help-19

[cosmic solar]

Is there a significant difference

I never use {} often

[fervent hawk]

it's just the LaTeX bot

$10^{-7}$ vs $10^(-7)$

[cosmic solar]

Ah

[clever fjord]

Biscuity

[cosmic solar]

Okay now part B of the equation

If you're able to help

[fervent hawk]

sure

km per million years

[cosmic solar]

So a My

[fervent hawk]

so we need to switch both

1million years = 1,000,000 years

now

4cm = ? km

so we know that 1km = 100,000cm

[cosmic solar]

Yeah

[fervent hawk]

and 4km = 400,000cm

so....

[cosmic solar]

Move the zero?

I mean decimal

Not zero

[fervent hawk]

we divided both sides by 100,000

yea

[cosmic solar]

I'm in auto pilot

Gotcha

[fervent hawk]

haha

[cosmic solar]

So would it go from 400,000 to .000004

[fervent hawk]

we have 0.000004km=4cm

[cosmic solar]

Okay sweet

[fervent hawk]

so we have

0.000 004km per year

now we have My

so we need to ×1,000,000

so we move the zeros again

[cosmic solar]

So it's .000004km x 1,000,000

[fervent hawk]

yep

[cosmic solar]

,calc .000004•1,000,000

[clever fjord]

The following error occured while calculating:
Error: Syntax error in part "•1,000,000" (char 8)

[fervent hawk]

use *

[cosmic solar]

Gotcha

,calc .000004*1,000,000

[clever fjord]

The following error occured while calculating:
Error: Unexpected operator , (char 10)

[fervent hawk]

and no comma

[cosmic solar]

okay lol

Thanks

,calc .000004*1000000

[clever fjord]

Result:

4

[fervent hawk]

weird

[cosmic solar]

That feels low

[fervent hawk]

,calc 1/100000

[clever fjord]

Result:

1e-5

[fervent hawk]

i bet we both have mistake on the cm to km part

[cosmic solar]

Isn't it 100,000

1 km is 100,000 cm

Right?

[fervent hawk]

yea

[cosmic solar]

Hmm

[fervent hawk]

so it's only 0.00001km = 1cm

we added too many zeros lol

that's why using those 10^(-5) are pretty useful in such case

[cosmic solar]

What is 1e-5 in decimal form

[fervent hawk]

0.00001

[cosmic solar]

Quick convo, how do you figure that 1e-5 is 0.00001

I understand the negative part

But the zeros throw me off

[fervent hawk]

oh ok, i usually count like this

$\underbrace{0.0000}_{\text{5 zeros}}1$

[clever fjord]

Biscuity

[fervent hawk]

or like this

$\underset{0}{e}$

$\underset{e}{0}.\underset{1}{0}\underset{2}{0}\underset{3}{0}\underset{4}{0}\underset{5}{1}$

[clever fjord]

Biscuity

[fervent hawk]

see which fits you better

[cosmic solar]

So when transferring a digit through decimal places using Euler's number you just count how many zeros you want to move over based on the Euler's number

[fervent hawk]

hmmm lemme check, i don't think it's euler number

[cosmic solar]

Like 3e+7 would be 30,000,000?

[fervent hawk]

just checked

[cosmic solar]

Oh, I was looking for a name for the "e" because I haven't been taught it, Google said Euler's sorry lol

[fervent hawk]

that e is not euler number

[cosmic solar]

Is it just e

Nothing fancy

No name

[fervent hawk]

right now, just treat it as a calculator expression

in maths, we would usually write that down as ×10^7

e.g. 3×10^7=30,000,000

[cosmic solar]

So counting the zeros like that is right

[fervent hawk]

it's something in the computer science field, you can look it up if you want 🙂

[cosmic solar]

I'm confused enough, thanks 😂

Okay anyways back on track

[fervent hawk]

so we have

[cosmic solar]

So wouldn't it be 40 Myr

[fervent hawk]

yea

correct

done

[cosmic solar]

,calc .00004*1000000

[clever fjord]

Result:

40

[cosmic solar]

Sweet

I'm gonna go back over this all and write notes

Thank ya for your patience and help

Much obliged pardner

[fervent hawk]

no problem!

[cosmic solar]

Have a good rest of your night :)

[fervent hawk]

you too!

you can type .close when you're done

[odd edge]

@cosmic solar Has your question been resolved?

[cosmic solar]

.close

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[cursive jackal]

cos(x) =-cosx
Is this true?

[cursive jackal]

cosx= cos(-x)

This is true

[crisp wadi]

cos(x) = -cos(x) for all x is not true
cos(x) = cos(-x) for all x is true

[cursive jackal]

19 question

Why did they write +/-

I guess because we can converse
Cos(A-π/4)

[desert marlin]

@cursive jackal

[cursive jackal]

But it gives the same answer

Yes austin 👋

My doubt why +/- they describe

[crisp wadi]

I can't really tell what you did in your work

So you expanded cos(pi/4 + x) knowing that it's equal to 1/2sqrt2?

[cursive jackal]

Yes i expanded

[cursive jackal]

Yes

[crisp wadi]

cos(pi/4 + x) or cos(pi/4 - x)?

[cursive jackal]

My doubt is why did they mentioned+/-

[cursive jackal]

Both gave same answer

1/(2√2)

[crisp wadi]

No, they are not the same when expanded too

Btw how did you get that one of them is equal to 1/2sqrt2

[cursive jackal]

19

[crisp wadi]

Yeah but the hint is telling you that the pi/2 could also be negative

So it's $\pi\cos A = \pm \frac{\pi}2 - \pi\sin A$

[clever fjord]

A Lonely Bean

[crisp wadi]

Hence the $\sin A + \cos A = \pm\frac12$

[clever fjord]

A Lonely Bean

[cursive jackal]

How does this happen?

[crisp wadi]

Hmm I have a better explanation than the one in the book

[cursive jackal]

Ohh i got it

U made clockwise

4th quadrant

Where tan cot gives positive value

[crisp wadi]

Yeah you can think of it as subtracting pi because it doesn't change the value of tan

Hence pi/2 could also become -pi/2

[cursive jackal]

tan(π cos a) = tan(π-πsin a) ?

tan(π cos a) = -tan(π sin a)

[crisp wadi]

So you got $\tan(\pi\cos{A}) = \tan\mathopen{}\left(\frac{\pi}2 - \pi\sin{A}\right)$

[clever fjord]

A Lonely Bean

[crisp wadi]

You can't just set the inputs equal to each other

tan(x) = tan(y) means that x = y + pik for some integer k

So here you get $\pi \cos A = \frac{\pi}2 + \pi k - \pi \sin{A}$

[clever fjord]

A Lonely Bean

[crisp wadi]

Rearrange like previously and you get $\sin{A} + \cos{A} = k + \frac12$

[clever fjord]

A Lonely Bean

[crisp wadi]

And now you need to decide on the possible values of k

Because sinA + cosA obviously has to be between -sqrt2 and sqrt2

And you will see that only k = 0 and k = -1 can work

Meaning $\sin A + \cos A = \pm\frac12$

[clever fjord]

A Lonely Bean

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[steep thicket]

What is happening from line 2 to 3?

[stark coyote]

it might be poor notation, the 3rd line's second fraction line should be the longest.

they are bringing all the factors into the fraction in the numerator from 2)->3)

then using a/b/c=a/bc to simplify the complex fraction from 3)-4)

[viscid flint]

ohh

it should be $\frac{\frac{x-2(x+1)}{2\sqrt{x+1}}}{x^2}$

[clever fjord]

hayley!

[odd edge]

@steep thicket Has your question been resolved?

[steep thicket]

ohhhh

Right yeah, fraction lines messed me up

thanks

[viscid flint]

yeah the original author was trolling

[steep thicket]

Yep thanks, makes sense now

.close

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[mystic saffron]

How do I find lcm and gcf? Also what’s repeated division

[nocturne ridge]

You can refer to it, I’m not sure.a. 45 and 189

For GCF:

The prime factors of 45 are 3, 3, and 5.
The prime factors of 189 are 3, 3, 3, and 7.
The common prime factors are 3 and 3.
So, the GCF is 3*3 = 9.
For LCM:

The LCM is found by multiplying all prime factors of both numbers, but only counting common prime factors once.
So, the LCM is 33357 = 945.
b. 12, 24 and 144

For GCF:

The prime factors of 12 are 2, 2, and 3.
The prime factors of 24 are 2, 2, 2, and 3.
The prime factors of 144 are 2, 2, 2, 2, 3, and 3.
The common prime factors are two times of 2 and one time of 3.
So, the GCF is 223 = 12.
For LCM:

The LCM is found by multiplying all prime factors of all numbers, but only counting common prime factors once.
So, the LCM is 22223*3 = 144.

[mystic saffron]

Thank you

What did I do wrong?

Oh nvm wrong answer wrong question

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[zinc coral]

i need helping finding the first derivative of y = sin(xy) using the implicit difference

[odd edge]

@zinc coral Has your question been resolved?

[tacit wasp]

Ok, LHS turns simply into y*'***, right? @zinc coral

[zinc coral]

yes

[tacit wasp]

Now, for the RHS you first need to use chain rule, and afterwards also product rule

[zinc coral]

so using chain rule, it would be

cos(xy) multiplied by x(y') + (x')y?

[tacit wasp]

Exactly

Now, x' is 1, do you agree?

[zinc coral]

yeah

[tacit wasp]

That's it, now you only have to rearrange stuff to get y'

[zinc coral]

alright lemme try it rq

alright

so its

cosxy(y) divided by 1-cosxy(y)?

[tacit wasp]

You should get this

[zinc coral]

alright thanks!

[tacit wasp]

Yeah, you've done very well 💪

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[rancid granite]

how should i approach this?

[willow zealot]

factorise the top

i surpose

actually

since you have the limit as x goes to 1

you want the (x-1) factor to cancel out

so you want (x-1) to be a factor of the top part

so use factor theorem

if F(a) = 0 then (x-a) is a factor of F(x)

where F(x) is a polynomial of degree 1 or greater

[rancid granite]

factor theorem?

[willow zealot]

yup

you shoulda learnt it way back

[rancid granite]

im sorry im kind of confused on that last part you said

[willow zealot]

but the idea is pretty simple

if (x-f) is a factor

then

you can write it as

(x-f)(other factors)

when x = f then the function will be equals to zero

ah a is a shit letter to use here

[rancid granite]

oh are you talking about

getting rid of (x-1)

?

because the limit approaches 1

[willow zealot]

thats the way for the limit to exist

yeah

you want the top to have the factor (x-1)

[rancid granite]

ok ok

hmm

could i divide the numerator by (x-1) somehow

[willow zealot]

you just want to find a such that the numerator has (x-1) as a factor

[willow zealot]

you could

[rancid granite]

idk why it's sideways

[willow zealot]

what are you trying here?

[rancid granite]

factoring?

[willow zealot]

why are you factoring 4x^2-4x though

[quartz oracle]

,rotate

[willow zealot]

if you dont know factor theorem your idea to divide numerator by x-1 is good

you can use long division for that

[willow zealot]

yeah

see what you get

then find a so that there will be no remainder

[noble forge]

well, you can just conclude that f(1) should be equal to zero

that should give you one value of a

remainder theorem imo is much efficient in comparison to long division

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[quartz oracle]

Can you send the entire original question?

(i) is right

[crisp wadi]

Looks correct

[earnest dagger]

.close

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[copper quarry]

How do I find the gradient of a time distance graph?

And what even is the gradient of a time distance graph

[tepid yacht]

The definition of gradient doesn't change, it's still the slope so find the slope

[copper quarry]

y2-y1/x2-x1?

[tepid yacht]

That is the formula for slope (terribly formatted though)

[quartz oracle]

and without parentheses

[copper quarry]

So I picked

()(0.2 - 0.16))/ (50 - 40)

[tepid yacht]

Those values are fine

[copper quarry]

Okay wait I’m gonna calculate it

[copper quarry]

I got 1/250

Or 0.004

[tepid yacht]

Sounds right

[copper quarry]

so what should i do then after getting this?

Hmm

.close

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[spare jewel]

Hello

[odd edge]

Please don't occupy multiple help channels.

[wooden python]

#help-14

!onechannel

[odd edge]

Please stick to your channel.

[wooden python]

.close

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[vast lodge]

2√2(5√2+3) yo guys how do I do this

[untold mist]

distributive property

nothing different

[quartz oracle]

you can distribute 2sqrt(2) over the sum

[vast lodge]

wait but like

do I do 2x5 or 2x2

[untold mist]

what

[sand night]

Bro does not know the distributive property

[vast lodge]

I separated into this(2√2)(5√2)

[untold mist]

what

wait

do you know what the distributive property is

[vast lodge]

do I multiply by the thingy inside the square root or outside

iknow but with squared roots idk how to do it

[untold mist]

a(b + c) = ab + ac?

[untold mist]

both

[vast lodge]

I dont do maths bro 😭

[sand night]

Ok start by just leaving the +2 until the end

Mutiply the first two things

[untold mist]

do you know surds at least

[sand night]

2√2(5√3)

[untold mist]

2

root 2 not 3

[vast lodge]

so 10 sqrt 10

[sand night]

.

What 2 times 5

[vast lodge]

10?

[sand night]

Yes

I meant sqrt 2 on both oops

[vast lodge]

so 10 sqrt 10

[untold mist]

no

not sqrt 10

[sand night]

What’s sqrt 2 times sqrt 2

[untold mist]

you multiply the roots together

[sand night]

What is 2 times 2 basically

[vast lodge]

sqrt4

[untold mist]

which is

[sand night]

Which is what

[vast lodge]

2

[sand night]

Yes

[untold mist]

now bring the 10 back (from 5 * 2)

10 * 2

[sand night]

Which

[vast lodge]

ohh so root times root and base times base

alr

[sand night]

2√2(2) now

@vast lodge ur not done

[vast lodge]

2√2(5√2+3)

its times 3

[sand night]

Oh it’s plus 3

[vast lodge]

6 sqrt 2

[untold mist]

good

[sand night]

ye

Now ur done

[vast lodge]

alr bois thx

[untold mist]

yw

[vast lodge]

now I js need to do it with fractions exponents and Im basically done

but yea i understand it now

[untold mist]

mhm gl

[vast lodge]

.close

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[shrewd sky]

Does 2/0 demonstrate a removable discontinuity or is it c

[weary pelican]

2/0 is "infinite" so not really continuous there

Or removable discontinuity either

[shrewd sky]

So 0 is not removable aswell?

[weary pelican]

Wait are you referring to 2 AND 0 or 2÷0?

[shrewd sky]

2/0

[weary pelican]

Which means...

[tender gulch]

Oh like when you plug-in?

[shrewd sky]

Yeah

[weary pelican]

When you plug in f(2)?

[shrewd sky]

Yes

[weary pelican]

Like I said, plugging f(2), 2/0 is "infinite" so not removable

[shrewd sky]

i understand

[weary pelican]

For 0, it's a different story

[shrewd sky]

wait is removable when there is a hole

[weary pelican]

Removable when there's a finite limit that can be added

So looks like a "hole"

Have you tried for 0?

[shrewd sky]

Yeah i get 0/0

[weary pelican]

Yes, but before plugging in 0

Keeping it in x form

x/(x²-2x)

Is there anything that can be simplified?

[shrewd sky]

Oh it becomes 1/-2

so it is e

[weary pelican]

What?

It's not the answer e

We've seen It's not continuous or removable for 2

[weary pelican]

For x=0 It's not defined originally because of 0/0

[weary pelican]

But it is removable because of 1/-2

[shrewd sky]

OH OK

so when you dont expand on it then its continuous

SO ITS A

And when you plug 2 in its infinite

[weary pelican]

Yep

Answer a

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[light widget]

Is having a leading 1 in every row enough to satisfy reduced echelon form?

[radiant merlin]

No

For the column of the leading one, all other entries must be zero

[light widget]

I fucked up then

This was the question

[radiant merlin]

This is what I get for the row reduced form

As you can see, the columns with leading 1 have all other entries turned to 0

[light widget]

Ugh

The thing is, I don’t know how it’s possible that I messed up

If the order of steps you do don’t matter

I must’ve done the arithmetic incorrectly

[radiant merlin]

If it's the reduced row echelon, then order doesn't matter because you always end up with the same matrix

If it's regular row echelon, it matters in the sense that it's not unique

[light widget]

there was a lot of negatives to cancel out some of the numbers

probably screwed up somewhere there

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[mystic saffron]

i dont get this

i dont get the division? ^

[nimble blaze]

what specifically about the division do you have an issue with

[mystic saffron]

i dont get why im dividing the thing im dividing i guess

[viscid flint]

the answer is essentially "because it gets us what we need"

[mystic saffron]

i understand but i feel like the numbers came out of thin air i dont quite undestand the rationale

(its my first time looking at addition formulae)

[viscid flint]

the rationale is that we'd like the formula for angle sum to be in terms of tan, since that's where we started

[mystic saffron]

okay

i dont know how to go about doing the division by myself

its very clunky?

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@mystic saffron Has your question been resolved?

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@mystic saffron Has your question been resolved?

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[mystic saffron]

im trying to prove something via proof by contradiction

[mystic saffron]

for all integers there exists a greater integer and there is no itneger between those 2

if we have a and its successor

so a and a + 1

by definition a < b < a + 1 where b in Z is not possible

but i dont know how to prove this

[low locust]

well what is your definition of integers

thats really what it boils down to

[mystic saffron]

thats all I have to do...?

[low locust]

what is your definition of integer

[mystic saffron]

a whole number

[low locust]

too imprecise

do you maybe have something like peano axioms?

[mystic saffron]

those are for nat numbers?

[mystic saffron]

Integers do not include fractions, decimals, or any numbers with a fraction

[low locust]

well yes and integers are defined as equivalence classes of pairs of natural numbers etc

so you can first prove it for naturals and then extend to integers

[mystic saffron]

we didnt learn about equivalence classes

[wooden python]

so then what did you learn

it sounds like you don't have a workable definition of Z

[mystic saffron]

like definition of sets, those tables for logic, proof stategies

[low locust]

if you dont know what Z is then you cant prove shit about it

[mystic saffron]

what am i missing?

[viscid flint]

a precise definition of the integers

[mystic saffron]

what is it?

[mystic saffron]

why is a whole number not ok

[viscid flint]

that's just another word for integer

[low locust]

what does "whole" number mean

you cant just define it by not being fractions etc

cause then you run into the problem of what these things are in the first place

[viscid flint]

you can probably make some kind of argument but it won't be precise and will probably be circular

[mystic saffron]

an integer is a fraction over 1 tho

[low locust]

proper fractions then. but that wasnt the point

[mystic saffron]

so is it good or bad to use the definition of integers?

because the contradiction is that a number cannot exist between a and a+1 because the integers are defined as not being fractions

so thus a < b < a + 1 is not possible

[low locust]

it is required to use a definition of integers

but what you gave arent precise mathematical definitions

[mystic saffron]

for the definition of integers?

[low locust]

you just gave me shit for calling integers not fractions btw

fractions are defined as quotients of integers

so we are back to the question of what they are

[mystic saffron]

Im not trying to be mean, im just genuinely bad at these things, sorry if i came across with poor taste.

[low locust]

(technically again equivalence classes of pairs of integers but whatever)

I didnt mean it as you being mean, sorry if you understood it that way. just noting it

but ok you said you knew peano axioms

yes?

[mystic saffron]

I looked them up

[low locust]

well ok then not

hmm yeah you cant really do anything here

call it obvious and move on

[mystic saffron]

Could i approach it with a < b - 1 < a?

[low locust]

no

[mystic saffron]

okay thank you for your help!

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[mystic saffron]

Non-repeating combinations
The number of combinations of n elements taken from k and k as well as groupings of the same number of elements is different, at least in one element, is calculated with the following formula:

Why are these two formulas for combinations without repetition equal. Can someone show me an example like when n = 5 k = 3

[mystic saffron]

Also in this example, why do you multiply 6 x 10, when the order doesn't matter
Example 1:
In how many ways can a commission composed of two men and three women be chosen from a total of four men and five women?
We choose: two men from a group of four men (C4) and three women from a group of five (C3).
• We calculate the number of five-person commissions that can be formed, composed of two men and three women:

<@&286206848099549185>

[odd edge]

@mystic saffron Has your question been resolved?

[leaden siren]

yess

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[shadow anvil]

does anyone understand how the 5 was simplified out in the final answer of the integral?

[low locust]

ln(something/5) = ln(something) - ln(5)

which is just another constant

[shadow anvil]

Ah I see, thanks

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[languid dew]

For the second line of the proof

why does the negative sign not apply to the i?

Ah I think I know why, because a^mn = a^m*n ?

[signal crown]

wdym

[languid dew]

So e^-itheta would that not be e^-(i)(theta)

hm I think I'm being stupid

I was going to say isn't it e^(-i)(-theta) but that's just e^itheta

So a^m(-n) = a^-mn?

[cold sage]

i mean, thats true, but whats your point?

are you asking why the - is specifically on the theta?

[odd edge]

@languid dew Has your question been resolved?

[languid dew]

nah I was just wondering how they could change the negative sign from the i to the theta

[cold sage]

-ab=a(-b), the order you do the multiplication doesnt matter here so you can move the -1 a and b into whatever order you want

the multiplication is commutative

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[languid dew]

Yeah thank you that helps

[languid dew]

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[wet wyvern]

How do I find the derivative of $-ln3(3^x)$

[clever fjord]

beautyiskeytosuccess

[cold sage]

you can express 3^x as e^(xln3) if thats easier to see how to differentiate, the -ln3 doesnt really matter since its a constant

just put it back after

[wet wyvern]

If a^x = (lna)(a^x) what does a equal?

[cold sage]

ln(a)=1, a=e

[wet wyvern]

Wait so what would the final answer be?

[cold sage]

i dont see how this relates to what was before

$-ln(3)\cdot 3^x=-ln(3)\cdot e^{xln(3)}$

[clever fjord]

AℤØ

[wet wyvern]

On my formula sheet it says to find the derivative of $a^x$ you have to do $(ln(a))(a)^x$

[clever fjord]

beautyiskeytosuccess

[cold sage]

no that would be the answer

$\frac{d}{dx} a^x=ln(a)\cdot a^x$

[clever fjord]

AℤØ

[wet wyvern]

Ohhh

wait no I meant because I’m trying to find the second derivative of -3^x and that is the first derivative

[cold sage]

$f'=-ln(3)\cdot 3^x$ then $f''=-ln(3) \cdot \frac{d}{dx}(3^x)$

oh wait sorry one moment

[wet wyvern]

👍👍

[cold sage]

is it (-3)^x or -(3^x)?

[clever fjord]

AℤØ

[wet wyvern]

It’s second derivative of (-3)^x

[cold sage]

i see, just need to rewrite it then one sec

[wet wyvern]

Kk ty

[cold sage]

actually

[cold sage]

if youre sure its this then the first derivative alone requires complex numbers

are you sure its not -(3^x)

[wet wyvern]

it’s probably that then bc we haven’t gotten to complex numbers yet

[cold sage]

aha, then yeah this is what you need

[wet wyvern]

Ohhhh ok thank you that makes sense to me now@

[odd edge]

@wet wyvern Has your question been resolved?

[odd edge]

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[somber rock]

Is $sqrt(

[somber rock]

Is $sqrt(3^0.6)

Do you multiply the square root number by three to get to the root of 6?

and the value inside is whatever to the power of 2

% the same as

[strong forum]

$\sqrt{3^{3/5}}$

[clever fjord]

Cxlyius

[somber rock]

Yes like that

[mystic saffron]

$\sqrt{3^\frac{3}{5}}$

[clever fjord]

Brandon H#1125

[somber rock]

$sqrt{3^{2/3}}$

[clever fjord]

0183x8204x1839x1047x1537

[strong forum]

wait 2/3 or 3/5

[somber rock]

2/3

[strong forum]

it can be rewritten as

[mystic saffron]

$c^\frac{a}{b} = \sqrt[b]{c^a}$

[clever fjord]

Brandon H#1125

[somber rock]

represent $c^\frac{a}{b}|$

[clever fjord]

0183x8204x1839x1047x1537

[somber rock]

as a value called

X

what if you square root X

[mystic saffron]

$\sqrt{x} = x^ \frac{1}{2}$

[clever fjord]

Brandon H#1125

[somber rock]

so $\sqrt{x} =\sqrt{ c^\frac{a}{b}}$

[clever fjord]

0183x8204x1839x1047x1537

[somber rock]

could it also be represented as $\sqrt{x} = { c^\frac{a}{2b}}$

[clever fjord]

0183x8204x1839x1047x1537

[somber rock]

right?

[quasi sparrow]

,tex .exp rules

[clever fjord]

riemann

[somber rock]

I understand

Just wanted to clarif

y

$\frac{a}{\frac{2}{4}}$

[clever fjord]

0183x8204x1839x1047x1537

[somber rock]

is equal to $\frac{a}{8}$

[clever fjord]

0183x8204x1839x1047x1537

[somber rock]

ty

.close

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[radiant shell]

how do i define a set in R^2 which is just all quadrants of the coordinate except for quadrant 4?

[radiant shell]

like does it have to be a union like $S = {(x,y) \in \mathbb{R}^2 : x \leq 0} \bigcup {(x,y) \in \mathbb{R}^2 : x > 0, y \geq 0}$

[clever fjord]

omgatriple

[radiant shell]

like it's just basically not the bottom right section

[weary pelican]

Well it can be simply an "or" statement

Quadrant 4 has x ... and y ...

[radiant shell]

i'm just trying to get a set definition to use it in a proof

[weary pelican]

yes

If (x,y) is IN quadrant 4, then what can be said about x and y?

[radiant shell]

x is positive and y is negative

[weary pelican]

yep

So the condition is of the form (A and B)

[radiant shell]

well it's basically the complement of that

[weary pelican]

So what's the negation of such a statement?

[radiant shell]

not a or not b

[weary pelican]

exactly

[radiant shell]

but how do i show that in a set definition

sorry im just new to this stuff rn

can i use logical or in a set definition?

[weary pelican]

$\vee$ is the logical "or", otherwise you can just write "or"

[clever fjord]

rafilou2003

[radiant shell]

so like $S = {(x,y) \in \mathbb{R}^2 : x \leq 0 \vee y \geq 0}$?

[clever fjord]

omgatriple

[weary pelican]

exactly

[radiant shell]

alr perfect thanks

.clsoe

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[winter breach]

The candidates A and B are the finalist for an award. A committee of 14 members will place their vote (in favour of one of the candidates) into a ballot box. Suppose that A receives 9 votes and B receives 5. In how many ways the ballot can be selected, one at a time, from the ballot box so that there are always more votes in favour of A. Explain your solution and print all such ways.

[sand night]

Uh

This might just be wrong

But if the majority has to be a

Then you could 14-8

Which is 6

And then total thing

2^6

[static totem]

what language

you make a recursive thing that builds a string and prints it

would be harder if it's like C

[winter breach]

mathematica

[static totem]

F

[winter breach]

I can just GPT it, but what's the soln to the probl

[static totem]

i'm not sure about how to count it

[winter breach]

https://en.wikipedia.org/wiki/Bertrand's_ballot_theorem

Isn't this problem that

[static totem]

looks like it

[winter breach]

A > B or p>q in the case of the wiki article

[static totem]

so you multiply the probability by (p+q) choose q

[winter breach]

not choose p?

13! / 8! - 13! / 9!

= 137280

[static totem]

choose p equals choose q

[winter breach]

surely they don't ask me to print all such ways

[static totem]

it's easy

except in mathematica

i've no clue how to mathematica

[winter breach]

137820 subsets?

[static totem]

i get 572

[winter breach]

can you show me your calculations

[static totem]

you're doing choose wrong

[winter breach]

show how you setup the soln

[static totem]

https://www.google.com/search?q=13+choose+8+-+13+choose+9

[winter breach]

Oh okayy

i wrote $\frac{13 !}{8 !}-\frac{13 !}{9 !}$

[clever fjord]

dgh

[winter breach]

i don't know why this should work

what does this calculate

does this not answer the question either

[static totem]

uh

it solves for the probability

if you multiply the probability by p+q choose q you get outcomes

[winter breach]

How many ways in total are there to draw all the ballots, ignoring the constraint?

14!?

[static totem]

yes

14 choose 9

[winter breach]

Why choose 9

[static totem]

you can;t tell the ballots apart

so 14! / 9!/ 5!

14 choose 9 is short for that

[winter breach]

According to the answer

It's 14!

[winter breach]

To this question

[static totem]

that's very dumb

[winter breach]

We are ignoring the constraint

That A should be strictly ahead

[static totem]

we have to guess if we can tell them apart, and common sense is that we can't, so they should have said it explicitly if they want 14!

[winter breach]

You mean with repetitions?

[static totem]

i assume it still works with the same solution

i don't know if i mean "with repetitions"

probably yeah

[winter breach]

asked in stackexchange

If we say {14!} = U (universal set), then we could use set theory to find the subset that contains all the votes where A > B, right?

[static totem]

so it's 24908083200 ways instead of 572?

i dunno it's dumb

[winter breach]

no that's just a leading question

to make me think

not the final answer or anything

[static totem]

it's the final answer, you multiply probability by 14!

it makes no sense to print so many

it makes sense to print 572

[winter breach]

,calc 4/14 * 24908083200

[clever fjord]

Result:

7.1165952e+9

[static totem]

no 14! is 87178291200

[winter breach]

Say there are 100 equally likely ways of doing something and you know the probability of meeting some condition is 3/4. Then how many ways meet the condition?

[static totem]

yeah

how many?

[winter breach]

,w 14! * 4/14

[clever fjord]

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Requested by dghf

[winter breach]

Let's see their answer

[odd edge]

@winter breach Has your question been resolved?

[odd edge]

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[shut mantle]

I don't understand

[tepid yacht]

Did you watch those videos I sent?

[mystic saffron]

when are they equal

do you know how to equate two things

[shut mantle]

yeah but they confused me more

[mystic saffron]

Look at this $=$

[clever fjord]

Brandon H#1125

[mystic saffron]

👉 =

[shut mantle]

look at what

[mystic saffron]

this

=

[shut mantle]

yes I see thay

that

[mystic saffron]

Use it for the problem

[willow zealot]

dont just shove an equal sign in their face with no explanation

[mystic saffron]

You have two sides of the $=$

[clever fjord]

Brandon H#1125

[mystic saffron]

you have two equations

put an equation on each side of the $=$

[tepid yacht]

Because those videos applied the same logic. The two equations you have are equal to y, therefore you can set the two equations equal to each other, like those videos

[clever fjord]

Brandon H#1125

[shut mantle]

3x+1=2x+6

[tepid yacht]

-2x

[mystic saffron]

those are not the equations the problem showed you

[tepid yacht]

You forgot a negative

[shut mantle]

the second video showed 2 examples which they did different ways for each example

[shut mantle]

wdym

[tepid yacht]

.

[tepid yacht]

.

You typed 2x

[shut mantle]

oh yeah

mb

3x+1=-2x+6

whats next

[tepid yacht]

Solve for x

Do you know how?

[shut mantle]

5x?

[tepid yacht]

That's not an equation

[shut mantle]

5x +1 = +6

[tepid yacht]

What should you do with that + 1 on the left?

[shut mantle]

move it to the other side which will make it a negative 1

[tepid yacht]

Then you have?

[shut mantle]

5x = 5

5÷5

= 1

[tepid yacht]

So x equals what?

[shut mantle]

1

wait It's 5

5x = 1

I think

[tepid yacht]

You know the x coordinate, you can plug that x value into either given equations to find y

[shut mantle]

ohh wait

[tepid yacht]

No

[shut mantle]

one sec

X

=

4

that's good right?

[tepid yacht]

Where did x = 4 come from?

[tepid yacht]

You have this

[shut mantle]

okay so

[tepid yacht]

What should you do to find x?

[shut mantle]

you replace the x with 1
3x+1
3(1)+1

=4

(1, 4)

[tepid yacht]

The equation is y =3x +1

Not just 3x+1

[tepid yacht]

But yes

That's the answer

[shut mantle]

so I'm finished

?

[tepid yacht]

.

[shut mantle]

tyyy

.close

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[odd edge]

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[lucid lily]

Hi

[fringe bough]

Hi

[lucid lily]

hi

[fringe bough]

Do you have a question or a problem you wanted help with?

[lucid lily]

I'm stuck man

I have an algebra eoc tmr

For algebra 1

And I don't know what to study

Because I don't know what type of questions will be on it

[tepid yacht]

Check the topics on your class syllabus

Study those

[lucid lily]

I'm no longer in algebra 1 it's a retake exam

Since that was 2 years ago

[tepid yacht]

The khan academy

Watch those videos, do the practice

[lucid lily]

Dang bro I have to sleep in and 1hr or 2 and I struggle bad with math and it's hard for me to really learn

[tepid yacht]

And algebra 1 is a lot of concepts, so better start studying then

[lucid lily]

Yea

Thanks tho guess ill go now that all I needed ig

[foggy mauve]

How is this not the right answer ;-;

I am confused

[quasi sparrow]

!help

[odd edge]

Please read #❓how-to-get-help

@lucid lily Has your question been resolved?

[odd edge]

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[chilly ridge]

This is the right Yes answer?

[rain tundra]

That is the criterion for a function

Each input gets mapped to exactly one output

I'm wondering why is Ursa Major a option

[chilly ridge]

They always be throwing a random ass choice

[rain tundra]

,w Ursa Major

[chilly ridge]

Like cheerios or some tomfoolery like that

[clever fjord]

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Requested by Normed#7467

[rain tundra]

LMAO

[chilly ridge]

Yeah

So itd be 4

[rain tundra]

Yeah

[chilly ridge]

Alr thanks

.close

[odd edge]

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[odd edge]

@chilly ridge Has your question been resolved?

[chilly ridge]

<@&286206848099549185>

[patent nimbus]

what do i do

[chilly ridge]

Wym

Oh for help

Confused on the options

[patent nimbus]

its dollars per year

[chilly ridge]

And what to put in the text box

[patent nimbus]

400

is that an option?

[chilly ridge]

I gotta type iy

It

[patent nimbus]

it decreases 400 every year

[chilly ridge]

Also this one is confusing:

[patent nimbus]

if x = 0 the point is 3
x=1 point is 5

x=2 point is 7

[chilly ridge]

Ah plug it in

[chilly ridge]

(3,0)

[patent nimbus]

0,3

[chilly ridge]

Or 0

Yea ty

[chilly ridge]

Top is 23 bottom is .02

[patent nimbus]

bottom 23 top 0.02

[chilly ridge]

Yea das what I meant

[patent nimbus]

i cant see the x intercept

[chilly ridge]

^

[patent nimbus]

Y=2/9X

[odd edge]

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[fast ivy]

im so lost pls 😭

o let me take the pic again

thank in advance 🙂

do i have to get the cub root of 27 and 125?

or would that be useless for a problem like this

pls anyone

[marsh elm]

It looks like it wants you to use the cube root formula

Which would use the cube root of 27 and 125

[fast ivy]

Oh

Wow i havent done that in a while

Ok thnx i do and show my work

[marsh elm]

Sorry, i mispoke, it isn't called the cube root formula. It's called the difference of two cubes.

[fast ivy]

Uh oh

so this one?

not good right

[marsh elm]

that's the formula

[fast ivy]

Oh ok perfect

i think i make a mistake

forgot to do 5^2 and put 25

[marsh elm]

yeah

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[odd edge]

@icy prairie Has your question been resolved?

[icy prairie]

<@&286206848099549185>

[icy prairie]

whatever i guess

.close

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[wooden python]

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[quartz gull]

hi im trying to figure out if ivt applies to this

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[viscid flint]

"empty set is a subset of every set" good, which one does that prove or disprove?

[odd edge]

@earnest dagger Has your question been resolved?

[viscid flint]

try it for some examples

like make up some sets A and B

ideally small ones

[wooden python]

you write "The empty set is a subset of every set."

[earnest dagger]

2 marks for one statement haha

i thought there would be like some equations or smth

[viscid flint]

no need for equations for that one

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[bold saddle]

Can someone explain what I'm doing wrong?

[mystic saffron]

Well the last line

For x > 2

Seems woefully wrong

[odd edge]

@bold saddle Has your question been resolved?

[bold saddle]

ah i see

it’s still partial tho

sorry my pc caught on fire had to switch to laptop

[mystic saffron]

Did you manually add that red dot at x = -1

Try removing it

It does say only add dots at breaks in the graph

[bold saddle]

no dots on x=-1

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[chrome zodiac]

please help

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[sand knot]

I need help w/ this

[sand knot]

I got till x^2 = -x^2+kx-k

2x^2-kx+k

aaaand im stuck.

[hoary marsh]

Derivatives?

[fallow tapir]

you see that is a quadratic in x?

[sand knot]

huh

[fallow tapir]

?

[sand knot]

wdym quadratic in x

[fallow tapir]

you know what a quadratic equation is?

[sand knot]

oh yes

[fallow tapir]

and is it one?

[sand knot]

looks like an equation to me

yeah ig so

[fallow tapir]

quadratic*

[sand knot]

yeah

[fallow tapir]

and both the curves are tangential

means they touch each other at a single point

[sand knot]

which means they touch at a coordinate but doesnt intersect

yeah

[fallow tapir]

so they have a single solution

[sand knot]

yeah

[fallow tapir]

the quadratic above has both the roots equal

do you understand that?