]

[soft zealot]

Copter

[lime crest]

no idea how to do this

[final saddle]

@lime crest Has your question been resolved?

[lime crest]

<@&286206848099549185>

[kindred mortar]

What have you tried ?

[analog kindle]

Think powers

Do you want an answer?

It's f(x)= ||a^x/2||

[lime crest]

not really anything

[kindred mortar]

try special cases

[lime crest]

m=n, etc doesnt get me anything

[lime crest]

what😭

i thought f(n) = 1 was the only answer

[lime crest]

isnt this not N -> N?

[analog kindle]

Shoot mb

[kindred mortar]

f(0) ? f(1) ?

[lime crest]

0 not in N

[analog kindle]

Sorry. My fault

[lime crest]

alg

[analog kindle]

Well since exponential funcs don't work...I'm kinda lost

F(4n)=(f(n))²

[lime crest]

yeah

[analog kindle]

F(10n)=f(n)³

F(x)=f(2(x+y))/f(y)..

Just stating random things atp

💔

Yeah so I sorta just messed around and got this

Can anyone cross check?

So ig f(x)=1 only

[lime crest]

hmm

[analog kindle]

I make dum mistakes regularly so check once 🙏

[south dirge]

Are you all trying random functions?

[analog kindle]

No.

[south dirge]

Oh you kept m as n

[analog kindle]

I'm spamming the property

Lmao

[kindred mortar]

@lime crest I have an idea but i think you won't like it

[south dirge]

Are you trying to analyze the function for various behavious?

As i did the same and i am getting a funny answer but yeah it is working

[kindred mortar]

nvm it wont work

[lime crest]

aw

[south dirge]

Well should i propose my method?

[steel cypress]

f(1)f(n+1) = f(2)f(n) ... ?

[lime crest]

f(n+1) = cf(n)

i got it yeyey

thanks

.close

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[median bay]

Linear (Old math): y = 2x + 3
(This makes a straight line on a graph).

[median bay]

Can Anyone tell what this mean

i ONLY KNOW BASIC MATH

[final tangle]

if you plot that relation on the xy-plane (aka cartesian plane)
you'll see a straight line

,w graph y = 2x+3

[soft zealot]

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[median bay]

ok

no i understand

[final tangle]

all points on that line will satisfy the relationship
of y = 2x + 3

[median bay]

thanks

[final saddle]

@median bay Has your question been resolved?

[final saddle]

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[hard blaze]

How is the blue angle equal to 20? is there something im not seeing, I know this is probably one of those angle rules but I can't figure out which one.

[open hill]

That F is mg meaning its direction is direct to the ground which is perpendicular to it meaning it creates a right angle
In that triangle the other angle would be 70 and since we know the object is perpendicular to the surface means that the other side of the angle would be 90-70 which is 20 degrees

[night raft]

thought you said you were gonna go 💔

anyways hi

[open hill]

Ello i saw physics

[hard blaze]

I have one confusion

[open hill]

Go ahead

Do yk Arabic perchance?

[hard blaze]

give me a second i need to sketch it

[open hill]

Alr

[hard blaze]

I should but I don't, learned how to read and write in school when i was younger and forgot everything now

[open hill]

Ah said that cuz of ur name

[hard blaze]

yeah i know its a common arab name

where u from

[open hill]

Yea it means a leopard

[open hill]

Eh id rather not say

[hard blaze]

all good

[hard blaze]

in the original image the 20 degrees are opposite eachother but in the sketch you sent 20 degree is opposite the 70 degree

is it supposed to be like that?

oh shit

i sent the wrong image

[open hill]

Oh

[hard blaze]

meant to send this

[open hill]

That angle is 70

Triangles add up to 180 degrees

[hard blaze]

oh wait ur right

[open hill]

Do u get it now?

[hard blaze]

Ohhhh i get it now one sec let me send one more sketch

[open hill]

I can explain it with other triangles too

[hard blaze]

@open hill hard to draw witha mouse but this is it right?

if not please correct me

[hard blaze]

drawing that second triangle makes it make a lot more sense now

[open hill]

U drew 90 90 and 70?

[open hill]

yea do u get how we get the 20 after finding the 70?

[hard blaze]

yes, is that not right?

[hard blaze]

yeah because a right angle is = 90

[open hill]

YESS

[open hill]

no it is just making sure

Okay thats it then

If ur done close the channel with .close

Goodluck with school

[hard blaze]

Thanks, I appreciate your help a lot. Have a good day!

.close

[final saddle]

Channel closed

Closed by @hard blaze

Use .reopen if this was a mistake.

[hard blaze]

wait

I need help with one more thing related to this question

.reopen

[final saddle]

✅ Original question: #help-36 message

[hard blaze]

where did he get sin 30 from?

[strange pelican]

probably typo

,w 3/sin(20 degrees)

[open hill]

Yea its 20

Sin(20)=3/ps

[soft zealot]

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Requested by mis.ter.x

[open hill]

Yea

[hard blaze]

ohh a typo

glad i got that cleared up, thanks once again guys..

This discord is a life saver

.close

[final saddle]

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[hard blaze]

This is a easy questions so I'm frustrated I'm not able to get it right, I know moment is = force*perpendicular distance

Now how do i find the force and perpendicular distance for the nut? do I break it down into its vertical and horizontal components?

[somber fog]

Rember, the horizontal component is calculated using the cosine.

[strange pelican]

find the perpendicular distance from the nut to force

[hard blaze]

Found that as 0,21

[strange pelican]

yh you can do it that way as well find the component of force perpendicular to spanner and mutiply 24

[hard blaze]

I converted 24cm into 0.24m

[hard blaze]

I'm gonna be honest how do i that? because i forgot

[strange pelican]

do yk how to break forces into components ?

[hard blaze]

yuh

[strange pelican]

hm.. so what troubles you

[somber fog]

Correct.

[hard blaze]

hold on just to confirm the vertical component is cos30=20x0.24 and the horizontal component is sin30x0.24 right?

[strange pelican]

you dot have vertical and horizontal components, here forces is downwards, so you have along the spanner and perpendicular to it
yh
moment = cos30x20x0.24

and force along = sin30x0.24

[somber fog]

Use that.

[zealous dew]

Hello anyone know? 1+1=y= x+79 - x2 = x + 7Maka x = 1 dan x =
-2 V = пt112(9-x2)2 - (x + 7)2dx V= п12(x4-18x2+81)-(x2 +14x +49)dx V = п/

[night raft]

make a seperate help channel since this one is occupied

[somber fog]

!occupied

[final saddle]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[hard blaze]

okay so corrrect me if im wrong the perpendidcular distance is the horizontal component which I calculated as 0.21 and the force is 20N?

[somber fog]

Correct!

[tired hill]

V = 333π /5

[somber fog]

!noans

[final saddle]

The purpose of this server is to help you learn; please don't ask for direct answers. Ask for guidance, explanations, or feedback instead.

[strange pelican]

yes

[tired hill]

ok

[hard blaze]

okay, but if we multiple those two values we get 4.8NM which is not the correct answer

the correct answer is A

[strange pelican]

huh

[hard blaze]

can I ask why you drew the triangle upwards? because i drew it the other way around

[somber fog]

Then, we need to use sin.

[strange pelican]

oh 0.24/2 = 0.12

[tired hill]

why sin and not cos

[hard blaze]

yeah same question i have here

[strange pelican]

0.12 * 20 = 2.4

[hard blaze]

why are you diving by 2?

[somber fog]

Because if it says that it is A we would be applying it to the component of the force that is perpendicular to the handle, not to the horizontal distance.

[tired hill]

oh ok

[hard blaze]

Is the line in blue this perpendicular to the handle that you are talking about ?

[somber fog]

Yeah!

[hard blaze]

I have another question, how do i find the line of action during questions like these? because I think thats what I struggle with the most.

[hard blaze]

And can you explain why we use sin again, which angle are we measuring from?

[somber fog]

The 30 one.

Since the vertival height is the opposite leg.

[hard blaze]

using that we get 20/24 which is 4.8, but the answer is 2.4? I know we're going in circles here but im trying to understand

[somber fog]

It's not that.

$$d = 24\text{ cm} \cdot \sin(30^\circ)$$, right?

[soft zealot]

Ga³¹Br³⁵I⁵³9000✞

[hard blaze]

is d, distance?

[hard blaze]

That gets the correct answer, but I don't understand why you're multiplying them

[somber fog]

The further you push, the more force you make, right?

[hard blaze]

yes, but which formula are you using I thought sin was opposite/hypo which is 20/24

Sorry if im sounding stupid, i hate this topic lol

[somber fog]

Don't worry.

[somber fog]

No, it is for distances.

[hard blaze]

distance is speed * time? neither of those quantities are relevant in this question.

[somber fog]

We use this formula: $$\text{Height} = \text{Handle length} \cdot \sin(30^\circ)$$

[soft zealot]

Ga³¹Br³⁵I⁵³9000✞

[somber fog]

Do you understand it better?

[final saddle]

@hard blaze Has your question been resolved?

[final saddle]

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[rugged merlin]

<@&268886789983436800>

[final saddle]

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[quartz swift]

Guys how exactly do we go about thinking about such questions??

[rugged merlin]

Relate to the definition of periodicity

That's your starting point

Could you define it?

[quartz swift]

Here if h was the period then f(x+h)= f(x)

In simple words functions repeats its values after a certain interval

But if all that is given in question is period is greater than h

[rugged merlin]

Sure

[quartz swift]

Then how do I relate the two?

[rugged merlin]

I mean it doesn't affect the definition itself. It's like me telling you that you may have a collection of sin(ax+b) functions with periods of at least pi. That fact didn't change the definition of sin as a periodic function

Might be better if you just start by questioning the parts at face value, though. For example, (A) is suggesting that for every single value h' larger than h, h' is a period of the function. Is this true when you apply it to, say, a sine function ?

[scenic pendant]

can you confirm that B and C are false ?

[quartz swift]

For ever h dash I mean

I don’t think so for every

But if every was not stated, then could A be the answer??

For example if they just used for some h dash

[south dirge]

Yeah!

[south dirge]

But again since every is mentioned, it isnt!!

[quartz swift]

Ah I see

B and C are what confuse me the most now

[south dirge]

Okay lets take the case of any function,

say f(x) = sinx

Here the periodicity is 2pi, and since h is less than 2pi,

[quartz swift]

Ohh wait, so my reasoning for why C could be the answer is, in B it states no period can exist , but in C we are not completely denying the possibility of a period existing

[south dirge]

Do you think for any value of x, sin(x+h) = sin(x)??

[quartz swift]

But in question they said it is periodic for some value

So ye I think C is a better bet

[south dirge]

Yup! for the first statement

[south dirge]

for C yes

[quartz swift]

But with none of these I feel a little unsure

[south dirge]

wait i didnt really follow?

Really sorry but could you elaborate a little?

[quartz swift]

I meant, with none of the statements are correct, I just feel a bit unsure with c

Which is something I struggle with for a lot of questions

So how can I verify or make sure what I pick is correct

[worldly spruce]

<@&268886789983436800> obviously hasn't learned from the timeout

[severe canyon]

Stop trolling or not helping <@&268886789983436800>

[south dirge]

wait this is trolling?

you can ping for this stuff?

[severe canyon]

Yup, he's been doing it for a while

[severe canyon]

Yeah

[south dirge]

Oh thats why it started to annoy me a little slowly😅

[tulip coyote]

If someone's being deliberately obstructive or unhelpful, yep

[south dirge]

Oh okay ty🙏

[south dirge]

Really silly doubt but here can one or more than one options be correct?

[quartz swift]

Nope

[south dirge]

Ah i see nvm

So did you understand how we ruled out B?

[quartz swift]

Yess

Now im just a tat bit doubtful about C or D , how do we eliminate D here??

[south dirge]

Okay so when we think about a periodic function, its got to be having a value of f(x1) = f(x2)

where x1 and x2 are not related by periodicity

[south dirge]

Think about this!

I would suggest drawing any rough sketch of a periodic function and observing this!

Well since you are kind of confused, try just simply drawing the graph of f(x)

Observe that sin(pi/4) and sin(3pi/4) are same!!

[midnight sky]

@languid hatch

[south dirge]

Tho pi/4 and 3pi/4 are not related to each other by period aka 2pi, they still are equal for some values of x only

[midnight sky]

Bro where did you go

[worldly spruce]

I do just want to say this. I am incredibly sorry ArstyVamp for interrupting in your help channel but this behaviour bothers me.

@languid hatch take this time to reflect on yourself. Trolling in your own help channel is one thing, and I just might (not really) understand it, since for some reason it's fun for you. But in reality you are wasting your own time, and, much more importantly, the time of helpers who volunteer here with no incentive, with their only wish being to try and help others.

BUT, jumping in into other active help channels is just incredibly selfish behaviour. By doing this, you are confusing the helpee, the helper(s) and simply making everyone lose the thread of the discussion. People come here because they expect a nice environment in which they can learn something new or understand something they are having trouble with. And people like you ruin that experience for so many others just for your own satisfaction. Think about this the next time you want to troll in other people's channels.

[midnight sky]

You told me you were supposed to teach me math

[quartz swift]

Ohh yesss

Makes sense

Understood it

Thank you soo much <<3

[south dirge]

Your welcome!

Anymore?

[midnight sky]

Just finished reading it

What did he do

He promised me to teach me math

[south dirge]

He was trolling unfortunately!

[midnight sky]

Now I feel like he was trolling with me too

Hard to believe people online

[south dirge]

Yeah thats sad

[midnight sky]

He's timed out?

[south dirge]

I think so

[quartz swift]

No, clear with it now

[worldly spruce]

I am genuinely baffled by how stupid you think we are

[south dirge]

Okey have a great day/night!!

[quartz swift]

Thankss u too, take care!!

[south dirge]

!done

[final saddle]

If you are done with this channel, please mark your problem as solved by typing .close

[quartz swift]

.close

[final saddle]

Channel closed

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Use .reopen if this was a mistake.

[midnight sky]

Wdym

[worldly spruce]

I don't even see the point in responding lol

[midnight sky]

I mean I don't need to stay in this shi server all I just wanted to say he was feeling sorry about it and he won't repeat this again that's if

It

[south dirge]

Lets leave this convo at this point, what part of maths you wanted help in?

[oak nimbus]

😴

[south dirge]

Sorry to inform you but he did repeat it

[final saddle]

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[stable viper]

Can someone verify my working out here?

[leaden moon]

you can't do this freely

there is still one more case you haven't considered

[stable viper]

the negative one?

hm

ok so is this fine now

[final tangle]

write full equations,
also don't forget the initial restrictions

[final saddle]

@stable viper Has your question been resolved?

[stable viper]

i see

so i just tke x = 0 and -2

ok thx

.close

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[final saddle]

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[delicate kiln]

Can someone spot where am I messing up?

[leaden moon]

,rccw

[delicate kiln]

My answer is 35.25 but the actual answer is 20.7

How

[leaden moon]

wait hold on

[delicate kiln]

Okay

[somber fog]

Let me see.

[leaden moon]

im just going to tell you that

you should not round after calculations immediately

[delicate kiln]

But even if it’s a rounding error this is way too large

[leaden moon]

because the error will grow larger and larger the more you round

[delicate kiln]

Oh wait I think I know

[leaden moon]

also this one is wrong

[delicate kiln]

How come

[leaden moon]

A is not 106.06 cm^2

[delicate kiln]

Oh I just didn’t add the area of a tectsngle

[leaden moon]

oh mb

[delicate kiln]

So it was the area of the triangle + rectangle

Nah I didn’t specify mb

[leaden moon]

writing like that could confuse people ngl

[delicate kiln]

Ye

Oh I think ik where I messed up idk let me just double check

[leaden moon]

hm

but i got the area of the triangle to be 35.35 exactly tho

[delicate kiln]

Wait what how

[leaden moon]

1/2(14.14)(5) is 35.35

also im not sure how that's cosine works

[delicate kiln]

I carried the decimal in my calculated

So the actual thing is 35.355339

[delicate kiln]

Ye I messed up here I’m jsut rechecking it cuz it should be 5/15

[leaden moon]

yep

[delicate kiln]

Okay I’m somehow getting 0.3 more than the answer

Is that cuz of rounding errors but that’s too large

[leaden moon]

.3 is normal for a rounding error tho

[delicate kiln]

Oh

Then how do I get it exactly to the answer

Do I do 4dp

[leaden moon]

it doesn't make it a big deal tho

[leaden moon]

you could try to round all of your calculations to 4 dp like you said

or just don't round until you get your final answer

[delicate kiln]

Oh alr

Okay I think I got it now lemme just recheck all my steps

Ty for ur help

[leaden moon]

np

[delicate kiln]

.close

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[quartz swift]

guys how do we find the value of terms in numerator in terms of n??

[final saddle]

@quartz swift Has your question been resolved?

[night raft]

write the numerator as a sum

do you know Stolz-Cesaro Theorem as well?

Also I assume c represents a constant here

[south dirge]

yeah i think so too!

[night raft]

basically this $\lim_{n \to \infty} \frac{a_n}{b_n} = \lim_{n \to \infty} \frac{a_n - a_{n-1}}{b_n - b_{n-1}}$

[soft zealot]

MxRgD

[quartz swift]

never heard of it

[quartz swift]

hmm i see

[night raft]

your $a_n - a_{n-1} = n^{\frac{1}{3}}$ and your $b_n - b_{n-1} = n^t - (n-1)^t$ in this case

[soft zealot]

MxRgD

[night raft]

then you can use binomal theorem in the denominator to evalute the limit

[quartz swift]

why didnt we first find the sum of numerator here??

[night raft]

our $a_n = \sum_{i=1}^{n} i^{\frac{1}{3}}$

[soft zealot]

MxRgD

[night raft]

i is just a starting index, so what would our a_n - a_n-1 be?

[night raft]

also the sum i gave here just represents the numerator

[quartz swift]

omgg yes n^1/3

[night raft]

yeah

[quartz swift]

i see

[night raft]

and our b_n = n^t right

so our b_n - b_n-1 must be?

[quartz swift]

n^4 - (n-1) ^4 ??

[night raft]

where did the 4 come from?

[quartz swift]

ohh wait mb mb its t

[night raft]

yeah

[quartz swift]

just messed it up with another limit question i was doing

[night raft]

so the limit we want to evaluate is just $\lim_{n \to \infty} \frac{n^{\frac{1}{3}}{n^t - (n-1)^t}$

[soft zealot]

MxRgD
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[night raft]

$\lim_{n \to \infty} \frac{n^{1/3}}{n^t - (n-1)^t}$

[soft zealot]

MxRgD

[night raft]

okay

[night raft]

@quartz swift this here

I'll let you do the rest, for the denominator you want to use binomial theorem

[quartz swift]

so t=1/3 or greater than 1/3??

[night raft]

how did you get t = 1/3

[quartz swift]

i took n power t out common, so as we know t tends to infinity would mean powers less than t would tend to 0, this way i got the expression as n power 1/3 by n power t , so for this limit to take a constant value, the powers should be equal and therefore i got t as 1/3

[night raft]

hmm

[night raft]

thing is I haven't done the question myself but just came up with the idea you need to do, do you have an answer key to check?

[quartz swift]

answer key isnt given but ill check online once

[night raft]

i think t might be too small

because 1/3 < 1

[quartz swift]

so i checked the answer, its 4/3

[night raft]

i see

did they show the method?

[quartz swift]

https://askfilo.com/user-question-answers-smart-solutions/q1-find-with-proof-all-possible-values-of-such-that-for-some-3331383134343937

this site

[night raft]

yeah they used the integral method

[quartz swift]

ohh i see

[night raft]

did you use binomial in the denominator?

$n^t - (n-1)^t$ turns into $n^t - n^t \left(1 - \frac{1}{n}\right)^t = n^t \left[ 1 - \left(1 - \frac{1}{n}\right)^t \right]$

[soft zealot]

MxRgD

[night raft]

then you can use binomial for (1-1/n)^t

you can approximate it as $(1-x)^t \approx 1 - tx$ for very small
$x$ since $\frac{1}{n} \to 0$

[soft zealot]

MxRgD

[night raft]

x here is just 1/n btw

[quartz swift]

so (n power t-1) into t

so 1/3 equals t-1

and we get 4/3

[night raft]

yeah

[quartz swift]

thankssss a lot

[night raft]

np

[quartz swift]

.close

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[pine sand]

Which theorem should I use here?

[halcyon ether]

No need for fancy theorems the only thing you need is 1/2height•base=area

I can see 5th grade chinese kid solving these

[pine sand]

My basic education was not good

[timber leaf]

Whats the point for this statement buddy

[pine sand]

So I'm studying on my own

[halcyon ether]

It's a joke, you're so lame dude

[strange pelican]

https://tenor.com/view/pepe-why-pepe-pepehands-crying-gif-12683546

[pine sand]

Joke was kind of personal😭

Why chinese?

[strange pelican]

are you chinese

[pine sand]

Noo

Why asking?

[timber leaf]

Thats kinda racist and stereotypes buddy

[halcyon ether]

Cuz that one popular problem with similar idea

[strange pelican]

you say it was personal

[halcyon ether]

For 5th grade

[timber leaf]

Why putting chinese in?

[south dirge]

Lets stick to the problem shall we?

[pine sand]

Can we talk straight to the problem only?

[strange pelican]

asian geo is tuff

[halcyon ether]

Yeah sure

[pine sand]

If i use this theorem?

[halcyon ether]

I mean yeah you can

That would be easier

[pine sand]

How will it help?

[halcyon ether]

It's not tuff they just teach kids hard geo for them to do olympiad

[pine sand]

If I draw a fancy line intersecting through d

[halcyon ether]

Okay so you can see using that formula, you can get AK/KD right?

[pine sand]

Right yes

Can I replace K with D?

[halcyon ether]

Okay so what's triangle KCB and ACD have in common

[halcyon ether]

This diagram btw

[pine sand]

Common is base

[halcyon ether]

Oh wait it doesn't work that well but eh whatever

[halcyon ether]

Yes so the areas ratio is the heights ratio

Do you see that

[pine sand]

Yes i can see

[halcyon ether]

You can see how AD/KD relate to the heights ratio

[pine sand]

But in our question?

[halcyon ether]

Just answer my question first I'll get into that later

[halcyon ether]

In case I cannot reply, you basically spam height to area ratio and base to area ratio to solve the problem

[final saddle]

@pine sand Has your question been resolved?

[final saddle]

@pine sand Has your question been resolved?

[final saddle]

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[radiant carbon]

how do we sub in values of x

2^x = 3 - 2x

suppose x = 0:

1 = 3

??

[south dirge]

see you are almost done with it

[south dirge]

this eqaution, isolate x to one side

[radiant carbon]

0 = 3 - 2x - 2^x

[granite sage]

You have to show alpha is between 0 and 1

It means you have to prove that the root (alpha) of this expression 2^x=3-2x lies between 0 and 1

[south dirge]

No no i meant 2^x + 2x = 3

[granite sage]

You can easily do it by intermediate value theorem

[south dirge]

well i think eren just answered your query

[granite sage]

Well I hope he know what is intermediate value theorem

And how to do it

[radiant carbon]

is that where the sign changes

[granite sage]

Yeah

[radiant carbon]

.close

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[nova talon]

Why does my calculator show this

It is the wrong answer

The answer is 10.18

How do I fix that?

[shadow marlin]

might be radian/degree conversion

[nova talon]

How do I make.it normal

I need it normal answer

[sturdy wasp]

Not even that

It appears to be gradians

[nova talon]

How do I get normal answer

[rugged merlin]

press shift

press setup

choose either DEG or RAD

[sturdy wasp]

If it’s 10.18 it will be deg

[rugged merlin]

whichever you consider to be the 'normal answer'

[nova talon]

I saw this

Now press what

[rugged merlin]

press 3

[nova talon]

It shows this

Is that good?

[final tangle]

,w 12 cos(32 °)

[dire oxide]

thats the ans

[soft zealot]

Results provided by WolframAlpha

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

Requested by ramonov

[nova talon]

How did u know what to do

Have u ever studied mathematics?

[vital crag]

Yea most helpers studied some college level math

[final saddle]

@nova talon Has your question been resolved?

[final saddle]

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[final saddle]

Please don't occupy multiple help channels.

Channel closed

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as this action is irreversible, and this channel may abruptly lock.

[next thorn]

Please don't occupy multiple help channels.

[strange pelican]

it was a bot

carvroomvroom

[next thorn]

It shouldn't occupy multiple help channels.

bad bot

Please don't occupy multiple help channels.

[strange pelican]

couldnt there be a verification system

for help channels

[modest sequoia]

theres not really a way that you can add like "2fa" to view certain channels however something that could work is everyone would have to react to a certain message from a discord bot in order to be able to even view the help channels.

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[strange pelican]

. yh apply that to available channels

[wooden vigil]

Can anyone help me with integrals. Its about disks and dishwashers around X-Axis and Y-axis

[wooden vigil]

Its in finnish

I am stuck at figuring out what should the start and end value be at the integral and I also can't use advanced calculator for this

Because its A section

You helping or not?

I meant that girl

Who reacted with skull

[drowsy epoch]

dw ignore her

[wooden vigil]

Okay

Btw this question is second year high school questiln

Not university

Basic course question

[deep condor]

since you are integrating dx, the bounds (start/end) of the integral are the bounds in the x-direction.
what i mean is, the region is bounded by x=1 and the y-axis (x=0), so x has to be between 0 and 1
=> the integral is from 0 to 1

[wooden vigil]

I put that, I wanted to ask just in case

[deep condor]

(later on, you may integrate dy, and in that case the bounds will be in the y-direction)

[wooden vigil]

Because I saw that there was only x = 1, so I put 0 as start value

[deep condor]

well, it is also bounded by the co-ordinate axes, yes? what are the equations for the axes?

[wooden vigil]

There is only equation which is e^x-2

And I gotta find the

Volume

I am calculating volume of integral around the X-axid

Axis

[wooden vigil]

No

For co-ordinates

Only one point was stated which is x =1

[drowsy epoch]

i think the last implication is wrong, y=e^x-2 intersections with y=0

[wooden vigil]

I might be in the wrong, I study in finnish

[wooden vigil]

Demonstration of the integral is this

[wooden vigil]

We don't calculate like this so idk

In my class

Idk about your classes

[deep condor]

but the region is bounded by the co-ordinate axes (koordinaattiakselien), these are also implicit equations

[drowsy epoch]

it's not a calculation, but a visualization of the region we rotate

[wooden vigil]

Aa

[drowsy epoch]

presumbly around x-axis?

[wooden vigil]

Yes

Not sy

Y

[deep condor]

good catch ty 🙇 although you agree the total integral is still from 0 to 1?

[wooden vigil]

This chapter and question is designed as X-axis

[drowsy epoch]

why?

oh i tranlasted the question

i see

[deep condor]

the region from 0 to ln(2) is still a bounded solid of revolution

[drowsy epoch]

i dont speak finnish

[wooden vigil]

Yea I didnt understand

[wooden vigil]

Revolution

?

[drowsy epoch]

I think i would split the integral?

[deep condor]

pyörähdyskappaleen = solid of revolution
(according to google translate)

[drowsy epoch]

i am afraid we would end up with the net volume if we integrate directly

[wooden vigil]

Yes

[drowsy epoch]

\color[HTML]{181A5E}
[ \pi \int_0^{\ln(2)}(2-e^x)^2\dd{x} + \pi \int_{\ln(2)}^1(e^x-2)^2\dd{x}]

[wooden vigil]

Where are you guys bringing ln(2)

[drowsy epoch]

actually we are squaring so it's redundant - nvm

[deep condor]

but it's good practice for what to analyze, so i support it

[wooden vigil]

I found the answer, its 0 to 1

I shouldn't have looked at it, but I didnt understand english

Sorry

[deep condor]

back to this: there are 4 equations for the bounds of this region. you know two of them (y = e^x - 2, and x = 1). the other two are from the co-ordinate axes - what are they?

[wooden vigil]

Its just one

[deep condor]

x=1 is an equation

[wooden vigil]

Like those two stated, plus the zero

So in total three I guess

I am not sure

[deep condor]

i think you have the right idea :)
the x-axis has the equation y=0, and the y-axis has equation x=0. does that make sense?

[wooden vigil]

Yes

[deep condor]

so since we have x=0 and x=1 in our equations, the bounds for our integral will be 0 to 1

then y = 0 and y = e^x - 2 is what we integrate

what is the formula you know for this integration?

[wooden vigil]

Its the

Rotating object

I also calculated but I ended up in this

[drowsy epoch]

-# you forgot a dx might get points off

[wooden vigil]

I forgot yea

[deep condor]

ok then ignore everything else we said for now, maybe it will come up later

[wooden vigil]

Why?

Did I do something wrong?

Aaa

Now I sew

Nothing yea

[deep condor]

basically, the real formula is $\int \pi(f(x) - g(x))^2$, where $f(x)$ is the upper function and $g(x)$ is the lower function

[soft zealot]

haseeb ♥

[wooden vigil]

We havent done that

This course

[deep condor]

but if one of the functions is y=0, then this formula does not matter, it just becomes $\int \pi(f(x))^2 ; \dd x$

[soft zealot]

haseeb ♥

[deep condor]

then no need to worry :)

[proud steppe]

You are missing some powers of e in the last step

[deep condor]

but this simplification doesn't seem right (last line)

lol what he said

[wooden vigil]

I missed some steps and looked at the answer but how does 4e become 8e?

[wooden vigil]

Hey

[wooden vigil]

I was doing it

Haha

I did it by 3+4

[deep condor]

nvm i see what you did

at the last step, you factored the 1/2 from the first term but not the -4e

[wooden vigil]

What should I have done?

I dont understand

So like 1/2(e^2-4e+15)

[deep condor]

second-last line should be pi * 1/2 (e^2 - 8e + 15)

because 4e = 1/2 * 8e

and you factored the 1/2

[wooden vigil]

Whaat

So like at the same time 1/2 is moved outside the box and it also

What

Yea I am tripping

[deep condor]

$\left(\frac 12 e^2 - 4e + \frac{15}{2}\right) = \frac 12(e^2 - 8e + 15)$

[soft zealot]

haseeb ♥

[deep condor]

but you wrote $\frac 12 (e^2 - 4e + 15)$

[soft zealot]

haseeb ♥

[wooden vigil]

Where is 15/2

[deep condor]

$7 \frac 12 = \frac{15}{2}$

[soft zealot]

haseeb ♥

[wooden vigil]

Aaa

Yea now I remember

So what I do to two?

[deep condor]

line number 6 becomes $\pi \cdot \frac 12 (e^2 - 8e + 15)$

[soft zealot]

haseeb ♥

[wooden vigil]

How

How

I am actually stupid

Or blind

Where

[deep condor]

you forgot to take 1/2 out of the 4e term

$\left(\frac 12 e^2 - 4e + 7 \frac 12\right) = \left(\frac 12 e^2 - \frac 12 8e + 7 \frac 12 \right) = \frac 12 (e^2 - 8e + 15)$

[soft zealot]

haseeb ♥

[wooden vigil]

I founf

Problem

So basically

I should have made 4 + 7/2, 8/2 + 7/2

[deep condor]

you mean 4/2 + 15/2

but yes

[wooden vigil]

I am gonna kirkify my pc atp

I cant fucning calculate this end

No I still end up square one

[wooden vigil]

What even is this

Bro

Like

I dont understand

[drowsy epoch]

just factored 1/2

[wooden vigil]

So what happens to remaining 3 1/2?

They just disappear

???

Bro chatgpt couldnt answer, this didnt work also, claude, mathgpt all same thing

I am gonna tear this computer apart soon like holy

[drowsy epoch]

you just kept the 4

but when you pull out 1/2 then 4 becomes 8

[drowsy epoch]

haseeb showed how, by writing every factor as a multiple of 1/2 so you see what remains after pulling out 1/2

[wooden vigil]

Okay so I pull two 1/2 at the same time?

[drowsy epoch]

no

you un-distribute the 1/2

[wooden vigil]

So I remove one 1/2, and all clones disappear into thin air

I guess

[drowsy epoch]

i guess you need to revise some algebra

[wooden vigil]

Why did chatgpt and any other format say otherwise I dont understand

[drowsy epoch]

Why would you blindly trust ai

[wooden vigil]

Because my own teachers use it

[drowsy epoch]

that doesnt mean they trust it

[wooden vigil]

Because I can't learn anything

I have reached aristoteles theory atp, I cant advance

[wooden vigil]

Whats that

[drowsy epoch]

a property

let me make a real life example

[wooden vigil]

How is it seen in this though

[drowsy epoch]

Imagine you order a menu that consists of 2 cheeseburgers and 2 french fries each, and that 5 times because you are at a party. Logically you can count the menu like 5(2+2) which is the same as counting each item separately 5(2)+5(2).

Both ways of counting lead to the same outcome

[wooden vigil]

Okay

Now I see

Wait

So like 1/2(e^2-8e+15)

And because 1/2 is factored in all, you can just make it one

[drowsy epoch]

yeah

[wooden vigil]

@drowsy epoch I am bit tired

I am not braindead patrick trust

I just happened to forget basic algebra

😭

[drowsy epoch]

Would be terrifying in calc 2

[wooden vigil]

I am in calc 3

I think

[drowsy epoch]

oh even worse then

[wooden vigil]

Sometimes happens

[wooden vigil]

It was all about how it was written

[drowsy epoch]

i figured

[wooden vigil]

Like I wrote it so that it got me tweaking out

Confusingly

@drowsy epoch

But will I lose points if I put it like this

[drowsy epoch]

happens when you have long computations

[drowsy epoch]

typos happen, but it's concerning if you say this

[drowsy epoch]

you might lose points indeed but like 0.5 to 1 at most

[wooden vigil]

The photo

[drowsy epoch]

mathematics is not about the correct result but how you get there

[wooden vigil]

Like that way

[drowsy epoch]

,w Integrate[(e^x-2)^2 * pi, {x,0,1}]

[soft zealot]

Results provided by WolframAlpha

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

Requested by 4nzon

[drowsy epoch]

uhm you still have the -4e

[wooden vigil]

I changed

[drowsy epoch]

well there you go then

[wooden vigil]

https://tenor.com/view/trey-lance-new-generation-letreylance-gif-25430953

I thank you personally for the help that you provided @drowsy epoch

Thank you comrade

[drowsy epoch]

you should thank @deep condor

[wooden vigil]

@deep condor I was bit stupid during the calculation, but I thank you

Thank you all

[deep condor]

not at all, im sorry i wasnt able to get that last point across

[deep condor]

well you did all the heavy lifting :P

[wooden vigil]

https://tenor.com/view/truman-show-gif-16260897409967297801

Thank you all.

@deep condor @drowsy epoch this was more dramatic than a hollywood movie

Imma close

Now

.close

[drowsy epoch]

distributivity is so heavy fr

[final saddle]

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[wooden vigil]

Come on man

Joke still

[drowsy epoch]

Oh this wasn't about you, sorry

I was just saying that what I did was not effortful as what haseeb did

after all he reviewed your work and spotted your error

that's all 😄

[deep condor]

well i did miss the point of intersection which is ._. but

good team effort

[wooden vigil]

Alright

Thanks

[final saddle]

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[timber leaf]

<@&268886789983436800>

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[timber plume]

what is this saying

[dense coral]

there's a c between a and b for which the tangent line to c is parallel to the secant connecting a and b

or if you prefer, the average rate of change between two endpoints is equal to the instantaneous rate of change at some point in between the two

[timber plume]

Ohhh okay

thanks 🙂

.close

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[umbral fable]

i understand how to solve homogenous second order DEs but these are nonhomogenous, i dont know where to start here

[umbral fable]

i understand how to find the homogenous solutions just set it equal to 0 and do the Q(s) factoring

but idk how to find the particular solution

[drowsy epoch]

I have a blue print if you want

[umbral fable]

sure

[formal trail]

you use the undetermined coefficients method described here https://tutorial.math.lamar.edu/Classes/DE/UndeterminedCoefficients.aspx

[umbral fable]

thank

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[ivory vessel]

in part e, i calculated Cov(X, Y) = -32.19, now for part f i need to calculate Var(X + Y), but Var(X + Y) = Cov(X, Y), and variance cannot be negative. is my covar wrong?

[ivory vessel]

this was how i calculated covar

[plucky rover]

What no

Var(X+Y) = Var(X) + Var(Y) + 2Cov(X, Y)

[drowsy epoch]

why can't cov be neg

[plucky rover]

That's not their concern star

They were concerned that variance would be negative

Cuz they misremembered the expression

[ivory vessel]

wait what

[plucky rover]

Yes

[drowsy epoch]

icmb

[plucky rover]

Var(X+Y) = Cov(X+Y, X+Y)

Now use bilinearity

Cov(X, X) + Cov (X, Y) + Cov (X, Y) + Cov(Y, Y)

[ivory vessel]

ahhhhh i misinterpreted the formula

[plucky rover]

Happens nw

[ivory vessel]

alright thanks

.close

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[fresh bobcat]

$$\text{my book:}$$
$$\int \sin{x} \dd x- \int \cos^2{x}.\sin{x} \dd x$$
$$-\cos{x} +\frac{\cos^3{x}}{3} + C$$

[soft zealot]

SimpleGamer14

[fresh bobcat]

could someone pls do out the integral for me? im confused as to how it got to the answer

[final saddle]

Show your work, and if possible, explain where you are stuck.

[vital crag]

Did you try anything

[fresh bobcat]

no, to me i just don't understand. i'll try it right now

[drowsy epoch]

What integral methods do you know?

[fresh bobcat]

functions of linear functions of x
integrals in which one part is the differential coefficient of the other part
integration by parts
integration by partial fractions

[drowsy epoch]

ever heard of substitution?

[fresh bobcat]

sorta, but i've only really done it with the linear functions of x (which you basically don't need substitution for)

[drowsy epoch]

I see

Do you wanna try it on this problem?

[fresh bobcat]

okay

[drowsy epoch]

Do you notice a special relation in terms of derivatives between cos(x) and sin(x)?

generally speaking

[fresh bobcat]

they are eachother basically

[drowsy epoch]

yes

[drowsy epoch]

So the idea would be to do a substitution for cos(x) for example or sin(x)

might try it out and see how it goes

[fresh bobcat]

alright

[drowsy epoch]

What's your progress so far?

[fresh bobcat]

about to do ibp on the integral
$$-\int , u \cdot \cos{x} , \dd u$$

[soft zealot]

SimpleGamer14

[brazen breach]

um

I don't mean to interrupt

[drowsy epoch]

Ok first what sub did you use?

[brazen breach]

the derivative of cosx is -sinx, so then the right can become -integral u^2 * -du on the right

[brazen breach]

sinx I'm assuming
use the higher power first or rather the one with the odd exponents should be the ones that end up as your du

[brazen breach]

you can't perform IBP on the integral because cosx is there, that's going to be treated as a coefficient rather than a variable involved in the integration, your method also disregards the fact that it is a variable in the first place

[drowsy epoch]

Yeah that sub u=sin(x) won't work out nice, so you can try u=cos(x) instead and see if this works out more nice

[brazen breach]

you're integrating with respect to u there, but you have an x

what I mean

[fresh bobcat]

yep i found it weird

we'll try cos

[drowsy epoch]

Also as long as the substitution is not 100 % executed you won't find a way to continue

[fresh bobcat]

yeah okay

[brazen breach]

yez, integration is essentially a whole lot of just doing anything until it works

[drowsy epoch]

but that gets better over time with experience

that's why I let you do some work first so you can get a better understanding of this concept

[fresh bobcat]

okay i got the answer :)
thx for the help and support
ima try the integral of sin^3{x} now so i'll come back here if i find confusion

[brazen breach]

note that sin^2(x)=1-cos^2(x)

because sin^2x+cos^2x=1

[fresh bobcat]

1/2 or

nvm

i was thinking of a diff one

[fresh bobcat]

cos^3{x} mb we just did sin

[brazen breach]

no that's the cos2x one

[brazen breach]

note that cos^2x=1-sin^2x

[fresh bobcat]

✅

aight bet we got it

gonna move onto cos^4{x} & sin^4{x}

[brazen breach]

oh

yeah about that

you need double angle formula for that

twice

[final saddle]

@fresh bobcat Has your question been resolved?

[fresh bobcat]

alr yay i got em right

now onto sin^5{x} & cos^5{x} 😅

same way as last time alright

i think im done w the help post

thx for the help <3

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[tropic crest]

Translation
Let xoy be a coordinate system/plane(?) (figure 1). There are 2 objects A and B undergoing uniform linear motion. at the start A is I =100 m away from B

Let the velocity of B be V_a = 10 m/s along the ox direction
the velocity of B be V_b = 15 m/s along the oy direction
a) After how much time since the start does the distance between A and B equal 100m again?
b) What is the smallest distance between A and B

I need explaination for a few things
1 How did they derive AB_1?
2 What is Δ' and how do they use it to derive the minimum distance as seen in the solution to b)
(

[timber leaf]

delta' là đỉnh thấp nhất của parabol

[tropic crest]

then?

im confused

[timber leaf]

delta' là d^2 min

bởi nó hỏi khoảng cách nhỏ nhất nên tìm nơi y có giá trị thấp nhất trong parabol