help-43

[lime kestrel]

bcz the following questions are wrong too then

the graph that is given if for the function w + in between

[compact pewter]

@lime kestrel Has your question been resolved?

[sullen canopy]

.close

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[subtle zealot]

your error cannot be larger than the first term you dont include

at least for alternating sums

[timid lodge]

as long as the non-alternating part is decreasing

[humble swan]

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[chrome compass]

can someone help me understand this

[chrome compass]

i have no idea on how to go about this

[kind viper]

by the looks of it, all they want you to do is to determine the equation of that green line...

[chrome compass]

oh

how do i do that

[half egret]

note that the equation E=bn+c is in slope-intercept form

[chrome compass]

right so b will be the gradient in this case right

i can find the gradient with any two points of x and y coordinates which fall on the line right

but only 1 point falls exactly on the line

im a bit confused on what to do

or can i take this point this point (0, 50) to calculate the gradient along with (4,60)

have i solved it right???

[kind crane]

Looks right yes

[chrome compass]

ok ty

.close

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[chrome compass]

.reopen

[compact pewter]

✅

[chrome compass]

i did this so far

im not quite sure if i did it right or what i should next

actually would it be right i use the x value of 2 here and substitute it into the equation i made earlier?

[kind crane]

Yes

Doesn't look like any other points are given so you have to use (2,50) to get the quadratic

[chrome compass]

right so this should tehcnically be correct

[kind crane]

Looks right

[chrome compass]

ok tysm

.close

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[warped oar]

Solve the pair of linear equations:
px + qy = p - q
qx - py = p + q

Eq(1) = p(x-1) = -q(y + 1)
Eq(2) = q(x-1) = p(y+1)
p and q are ALWAYS non-zero.

(a) If x is not 1, then p(x-1)/q(x-1) is defined.
(b) If y is -1, then -q(y+1)/p(y+1) would be undefined.
But defined n,eq undefined.

Similarly, if x = 1 and y is not -1, we would get another invalid case.

x = 1 and y = -1 is a valid solution.

x n,eq 1 and y n,eq -1 is not a valid solution since this would lead to a contradiction that p = q = 0.

Is this correct?

[kind viper]

i will say this for the N'th time

do not write neq =

write != or just neq

break that habit

anyway, am i to understand that p ≠ 0 and q ≠ 0 are both stipulated from the start?

[warped oar]

Yes.

[kind viper]

k

i will once again say that, even if it's correct, it's definitely too complicated.

like it looks correct-ish at a glance but it's not worthwhile to go through all of this ugly legwork just for a linear system

is there a reason why you aren't happy with more conventional linear system solution methods, like substitution or elimination?

[warped oar]

I know, I could have just multiplied the first equation by q and the second by p.

[kind viper]

yes

that would have been much less painful

[warped oar]

Ok.

Is it correct though?

The method, the steps.

[kind viper]

you have my begrudging affirmation.

idk, maybe you get a kick out of maximizing the complexity of your solution to a problem.

[compact pewter]

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[ebon lark]

how to make reasons for 3,4,5?

[ebon lark]

what r the reaosns?

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[silk turtle]

Does someone how to do this. Ive tried to do the monotonic part but I cant do the inequality

[boreal nimbus]

if you can’t do the monotonic part then maybe it’s not monotonic

[hybrid rock]

did you use a graphic utility perchance to confirm ur results

[silk turtle]

I never had results

[hybrid rock]

do you think it's bounded or not

[sullen canopy]

its incredibly obvious with a graphing utility so probably shouldnt (until check)

[hybrid rock]

it's

🤯

[silk turtle]

But how would I do it without a graph

[hybrid rock]

have you figured out whether it's bounded yet

[silk turtle]

no

[hybrid rock]

take the limit of the function

try figure out what's the maximum and minimum value of the function

if you can figure out there's a maximum and minimum

then it is bounded cuh

if not

then oh well such is life

[silk turtle]

is the limit 0

[hybrid rock]

as you tend to positive infinity yh

what about in the OTHER direction now

[silk turtle]

wouldnt it also be 0

[hybrid rock]

hmmmmmmm

are you sureeeeeeeeeeeeeeeeeeeeeeeee

[silk turtle]

going to negative infinity you still get 0 on the bottom

[boreal nimbus]

it is a sequence a_n

[hybrid rock]

oh shi mb

mb mb

[boreal nimbus]

you do not care about negative n

[hybrid rock]

mb mb oopsy poopsie

[silk turtle]

How would I find the max of the sequence

[hybrid rock]

just guess bro

[sullen canopy]

what are you on about

[hybrid rock]

i'm jesting abt mate

if u analyze for monoticity

it becomes obv what the max is

[boreal nimbus]

nobody cares what the max is

[hybrid rock]

NOOOOOOOOOOOO I CARE BECAUSE WHAT IF

WHAT IF LIKE

WAAAAAAAAAAAAAAAAAAAAAAAAAAAAA

[sullen canopy]

please stop trolling

[hybrid rock]

i'm sorry banana steeler

anyway @silk turtle start taking the derivative and see what happens when n<9 and n>9

and make some sexy analysis

[silk turtle]

ok

[hybrid rock]

love you mate <£

[boreal nimbus]

this does not help you…

[silk turtle]

I got

[silk turtle]

Then how am I supposed to do this

[sullen canopy]

i think this is wrong

[hybrid rock]

huh

[silk turtle]

n* (e^-n/9) = n'(e^-n/9) + n(e^-n/9)'

oh

[hybrid rock]

bro if u take the derivative you can see that for x < 9 the function is increasing and for x > 9 then the function is decreasing

Mqnic_ is tryna hate on me cuzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

[silk turtle]

is this how you would prove it using derivative

[hybrid rock]

for n < 9, f'(x) > 0, for n > 9, f'(x) < 0, badabing

badaboom

tho that also probably looks right i didn't acc read it

[silk turtle]

but I dont know I would get that without your help

.close

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[devout mountain]

what does this mean

[solid bison]

the magnitude of f at infinity?

depends on the context of everything else

[devout mountain]

but f is a func not a vect ??

how

i don't get it

[solid bison]

what is f

[hushed magnet]

the infinity norm of f

[devout mountain]

a function

[hushed magnet]

aka supremums norm

sup |f(x)|

over all x in your domain

[devout mountain]

ok so what if we replace infinity by any other number

like 6 7 or anything

what would that mean

[hushed magnet]

$\norm {f}_p = \left(\int |f(x)|^p dx\right)^{1/p}$

[boreal girder]

Denascite

[hushed magnet]

where the integral is over your domain

and you assume it exists

[devout mountain]

yeah what would this represent in a graph

[drowsy summit]

the ⭐ mother of all norms ⭐

[hushed magnet]

area under the curved but weighted

there is no "nice" visualization

at least I dont think there is

[devout mountain]

okay thank you

one last thing

do u have any article or something that have more infos on this

[hushed magnet]

on what

norms?

[devout mountain]

yeah

[hushed magnet]

like any real analysis book

[winged lion]

you can also just visualize with desmos and observe what happens
https://www.desmos.com/calculator/tfl3fuxbwg

[devout mountain]

alr thanks

[hushed magnet]

the integral bounds should be fixed

eg from 0 to 1

and then you can let the function be in terms of p

you'll see that it gets closer and closer to the sup norm

[compact pewter]

@devout mountain Has your question been resolved?

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[quartz yoke]

Um hello

[quartz yoke]

Hello someone pls help

I will share what happened

Basically im in 10th grade

And i dont know any math

I dont even know like 5th grade math or 6th grade math

Like im so scared

I dont think i can graduate or do anything

I am horrible at math

I used to be really good

Good

But i got a bad teachers overtime and my teachers wouldnt even teach

Like theyd just make us do ixl and like

Ive had teachers who cared more about joking around with the students and letitng whatever then like teaching the students and Um also when

Like covid happened in 2020

Like it was hard to learn the math on zom

Zoom

Sometimes my teachers would glitch and i would fall asleep in like all the live zoom classes

And also im to blame because im im just im not that good anymore like im scared of numbers

When i see a problem

For example like

12+x-y=xy27

I dont know if thats even a equation i just made it up

But im so terified of it like i start geting really scared 😢 i have panic attacks

So what exactly do you need?

Because of math

Oh i was wodnering if

Like

I dont know i dont have money to afford a tutor like maybe someone could help me 😦 Like help me like what

Do i need to learn

to succeed

Like

Do i need to know fractions or

I mean math is very general and necessary everywhere

[quartz yoke]

Yeah you should

10th grade means you are how old?

Okay 😢 I will try learning that

Im 16

But i feel terribly behind because i dont even know basic math or algebra

[quartz yoke]

Okay if you have any question in specific mention it and I can help you solve it

Or like graphing or anything

Thank you

[quartz yoke]

What about algebra or basic math confuses you

Like be specific

Where do you get lost

That way I can help you

Thank you monib you are a very kind soul thank you for helping me also this is i dont use discord I still am firguing it out and but i Know its a like where you can talk to people and im shocked on how nice some people are like thank you for helping me 😭 We need more kind people in this world thank you

Okay so I think like for me its like the letters

Like i always thought that letters were for english like and then they started adding to math

[quartz yoke]

No worries 😭

Adding it to math

And i get confused like

Thank you

[quartz yoke]

Letters aren't that complicated, basically replace the letter with a number and it's the same

Ahh i see it makes sense now like solve for x for example its like a number

Like 10 + x = 15

If x = 4
And then you replace it for anything like 2x + 4 it's just 2. (4) + 4

So x would be OHH qwiat Hod on

[quartz yoke]

Then x equals 5

Yes!!!

Thank you 😭 😄

Im learning now

Pass the 15 to the other side by doing subtraction and solve it

15 - 10 = 5

Ahhh i see

Thank you! 😄

Yeah

That makes sense

No problem you don't have to say thank you 😭

What else do you not understand

Sometimes you have to figure it out like x2 + 5x - 5 = 0
Then there's formulas involved and it's just steps of putting everything in the right spot

I feel so embarrased by it and sad but honestly like everything 😢 Everything in math confuses me ive always been better at english but actually im bad at english too. My teacher gets mad at me because i use emojis in my essays but i never use periods because i feel bad because it sounds mean like and that is why i said that. Like it sounds mean vs and that is why i said that, like someimtes i get sad because it sounds mean so i use the comas and try to avoid using so many like serious and now im failing english too WAHH IM FAILING ENGLISH AND MATH But um yes like everything about math scares me but im slowly learning

Im sorry im yapping

[quartz yoke]

Ohh i see

It's okay 😭

Oh no i think im cooked because that equation scared me like i think thats why im scared of math theres so many

Nubmers and letters and forumulas

It gets so overwhelming maybe its just me

I need to practice more

Its like a sport

Like you have to rpactice and stuff and like do it regulary 😕

Yes yes

Practice it out and it'll be easy

[charred vine]

Dont listen to monib he failed maths

[quartz yoke]

Ask your teachers if they can give you basic work of stuff they've already gone through and consider not necessary to explain anymore and then practice it out

Thank you i appreciate it so much thank you wow i wasnt Oh like i wasnt expecitng anyone to actually take me seriously thank you so much im so glad I ran into a nice person and not scary i rememebr on youtube i saw servers were scary some people are mean thank you for being kind

[quartz yoke]

IM ACTUALLY FANTASTIC IN MATHS

Oh no what hapepnd no I

NO SHES LYING DW

[quartz yoke]

Okay thank you

I've passed maths every semester

Yay im happy for you 😄

And you too Rylee thank you both for helping

[quartz yoke]

she did nothing but slander me 💔

[charred vine]

you're welcome I helped as much as I could

:)

I will always help you

[quartz yoke]

... outrageous

I hope i can pass in math because its currently my worst subject and english as well im failing too idk if ill graduate 😭

Thank you boh

both

[quartz yoke]

Noo i im sor

😭

But thank you

Im gonna study

Its fine you're good

Okay if you don't understand something open up another ticket

I heard that khan academy or like youtube is good too

Yeah Khan academy is good for maths

[charred vine]

I utilise websites online and watch youtube videos to break down topics

if you're a visual learner it'll help

[quartz yoke]

And some youtube channels also are decent

Thank you both! 😄 Im so happy this is really motivating

While they solve their example that they put up

You make another similiar to it and solve it

Ahh i see got it

Following their steps

Yeah

[charred vine]

no worries you cheeky monkey 😄

[quartz yoke]

?GPDNAJKFASLN:MSA

Aww hahahah 😂😄

Yayy

Yes thank you!

Okay ill do that and yes khan academy and youtube

I think its possible i can catch up on math if i just

Okay perfect and if anything open up another ticket

Watch study and practice

Thank you 😄

Yeah but study a lot

[charred vine]

Practice makes perfect, you got this!

[quartz yoke]

Cause you're a few years back

So take your time understanding it

Yes yes definietly 🥲

Also don't use emojis

[charred vine]

never be afraid to ask questions, it'll be your biggest setback

[quartz yoke]

Practice your english as well

Yes thank you and also my mom is a math teacher its funny because like i should be good at math but im really bad so I can also help I can I meant i can also ask for help too

Thank you yes

Yes

😄

Yes thank you you both you both are so kind and caring thank you!

Okay, say .close to close this ticket if you're done 🥰

This really helped and motivated me and im so grateful

Thank you!

Okay

No problem

Bye friends!

[charred vine]

bye bff for life

[quartz yoke]

Thank you monib and thank you Rylee

Bye friend

Bye bye! 😄 Thank you so much you both!

.close

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[radiant fable]

im honestly so confused on the concave questions

[radiant fable]

like im confused past (4 ,3) on if it counts as up or down

[rigid perch]

this is the general rule

[radiant fable]

so past the point (4,3) there would be no concave right?

[rigid perch]

why wouldn't there be?

[radiant fable]

well there is no full curve i think

[rigid perch]

we don't need a "full" curve for these, even a "half" curve still counts

[radiant fable]

oh damn

so the upward concave then would be (1,4) and (5,7) and downward would be (0,3) and (3,5)?

[rigid perch]

your intervals of concavity should not overlap

[radiant fable]

wait wym overlap?

[rigid perch]

you have some points which are in both your concave up and concave down intervals

[radiant fable]

alright i think i got it this time

up would be (2,4) and (5,7). Down would be (0,2) and (4,5)

alright it was right thank you very much

.close

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[compact pewter]

@strange pendant Has your question been resolved?

[nova ocean]

@strange pendant maybe I can help or you have done it?

[strange pendant]

I havent

I would appreciate it

[nova ocean]

Ok wait a min

[strange pendant]

ping me

[nova ocean]

The first part

Had to use calc for trigno values

Let me know if you don't understand a thing @strange pendant

2nd oart

*part

For the 3rd part I don't understand if the y axis is vertical distance or vertical component of velocity

If it is vertical distance then it will be a parabolic path with its vertex behind the y axis

[strange pendant]

is this projectile motion

can you explain

[nova ocean]

Yes this somewhat less than a half path of projectile motion

Gravity is acting and no interaction in horizontal way

[compact pewter]

@strange pendant Has your question been resolved?

[strange pendant]

why 50, D is 5m bro

also, include the units , is not just numbers

[nova ocean]

Not when i remove decimal of 0.8 i have to multiply numerator with 10

That's why it's is 50

50 by 8 is same as 5 by 0.8

@strange pendant

Everything in units is correct

[strange pendant]

,w 5/0.8

[boreal girder]

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[strange pendant]

what is angle alpha

[nova ocean]

It's is given in question

[strange pendant]

alpha is not given

[strange pendant]

no? I dont see it

[nova ocean]

See between the house top

Where the ball is at the edge

[strange pendant]

so?

[strange pendant]

yes but is alpha

is not in degrees or radians

[nova ocean]

Doesn't matter because angle is not asked

[strange pendant]

but we need it to find the velocity and decompose the velocity vector in x and y direction

@nova ocean

there is no velocity in x direction bro

just velocity in y direction I think

[nova ocean]

Yes there is thats why it can move to point D

[nova ocean]

It's given that it have been moving with constant velocity on the top of hous

Imagine a real scenario where the ball falls from slant top and where it will hit

[strange pendant]

I dont get it

how did this happen?

we dont know angle alpha

[strange pendant]

but we dont know the angle? how are you decomposing the velocity into x and y directions?

[strange pendant]

but your fraction says 50/0.8 Wtf

[nova ocean]

By supposing an angle alpha

[strange pendant]

you found vy first

before finding vx?

[nova ocean]

The . Is cut by a small line

[strange pendant]

? what

[nova ocean]

It's a Lil notation to show you remove the decimal and multiply numerator with 10

[strange pendant]

the fuck?

[nova ocean]

I found neither first i solved for the angle

[strange pendant]

I am assuming is not a widely accepted notation

[strange pendant]

how

[nova ocean]

Yes

[strange pendant]

how is yellow happening

[strange pendant]

this purple is the first step then

how is tanalpha = 1.36?

no, yellow is first step

[nova ocean]

The v is cancelled the expression shows calculation for angle but it was complex so I used tan function in calculator

[nova ocean]

Calculator

What's your grade?

[strange pendant]

I dont get it

[nova ocean]

You know trigonometry?

[strange pendant]

yes, only the basics, soh cah toa

[strange pendant]

tan = sin/cos. so what?

[nova ocean]

It's used in solution

[strange pendant]

no, u used vy = vsinalpha and vx = vcosalpha
then tanalpha = vy/vx

dunno why

[nova ocean]

Yes

Because

[strange pendant]

because the vs cancel

so its valid.

but we dont know vsinα

and we don't know vcosα

[nova ocean]

Vel is distance over time and time cancel so it becomes distance of pendicular over horizontal which is tan

If you don't understand I ll start from basics

[strange pendant]

I dont understand how you found tanalpha = 1.36 bro

,w 5/0.8

[boreal girder]

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[strange pendant]

5/0.8 = 6.25

cosα = 6.25 m/s

[nova ocean]

Some conditions are fixed in question like distances and time which makes the unknown angle and velocity to be found there are many approaches, i first found the angle then the velocity

[nova ocean]

You got it wrong velocity multipled cos of alpha is 6.25

[strange pendant]

vcos(α) = 6.25m/s

[nova ocean]

Yes

[strange pendant]

vcos(α) = 6.25m/s

[nova ocean]

Yes

[strange pendant]

but you wrote other stuff in your paper

you made mistake?

Y or N

[nova ocean]

N

[strange pendant]

?

[nova ocean]

N

[strange pendant]

oh ok I see

I see

[nova ocean]

Vcos alpha is only horizontal velocity

[strange pendant]

and for Vy you used free fall

[nova ocean]

Vsin alpha is only vertical velocity both components make the velocity vector which makes the ball go on a certain lath

[nova ocean]

Yes

The gravity will only influence the vertical velocity

[strange pendant]

,w (10 - 9.8 * 0.8)/(0.8)

[boreal girder]

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[strange pendant]

h = t(vo + g)

h/t - g = vo

,w 10/0.8 - 9.8

[boreal girder]

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[strange pendant]

are you sure your Vy is correct

v.sin(α) = 2.7m/s

v.cos(α) = 6.25m/s

,w (10/0.8 - 9.8)/(5/0.8)

[boreal girder]

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[strange pendant]

I am not getting tan(α) = 1.37

I am getting tan(α) = 0.432

@nova ocean

[nova ocean]

Your 2nd equation is wrong

@strange pendant

[nova ocean]

Where have you got this formula, this is so wrong

[strange pendant]

h = 1/2 . g . t^2

[nova ocean]

This is when

Initial velocity is zero

Not in your question

[strange pendant]

10m = 1/2 . 9.8m/s^2 . (0.8)^2

[strange pendant]

what

[nova ocean]

The d expression which is correct to apply in your case

Distance= initial velocity × time +0.5 g × time²

[strange pendant]

,w 10/0.8 - 1/20.89.8

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[nova ocean]

This formula turns to what your are saying when initial velocity is zero

[strange pendant]

I get v.sin(α) = 8.58m/s

v.cos(α) = 6.25m/s

,w (10/0.8 - 1/20.89.8)/(5/0.8)

[boreal girder]

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[strange pendant]

I get tan(α) = 1.3728 bro

,w (10/0.8 - 1/20.810)/(5/0.8)

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[strange pendant]

you used g = 10m/s^2

tan(α) = 1.36

,w arctan(1.36)

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[strange pendant]

I got it bro

what about b)?

[nova ocean]

Nice

[nova ocean]

.

[nova ocean]

⬆️

[strange pendant]

yep

[strange pendant]

displacement is y axis and time is x axis

for c) I mean

how would u draw it?

[strange pendant]

wdym

why not we plot the velocity over time graph and the displacement over time?

[strange pendant]

lets just do both, no?

[nova ocean]

Take time as x axis and displacement as y axis on a graph then it would satisfy y=v*sin(alpha )*x + 0.5gx² where x is time and y is vertical displacement

It would look like a downward parabola

And we know at time zero y is 10 and at time 0.8 y is 0

So plotting will be esay

*easy

[strange pendant]

can you help me do the drawing

[strange pendant]

any other points would you plot?

[compact pewter]

@strange pendant Has your question been resolved?

[nova ocean]

@strange pendant

[strange pendant]

how?

[nova ocean]

The 2nd equation tells us how height is changing with respect to time

[nova ocean]

.

[compact pewter]

@strange pendant Has your question been resolved?

[strange pendant]

how did you got to this function?

like how did you get there

[strange pendant]

what points should I be plotting on this function?

[tired bear]

i think you overcomplicated part a

or did something else

didn't they ask for velocity vector at the instant it leaves the roof of sth

[tired bear]

something like this for part a

the numbers look like a pain to calculate

so I hope you are allowed a calculator

[strange pendant]

I am

[tired bear]

then it's fine

you almost get an integer for alpha in degrees

just report what you get

[strange pendant]

bro, is not possible to have -H

we cant have negative height

[tired bear]

displacement is negative

moving down the y axis is negative with normal conventions

if you want you can take going down the y axis as positive too

you will get the same result as every term becomes positive

in the formula s = ut + 1/2 at², s is the displacement

[nova ocean]

I did calculate the initial velocity and both approaches are same squaring adding and square root is the same work as for solving the angle but i didn't know before he needed a simplified solution

And what do you think about the graph is it correct?

[tired bear]

pretty sure no

x should be (5, 0)

we need to clarify a) first

and @strange pendant hasnt been here for a while

[nova ocean]

He said it was vertical displacement over time graph

It should be correct on this statement

[tired bear]

oh time

[nova ocean]

I think what you are saying is the projectile path graph

[tired bear]

mb

[nova ocean]

Np

[tired bear]

ok yeah seems right

i think you need a 9.8 instead of a 9.5 though

[nova ocean]

Oh yea I typed it wrong

[compact pewter]

@strange pendant Has your question been resolved?

[strange pendant]

I think what tatakae did for a) and b) is correct, no?

problem is he left without helping me with c)

@nova ocean

sir do you mind helping me with the graph

[strange pendant]

so this is a displacement over time graph?

[strange pendant]

.close

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[nova ocean]

@strange pendant man I was sleeping

If you Still need help ping me

[strange pendant]

@nova ocean

help me with c)

.reopen

[compact pewter]

✅

[nova ocean]

I think the question is asking for two graphs

Blue is vertical displacement with respect to time graph

Red horizontal displacement with respect to time graph

[strange pendant]

how did you do it

[nova ocean]

And when we eliminate time from blue and red equation we left with vertical displacement wrt horizontal displacement graph green graph showing trajectory of the projectile

[nova ocean]

We some equation independent in there direction

Treat the ball independent in x and y direction

Then apply the simple linear kinematics equations in that direction

The ball moving linear in x direction and linear in y direction

We see a projectile trajectory when we combine those two parameters

This is the understanding part

For applying we have main two equations in linear motion v=u+at and d=ut+0.5at²

2nd shows how displacement changes when time changes

Which is asked in question so we place displacement on y axis and time on x axis

@strange pendant

[solid wren]

e

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[strange pendant]

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[strange pendant]

for vertical displacement, are you sure you did it correctly?

@nova ocean

the graph

shouldnt it be y(t) = Voy * t - 0.5 * 9.8 * t^2

where Voy = - v. sin(alpha)

ohh, I just noticed v . sin(alpha) = 8.58 m/s

so Voy = -8.58m/s

but why the 10 ?

delta x = xf - xi
xi = 0
xf = 5m
delta x = 5m
delta y = yf - yi
yi = 10
yf = 0
delta y = 0 -10m

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[nova ocean]

Initially when x is zero ball is at height 10m so we have to add 10 m because i suppose up is positive direction and negative downwards

[nova ocean]

Otherwise it won't correlate with the question given

Sign convention doesn't matter until you are doing it Right

But the graph we are plotting will be respect to origin so it will be

∆y = y - 10 where y is general displacement between 0 to 10

So ∆y = vsin(alpha)×t-0.5*9.8t²

Which would bring us to that equation

[signal mist]

@nova ocean You might want to close this channel (unless you actually need it)

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[potent ore]

What would be the shortest distance from the orgin to f(x)=e^x

[potent ore]

pretty sure i use distance formula

e^x is the change in y for it

d = sqr ((x2-x1)^2 - (e^x)^2))

would I just use (x) for (x2-x1) since its f(x)=e^x

[cerulean steeple]

yes

[potent ore]

d = sqr((x^2)-e^2x))

idk what to do from there

[signal mist]

This is screaming advanced Polar Coordinates

[potent ore]

lowk never learned them but its on my calc practice 😭

[signal mist]

[acoustic yarrow]

perhaps use + instead of -

[potent ore]

ohh yeah

[cerulean steeple]

you want to find the minimum of it, so just differentiate and set it equal 0

[potent ore]

could I use chain rule for the square root if I turn it into ((x^2)+e^2x))^1/2

[signal mist]

Wait…

[acoustic yarrow]

why are u subtracting them

[potent ore]

mb

meant + xd

[signal mist]

The order pair for f(x) = e^x is (x, e^x)

That means the Radius = sqrt(x^2 + e^2x)

(e^x)^2 = e^2x

[acoustic yarrow]

so you have sqrt(x^2+e^2x)

now differentiate it using chain rule

[potent ore]

(2x+2e^2x)/2(x^2+e^2x)^1/2

Then I would set this equal to 0?

[acoustic yarrow]

yeah

let me check ur derivative

,w derivative of sqrt(x^2+e^2x)

[potent ore]

would I plug anything into x?

[acoustic yarrow]

okay looks the same

you equate it to 0

solve for x

wait

,w derivative of sqrt(x^2+e^(2x))

[potent ore]

i did it wrong

[mint furnace]

this doesnt look right

[boreal girder]

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[acoustic yarrow]

so u r solving for -x = e^2x which you can numerically approximate

[potent ore]

what do I do with the denominator?

oh

multiply right

since its set to 0 it cancels

[acoustic yarrow]

yes

[potent ore]

im confused on how I would approximate it

if i take ln would it be -lnx = 2x

[acoustic yarrow]

you cant have closed form solutions for this

just use a calculator

,w -x = e^2x

,w -x = e^(2x)

[boreal girder]

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[acoustic yarrow]

holy shit wa

,w approximate -x = e^2x

,w approximate -x = e^(2x)

[boreal girder]

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[acoustic yarrow]

cooked

okay we have our x value here

plug this into the distance equation

[potent ore]

ohohh

so on my ti84 i could just graph both lines and go to where it intersects then plug dthat in

okay

tysm for the help

[signal mist]

Actually. That makes so much sense

[potent ore]

MIGHT be cooked for my exam but some of its making sense 😭

[signal mist]

If you tilt your head 45 degrees counter clockwise, it looks like a hyperbola dipping symmetrically

[potent ore]

.close

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[compact pewter]

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[willow nacelle]

In the second question, can I do alpha + beta = -b/a and then make it -a/b

[safe silo]

first solve the alpha beta more

[willow nacelle]

I don't need to solve to find alpha right?

[spark folio]

theres no need to solve for these

[safe silo]

it will become this

[willow nacelle]

Since we know alpha + beta = -b/a

[safe silo]

yes

[willow nacelle]

Oh that's what u mean

Can I do -a/b that's what am asking

Yall getting what I tryna say?

[spark folio]

Yes. This works

[willow nacelle]

Tysm

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[idle shard]

A (1,1,1) and B(1,-4,1) on a 3d coord system

[idle shard]

what is magnitude of projection of OA onto oB?

so the formula is absollute value of (oa dot ob)/magnitude of ob

and then i have $$\frac{|1-4+1|}{\sqrt18} $$

[boreal girder]

꧅

[idle shard]

nvm got it

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[quartz yoke]

Can someone check if this is correct

[quartz yoke]

I got (a) and (c) correct
But( b)is supposed to be 27.9 and (d) is 51.3

I put 28 for( b)
And 51.4 for (d)
Because thats the answer I get and I didnt round it wrong

[compact pewter]

@quartz yoke Has your question been resolved?

[quartz yoke]

<@&286206848099549185>

[hexed ferry]

im reading it

[quartz yoke]

Oo oki

[hexed ferry]

your work looks good but im plugging it in the calculator to see

[quartz yoke]

Oki

[hexed ferry]

what probably happened is you rounded early

but im seeing

[quartz yoke]

Oo I see

[hexed ferry]

yea i think thats what happened

[quartz yoke]

Where did I round early

[hexed ferry]

this long decimal looks like it was rounded

same thing here

[quartz yoke]

I round it to make it easierto write usually when im calculating I dont round it up

Let me try again

[hexed ferry]

ok try without rounding until the lasts tep

step

[quartz yoke]

This is the answer I got for thus

[quartz yoke]

And for this

[hexed ferry]

well maybe whoever wrote the solution rounded down i guess

kinda weird

[quartz yoke]

🥲ye

Oki thanks for the help

[hexed ferry]

yea np

[quartz yoke]

Have a nice day!

.close

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[compact pewter]

Please don't occupy multiple help channels.

[ivory stump]

.close

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[carmine garden]

Trying to find the radius and interval of convergence here

[carmine garden]

so we have $\lim_{n \to \infty} \frac{x^{n+1}}{\sqrt{n+1}} \cdot \frac{\sqrt{n}}{ x^n}$

[winged lion]

we had

[quartz yoke]

a failed to render

[carmine garden]

by the ratio test

[boreal girder]

What a wonderful world !

[carmine garden]

which gives us $x$

[boreal girder]

What a wonderful world !

[carmine garden]

Which has to lie between -1 and 1

so $(-1,1)$ is the interval of convergence

[boreal girder]

What a wonderful world !

[carmine garden]

and the radius is 1

is that right

[winged lion]

what about the endpoints

[carmine garden]

Have to study that bit

*bit

will do that

thanks

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[carmine garden]

.reopen

[compact pewter]

✅

[carmine garden]

wait

when x=1 it diverges

when x=-1 converges via the alternating series test

[winged lion]

ok

[carmine garden]

thanks

.cloe

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[winged lion]

.cleo

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[floral kelp]

Guys, do we differentiate the equation of the circle to solve letter d?

[floral kelp]

how to differentiate the equation of circle? it has both x and y and im confused now

[winged lion]

you can differentiate implicitly

[floral kelp]

what does implicitly means

[winged lion]

an implicit equation is what you have now

like you didnt solve for y

you have like f(x,y)=0 instead of y=f(x)

but you can still differentiate both sides applying d/dx

for example

x+y+1=0 so d/dx (x+y+1) = d/dx 0 so 1+y' = 0 or y' = -1

[floral kelp]

i still dont understand

[floral kelp]

d/ dx can differentiate both x and y variables?

[winged lion]

yes

you always did

[winged lion]

y is a function of x

and you know that you can differentiate them just as well wrt x

[floral kelp]

sorry but what does d/dx mean?

[winged lion]

it's an operator, which means i am now to take the derivative of something with respect to x

but now i am asking, why do you need to differentiate

you have a circle C and a point P on C, you now want to find the second point Q on C so that the line PQ is parallel

to the x-axis

so that is nothing more than just y = some number

that line goes certainly through P so some number must be 2

y = 2

[floral kelp]

im doing letter d

[winged lion]

ohh mb

ah ok isee

[floral kelp]

wait what does with respect to x means

[winged lion]

you differentiate after x

[floral kelp]

i understand dy/dx but i dont understand if we are to differentiate y^2

in y^2, there is no x right

[winged lion]

y^2 is a function of x

so it's not a constant

y^2 = (y(x))²

you will have to apply a special rule here

imagine you had (sin(x))²

how would you differentiate that

[floral kelp]

uhhmm

i havent studied that

[winged lion]

oh well maybe you arent supposed to use derivatives

use geometry

[floral kelp]

okkk im going to try

[floral kelp]

thankuu so much!

[winged lion]

wait lol

i think you can use this

the purple segment is perpendicular and we know that the perpendicular line of a line has slope -1/m

[floral kelp]

ohhhh i get itt

[floral kelp]

thankuu soso much!

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[tough fable]

AB = 8
DC = 17
BCA = ACD
BC = ?
How do i get BC all i did was find AH by pythagoras theorem

[woeful schooner]

,rccw

[woeful schooner]

1 thing that comes to mind is using the area
Area of the rectangle ABCH = 2 * the area of the triangle ACH (because $\triangle ACH \cong \triangle BAC$) and then you can set that equal to the $2 \cdot (area(\triangle ACD) - area(\triangle CHD))$

[boreal girder]

@woeful schooner

[woeful schooner]

$8 \cdot x = \frac{1}{2}(15 + x)(8) - 4\cdot x$

[boreal girder]

@woeful schooner

[woeful schooner]

$8 \cdot x = (15 + x)(4) - 4 \cdot x$

[boreal girder]

@woeful schooner

[woeful schooner]

$8 \cdot x = 60 + \cancel{4 \cdot x} - \cancel{4 \cdot x}$

[boreal girder]

@woeful schooner

[tough fable]

Oh woooow

So x = 60/8?

[woeful schooner]

I think so yea

unless I made some dumb mistake lol

[tough fable]

Wow thanks

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[primal jay]

sin θ and -cos θ are two solutions for function √3x²-x+k=0. What's the value of k?

[woeful schooner]

Are you aware of the properties of sum and product of roots of a quadratic?

[primal jay]

sum is -b/a, product is c/a?

[woeful schooner]

sum is -b/a

but yes

Have you tried using them here?

[primal jay]

Huh. I'm not aware of the properties, maybe I should try it.

[woeful schooner]

.?

[primal jay]

my original approach BTW.

It peobably works, but I want to see if there's a less hideous approach.

[woeful schooner]

Oh wow I have 0 clue what's going on lmao

[primal jay]

I tried pluging in the two solutions into the original function and factor it out.

[woeful schooner]

Ok where did k go then?

[primal jay]

Plug the value of θ back into the original function can get me the value of k (which I haven't done yet)

[woeful schooner]

Oh wait you made them equal, yea I don't think that's how this works

[primal jay]

Done.

.close

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[chilly basalt]

<@&268886789983436800> scam

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[idle shard]

so A is a matrix 2x2

[idle shard]

when can i say that A^n is equal to the inside numbers to the nth power

[azure vault]

when A is diagonal

[idle shard]

like this case on the right hand side

oh ok

fr

ty

[azure vault]

I think that's the only case

[idle shard]

ty then

.close

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[turbid surge]

$\int_{-\infty}^{0}e^{x}sinxdx$

[boreal girder]

prograce

[azure vault]

!status

[compact pewter]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[turbid surge]

$= lim_{M \to -\infty}\int_{M}^{0}e^xsinxdx$ ?

improper integral

[winged lion]

did you mix the bounds

[turbid surge]

wdym

[winged lion]

here -inf is a lower bound

[turbid surge]

yes i mixed them

[boreal girder]

prograce

[winged lion]

well either way you need ibp

[turbid surge]

is this correct >?

[winged lion]

yes

[turbid surge]

i continue by myself

[azure vault]

Or complex numbers

[turbid surge]

No complex numbers in my course

i got $2 \int e^xsinxdx=-e^xcosx$

uh

[boreal girder]

prograce

[turbid surge]

what can i do

now

what does this mean

i remember i saw something like this before but forgot what they did

idk

[winged lion]

did you forget the bounds?

[turbid surge]

no im calculating the undefinite(?) integral and then use NL

[winged lion]

well something went wrong then

[turbid surge]

Since the function is continuous

[turbid surge]

oh

wait

i messed up

Nooo

Now

[winged lion]

seems to be it

[turbid surge]

nice

.solved

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[fresh ginkgo]

why can u use lopital here? f is continous on [0,1]

[barren horizon]

is it in the form of 0/0 or ∞/∞?

[fresh ginkgo]

But how?

alpha > 0

U can't estimate the interval with 1,0

[barren horizon]

oh "can", mb I thought you said "can't"

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@fresh ginkgo Has your question been resolved?

[vernal fossil]

oh wow, whoever made that solution did not bother trying to be more explicit

ill try to look into it

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[short sphinx]

help

Simplify the ratio 300 : 25

this one firstly

[potent star]

12:1

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@potent star Has your question been resolved?

[potent star]

<@&286206848099549185>

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@potent star Has your question been resolved?

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[rich jay]

can someone help me solve these?

[rich jay]

like I know how to find the tops but I'm not sure about the final answer

[near crown]

There's 3 nontrivial elements which must be divided somehow among sets of size 1 and 2

3 singletons is impossible (that generates the discrete topology)
3 sets of size 2 does the same
2 singletons is possible and generates the topology you gave
2 sets of size 2 is also possible and generates the topology you gave

so you've found every possible way for 5

[rich jay]

yes 5 is done

but for 6 and 7

I feel like there is more than just 3 for each

[near crown]

Same argument

Having 3 singletons or 3 sets of size 2 automatically generates discrete

So you can have at most 2 and 2

There should be... 6 ways to do that?

I think

[rich jay]

3 each

[near crown]

There's no examples with 7

[rich jay]

nope

here it says how many ways each element should have

29 in total for all of them