help-0

[sharp thorn]

same as $t^2 - 4t = 0$

[ocean seal]

bettim

[shadow sparrow]

could you even divide both sides by 4?

[sharp thorn]

then it will give you $\frac{1}{4} \cdot t^2$ which is hard to work with

[ocean seal]

bettim

[shadow sparrow]

Yeah, I'm kinda just confused on the best way to go about it here

[sharp thorn]

ye

[shadow sparrow]

I know that when its t^2 you can just square root both sides

[sharp thorn]

you take t out

[shadow sparrow]

To get it to t

t(t-4)?

[sharp thorn]

$t(t-4) = 0$

[ocean seal]

bettim

[sharp thorn]

so you have 2 solutions for t

[shadow sparrow]

Then you would what from there, though?

Like, divide the equation inside?

or

[sharp thorn]

find for what values this equality holds true

so we have two terms

[shadow sparrow]

Ah

[sharp thorn]

$t \times (t-4) = 0$

[ocean seal]

bettim

[gilded magnet]

12t•t-48t=0

[shadow sparrow]

So its less a solve at this point, but just logic it out

?

[sharp thorn]

if you were to go by logic

you take two cases,

[shadow sparrow]

Its either 0

or

4

[sharp thorn]

case 1 : divide by t on both sides
case 2: divide by (t-4) on both sides

then you will get

case 1: t=0 and case 2: t-4 =0

so you get your two solutions

[gilded magnet]

12t is 48 when t is 4 and then there's another t...so that's 48t

[sharp thorn]

what are you even doing

[gilded magnet]

Zero boom

And then ofc there's 0

[shadow sparrow]

He's solving it by figuring the value of t, same way we are, I think basically

just different.

[gilded magnet]

I mean it's straightforward if ur familiar with 12's table

[sharp thorn]

okay i get ittt it uses logic... fine here but in some cases you cant get it when you have rationals and stuff

[shadow sparrow]

I just forget sometimes some of this basic stuff lol

when doing the complicated calculus stuff

[sharp thorn]

i did 2 + 11 = 22 once so its common ig

[gilded magnet]

Calculus is another opportunity to master ur basics

On the go

[lone heart]

@shadow sparrow Has your question been resolved?

[lone heart]

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[viral hamlet]

can anyone solve this for me
find sum of arithmetic series: 28, 39, 49 ... 566
I am literally pretty much 10000 percent sure that is not an arithmetic series

[tacit arch]

Show the original question. Screenshot or picture is best

[viral hamlet]

ok

not that it would help

[sharp thorn]

not an AP

probably not an GP either

could be AGP idk im dumb

[viral hamlet]

my math teacher dude guy thingy just confirmed that it is in fact not an arithmetic series

[sharp thorn]

not all teachers are exceptional

[tacit arch]

Do .close if you're done

[viral hamlet]

.close

[lone heart]

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[steel robin]

how do I find cot (-pi/6) using reference angles

[steel robin]

i am confused about reference angles and i missed this lesson

[sharp thorn]

what is $\cot(-x)$

[ocean seal]

bettim

[steel robin]

1/-tan(x)

-1/tan x

i mean

[sharp thorn]

so ?

$-\cot (x)$

[ocean seal]

bettim

[steel robin]

do i put -pi/6 as x

[sharp thorn]

x as $\frac{\pi}{6}$

[ocean seal]

bettim

[sharp thorn]

coz we took the - outside

[steel robin]

okay

i forgot to mention i have to do this without a calculator

thats the issue im having

[sharp thorn]

it does not require a calc i suppose

$\pi = 180$

[ocean seal]

bettim

[sharp thorn]

so what is

$\frac{\pi}{6}$

[ocean seal]

bettim

[steel robin]

30

[sharp thorn]

yea

what is cot 30 degrees

?

[gilded magnet]

√3

[steel robin]

right

[sharp thorn]

yea but it was his question

[gilded magnet]

Lol

Haha

[sharp thorn]

so - cot pi/6 = - sqrt(3)

[steel robin]

hmm ok

does that method work every time ?

i see other people using different methods

[gilded magnet]

Cos and sec absorb negative sign

[steel robin]

u mean cot?

[gilded magnet]

Rest of em excrete it

[sharp thorn]

no cosine and secant

$\cos (-x) = \cos (x)$

[ocean seal]

bettim

[steel robin]

what would i do for a problem like cos = 3/5 and they tell me that theta is in quandrant 4

how would i use the quandrant

or would i just use pythagrean identity

ohh wait we know its in the fourth so we know sine is negative

[lone heart]

@steel robin Has your question been resolved?

[steel robin]

i have another question

[lone heart]

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[earnest lintel]

y = x. lnx curve, x-axis, x=1 line and x=e line
Find the area of the region between

[alpine sable]

Draw all of that out first?

[wet nest]

Integrate y= xlnx with limits x=1 to x=e

[earnest lintel]

I don't know how to solve

[earnest lintel]

can you solve it for me?

[wet nest]

Don't you know how to Integrate?

[earnest lintel]

I don't know integrals with lnx, sorry my friend 😦

[earnest lintel]

is this the answer?

[wet nest]

Put the limits

X=1 , x=e

[earnest lintel]

dude i have no idea how to do it

this damn thing is like an olympic question

[wet nest]

Haven't you studied definite integration?

[earnest lintel]

or am i stupid

[wet nest]

Its far away from even touching the level of olympiad question

[earnest lintel]

not yet but this problem needs to be solved

[wet nest]

e^2/2 lne - e^2/4 -(1/2ln(1)-1/4)

[earnest lintel]

sorry for bothering you bro could you show me the solution steps?

[wet nest]

I can't really explain if you haven't studied definite integration

[earnest lintel]

thx buddy can you solve my next question too?

[earnest lintel]

is this the solution?

[wet nest]

Yes

[lone heart]

@earnest lintel Has your question been resolved?

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[earnest lintel]

solve the integral for n=4 with the help of "Trapezoidal Rule" plz

[earnest lintel]

@wet nest dude this last question can you help me?

[lone heart]

@earnest lintel Has your question been resolved?

[lone heart]

@earnest lintel Has your question been resolved?

[heady void]

ok

so what is the formula for the trapezoidal rule

[earnest lintel]

I don't know

[heady void]

ok I want you to imagine a function first

with bounds a and b

and then we have an area under the curve(function)

and we divide it into n parallel strips

[earnest lintel]

is this the answer dude?

[heady void]

yeah

I'm basically guiding you to the answer

[earnest lintel]

I was expecting a numerical solution

[heady void]

huh

[earnest lintel]

like this one

[lone heart]

@earnest lintel Has your question been resolved?

[lone heart]

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[lilac jolt]

Just curious. according to the Pythagorean identity, "sin²(x)+cos²(x)=1". how?

[subtle birch]

draw a triangle

and label the sides by some variable

[lilac jolt]

okay

i did a b c

[upbeat hornet]

then consider an angle theta in the triangle

rewrite each side in terms of it

[lilac jolt]

idk how that works. what topic is that? I'm bored and want to study random topics in math

[upbeat hornet]

trigonometry

[alpine sable]

I have a doubt
Could anyone help me with the Architectural doubt
A car has to go on a ramp to the parking floor
What angle should they put the parking ramp with respect to parking floor. The height of the parking floor from ground is 182.88
If it has to not bump the car with ground clearance 12.7, 15.24, 17.78 cm and car of length 241, 269, 297 cm

[upbeat hornet]

consider b and a: can you rewrite them in terms of c and theta?

[upbeat hornet]

go to #help-8

[alpine sable]

This is a real life doubt.

[upbeat hornet]

1. usually in English we say “question”
2. please go to #help-25

[lone heart]

@lilac jolt Has your question been resolved?

[lilac jolt]

I do not know how to rewrite them in terms of c and theta sorry

I only studied limits of trig functions and derivatives

that is all the trig topics I know

[upbeat hornet]

This follows from trig ratios

[upbeat hornet]

you’ll want to look into compound angle formulae

[upbeat hornet]

and you could check your school syllabus and find out what’s taught after that

[lilac jolt]

c is my Hypotenuse

does that help with anything I'm about to do

[upbeat hornet]

so can you rewrite them in terms of c and theta?

[upbeat hornet]

yes

sohcahtoa

[lilac jolt]

how do I know which one of them tho? doesn't that only work with sin cos tan

[upbeat hornet]

you can do that here

[upbeat hornet]

how are you doing that and not know how to do trig ratios

[lilac jolt]

idk, my calculus teacher just straight up went for trig limits

does the Pythagorean formula has to do with yhis

[upbeat hornet]

yes

[lone heart]

Channel closed

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[lilac jolt]

.reopen

[lone heart]

✅

[lilac jolt]

I seriously have no idea how to do this

[carmine reef]

Make c 1

[queen river]

i think youre supposed to learn this

before calculus

maybe your teacher assumed that you have knownthis already

[lilac jolt]

yeah I didn't pay attention on math before this

I just learned that I am actually into math

so

I missed out big time

[upbeat hornet]

you’ll want to look over all learned material and see what you’re not confident with

but in this case, sohcahtoa is what you’ll need for this

[lilac jolt]

a/b?

[upbeat hornet]

can you make it into an equation

[lilac jolt]

$c=\frac{a}{b}$

?

[ocean seal]

Sterling

[carmine reef]

nah

a/b would be tan θ

[lilac jolt]

oh okay

why did we use tan tho

tbh I just guessed a/b because I don't see any c in there

[carmine reef]

Or well

In your diagram tan θ would be b/a

[carmine reef]

this one

[lilac jolt]

isn't that cotangent

[carmine reef]

Nah

Tangent is opposite over adjacent

b is opposite, a is adjacent

[lilac jolt]

oh it's because our triangle has diff letters

[carmine reef]

yeah

[lilac jolt]

wait I'll make a new triangle with the same variables so I won't get confused

so what happens after tan theta = a/b

[upbeat hornet]

this is a correct equation, can you rewrite a in terms of c and theta using trig ratios?

[carmine reef]

so forget about the a/b thing, you want a way to relate c and a now

a/b = tanθ relates a and b

[lilac jolt]

I think I'll comeback to this question after I have a background knowledge about the topic because I need to occupy another channel for a more important question for class. I'm sorry but I really appreciate the help

Thanks!

.close

[lone heart]

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[thick heart]

so guys hello

[lone heart]

Please don't occupy multiple help channels.

[thick heart]

isnt it meant to be y=-root ?

not x=?

[echo socket]

y = -sqrt(R^2 - x^2) would yield the semi circle that is entire below the x-axis

,w plot y = -sqrt(1 - x^2)

[ocean seal]

Results provided by WolframAlpha

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Requested by A Lonely Bean#7998

[upbeat hornet]

Please don’t occupy multiple help channels. Close the ones you opened before

[thick heart]

its different questions

[carmine reef]

you can't write that graph with y being a function of x, it doesn't pass the vertical line test

[echo socket]

Still

[thick heart]

ok

[worldly scarab]

type different questions in the same help channel

just label them

[thick heart]

kk

[thick heart]

so then i cant sketch?

[carmine reef]

?

[thick heart]

wdym i cant write?

[echo socket]

You can sketch it

[carmine reef]

you can't write y as a function of x

there's no function that would work

[echo socket]

But you can freely say x is a function of y

[carmine reef]

since every y value has only 1 corresponding x value

[upbeat hornet]

semicircircle

[thick heart]

ok so samething ?

.close

[lone heart]

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[blazing quest]

does anyone know where the multiply by 2 comes from?

[upbeat hornet]

it comes from h(x)

[queen river]

chain rule

[blazing quest]

ahh ok makes sense

[blazing quest]

thank you

.close

[lone heart]

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[stuck igloo]

if the slant height of a cone is three times as long as its base radius and the cone is 12 cm high. Can someone help me find what is the slant height of the cone?

[upbeat hornet]

Hi creep, what work have you done so far?

[stuck igloo]

I have drawn a diagram of the cone with each sides labeled

[upbeat hornet]

Can you show it?

[stuck igloo]

its a bit complicated

uh

its drawn on discord jamspace

which i have opened right now

[upbeat hornet]

where’s that

[stuck igloo]

you need to voice call with someone

to open it

my friend and i are struggling with this question

[upbeat hornet]

can you take a screenshot and put it here

[stuck igloo]

we want a step to step guide

aight bet

my friend drew it

he cant rlly draw

[upbeat hornet]

try using pythagoras’s theorem

[stuck igloo]

ye we tried it

we got x=4

[upbeat hornet]

can you show your steps

[stuck igloo]

soo

(3x)^2 = 12^2 + x^2

9x^2 = 144 + x^2

divide 9 to both sides

x^2 = 16 + x^2

what

[upbeat hornet]

check that step again

[stuck igloo]

uh

[safe tartan]

If you divide something, you must do for all terms

[stuck igloo]

oh

[safe tartan]

Here, it’s easier to minus x^2 from both sides then dividing

[stuck igloo]

nah thats what i meant

so

[safe tartan]

So

[stuck igloo]

8x^2 = 144

we need help to find the radius of the cone

to find the slant height

[upbeat hornet]

you can solve for x from here

[stuck igloo]

divide both side by 8

x^2 = 18

square root both side

x = radical 18

[upbeat hornet]

$$ x = \sqrt{18} $$

[ocean seal]

(a + b)^2 = a^2 + b^2

[upbeat hornet]

and now you can get the slant height

[stuck igloo]

uh

how

[final nimbus]

@stuck igloo Since the Slant heigh is 3 times more then the base's radius you simply do 3(square root of 18)

[stuck igloo]

shut yo ass up

u aint no proffesional

[final nimbus]

and converted into cm is 12.73cm

.close

[stuck igloo]

tysm @upbeat hornet

.close

[lone heart]

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[upbeat hornet]

I’m not a professional either

[final nimbus]

u are

[stuck igloo]

seems like u are

[final nimbus]

grandmaster

yes

[stuck igloo]

fr

moses is the guy who did the art

[lone heart]

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[crude bluff]

would the red part for example return a true or false value?
(<=D is just a name for a set of relations)

[upbeat hornet]

this looks like the definition for transitivity

[crude bluff]

yes i tried making one myself but idk if its correct

[upbeat hornet]

either a thing is in a set or it is not

so it could be true if it is in the set or false if it is not

[crude bluff]

oh okay, so it seems i could use that as a correct definitiion?

[barren shuttle]

yes

[crude bluff]

i thank both of you :)

what commad to use if my quesiton is done?

[barren shuttle]

it's .close

[crude bluff]

ty

.close

[lone heart]

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[steady basin]

bit stuck on what to do here since you can't divide a vector

[lone heart]

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

[steady basin]

my work is there

[upbeat hornet]

sorry, didn’t see

[steady basin]

np

[upbeat hornet]

you could try splitting v into components

[steady basin]

true

ill do that

[steady basin]

like this?

dont think ive done that right

[upbeat hornet]

For angular velocity, you’ll want to resolve into components perpendicular and parallel to the original vector

[steady basin]

icl im kinda stuck

[upbeat hornet]

here’s what I’m thinking

[steady basin]

but theres 3 directions

i j k

[upbeat hornet]

j can be neglected because everything is happening in the ik plane

[steady basin]

right

so lets resolve for i first

we have a 2 on the lhs and a 1 on the rhs

[upbeat hornet]

this is more like what I was thinking:
$$ 2i - k = a(i - k) + b(i + k) $$ where a and b are scalars

[ocean seal]

(a + b)^2 = a^2 + b^2

[upbeat hornet]

we have to do this because 2i - k is not a scalar multiple of i - k, nor is it perpendicular

[steady basin]

Oh lemme try

[steady basin]

just bit unsure on where the i + k comes from

[upbeat hornet]

It is a vector perpendicular to i - k

[steady basin]

got this

[steady basin]

do i sub in a and b now?

[upbeat hornet]

I’m not sure what you mean, but you can now use the perpendicular-to-(i-k) component to compute angular velocity

[steady basin]

sry wdym by that

[upbeat hornet]

what is the definition of angular velocity that you know

[steady basin]

its the rate of change of angular position

[upbeat hornet]

then you can do that here

[steady basin]

we dont know what r^2 is tho

[upbeat hornet]

r^2 is the squared magnitude of the vector

I think

[steady basin]

lemme try

@upbeat hornet

[upbeat hornet]

oh, forgot angular velocity is a vector

in that case, looks right

[steady basin]

sick

thanks mate

.close

[lone heart]

Channel closed

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[steady basin]

.reopen

[lone heart]

✅

[steady basin]

@upbeat hornet sry mate had one last thing to ask if u dont mind

sry sry

any idea for this? i have the latter from my notes

[upbeat hornet]

!show

[lone heart]

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

[upbeat hornet]

!status

[lone heart]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[steady basin]

ibr idk where to start

so 1

do i diffirentiate r hat in terms of cosine and sine?

[upbeat hornet]

this is the whole question?

[steady basin]

sry

[upbeat hornet]

this is the whole question?

[steady basin]

yes

[upbeat hornet]

the question is asking how fast the unit vectors change with time

maybe drawing them will help

[steady basin]

.close

[lone heart]

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[spare canopy]

why is x=-4 not an solution?

[upbeat hornet]

try putting it into the first term of h(x)

[spare canopy]

.close

[lone heart]

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[round forge]

Hi! I have a few questions in the image below. I’m relatively new to calculus but took it upon myself to start learning some real analysis, and I’m curious about the nature of integrals and some things regarding the dx notation outlined below. First off, is the sum in A equal to a definite integral? Does the notion of integrating over a bound of dx even make sense? If no to either of those, why? Question B and below are already fleshed out, just would like an answer is possible.

[lone heart]

@round forge Has your question been resolved?

[tacit arch]

What resource are you reading

[round forge]

Real and Functional Analysis by Serge Lang, but these questions are my creation. Such material isn’t really covered

[tacit arch]

... that's a graduate text

[round forge]

Because this is self taught I’ve really gone full steam ahead and stuck to topics relating to calculus, I just find the area of math very interesting.

But my questions?

[tacit arch]

Maybe pick a real analysis book before reading a functional analysis book

[round forge]

I found the wrong one, I don’t have the book with me but the design is the same as this one. It is introductory real analysis

The very basics of it

[tacit arch]

Most of what you've written is undefined. There's no point in answering "what could this be" for notation you just made up

[round forge]

See this is just not the way to answer a question

Whyyyy is it undefined?

I didn’t know that

Why can I not put dx in my bounds of integration?

Etc etc

[tacit arch]

It absolutely is

[tacit arch]

Because nobody's found a use for it

[sly mantle]

the things you wrote are just simply nonsense and its hard to answer further than that

[tacit arch]

You can try defining it yourself, but it's probably not gonna be well defined

[round forge]

So it’s a really small number

But no it’s not

But we can do algebra with it

But we shouldn’t

[sly mantle]

its like stringing together english words with zero care for structure and asking others why your string of words is nonsense

[round forge]

Idk why math peeps act with such disgust about the question lol

It’s very confusing and not made clear until… well I don’t know

It being “dx”

[tacit arch]

Nobody's disgusted. We're just telling you it's nonsense

[tacit arch]

That's much more useful than inventing uses for it and claiming it has some meaning

[sly mantle]

you might probably finish high school knowing how to compute integrals, write a few fancy symbols, and a few fuzzy notions of what they represent, but thats pretty much about as far as you can actually think. high school really doesnt prepare you to look under the hood at the formalism, ie why things work out as we like, and in particular why they make integrals works

at that point, provided youre actually interested in looking under the hood, you may wanna crack open an intro real analysis book

[safe tartan]

Bruh no need to do him like that 😭😭

But yeah you’re writing some weird stuff. Can’t just stick certain notation into places.

[lone heart]

@round forge Has your question been resolved?

[round forge]

Haven’t once heard why. Thanks for absolutely nothing. Maybe even less than nothing, because it took energy to sigh heavily each time I saw another response

[lone heart]

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[vale laurel]

.reopen

[modern maple]

I have no idea how to do this

[vale laurel]

Do you have the cords for the ends ?

[modern maple]

No

[north canopy]

do u know rise over run?

[modern maple]

He’s

Yes*

[north canopy]

find some reference points and use them for rise over run

[modern maple]

I did that it was wrong

[north canopy]

how so ?

could u show some work ?

[lone heart]

@modern maple Has your question been resolved?

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[graceful ether]

$\lim _{x\to \infty }\left(ln\left(x^2+1\right)-5arctan\left(x\right)-2ln\left(x\right)\right)$

[ocean seal]

Penca53

[graceful ether]

how is it possible that the two lns are cancelling out?

[lament forge]

well $\ln(x^2)=2\ln(x)$

[ocean seal]

bee [it/its]

[graceful ether]

and the plus one?

[lament forge]

well if x is very big the + 1 probably doesn't matter much...? given how slowly ln grows at large numbers

[north canopy]

combine the lns

[lament forge]

oh yes that's a good idea

then you get $\ln\left(\frac{x^2+1}{x^2}\right)$ (i think)

[ocean seal]

bee [it/its]

[graceful ether]

yes

[lament forge]

and that inside is the same as 1+1/x^2

[graceful ether]

which is 0 (ln result)

cool, thank you very much

.close

[lone heart]

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[cerulean elm]

-help

[cerulean elm]

am i allowed to use HR twice?

also am i solving this correctly

[fleet vale]

you can't use HR anymore

since you'd get 0 in the denominator

and yes you've solved the limits

,w limit to -infinity of (x-1+(2x/(x^2+1)))

[ocean seal]

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[fleet vale]

,w limit to +infinity of (x-1+(2x/(x^2+1)))

[ocean seal]

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

Requested by ! Ilya#2861

[fleet vale]

would be + inf

[cerulean elm]

aight

here in 3 a

can i just do f(x)-y(D)

or do i have to do long division to find the eq of the oblique asymptote

since it says to show that its an OA

not to deduce it

[fleet vale]

i would assume it's just to calculate it

[cerulean elm]

through long division?

how do i do long div on that train wreck of a function 😭😭

[fleet vale]

i would just divide every term by x on its own

so you get lim to + or -inf of 1-1/x+2/(x^2+1), which is quite easy to solve

[cerulean elm]

i dont quite understand

where did the 1-1 come from

also the x+2

[fleet vale]

you know how to find the oblique asymptote?

[ocean seal]

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Upgrade to WolframAlpha Pro!

Requested by ! Ilya#2861

[fleet vale]

bruh

[cerulean elm]

long division no?

[fleet vale]

lim to inf of f(x)/x is the formula for the a in y=ax+b

with y the OA

well

I do remember another way to calculate them

[cerulean elm]

wait

[fleet vale]

you might be able to do it with long division, the formula i gave is another formula for the OA

[cerulean elm]

(x^3-x^2+3x-1)/(2x+1)

i do long div

wait let me try

[fleet vale]

yes

then you would to Q(x) - R(x)/dividend?

[cerulean elm]

fun

is this the same answer

its supposed to be y=x-1

according to the question

[safe tartan]

Is this long division

Well first off you doing it wrong

Oh nah wait it might be right

I think you got something wrong in the second step

-x^2-x^2/2=

[cerulean elm]

idk i was following an example given by my teacher

[cerulean elm]

(-x²/2)(2x+1)?

[safe tartan]

What

[cerulean elm]

the second step

[safe tartan]

Subtraction

[cerulean elm]

oh

idk i did it in my head

might be wrong

wait

[safe tartan]

-3/2x^2

But you wrote -x^2/2

Cuz you added

[cerulean elm]

oh wait

i added it

mb mb

man i hate long division

so much room for error

[safe tartan]

Lmao yeah Ight gl 4am gotta sleep

[cerulean elm]

gn

thanks for the help

smths still off

[lone heart]

@cerulean elm Has your question been resolved?

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[cerulean elm]

.close

[lone heart]

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[dapper echo]

Not sure how first denom became second

[dapper echo]

-22+16 doesn't = 3

[echo socket]

How would you simplify 4^2 - (2x + 22)?

[tacit arch]

-2(x+3)=?

[dapper echo]

.close

[lone heart]

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[dapper echo]

im too stupid

[lone heart]

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[wise dirge]

can you plot the graphs?

[echo socket]

One example is insufficient

By "mutually directed" you mean perpendicular?

Draw any two perpendicular lines near their intersection point

Yeah

Here I am showing you two lines' graph near their intersection point

Here I am showing you the same lines but somewhere else

However you draw the graphs, just make sure you include the intersection point

Yes

But first start with the graph

Sure, anything will work

Let's say the intersection point is (x0, y0)

Can you also show the points (x0 + 1, y0 + k1) and (x0 + 1, y0 + k2)?
(They should lie on the lines)

This is why it would be better to draw an arbitrary graph (on paper as well)

Let's label the intersection point as $C(x_0, y_0)$

[ocean seal]

A Lonely Bean

[echo socket]

On the lines there also lie the points $A(x_0 + 1, y_0 + k_1)$ and $B(x_0 + 1, y_0 + k_2)$

[ocean seal]

A Lonely Bean

[echo socket]

Should be something like this

Right

Let's now consider the length of AB, it should be $\abs{k_1} + \abs{k_2}$

[ocean seal]

A Lonely Bean

[echo socket]

Wait let me phrase it this way

If we connect the points A and B and draw a line crossing C perpendicular to AB, which, let's say, crosses AB at some K

Then we get this

Now, it should be obviously that CK = 1, AK = |k1| and KB = |k2|

According to Pythagorean theorem, AC = sqrt(1 + k1^2) and BC = sqrt(1 + k2^2)

According to Pythagorean theorem (yes, applying it once more), we get that 1 + k1^2 + 1 + k2^2 = (|k1| + |k2|)^2

It's the traditional proof

[echo socket]

From here you can expand and that 2 + k1^2 + k2^2 = k1^2 + k2^2 + 2|k1k2| and |k1k2| = 1

Meaning k1k2 is either 1 or -1
How do we know it's -1? If it was +1 then we would be dealing with two identical lines

Proof finished

Yes

[lone heart]

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[strange badger]

need help pls

?

[echo socket]

Consider applying law of cosines in the triangle BAD, but you will first need to find the length of BD using Pythagorean theorem

[strange badger]

ohk

bd=20

20/2=10

?

[echo socket]

Right

[strange badger]

idont know what to do next

[echo socket]

What you can do is drop a height from A onto the rectangle

Let's say the center of the rectangle is K

Then KAD is a right triangle

What's sin(KAD)?

Given that the side opposite to the angle KAD is 10 (half of 20)

And the hypotenuse is given as 14

[strange badger]

hmm

not sure

?

@echo socket

10/14

?

??

.close

[lone heart]

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[strange badger]

.reopen

[lone heart]

✅

[strange badger]

@echo socket

?

.close

[lone heart]

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[alpine sable]

what happened

[lone heart]

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[alpine sable]

hello <@&286206848099549185>
i would like help with math problems relating my scholarship math exam. i haven't studied math in about 2 years cause i was taking a gap year and suddenly decided to apply for a scholarship last minute. could somebody help walk me through some problems?

[stone oxide]

i can try

[stone oxide]

there is a high liklehood that i dont know it thoo.

[royal plank]

anyway, pls make sure to make a separate channel for each problem so ppl good in one field can help you better

[alpine sable]

so sorry, i'm a bit confused

[royal plank]

just post the first problem you want help with

[stone oxide]

ye

[alpine sable]

ohh okay

[stone oxide]

how do u get the helpful rank

[royal plank]

helping

[stone oxide]

is there an official process

or do they just see who helps a lot

[alpine sable]

the numbers inside the brackets just refer to the answer sheet so don't mind it

[royal plank]

no glue, maybe message count, maybe they see you being active
tbh I am surprised you don't have it yet with 2k messages

[royal plank]

alright, do you generally know how to approach this?

[stone oxide]

ok thx

[alpine sable]

i don't remember much about sequences. are they complicated?

[royal plank]

they can be, but this one is simple because its only made out of 3 distinct elements

[alpine sable]

oh i see

how can i approach this

[alpine sable]

whenever you're available to help please ping me, the server is a bit complicated sorry

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

@alpine sable Has your question been resolved?

[tacit arch]

This almost looks like a question. I suggest closing and opening since this channel is cluttered with things unrelated to your question

Just post your question in the first message

[lone heart]

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[pliant cypress]

How do I solve a limit with this form (1/0)? Can't direct substitute, can't factor. Can't use l'hopitals rule either

[gleaming granite]

you have to find the one sided limit and you can't directly solve for this q

[pliant cypress]

Yep, got that. Is it something to do with the vertical asymptote that I can use to find the limit?

e.g. vertical asymptote at x = 3 corresponds to infinite limit at x = 3?

[gleaming granite]

yeah pretty much

[gleaming granite]

do you need to know how to write steps for this type of question on a test?

[pliant cypress]

No just wasn't sure how to solve infinite limits

[gleaming granite]

okay 👍

[pliant cypress]

Thanks for the help

.close

[lone heart]

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[next arch]

Hi, I'm stuck with this question, can anyone help me?

[vapid shuttle]

what is the question?

[next arch]

the picture

[vapid shuttle]

the picture is just a math expression

with no words

it'd be as if I put

[next arch]

oh erm..

[ocean seal]

AustinU

[next arch]

solve

[vapid shuttle]

solve what?

[next arch]

the math

[ocean seal]

AustinU

[vapid shuttle]

solve the math

[next arch]

but theres no x in that expression

[vapid shuttle]

my point is that there is no question

it is just a random listing of numbers inside square roots

without asking you to do anything

[ocean seal]

AustinU

[vapid shuttle]

solve the math

doesn't mean anything

[tacit arch]

,tex .original

[ocean seal]

riemann

[next arch]

let me type it in here

√3+√5.√2

[rose sigil]

it’s just a paper that’s conpletely blank except that it has √3+√5.√2 on it?

[tacit arch]

That's not a picture or screenshot

[wind cloak]

Are you meant to simplify it?

Start by multiplying the sqrt(2) inside

You'll be able to write the inner term as a complete square

[next arch]

no, there re more but i just stuck with that

[rose sigil]

it’s also wrong now

[vapid shuttle]

Are there words on the paper?

[next arch]

on a file

[vapid shuttle]

perhaps words that idk.. ask a question?

are there words on the file?

[next arch]

√5.√2 first?

[tacit arch]

,tex .original

[ocean seal]

riemann

[wind cloak]

no

[surreal meadow]

post picture of file first?

[wind cloak]

$\sqrt{3 + \sqrt{5}}\cdot \sqrt 2$

[ocean seal]

NEONPerseus

[vapid shuttle]

solve the math for me: 51089(1)

[wind cloak]

Multiply sqrt(2) inside the root

[vapid shuttle]

exactly

[next arch]

Can I square both √3+√5 and √2? it gonna be 3+√5 . 2

[surreal meadow]

i mean sure

go off

but what is the question asking you to do

[rose sigil]

i think the instructions are actually:
find a polynomial with integer coefficients with the following roots

[next arch]

but i cant do more if it be 3+√5 . 2

[surreal meadow]

realistic

what is the question asking you to do

[tacit arch]

Solve it assuming collatz conjecture

[next arch]

do the math expression:

[surreal meadow]

assume x = sqrt(3 + sqrt(5))*sqrt(2)
prove the riemann hypothesis

[surreal meadow]

do you have a picture with the instructions included

[tacit arch]

,tex .original

[ocean seal]

riemann

[next arch]

it just like 1+1 =? but it change to what is 1+1

with no equal, just solve it like normal

[surreal meadow]

well 1+1 = 1+1

[next arch]

my teacher gonna yell me if i do this 💀

[surreal meadow]

we can't know what the right answer is without the actual instructions

[tacit arch]

,tex .original

[ocean seal]

riemann

[tacit arch]

Only explanation is you're taking a test

[rose sigil]

1 + 1 = 1 + 1 + 10 - 10

solved

[next arch]

oh I know

Is that correct?

[surreal meadow]

it very well could be

if only we knew what the question was asking so we could explain

[next arch]

can u example for me a math expression with the question?

[surreal meadow]

i don't know what you're asking

[next arch]

u telling u need the question

but that is the question

[vapid shuttle]

That is not a question

[next arch]

uh...

[vapid shuttle]

Do you think this is a question

5175227181

Is that a question?

Or just a listing of numbers, with no statement?

[next arch]

but mine has plus and times

[vapid shuttle]

5+5*2

Is this a question?

[next arch]

ye just solve it like normal, as i told

the question is my text and the picture is the math expression

[rose sigil]

.-.

[tacit arch]

We don't know what you mean by nirna in

Only you do

[next arch]

._.

[vapid shuttle]

What if I normally “solve” 5+5*2 like this

5+5*2-(17/17)+ln(e)

We don’t know what you mean by solve “like normal”

When we don’t know what the question is

[next arch]

i told u the question is really same as my text, nothing more, here

oops wrong one

[surreal meadow]

if only you could have done that 20 minutes ago

[next arch]

!!!!

[surreal meadow]

ok never mind

let's move on

[next arch]

oke

[surreal meadow]

what have you tried towards solving this

[next arch]

but really, idk what question do u guys need

[next arch]

the calculation i just sent?

[surreal meadow]

let's say $x = \sqrt{3 + \sqrt{5}}\cdot \sqrt{2}$

[ocean seal]

maximo

[surreal meadow]

what is x^2

[next arch]

x^2?

[surreal meadow]

square the right side

[next arch]

3 + square root of 5 . 2

[surreal meadow]

use parentheses please

but i get what you mean

$x^2 = (3+\sqrt{5})\cdot 2$

[ocean seal]

maximo

[next arch]

ye

[surreal meadow]

what can we do now

[next arch]

so just times 2 in both 3 and square root of 5?

[surreal meadow]

yes

$x^2 = 6 + 2\sqrt{5}$

[ocean seal]

maximo

[next arch]

ye

[surreal meadow]

so what is x

[next arch]

ermm

i cant type

[next arch]

but just square root this

[surreal meadow]

yes

[next arch]

the right side

[surreal meadow]

so $x = \sqrt{6 + 2\sqrt{5}}$

[ocean seal]

maximo

[next arch]

done?

or we can do more

[surreal meadow]

i don't believe we can do any more, but i may be mistaken

[next arch]

alr thank you

I can do u it now

[vale wigeon]

you can do a stupid trick

6 + 2 sqrt(5) happens to be 5 + 2 sqrt(5) + 1, or (sqrt(5) + 1)^2

[next arch]

Identity 1, ye I did that

[lone heart]

@next arch Has your question been resolved?

[lone heart]

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[fast reef]

Don’t know what I’m doing and just need the answer

[fast reef]

<@&286206848099549185>

.close

[lone heart]

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[dapper lynx]

Hey math people!

[dapper lynx]

Its been a while since limits

How do I do this, again?

Note: This is part of solving a larger problem:

Can I use substitution for this? Like...

If I compute the limit of 0/y as y->0 I get 0 (via l'hopital's rule)

Can I then substitute sin(0/y) for sin(u) as u->lim(0/y)?

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@dapper lynx Has your question been resolved?

[dapper lynx]

.close

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[quartz panther]

What do they mean by find the co-ordinates of the point on the curve where the gradient is minimum

ik how to find stationary points if that helps

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[deep crater]

Eight teachers are lined up to buy tickets to a rock concert. How many possible arrangements of teachers are there if Mr. Ben or Mr. John buy the 4th ticket

[wanton valley]

!status

[lone heart]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[deep crater]

So for this question

It uses the word OR

Does this mean we add two possible outcomes numbers?

I did this so far:

(7 x 6 x × 1 × 5 × 4 × 3 × 2 × 1) +(7 x 6 x × 1 × 5 × 4 × 3 × 2 × 1)

Would this be correct?

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[placid zinc]

Yeah I agree with that

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[mellow grail]

What have u tried?

Mhm

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[trail remnant]

Solve the equation to get x in terms of y:

dy/dx = 16 - 9y^2

I integrated the right expression in terms of x, this got me:

16x -9xy^2

Took x out as a factor

y/x = 16-9y^2
x = y/(16-9y^2)

Obviously this isn't right as you can't integrate the right hand side with the ys in terms of dx.

[trail remnant]

Btw the reason I did it that way is cos I had no idea for a different method. I forgot differential equations

[hard mountain]

Looks like a separable ode

Think you can move all y terms to one side of the equation and x terms to the other side

dy 9y^2 = 16 dx

Then integrate both sides

3y^3 = 16x

[trail remnant]

I thought you couldn't subtract or add terms in the context of a differential equation

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[tepid flare]

Hey there, im a bit stuck on the part where its asking for what the condition is equal to (my current answer is incorrect) Thank you.

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[lilac jolt]

$\frac{1}{1√3}$

[ocean seal]

Sterling

[lilac jolt]

can this be rationalized

[subtle birch]

Do you mean $\frac{1}{\sqrt{3}}$

[ocean seal]

B-eard

[royal plank]

what does the 1 in the denominator mean, did you meant to write whats above?

[lilac jolt]

no

sorry it was just an example let me change it to

$\frac{1}{2√3}$

[ocean seal]

Sterling

[lilac jolt]

I was wondering if u can rationalize something that looks like that

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@lilac jolt Has your question been resolved?

[lilac jolt]

<@&286206848099549185>

hiiiiiiii

[safe tartan]

I mean you can just times by root 3

[lilac jolt]

thanks

[undone mango]

😮 idk if it's right

[lilac jolt]

.close

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[alpine sable]

Hi so i have to calculate the ratio of the area for picture B

So i have to calculate area cricle*x=area square

I allready solved a but dont know how to do B

[median oar]

,rotate

[safe tartan]

I’m not quite sure what you’re asking but first let x be the side length of the square

And the radius of the circle would be half of the diagonal of the square

Which you can find using pythag

[alpine sable]

Yes ok

[safe tartan]

And then you know both areas and can do what you want with that

[alpine sable]

Ok 1 sec

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[formal tide]

how do i factorise 8m squared - 200 m squared?

[wet lark]

$$8m^2-200m^2$$

[ocean seal]

gekka

[wet lark]

?

[formal tide]

yep

wait

is it

[wet lark]

you dont have to factor, you just combine them

[formal tide]

2msquared (2+10)(2-10)

[formal tide]

i have to

its literally

thje question

[wet lark]

then use the definition $a^2-b^2=(a+b)(a-b)$

[median oar]

You can first factorise the units

[ocean seal]

gekka

[median oar]

(8-200)m²

[safe tartan]

Prolly he wrote the question wrong

[wet lark]

or that

[formal tide]

it is the question

why is it not 2m squared (2+10) (2-10)

[safe tartan]

U sure

[lament forge]

(wait how is that "a definition")

[formal tide]

oh right

i did do it wrong

the 200 is n

but thats the only difference

[safe tartan]

Yeah thought so

[lament forge]

$8m^2-200n^2$

[ocean seal]

bee [it/its]

[wet lark]

idk i just call it that without thinking 💀

[safe tartan]

Lol

Yeah so just take out the hcf

$8n^2-200n$

[ocean seal]

ㅠㅠ

[formal tide]

bro what

[wet lark]

where’s the square 💀