help-13

[gritty viper]

yeah

[visual berry]

this is a much more boring result i completely missed

thanks

[gritty viper]

np

[visual berry]

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[split crest]

we know that vectors (3,4,2) and (1,1,1) are solutions of the system Ax=b; Prove/find a contradiction that the vectors (4,5,3) and (5,7,3) must necessarily be the solution aswell. If yes, prove it, if not, find some system of equations where the vector isnt solution

[split crest]

1. Yes, because (3,4,2)+(1,1,1) is 4 5 3
2. also yes cuz i could express the 5 7 3 as LC of those before

[sharp lotus]

Wouldnt A(4,5,3) = A(3,4,2) + A(1,1,1) by linearity?

= 2b so it is only a solution if b = 2b i.e. b = 0?

@split crest ?

[split crest]

I dont know

it was in my test

that is how I answered

@sharp lotus

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[hoary vessel]

can someone please explain why bessel's correction involves subtracting 1 other than any other number?

[cedar kiln]

@hoary vessel Has your question been resolved?

[crimson delta]

do you mean why it doesn't subtract 2 or 17 in the denominator?

the math just works out that way

[hoary vessel]

like why could -1 give a more unbiased answer than those yeah or even the original without any subtractions

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[untold onyx]

i thought e^x ≠ e^2x

why we can do u substitution for that too

[fiery whale]

because they replaced dx with du

u=e^x, so du = e^x dx, so dx = du / e^x

substituting that too gives the result at the bottom

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[hasty rapids]

I need help on this problem

[hasty rapids]

This is my work shown

I wasn't sure what to do with a, but since it represented a constant I thought I could just put that outside the integral

This is calc II, trig substitution unit

[stable osprey]

you've gotta update your bounds

for the sub

I think

[cosmic steppe]

You have to

[stable osprey]

(im in calc II, so my opinion is not very valid yet)

he says its true tho

[cosmic steppe]

The power of being better than the university kids what can I say :)):):):):):

[hasty rapids]

But if I take the substitution, and then unsubstitute it for my final answer, wouldn't it be fine?

[cosmic steppe]

I wouldn't unsub unless it somehow makes it easier

[hasty rapids]

Hmm

I don't know how to update bounds

I forgot

[stable osprey]

well if your bounds are normally x,

then you can replace x in x=atan(theta)

so a = .. atan(theta)

i guess

that works out nice

[cosmic steppe]

They need to be theta bounds

[stable osprey]

mhm

[hasty rapids]

So in this case if my bounds are 0 and a

And with substitution, I change x = atan(theta)

Would I do arctan(x/a)

[cosmic steppe]

arctan(0) and arctan(1)

[hasty rapids]

With x being the upper and lower bound

[stable osprey]

replace x with a

[cosmic steppe]

pretty much yeah

[stable osprey]

and yes

[hasty rapids]

Go it

What am I supposed to do with the a?

[stable osprey]

it just disappears

when a = a*tan(theta)

divide by a

gone

[hasty rapids]

?

When I substituted everything

I was left with the equation

8* integral(upper: pi/4, lower: 0 // (a^-3)(cos(theta)) )

Why would I divide by a?

[stable osprey]

maybe i dont know what u mean by this

[hasty rapids]

Can I put the a outside the integral?

[stable osprey]

the a^3?

8/a^3

it was already out

idk how u pulled it back in

[hasty rapids]

This is my new work

[stable osprey]

or why*

yea its a constant

[hasty rapids]

So it doesn't matter?

[stable osprey]

nah yoink it out

[hasty rapids]

Got it

[cedar kiln]

@hasty rapids Has your question been resolved?

[hasty rapids]

OH

I see what I did wrong

I didn't integrate sin(theta)

Wait yes I did

I think I got the same answer

Umm

It's still the same answer that I inputted

Even though I did it a different way

sin(pi/4) is root(2)/2 and sin(0) is 0, right?

I don't see which step could've gone wrong

[stable osprey]

ahh

wow

i did not see that

a has performed a vanishing act

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[zinc vortex]

A suitcase is pulled 50 ft along a horizontal sidewalk with a constant force of 30 lb at an angle of 30° above the horizontal.

[zinc vortex]

I need to calculate the work

using the dot product

[broken nest]

could u help me

#help-23

[cedar kiln]

@zinc vortex Has your question been resolved?

[faint dirge]

F•d, given constant force if you want simple work

F•d=FdcosØ, which has everything you need for your answer in ft-lbs

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[hollow garnet]

In the middle it says ln |u(x)|, what does u(x) mean?

I know that ln |u| derivitive is 1/u

But here its u'/u

And I dont really understand when derivtiive of ln is 1/u vs u'/u

[glad kestrel]

you've just been told to memorize the d/dx ln|x| = 1/x, but if you have an inner function, you must apply the chain rule

u(x) represents the inner function

[hollow garnet]

Oh

So it's technically always u'/u but

If there isnt anything crazy inside then u' just gives us 1

Is that right

[glad kestrel]

correct, d/du u = 1

[hollow garnet]

Thank you

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[crimson sedge]

volume = m/d

83.4

37.6mm to cm is 3.76

[runic garnet]

What do u need help with

[crimson sedge]

1.06 * 3.76 = 3.99

83.4/3.99 = 20.92

20.92cm = 0.209m

https://tenor.com/view/supa-hot-fire-ooooh-rap-battle-jump-crowd-surf-gif-4557024

It was fucking right

0.209m was right

I have done zero studying for chem

all i do is win win win no matta wut

[cerulean sail]

GOT MONEY ON MY MIND I CAN NEVER GET ENOUGH

Sorry just had to 🔥

[crimson sedge]

EVERY TIME I STEP UP IN BUILDING EVERY BODYS HANDS GO UP

AND DEY STAY THERE

[cerulean sail]

Damn that reminds me to add that to my 2010s playlist

Funny enough I’m listening to that playlist right now

[crimson sedge]

87.3 - 54.8 = 32.5ml

V=32.5ml

M/V=D

627/32.5=19.3

Guess what

It was wrong.....

PSYCHE IT WAS RIGHT FIRST TRY

https://tenor.com/view/supa-hot-fire-ooooh-rap-battle-jump-crowd-surf-gif-4557024

[runic garnet]

https://tenor.com/view/woo-pop-smoke-gif-18591273

[crimson sedge]

GET STURDY

.close

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[unreal ferry]

Need help with this

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[gritty shore]

Can someone please help simplify this complex fraction to evaluate the limit

[latent bloom]

,rccw

[gritty shore]

?

Would the top of the fraction equal to 5- X+3

<@&286206848099549185>

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[naive sleet]

help

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[naive sleet]

<@&286206848099549185>

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[latent bloom]

Remember here that f(x) is a function of x only

y and z are constants

Differentiate and solve

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[drowsy glen]

hi

[buoyant latch]

What’s your question?

[drowsy glen]

this thing

i am not able to understand

i think the answer is "A" am i right?

[crimson sedge]

no

[drowsy glen]

then whats right answer?

[crimson sedge]

.

[drowsy glen]

tan theta= opp/adj

sin theta=opp/hyp?

[wraith dagger]

عبد الرحمن

[drowsy glen]

no

whats the answer?

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[jagged charm]

I've : $h'(x)=e^{-x}[\sqrt{2}cos(x-\frac{π}{4})-1]$

How can I justifie than :
On $[0;\frac{π}{2}]$, $\sqrt{2}\cos(x-\frac{π}{4})-1≥0$ and then on : $[\frac{π}{2};2π]$, $\sqrt{2}\cos(x-\frac{π}{4})-1≤0$ ?

Please help me ...

[wraith dagger]

Pierre de Fermat

[limpid mesa]

My opinion is

as we know, cos(x) monotonic decrement when $x \in [0,\pi]$

[wraith dagger]

SUM

[limpid mesa]

cuz $\sqrt{2}\cos (\frac{\pi}{4})-1=0$

[wraith dagger]

SUM

[limpid mesa]

therefore when $x=\pi /2$, it is 0

[wraith dagger]

SUM

[limpid mesa]

so when $x<\pi /2$, it is bigger than 0

[wraith dagger]

SUM

[limpid mesa]

when $\pi>x>\pi /2$, it is smaller than 0

[wraith dagger]

SUM

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[drowsy quartz]

how do i find the arg of -1-sqrt(3)i

[rough heron]

you can draw a diagram

that'll probably help a lot

[deft moon]

convert it into polar form

[rough heron]

the argument is just the blue angle here

just remember to negate it

as it's going under the x-axis

[rough heron]

to do that you need the modulus and the argument though

i think using arctan here is simpler

[drowsy quartz]

so answer is negative because the angle is under the x axis

[deft moon]

multiply and divide by 2
2{cos(-pi/3)+isin(-pi/3)}

[rough heron]

what do you mean multiply and divide by 2

[drowsy quartz]

arg is tanthita=y/x right

when z=x+yi

[rough heron]

i wouldn't solely rely on that

that is true for the first quadrant i.e. x and y are positive

but it becomes a bit more fiddly with other quadrants

[drowsy quartz]

i see

so best way to do it is draw diagram?

[rough heron]

i would say so yeah

so there's absolutely no confusion

[drowsy quartz]

okayu thanks

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[ebon scaffold]

Hi

[ebon scaffold]

sry for coming again

I hv a question

I'm not so sure how to do this

Is this wht I do for a?:
a) 80 * 3.142 =251.36

Or did I do tht wrong?

<@&286206848099549185>

Oops, mb its only been 13 mins

sry

[ebon scaffold]

Anyone ble to help, tho?

[quiet plover]

yes its correct

Circumference = $2 \times \pi \times r = \pi \times d$

[quiet plover]

= 3.142 * 80 cm = 251.36 cm (or) 2.51 m

[ebon scaffold]

Ahk, ty for the help

How about B?

I'm not so sure how to do tht

[quiet plover]

hmmok

[ebon scaffold]

Oh wait just 2.51m * 100

[quiet plover]

now what does one rotation mean?

[ebon scaffold]

when it turns whole once

[quiet plover]

yess

that means one rotation covers distance equal to the circle's circumference

one rotation -> 2.51 m

or this way

2.51 m -> 1 rotation

then 1 m -> ? rotations

try to find that

then you can find rotations needed for 100 m

[ebon scaffold]

Ohh

[ebon scaffold]

I'm not rlly so sure ho wot do tht

how to do tht

[quiet plover]

2.51 m $\rightarrow$ 1 rotation\\
$\frac{2.51 m}{2.51} \rightarrow \frac{1}{2.51}$ rotation\\
$1 m \rightarrow \frac{1}{2.51}$ rotation

[ebon scaffold]

hm

So 1m is 0.398406374501992

I do 0.398406374501992 * 100?

[quiet plover]

yes

[quiet plover]

yes, exactly

[ebon scaffold]

Ahk

Thats 39.8406374501992

and it to the nearest whole number

is 40

Yes it worked, thankyou for your help

[quiet plover]

welcome (:

[ebon scaffold]

ngl its kinda cool how u made tht img

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[quiet plover]

its called latex
its mostly used in this server to depict stuff like fractions, exponents, and so on

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[tame hare]

for this question, are the two circles of equal radius

im not sure if the diagram is trying to trick me

call the radius of the top circle a and the bottom circle b

let R be the midpoint of PQ

let S be the very top of the diagram (where the smaller circle and the biggest "whole" circle intersect) and T be the very bottom of the diagram (where the bigger circle and the biggest "whole" circle intersect)

using power of a point, PR * RQ = SR * RT

since we stated that R is the midpoint of PQ and PQ is 6 this means PR and RQ are both equal to 3

SR and RT are equal to 2a and 2b respectively since they are the diameters of the top and bottom circle respectively

[tame hare]

therefore 4ab = 9

ab = 9/4

let O be the center of the biggest circle (the entire thing)

let x be equal to RO

using pythagoras PO = sqrt(x^2 + 3^2) therefore PO = sqrt(x^2 + 9)

PO is a radius, but so is SO

therefore 2a+x = sqrt(x^2 + 9)

ok i see where i went wrong nvm

.colose

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[drowsy quartz]

@rough heron

[drowsy quartz]

θ = tan-1(b / a) if z lies in the first or fourth quadrant
θ = tan-1(b / a) + 180° if z lies in the second quadrant
θ = tan-1(b / a) - 180° if z lies in the third quadrant

just found this, seems to work and is handy to know

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[mint moth]

How is <c not 60 degrees?

[mint moth]

I did 60+60+c=180 (because co-interior angles=180)
120+c=180
c=60

.CLOSE

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[ruby lion]

that was agressive

[cedar kiln]

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[tame hare]

I suck at geom how to do

[tame hare]

wait oops

semicircle + semicircle - triangle

ooooooooooooooooooooooooops

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[sick sparrow]

Positive integers $p$, $a$ and $b$ satisfy the equation $p^2 + a^2 = b^2$. Prove that if $p$ is a prime greater than 3, then $a$ is a multiple of 12 and $2(p+a+1)$ is a perfect square.

[sick sparrow]

please help

[wraith dagger]

mchw

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[thorny sun]

Show that the function f : C → C given by f(z) = z^2
is continuous on C

[thorny sun]

hi guys i have no idea how to approach this ;-;

[tropic oxide]

have you ever worked with the concept of continuity before

[thorny sun]

only for points

[random shale]

@thorny sun do you get given lecture notes?

Usually the lecturers will give you nice theorems / definitions that you can apply to solve these types of questions

[thorny sun]

yep but theres no mention of continuity on C

we were taught abt diff and holomorp

[cedar kiln]

@thorny sun Has your question been resolved?

[random shale]

These are what my notes say

[cedar kiln]

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[subtle sphinx]

help

<@&286206848099549185>

[earnest pollen]

I hope it's clear @subtle sphinx

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[ocean halo]

can anyone explain this to me? ik the answer (2.5) but i don't think i understand it

[ocean halo]

this is highschool math if that matters

[acoustic shore]

you can solve this alegebraically. you can add and subtract vectors like normal variables

[ocean halo]

see look

a + t b
a + (3t -5)b

t = 3t - 5
5 = 2t
t = 5/2

i messed around and i got this which is right but what happened to the a and b? this is the only part that i don't understand. i'm sorry but math is my WEAKEST point.

[acoustic shore]

wdym by what happened to a and b

[ocean halo]

how did "a + (3t -5)b" become "t = 3t - 5" 😭

[acoustic shore]

ooh

ok so see

they ve given you a condition

the two vectors

are equal

now substitute the expressions of the vectors

what equation do you get?

[ocean halo]

a + tb = a + (3t-5)b?

[acoustic shore]

yes

now you can move forward from that

[ocean halo]

so we need to get rid of a and b

right?

[acoustic shore]

yes

[ocean halo]

can i just cancel a?

[acoustic shore]

in this case its easy

[acoustic shore]

yes, you can subtract a from both sides

what equation do you get after doing that?

[ocean halo]

okay

tb = 3tb - 5b

after expanding

[worldly iron]

AB=CD if and only if the components of both vectors are equal

use this principle to calculate the value of t

[ocean halo]

should i switch the -5b and tb?

[worldly iron]

3t-5=t

[ocean halo]

i get this but there's one small part that i don't get

[ocean halo]

what happened to the b if u don't mind me asking?

[worldly iron]

a and b here are unit vectors

[ocean halo]

unit vector means 1?

[acoustic shore]

ah right this can also be solved using components

[acoustic shore]

not necessarily

@ocean halo basically the main point is that the two vectors are linear combinations of a and b

[ocean halo]

that's not part of my syllabus so idk what that is lol

[ocean halo]

okay

[acoustic shore]

components are basically how much part of the vector is in that direction

so say i have a vector

(2, 3)

[worldly iron]

r u sure about that?

[acoustic shore]

now i say, what is its x component?

that is 2, because the vector is 2 units in the x direction

same goes for y

[ocean halo]

2?

okay

[acoustic shore]

yes, its only a linear combination

[ocean halo]

makes sense

[acoustic shore]

yup

but its not just in x and y directions

say i have another vector, (1, 5)

now i say, what is the component of (2, 3) along (1, 5)?

[worldly iron]

In some textbooks, they also count a,b,c instead of caartesian axes

[acoustic shore]

thats just convention

[ocean halo]

no idea 😭

[acoustic shore]

but i think unit vectors are represented by hats

[ocean halo]

this is too advanced for me, when do people generally take this

u guys seem very smart lol

[worldly iron]

the dot product of then

[acoustic shore]

it will take some calculation but you get the point

[ocean halo]

yeah i do

[acoustic shore]

well the dot product divided by the magnitude of the second vector

[ocean halo]

i think i understood the question now, i just need to practice vectors a lot

thanks u guus

guys*

[worldly iron]

bruh, this is too simple TBH

It's not rocket science

[acoustic shore]

then just stick to the normal algebraic method

[ocean halo]

it's not part of my IGCSE syllabus so never heard of it before

[ocean halo]

much easier

[acoustic shore]

you have the equation tb = (3t - 5)b. you can cross both the sides with 1/b

[worldly iron]

well, yeah the projection of that vector damn

[acoustic shore]

are you aware of cross products?

mhm

dot product is projection multiplied by length of the vector you re projecting on to

and the magnitude of the resultant vector

[worldly iron]

@ocean halo read these:

https://en.wikipedia.org/wiki/Cross_product
https://en.wikipedia.org/wiki/Dot_product

[acoustic shore]

i meant dot. my bad

dot both the sides with 1/b

[ocean halo]

tb = 3tb - 5b. i switch the tb and -5b so 5b = 2tb. divide both sides by b to get rid of it then we will have t = 5/2 which is our ans

[ocean halo]

sounds interesting tbh, i'll give it a read

[acoustic shore]

yes

[ocean halo]

do people generally take this in college? or HS?

[ocean halo]

got it now

[acoustic shore]

more specifically you d have to take the product on both the sides with 1/b, because vectors can be multiplied in two ways

[ocean halo]

yup

[acoustic shore]

read the article sent by @worldly iron

[worldly iron]

well, here in Bangladesh we study them right after primary school

[ocean halo]

will do so

[ocean halo]

woahhhh

i think i'll take this in A levels (12th grade)

[acoustic shore]

omg. here in india we dont study about vectors before 11th grade (i am in 10th grade but i ve already studied them lol, i really like maths so)

[worldly iron]

Dude, you are an Indian?

[ocean halo]

i just checked, i'll take it in the 12th grade ONLY if i take further math lol

[ocean halo]

woahhh

[acoustic shore]

yes

[worldly iron]

Lets be friends then

[ocean halo]

i thought u were a college student or sum bro 😭

keep it up G

[acoustic shore]

haha sure

[acoustic shore]

lmao, i do think that in asia education in lower grades is a bit more advanced

[worldly iron]

Being an Asian is a next level torture for Americans lmao

[ocean halo]

i heard that a lot

[acoustic shore]

haha

[ocean halo]

😭

[acoustic shore]

@ocean halo if you re doubt has been resolved you can close the channel

[ocean halo]

oh didn't know i could do this

sure

[acoustic shore]

use .close

[ocean halo]

thank u guys sm

[acoustic shore]

yw

[ocean halo]

have a good day/night!!!

[acoustic shore]

read more on dot and cross products

[ocean halo]

.close

[cedar kiln]

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[obsidian tundra]

which method to apply for this to find convergence.

[obsidian tundra]

nvm

.close

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[obsidian tundra]

.reopen

[cedar kiln]

✅

[obsidian tundra]

nvm couldnt find

[red pumice]

do you think it should converge?

what does your intuition say

[obsidian tundra]

converges or diverges? quesion is this

ah wait

like i am not sure because of sin it makes me mix , but i think it will converge

[red pumice]

exactly it will converge

[obsidian tundra]

but dont know which method to prove

[red pumice]

$\sum_{n = 1}^{\infty} \frac{1}{n^2}$ converges

[wraith dagger]

heavy

[red pumice]

and

$0 \leq |(-1)^n \sin(n)| \leq 1$

[wraith dagger]

heavy

[obsidian tundra]

uhhh

it is not a test yes?

just logical answer

or hm

okay thanks man

.close

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[zenith cipher]

i got this 1^oo case and while i used euler i got to the point where i don't know how to continue

i have e to power lim which results in a 0*oo and i can't use l'hospital either

[obsidian tundra]

(3+5)/ 2^n and 2^n goes to infinity then it becomes 8/inf and it gets closer to zero. i am not helper but this is it i think

[zenith cipher]

isn't it a sum that it's raised to power n, i don't think you can use that property

[obsidian tundra]

holy, my fault sorry sorry

[mossy mango]

ok rbit

ur wrong

[zenith cipher]

i got to this point and i don't have a clue how to continue

[obsidian tundra]

if this is true

use this

[zenith cipher]

a is oo and if i use oo in f(x) it's going to be 1 and in g(x) it's going to be oo which still results in 1^oo

i'm not sure either

[obsidian tundra]

1^inf is 1

i think ,what else it can be

[crimson sedge]

1^inf is not always 1

[obsidian tundra]

what the hell

[gilded elm]

achkually inf is not a number so that's undefined

[zenith cipher]

i'm not sure how to continue that in case it's correct

[cedar kiln]

@zenith cipher Has your question been resolved?

[cedar kiln]

@zenith cipher Has your question been resolved?

[cedar kiln]

@zenith cipher Has your question been resolved?

[dire geode]

factor out one of the 1/3^n or 1/5^n

[zenith cipher]

ok, i did with 5^1/n

[crimson sedge]

can you show?

@zenith cipher

[zenith cipher]

didn't work out

[zenith cipher]

what about this, is it wrong?

[crimson sedge]

seems a bit complicated, are you not allowed to use lhospital?

[dire geode]

Show it

[zenith cipher]

Show it
@dire geode

is it correct this way?

[zenith cipher]

sadly not, it's a series of functions not function limits

[crimson sedge]

a series of functions? if a real function f(x) has a limit for x->inf, then the sequence f(n) has the same limit for n->inf

[zenith cipher]

yeah but i ve been told for 5 years that i'm not allowed to use l'hospital, if i have to, then i need to create a function that is defined in R or sth and it's still not wanted by some teachers

[dire geode]

,rotate

[dire geode]

that's on the right track. keep going with it. remind yourself the limit definition of e

[zenith cipher]

that's on the right track. keep going with it. remind yourself the limit definition of e
@dire geode what about this?

[dire geode]

,rotate

[cedar kiln]

@zenith cipher Has your question been resolved?

[cedar kiln]

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[elder elm]

perpetually confused on how to solve dis

[wraith dagger]

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

[elder elm]

?

[gilded elm]

sorry the f(x) x should be f(x) dx

[elder elm]

So would my a be 5(x)^2 and my b be 6()^5?

[gilded elm]

that would not work

[elder elm]

Why?

[gilded elm]

you didn't think sufficiently

the limits here definitely should not contain variables

[elder elm]

What type of problem is this?

?

[cedar kiln]

@elder elm Has your question been resolved?

[elder elm]

so a = 3, b = 5, but what's f(x)/

[elder elm]

.close

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[high kernel]

Can someone help this is what I got

[high kernel]

P is for period

Here’s the graph

[cedar kiln]

@high kernel Has your question been resolved?

[high kernel]

<@&286206848099549185>

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@high kernel Has your question been resolved?

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[crimson sedge]

you cannot

[dull oxide]

a test question...

why you asking us for test help?

How much time you got left?

[cosmic steppe]

Ayo

[dull oxide]

Still around mr @tiny spear?

[slim hearth]

.close

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[latent bloom]

[cedar kiln]

@narrow cove Has your question been resolved?

[dire geode]

.close

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[burnt moss]

I do not know how to get to this answer

Do absolute signs act as parentheses?

[true wasp]

yes, or sort of, you can introduce a positive constant inside and subtract another from its definition.

[burnt moss]

I tried treated the absolute signs as parentheses and I ended up with -6x^2/5+ 2x/5-14/3 = 0

or did you mean substract everything in the brackets together on the other side?

[true wasp]

before that, I recommend you to plot the one with the absolute value.

Because then it should be clearer how to tackle that one

I mean, that find that case were you can remove the absolute value and substitute for the appropriate one

and after that you will just have to make both sides equal :)

[burnt moss]

Okay thank you!

.close

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[gilded elm]

how do I show sqrt(x) is continuous on [0, 1/4]? I can't find an upper bound for it

[dire geode]

What

It's monotone

[gilded elm]

oh

is that actually all I need

oh right

sigh

real analysis

i got the rest

myself

[cerulean sail]

Mind you, showing continuity from first principles doesn't seem too hard!

[gilded elm]

I spent 4 pages on it

I must have made an algebra mistake

ngl intended to show u.c. but I can just apply that one theorem

anyway

coose

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[crimson sedge]

This is the question, it's about inverse functions

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

<@&286206848099549185>

[icy stream]

What is the inverse of multiplication?

(The exchange rate is being multiplied by D_US

[crimson sedge]

division

[icy stream]

Correct, now what is the inverse of 1.5226*D_US?

[crimson sedge]

well, I did this

[icy stream]

Mostly correct

Just note:

You need D_C, and you have D_US, It seems that you have assigned D_C as Y and the other X however, you seem to have swapped them. (I assume that your original is f(x)

[crimson sedge]

oh

thank you!

[icy stream]

Your algebra looks confusing to me, just give a moment...

Okay, You are trying to find D_US as D_C so it would be what is the D_US value turned into D_C using the conversion rate... D_C is 1.5~ times more valuable than the D_US so we would want, divide the D_US by 1.5~ to find D_C

[crimson sedge]

yes

[icy stream]

It was your final answer that was throwing me off because we are trying to answer for D_C not D_US.

[crimson sedge]

so... is it correct?

[icy stream]

$D_{C}=\frac{D_{US}}{1.5226}$

[wraith dagger]

박상민

[crimson sedge]

Thank youuu

[icy stream]

It may help to indicate what X and Y are, or just directly use D_C and D_US... I always make little mistakes when it comes to algebra...

[crimson sedge]

nt

.close

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[sleek yoke]

I thought I got it but I'm still lost

[sleek yoke]

Could someone explain how I'd draw the graph out for it?

Azo was right about f(0) = -4 but tbh I still don't get how he got there

[zenith sail]

You're given one point on the graph of f: f(4) = 0

so start with that

The graph you're shown is the derivative

Do you know what that means?

[sleek yoke]

that'd be the slope right?

[zenith sail]

Right

So see how between x=3 and x=4, you have f'(x) = 3

[sleek yoke]

so to get from x =3 to x =4 you go up 3 right 1

[zenith sail]

You know f(4)=0, and between x=3 and x=4, the graph of f has a slope of 3

right, which means what do you have to have for f(3)?

[sleek yoke]

thats where u lost me

lmao

[zenith sail]

You're exactly right with this

And you have f(4) = 0

Which means this segment you're talking about goes from (3,?) to (4,0)

[sleek yoke]

oh wait what is it -3

[zenith sail]

Yeah, exactly

[sleek yoke]

and then just do that for every point

[zenith sail]

Yeah pretty much. It says the graph of f is continuous, so if you're gonna continue working left, now you're going from (3,-3)

[sleek yoke]

i can't remember the last time i've felt this dumb

ahahaha

[zenith sail]

Lol, you got it now?

[sleek yoke]

long day i'll blame it on that

yeah fs

thanks so much

haha

[zenith sail]

Np 👍 You'll probably actually want to draw the whole graph

so you can do the integral at the end

[sleek yoke]

yeah thats the plan i already have it going

oh wait btw

[zenith sail]

yep?

[sleek yoke]

am i just evaluating the integral for c

as in finding area between x axis and curve

well not curve but lines

[zenith sail]

oh my bad, that's the integral of f'(x)

[sleek yoke]

as in i'd get a numerical value?

[zenith sail]

yes

But it's f', so actually for that you'll just use the f'(x) graph you're given

[sleek yoke]

oh what

how would i do that

[zenith sail]

It's the integral of f'(x)
not f(x)

[sleek yoke]

just do it as rectangles?

[zenith sail]

Yeah exactly

(and remember the ones below the x-axis are negative)

[sleek yoke]

yessir

or maam my fault

[zenith sail]

Lol

[sleek yoke]

that was sm easier than i was making it out to be

[zenith sail]

np 👍

[sleek yoke]

needed that walk through

[zenith sail]

glad it helped

[sleek yoke]

thanks so much again, really appreciate it

fs have a good one! :)

[zenith sail]

You too!

[sleek yoke]

yeah just finished the question, -4, -5, -1

ffs no idea how i got accepted to this uni for science 😭

doesn't always show bahaha

[cedar kiln]

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[spring coyote]

guys

to determine homogenity

my homework answer said alpha = 6 (level of homogenity)

but how can lambda be extracted here to power of ^6?

.close

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[mental atlas]

Using the combination formula, $n \choose r$ = $\frac{n!}{r!(n - r)!}$, can someone walk me through how we are able to simplify $2n \choose n$$n \choose 2$ to $\frac{(2n)!}{(n-2)!n!2!}$ from $\frac{(2n!)}{(n)!n!} * \frac{(n)!}{(n - 2)!2!}$?

[wraith dagger]

phamous

[mental atlas]

I'm not sure how to cancel like terms with $\frac{2n!}{n!n!} * \frac{n!}{2!(n - 2)!}$

[wraith dagger]

phamous

[dull oxide]

n!

[mental atlas]

I'm guessing we are allowed to cancel one of the n!

since it is the same base

[dull oxide]

You're basically done

[mental atlas]

so we are left with $\frac{2}{n!} * \frac{n!}{2!(n-2)!}$

[wraith dagger]

phamous

[dull oxide]

Where did the (2n)! go?

[mental atlas]

is (2n)! not the same as 2n!?

lol man i need to sleep

of course

we need to compute 2n first before we take the permutation of that

[cedar kiln]

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[crude sigil]

part (c)

can someone help

[ember geode]

what have you tried so far

[crude sigil]

I have done part a and b

Found the roots to be

3+4i

and

-3-4i

part b

ik u have to use quadratic formula

and discriminant formula I think

I just cannot remember exactly...

[ember geode]

Have you tried using the quadratic formula

[crude sigil]

idk how to with discriminat

i forgot

@ember geode

can u help?

.close

[cedar kiln]

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[cedar kiln]

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[wide ether]

what is focus conic section

[wide ether]

in conic section*

[crimson sedge]

A focus is a fixed point in the interior of the conic section, it is a reference point that helps define some of the properties of that conic section, for example

In an ellipse, for example, there are two foci

any point on the major axis of the ellipse that is equidistant from the two endpoints of the minor axis can be considered a focus

parabolas and hyperbolas have similar definitions

[wide ether]

ooo

what is the minor axis exactly

[crimson sedge]

This basically

[wide ether]

is it 90°s to the crosssection of ellipse or parabola?

[crimson sedge]

a is the major axis

b is the minor axis

F_1 and F_2 are the foci

this is an ellipse

[wide ether]

....

[crimson sedge]

i think the formal definition would be something like

[wide ether]

where did the cones go 😭

[crimson sedge]

The minor axis of an ellipse is the line that passes through the two endpoints of the shortest diameter of the ellipse and is also an axis of symmetry of the ellipse, if i remember correctly

[wide ether]

the mazor axis is the one passing through the double napped circular cone right

[crimson sedge]

you need to elaborate on this tho, wdym

[wide ether]

oooo

that makes sense!!!

[wide ether]

nvr mind i was wrong

[crimson sedge]

seemingly this is more about cross section and stuff, so like i think you want to hear some other definitions or something

[wide ether]

ok that makes sense

no no

thank you

i was just reading and the word focus was confusing me tysm

.close

[cedar kiln]

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[crimson sedge]

also sorry for the confusion, but what i said here is actually incomplete. a is the semi-major axis and b is the semi-minor axis, 2 times the length of a and b would give u the actual major axis for both

so basically the diameter if you will

[wide ether]

.reopen

[cedar kiln]

✅

[wide ether]

oh yea true

.close

[cedar kiln]

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[wide ether]

tysm agaij

again

[crimson sedge]

oh okay, just think of foci as like, fixed points that have nice properties that define what those cross sections (ellipses, parabolas, hyperbolas) are. like being equidistant with reference to something else n stuff

[crimson sedge]

no worries!

[wide ether]

ok now that .... is confusing

ill just try and do my project....for now

[crimson sedge]

a visual explanation about something that is inherently geometric is like necessary haha

me just vomiting words at you won't help

let me look up some video for you

[wide ether]

.reopen

[cedar kiln]

✅

[crimson sedge]

https://www.youtube.com/watch?v=QR2vxfwiHAU

i skimmed this video and i think they explain it really neatly

[wide ether]

can i also ask bout my project

thank you so much btw

[crimson sedge]

ah sure ofc

[wide ether]

it says use focal property of ellipse to construct ellipse

it means i just have to draw it right

[crimson sedge]

oh yeah, foci basically define ellipses, so make sense

[crimson sedge]

yeah

were u provided with some numbers or something

[wide ether]

nope

[crimson sedge]

like what the foci are

well if you weren't then ig we can make the numbers up ourself

[wide ether]

YEA!

we can!

[crimson sedge]

oh btw

This method of constructing an ellipse using the focal property is known as the "focal chord method" if my memory serves me right

[wide ether]

oh my god thank you so damn much

[crimson sedge]

wait is it

[wide ether]

lmao

ill search

[crimson sedge]

err nvm i must be confusing terms

oh its the focal point method

but the videos online are kind of dogshit about it

[wide ether]

mb i should do a different project

[crimson sedge]

how can u switch between projects this easily lmaoo

aren't they assigned or something

[wide ether]

any one from section B or C

[crimson sedge]

Anyways your project is totally doable, you just have to take out a ruler and do a lot of measurements. Like you have to check if the foci are equidistant and go from there to building your ellipse

[wide ether]

ive final exam in 15 days and they just said this....and vanished....

i see thank you so much ill try to make sense of it after watching the videos then

or maybe

number 22

[crimson sedge]

wait i will go video-hunting for you

let me try and find some suitable videos

[wide ether]

percentile
draw inferences of percentile

maybe i can just write in it?

is it ok to ask which one will ne the fastest one....im trying to get it over with today....

tbh maybe number 23 but theres nothing relating to purchasing power in our book

[crimson sedge]

im confused by what you are trying to say

ah

you are talking about the other question(s)

okay

i mean

[wide ether]

do you think i can understand this by today?

[crimson sedge]

oh yeah definitely

[wide ether]

ok then

[crimson sedge]

you just need to watch a bunch of videos here and there

https://youtu.be/TBK6TFucgWI

[wide ether]

bet

[crimson sedge]

the music to this video is a headache but i think it illustrates it well?

[wide ether]

ill complete the ones im watching then watch urs thank you so much

[crimson sedge]

aighty good luck you got this

[wide ether]

thanks a lott

.close

[cedar kiln]

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[cedar kiln]

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[spare fiber]

How can we find area of a circle by integration?

[long arrow]

y = sqrt(r^2-x^2)

-r <= x <= r

integrate

multiply by 2

[spare fiber]

Why are we doing this step? Can you elaborate please?

[long arrow]

equation of the circle with center (0,0) and radius r is x^2 + y^2 = r^2

we want to have function of one variable (because it's easier to do integration then, but double integral would work as well)

this is why we do

y = sqrt(r^2 - x^2) (in fact it should be + or -, but let's asssume it's +)

it represents semcircle with center (0,0) and radius r

2 x semicircle = circle

[spare fiber]

OKay. thanks!

.close

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[spare fiber]

What is a skew line?

[cedar kiln]

@spare fiber Has your question been resolved?

[spare fiber]

<@&286206848099549185>

[lusty grotto]

did you try googling

[spare fiber]

can't understand the definition there

Would be better in simpler words

[clear swallow]

What is the definition given in google?

Skew lines are a pair of lines that do not intersect and are not parallel to each other- is what is given in google

Basically skew lines are 2 or more lines that don't overlap or cross each other, but also not parallel to each other either

[lusty grotto]

and this is not simple words?

[clear swallow]

Eh, I tried explaining it simpler

[spare fiber]

How can they not intersect and not be parallel too?

[lusty grotto]

oh wait sorry i thought u were OP

[clear swallow]

Haha

I'm new here

And also an pre-undergraduate

so

[lusty grotto]

one line can be like on the top of the other

like the rungs of a ladder

[clear swallow]

What do you mean on top?

[clear swallow]

They would be parallel to each other then

[lusty grotto]

okay not on top but on the side

[clear swallow]

So they are not skew lines

[spare fiber]

so, skew lines are in 3D and not in 2D?

[clear swallow]

Yep

[lusty grotto]

yes yes sorry

lol

mb

imagine like a twisted ladder ig

[clear swallow]

Google "skew lines" and go to images to understand more I guess

[spare fiber]

Damn, someone told me that skew are in 2D too but they teach that in higher studies

[lusty grotto]

as am i

[clear swallow]

What grade?

[spare fiber]

Thanks though!

[clear swallow]

I myself have never heard of the term "skew lines", so I may be wrong yeah

[lusty grotto]

well by pre-undergraduate i meant ive finished schooling and am yet to enter university and start an undergraduate course

[clear swallow]

Ah

Alright-

My bad

[lusty grotto]

are you already in university

[clear swallow]

Haven't finished schooling yet 💀

[spare fiber]

same here

[clear swallow]

I'm here to help people in middle school and under I guess

From the concepts I know

[spare fiber]

.close

[cedar kiln]

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[severe void]

i've got two attempts left for this question. i was taking the integral of v(t) but it's marking it as wrong, was wondering if someone could help me w that

[spare fiber]

I think there might be some error in the integration part as there's a +C which is a variable, which is not possible to know

[severe void]

how should i incorporate the r(0) = <3,4,4>, or should I?

[cedar kiln]

@severe void Has your question been resolved?

[cedar kiln]

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[latent fox]

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