help-33

[dusky lodge]

HELP

WITH

STATS

[marsh citrus]

@dusky lodge Has your question been resolved?

[dusky lodge]

NO ONES ANSWERED IT

<@&286206848099549185>

<@&286206848099549185>

SOMEONE

HELP

@hushed egret

@worn nimbus

@main idol

@oak zodiac

@rustic flume

[main idol]

You need to stop

Don't ping individual people

[dusky lodge]

pls help

someone

[main idol]

And just be patient

[dusky lodge]

20 MINUTES

PPL ABOVE ME HAVE GOTTEN HELP

AFTER I ASKED

[main idol]

Yea well pay for a tutor then

[dusky lodge]

omds

[marsh citrus]

@dusky lodge Has your question been resolved?

[marsh citrus]

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[icy dawn]

someone please help im really stuck

[main idol]

do you know the distance travelled for harry at 60 sec?

[icy dawn]

yes

it is 120

and for scarlet it is 200

@main idol

[main idol]

do you know what ratios are?

[icy dawn]

no

[main idol]

it's just the fraction of two numbers

or division of one number to the other

a:b means $\frac{a}{b}$

[elfin berry]

riemann (eric tao for honorable)

[main idol]

don't forget to simplify

[icy dawn]

wait so i ÷ both numbers by what?

[main idol]

what are a and b?

use words or numbers

[icy dawn]

a is 200 and b is 120

[main idol]

correct

[main idol]

plug that into the fraction

[icy dawn]

200 over 120

[main idol]

right

[main idol]

.

[icy dawn]

ah

[icy dawn]

so it would be 2 over 3?

[main idol]

how'd you get that?

[icy dawn]

simplify

[main idol]

explain your process

[icy dawn]

120 - 3 200 - 2

same time table

lowest number

[main idol]

i don't know what this means

where did 2 and 3 come from?

[icy dawn]

simpliflying

to the smallest number

[main idol]

you said that already

[icy dawn]

what do i simplify to?

@main idol

[main idol]

https://www.cuemath.com/numbers/simplifying-fractions/

do that with $\frac{200}{120}$

[elfin berry]

riemann (eric tao for honorable)

[icy dawn]

alr 1 sec

oh ok

200/120-100/60-50/30 / 25/15

so it would be 25 over 15? @main idol

[main idol]

you can still simplify further

use a calculator to check your final answer

[icy dawn]

7.5? it would be if i simplifly more

[main idol]

simplest form means both top and bottom are integers

[icy dawn]

bro im sorry im so confused

[main idol]

7.5 is not an integer

[icy dawn]

but how do i simplifly more

because 15 ÷ 2 = 7.5

[main idol]

25 and 15 have one factor in common

[icy dawn]

5

wait so it would be 5 over 3

@main idol

[main idol]

,calc 200/120

[elfin berry]

Result:

1.6666666666667

[main idol]

,calc 5/3

[elfin berry]

Result:

1.6666666666667

[main idol]

yea

[icy dawn]

alr

tysm

.close

[marsh citrus]

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[gray shale]

Hum how can I solve that

[lime relic]

👋 trying to get x on one side if reading correctly

[gray shale]

That's the difficult part x)

I thought about transforming the sin(x/3) in a cos (x/3 -pi/2)

But I'm not sure about this expression

[lime relic]

Well if your trying to get x on one side have you thought about dividing everything by cos(x/3)?

[gray shale]

Hum

Then we have tan(pi/3)<3

[lime relic]

Keep the x in you would get 1<=tan(x/3) then do tan^-1(1)<=x/3 times out by 3 and hey presto x on its own with a number on the left

[gray shale]

Ok thx I got it

[lime relic]

Should leave you with a solution of (3pi)/4

[gray shale]

.close

[marsh citrus]

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[twilit hazel]

how do I write Q(P)= 1000 - 40 P as P(Q) ?

[twilit hazel]

work so far: Q=1000 - 40P, 40P=1000-Q, P=(1000-Q)/40

now what

[lime relic]

That’s it your p function is in terms of Q

[twilit hazel]

so I solved for P(Q) correctly?

[lime relic]

This p(Q)

[twilit hazel]

Nice

[lime relic]

Yhea should have done

[twilit hazel]

thank you

.close

[marsh citrus]

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[marsh citrus]

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[atomic solar]

Let A={1,2,3 ... 10}
X={f:A->A / f is bijective}
Let R a relation in X defined by: fRg if it exists n in A / f(n)=1 and g(n)=1

Let ld:A->A / ld(n)=n
and Y={f in X:f({1,2,3}) c {1,2,3,4,5} and f R ld}

[atomic solar]

find the cardinal of Y

Ive thought about it for a while, but I cant get to do it

[marsh citrus]

@atomic solar Has your question been resolved?

[marsh citrus]

@atomic solar Has your question been resolved?

[civic moss]

@atomic solar so let me understand

A is {1, ..., 10} and X is the set of all permutations of A

[atomic solar]

X is the set with f function, f is bijective and its domain and image is A

[civic moss]

yes, that's what a permutation is

ok

and R basically says two functions are related if they map the same element to 1

and then id is the identity permutation, which maps everything to itself

ok now Y is the set of all functions which map {1, 2, 3} inside {1, 2, 3, 4, 5}, and are related to id; in other words map 1 to 1

@atomic solar is this all making sense?

[atomic solar]

oh wait

I havent thought of it like the identity

your right

yes I think I understand up to that

[civic moss]

cool

and so they ask for the cardinality of Y

in other words, how many such functions are there

so right now you're working with {1, 2, 3} mapping inside {1, 2, 3, 4, 5}, except 1 must map to 1

so your freedom is restricted; you're finding functions which map {2, 3} inside {2, 3, 4, 5}

[atomic solar]

right

[civic moss]

so for 2, there are 4 choices, and then for 3 there are 3 choices (since one choice was taken)

so the number of total possibilities is 4 * 3 = 12

[atomic solar]

12+1 is necessary bc of the 1?

[civic moss]

the 1 doesn't matter though; 1 is forced to map to 1 in all cases

[atomic solar]

k, ty then

[civic moss]

np

[atomic solar]

.close

[marsh citrus]

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[marsh citrus]

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[crimson pendant]

The inverses trip me up

Can I just cancel the inverse and say it's 32

[marsh citrus]

@crimson pendant Has your question been resolved?

[crimson pendant]

<@&286206848099549185>

[marsh citrus]

@crimson pendant Has your question been resolved?

[marsh citrus]

@crimson pendant Has your question been resolved?

[marsh citrus]

@crimson pendant Has your question been resolved?

[tight furnace]

Nah

The only time you can cancel things in a fraction is when you have something multiplied by both sides

[tight furnace]

This isn't solveable unless you're also given that f^-1(2x)/f^-1(x) is constant for all x

[marsh citrus]

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[marsh citrus]

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[marsh citrus]

Please don't occupy multiple help channels.

[spark otter]

Hello, do you know about the property of exponents : (y^n)^m = y^(nm) ?

well this is the property you have to use :)

[sage heath]

uhh…

[junior bobcat]

yupp

[jade sage]

What's with uhhh

Math does not vary from country to country

[spark otter]

maths is universal m8

[jade sage]

It's fixed.

That doesn't effect it too

[weary ibex]

.close

[marsh citrus]

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[cursive relic]

Hey, how do i find the area of a parallelogram by using vectors? i have the given coordinates:

[upper briar]

i think cross product gives u area

length of cross product

[cursive relic]

ok

and then im guessing that the half of it

since its a triangle

[upper briar]

w8w8

u asked for parallelogram

so its not half

[hushed egret]

cross product gives exactly the parallelogram

[cursive relic]

oh, i thought it only gave half of it

[hushed egret]

you have misthought

[cursive relic]

[upper briar]

[cursive relic]

im just tryna get by

[upper briar]

as i always

[hushed egret]

its okay

happens to the best of us

[cursive relic]

😢

cant wait for next year

[upper briar]

more math?

[cursive relic]

yep

last year

supposed to be calculus and more graphical stuff

[upper briar]

yay

[cursive relic]

wait tho

im tripping then

cos the crossproduct is just this

[sturdy schooner]

Thats dot product

[hushed egret]

thass dot product my mans

and it doesnt give area

[cursive relic]

ok language barrier

[sturdy schooner]

Cross product id a × b = ||a|| ||b|| sin(v)

Bruh

[hushed egret]

LOL

[cursive relic]

yeah

i figured so

[hushed egret]

||a x b|| = ||a|| ||b|| |sin(theta)|

mm

[sturdy schooner]

Is there an echo in here?

[upper briar]

its more or less exactly the same as using 2 lengths and the angle between to get the area of triangle

but *2 for parallelogram

[hushed egret]

you need a

norm

on

the LHS

Olly

[upper briar]

lol

[sturdy schooner]

Meh depends on the definition

Some say its a vector

Some say its just the magnitude

[hushed egret]

well if you define it as the magnitude

you are morally in the wrong

[sturdy schooner]

XD

[hushed egret]

cross products are morally wrong anyhow

but what can you do

[upper briar]

moral highground

[sturdy schooner]

Ghandi was supposedly morally right

Look where that got him

[hushed egret]

[cursive relic]

so how wrong is this now

[sturdy schooner]

That is some sussy notation tbh

[cursive relic]

wym

wdym sussy

[sturdy schooner]

The dot for cross product

Very sussy my friend

[cursive relic]

isnt cross product x1y2+x2y1

[sturdy schooner]

It looks scarily like you took the idea of dot product. Applied it to cross product and then just said that it was equal to the sin(v) instead

Actually I don't know tbh

Let me think about it

[cursive relic]

our teacher told us that the cross product is just multiplying across and can be written like i have

[sturdy schooner]

Gimme uno secondo I'm just trying to work it out

[hushed egret]

yeah no thats

[sturdy schooner]

sqrt((y2 - y1/2)^2 + (x2 - x1/2)^2) * sqrt(x1^2 + y1^2) should give the parallelogram

[hushed egret]

completely not right

[sturdy schooner]

It might be able to be simplified

A lot

,w simplify sqrt((y_2 - y_1/2)^2 + (x_2 - x_1/2)^2) * sqrt(x_1^2 + y_1^2)

Shut hp

[elfin berry]

Results provided by WolframAlpha

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

Requested by Olly#1130

[sturdy schooner]

Nope

That didn't get much simpler

[hushed egret]

,w norm of (a, b, 0) cross (c, d, 0)

[elfin berry]

Results provided by WolframAlpha

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

Requested by 夢雪#2250

[hushed egret]

[sturdy schooner]

[hushed egret]

looks pretty simple to me

[sturdy schooner]

Determinant in 2 dimensions is just ad - bc

Idk how I got my long ass thing

But im pretty sure I'm right

[hushed egret]

oh thats right determinant works too

[cursive relic]

i got this

[hushed egret]

,w 11 - 32

[sturdy schooner]

I feel like you just disrespected yourself so badly

[hushed egret]

what me?

noo

theres no way

[sturdy schooner]

Dont worry sometimes when I'm not thinking I type 2^2 on my calculator

[cursive relic]

i was deadassbout to say this

cos i check notes from a mate

and he said u can just use that

[hushed egret]

ye

go for it

[sturdy schooner]

Yes it's right

[cursive relic]

😩

ansewr was right in front of me

ffs

[sturdy schooner]

Sounds like a romcom

Without the com

[hushed egret]

where is the rom

[sturdy schooner]

Idk I'm not a computer scientist

[hushed egret]

[cursive relic]

.close

[marsh citrus]

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[buoyant dagger]

Hey guys, what am I doing wrong here?

[stoic saddle]

,calc 150/25

[elfin berry]

Result:

6

[stoic saddle]

taken at face value, apparently nothing. are you getting any error messages when trying to submit this?

maybe it wants you to simplify the thing?

[buoyant dagger]

I did the word problem correctly?!

[spark otter]

simplify 1.5/2 into 3/4 maybe ?

[buoyant dagger]

Holy shit I did

[stoic saddle]

ok so like. there's a big difference between

"Am I doing something wrong here?"

and

"What am I doing wrong here?"

the latter implies that you think, or have been told that, there is indeed something wrong.

and people might get weirded out when that's not the case, and go look for minor details and may not even find any.

[buoyant dagger]

Yeah I thought I definitely did something wrong

[stoic saddle]

if you thought you definitely did something wrong but have no concrete thing to point at that you think you did wrong, that's called second-guessing.

and so you should say "I'm second-guessing myself on this problem" or something similar to communicate this fact.

[buoyant dagger]

Okay I will

I am second guessing myself

@stoic saddle any idea?

Am I doing something wrong here ?

<@&286206848099549185>

Like I don't know whether or not to write

425 * 31t

[stoic saddle]

S(t) = C(t) * D(t) is correct

[buoyant dagger]

Or 400 * 30t(25 + t)

[stoic saddle]

however then writing 425 * 31t is fairly blatantly wrong

C(t) = 400 + 30t and D(t) = 25 + t, so C(t) * D(t) = (400+30t)(25+t)

if you wish to simplify it, you can, but it does not appear strictly necessary

[buoyant dagger]

Ahhhh

[stoic saddle]

one must not overcomplicate things

[buoyant dagger]

Thank yiu

You

[buoyant dagger]

Thanks

.close

[marsh citrus]

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[still temple]

math for ppl

[still temple]

help plz

[rigid crown]

Hi @still temple, what level math is this?

[still temple]

5th

[rigid crown]

5th grade? 😄

[still temple]

am in 5th

[rigid crown]

Ok

First you want to find how many 10s there are in 14.702

[still temple]

ok

[rigid crown]

I will paint you a picture, give me a second 😄

[still temple]

ok thank you so much

[rigid crown]

In this number 123.456, there are 1 100s, 2 10s and 3 1s

[still temple]

ok thats were i was stuck thank you!

[rigid crown]

That can be written as (1 x 100) + (2 x 10) + (3 x 1)

Does that help?

If your question was answered, please do ".close" to free the channel for next person. Otherwise feel free to ask me anything 😄

[still temple]

yes so much thank you!

[rigid crown]

You're welcome 😄

[still temple]

.close

[marsh citrus]

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[still temple]

.reopen

[marsh citrus]

✅

[still temple]

.close

[marsh citrus]

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[stray trout]

Find the density of a piece of wood weighing 189g and having a volume of 210cm³" Can anyone help?

[stray trout]

D=M÷V so is it 189÷210?

[worn nimbus]

yes

[stray trout]

Ty

.close

[marsh citrus]

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[marsh citrus]

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[hidden tartan]

Help

[dire beacon]

You literally put $x+/Delta x$ in the boxes. Don't over think it.

[elfin berry]

The Mask of Eternity

[hidden tartan]

Bro I don’t know how I’m going insane to much words

[dire beacon]

You're good, just take it slow. The function is $f(x)=7x^2-9x$

[elfin berry]

The Mask of Eternity

[dire beacon]

To get $f(x+\Delta x)$ wherever there was an x before, you replace it with $x+\Delta x$

[elfin berry]

The Mask of Eternity

[hidden tartan]

I sound so dumb but I tried that and got it wrong

[dire beacon]

Nope. So what is $7x^2$ when you replace the $x$ with $(x+\Delta x)?$

[elfin berry]

The Mask of Eternity

[dire beacon]

It would be $7(x+\Delta x)^2$ right?

[elfin berry]

The Mask of Eternity

[dire beacon]

And similarly, if you replace the $x$ in $9x$ with $x+\Delta x$ you get $9(x+\Delta x)$.

[elfin berry]

The Mask of Eternity

[dire beacon]

So $f(x+\Delta x) = 7(x+\Delta x)^2 -9(x+\Delta x)$

[elfin berry]

The Mask of Eternity

[hidden tartan]

Holy bro to think I was good at math at a point

[dire beacon]

It's just substituting terms. Just takes practice.

[hidden tartan]

How will I add the triangle to the problem

[dire beacon]

Can you take a screenshot of more of the screen?

There should be an option for Greek Letters. You're going to have to learn them. The "triangle thing" is a capital Delta.

[hidden tartan]

I see it now

So like this

[dire beacon]

You saying that it says it's wrong?

[hidden tartan]

No was just asking it was right

[dire beacon]

Oh yeah. Submit that bad boy.

[hidden tartan]

Now I need to simplify

[dire beacon]

So do you know how to \textbf{Foil} the term $(x+\Delta x)^2$?

[elfin berry]

The Mask of Eternity

[hidden tartan]

Not really

[dire beacon]

Okay. Just a heads up. Calculus is going to be really hard for you if you don't remember your Algebra.

[hidden tartan]

I haven’t done math for 3 years forgot it all

[dire beacon]

$(x+\Delta x)^2=(x+\Delta x)(x+\Delta x)=x^2+x\Delta x+x\Delta x + \Delta x^2=x^2+2x\Delta x+\Delta x^2$

[elfin berry]

The Mask of Eternity

[dire beacon]

So
$7(x+\Delta x)^2 = 7(x^2+2x\Delta x + \Delta x^2)=7x^2+14x\Delta x+7\Delta x^2$

[elfin berry]

The Mask of Eternity

[dire beacon]

and $9(x+\Delta x) = 9x+9x\Delta x$

[elfin berry]

The Mask of Eternity

[hidden tartan]

You’re very smart

[dire beacon]

Subtracting them we get,
$7x^2+14x\Delta x+7\Delta x^2 - ( 9x+9x\Delta x)$

[elfin berry]

The Mask of Eternity

[dire beacon]

distribute the minus sign into the parenthesis in the second half.

$7x^2+14x\Delta x+7\Delta x^2 - 9x-9x\Delta x$

[elfin berry]

The Mask of Eternity

[dire beacon]

And combine like terms

[inner lantern]

dude what two numbers add to 3 but multply to -20

[dire beacon]

$f(x+\Delta x)=7x^2+5x\Delta x+7\Delta x^2 - 9x$

[elfin berry]

The Mask of Eternity

[hidden tartan]

For this problem the 9x came out wrong

[dire beacon]

Show me

[dire beacon]

It's $9x\Delta x$

[elfin berry]

The Mask of Eternity

[dire beacon]

Just put 9 in the box.

You really need to review your Algebra man.

[hidden tartan]

I do man

After this semester I’m not gonna need math classes so ima be free from this

[dire beacon]

Gtg good luck man.

[hidden tartan]

@dire beacon I appreciate everything man

[marsh citrus]

@hidden tartan Has your question been resolved?

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[lone timber]

please check if my answer is correct

[marsh citrus]

@lone timber Has your question been resolved?

[lone timber]

<@&286206848099549185>

[marsh citrus]

@lone timber Has your question been resolved?

[marsh citrus]

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[long cape]

Did I answer these correctly?

yes I did

.close

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[proven ocean]

what formula do i need to use in order to solve this?

[marsh citrus]

@proven ocean Has your question been resolved?

[late geode]

consider stuff like equation of a parabola

[still temple]

Yeah.

Was typing that.

[elfin berry]

3317

[still temple]

That's for the arch.

Plug in the values and solve.

[late geode]

you can start with something more convenient

as you're given the x-intercepts

[marsh citrus]

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[mild pulsar]

I have no idea how to go about this

if someone could point me in the right direction thatd be great

[smoky terrace]

invertible = inverse?

[mild pulsar]

yeah

[smoky terrace]

i dont really understand what it means for f to be inverse

[mild pulsar]

you misunderstand

f has an inverse

meaning its bijective

[smoky terrace]

I have no idea since i didnt study this

Sorry

[mild pulsar]

algd, thanks anyway

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[jolly sigil]

I'm totally blanking, how do you find the range of a function again? My professor drew a graph for this but I want to do it algebraically

[proven timber]

Consider the possible outputs that a square root function can give

[jolly sigil]

hmm

ohhhhhh

wait

wouldn't it be like, what I can't input?

[proven timber]

The range is just the outputs

[jolly sigil]

right

I know that part

but there's a restriction no?

[proven timber]

3 - 4x can be any real number with the right x, so the range of √(3 - 4x) is gonna be the same as the range of √x

[jolly sigil]

oooo

[hardy slate]

ignore me

[marsh citrus]

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[lethal oriole]

Why?

[late geode]

by definition

[proven timber]

a^x and log_a(x) are inverses by definition

[lethal oriole]

Yes i understand that

But this doesn't seem logic

[proven timber]

If f and g are inverses, then f(g(x)) = g(f(x)) = x

a^(log_a(x)) = x and log_a(a^x) = x

[lethal oriole]

AAAAAAH

Thanksss

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[glossy swallow]

Imagine a typical deck of cards with an additional 2 suit(s) say: horseshoes and stars. Each new suit still has
the normal 13 denominations as the original suits. Your new expanded deck then has 78 total cards and a
total of 6 suits.
If 5 cards are randomly selected without replacement from your deck of 78 card deck. Find the probabilities of
the following

[glossy swallow]

c. 3 Kings and 2 ♢s

[tired pivot]

Hey, this message comes out a bit terse, but I'm just trying to establish a baseline of where we should start

Can you find the probability if it was just 3 kings in 5 draws?

Can you find the probability if it was just 2 diamonds in 5 draws?

Are you able to find the probability of 2 independent events both occurring, given the probabilities of those independent events?

[marsh citrus]

@glossy swallow Has your question been resolved?

[glossy swallow]

yes

for kings

(6C3x72*66)/78C5x2!

i think

[sleek lake]

it's only 2 cases

3 non diamond kings or 2 non diamond kings

[marsh citrus]

@glossy swallow Has your question been resolved?

[glossy swallow]

you just sum the cases and its done

[open plume]

Did you solve the problem or do you still need help?

[glossy swallow]

i sort of just went to do other ones

[glossy swallow]

i havent done it yet

[open plume]

I would proceed via casework based on how many of the Kings are ♢s.

[glossy swallow]

1

there is one king of diamonds

[glossy swallow]

for this question do you find the case of one of the 3 kings you select are diamonds and then the case where the three kings arent diamonds

is that all?

[open plume]

There are two cases:

1. 0 Kings are ♢s
2. 1 King is a ♢

[glossy swallow]

you cant have 2 kings of diamond can you?

[open plume]

Oh, right.

I forgot that it's a deck of cards :p

[open plume]

Yep.

[glossy swallow]

ok let me see if i can figure out these

case for no kings being diamonds

is

(5C3x13C2)/(78C5)

?

[marsh citrus]

@glossy swallow Has your question been resolved?

[marsh citrus]

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[versed linden]

how do you solve the second part?

[hidden plaza]

Draw a triangle

You know we’re in the third quadrant so sin and cos are negative

Like this and you know the sides

[versed linden]

okay but then how do I sub in the values?

cause i need the angle a and b individually right?

[velvet gate]

in this case you dont

[versed linden]

so i don't use the formula sinacosb+cosasinb?

[velvet gate]

you dont

you use the pythagorean theorem

[velvet gate]

on this triangle

[versed linden]

okay so sin(a+b) is 3/5?

[velvet gate]

nah

[velvet gate]

think of what tan(a+b) represents here

[versed linden]

what 💀

opp/adj..???

[velvet gate]

ok cool

and tan(a+b) = 3/4

so we can write the opposite side of that triangle as 3x, and the adjacent side of that triangle as 4x

now, think of what sin(a+b) represents

[versed linden]

opp/h

[velvet gate]

so whats the hypotenuse

[versed linden]

5

x?

[velvet gate]

yes

now, remember that sin(x) will be negative, becuase it is third quadrant

[velvet gate]

now find sin(x) from this

[versed linden]

oh so -3/5?

[hidden plaza]

Yeah

[versed linden]

ahh i see thankss

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[bronze drift]

Given positive integer x, is there a way to approximate the number of times digit 2 appears in integers from 1 to x?

[bronze drift]

Or if not (or it's not that easy), is there a way to prove that for all x such that x has more than 6 digits (and no zeros following) the number of times digit 2 appears from 1 to x is strictly greater than to other digits (0, 1, ..., 9)?

no I mean

like

[tacit trail]

Oh digit

My bad

[bronze drift]

1, 2, 3, ..., 12, etc

so yeah, digits

e.g. in 22 it will be twice

[tacit trail]

Theres probably a way

[jade sage]

I mean using python, yeah! 😄

[tacit trail]

What is the full problem that you are trying to solve?

[bronze drift]

generally, I'm given x and I need to find the digit which appears most times in integers from 1 to x

if few digits appear equal number of times then I need to take the greatest one

and I have a conjecture that for all x with more than 6 digits, 2 appears most times (idk why yet but am trying to prove it)

[bronze drift]

x can have up to 10^6 digits

in general

[tacit trail]

I mean from 0 - 9 there is one 2

From 10 - 99 there is 2 * 10 + 2* 9 = 19 2's

Bu also every other digit appears the same amount

Except 0

[bronze drift]

okay, my conjecture is false

rip

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[clever tangle]

why is the green part d(sin(theta))?

[trim quest]

It's not the green area, just the height of the triangle

the y-coordinate of a point on a unit circle is equal to the sine of the central angle theta

so d(sin(theta)) is a small change in the y-coordinate corresponding to a small change in theta

[clever tangle]

I don;t get this part

[trim quest]

That's basically just the definition of sin

This video might be helpful if it doesn't make sense
https://www.youtube.com/watch?v=1m9p9iubMLU

[clever tangle]

ok

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[clever tangle]

.reopen

[marsh citrus]

✅

[clever tangle]

ok why are these triangles similar

thay have the same angle theta

[nova crescent]

ye and they both have a right angle

[clever tangle]

so this is the explanation?

[nova crescent]

for similar triangles?

[clever tangle]

of why these 2 are similar

[nova crescent]

yeah

you know what similar triangles are defined as?

if you have two of the same angles

[clever tangle]

wait

[nova crescent]

so now you have theta and a 90 angle

[clever tangle]

but we were not given theta before that

[nova crescent]

ya but theta can be anything u want

if its 30 degrees, then the other triangle's theta is also 30 degrees

[clever tangle]

ohhh

ok

[nova crescent]

it's set as theta, a variable, because it's meant to convey that the angle can be anything

[clever tangle]

I get it now

thx

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[errant osprey]

how

[sharp vessel]

Do you know how to sketch graphs?

These are both parabolas.

[hexed laurel]

ok so u like use khan acadamy

[marsh peak]

To graph it, first graph f and g and just highlight the area between enclosed by them

To find the area, you just need to evaluate the integral of |f - g| from x1 to x2 where x1 and x2 are the points where f = g (x2 > x1)

[errant osprey]

but wont that only give stuff above the x axis

[errant osprey]

not that part 😭

[marsh peak]

No

[errant osprey]

oh nvm then

idk why i thought it would be only above x

mb

ty

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[calm hollow]

.

[timber tundra]

"Every odd integer can be written in the form 2m+1, for some integer m"

[timber tundra]

I wrote: Odd(x) → ∀n ∈ Z, x = 2n ± 1

[marsh peak]

It says "for some", not "for all"

[timber tundra]

if I write like this, Odd(x) → ∃n ∈ Z, x = 2n ± 1
it's right?

[twilit arrow]

yeah

you could clarify that $(\forall x\in\mathbb{Z})\text{Odd}(x) \implies \exists n \in \mathbb{Z} : x = 2n+1$

[elfin berry]

maximo

[twilit arrow]

also the statement is for “2n+1”, not necessarily plus or minus

[timber tundra]

oh okay, thx 😄

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[quaint chasm]

How can I definitely state something with just one direct proof. E.g a number is even when the modulus = 0 (no remainder). So I go to direct proof of 2 / 2 = 0. Now at what point can I conclude that this proof holds?

[hollow sparrow]

That's for one example

a proof generally does it generically

like "Let x be an even number. Then x = 2k for some integer k" then you work out to show that your proof holds for x

[quaint chasm]

Even so, how this in general is considered proofed just by one direct proof.

Is there a threshold or like a general acceptance to how many types of proofs need to be done for a definitive proof?

[hollow sparrow]

well if you prove it for one generic element then it proves it for all numbers.

For your example, you're trying to show that a even number modulo 2 equals 0 right?

[quaint chasm]

for example

[quaint chasm]

I guess so - it depends on your definitions, right? I mean if the definitions are correct and they don't change only the input does then its safe to assume (after one proof) that output will always be constant following definitions.

[hollow sparrow]

yeah that's kind of the idea

we can prove all day and night that 2 is even, 4 is even, 6 is even

but it'll be easier to prove that a generic even number's remainder will be 0 when divided by 2 right

so let's walk through a proof

[quaint chasm]

yep

[hollow sparrow]

we want to show that if x is even, then $ x \equiv ( 0 mod 2)$

So we start off with defining x

so Let x = 2k for some integer k

sorry I guess the bot is broken

let me try something

$ test $

darn lol

okay give me one second, I'm going to write it up and screenshot it

[quaint chasm]

I got latex running its ok

[hollow sparrow]

lol okay

so we have x ≡ (0 mod 2). We're trying to prove that if x is an even number then this congruency holds

This is the same thing as saying 2 | (0 - x) or 0 - x = 2j for some integer j.
If x is an even number, then let x = 2k for some k in the integers.

So then we have 0 - 2(2k) = 2j ==> (0 - 4k) = 2j ==> 2(0 - 2k) = 2j .

In other words it's still even no matter what we put in for k

so this shows that it will be even

[quaint chasm]

Yep, clear got it thanks 🙂

[hollow sparrow]

np

any other questions?

fwiw direct proofs are just by practice. Find things you know to be true and try to prove them. Like showing that f(x) = 2x + 3 is injective (one to one)

practice makes perfect 🙂

[quaint chasm]

I might drop my solution for a problem later here associated with this. Want me to tag you? 🙂

[hollow sparrow]

I'm about to head out for a bit. But if you post it and I"m around I'll look out for your name :)_

[marsh citrus]

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[orchid kestrel]

I'm going to ask whether the following 4 algebraic expressions are rational or irrational.

[wise jackal]

those look rational to me!

[late geode]

yes

[elfin berry]

TheUnknown

[orchid kestrel]

Had a hard time making the damn equation 😂

[orchid kestrel]

Is that rational or irrational?

[late geode]

in the denominator, what's that radical covering

[orchid kestrel]

x

[late geode]

use \sqrt{}

[elfin berry]

TheUnknown

[wise jackal]

is any info given about x?

[orchid kestrel]

Nope

[late geode]

have you tried determining whether that could be expressed in the form
polynomial/(another polynomial)

[orchid kestrel]

Yes, its polynomial / another polynomial. ie.. P(x)/Q(x)

[late geode]

what's your p(x) and q(x)

[orchid kestrel]

The values aka solutions?

[late geode]

well you said it can be expressed in the required form

what are you two polynomials

[orchid kestrel]

The chapter is about polynomials. The question is State whether each of the following expressions is a rational expression or not

[late geode]

I know

[orchid kestrel]

I don't get what you mean there

[late geode]

what did you mean by

Yes, its polynomial / another polynomial. ie.. P(x)/Q(x)

[elfin berry]

TheUnknown

TheUnknown

[late geode]

what's your definition of polynomial

[orchid kestrel]

¯_(ツ)_/¯

[late geode]

because those aren't polynomials

[orchid kestrel]

Lets forget the polynomial part. Are those rational expressions or not?

[late geode]

...

you can't forget about something that's crucial to determining whether something is a rational expression

[orchid kestrel]

That doesn't seem crucial, does it?

[late geode]

it does ...

[orchid kestrel]

Alr wait

[late geode]

the definition of rational expression involves polynomials,
hence you'd need to know what polynomials are to determine if something is a rational expression

[orchid kestrel]

How about this, is that rational or not? : $\frac{{x^2}+6x+9}{{x^2}-9}$

[elfin berry]

TheUnknown

[late geode]

identify whether the numerator and denominator are polynomials

and/or whether manipulation can be performed to get a fraction of two polynomials

[orchid kestrel]

Yes, the numerator and denominator are polynomials.
I don't think manipulation can be performed.

[late geode]

well if they're already polynomials, no additional work is required and you can say for certain that it's rational

(by definition of a rational expression/function)

[orchid kestrel]

Uhmm I see

So the first one can be said is irrational as its not polynomial. Right?

[late geode]

well you'd want to be more rigorous

[orchid kestrel]

Lets not go into the edge cases. Keep it simple. It says so in the book that its irrational.

[late geode]

just because you don't start with a fraction of two polynomials doesn't necessarily mean the expression isn't rational

considering edge cases and being rigorous is important

consider a simpler example with numbers

[orchid kestrel]

It doesn't ask for a definitive answer that holds true in all cases. Also considering its low grade math for education

[late geode]

I know

my point is, just because you see
nonpoly/nonpoly doesn't mean you should blindly jump to the conclusion of irrational

[orchid kestrel]

Ofcourse. But in this specific situation/question, its okay. Right?

[late geode]

eg just like
sqrt(28)/sqrt(7)
you shouldn't blindly jump to the conclusion that's an irrational number
just because the numerators and denominator s themselves aren't integers/rational

[elfin berry]

TheUnknown

[late geode]

same question

[orchid kestrel]

Yes, also considering if it aint polynomial it aint rational (i guess)

[late geode]

are the numerator and denominator polynomials

[orchid kestrel]

:l

[orchid kestrel]

Yes they are

[late geode]

so you have your answer

[orchid kestrel]

Well, why are we neglecting that sqrt(3) is irrational?

[late geode]

note that you're dealing with polynomials

[elfin berry]

TheUnknown

[late geode]

and not rational numbers

[orchid kestrel]

That means ANY polynomial divided by another, results in rational expression?

[late geode]

you don't care if the coefficients or constants are irrational when dealing with rational functions/expressions

yes, by definition

[orchid kestrel]

👍

[late geode]

Ofcourse. But in this specific situation/question, its okay. Right?
if they're not trying to trick you yeh

[orchid kestrel]

Can we ignore that part? Consider this just an expression and then does it make it irrational? As sqrt(3) is irrational.

[late geode]

you don't care if the coefficients or constants are irrational when dealing with rational functions

[orchid kestrel]

rational functions?

[late geode]

rational functions/expressions

functions makes it less likely to conflate these with rational numbers

all you care about is whether

are the numerator and denominator polynomials
(or whether manipulation can be performed to get that)

$\frac{\pi x^3 + ex^2 - \sqrt{7}}{x^2 - \pi}$

[elfin berry]

ℝamonov

[late geode]

doesn't matter how many irrationals are present here

the numerator is a polynomial
the denominator is also a polynomial
this is a rational function/expression

[orchid kestrel]

So I just call it a law of maths? P(x)/P(q) is always rational

[late geode]

it's literally the definition

which should have been taught/given to you

[orchid kestrel]

Yeah lol

[late geode]

and what youll see when looking it up

[orchid kestrel]

Still had doubt regarding the irrational coefficients

[late geode]

hence why I also mentioned the importance of knowing the definition of polynomial

[orchid kestrel]

👍

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[inner jacinth]

I need to prove $$A \psi(X) = \lambda\psi(X)$$

[elfin berry]

Leonastos

[inner jacinth]

And am stuck to this step

$$A\psi(X) = ABX$$
$$\lambda\psi(X) = BAX$$

[elfin berry]

Leonastos

[sharp mortar]

isn't E_{lambda}(A) the eigenspace of A with eval lambda?

[inner jacinth]

yeah

[sharp mortar]

is lambda any eigenvalue or one that satisfies this

[inner jacinth]

yeah it verifies that

[sharp mortar]

ok you should use that fact

X satisfies (AB - BA)X = 0

[inner jacinth]

ahhhhhhh

thank you a lot

[sharp mortar]

np

[marsh citrus]

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[still temple]

What's the possibility to get a Bingo within 5 draws?

[still temple]

0.000017 = 1 in 58 Thousand Right?

[sage heath]

what is a bingo, explain rules

[late geode]

,calc 1/0.000017

[elfin berry]

Result:

58823.529411765

[late geode]

,W C(75,5)/292

[elfin berry]

Results provided by WolframAlpha

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

Requested by ramonov#0921

[still temple]

HEy Deep you are everywhere

Its drawing a number but you dont put the number back

[sage heath]

[still temple]

like lotto if you call it that in english

[sage heath]

hmm 🤔

well Ramonov alr verified it ig

[still temple]

you need picture right

[sage heath]

oh okay i get it now

[still temple]

is this really a verification? you just made the frac in 1 to ...

test

Laptop down in mobile know

[late geode]

0.000017 = 1/x,
solve for x

[still temple]

What r U doing ramonov?

[late geode]

?

[still temple]

Im asking what r you doing

[late geode]

you were asking whether

0.000017 = 1 in 58 Thousand Right?

I queried the bot to check that

[still temple]

My Question is Not If 0.000017 is 1 in 59 thousand

[still temple]

Thats The original Question

[late geode]

then why was the "question" in there with the 1/58000 or 1/59000 in there,

what are the exact rules of this variation of bingo

[still temple]

I was asking for someone whou could validate The solution

[late geode]

are the stars relevant

[still temple]

I played Bingo today, i Made The stars on it

The star in The middle is relevant

ITS Like a joker

Sorry my mobile is

writing like this, now I'm back to laptop

What's the possibility to get a Bingo within 5 draws?

[late geode]

are you allowed diagonals

[still temple]

wow

thats a GOOD Question

no im stupid

😄 I already did calculate the diagonals

thought for a second i missed them

[late geode]

how many balls are there

[still temple]

in this Bingo 75

Thats why 75 above 5, because you draw 5 out of 75 in this question

What's the possibility to get a Bingo within 5 draws?

[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

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[prisma nova]

How do I rationalize the denominator

[wise jackal]

you should multiply by the conjugate of the denominator

(the conjugate of a - b is simply a + b)

[prisma nova]

so sqrt(5)+sqrt(6)?

[wise jackal]

yep

when you multiply it out, you’ll notice something

the roots will be gone

[prisma nova]

that works even with something more complex?

[wise jackal]

depends how complex you’re talking

[prisma nova]

say sqrt(x)-(2/sqrt(x)) as the denominator

[wise jackal]

hmm

$\frac{1}{\sqrt{x} - \frac{2}{\sqrt{x}}}$

[elfin berry]

Kihei

[wise jackal]

I suppose you could simply multiply by sqrt(x)/sqrt(x)

[prisma nova]

makes sense...

[wise jackal]

so that just leaves sqrt(x) over x - 2?

however, perhaps you meant something like $\frac{1}{\sqrt{5} - \frac{2}{\sqrt{6}}}$

[elfin berry]

Kihei

[wise jackal]

and in that case you should multiply by the conjugate

[prisma nova]

wait so I can't use conjugate if there is a variable instead of a value?

[wise jackal]

no you can use anything

[wise jackal]

but in this case it’d be smarter to just multiply by sqrt(x)

as x is the same number throughout the expression

[prisma nova]

oh makes much more sense

thanks man

[wise jackal]

np 👍

[prisma nova]

.close

[marsh citrus]

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Closed by @prisma nova

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[marsh citrus]

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[whole linden]

wdym difference? they're just 2 different formulae

well if you know base and height, you use the formulae that has b and h
if you know the sides, you use herons

because you don't know the height

ofcourse you could find it using some other methods

in most/all cases, first

[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

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[west night]

I need some help understanding what this assertion is saying

[echo bough]

do you understand what the first line means?

[west night]

theres a sort of range from c where that inequality is true

[echo bough]

yeah so it means what follows is true around point c

[west night]

supposedly theres an error in logic, im trying to see if I have the right understanding of the assertion itself

so i can find the error

[echo bough]

second line just tells you that around point c

f is between h and g strictly

then we know that at point c all 3 functions have limits

and the assertion is that under these conditions

the inequality stays true also for the limits

[west night]

Thats what I understood from it, but I dont see how theres an error

the assertion makes sense

[echo bough]

its a subtle one

see that the first inequality is true around c

but not at c

[west night]

oh so is it because in a limit you dont go to the actual point

so technically they can all have the same limit

[echo bough]

yeah but if it was

|x-c|<p

so x can be equal to c

that would mean that the functions would be defined at point c

and that their values would be strictly ordered

[west night]

not sure what that means

[echo bough]

like h(c)<f(c)<g(c)

[west night]

oh ok

[echo bough]

oh actually nevermind we dont know if they are continuous

the real argument is as you said, the limits could be the same

like if you take h(x)=0

f(x)=x^2

and g(x)=|x|

they fullfill the assumptions

yet all the limits at 0 are 0

[west night]

but they would all equal 0 at f(0)

doesnt that contradict the first inequality

[echo bough]

the first inequality is for |x-c|>0

it doesnt mean anything for

f(c) h(c) and g(c)

like i could take the same examples and assign any values to f(0) h(0) and g(0)

and it would still work

the limits dont care about whats happening at the point

unless the function is continuous

[west night]

so the inequality only applies to the "range" around c, not to c itself

[echo bough]

yeah

like theres no hypothesis on whats happening at c here

just around

as close as you want but not c

[west night]

and since limits dont care about whats at c, we can just say that the functions around c still fulfill the inequality, but the limits might be at the same place

[echo bough]

yeah as in the example i gave

and usually a rule is that

[west night]

so then the limit inequality would use <= rather than <

[echo bough]

inequalities always become loose after going through a limit

[west night]

and the function inequality stays as <

[echo bough]

yeah

why would it change

it was assumed true

its still is

[west night]

are you referring to the limit or function inequality?

[echo bough]

function

like things dont change in maths, usually when we say they do its because we are looking at a close related thing

like here i said the inequality changes

but really its the inequality of limits related to the function inequality

its 2 different things

so they can be different

(or the same)

[west night]

finally I understand it