help-36

[exotic shale]

is tthere no standard one

[desert mantle]

depends what you mean by standard

a lot of courses define e^x by its taylor series

but then what you are trying to do is kinda pointless

[final saddle]

@exotic shale Has your question been resolved?

[exotic shale]

im trying to find something

how was e calculated

did we use a specific defintion?

[desert mantle]

the original historical def was lim n->infty of (1+1/n)^n afaik

(thats another way to define e^x, as the limit (1+x/n)^n for n->infty)

[exotic shale]

ok anyways

so for this

when doing the limit

am i supposed to choose an a

as center

or i leave it as a

?

[final saddle]

@exotic shale Has your question been resolved?

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[short wraith]

uhhh is this question bugged or smth cuz im completely clueless on how to approach this
like im trynna make a simultaneous equation but uhh idk dude

[true citrus]

First start with finding how the ball should move with respect to both time and initial speed.

Use the fact that there are no forces in the x axis.

[short wraith]

so for horizontal s = ucostheta t and for vertical s = usintheta t - 4.9 t^2

[true citrus]

We may work with ux and uy so

$$s_x = u_x t$$
$$s_y = u_y t - \frac{g}{2} t^2$$

[soft zealot]

Qwert

[true citrus]

Now u_x should be simple enough to solve with respect to time.

[short wraith]

but we dont know time though
and if i go simultaneous equation route i get 2=6vy/vx - 4.9(6/vx)^2

[true citrus]

For now see that at time at time 9/u_x, s_y = 5

[short wraith]

wait how did you get s_y = 5

[true citrus]

It is 6(the height of the house) -1. And you get 6 by using the 45 degrees to form a triangle.

[short wraith]

ohhh yeah
yeah i just saw that

Thanks
i think ill do it from here : )

[true citrus]

Alright then np.

Bye.

[short wraith]

Bye

[cosmic warren]

hmm I think you need one more equation since there's 3 unknowns. v_0, theta, and time.

the third equation is based on the condition of the minimum velocity needed

i.e. v_y would be 0 at the peak of the trajectory

[short wraith]

yeah i got one 9/ux = t
one is 5 = vyt - g/2 t^2
other is 0 = vy - gt

[cosmic warren]

ok bet

[short wraith]

my answer is coming 13.32
could u confirm please?

[cosmic warren]

uhh imm on my phone rn lemme get my laptop, it'll be easier

[short wraith]

yeah sure : )

[cosmic warren]

yup 13.32!

@short wraith

[short wraith]

yooo lesgoo and angle 48.01 right

[cosmic warren]

I get 48.04 but probably only cause I put in an estimated form rather than the exact form into arctan.

[short wraith]

oh that makes sense
thanks alot dude

[cosmic warren]

np

[short wraith]

have a good day
bye

[cosmic warren]

cya!

.close if you're finished 🙂

[short wraith]

.close

[final saddle]

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[warm python]

Am I missing something here ?
(i) Let $(a_n)$ be bound below by $a$ and $(b_n)$ be bound by $b$.
\
$\abs{a_n}<a \forall n \in \N; \abs{b_n}<b \forall n \in \N \implies \abs{a_n}+\abs{b_n}<a+b \implies \abs{a_n+b_n}<\abs{a_n}+\abs{b_n}<a+b \forall n \in \N$

[soft zealot]

wai

[warm python]

Like this is from a section on cauchy seqeunces, which is confusing me[ As in this requires no cauchy convergence does it?]

[worldly mesa]

you are right

[scarlet sequoia]

You have the idea, but I wouldn't use strict inequalities when using triangle inequality

this one especially

the rest is correct

[warm python]

thanks!

.close

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[next thorn]

ABC is a right angle triangle on B (angle B = 90)
AB = 6
BC=8
D is a midpoint of AC.
whats the component of BD in the direction of AB

[next thorn]

IDK why i got this wrong so ill just tell you guys what i did

OK I WROTE THE 8 IN ARABIC

AS;JKDSA]

here we go

anyways, the component of BD in the direction of AB is magn of BD * cos(angle between them)

the angle between them is 45 so lets work on the length of BD

I used the cosine

[edgy mauve]

Arba

[edgy mauve]

So what do u get after this

[next thorn]

cos(45) = ( (BD)^2 + (BA)^2 - (AD)^2 ) / 2....

okay i see what i did wrong

i wrote 2 * 5 * 7 instead of 2 * bd * 6 on the denominatoir

[ember jungle]

The answer is أ

[thin cloud]

that angle isn't 45 degree tho

[next thorn]

why wouldnt it

[thin cloud]

BD is median not a bisector

[next thorn]

doesnt BD half that 90 degree angle

[thin cloud]

no....

[next thorn]

oh

[edgy mauve]

That's when perpendicular and base r equal to eo

[next thorn]

oooh

[edgy mauve]

Or u might call it opposite and adjacent

[next thorn]

ok i can get the angle A then solve again

let me retry

[ember jungle]

Place the triangle on a coordinate plane with ب at (0,0), أ at (6,0), and ج at (0,8). The midpoint هـ of أج is then found by averaging the coordinates, giving هـ ( 3 , 4 ). The vector بهـ is therefore (3,4). Since the direction of أب lies along the x-axis, the component of بهـ in the direction of أب is simply the x-component of this vector, which is 3.

[thin cloud]

!nosols

[final saddle]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[ember jungle]

This is explaining. Apologies if it seemed like just giving the answer.

[terse sorrel]

you can also just use cosine rule in triangle abd

abd

[next thorn]

ok i got 25 for BD now onto that angle

[thin cloud]

yeah you gave the answer you found

so i thought

[terse sorrel]

find bd from that

and then use sine rule

[edgy mauve]

U mean 5

Bd²=25

[next thorn]

I was wondering what was wrong with my calculations

[thin cloud]

there's a theorem for that...

[edgy mauve]

What do u get from here

[edgy mauve]

That the half of hypotenuse is the length of its median from opposite vertex

[thin cloud]

yeah bruhhh, I don't know how to word that

[next thorn]

from bd = 5? i can find the angle between bd and ba now

and multiply that by 5

[next thorn]

wahr?

[thin cloud]

tbh we only need AB to do this problems

[next thorn]

elaborate?

[edgy mauve]

U can, yes

[edgy mauve]

Using coordinates?

[edgy mauve]

Yea

[thin cloud]

BDA is issoceles triangle at D

[next thorn]

yeah i got 771. what a beautiful angle

[thin cloud]

so...

[edgy mauve]

No way

Can u show ur work

[thin cloud]

Its projection onto BA is just mid point BA

[edgy mauve]

Oh nice,yea

[next thorn]

oooooooh

yes

makessense

yeah i got it

I cant believe it took me this long

its stupid

there was another question

about...

the shape with 6 sides

what do you call that

this thing

[edgy mauve]

Hexagon

[next thorn]

each length is 2cms long, what is | ab x af | ,

[ivory bear]

a fellow ||jee ||aspirant?

nice

[next thorn]

what i did...;

[thin cloud]

dang,yellow font in white background

[edgy mauve]

Nope i m not fortunately or unfortunately

[thin cloud]

nice choice

[ivory bear]

why

i thought you were

[edgy mauve]

Is?

[next thorn]

i connected e and b and assumed it was a parallelogram 🤩

im typing.

[edgy mauve]

B4 that uk how to determine the vertex angles of regualr polygon?

[edgy mauve]

I m not,but what made u think so?

[next thorn]

you mean their value when they're all equal?

no but

ik that each anglein a hexagon is 120

[edgy mauve]

These r vertex angles

[next thorn]

yes each of those is 120

it mentions that the shape is منتظم which means that they're every angle and side is equal

[next thorn]

good to know.

[edgy mauve]

Alr yes

[edgy mauve]

Noted,new word

[next thorn]

|ab x af | = 2 * 2 * sin(120)

[edgy mauve]

Yeah

[edgy mauve]

As for this

[next thorn]

🤩 im so smart with my assumptions

[next thorn]

what?

[edgy mauve]

If u wanted to form a parallelogram u should hv joined b,d and a,e

Tho i dont know where this takes u

[next thorn]

idk it was random 🤩 i needed a parallelogram to use AxB apparently. dont mind my decisions 🤩

[next thorn]

how? wont that be a

what do you call it

[edgy mauve]

Rectangle

[next thorn]

two sides are equal and the other are equal but are not equal to the first two sides

yes that

[edgy mauve]

Yeah rectangles

[next thorn]

how is that a- oh ig a rectangle is a parallelogram

[edgy mauve]

Rectangle is a type offl parallelogram ,the only property it neglect is that the diagonals r not equal

[next thorn]

why cant we connect eb and say that bafe is a parallelogram tho

[edgy mauve]

Bafe would be an irregular quadrilateral

In a parallelogram, opposite sides r equal

Opposite angles r equal

And the diagonals bisect eo

These properties cant be seen in BAFE

[next thorn]

?

they are????

💀

[edgy mauve]

Yes

[next thorn]

i feel like i shouldve known this a bit earlier

oooh thats why the parallelogram vector property works

[thin cloud]

yes actually

[edgy mauve]

Maybe u r getting confused with the english terms

U r supposed to know it

[next thorn]

idk i finished cross and dot product and i didnt know that hte sides are equal 😭

[craggy plank]

[next thorn]

ok so theres another question i got wrong but idk which one

and i dont access to the rest of the exam so

ig later.

got

off to equations i go

goodbye and ty people

.close

[final saddle]

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[edgy mauve]

That's a part of geometry

[next thorn]

i never studied that

i only studied trig

[edgy mauve]

I think u did learn ,but forgot or mixed it up

[next thorn]

forgot 100%

[edgy mauve]

Oh

[edgy mauve]

Lemme try this
'Afwan'

[final saddle]

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[golden cave]

18sqrt(5)

i got

[severe verge]

wrong

[craggy plank]

What did you do to get this answer?

[golden cave]

understood error

still dont get how to do it

[sullen gale]

how did you get 18sqrt(5) then

[golden cave]

v

drop a perpendicular from b to DC and from a to DC?

[golden cave]

i was stupid lol

did random stuff

[golden cave]

did that

[golden cave]

ye?

[meager hedge]

Let h the height

[golden cave]

ye

did that

[meager hedge]

You have : x^2 + h^2 = 7^2
(8-x)^2 + h^2 = 9^2

[golden cave]

ye

[meager hedge]

Meaning

[golden cave]

you can solve for h

[meager hedge]

7^2 - x^2 = 9^2 - (8-x)^2

You find x, then h

Then the area is (8-x)*h

[golden cave]

yea

[meager hedge]

All good ?

If you did all that you should be set

[golden cave]

x=2

h=sqrt(45)

[meager hedge]

Good

[golden cave]

so

18root(5)?

[meager hedge]

Yup

[golden cave]

bru

[meager hedge]

What ?

[golden cave]

i had it the entire time lol

but i did it in 2hrs

[meager hedge]

Organisation is key

x^2 + h^2 = 42
y^2 + h^2 = 26
x+y+4 = 12

So y = 8-x

So : 26 - (8-x)^2 = 42 - x^2

Solve for x then y then h

Área = h(12-1/2(x+y))

[golden cave]

ok'

[meager hedge]

x = 5
y = 3
h = sqrt(17)
Area = 8.sqrt(17)

[golden cave]

we find AC

[meager hedge]

Aaah yes

My bad

[golden cave]

root(42)?

[meager hedge]

AC^2 = (4+3)^2 + 17 = 49+17 =66
AC = sqrt(66)

[golden cave]

(4+y)^2

ye mb

i did 4+3=5

lol

[meager hedge]

It’s ok

It’s always the same thing just do right triangles, organize your equations to be solved easily … and solve

[golden cave]

ok

[golden cave]

for this

[golden cave]

wait

3 variables need 3 equations?

<@&286206848099549185>

[ivory bear]

for sure

[golden cave]

ok

[ivory bear]

thats true regardless through and through

[golden cave]

ye

[golden cave]

for this i only got 2 and cant get 3rd

[severe verge]

notice the isoceles triangles?

[golden cave]

where

AC?

and AD?

[severe verge]

∆ABP and and ∆PCD

[golden cave]

AB , DB

oh yea

bro

[severe verge]

use this to calculate angle APD

[golden cave]

ok

[golden cave]

90

took long enough

[severe verge]

alr nice

now ∆APD is a right triangle

you have M as AD's midpoint

what should x be?

[golden cave]

height?

[severe verge]

remember Thale's theorem?

[golden cave]

uh

yea

[severe verge]

use that to find x

[golden cave]

ok

10?

[golden cave]

i remember u

[severe verge]

nope

[golden cave]

bruh

[severe verge]

[golden cave]

20?????

wait no]

[severe verge]

it's just 20

[golden cave]

BURh

ok'

ty

carbonized

no right triangles 😭😭 that means more geometry than algebra

[severe verge]

interesting...

[golden cave]

my old acc got deleted lol

[severe verge]

damn

[golden cave]

alr

with da question

[golden cave]

btw i thought u stopped helping

and u left the serv.

it is

[ornate tree]

Which question are we dealing with rn?

[golden cave]

that

[severe verge]

uni is killing me

[golden cave]

uni?

[severe verge]

university

[golden cave]

oh

[ornate tree]

pinned

[golden cave]

ok

ty

why so many math channels

i've seen times when there were 2

alr to the question

wish it was in the center it would have been (24+32)/2

[thin cloud]

Sometimes there're non

[golden cave]

...

[golden cave]

what the emoji

i got 20root(2)

am i correct?

[severe verge]

yes

[golden cave]

ok

last one

took 3 days for 15 questions 😭😭😭

[severe verge]

[ornate tree]

@severe verge pin the question :))

[golden cave]

its not 7

[golden cave]

im an idiot

i put -7 as a response

is it 7?

[final saddle]

@golden cave Has your question been resolved?

[golden cave]

<@&286206848099549185>

i need help

i found a pair of similar triangles

AA congruency

similarity mb

[severe verge]

oh wow I figured it out

[golden cave]

?

[golden cave]

wym

i think its 6

[severe verge]

it's 7 😭

[golden cave]

i got that but put -7

[golden cave]

anyway

i gtg

eat

ty carbonized

[severe verge]

it's that simple???

I am stupid

[golden cave]

lol

i did smth like that

[golden cave]

..

.close

[final saddle]

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[golden cave]

ty

[severe verge]

no problem

[final saddle]

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[gray acorn]

substitution by part for integral calc

[gray acorn]

i used to have a method thats like

you make a table

i thinbk theres a name or acronym for it

what is it if anyone knows

[worldly mesa]

integration by parts

[dense coral]

LIATE?

I never used the acronym though ngl

I always did parts by vibes

integration by vibes

[tulip coyote]

(there are also a few permutations/swaps of the letters in that too, e.g. ILATE etc etc )

[dense coral]

icic

[gray acorn]

😭

integration by vibes

okay yeah ty

.close

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[gray acorn]

lol

3h of sleep made me say that

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[prisma gulch]

Can someone explain this to me? I literally did this question multiple times and yet i still cant get that answer.

[final saddle]

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

[prisma gulch]

I have no idea my teacher assigned this for us due monday and all they said was the answer is as shown y8/a10 i did the question many times and i still cant get the answer

am i supposed to send the wrong answers

[late rose]

show us your working so far

even if its wrong

there might be a careless mistake

[prisma gulch]

why is the image sideways mb

<@&286206848099549185>

[late rose]

So in this case i think it would be best to combine the fractions on the left and right as much as possible

,tex

\begin{align*}
&\frac{2^{-2} \times a^6 \times y^{-8}}{b^{-4} \times x^7} \times \left( 2 \times \frac{a^8 \times y^{-16}}{b^{10}} \right)\
&= \frac{2^{-2} \times a^6 \times y^{-8} \times 2 \times a^8 \times y^{-16}}{b^{-4} \times x^7 \times b^{10}}\
\end{align*}

[late rose]

try to simplify that

[ornate hawk]

Sorry- how did you go from y^16 to y^10? Am I missing smth?

[prisma gulch]

mistake

[late rose]

and then for the fraction on the right, try to simplify this (first step done for you)

\begin{align*}
&\left(\frac{a^{-4} \times y^{12}}{b^{16} \times x^{-18}} \div \frac{x^{15} \times y^{60}}{a^{30}}\right) \times a^6\
&= \frac{a^{-4} \times y^{12}}{b^{16} \times x^{-18}} \times \frac{a^{30}}{x^{15} \times y^{60}} \times a^6\
\end{align*}

[ornate hawk]

And then you got y^18, which would be wrong as you have y^16, not y^10

All good, though. Just fix that, and you got it 👍

[final saddle]

@prisma gulch Has your question been resolved?

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[finite ocean]

How exactly do I go about this?

[hot osprey]

Answer: 0

[neon pewter]

i think he is a troll

[hot osprey]

ah..

He also left the server..

[final saddle]

@finite ocean Has your question been resolved?

[hot osprey]

just do ✅ since he left the server

[final saddle]

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[worthy patio]

Doesn't the divergence test say that this is divergent?

Because the limit does not equal 0?

[formal trail]

the divergence test says that a series will diverge if the terms being summed don't converge to 0. but this is the sequence of partial sums, not the sequence of terms being summed

[worthy patio]

um.. what's the difference

[formal trail]

if we have a series $\sum_{n = 1}^\infty a_n$ then $a_n$ is the sequence being summed and $s_n = \sum_{k = 1}^n a_n$ is the sequence of partial sums

[soft zealot]

κλαοδ ☁ (cloud)

[final saddle]

@worthy patio Has your question been resolved?

[final saddle]

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[autumn parcel]

If I have a matrix E = [1 over -3] and im asked for 2E would I multiply each value in E by 2, or multiply E by E in a row?

[formal trail]

multiplying a matrix by a scalar means multiplying each entry individually

multiplying E by E would only come out of E^2 (assuming it even has the right dimensions to multiply by itself)

[autumn parcel]

ah

[autumn parcel]

Alright thanks

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[remote stream]

why doesn’t this work

[tepid narwhal]

when you use U-substitution, you cannot have x and u variables exist at the same time

if you want to use it, Let U be the main integrand

[remote stream]

oh so i cant have dx = u/x du cause there are both u and x

[tepid narwhal]

tryna find as x express as u

the first step was correct

[tepid narwhal]

you can let u express as x, but when substitute into the integrand, you cannot have both variables

[remote stream]

y though

[tepid narwhal]

u substitution doesnt work like that

[fiery bluff]

huh
looks like it could work, lemme check if the answers are the same

[remote stream]

i think it does 😭

holon imma differentiate

my answer

[tepid narwhal]

If any original variable (like x) remains, the integral becomes a mix of two different variables and cannot be solved using this method, indicating an incorrect substitution was chosen.

---- Wiki definition of U-sub

[remote stream]

i just dont understnad why u sub wouldnt work like that

[remote stream]

yeah but it doesnt tho cause the Us cancel

[tepid narwhal]

no but u have 2 variables 【IN THE INTEGRAND]

[tepid narwhal]

if 2 variables just exist, it wouldn't work as the text says

[fiery bluff]

yeah the answer checks out

[fiery bluff]

it's fine, just pretend x is a function of u

[tepid narwhal]

also your integrand as x

and you're from du

[remote stream]

is there a better way to do this

[tepid narwhal]

this is very wrong

[remote stream]

but im not integrating x

wait

[tepid narwhal]

you cannot integrate x as respective as DU

[remote stream]

i am

[remote stream]

but i swap it

so its fine

[fiery bluff]

yeah x was substituted for u before integrating

[remote stream]

i swap it back to u then i integrate

[fiery bluff]

it's just doing the manipulation with x and u

[tepid narwhal]

this step is horribly wrong thats my conclusion

[fiery bluff]

you can think of x as sqrt(u^2+16)

[tepid narwhal]

just very wrong

[fiery bluff]

i think it works

[remote stream]

alr

whats the better way

to do this

[fiery bluff]

you can do your manipulation outside the integral but this is fine too

you can write x(u) to highlight that x is a function of u

[remote stream]

how would u do that

[fiery bluff]

$dx=\frac{u}{x(u)}du$

then

$\int\frac{u}{[x(u)]^2u}du$

$\int\frac{1}{[x(u)]^2}du$

$\int\frac{1}{u^2+16}du$

[soft zealot]

Element118

[fiery bluff]

that's if you want to be very clear what your intent is

[remote stream]

oh alright

isnt u usually a function of x tho

[fiery bluff]

you can be even more clear by literally writing "x is a function of u"

[fiery bluff]

there's a relation that relates them u^2=x^2-16

so you can treat this as u as a function of x, or the other way around

[remote stream]

oh okay that makes sense its like implicit differentation

ty

.close

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Available help channel!

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[tardy hamlet]

Hello I just need help with 3 questions

[tardy hamlet]

,rotate

[tired walrus]

ok so which of these many questions would you like to start with

[tardy hamlet]

I would like to start with 4

[tired walrus]

ok, so you need to write down the equation of the line thru these points

[tardy hamlet]

Yes

[tired walrus]

does it say what form they want?

slope-intercept, point-slope, something else?

[tardy hamlet]

In point slip form

[tired walrus]

ok cool

so can you find us the slope of this line first & foremost

[tardy hamlet]

Yes I will try

[willow cloud]

y=mx+b

[tired walrus]

aight go ahead and do it and show me your answer AND calculations

[tired walrus]

op just said she needs it in point-slope form so thats kinda misplaced right now.

[willow cloud]

which math is it

what level

also how can i mkae a new chat for help on my own problems i cant figure it out

[tired walrus]

read #❓how-to-get-help for instructions

you type in any help channel that doesnt have a name on it

when you do, it will be moved and have your name on it and then you will have claimed it

@tardy hamlet ping me when you're ready, finding the slope is just one step in the problem

[tardy hamlet]

Sorry I’m really bad at fractions

So it’s taking me a bit 🥲

[tired walrus]

ok

[tardy hamlet]

Wait I’m stumped

Am I doing this right???

Or do I have to get rid of the fractions first

[tired walrus]

first, this should be m= and not y=

[willow cloud]

@tired walrus if ur not too busy can you look at mine too #help-45

[tardy hamlet]

Thanks

[tired walrus]

... i will look at it if and only if i feel like doing so

@tardy hamlet you did the numerator in a slightly wonky way (could have taken common denom as 4 rather than 8) but no screw up yet

(-14/8)/(-13/8) is where you're at with the slope

simplify further

[tardy hamlet]

Oh yes

I forgot about that thank you

That leaves me with (-7/2)/(-13/8)

[tired walrus]

uhh no it doesn't

numerator by itself would simplify to -7/4

but also you kinda don't need to do it

you can just multiply the big numerator and denominator by -8 and jump straight to 14/13 as your slope

wait.

ah fuck.

[tardy hamlet]

What happened

[tired walrus]

ok sorry i only now discovered that you put the numbers in all the wrong places.

[tardy hamlet]

Oh shoot

[tired walrus]

and uhh you will have to erase all of this.

[tardy hamlet]

Mistakes happen 🥲

[tired walrus]

sorry, not fully woken up yet cause i have not had my entire cup of morning coffee

[tardy hamlet]

Don’t worry bro, you’re still doing pretty good

[tired walrus]

remember m = (y2-y1)/(x2-x1)

so the numerator needs to have the y's and the denominator needs to have the x's

[tired walrus]

don't call me "bro" please.

[tardy hamlet]

My bad uhh what should I call you???

[tired walrus]

i'm a girl and don't like it

[tired walrus]

just my name is fine

[tardy hamlet]

Alright bet thank you for letting me know

🙂‍↕️🙂‍↕️🙂‍↕️

[tired walrus]

$m=\frac{\frac52-\frac32}{\frac34-(-\frac78)}$

[soft zealot]

Ann

[tardy hamlet]

I will solve this rq 🙂‍↕️🙂‍↕️🙂‍↕️

I’ve got -1/(13/8)

@tired walrus sorry but is this correct?

Sad times

Is the -1 actually 1

Yeah it is

Whoops

Do I do keep change flip???

[tired walrus]

8/13 should now be the correct slope unless i fucked up in giving you directions

you're now ready to fill in the numbers in point slope form

im on my way to work and on the bus rn so might not respond immediately

[tardy hamlet]

Sorry to trouble you while ur busy Ann but thank you for helping me out 🙇🙇🙇

This should be correct???

Welp ima hope I’m correct on that

[tired walrus]

yes this is correct

[tardy hamlet]

Yessirrr!!! 🥹

I did it whew

Thank you 🙂‍↕️

It may be slightly troubling but would you be able to help me question 15-16? It’s alright if you’re too busy to do so

[tired walrus]

er. can you also not call me "sir" please

on account of me being a girl

[tired walrus]

can you repost these

[tardy hamlet]

Sorry that wasn’t me calling you a sir, it was one of those uhh things where you say like “yeppie” or some sort of exclamation, just for clarification 🙇🙇🙇

Sorry again and I’ll try not to it again 🙇🙇

[tired walrus]

if you have to, why not "yes ma'am" or something

[tardy hamlet]

Alr bettt

[tired walrus]

right

so conceptual question

[tardy hamlet]

Yes

[tired walrus]

if you have a line given by an equation (in any form), and a point,

what does it mean when we say the point lies on the line?

[tardy hamlet]

That’s the uhh (x,y)?

[tired walrus]

... not what im looking for here

well yes the point is given by its coordinates

but what exactly does it mean for it to lie on the line, algebraically speaking

[tardy hamlet]

Uh is it one of those slope formulas???

[tired walrus]

im looking for a complete sentence here

not just a namedrop

[tardy hamlet]

Okay bet I got this

Is it a point slope formula?

Okay wait that’s stupid

Does it mean that the equation is true?

[final saddle]

@tardy hamlet Has your question been resolved?

[tardy hamlet]

@tired walrus uhh are you too busy to continue???

I will take that as a yes

<@&286206848099549185>

[ornate tree]

Which question are you at?

[tardy hamlet]

15 and 16

[ornate tree]

you mentioned that there are three

alright

[tardy hamlet]

🙂‍↕️

[ornate tree]

Had Ann started 15 yet?

[tardy hamlet]

No

She did try to help me understand it

[ornate tree]

Alright, have you tried plugging that point into the function?

[tardy hamlet]

Uh no

[ornate tree]

Let's give it a try

[tardy hamlet]

Alright bet

[tardy hamlet]

Would it be like this

[ornate tree]

yes, and replace x with a

[tardy hamlet]

Okay betty

I will solve

Uhh I got 1

[ornate tree]

what happened in the third equation?

[tardy hamlet]

I added 6 to the other side

[ornate tree]

yes, that's legit

[tardy hamlet]

Yessir

[ornate tree]

how about the 3/4 beneath 3/4

[tardy hamlet]

Division

And it like goes to the 12

So it’s like 12/3/4

Sorry don’t mind my uhh horrible equation organization

[ornate tree]

$\frac{12}{\frac{3}{4}}$

[soft zealot]

This is sad 😢

[tardy hamlet]

Yes

[ornate tree]

So the problem is this

can you simplify it again for me?

[tardy hamlet]

Yes

The 12/3/4???

Okay betty

[ornate tree]

yep

[tardy hamlet]

Wait is it keep change flip

16???

[ornate tree]

yep

[tardy hamlet]

Wow

[ornate tree]

and that's the answer

[tardy hamlet]

Thank you bro 🙂‍↕️🙂‍↕️🙂‍↕️

[ornate tree]

no worries

last one

last one?

[tardy hamlet]

Yes

[ornate tree]

Damn, that's a long question

[ornate tree]

pinned

[tardy hamlet]

Yeah it’s a lil hard for me 🥲

Wow rip dumbledore

Uh fam-?

[ornate tree]

Sorry, I'm helping at two channels simultaneously 💀

[tardy hamlet]

Wow multi tasking new level how the heck do you do that

[ornate tree]

https://discord.com/channels/268882317391429632/903463355619110912

lemme check ur question

[tardy hamlet]

Alrighty betty 🙂‍↕️

Erm hola pls help za poor me

<@&286206848099549185> just one question/ problem and I need sleep

[frosty fossil]

hi

what is the question

[tardy hamlet]

Hello Ty a k you

[frosty fossil]

all parts?

[tardy hamlet]

Maybe the part of a and perhaps guidance on the others

The others I think I’ll be good on

Just need some answer checking or you can pass that

I don’t mind 😛

[frosty fossil]

think about what happens at the beginning

when she hasn't read any pages

[tardy hamlet]

0,0???

[frosty fossil]

yea

[tardy hamlet]

Wow

How cruel

[frosty fossil]

lol

[tardy hamlet]

Okay I’m solve this rq and pls check if I get anything wrong cuz I always mess up

Okay erm

I got stuck

On d what happens and is c even correct?

@frosty fossil

[frosty fossil]

c is correct although it would be faster to plug in the other point in point slope form

in d, set y = 30

you just multiplied y by 30

[tardy hamlet]

Wait what

Wait what would the formula be for uh d???

Wait is it 30=2/5-0

[frosty fossil]

30 = 2/5 * x

[tardy hamlet]

That’s multiplication right 🤔

Wait

[frosty fossil]

yea

[tardy hamlet]

This????

Would it be 75

Pls be 75

Ima say it is

Thank you

Tysm I want to sleep

.close

[final saddle]

Channel closed

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[vital breach]

it's an easy question but I seem to be getting 80 as the answer

[vital breach]

12+36+24+8

but the notes i'm referring to say 72 is the answer, could someone help confirm?

[gentle barn]

,calc 160-(48+12+4+24)

[soft zealot]

Result:

72

[gentle barn]

Where comes this set of numbers?

[final saddle]

@vital breach Has your question been resolved?

[vital breach]

oh I divided the shape into sections and then got the areas

and then divided all of them by 2 and added them

so the areas I calculated were 24+72+48+16

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[unborn rock]

Hi, I'm stuck on this problem.

[plucky rover]

Well let's start with labelling the points so we can talk about the sides more clearly

[unborn rock]

ok I will label them for you

[plucky rover]

Cool

Now what do we know about BC

[unborn rock]

it's 6 cm

[plucky rover]

Good

And what do we know about AB and AC

[unborn rock]

I also know that AB is 10cm due to pythagorian theorem

[plucky rover]

Why do you know that

[unborn rock]

AC = 18 - AB
AB ^ 2 + 6 ^ 2 = AC ^ 2

[plucky rover]

That would give AC as 10

Not AB

[unborn rock]

o

yes

alright

[plucky rover]

Anyway

Now I want you to draw a right triangle using A and C as two of the vertices

[unborn rock]

okay

like this, right?

[plucky rover]

Yes

[unborn rock]

hmm

[plucky rover]

Let's call that vertex O

Now if you take the area of ABC, AEC and ACDE and add them up, you get the original area back

[unborn rock]

really?

[plucky rover]

Typo

[unborn rock]

ACED?

[plucky rover]

ABC and AEC takes care of the part that's on the "lower layer"

[unborn rock]

the square ACDE?

[plucky rover]

DE my bad

And ACDE takes care of the "upper" layer

[plucky rover]

It isn't a square necessarily

[unborn rock]

oh ok I meant a quadrilateral

[plucky rover]

Ye

Now you want to find the distance CE

You already know CO

And AOE is a right triangle

[unborn rock]

AOE is right triangle, and I know
AO = 6, but I dont know AE yet.

[plucky rover]

You can find CE the same way you found AB

Using the triangle CDE

Cuz CE + DE is 18 again

And CD is 6

[unborn rock]

CE + DE = 18?

[plucky rover]

Oh okay we didn't need to do the covering thing, could have just split it into triangles from the start

[plucky rover]

Cuz it's one side of the rectangle if you unfold it

[unborn rock]

let me cut out a rectangel rq

[plucky rover]

I need to leave sorry

[unborn rock]

oh

ok ok

[plucky rover]

But yea your goal now is to find CE

[unborn rock]

alright

[plucky rover]

Good luck

[unborn rock]

thank you

[plucky rover]

Tag me and I'll check back when I can

[unborn rock]

thanks 👍

[unborn rock]

boom 💥 I got it thanks bro

:)

.close

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

[tranquil pine]

why a point has no radius, but a circle has?

[tired walrus]

let's turn that upside down: why should a single point have a radius?

[tranquil pine]

because it has to have some lenth, some measure of it?

how does any line segment have any length ?

[tired walrus]

oh, i guess we're going down to the basics with maybe a strong philosophy flavor...

if a single point even has a length, its length is zero.

[tranquil pine]

is it an assumed thing , like axioms in maths or is proven?

[queen trench]

Huh😭😭😭

[tired walrus]

the notion of length itself is a primitive (one does not question, for example, the validity ipso facto of assigning real numbers to pairs of points on the plane), but perhaps such properties as additivity (if A, B, C lie on the same line in that order then AB+BC=AC) are taken as axioms

there are iirc several different (but equivalent) axiom sets for Euclidean geometry

[ornate tree]

What is the definition a circle?

[ripe jewel]

a set of all points equidistant from one point, that point being the center of the circle

oh wait was that a prompt

[ornate tree]

yeah, but I was expecting a different person to answer this LOL

[ripe jewel]

sorry if i wasnt suposed to answer

my bad!

[ornate tree]

nah, it's alright

keep that on the board

[ripe jewel]

you can prove some primitive things as theorems though

like that R is equinumerous with the points on a line

and i've seen a definition of length that only takes unit length as primitive

it was clever

[final saddle]

@tranquil pine Has your question been resolved?

[final saddle]

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• Show your work, and if possible, explain where you are stuck.
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[harsh stratus]

hello

[harsh stratus]

in need of help with this problem

thinking I want the curve to be a sine curve

y = A * sin(kx) + b

I've managed to solve for A

(5 - 1)/2

but don't know how to proceed

[woven ledge]

!showwork

[final saddle]

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

[harsh stratus]

what 😄

[woven ledge]

like just show what you did

so its easier to help

[harsh stratus]

but I did show my work

[edgy mauve]

The minimum point and maximum would hv at least one same coordinate with opposite sign if it was sine graph

If axis is taken as x or y axis

[harsh stratus]

oh

but

what I want to achieve is a graph that looks like this

picasso

[woven ledge]

Asin(k2pi/3) + b = 5
Asin(k5pi/3) + b = 1

Akcos(k2pi/3)=0
Akcos(k5pi/3)=0

[harsh stratus]

alrighty

today just wasn't my day

thank you for your help everyone

.close

[final saddle]

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[woven ledge]

you can do it!

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[quasi plume]

how do I do 3d?

I know orthogonal means p dot q = 0 and parallel is if they're both scalar multiples of each other

no clue how to apply it here tho

[final saddle]

@quasi plume Has your question been resolved?

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[harsh solstice]

If (a^2 b^2 + b^2 c^2 + c^2 a^2 - abc(a+b+c)) = 0, prove that a = b = c

[worldly mesa]

!status

[final saddle]

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

[harsh solstice]

I must do this by analysing the dance of a three real numbers.

[worldly mesa]

dance?

[valid carbon]

why are my numbers dancing

[spring haven]

this isn't strictly true, you can have for eg. a = b = 0, c != 0

[valid carbon]

did i accidentally open cocomelon instead of 3b1b

[harsh solstice]

Let a, b and c be positive numbers.

[harsh solstice]

The are sewed together and kept close to each other, and therefore influence each other.

[worldly mesa]

!original

[final saddle]

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

[spring haven]

Consider the substitution u = ab, v = bc, w = ca

[harsh solstice]

What?

[worldly mesa]

do you have a screenshot?

It seems like there is additional information

[harsh solstice]

u^2 + v^2 + w^2 - root(uvw) (a+b+c)

[spring haven]

expand the bracket first

[final saddle]

@harsh solstice Has your question been resolved?

[final saddle]

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• Be polite and have a nice day!

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

[fathom stream]

Can someone help me understand these trransistors.

how does one tell which is P channel and which is N channel and then what family of transistor it is just by looking at the transistor

[fathom stream]

i was toldthat for p channel the arrow points outwards but then what about the 4th transistor in top row

[whole halo]

it does sort of look like theyre all competing ways to write down a transistor, so your best option is just to remember all of them

[fathom stream]

ddamn

[whole halo]

the arrow thing isnt even consistent only looking at 1 and 5

[fathom stream]

alright

thanks

[whole halo]

np

[fathom stream]

.close

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

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

[soft heart]

how to start this

[valid carbon]

press f

[soft heart]

one doubt left for today

[valid carbon]

!status ?

[final saddle]

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

[valid carbon]

oh 1?

[tired walrus]

make a table

[soft heart]

ok..but i want to know when can i make a table

[tired walrus]

        | Allocated | Score % | Marks scored
--------+-----------+---------+--------------
Theory  |           |    60   |              
--------+-----------+---------+--------------
Project |           |   ???   |              
--------+-----------+---------+--------------
TOTAL   |    180    |    62   |    

[tired walrus]

honestly i have no idea how to give an exhaustive answer

without also being completely un-informative

i will pretend that you twisted my arm until i gave you an answer, so i will say this:

tables are a tool for organizing data

generally if you SEE a way to tabulate the things that a question tells you, then it's not a bad idea.

it can open your eyes to possibilities like what to make a variable and what equations to write down.

[soft heart]

I have no idea how to calculate project % score

[tired walrus]

you dont get there directly

so you dont yet know how to calculate project % score.

what CAN you calculate?

[tired walrus]

,calc 135*0.6

[soft zealot]

Result:

81

[tired walrus]

ok so far so good.

how many marks do we want to score in total to have 62% out of 180?

[soft heart]

111.6?

[tired walrus]

,calc 180*0.62

[soft zealot]

Result:

111.6

[tired walrus]

yup

ok good that means you can put 111.6 into the bottom right cell in the table

[soft heart]

yes

still can't figure out

project marks will be 30.6

what about %

of project score

my phone's battery is about to die

please reply

[tired walrus]

30.6 out of 45 is what %?

[soft heart]

32%

?

[tired walrus]

thats kinda low, are you sure?

30.6 is ___% of 45

ok i guess your battery's dead now.

[soft heart]

68%

did it digitally..by coming into the charging room

bue

bye

.close

[final saddle]

Channel closed

Closed by @soft heart

Use .reopen if this was a mistake.

[final saddle]

Available help channel!

Send your question here to claim the channel.

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

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

[proud igloo]

$$x''+16x=0$$
How can we solve this without method of undetermined coefficients

[soft zealot]

Nyxzore

[proud igloo]

x' = dx/dt

Without

By this point I had only learnt direct integration and method of separation of variables

[loud sundial]

If you really don't want to use the characteristic equation, then you can do $$x'' x'+16xx'=0 \implies \dv{t} \left(\frac{1}{2}x'^2+8x^2 \right)=0$$

[umbral hamlet]

method of undetermined coefs is moreso for nonhomogeneous solutions, the analogous strategy here is just "guessing" ig

[soft zealot]

Civil Service Pigeon

[proud igloo]

This looks solid I'll try it ty

Maybe I'm stupid but I can't think what to do from
$(x')^2+16x^2=2A$

[soft zealot]

Nyxzore

[worthy wren]

separation of variables

anyways, what u would do here ideally isnt method of UC but using an exponential solution x=e^rt and plugging it into the ODE which gives u the characteristic equation

[proud igloo]

Ik 😭 but I have to do it without it

[proud igloo]

Also doesn't separation of variables not work with a non linear eq

[worthy wren]

???

it works for first order odes

if u have the form x' = f(t)g(x)

try turning it into that form