help-33

[trail cove]

its hella weird but like its like 1 proof ig

[tacit fjord]

implicit encouraged usage of chatgpt

is. bad.

[crystal lintel]

or encouraged responsible use of chatgpt

[tacit fjord]

sorry to deviate, split up what union.

[trail cove]

So here

I am shouldnt use words

but to complete the chatgpt proof i think i need to no?

[tacit fjord]

doubt.

which line are u referring to

[trail cove]

3rd

[tacit fjord]

x in A u B <=> x in A or x in B

does this help?

A \ B = A n B' (idk if u can use this)

[trail cove]

i dont think this is useful

[trail cove]

yeah but i cant use words

[tacit fjord]

that is all expressible symbolically.

what do you think cannot be.

[trail cove]

oh so i use ^

and the upside down on?

[tacit fjord]

well yes.

[trail cove]

yeah i just need to replicate the chat gpt proof

my brain is fried sorry

I dont get this

[tacit fjord]

whats 'this'

[trail cove]

step 5 to step 9

well actually i get 5 and 6

not 7 to 9 though

and i dont konw how to write this in a direct proof

[tacit fjord]

so do you not get the reasoning?

i take it or

get how to write them symbolically

[trail cove]

this

i dont get what its doing

i dont get the reasoning to write them properly

[tacit fjord]

have u got a better zoom for the gpt proof

[trail cove]

yep

[tacit fjord]

ok, so gpt aside

you understand

that to show X subset Y

the usual approach is

assume x in X

show x in Y

[trail cove]

yea

[tacit fjord]

right? I'm sure they're using this approach, although its convoluted

because the sets are not simple

right so theres this

[trail cove]

This is the claim btw

[trail cove]

Yeah

since it originally a complement

[tacit fjord]

and then demorgan turns this into a NOT X and NOT Y statement right

[trail cove]

yea

[tacit fjord]

x not in X and x not in Y

So the conditions at the beginning of 5 and 6

happen at the same time

and they want to combine this back into 1 statement

=======================
x not in X => P
x not in Y => Q

We now want to make a claim that goes
x not in X and x not in Y => ???????

=================

specifically, it looks like this
x not in X => C or D
x not in Y => E or F

======
so

(x not in X) AND (x not in Y) => (C or D) AND (E or F)

that make sense?

and then they are most likely distributing that AND over OR

[trail cove]

so if its not in X that implies thats its in C or D?

[tacit fjord]

oh, I mean C, D, E, F to be statements or propositions

[trail cove]

honestly i dont get this proof

[tacit fjord]

show what your symbols are for 1-4

[trail cove]

i havent written 1-5

only the beginning

[trail cove]

how would you state 5 and 6 in one step though

[tacit fjord]

tbh, are you able to prove that statement yourself (without following the chatgpt proof)

[tacit fjord]

(P => Q) and (S => R)

[trail cove]

maybe, i don't know set differences all that well, but other than that i think i could

[tacit fjord]

x in A \ B <=> x in A and x notin B

[trail cove]

yeah i get that

[tacit fjord]

well honestly - theres basically only one proof for this

its possibly worth just doing it yourself and then comparing notes

that might clear up some confusion

[trail cove]

ok ill try

is it ok if i @ u if i got more questions?

[tacit fjord]

yh

[trail cove]

@tacit fjord i dont think im dojng this right

[tacit fjord]

dont do a notin B

do not (a in B)

this is wrong, pretty sure.

same story, not convinced this holds

ur assuming rules for x in X transfer to x notin X, and thats not the case.

,,\lnot\lor\land

[tacit fjord]

you should be using these symbols

not or and

[trail cove]

ok

[trail cove]

whys that one wrong?

[trail cove]

yeah i didnt know for that

[tacit fjord]

write it out with logical nots, and u should see why it doesnt follow

[trail cove]

ok ill try again

[trail cove]

so you want me to write it with logical operators and not the union symbols and such

[tacit fjord]

well ofc u need the unions and setminus

and in

just dont use notin since that seems to be tripping u up

[trail cove]

so write it with complements?

[tacit fjord]

,,x\not\in X \iff \lnot(x\in X)

[tacit fjord]

i mean to say you should be using the right hand side notation

[trail cove]

oh that

i see

[tacit fjord]

to correct your mistakes in here

[trail cove]

ok imma eat first rq

[marsh citrus]

@trail cove Has your question been resolved?

[trail cove]

So to restate the complement i shoudl write $\lnot(x\in {})$

[elfin berry]

42

[trail cove]

Ok lemme do it and ill send an image

[trail cove]

Ok im messing up

[trail cove]

@tacit fjord this has to be wrong

I dont know how to work with rhe set differences

So if x is in A-B then x is in A, if x is not in A-B then x is in B

[trail cove]

@arctic hare can i get extra help

[marsh citrus]

@trail cove Has your question been resolved?

[trail cove]

.close

[marsh citrus]

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[solar crystal]

someone please draw the graph

i got this

[solar crystal]

this the question

[solar crystal]

this the asnwer

<@&286206848099549185>

<@&286206848099549185>

[marsh citrus]

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[solar crystal]

<@&286206848099549185>

[marsh citrus]

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[feral cloak]

Hi

[feral cloak]

How does sigma i = 1 approaching n for 3/n

becomes jsut 3

I thought you take 3 out

but then 1/n will just be 0

so it will end by being 0

[bitter solstice]

it's a sum not a limit

$$\sum_{i=1}^N \frac{3}{N} = 3$$

[elfin berry]

OssihLikesBlue

[bitter solstice]

Think about it, you split 3 into N parts and now you're adding it up N times

[marsh citrus]

@feral cloak Has your question been resolved?

[feral cloak]

Got it thanks

[marsh citrus]

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[fallen dagger]

how do i solve this using elimination

[fallen dagger]

i have no clue since it uses fractions

[vague jasper]

you know you can multiply both sides to get rid of fractions, right?

[fallen dagger]

wait whaaat

what do i multiply by tho

[vague jasper]

I mean both sides of the equation

[feral cloak]

just subtract the both equations

x/2 and x/2 will cancel out

and then just solve for y

[fallen dagger]

ok im actually concerned how i didnt see that

give me a sec

[feral cloak]

lmao It's fine it happens

[fallen dagger]

so i end up with y-3/3 = 1 and -(y+9) = 0

i know the number after the equal sign is 1

but how in the world do i subtract -(y+9) from y-3/3

[feral cloak]

no I meatn like

(y-3)/3 + (y+9) = 1

mulitply both sides by 3

y-3 + 3y+27 = 1

[fallen dagger]

oh

huh

i didnt know you could do that

or at least i dont remember you coudl do that

[feral cloak]

you can

it's an easier way of doing it

[fallen dagger]

am i supposed to multiply the 1

at the end

actually nvm ill just ask my teacher tmrw

.close

[marsh citrus]

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[marsh citrus]

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[lapis fjord]

Is my answer to question 3 rigorous enough

[marsh citrus]

@lapis fjord Has your question been resolved?

[marsh citrus]

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[lapis fjord]

.reopen

[marsh citrus]

✅

[marsh citrus]

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[marsh citrus]

@lapis fjord Has your question been resolved?

[marsh citrus]

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[still temple]

Hi, it says: If...., calculate.... Resolution:
why is this step done?

[past maple]

Which one?

[still temple]

the one that is in a circle

[past maple]

To obtain (sen^3 x + csc^3 x)². Since it equals sen^6 x + 2 sen^3 x csc^3 x + csc^6 x, they added 2 sen^3 x csc^3 x to obtain that number

[still temple]

ohh I get it
why 2 sen^3 x csc^3 x = 2

oh'

I get it

2(1) = 2

[past maple]

Yes

[still temple]

thanks for the help

👍

.close

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[still temple]

.close

[marsh citrus]

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[still temple]

how do i do this question?

[still temple]

i thought the limit would be zero but it is not?

my answer key says the left boundry for the inequality would be 0 but when i put that for the right on too it says its not 0

its (x-1)^2

if its looks confusing

[marsh citrus]

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[still temple]

<@&286206848099549185>

[marsh citrus]

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[still temple]

how do i do this question?

[still temple]

i thought the limit would be zero but it is not?
my answer key says the left boundry for the inequality would be 0 but when i put that for the right on too it says its not 0
its (x-1)^2

<@&286206848099549185>

[sly zephyr]

!15min

[marsh citrus]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[spark siren]

hmmm, 1 <= f(x) <= 6 -> 1/6 <= 1/f(x) <= 1, multiply by (x-1)^2 with x not equal1 will give you two inequalities, but the limiit for both would be 0, i guess.

[still temple]

why doesn't this work?

[spark siren]

how should i explain something what i do not know? who says, that this wont work?

explain why it should not work, then we can discuss it.

i say it works.

[still temple]

i dont know

the thing says its wrong

🥲

[spark siren]

who is the thing? and what does the thing exactly say?

[still temple]

it syas

you have to use squeeze therom

and the left bound it correct as 0

but the right bound is not

???

[spark siren]

this argument is a ontradiction. if the right bound limiit is not 0 the you cannot use squeeze theorem. that does not make any sense. sorry. can you post a photo?

[marsh citrus]

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[marsh citrus]

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[still temple]

Can someone please help me in #1155953228710674433 ? I need to make sure about something

[wispy harbor]

wait isn't this feix channel rn?

[still temple]

That's my username but idk what to say. I need help in #1155953228710674433 but got none yet

[sour shell]

yeah, we sent the message at the same time lol. Please help him first

[still temple]

What I need is a simple opinion if Im correct or not, I can do it. Thank you 🙂

This is what I need

@sour shell

@wispy harbor

How is that 100?

It can't be 100

@sour shell You there?

[sour shell]

Can't help ya with that XD

[still temple]

Why?

[ashen glen]

there isnt more info given?

wdym how is that 100

its an obtuse angle

[sour shell]

exactly my thoughts either

[still temple]

But it wont add up

[ashen glen]

what wont add up

[still temple]

The inside angles wont add up to 360.

C must be 100 too

a is 20

Lemme show you from the book

[ashen glen]

show me the full original question

[still temple]

Idek what to ask

There are like too many things that dont add up there

[ashen glen]

do they give you angle b?

the inner angle

[still temple]

No

[ashen glen]

ok hold on

[still temple]

What is given is only 100 and the 20

The others are just ink I put

[ashen glen]

inside angle b is 260

split the shape into 2 triangles

you get angle a is 20

angle b is 1/2 of 260 which is 130

you get that 1/2 angle c is 30

bc triangle angles add up to 180

[still temple]

So what is angle c then?

[ashen glen]

130 + 20 + c = 180

solve for c you get that angle c is 30 degrees for one of the triangles

or 60 for the full angle

[still temple]

Lemme see 1 more time

So what are the info you found?

What is c and b again?

[ashen glen]

hold on

im drawing it for you now

[still temple]

I just dont think the inner angles add up to 360

They didnt add up to 360

[still temple]

Shouldn't C be 100 though?

That's what confused me in the first place

[ashen glen]

C isnt the same angle

because the lines are different for c when compared to b

you can see that by the double line on the c lines

and the one line for the b lines

[still temple]

Oh so they're not identical to be the same

[ashen glen]

in the picture c looks like an obtuse angle

hold on

does it say if the picture is accurate?

[still temple]

I got confused because there was an excercise last year I had with a similar shape but the angle C was the same as the 100, but different angle degrees which I forgot

[still temple]

Idk what abtuse angle means. Lemme translate it so I understand it

[ashen glen]

i dont think c is the same angle

obtuse means its bigger than 90 degrees

[still temple]

Oh yea but it isnt then

[ashen glen]

i think my work is correct

[still temple]

But why did I think it was 💀

[ashen glen]

but the picture in the text book looks like its bigger than 90

im getting that c is 60 degrees

[still temple]

Wait, C in the textbook looks like abtuse

[ashen glen]

yeah bigger than 90

which cant be possible

[still temple]

💀 what do I do?

[ashen glen]

wait

yeah i think im right

[still temple]

Wait 1 min

[ashen glen]

i think this is correct

the lines for angle c are different from the ones for angle b

its different angles

i think the picture in the textbook isnt accurate i think its just to give a rough idea of the shape

[still temple]

It is over 90

It isnt 60

[ashen glen]

im 99% sure it is

does the problem say that the picture is accurate?

i dont think it was drawn to be accurate

[still temple]

What I can tell is that the angle that says 100 is not right. It must be 120 I think

[ashen glen]

so bro

that means

[still temple]

Info isnt accurate.

[ashen glen]

the picture is not accurate they just want you to solve it using the numbers they gave you

so my picture is correct

[still temple]

The problem says find the angles of the letters.

[ashen glen]

yes

thats the angles

[still temple]

But the angle that says 100 cant be 100

It is not 100

It's more

[ashen glen]

thats bc the picture is not drawn to scale

its just an example of the shape

they dont want you to measure the angle with tools they wanted you to solve it using math

[still temple]

That info problem happened only in this excercise. The others are correct

I have measured them

Probably a typo

Look

For it to be correct it has to be 120 or 140

Lemme check

UGH this is making me vomit

Lemme ask an AI

AI is no help either

@ashen glen you were right but...

C is not 60 degrees!!!!

It cant be 60 degrees

@ashen glen Do you have a protractor?

Does anyone in here have a protractor? I dont atm

It's night

[marsh citrus]

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[marsh citrus]

@still temple Has your question been resolved?

[marsh citrus]

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[unkempt tartan]

how can i solve for x

[old thicket]

i'd square both sides.

gives you: x^2 + x^(1/2) = 18

could be wrong.

[marsh citrus]

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[wooden grotto]

Could someone help review my problems and tell me if im on the right track?

[old thicket]

what's the middle symbol "|"?

[wooden grotto]

does not divide.

[marsh citrus]

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[wooden grotto]

.close

[marsh citrus]

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[echo folio]

How do we simplify (16+4t^2+1/4t^4)^1/2??

[echo folio]

We can't just distribute the power of 1/2 to all terms right

What should we do

[inland cape]

You can distribute the sqrt to each term

[floral linden]

you can distribute the square root into the numerator and denominator, but not to each term

are you sure the numerator is correct?

[echo folio]

Oh its actually (16+4t^2+0.25t^4)^1/2

to be clear

[inland cape]

Okay let’s ignore the root and try to factor

Maybe that will help

[inland cape]

Oh yeah mb thanks

[floral linden]

you can factorise this and make it a perfect square. The denominator is already a perfect square, so that's easy to raise to the power of half.

[marsh citrus]

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[stuck spade]

the question is confusing me

[marsh citrus]

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[full comet]

How to find the inequalties in cartesian coordinates

The shape is like icecream

or parachute

I believe

Something like this

How do I write the equation of the cone, and inequalities in a way that satisfies this shape?

[marsh citrus]

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[spark vale]

can someone help me w this

[marsh citrus]

Please don't occupy multiple help channels.

[waxen dust]

Why'd you make 2 channels 5 minutes apart

[marsh citrus]

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[scarlet schooner]

I need help with b

[stoic saddle]

,rccw

[stoic saddle]

!status

[marsh citrus]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[scarlet schooner]

2

[stoic saddle]

show work

[scarlet schooner]

i just started using guess and check from then

[stoic saddle]

1. 19 + x is not necessarily equal to 26+13+y
2. there is no guess and check needed here

[scarlet schooner]

oh then how should i solve it?

[stoic saddle]

the sample size is 100

so the median is the value between the 50th and 51st data point (sorted in ascending order obv)

you need both of those to be 2 hours

so 19+x must be at least 51

19 + x ≥ 51

[scarlet schooner]

oh so x must be more than or equal to 32

how do i check tho

[stoic saddle]

oh wait no hold on

sorry i misread the problem

you want the median to be 2.5 hours not 2

[scarlet schooner]

yeah

[stoic saddle]

this means that the 50th data point needs to be 2 and the NEXT one needs to be 3

so you were right and 19+x is exactly 50

[scarlet schooner]

oh yeah

[stoic saddle]

and x+y = 37 as you found earlier...

[scarlet schooner]

so y=6?

[stoic saddle]

yeah looks like it

[scarlet schooner]

how to check if its correct tho?

[spark vale]

my phone started glitching and it told me it closed

[marsh citrus]

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[modest ermine]

hi I'm a guy who recently discovered his passion towards mathematics but since I currently suck at math, I wanted a roadmap for my journey from chat GPT and they gave me this:

1. Arithmetic: Basic operations (addition, subtraction, multiplication, division), fractions, decimals, and percentages.
2. Algebra: Solving equations and inequalities, graphing linear equations, factoring polynomials.
3. Geometry: Properties of shapes (lines, angles, triangles, quadrilaterals), area and perimeter calculations.
4. Trigonometry: Relationships between angles and sides in triangles (sine, cosine, tangent).
5. Probability and Statistics: Calculating probabilities, analyzing data sets (mean, median, mode).
6. Calculus: Differentiation (finding derivatives), integration (finding antiderivatives).
7. Linear Algebra: Matrix operations (addition, subtraction, multiplication), solving systems of linear equations.
8. Discrete Mathematics: Logic and proofs, combinatorics (counting principles), graph theory.

Please note that this is a general overview and the difficulty level can vary for each individual based on their aptitude and prior knowledge in mathematics.

To earn a math diploma or degree at an undergraduate level or higher, you would typically need to have a solid understanding of all these concepts along with additional advanced topics such as:

9. Differential Equations: Solving ordinary differential equations using various techniques.
10. Real Analysis: Rigorous study of limits, continuity, differentiation and integration.
11. Abstract Algebra: Study of algebraic structures like groups, rings and fields.
12. Number Theory: Properties of integers including prime numbers and modular arithmetic.
13. Mathematical Logic: Formal systems for reasoning and proof theory.
14. Complex Analysis: Analyzing functions of complex numbers using techniques from calculus.

Is it valid? If yes could you modify

Opologies for making it so long and thank you for helping a fellow out

[cloud iron]

Looks like a pretty standard course sequence

Stuff gets crazy after calc and linear algebra because there’s so many different directions that math branches into

Also as a rule of thumb, never use chatgpt for actual math

[modest ermine]

yea

well thanks mate

is there any tip or advice for me?

[cloud iron]

Algebra, geometry, more algebra, trig/precalc, calc is the typical progression in american high schools, with stats thrown in randomly somewhere after algebra II

Myself in college then did calc, discrete, linear, abstract, real analysis but at that point in math education you can mix things up more

[modest ermine]

mm hm

thank you very much

[cloud iron]

What level do you currently find yourself at?

[modest ermine]

near noobie

[cloud iron]

Which math classes have you taken before?

[modest ermine]

school classes nothing more because i hated the subject back in the day

[cloud iron]

Look into some algebra and geometry until you have a solid enough foundation to move towards trig and precalc level analysis

Khan academy is a really good resource for a large variety of math courses (among other subjects)

[modest ermine]

thanks

[modest ermine]

that was what im looking for

[modest ermine]

sure thing

[cloud iron]

Check out Khan Academy’s Algebra I course, see what you already know and what you haven’t seen before

If you already know most of it, try geometry and Algebra II

[modest ermine]

ok

[cloud iron]

If you know that, precalculus or statistics

[modest ermine]

does it matter to choose which one (or even which one first?)

[cloud iron]

Statistics is sorta its own thing that you can start really anywhere after algebra II

If you get into data analysis you’ll want to be good with statistics and calculus, so looking into stats somewhere between algebra and calculus is good

[modest ermine]

for ai development which im learning that will be a good idea

[cloud iron]

I don’t know a whole lot of computer science but being strong in calculus and linear algebra I’ve heard are essential

statistics is always good in life in general

[modest ermine]

ai is the fancy term of statistics

but that was some good stuff you've shared with me, im grateful

.close

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[mild dawn]

how can this be true?

[mild dawn]

,rotate 180

[mild dawn]

if we take radius of the circle on the left, minus distance from core of both circles, minus again radius of the right circle, this will always be a negative number

that makes no sense to me

furthermore AGAIN this has to be wrong, m is supposed to be perpendicular to l, how isn't m then y = -1/x + 1 ?

[marsh citrus]

@mild dawn Has your question been resolved?

[mild dawn]

please just tell me if this is completely bullshit

it has to be wrong since m is not even perpendicular to l

but maybe i'm missing something

[marsh citrus]

@mild dawn Has your question been resolved?

[marsh citrus]

@mild dawn Has your question been resolved?

[mild dawn]

.close

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[gaunt locust]

Hello, I'm trying to find a curve in the realm of "as X approaches 0, Y approaches 0." Based off that curve given a domain 0 < X < Arbitrary number I can get a value between 1 and 0.

Purpose for this is programming the throttle of rocket as it's apoapsis approaches its target. But I'm having a hard time deriving something like this. My math level is PreCalc+AP Physics
Y is throttle and X is the difference between current and target Apoapsis.

[marsh citrus]

@gaunt locust Has your question been resolved?

[gaunt locust]

<@&286206848099549185>

[marsh citrus]

@gaunt locust Has your question been resolved?

[marsh citrus]

@gaunt locust Has your question been resolved?

[whole sleet]

y = x

[marsh citrus]

@gaunt locust Has your question been resolved?

[open relic]

Hello. Yes as Kaynex mentioned a simple equation y = kx satisfies that
y(0) = 0 and it can give you a number between 1 and 0 if you choose certain k

[marsh citrus]

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[noble cedar]

how to get this answer?

[noble cedar]

im confused how 7pi/6 turns into pi/6

[marsh citrus]

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[trim minnow]

Need help w partial decomposition...

[trim minnow]

will send photos

I just need help with the first step

i can integrate it fine but I struggle to decompose the fraction like writing A/x^2+1 + B/x+5

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

yo someone plz

ill be up a while so join when u can

i know yall are slammed rn

<@&286206848099549185>

<@&286206848099549185>

so does no one know how to do this either or what lmao

[floral linden]

the decomposition in the first one would be $\frac{2x+2}{1+x^2} - \frac{2}{x+5}$

[elfin berry]

nalin

[trim minnow]

so how though

is there a formula for this or something

[floral linden]

there isnt really a formula

you just have to see what works

[floral linden]

at least as far as i know

[trim minnow]

yeah but how did you know it was 2x+2 for the first one and 2 for the second

[zealous shuttle]

if there's a linear at the bottom then make it a constant at the top, A, if there's a quadratic at the bottom then make a linear at the top, Bx+C,

(12x+8)/((x+5)(x²+1)) = A/(x+5) + (Bx+C)/(x²+1)
12x+8 = A(x²+1) + (Bx+C)(x+5)
12x+8 = Ax² + A + Bx² + 5Bx +Cx + 5C
12x+8=(A+B)x² + (5B+C)x + A + 5C
match coefficients
A+B = 0
5B+C=12
A+5C=8
solving gives
C=2
B=2
A=-2

[floral linden]

yeah this is how i do it too

[trim minnow]

ahhhh ok

so since its x^2 as the first term in the denominator you do Ax+B

[zealous shuttle]

yea

[trim minnow]

so the second one would be A/x-3 + B/x+2 ?

[zealous shuttle]

however if its factorisable
like if its x²-5x+6 or something
then write it as linear products first, (x-2)(x-3), Ax+B and stuff is for non factorisable quadratics

[zealous shuttle]

yes

[trim minnow]

got it

if its factorable then you would do it the same was as the second one. break it down into 2 in the denominator then its just A/x-3 + B/x+2

[zealous shuttle]

yea like that

[trim minnow]

ok great

Thanks for the help

[zealous shuttle]

all good mate

[trim minnow]

@zealous shuttle @floral linden

.close

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[still temple]

In third line 10 with the power of -24 changed to 10 with the power of -23 how and why?

[humble pivot]

24.30 = 2.43 x 10. so you can write the multiplication as
(2.43 x 10) x 1.66 x 10^{-24}
then rearrange to get (2.43 x 1.66) x (10 x 10^{-24})

this is 4.0338 x 10^{-23}

(then they rounded)

[still temple]

Ohh thx

[humble pivot]

[still temple]

Another question can you Guess the language?

[humble pivot]

nope

[terse turtle]

thai innit

[still temple]

Damn thats right init

Thx for help

.close

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[mild dawn]

i am not sure how i can interpret x(t) = 0 to become the possible solutions for the first 2 steps of this answer

[mild dawn]

we take the inverse sin of both sides of the equation and then rearrange, i understand that

but how can i determine which values of t lie in the interval based on this

this would translate to

these two points

,rotate 180

,rotate

[mild dawn]

.close

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[boreal lintel]

hello

[boreal lintel]

is this correct?

[humble pivot]

Yeah. Probably dont need the last sentence

[boreal lintel]

oh okay.

thanks boss!

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[vivid cipher]

I wrote a proof for a problem in Spivak's Calculus and was looking for feedback on it. My main question I had was if my use of without loss of generality was appropriate. I was trying to express it doesn't matter if I started with 0<a or 0<b

[brisk scarab]

but don't u wanna have both a and b more than 0, simultaneously?

a and b are in P, therefore
a > 0
a + b > b > 0
i.e. a + b is in P

i think that completes the proof

[vivid cipher]

yeah i meant in the sense that the way i was trying to state without loss of generality was to express that it wouldn't make a difference if i started with

a>0 compared to b>0
a+b>b>0 b+a>a>0

is there a better way i could've phrased it?

[brisk scarab]

i don't believe u lose any generality even if you don't mention that phrase

also did u intentionally align these 2 b's!?

more importantly, if so, then how!

[brisk scarab]

i think honestly i would just start with whatever variable i want... it won't matter

[marsh citrus]

@vivid cipher Has your question been resolved?

[vivid cipher]

yeah i just manually used the spacebar

[vivid cipher]

when would it be appropriate to use without loss of generality?

oh i think i see it
is it because in this instance a>0 and b>0 , so there is no loss of generality?

[brisk scarab]

I would imagine when, for example, if u have two numbers and a positive difference between them, then you can write
x - y = d
assuming x > y without loss of generality.

in cases where it would actually matter which is the bigger number, as otherwise the difference will no longer be positive for above example...

I just feel like in our question here beginning with any case is really strictly the same so it doesn't matter at all

[vivid cipher]

thanks

[marsh citrus]

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[karmic forge]

can you help me with this question

[naive tundra]

Just multiply 3 by itself till u get 90

[karmic forge]

multiplied it until it became 81

[young sigil]

that is good

x is how many times you multiplied 3

[karmic forge]

alright

[naive tundra]

Yup

[karmic forge]

so it would be 3^4?

[naive tundra]

Or you could divide 90 by 3 then estimate it

Wait but u couldn’t actually get 90?

Because it doesn’t reach 90?

[karmic forge]

thats where im stuck

but at the same time. it says approximate, if that helps

[naive tundra]

Oh

So should it be in decimal?

Like the power?

What grade math is this😭

[royal blaze]

the answer is 4.095 i think

[karmic forge]

alright, and it needs to be to the nearest interger so its 4

[royal blaze]

ok

[karmic forge]

correct thanks

[royal blaze]

np

[karmic forge]

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[umbral python]

how is it not that

all I ddi was plugin 5 and then plugged in 5,1

and then found the average

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[past badge]

@arctic hare

[desert dirge]

poor helper, always being pinged

[marsh citrus]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[vagrant gull]

are you familiar with transformations rules?

[past badge]

I've never learnt it, my teacher just put it on

[vagrant gull]

Wdym just put it?

[past badge]

most of the answers i had to just guess

[past badge]

like no one in the class has learnt it

and its due in tmrw

[desert dirge]

you werent taught the stuff youre being tested on?

[past badge]

yep

[desert dirge]

strange

[vagrant gull]

,tex .transformation rules

[past badge]

exactly

[elfin berry]

Akira 🍉

[vagrant gull]

take a look at these

[vagrant gull]

you sure you didn't learn these things?

[past badge]

positive

learning about box plots atm

[desert dirge]

interesting

[vagrant gull]

yes horixontal translation right 6 units so which one do you think matches?

[past badge]

a or d right

OH

[vagrant gull]

close

[past badge]

wha

is it one of them?

[vagrant gull]

mhm but think about which one is right

[past badge]

a

[vagrant gull]

no

[vagrant gull]

look here again

[marsh citrus]

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[iron helm]

Can someone help me with this I don't have an available calculator at hand does someone know how to solve this and where I can find the correct calculator for this problem.

[stoic saddle]

http://desmos.com/

don't forget to put it in degree mode

[iron helm]

how do you put it in degree mode

[wet holly]

click on the tool icon

[iron helm]

thank you

[wet holly]

np

[iron helm]

so how do i figure out the answer

with desmos calculator

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[echo wagon]

@arctic hare How do I solve the problem: "too+too+spot what is the value of "t"" I don't even know where to start?

[marsh citrus]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[echo wagon]

.close

[marsh citrus]

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[stray edge]

I don't understand the last few steps here

take the example

6x ≡ 15 (mod 21)

gcd(6, 21) = 3, which implies there is a solution

can rewrite as 6x + 21y = 15

2x + 7y = 5

2x ≡ 5 (mod 7)

I can just quickly inspect a solution x = 6

but

the rest of this shit I dont understand

why is there d = gcd(6, 21) number of solutions

why are the solutions this weird ass form etc

[stoic saddle]

they basically tell you to solve this smaller-modulus congruence first and to then lift the solutions back up to mod 21

there's gonna be 3 of those

[stray edge]

why?

okay lets work generally maybe

i have

ax ≡ b (mod m)

if d = gcd(a, m) divides b

then i can rewrite my shit like

a/d * x ≡ b/d (mod m/d)

[stoic saddle]

6, 13, 20 in your example

[stray edge]

I understand the rewirting from here

but then im lost

[stoic saddle]

every residue k mod m/d lifts to d different residues mod m basically

k mod m/d corresponds to k, k+m/d, k+2m/d, ... k + (d-1)m/d mod m

[stray edge]

would u be able to use a bit different lanague like

idk what residues mean

[stoic saddle]

number

[stray edge]

would u be able to say that again like

with more english

also dont get this

a/d * x ≡ b/d (mod m/d)

i get to here and then I dont understand

wtf is all this x' shit comign from

[stoic saddle]

x' is the solution of the congruence (a/d)x ≡ c/d (mod m/d)

[stray edge]

yeah but why

is it not

x

😭

or is x' just a general solution

[marsh citrus]

@stray edge Has your question been resolved?

[marsh citrus]

@stray edge Has your question been resolved?

[marsh citrus]

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[west mango]

ans is B but dont know how to solve it

[drifting trout]

Have you learned about the quadratic formula?

If $ax^2 + bx + c = 0$, the solutions of the equation are $$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

[elfin berry]

thedude365

[west mango]

thanks

[drifting trout]

Of course

[stoic saddle]

do you know generally how to solve quadratic equations?

[marsh citrus]

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[frank orbit]

Question:

[frank orbit]

Is this diagram the same thing?

Cuz idk what I did, R=400

[marsh citrus]

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[frank orbit]

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[neat siren]

yo i wanna clarify some doubts, so i understand why asin(-x) = -asinx
acos(-x) = π-acosx
atan(-x)=-atan(x)
but I don't understand why acot(-x) = π-acotx?? π-A lies in the third quadrant and cot,tan are positive int he third quadrant then why does it yield a negative ratio?

[lofty fulcrum]

Even and Odd functions.

[neat siren]

elaborate pls

[lofty fulcrum]

An even function is where the function is symmetric about the y-axis, such that if we were to horizontally reflect it's position/orientation would remain the exact same. Picturize a parabola y = x^2. Its SYMMETRIC about the y-axis. Do not confuse the degree for functions being even or odd that is a common misinterpretation. f(-x) = (-x)^2 is the same thing as f(x) = (x)^2. Odd functions on the otherhand -f(x) = f(-x). Picturize a linear function about the y-axis. We know its not symmetric through observation.

Do NOT confuse even and odd functions with the power of a function this is a common misconception. The power of a function has nothing to do with even and of functions. The behavior on whether a function is symmetric.

[neat siren]

okay but i don't know what that has to do with inverse trig functions?

[lofty fulcrum]

it can be any function. Let me ask you this cos^-1 symmetric about the y-axis?

[neat siren]

yes it is

[lofty fulcrum]

Nope.

Its not symmetric.

[neat siren]

ohhh i thought you meant cosx not acosx

mb

yeah it's not symmetric

[lofty fulcrum]

mk, so because we know its not symmetric its demonstrating odd behavior, like the linear function y = x and so we would then use -f(x) = f(-x)

[neat siren]

mhm

sooo

i wanna know why acot(-x) is pi-acotx

you know that the trignometric ratios are defined by a circle and a whole rev is 2pi rad

pi-A where a is an acute is positive for cotA

[lofty fulcrum]

mhmmmm.

[neat siren]

wait uhh

nvm hold on let me get that correct

nvm bruh i got it now i was making a simple mistake

thanks for your help though i understood it a bit

.close

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[torpid wind]

how can i tell whats parallel and perpendicular?

[dry prawn]

What are the definitions of parallel and perpendicular that you're working with?

[torpid wind]

i'm taking geometry but i'm not sure if that helps

[dry prawn]

That doesn't answer my question

[marsh citrus]

@torpid wind Has your question been resolved?

[marsh citrus]

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[neat elk]

help. i only got the first two i dont know what everything else would be

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@neat elk Has your question been resolved?

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[rapid orchid]

**please help me out with this question **
For the transformation
x=e^(u)cosv
y=e^(u)sinv
show that (∂(u,v))/(∂(x,y))= e^(-2u)

[brazen meadow]

what is ∂(u,v) definition?

[rapid orchid]

it's partial differentiation

[brazen meadow]

I didnt take calc 2 completely yet 😓 sorry

then I dunno rly how to partially differentiate

[rapid orchid]

thank you for reaching out

**please help me out with this question **
For the transformation
x=e^(u)cosv
y=e^(u)sinv
show that (∂(u,v))/(∂(x,y))= e^(-2u)

[ancient slate]

So you want to calculate the jacobian, right?

[rapid orchid]

yes

[ancient slate]

What do you have so far

[rapid orchid]

im getting stuck at the determinant

[ancient slate]

I understand that, but I need to know where exactly

[rapid orchid]

∂x/∂u = e^u cosv
∂x/∂v = -e^u sinv
∂y/∂u = e^u sinv
∂y/∂v = e^u cosv
the partial derivatives that i got were these

[ancient slate]

Okay

and what do you get when you try to set up the determinant part

[rapid orchid]

putting it the matrix, hence the det
it should be e^u * cosv * e^u * cosv - (-e^u * sinv) * (e^u * sinv)

[ancient slate]

ok good

and what does that give you

[rapid orchid]

(e^u)^2 * cos^2 v + (e^u)^2 * sin^2 v

how do i approach the next step to prove it = e^-2u

[ancient slate]

wait a moment

you can still simplify that

[rapid orchid]

how so

[ancient slate]

think pythagorean theorem

look at the common factor

[rapid orchid]

1-cos^2 v?

[ancient slate]

$e^{2u} \left( \cos^2 v + \sin^2 v\right)$

[elfin berry]

TooManyCooks

[ancient slate]

i hope something is clicking by now

[rapid orchid]

oh yeaaaaaa

and with the recirprocal it just comes down to e^-2u

perfect

[ancient slate]

that's right. just use the inverse property of jacobians

[rapid orchid]

yesss thank you so much!!!!

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[nimble ridge]

Can anyone help explain this?

The last 9 calls to a customer support line had the following lengths (in minutes): 5, 23, 24, 25, 26, 27, 29, 30, 31. Which measure should be used to summarize the data?

the answer is median, but why median and not mean?

[cloud iron]

What are the mean and median of that data set?

[nimble ridge]

median 26
mean 24.44

[cloud iron]

Now just looking at the data set—forget about mean and median for a minute—what do you think would be a good ‘typical’ value of that set

Like if you called that customer support line having seen this data, how long would you expect to be on the call?

[nimble ridge]

whole number

[cloud iron]

Which number?

[nimble ridge]

26

[cloud iron]

Like would you expect to be there for closer to 20 or closer to 30

This is a weird example for this kind of problem because they are quite close, but in some cases you will get a mean and median that are very far apart

[stoic saddle]

i think that giving you the numbers is a bit misleading

the implication is that different sets of numbers would "call for" different summary measures but this imo is idiotic

it is probably more sensible to consider the SOURCE of this data

namely that they are call durations

and you as a customer probably care about the median (50% of calls take at least this long, and YOUR call has a 50% chance of taking at least this long) rather than the mean (a hundred thousand people called in and this is how many minutes the company's reps have spent talking to them in total)

[cloud iron]

In general, if you have a set with outliars on one side you’ll want to use median, because outliars have a big effect on the mean but a very small effect on the median

Typical wage is an example where you see median a lot—people talk about median wage more than mean wage because the wage distribution is generally very heavily skewed

Idk if you’ve done much with distribution skew yet

[nimble ridge]

the outliar that you talking about is 5 in my case right?

[cloud iron]

correct

[nimble ridge]

I get it

[cloud iron]

That’s what’s making your mean lower than one might expect it to be

Without the 5, your mean is 26.5

Without the 5, the median is also 26.5

So you can see how much that outliar effects each

[nimble ridge]

it doesn't matter what type of data it is, right? like (durations, money, temperature, etc)

[cloud iron]

Some data types generally exhibit more outliars than others but generally speaking yes this applies to any

Do you like celsius or fahrenheit?

[nimble ridge]

celsius in my country

[cloud iron]

So you record temperatures for five days and get this: 26, 27, 22, 25, and -3

Your mean there is 19.4, while your median is 25

25 would probably be a much better estimation for what a typical day that week was like

[nimble ridge]

I get your point

thank you sm

[cloud iron]

[nimble ridge]

.close

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[marsh citrus]

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[oblique cape]

So, I have some combinatorics homework and would love to understand why my attempt at an solution turned out so wrong. To the question:
A group consists of 10 women and 15 men. Calculate the probability that a random pick of 5 people will result in at maximum two women.
My failed attempt:
So my initial idea was to calculate the complemental to a maximum of two women which would be at least 3 men. To calculate this complemental probability I wrote down (C(15, 3)*C(22, 2))/(C(25, 5) which gave a very wrong answer. Am I missing something obvious here or does this simply not work?

[oblique cape]

<@&286206848099549185>

[sleek lake]

that's not the right complement, i would say "at most 2 men" would be the opposite
or "at least 3 women" maybe you just meant at least 3 women idk

but like, that doesn't help

the main problem is it simply doesn't work, you overcount the same groups

[oblique cape]

Yeah you now made me realise that my complement is just plain wrong

[sleek lake]

if from the start it asked for at least 3 men, (C(15, 3)*C(22, 2)) would count the same choice again and again

[oblique cape]

Wait I dont quite get that

How do I count the same groups

[sleek lake]

e.g. m1,m2,m3,m4,m5
if you choose 2,3,4 out of 15, and add 1,5 out of 22 you get that
if you choose 1,4,5 out of 15, and add 2,3 out of 22 you get that again

and again and again, every way to end up with 12345 is counted

[oblique cape]

Ooh now I get it

So this approach to these type of questions just doesnt work

[sleek lake]

yes

[oblique cape]

I have to split it up in different scenarios with 0, 1 or 2 women

Because thats how my teacher did it

[sleek lake]

yes, there's no alternative

[oblique cape]

Well thank you so much🙏

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[pallid agate]

what

[split atlas]

What part of the question are you having trouble with?

e.g. can you recall the definition of that crossed out circle (the null set), or what that big P means (power set)

or is whats stumping you is exactly how to apply the power set to sets

[pallid agate]

what does the cursive P mean

I think I was sick during the day the professor talked about that

[split atlas]

ah, got it, so:

The cursive P is the power set function: it takes in as input a set, and returns as output a set containing every possible subset of that input set.

So for example:

P({0,1}) = {null set, {0},{1},{0,1}}

[pallid agate]

ok

so is it option 4?

wait no

idk

[sleek lake]

it always has 2^n elements

4 in this case

also yes option 4 is right

[split atlas]

If you'd like a refresher on basic terminology this article might help: https://www.mathsisfun.com/sets/power-set.html

[pallid agate]

what is the difference between {null set} and null set

[sleek lake]

the brackets essentially

[split atlas]

{null set} is a set who's one and only element is the null set.

[pallid agate]

oh ok

[sleek lake]

so it's not empty

it has 1 element

[pallid agate]

so the {1} is a set whose only element is 1

[sleek lake]

yeah

[pallid agate]

ok

this is making more sense

my professor teaches so fast

and I am ADHD so

like half the stuff he teaches goes through my head

thank you for the help

👍

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[brittle cloak]

help plss

[marsh citrus]

Please don't occupy multiple help channels.

@brittle cloak Has your question been resolved?

[bright jay]

Don't open multiple channels, stay in #help-13

.close

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[pallid agate]

uh

what does the sideways U without the bar mean

[proper zodiac]

"is a subset but not equal to"

[pallid agate]

wait so what does the U with the bar mean

.close

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[restive sun]

subset but can be equal to

[marsh citrus]

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[devout mauve]

what do you think

[pallid agate]

uh

well

is it all 4

[sleek lake]

which one is dubious?

[pallid agate]

the 3rd one?

[sleek lake]

it's describing points on a circle

[pallid agate]

yeah

[sleek lake]

there's infinite points on a circle

[pallid agate]

oh