help-0

[wide talon]

so prove it by multiply the parenthesis in different orders 🙂

[midnight marsh]

or is it unsolvable

[distant bay]

Ok that’s so much simpler thank you sir

[distant bay]

Is it cool if you check if I did 9a correctly, my textbook is inaccurate since it’s a dated textbook.

[wide talon]

sure

what did you get?

[midnight marsh]

<@&286206848099549185>

i posted it 15 mins ago

reposting now

[distant bay]

I got this

[wide talon]

nope, doesn't look right

to make it easier for yourself, multiply 2pi into the parenthesis

on both the terms

[lapis harness]

x+y/t1+t2=42 6/17 , x=30t1, y=60t2

you should solve it

youre looking for x/x+y

[distant bay]

Ok thank you

[distant bay]

How should 2pi be in the variable or 3.14 form?

[wide talon]

always leave it as pi

unless a question / teacher says otherwise

😄

[lapis harness]

its not engineering 🤮

[glass lichen]

pi isnt a variable

[distant bay]

Ok thank you

[distant bay]

My bad

[midnight marsh]

i’m looking for how much of the whole distance he travelled so, d1/total distance

[lapis harness]

the t1 or t2 will cancel out

[midnight marsh]

i got to where you got in the first box

now how do i solve for the 2nd box

@lapis harness

[distant bay]

That’s what I got this time

[lapis harness]

@midnight marsh

[wide talon]

looks way better 😉

[midnight marsh]

@lapis harness i see

[distant bay]

Thank you 🥺

[midnight marsh]

@lapis harness

that’s what i get

[lapis harness]

you have x

and t1 in terms of t2

substitute

[midnight marsh]

how do i have x?

[distant bay]

is it cool if I ask another theory question

[lapis harness]

look at the begining

[midnight marsh]

x = 30t1?

[lapis harness]

😉

[midnight marsh]

then i’m left with 60t2 @lapis harness

after i cancel out

but i dont know t2

[lapis harness]

https://cdn.discordapp.com/attachments/490557019623915520/839982340356702238/unknown.png

compare

those two

equations

[midnight marsh]

t1*42 6/17 = x?

@lapis harness i’m so confused

[lapis harness]

\

[midnight marsh]

yes i know that

[lapis harness]

so you can get t2 in terms of t1 ?

[midnight marsh]

so 30t1 = 42 6/17*t1?

i dont know t1 or t2

i’m so confused

wait

if you expand those brackets

its all wrong

[lapis harness]

ok look

we have this right

[midnight marsh]

@lapis harness you get 42 6/17t1 = 30t1

[midnight marsh]

yes we have hats

this

[lapis harness]

the only thing

holding us back

is the t2

so

if you could get

t2 in terms of t1

[midnight marsh]

what about t1 though

[lapis harness]

you would solve the question

[midnight marsh]

we dont know t1 either

[lapis harness]

you can cancel it out

[midnight marsh]

ok this is too fast

how do we get t2 in terms of t2

t1

[lapis harness]

thats what we wanna find

[midnight marsh]

yes

so how?

[midnight marsh]

how

[lapis harness]

so we manipulate the equations

[midnight marsh]

what the

[lapis harness]

multiply the brackets one variable on right 2nd on left the usual stuff right ?

[midnight marsh]

yes

and you took away 40 from both

i mean 30

dont you have to take away 30t from both

[lapis harness]

im confused

[midnight marsh]

i’m more confused

[midnight marsh]

thats all correct

the 2nd line i understand

how did you go from 2nd line to 3rd line

[lapis harness]

if you have ax=by to get y you divide by b right so you get a/b x = y

[midnight marsh]

yes

correct

[lapis harness]

you just divide by the thing next to your t2

[midnight marsh]

so you divided by what?

[lapis harness]

(12 6/17)/(17 11/17)

[midnight marsh]

ah ok i see now

now you get t2 in terms of t1

[lapis harness]

so you plug it in the blue equation and cancel the fraction

theres your answer

[midnight marsh]

but then you need to solve for t1 @lapis harness

@lapis harness

[outer cove]

hey guys is the answer 240? I finished I just wanna make sure

[midnight marsh]

hello

@lapis harness you need to solve for t1 lol

[lapis harness]

thats why

you dont need to solve for t1

🙂

[midnight marsh]

but dont they both cancel out

wait

why do you just stick 42 in there @lapis harness

i get everything else

[wide talon]

yes

[outer cove]

Thanks!]

[lapis harness]

you sub in for t2 your value in terms of t1

and you get 42 t1

instead of 60 t2

[midnight marsh]

12 6/17 t1 = 17 11/17 t2

[lapis harness]

yes if you divide both sides by 17 11/17 you get t2 = 0.7 t1

and

you sub taht

[midnight marsh]

@lapis harness you are just an alpha

at match

maths

[midnight marsh]

still dont get 2nd to 3rd line

everything else makes PERFECT sense

[lapis harness]

you move the t1 parts to the right and t2 parts to the left

[midnight marsh]

@lapis harness never mind i got it

lol

i got it

[lapis harness]

🙂

[midnight marsh]

i read it properly

you switch it

then minus them both

then you land up with that

then you realise that @lapis harness is really good at math

[brave fossil]

how do i do these?

[full wasp]

yo wth i think someone posted these exact same questions a few days ago

[brave fossil]

oh foreal?

probably goes to my uni

[full wasp]

lol thats interesting

well whenever i see questions like these my first instinct is to get one side to equal 0

because then u can factor and use zero product principle

[brave fossil]

so how would i go about getting one side equal to 0?

do i cancel the sin on both sides?

[full wasp]

no thats bad

never cancel on both sides

if you do that its really bad because you exclude solutions

[strong furnace]

you can in this case tho

because they have defined cot(theta)

[full wasp]

the only time its safe to cancel on both sides is if youre 100% sure its not gonna equal 0

[strong furnace]

#help-2 message here's the old post btw

[full wasp]

i still dont think u can cancel sin(θ) like arent we gonna lose 0 and pi

[strong furnace]

can cot(theta) be defined for 0 and pi?

[full wasp]

😔 i stand corrected

[strong furnace]

although not cancelling is the correct and consistent way of solving equations

[full wasp]

this is what i wrote for b) the last time

[bold lance]

would smn mind helping me with a vector qu

[full wasp]

ok sounds good

[bold lance]

if anyone could help with b it would be appreciated

[upbeat locust]

ill give it a go!

[full wasp]

u need to show that NM is a scalar multiple of NZ

thatll prove that NMZ is a straight line

[bold lance]

how do i do that

[upbeat locust]

exactly!

[full wasp]

find NM then find NZ then show that NZ = q * NM where q is any real number

[upbeat locust]

try make a vector in terms of a and b for PY?

you know that M is the midpoint for PY

[bold lance]

i think py is -3b+A

so PM/MY=a-3b/2

[upbeat locust]

woldnt that make the b vector point straight in the opposite direction?

[bold lance]

i mean PM or MY

[full wasp]

py = a - 3b is right

[bold lance]

how is b+a-3b/2 a multiple of -2b+2a

[full wasp]

i think u did something wrong

[bold lance]

mm same lol

i have no idea where ive gone wrong

oh nice ive got it

[alpine sable]

can someone walk me through how to do this pls

[woeful pulsar]

is this "find x"?

do you know cosine rule?

[alpine sable]

could you explain that to me

[bold lance]

c^2 = a^2 + b^2 − 2ab cos(C)-cosine rule

[upbeat locust]

same, just a biiit to late

[woeful pulsar]

idk can easily search "cosine rule" and figure what to plug in?

[bold lance]

@alpine sable literally just plug in the values

[alpine sable]

okay thanks guys

[haughty plaza]

is this correct?

I got 0

[hushed warren]

Hello guys

I need your help

I have math question which contains max min problem and I want to throw it, can you help me

?

80 / 5000

Translation results

The closest point of the function f (x) to the point A (a, a) is B. accordingly | AB | ?

[oak lodge]

is this a correct way to do hypothesis testing? or is the >= sign for the halpha?

[lucid arrow]

!Help

[wise jewel]

Does anyone know how I'd go about learning the volumes and surface area formulas for 3d shapes? there are so many of them and I have a test tomorrow in which we aren't provided a key for them 😭

[civic crypt]

For all prisms the volume is V=B*h. For all pyramids the volume is V=B*h/3

For frustum (pyramid cut at the top) you take full pyramid, and remove the small part.

What remains is the ball: here you remember the full volumne, the cut from the middle, and the slice.

---

For the ball you also learn the 3 surface formulas.

---

Prism surfaces are easy. 2*B + all_vertical_sides. Pyramid is B + all_side_triangles.
The side triangles are computed by the help of the pythagorean theorem on some right triangles in there.

@wise jewel

[wise jewel]

@civic crypt these are my current notes on surface area formulas

Rectangular Prism: SA = 2lw + 2lh + 2wh
Rectangular Pyramid: SA = ½(lp) + B
Cylinder: SA = 2πr² + 2πrh
Trapezoid: SA= hp + 2B
Cone: SA = πr^2 + πrl
Triangular Pyramid: SA = ½(lp) + B
Sphere: 4πr²
Hemisphere: 3πr²

ive got the volume formulas nailed down i think

[civic crypt]

Hemisphere is just half the sphere, lul. You dont memorize that 😄

[wary stream]

No, it's not. The formula isn't

[wise jewel]

oddly enough someone else said its half too

[sour lynx]

i need help on a whole work sheet cause i forgot how to do this

[civic crypt]

Cause he made a typo

[sour lynx]

its probabilities

[wise jewel]

but my notes say its 3pi*r^2

not 2pi*r^2

[sour lynx]

can someone help me

lmfao

[civic crypt]

@sour lynx First read #❓how-to-get-help

[wise jewel]

@civic crypt also when i search online it says the surface area of a hemisphere is " 3πr2" ?

[civic crypt]

It might be the hemisphere with the base?

[wary stream]

That

It's because of that reason

[wise jewel]

hm, so lets say the hemisphere is connected to, idk, a cylinder for example. in that case, would i make it 2πr^2 since the base is not facing the air?

[wary stream]

Normally a hemisphere is a closed shape

I think

[civic crypt]

I would say it is normally open.

hemisphere litterally means half of the sphere

[wise jewel]

well regardless, when it is closed (and assuming by closed you mean connected to something) the surface area formula would be 2πr^2 and when it is open it would change to 3πr^2, right?

[wary stream]

What about the case of a square pyramid on a cube?

[civic crypt]

wdym?

[wary stream]

Flip it, open hemisphere is 2πr^2, and closed is 3πr^2

[wary stream]

If a square pyramid is on a cube, would you include the base of the square pyramid in the calculation?

[civic crypt]

OK, but you dont learn these formulas in memory. Sphere is 4πr^2. You only remember this.
Open hemisphere is half of that. And for closed you also add a base circle which is r^2π to the half.

[wary stream]

Kinda like the idea of a hemisphere on a cylinder

[civic crypt]

Usually not, and you wouldnt include the top base of the cube either.

[wise jewel]

@wary stream but doesn't this show an open hemisphere as 3pi*r^2 ?

[wary stream]

If it's closed, it has a base

[civic crypt]

Open means the blue face is missing.

[wise jewel]

wait so does open mean it is connected to a different shape?

i might have mixed the definitions of open and closed

[civic crypt]

Open just means the blue is missing.

Closed means the blue face is there.

[wise jewel]

an open hemisphere would be a hemisphere connected to another shape though, wouldn't it?

the base can only be missing if its connected to another shape id presume

[civic crypt]

Well it can be missing if you say it is missing.

If you say it is not missing than it is not missing.

[wise jewel]

well we're not finding the surface area or volume of a bowl

[civic crypt]

You sometimes do.

[wise jewel]

not in my grade we're not

[civic crypt]

It is classical task to find the surface area of a spherical cap

[wise jewel]

hahaha not in geometry level 1 though 😂

[civic crypt]

https://en.wikipedia.org/wiki/Spherical_cap

[civic crypt]

That is basic geometry.

[wise jewel]

right

well we havent done that yet

but currently the only time ive seen a hemisphere with an open base is when it is connected to another shape

[civic crypt]

Anyways, cyllinders and prisms behave the same.

You dont memorize the formulas. You just know that V=B*h, and for the SA you compute the 2 bases and the sides.

Same, cones and pyramids behave the same.

[wise jewel]

like this

^^ this counts as an "open hemisphere" right?

[wary stream]

I think that it would specify

[civic crypt]

This is 99% open hemishpere + open cone

[wise jewel]

@wary stream here my teacher solves it without the base, so I'd assume so

@civic crypt wdym by "99%" ?

[civic crypt]

You can always ask the teacher to clarify if the base of the sphere and cone are included in the shape

[civic crypt]

OMG

[wise jewel]

true

[wary stream]

I mean if I run a plane through the intersection of the two objects to separate the two, I would consider them to have a base

[wise jewel]

but you're not running a plane through it nor splitting them apart

that shape is one entire shape

but can be seen as a cone and a hemisphere

[civic crypt]

99% chance that the task ask you to consider open hemisphere.

[wise jewel]

@civic crypt we haven't been asked anything like that at all yet so I'd assume it's not in my test tmrw

even if it is at least i know it'll be 3pi*r^2

[civic crypt]

Not really. I saw that same definition on wiki.
The plane just defines where the shape gets cut

[wise jewel]

and not 2pi*r^2

and that's what matters

regardless, i think i figured out what it was I was looking for, I suppose I will just have to memorize the other stuff (except spheres and hemispheres)

@wary stream @civic crypt ty!!!

[ashen wave]

can anyone help me make a histogram?

[wary stream]

Honestly, it's been years since I've done geometry. All I deal with is imaginary numbers and phasors

[civic crypt]

I mean, you have the point. It is ambiguous.
I think I provided the correct interpretations with 95% probability.
But you can always argue it is ambiguous and you will be right.

[wise jewel]

@wary stream just assume you're trying to explain geometry to a baby in my case lol

never even heard the word "phasor"....so yeah LMAO

just looked it up and the definition looks to be in a different language hahaha

"a complex number representing a sinusoidal function whose amplitude (A), angular frequency (ω), and initial phase (θ) are time-invariant."

LIKE WHAT

😂

[civic crypt]

Read #❓how-to-get-help first

[wise jewel]

the only word i understand from that explanation was "number"

[sour lynx]

i dont know how to do simple probabillity and i have a whole worksheet on it please elp

help*

[ashen wave]

alright my bad

[sour lynx]

can someone show me or something

[wary stream]

Eigenvalues and eigenvectors and orthonormal are big words too

[wise jewel]

@wary stream thought you were speaking german for a second 💀

[sour lynx]

lmfao

[ashen wave]

is this channel being used?

can anyone help me make a histogram

[compact nexus]

by hand or in a program?

[civic crypt]

@ashen wave What is the exact question?

[ashen wave]

by hand

It says make a histogram for the following data set: 12, 14, 14, 14, 16, 18, 20, ,20, 21, 23, 27, 27, 27, 29, 31, 31, 32, 32, 34, 36, 40, 40, 40, 40, 40, 42, 51, 56, 60,65

[civic crypt]

A histogram can group different values, or it can show each value in its own bar.

I think you need to show each in its own bar?

[compact nexus]

I would assume so, it doesn't mention any binning

[ashen wave]

yeah I think so, thats what we usually do

[civic crypt]

If you usually do, this means you saw couple of examples of this already. What is the problem then?

[ashen wave]

oop

I dont know I dont pay attention T-T

[compact nexus]

What are the y and x variables in this image?

[fringe kernel]

Question please

Like we want a relationship between x and y

[ashen wave]

erm...what do you mean? theres multiple

[ashen wave]

no he's helping me lol

[compact nexus]

What does x represent

What does y represent?

[ashen wave]

y= frequency

in your graph

[compact nexus]

Yes, explain what frequency means

[ashen wave]

erm.. like the rate of something

[compact nexus]

in this instance, freq = the count of data with respect to x

[fringe kernel]

Ya

[ashen wave]

alright

[fringe kernel]

Like how many times the x value repeated

[compact nexus]

looping back do your original data, x = 14 three times, so y = 3

[ashen wave]

OH

OHHHH im getting flashbacks from like 4th grade lmao

[fringe kernel]

Where is x .= 14

[ashen wave]

ok yeah that was a big "ohhh" moment

[compact nexus]

No worries, sometimes y is labeled as frequency or count

[ashen wave]

ok I think I got it let me make the graph and ill upload it

[tacit bay]

I think im slow but i forgot how to do this

Do i use the unit circle to answer this

[wise jewel]

im so confused on how to determine whether or not something is a length or a width

is length the longer side of something?

[alpine sable]

@tacit bay option 1 is correct because sin&csc are +ve in 2nd quadrant and tan&cot are +ve in 3rd quadrant so 4th quadrant is only option where cot&csc both are -ve.

[tacit bay]

Oh my goddd i feel stupid now

Thank you

So much

[alpine sable]

@wise jewel you can't say by looking at the number that this is the length and this the width.
You have to visualise it or unless it's not given in the question..

[flat vigil]

how to do this?

e

[wary stream]

Alternate exterior angles

And sum of angles on a line equal 180

[flat vigil]

thx I cant understand my teacher

[acoustic zinc]

For 8 a) iii), what would the sketch look like?

I just want to confirm my answer since I got the same answer for i) and ii) as my textbook, but our graphs for iii) are very different

[unreal depot]

Can someone help me out with these

[green hazel]

I need some assistance

[stiff moth]

what rule do you need to use?

[alpine sable]

how can i solve a radical equation with the 3 on top

so x = 25

[green hazel]

i need to use the rule of

I need to use power rule

[glass lichen]

Yes and chain rule

[green hazel]

i don't know power rule

I don't know chain rul

esorry

I didn't learn it

Im in pre calc

[glass lichen]

Then learn them before attempting a differentiation question

[green hazel]

I don't want to do calculus

I just wana kill myself

ive learned so much shit alread

ywhy do i have to learn more shit

[glass lichen]

Newsflash, learning is life long

[green hazel]

wherever I see h(x) I plug in -1 and wherever I see g(x) plug in 3
then u get the function for f(x)

[glass lichen]

$f'(x)=2h'(x)+2g(x)g'(x)$

[ocean seal]

moshill1

[warm belfry]

$2+139⁵⁶= ???

$f'2+139⁵⁶= ???

[full wasp]

bro that is a chunky calculation

[warm belfry]

$2+139⁵

[warm belfry]

sorry

[worn rapids]

Find Absolute minimum and maximum within vertices (0,0) (0,2) (2,0).

$f(x,y)=x^2+y^2-2x-2y$

[ocean seal]

Orubieso

[worn rapids]

need help w/ this ^ pls, thx

[full wasp]

have u tried implicit differentiation

[lapis harness]

well start off by calculating gradient

[full wasp]

^ and do that via implicit diff

[sly mantle]

finding grad f doesn't involve implicit diff

[full wasp]

shid am i stupid

(i think im stupid)

[worn rapids]

I'm not sure if I'm missing any points of evaluation
So far I have 6 points evaluated

kinda blurry

[lapis harness]

can't see anything but if you've already found your points just plug them into the determinant to see whether they're maxim/min

[wise jewel]

if im trying to figure out length vs width, then how would I be able to "visualize it" when the shape can be looked at in 2 different ways?

in the case of a 3D shape

if i need to find the surface area of a rectangular prism for example, the formula is 2lw * 2lh * 2wh

how can i know what the length and what the width are?

[wise jewel]

<@&286206848099549185>

in a shape like this for example

[alpine sable]

How to be good at maths ?
I get my arse whooped by my mommy

[wise jewel]

@alpine sable I mean I searched online and it said the same thing

But if that’s the case, why does my teacher put 8 (the shortest side) in for the length in the surface area formula?

Someone above said what she did was correct though, lemme quote that they said “you can't say by looking at the number that this is the length and this the width. You have to visualise it or unless it's not given in the question..”

Ah ok

Yeah true since I get the same answer regardless of what number I put there as long as I do the rest of the formula correctly

[young ocean]

Q: What are the coordinates of of the third segment from Point A?

How would i go about solving this question?

[west nimbus]

wait oops someone else using this channel

[toxic dust]

@alpine sable can you help me here since someone else is in the otehr chat

[alpine sable]

part c divide both the top and bottom by sqrt(x)

1/(1+sqrt(x)) and you can plug in x=0

[toxic dust]

that gives me 1

[ocean hearth]

yo where can I get help??

[alpine sable]

yeah thats the answer

[alpine sable]

ask in an unoccupied channel

[toxic dust]

Wait so i just divide by Sqr x

[ocean hearth]

Ight

[alpine sable]

#❓how-to-get-help

[alpine sable]

divide the numerator and denominator by sqrt(x)

[ocean hearth]

fack i dont have permission

[toxic dust]

the top cross out and the bottom ur left with x no?

[alpine sable]

no

[toxic dust]

right

[toxic dust]

ohhh

[alpine sable]

for part d the numerator has a negative sign and the denominator has a positive sign

[pale cargo]

unoccupied ?

[alpine sable]

yeah think so

[toxic dust]

@alpine sable

[toxic dust]

Sorry give me one sec

[alpine sable]

answer for part d is -1

[toxic dust]

I got -1

look at last line

[alpine sable]

k

[toxic dust]

So its right then

cause i choose a value < -4 which was -5 and subed it in

[alpine sable]

the work isn't right, you wouldn't plug in x=-5

you would consider a number slightly smaller than -4

[toxic dust]

-3?

[alpine sable]

no like very slightly

something like -4.001

[toxic dust]

I get positive 1

[alpine sable]

so as x approaches -4 from the left, x+4 is negative and |x+4| is positive

[wild shard]

Hello

[alpine sable]

how'd you get that

[wild shard]

is it possible to solve for theta in this equation

https://i.gyazo.com/thumb/1200/2814cfcfda82a56146d4d84ee405f602-png.jpg

[alpine sable]

repost this in an unoccupied channel

[toxic dust]

-4.01 + 4 / -4.01 + 4

[alpine sable]

you forgot to take the absolute value on the bottom

[toxic dust]

🙈

how about b) am i on the right path?

[alpine sable]

yeah that's right

[harsh acorn]

i did not understand what does this question mean

[alpine sable]

You have to find out the number of ways the marks can be allocated here

[harsh acorn]

yep

how did u know lol

next month is HKIMO and it is so different than our national exams

wdym

[alpine sable]

Dude highest marks are 28*4 lowest marks is zero. Now just think how many people you need to have 3 people with same marks

[harsh acorn]

oh

what does "how many people you need to have 3 people with same marks" mean

im not native speaker and it looks complicated for me

[alpine sable]

That no matter what the situation, there would be 3 people with the same marks

Out of the given candidates

[harsh acorn]

oh i get it

Azerbaijani

my second language is Turkish

english is 3rd

anyway

how can i find how many numbers are there in [1,27]

1 to 27

oh right

lets say 1,2,3...26,27 how much numbers are there

is there formula for that

[solar cradle]

are you asking for the sum of the integers in [1,27]?

If so yes, it's n(n+1)/2

[harsh acorn]

oh thank you

oh wait i did not ask for that :s

[stark lantern]

27 numbers

[strong furnace]

the number of natural numbers between a and b including a and b is b-a+1

[harsh acorn]

well i prefer english one bcs google translate is not accurate

[stiff forge]

can anyone help explain what a jordan block dot diagram is and it's function in abstract linear algebra?

[harsh acorn]

oh answer is basically 3 x 28?

ohhh i get it now

yep yep i get it

yep im in secondary 2

lmfao

what a coincidence

which country?

allright

heat round first

$\frac{1}{n+1}$ how can I decompose this?

[ocean seal]

Hyl1s

[covert glade]

Can someone help me please

[alpine sable]

Decompose?

[harsh acorn]

i mean $\frac{1}{n}+\frac{1}{x}=\frac{1}{n+1}$

[covert glade]

sorry

i didnt realize smoeone was currently asking a queston

[alpine sable]

Channel occupied please move on to some other one

[covert glade]

i apologize

yea

[alpine sable]

What do you want to do with this

[ocean seal]

Hyl1s

[alpine sable]

Oh ok I guess move 1/n to RHS

[harsh acorn]

I mean i want to decompose RHS to similiar type of LHS

$\frac{1}{n+1}=\frac{1}{n}+\frac{-1}{n(n+1)}$

[ocean seal]

Hyl1s

[harsh acorn]

i am so stupid lol

[alpine sable]

Ok this was what u meant

Well taking 1/n to RHS would've been same

[harsh acorn]

yep it was stupid question

[harsh acorn]

i think it is topic of physics

[rich basin]

It's also a highly unrealistic question. Such an object would reach terminal velocity long before the speed of 5km / s.

(also, why the rocket would need to be qualified as chinese seems out of place)

[stark lantern]

apparently a recent chinese launch is falling back into earth

could be why

[rich basin]

Oh, really? I have to check if someone actually estimated the speed reaching 5km / s then.

[harsh acorn]

Find the remainder when $2018^{8012}$ is divised by 7

whut

[ocean seal]

Hyl1s

[harsh acorn]

is the answer 2

remainder of $\frac{2018}{7}$ is 2

[ocean seal]

Hyl1s

[stark lantern]

No it's not 2

3^2 = 9 but 3^2 mod 7 is not 3

do you know modular arithmetic?

[harsh acorn]

i searched a bit yesterday

ik a bit

[gray isle]

,w 2018 mod 7

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by ramonov#0921

[stark lantern]

He's asking 2018^8102

[strong furnace]

the answer is 4 btw not 2

[harsh acorn]

,w 8012 mod 7

[ocean seal]

Results provided by WolframAlpha

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

Requested by Hyl1s#3863

[tranquil flint]

how does the last time change to 4 - 5 on the interval

[harsh acorn]

okay i understand how to calculate but in exam calculator is now allowed

how can i calculate this by hand

[stark lantern]

I'll give you a hint: 2018 = 2 mod 7 and 2^3 = 8 = 1 mod 7

[strong furnace]

product of remainders is what you'r supposed to use

[stark lantern]

you can also use the binomial theorem to expand (2016+2)^8012 if you know that

[oak chasm]

@tranquil flint Sorry, channel is busy. #help-4 is open if you hurry.

[pale cargo]

Yeah but it's mostly maths so that's why i asked here

[harsh acorn]

math is language of physics ofc it will be

[pale cargo]

• the physics server is just a mess

[harsh acorn]

but formulas :s

[pale cargo]

everyone ghosts everyone

so i thought maybe someone here had some knowledge

[pale cargo]

exactly

it's a question i found on a twitter page

[harsh acorn]

i didint understand it

[pale cargo]

ik but just do the maths right hahahahha

[harsh acorn]

should i find 8012 = x mod 7?

[stark lantern]

if you aren't familiar with the binomial theorem, I suggest you go and learn the basics of modular arithmetic first. You wouldn't understand the method otherwise. If you do know BT, I can give an alternative method

[harsh acorn]

idk any of them

better learning now then

[stark lantern]

https://brilliant.org/wiki/modular-arithmetic/ this is pretty good for starters

[pale cargo]

So this is no unoccupied again i guess?

ill repost

[rich basin]

Looks like it is orbiting at around 7km/s. Someone probably thought it could maintain similar velocity on reentry...

[rich basin]

Are you interested in a calculation given those premises, or what would be a realistic scenario?

[pale cargo]

given those premises

[stark lantern]

this is a physics question, let's just assume the atmosphere doesn't exist

[pale cargo]

hahhahha okay

cuz it said air resistance is compensated so yeah

[stark lantern]

$\frac{m{v_f}^2}{2} = \frac{m{v_i}^2}{2} + mgh = E$
E/4184000 would be kg TNT equivalent

[ocean seal]

error 404

[stark lantern]

probably

I'm sure all the energy isn't converted into "impact effect" but it's convenient

[oak chasm]

I think it's pretty clear that the question is assuming the impact is completely elastic.

[fervent charm]

I m preparing for IIT can u help me in maths

[alpine sable]

#competition-math

[alpine sable]

Me too. Which class r u in

[harsh acorn]

can someone explain me how to solve this?

[strong furnace]

I am pretty sure you can solve this using vectors and the formula for internal ratio

[vale wigeon]

is_your_space_bar_broken_blue_guardian

[harsh acorn]

bad thing is idk what is formula for internal

[alpine sable]

how do u find the period of this tan graph?

[strong furnace]

If a point P internally divides the line AB in the ratio 1:m P=(mA+B)/(1+m)

[harsh acorn]

what is the name of theorem

formula for internal ratio?

[strong furnace]

Section formula

[alpine sable]

What do you think is the min amount after which the graph repeats itself

Start at any point (say origin) and see after what value will the shape repeat

@alpine sable

here?

Yeah so what do you think is the period

pi/4+pi/2=3pi/4

Um no

You need b

3pi/4/2=3pi/8?

[grand kelp]

The period is 3*pi/8

[alpine sable]

See if f(x) is periodic after a,

Then f(bx) is periodic after a/b

Since graph is tan(bx)

[grand kelp]

But a is zero

[alpine sable]

It's periodic after π/b

[grand kelp]

Tan(bx) is periodic everywhere

[dense mirage]

Need help

How to I turn 50 3/2 into a mixed radical

[alpine sable]

Dude...

[grand kelp]

Do you mean $50^{\frac{3}{2}}$?

[ocean seal]

NickPro

[dense mirage]

Yes

[grand kelp]

@dense mirage

Okay

[dense mirage]

I got 250 root of 2 and the 2 inside

Idk how to show u

[grand kelp]

So by definintion of a fractional power, $50^{\frac{3}{2}} = \sqrt{50^3}$

[ocean seal]

NickPro

[dense mirage]

Ye

Into a mixed radical

So my coefficient was 250

And the root of 2

My answer

[grand kelp]

And what's the problem?

[dense mirage]

What is the answer turning it into a mixed radical

Am I right or wrong

@grand kelp

[grand kelp]

Right

[dense mirage]

Wtf my answer key is wrong

It said 125 coefficient swaure root of 2

Mine is 250 coefficient swaure root of 2

[grand kelp]

square*

[stark lantern]

125root2 is correct

[dense mirage]

How

[stark lantern]

you got till 50sqrt(50) right?

[grand kelp]

It cannot be correct since this has to be a muliple of sqrt(8)

@stark lantern Yes, and 50*5 = 250

[stark lantern]

oh wait

nvm

Im wrong

[dense mirage]

50 x 50 x 50 is 125000 and 250 x 250 x 2 is 125000

[stark lantern]

I should just go to sleep lmao, 50 times 5 = 125 🤦

[ocean seal]

Chai T. Rex

[oak chasm]

,w simplify 50^{3/2}

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[harsh acorn]

are u guys done?

[grand kelp]

we are

[harsh acorn]

which formula should i use for this?

[woeful pulsar]

shoelace

[harsh acorn]

which grade's topic is this?

[grand kelp]

You can use Heron's formula or the cross product of two vectors

[alpine sable]

11

[harsh acorn]

wow

i love international olympiads lol

[woeful pulsar]

heron's when you have coordinates? that's not very cash money

[oak chasm]

@harsh acorn Get the lengths of all three sides and use Heron's formula.

[harsh acorn]

is it 1

[woeful pulsar]

those circled numbers are 1, the area is not 1

[harsh acorn]

yep i was asking for circled ones

[grand kelp]

@woeful pulsar I mean, if you haven't studied matrices, that's the only option

[harsh acorn]

i know what is matrics but it is absoluetly not topic of low grades lol

[grand kelp]

Can you use Heron's formula?

[harsh acorn]

yep

[alpine sable]

Lol this is Olympiad!

[harsh acorn]

i can find sides by S^2=root of y^2+x^2

[woeful pulsar]

cross product is pretty fine too

[harsh acorn]

i mean

magninute of sides

[woeful pulsar]

area and cross product has quite a bit of relation

[harsh acorn]

not area

[alpine sable]

U would've to form vectors

[woeful pulsar]

not that bad, given we have coordinates

[alpine sable]

Matrices is easier

[woeful pulsar]

I just don't like random square roots appearing

[harsh acorn]

HKIMO 8TH past paper

[alpine sable]

Dude have u heard of jee

[harsh acorn]

yep

[grand kelp]

You can find the distance between one of the vertices and the opposite side and just use the base-height formula

[harsh acorn]

but there are stuff in your criculum with stuff in jee

but in us nop

anyway

[alpine sable]

Yeah our papers make us cry

[harsh acorn]

can someone solve the problem step by step?

[alpine sable]

Whatelse do u need.¿

[grand kelp]

Gimme a sec

[alpine sable]

That's unnecessary. You would have to write eqn of line too for perpendicular distance

[harsh acorn]

why spanish tho

[plush belfry]

si

[plush belfry]

enserio?

[grand kelp]

@harsh acorn

[harsh acorn]

yep i understand

[grand kelp]

It would probably take forever to use Heron's formula for this

[ocean seal]

Chai T. Rex

[grand kelp]

That's the expansion of the cross product formula isn't it

[oak chasm]

Probably.

[grand kelp]

Using vectors you can find the area of any polygon

[harsh acorn]

is the opening like $\frac{1}{2}(x1y2+x2y+x3y1-x1y3-x2y1-x3y2)$?

[ocean seal]

Hyl1s

[grand kelp]

you can use x_1 for the subscript

[harsh acorn]

is the answer 1.5

[grand kelp]

It isn't

I have shown you geometrically that it's exactly 1

[harsh acorn]

i tried to solve with matrix

but why i get 1.5

[grand kelp]

Try a simpler version with cross products

[harsh acorn]

k

[dense mirage]

Yo

Nickpro

How do I turn this into a mixed radical

All I know is that 3/4 turning it into a 4/3 to make the exponent positive

So 4/3 and 7/2 as an exponent

[grand kelp]

That's great already

[dense mirage]

How do I turn into a mixed rsdical

[harsh acorn]

first write -3.5 as -35/10= -7/2 (you reverse the base) and you get 7/2 on the power

[grand kelp]

$(\frac{4}{3})^{\frac{7}{2}} = \sqrt{(\frac{4}{3})^7}$

[ocean seal]

NickPro

[harsh acorn]

oh right

[dense mirage]

I cant use a calculator btw

[harsh acorn]

no need to calc

[grand kelp]

You can use the property of square roots to find that this is equal to $\frac{\sqrt{4^7}}{\sqrt{3^7}}$

[ocean seal]

NickPro

[grand kelp]

The root at the top opens up just fine and that is 128

(2^7)

$\sqrt{3^7} = 3^3\sqrt{3} = 27\sqrt{3}$

[ocean seal]

NickPro

[grand kelp]

@dense mirage Does that work for you

[dense mirage]

I understand that

But the answer key shows

It's T

64 3 81

[ocean seal]

Chai T. Rex

[grand kelp]

Why does it scale everything down by a factor of 2

[oak chasm]

Not sure why they keep giving answers that are off by a factor of 2.

[dense mirage]

@oak chasm how did u go from 27 Square root of 3 to 8

To 81

[ocean seal]

Chai T. Rex

[oak chasm]

So, 81 is the new denominator.

[alpine sable]

I have written opening below in the same pic

[smoky barn]

x : y = 5:9

x+y if y-x = 52

can someone explain how to do it?

[ocean seal]

Chai T. Rex

[smoky barn]

ohh thanks

[oak chasm]

No problem.

[smoky barn]

so my answer is X = 5y/9 and Y = 9x/5

am I correct?

[vale wigeon]

no, that's not the answer

[smoky barn]

oh

[vale wigeon]

and also, you should not just capitalize math notation carelessly. math is case-sensitive.

[ocean seal]

Chai T. Rex

[vale wigeon]

also, you should read and understand what chai t. rex is asking you to do

and do that

[smoky barn]

okay im gonna revise it again

does negative numbers count as pure numbers?

[alpine sable]

how do i do this?

[quaint trout]

Uh

[stark lantern]

I assume by "pure" number he meant a number without any variables(x or y). So it's fine if x+y is -ve

[quaint trout]

First go to first grade and practise writing. Then ask again.

[smoky barn]

ahh okay I got my answer then

[alpine sable]

wym?

[smoky barn]

thanks

[quaint trout]

I can't tell what that says at all

[alpine sable]

First go to first grade and practise reading. Then answer again.

[quaint trout]

😂

Okay

[stark lantern]

What did you get as x and y tho? Neither should be negative

[smoky barn]

I got Y=117 and X=-65

did I do something wrong?

[stark lantern]

Is the equation y + x = 52 or y - x=52?

if it's the latter you should have got +65 instead

[oak chasm]

@smoky barn You're getting close.

[smoky barn]

wait no the equation is x+y if y-x = 52

[oak chasm]

@smoky barn You got one of the numbers y = 117 and x = -65 wrong.

[smoky barn]

I see

[dense mirage]

Is the answer for y right?

[oak chasm]

@dense mirage Sorry, I think the channel is still busy.

[dense mirage]

I got 2 to the power of 178

[smoky barn]

yea I cant figure it out :/

[oak chasm]

@smoky barn Just redo your work.

You got very close the first time.

Unless you're saying you redid it.

In which case, show your work.

[smoky barn]

okay im gonna redo it again

[fiery turret]

yo i got a math test on trigonometric functions in like 4 hours and i got no clue what i'm doing man

here's some examples

[smoky barn]

I think X = 65 im not sure

[stark lantern]

correct. you can always verify by plugging the x and y values back into the original equation to see if they satisfy the conditions

[smoky barn]

ahh thanks

[golden violet]

hii guyys could anyone help me with this log qns

[surreal meteor]

"We believe in a woman's right to control her body, and she deserves this right no matter where she lives, even if she's still living inside her mother's womb. Feminists for Life" so would yall say that this is ethics of duty or ethics of utility?

[quaint trout]

@surreal meteor what da fuq

[manic quail]

Have you tried anything yet?

[quaint trout]

This is a math and cat server sir

[golden violet]

well tbh ik how to do these kind of qns, but the english kinda fumbled me

[quaint trout]

The half life being 8 days means after 8 day, the number of atoms is half what it was originally

So N(8) = N_0 / 2

[surreal meteor]

Mb

[golden violet]

make sense?

[quaint trout]

No

[stark lantern]

it should be $\frac{1}{2} = e^{-\beta t}$

[ocean seal]

error 404

[stark lantern]

because it's n(8)/n_0

[golden violet]

ahh

@ocean seal could u further explain why’s that

[stark lantern]

@ocean seal is a bot lol

[golden violet]

LMAOO oops

[manic quail]

$\frac{N_0}{2}=N_0 \cdot e^{-8 \beta}$

[ocean seal]

verysadperson

[manic quail]

Does that make sense, @golden violet ?

[golden violet]

yea i think it does

lemme give it a shot

[ionic jewel]

texit writes all our math and takes pictures of it to send here

hes a very neat writer

[golden violet]

ahh i get it

thankss dudes

help alot

[harsh acorn]

$$\frac{(n-2)*180}{n}=12n+6$$ and $$180n-360=12n^2+6n$$

[ocean seal]

Hyl1s

[harsh acorn]

am i right?

[oak chasm]

@harsh acorn Yes.

[harsh acorn]

i tried to solve for n but answer is not integer

idk why

,w solve 180n-360=12n^2+6n

[ocean seal]

Results provided by WolframAlpha

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

Requested by Hyl1s#3863

[harsh acorn]

oh

wait

what

[maiden pumice]

Lol

[fallow igloo]

xd

[harsh acorn]

but it was giving me 2.2525... lol

[loud frigate]

How do I solve the equation $x^2-8x-9=0$ with the algebra methode?

[ocean seal]

TeddyA

[fallow igloo]

use the quadratic formula

[harsh acorn]

use quadratic formula or viet theorem

[oak chasm]

You can also complete the square.

[harsh acorn]

viet is easier

[fallow igloo]

indeed

[loud frigate]

No because it says I should use algebra

[harsh acorn]

it is algebra

[oak chasm]

All of these methods are algebraic.

[fallow igloo]

quadratic formula is systematic and always works, other methods require a previous think and can save you time

[harsh acorn]

$$x^2-8x-9=0$$ and $$x_1+x_2= 8$$ $$x_1*x_2=-9$$

[ocean seal]

Hyl1s

[fallow igloo]

?

[harsh acorn]

as you can see answer is $$x_1=9$$ $$x_2=-1$$

[ocean seal]

Hyl1s

[harsh acorn]

yep you can use quadratic formula too

i think it is faster

which formula should i use for this problem?

ik how to solve by hand

[oak chasm]

@harsh acorn Select the positions of the girls.

[harsh acorn]

i just want to know formula

[oak chasm]

The boys will take the remaining positions.

So, how many ways are there to place the girls?

[vale wigeon]

stop. no. bad.

[harsh acorn]

you mean i should find by myself?

so i can understand very well or what

[vale wigeon]

you should not fixate on knowing "the formula" as much as youre doing rn

also this question is all kinds of ambiguous

like, are the boys and girls all distinct from one another? or can we swap two of the girls without getting a different arrangement?

[harsh acorn]

if they are indepedented from each other then answer is 8! right?

[vale wigeon]

and if they are all distinct then why even mention that theres 2 boys and 6 girls as if that's of any relevance to the problem?

[harsh acorn]

good point

[vale wigeon]

there don't seem to be any restrictions along the lines of "the two boys must not stand together" or something

[harsh acorn]

so if they are distinct answer is 8! but if they are like a group of boys-girls answer is 2

right?

[oak chasm]

What are the two arrangements, using G and B in like BBGG.... format?

[harsh acorn]

i consider B as all the boys G as all the girls

BG and GB

:s

[oak chasm]

No, do it with individual children.

There should be eight children.

What are the two arrangements of eight children?

Like, BBGGGGGG and GGGGGGBB?

[harsh acorn]

yep

[oak chasm]

What about BGBGGGGG?

[harsh acorn]

if we consider question as this it goes to 8!

as i know

[oak chasm]

No, it doesn't.

Because if you switch the two boys, the arrangement is the same.

[harsh acorn]

oooh

BBGGGGGG
BGBGGGGG
BGGBGGGG
BGGGBGGG...

like that

right?

[oak chasm]

Right.

But that's the long way.

[harsh acorn]

is the answer 8+7+6...+1?

[oak chasm]

No, because you also have GBBGGGGG.

Again, counting them all up is the long way.

Oh, wait.

[harsh acorn]

i am confused

how can i find it without counting then

[oak chasm]

I mean individually.

Each case.

[harsh acorn]

from this type there are 8 times

[oak chasm]

How did you come to 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1?

Oh, OK.

Yes, I see.

But from that one, there are only 7 ways.

[harsh acorn]

yep

[oak chasm]

So, 7 + 6 + 5 + 4 + 3 + 2 + 1

But there's another, more general way.

Do you know about what 12C3 means?

[harsh acorn]

no i dont

[oak chasm]

OK, it means you have 12 things to choose from, and you want to choose 3 of them.

[harsh acorn]

okay

[oak chasm]

OK, so we have 8 positions to choose from.

And we want to pick 2 of them for the boys to stand in.

Then we have 6 positions left over.

And we want to pick 6 of them for the girls to stand in.

[ocean seal]

Chai T. Rex

[harsh acorn]

equals to 48C12?

[oak chasm]

No.

[ocean seal]

Chai T. Rex

Chai T. Rex

[oak chasm]

Does that make sense?

[lucid arrow]

Can somebody help me?

[oak chasm]

@lucid arrow Sorry, channel is busy.

[harsh acorn]

yep it does

[oak chasm]

OK, do you know what the ! means?

[lucid arrow]

Oh okay

[harsh acorn]

8! is all possibility 6! is girl's all 2! is boys

3!=3x2x1

[oak chasm]

No, not exactly.

The girls aren't in the picture.

8C2 is about 8 positions and where to put the boys.

So, let's say there were three groups.

10 red flowers, 2 green flowers, 5 yellow flowers.

How many arrangements where the same color flowers are indistinguishable from each other?

[ocean seal]

Chai T. Rex

[harsh acorn]

ooh i get it

now we will write them as (17!)/... x ... x =

and solve?

[oak chasm]

Yes.

[ocean seal]

Chai T. Rex

[harsh acorn]

0! was 1 right?

[oak chasm]

Yes.

[harsh acorn]

but it is stil messy isnt it

[oak chasm]

Right. You can also cancel the (7 - 2)! with the 5! on top.

[harsh acorn]

oh yep

[oak chasm]

Instead of the 5! on bottom with the 5! on top.

But yes, that's right.

,w Binomial[17, 10] Binomial[7, 2] Binomial[5, 5]

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[oak chasm]

The parentheses with two numbers written above and below each other with no fraction line is another way to write nCk.

It's called a binomial coefficient.

You may have heard of it from earlier algebra.

[harsh acorn]

yep

so answer is 408408?

[oak chasm]

Yes, that's right.

Lots of arrangements.

[harsh acorn]

is this equal to 1

[oak chasm]

Yes.

nCn = 1

nC0 = 1

[harsh acorn]

so answer is 28

[oak chasm]

Because there's only one way to choose them all.

And there's only one way to choose none of them.

,w Binomial[8, 2]

[ocean seal]

Results provided by WolframAlpha

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

Requested by Chai T. Rex#7323

[oak chasm]

Yes, the answer is 28.

[harsh acorn]

for this question answer is 8C3 * 5C5?

[oak chasm]

Yes, that's right.

[harsh acorn]

well now it looks so easy lol

[oak chasm]

Pick the positions of the math books. From the remaining positions, pick the positions of the English books.

[harsh acorn]

thank you so much

[oak chasm]

You're welcome.

[harsh acorn]

,w Binomial [8,3] Binomial [5,5]