help-0

[fleet steeple]

how

[tight locust]

except you replace the 10s with 5s

[fleet steeple]

how does that work

[tight locust]

1234 (in base 5) = 1* 5^3 + 2*5^2 + 3*5^1 + 4*5^0

[glass lichen]

subtract off integer powers of 5 and the number of times you subtract them off is the digit of the number in that base

[fleet steeple]

125+50+15+4 does not equal 1010 tho

[glass lichen]

or you could just give him the answer and not let him think about it at all

[tight locust]

he wanted an example

[glass lichen]

where are 50 15 and 4 coming from?

[fleet steeple]

2

2*5^2

3*5^1

[glass lichen]

right, so the 3rd digit from the right is a 2

[tight locust]

this is 1234 in base 5, not 1010 base 5

[glass lichen]

cause you need 2(5^2)

[fleet steeple]

hmm let me try right in base 10, 1010

it would be 1*10^3 + 1 times 10^1

[glass lichen]

yes

[fleet steeple]

but i thought it had to be

1+2+3+4

[glass lichen]

and 0 lots of 10^2 and 0 lots of 10^0

[tight locust]

no. i was just giving you that as an example

[jade birch]

this is making my brain go reeeee

[tight locust]

this is right

[fleet steeple]

ok

so then what

we just subtitute?

[tight locust]

yes

[fleet steeple]

so it wuld be 5^3 + 5^1

[tight locust]

yes

which is?

[fleet steeple]

130

[tight locust]

congratulation

[fleet steeple]

but how did they know to write in base 5

[tight locust]

how many even digits are there

in base 10

[fleet steeple]

uhm in confused on what you are asking

[tight locust]

what are digits

[fleet steeple]

there are 2?

[tight locust]

0 1 2 3 4 5 6 7 8 9

in base 10 of course

[fleet steeple]

yuh

[tight locust]

now how many of those are even

[fleet steeple]

5

[tight locust]

right

[fleet steeple]

how do they coorelate the base 10 to base 5 tho

*not how do they get it from it

but how do they see it needs to be written from base 5

[tight locust]

because symbols are arbitrary. you could just as easily write 0,1,2 as you could a,b,c or !,@,#

so it's just replacing the symbol with a different symbol

[fleet steeple]

ok

what would a similarproblem look like?

[tight locust]

The increasing sequence 0, 5, 50, 55 contains all digits that are divisible by 5. The kth number in this sequence is 5050. What is k?

@solar mural go away

[jade birch]

lol

[fleet steeple]

so there are 1011 sequences

but we need to do something with it

wait

wait

nvm

there is not

there would be like 1003?

in base 10 that would be

10^3 + 3*10^0

so base 5 it would be

125+3?

128?

i probably did it wrong

[tight locust]

not quite

look at the sequence. how many different digits did i give you?

[fleet steeple]

4

[tight locust]

no

[fleet steeple]

wait

sry

6

[tight locust]

no

[fleet steeple]

:///

0,5 ,50, 55,

1 2 3 4 5 6

0 5 5 0 5 5

[tight locust]

how many DIFFERENT digits did i give you

[fleet steeple]

2

[tight locust]

yes

[fleet steeple]

so what do i do with that-

[tight locust]

so if you're counting with only two distinct digits, that means you're in

?

[fleet steeple]

base 10?

[tight locust]

base 10 has 10 distinct digits

[fleet steeple]

bas e2

base 1

[tight locust]

base 2

yes

[fleet steeple]

but how

0, 1

is base 1 right

[tight locust]

no

look at base 10 digits: 0 1 2 3 4 5 6 7 8 9

how many numbers are in that list?

[fleet steeple]

10

[tight locust]

yes

[fleet steeple]

ok

[tight locust]

so base n has n digits (you have to count 0)

[fleet steeple]

so base 1 = 0

digits

[tight locust]

eh not really

base 1 is a bit of an exception

in that you just use tally marks

like 111 would be 3

but don't let that confuse you

[fleet steeple]

ok

sorry this is taking so long, this is an entirely new concept

[tight locust]

ok

it's cool

[alpine sable]

are there any duplicates between 000001 and 999999?

[tight locust]

@alpine sable go away

[fleet steeple]

ok so

0, 5, 50, 55 end = 5050

k=?

so

written in bae 2

base 2*

so

what do i do next

5050/5?

1010

10^3 +1*10^1

so 2^3 +2?

that doesnt seem right

[tight locust]

no you got it

what's 2^3 + 2

[fleet steeple]

10

[tight locust]

good job!

[fleet steeple]

10 esems like a small number

[tight locust]

0, 5, 50, 55, 500, 505, 550, 555, 5000, 5005, 5050

[fleet steeple]

oo

ttyyyy

smmm

i understand nowww

[tight locust]

👍

[deft scroll]

hello guys

ill try to translate the quesiton i was igven to english

so 2.5 kg of steak for example, will cost 28.75 usd

thats brand A

brand B sells 12kg for 119 usd

how do i figure out how much discount i should give brand A for it to be just as cheap as brand B

i figured it out, but im 100% sure theres a smarter way that you guys know of...

[velvet pelican]

For 2 brands to give you the same value for money, you must have the price/weight to be equal

[deft scroll]

no?

it just has to be the same price per kg

[velvet pelican]

yes, the price divided by the weight have to be equal

so the price per kg is equal

[deft scroll]

yes.

how do i figure that out

how much % discount i should ive brand A so the price per kg is equal to brand b

cause my way took way too long

[velvet pelican]

What is Price/Weight for B?

[deft scroll]

12kg for 119 usd

[velvet pelican]

as a fraction?

[deft scroll]

bruh wdym, it is how its stated

u buy 12 kg for 199 usd

119**

[velvet pelican]

If you divide 119 by 12, what to you get

[deft scroll]

9.9166666

[velvet pelican]

Yes

[deft scroll]

the other is 11.5

[velvet pelican]

So if you divide Price of A by 2.5 you get the same thing

[deft scroll]

then i found the difference

[velvet pelican]

That's longer

[deft scroll]

no i get 11.5

[velvet pelican]

for them to have the same value for money, they both must be 9.91666

[deft scroll]

yes.

[velvet pelican]

So you need to find a price

that when you divide price/2.5

it gives you 9.916666

[deft scroll]

x/2.5=9.916666

jesus, thanks man

[velvet pelican]

Yes

welcome

[deft scroll]

why didnt i think of that

ffs

[velvet pelican]

And from the price you get the discount

[deft scroll]

u just divide the difference by the original price right?

[velvet pelican]

to get the %, yes

[deft scroll]

nice

thanks again

[velvet pelican]

welcome

[deft scroll]

got it set up nicely now lol

i hate showing work

[velvet pelican]

Yes, well done!

[deft scroll]

🙂 thanks, time for bed

cya

[velvet pelican]

cya

[thorn kindle]

What language is that

Spanish?

[velvet pelican]

[thorn kindle]

French?

Arabic?

[velvet pelican]

Not french or arabic

[thorn kindle]

How do you know

[velvet pelican]

I know a bit of french and how arabic characters look

[thorn kindle]

Wow

👏

😫

[velvet pelican]

Yes

now you have to find a non zero vector such that Mv = 0

where M is that matrix

v is your vector in R^4

and 0 is the zero vector in R^4

Essentially a system of linear equations

[thorn kindle]

What? Isnt (0,0,0,0) the zero vector

As opposed to the 0 scalar

[velvet pelican]

Yes

[velvet pelican]

I am representing it as 0

[thorn kindle]

Don't do that. It's misleading

The zero vector is a completely different thing from the zero scalar.

It's a vector

Lol!

[frank cave]

Consider a polynomial p(x) = a_0 + a_1 * x + a_2 * x^2 + a_3 * x^3 + ... + a_n * x^n + .... This is an "infinite polynomial.. Find the values of a_k such that p(0) = p'(0) = p''(0) = ... = p^k(0) = 1 for all k = 0, 1, 2. I know this is a power series but how am I supposed to find a_k?

[alpine sable]

Do you guys no decimals

[thorn kindle]

@frank cave differentiate the polynomial

[alpine sable]

Is anybody working in here

[frank cave]

ok so i found that a_0 = 1 right? @thorn kindle

cuz if u plug in 0 for x you just get a_0 = p(0) so a_0 = 1

if i differentiate the polynomial I get like $a_1 + 2 * a_2 * x + 3 * a_3 * x^2 + ... + (n * a_n) * x^n-1 + ...$ @thorn kindle

[ocean seal]

oof

[thorn kindle]

Yep

Now it has to be 1 when x is 0

[frank cave]

ohh wait.

ohh so all $a_k = 1$ basically

[ocean seal]

oof

[thorn kindle]

Im sorry

Keep differentiating and youll find the pattern

Because when you differentiate you get new coefficients

[frank cave]

ah ok lemme try that

so rn i have $a_0 = 0$ and $a_1=1$

[ocean seal]

oof

[thorn kindle]

a0 = 1, a1 = 1, a2 = 1/2, a3 = 1/6

Etc etc

In general:

a_n = 1/(n!)

[frank cave]

ah ok i see

Wait but let's say i have the same infinite polynomial but now the constraints are s(0) = 0, s'(0) = 1, s''(0) = 0, s'''(0) = -1, s^4(0) = 0, s^5(0)=1, and so on. If I differentiate, I get a_0 = 0, a_1 = 1, a_2 = -1/6 but I dont see any pattern @thorn kindle

[thorn kindle]

a_2 should be 0

because s''(0) = 0

0, 1, 0, -1/6, 0, 1/120

sin(pi/2 * n) * 1/(n!)

isn't that cool?

[frank cave]

how tf did u get that pattern so quickly

[thorn kindle]

the sine function OSCILLATES!!!

[frank cave]

o wow

pretty neat

thanks for ur help

[alpine sable]

i just wanted to make sure, does y represent what a slope field look like and y prime represents the slope at the point on the slope field?

[thorn kindle]

yep

[alpine sable]

k, thx

[thorn kindle]

sorry i still had my caps lock on

as you can see it's pretty amazing that the sine function OSCILLATES!!!

@frank cave so sorry

pi/2 *n

not pi/4

90 degrees, 1/4th of a circle. radians always mess me up.

it's off by a factor of 2

[frank cave]

got it thx

[slate narwhal]

Hi,
In what cases Tr(AB) = Tr(A)Tr(B) is true?
Does the fact of [A,B]=0 help in something?

[thorn kindle]

Why are you bringing stats into math server

Math is analysis and number theory not actual numbers

[paper temple]

If i have 2 points (-2,5) and (3,9) to find the magnitude is it the diffrence in the coordinates then pythag? or is it -2i+3i, and 5+j9j making i+4j

,rotate

[paper temple]

Question 3

[thorn kindle]

Yeah just find dy and dx and then take the arctangent of the ratio

That will give the angle of the vector up to the sign

[paper temple]

sorry is this in answer to my question?

[thorn kindle]

Yes

[paper temple]

why would i diffrentiate?

[thorn kindle]

Sorry

By dy and dx i mean the change

[paper temple]

havent done arctangent yet

[thorn kindle]

you should know what the arctangent is if you're doing vectors

This is first day trig

Not being rude, just honest

[paper temple]

oohhhh

inverse tan

sorry i had never heard of it be called arc tan you mean tan^1(

[thorn kindle]

yeah lol

[paper temple]

why do i need angle?

[thorn kindle]

wait do you need it in polar or rectangular?

[paper temple]

wait r we talking about q2 or 3

[thorn kindle]

3

[paper temple]

ok good

why do i need angle

[thorn kindle]

do you know what a polar form is

[paper temple]

no

[thorn kindle]

there's two ways to describe a 2D vector:

by horizontal and vertical position

[paper temple]

yes i and j

[thorn kindle]

and by magnitude and angle to the x axis

[paper temple]

oh

yes makes sense

so i cant really magnitude in i and j?

[thorn kindle]

no

i and j is rectangular (Cartesian) coordinates

[paper temple]

no as in a cant or no im wrong

[thorn kindle]

you're right

[paper temple]

ok so i have to convert to magnitude and angle

[thorn kindle]

no not really

find the dy and dx and divide by the length of the hypotenuse

this is called "scaling"

thus the hypotenuse becomes equal to 1

and the legs of the triangle are decreased in due proportion

[paper temple]

so divide both 5 and 4 by hyptoenuse

[thorn kindle]

yep

[thorn kindle]

yep

5/sqrt41 i + 4/sqrt41 j

[paper temple]

ok and thats the magnitude?

[thorn kindle]

no that's the unit vector

[paper temple]

ok so now

[thorn kindle]

the magnitude is sqrt(41)

which is the hypotenuse

[paper temple]

and multiple of them is parallel?

[thorn kindle]

yes it will be parallel

we scaled down the triangle so the lengths decreased and the angles will remain the same

[paper temple]

so the answer is just 5/sqrt41i and 4/sqrt41j

[thorn kindle]

yep

[paper temple]

ok thanks i defo need to read up on vectors

[thorn kindle]

vectors are just triangles.

literally

[paper temple]

yeh my teachers shit he just tells us stuff

like rather than showing the bigger picture

cos i is length j height hyptoenuse is pythag

yes mate thanks for asking

[queen wing]

Try thinking: 1/2 probability implies that it is most probable that both the scenarios of head and tails will be equally distributed.

b) and e) would imply that a probability of 1 to 0 is by comparison more prbable.

And b) and c) suggest a 3 to 4 probability for one of the sides, and a 1 to 4 probability for the other- You know also this isn't the case.

[alpine sable]

So I am trying to solve this equation but I keep getting 2 and its wrong...

[queen wing]

Do you know what the "|" are?

[alpine sable]

absolute value

[queen wing]

They make everything inside them positive

No

[alpine sable]

ya but two would still work because we aren't going into the negitives right?

[queen wing]

How did you re-write the equation without the |'s?

[alpine sable]

x+1+x-2=3?

[queen wing]

Read what I wrote again. In my third message I meant b) and c) are wrong, since the say the same thing inversely.

[alpine sable]

wait the -2 could be negitive right?

[queen wing]

I wrote d) again by accident

[queen wing]

Nothing within a | can be negative

[alpine sable]

oh

so what I wrote before would be correct

[queen wing]

|-10| = 10

The thing is, you need to keep the |'s because you still can't solve what's within them.

[alpine sable]

bruh I'm tryna solve this too, I hate absolute value

I think I am being scammed...

what

[queen wing]

@alpine sable I suggest you post your problem

[alpine sable]

no no I'm trying to do the same as Snezel

yeah with numbers it's easy, a bit harder with x

no but I wanna solve that too

and what I was saying is that you can't just remove the second absolute value and change it to x + 2 for example

ok so if x is less than 0 2 wont work right?

[queen wing]

You don't know if x is positive or negative

[alpine sable]

that's what I'm saying

it's not as easy as just inverting every - you find or something xD

so would it be something like -1<x<2

?

or x>2

no it wouldn't be <= to -1 we don't want it to be = to negitive 1 @final goblet

oh it would be positive nvm

thanks everyone!

not sure I understand his method xD

personally I'd divide it in three different cases

[queen wing]

Either |x+1| or |x-2| have to equal to 0

[thorn kindle]

Four

[alpine sable]

huh wouldn't it be - + and 0?

[alpine sable]

there's no interval where the second one is positive and the first one is negative I think

Should be like this

inside the rectangle

[alpine sable]

so?

[queen wing]

And the same x value that made one of the two a 0 will make the other one equal to 3.

And it can be more than 1 x value

[alpine sable]

mh I'm lost

[alpine sable]

why is this

[queen wing]

Try the equation with x = -1

Then with x = 2

[alpine sable]

oh ok

after that what would one do?

[queen wing]

The thing is, x = 1 doesn't work.

x = -1 and x = 2 are the only possible answers.

Oh, and x = 0

So, there are three possible solutions.

Two you find because they are the range of possible x values.

[alpine sable]

but why do we want them to be 0 anyway?

[queen wing]

One you find by trying the values in the middle

[queen wing]

Forget the way I tried to explain it.

It's just your way to find the range

Which gives you two of the possible values.

The third, you just find by testing integers within that range.

[alpine sable]

is the way I was doing it wrong?

[queen wing]

I can't figure out what you were doing.

[alpine sable]

I was trying to figure out when each of the two values was positive or negative

so that I could remove them in the correct way depending on the interval

like if in a certain interval they're both positive I'll just remove them and solve the equation as normal

[queen wing]

For that, you will realise that if you set x to a value that cancels out either of the absolute values, your result will be correct.

[queen wing]

Both what?

[alpine sable]

both the contents of the abs values

[queen wing]

Absolute values are by definition positive

[alpine sable]

I said the contents

aka x+1 and x-2

[queen wing]

Well, that is just the wrong approach

[alpine sable]

why?

[queen wing]

Because it doesn't work that way. You are interested in the left part of the equation being equal to the right part.

Nothing else.

[alpine sable]

what do you mean it doesn't work that way

I don't want to argue I just wanna understand

just to be clear

[queen wing]

Well, the concept of "I want to see when the values in there can be positive or negative" sort of sounds to me like it comes out of nowhere. There is no reason to be looking for that, instead of looking for what could be a range.

Which may be entirely positive or entirely negative, in some cases.

[alpine sable]

the reasoning behind it is that if I know that when the value is negative then I change the sign and basically transform |x+1| in -(x+1) and when it's positive I just leave it as x+1

[queen wing]

Still no need for that. Assessing the usefulness of the |'s gets us no closer to finding the answer.

[alpine sable]

I mean I'm telling you this because I'm seeing a video where this is applied

idk I guess it's wrong

the video is in italian but I think you can see what he does

[queen wing]

Qui li tratta individualmente per spacchettare meglio il problema. Questo ci sta.

[alpine sable]

plot twist

[queen wing]

(Sorpresa, sono Italiano anch'io)

[alpine sable]

top

[queen wing]

Vabbè, non so dirti altro.

[tight locust]

spaghetti

"Insanity is doing the same thing over and over again and expecting different results."

-Albert Einstein

try using curly brackets

,w determinant of{{0.8-a,0.5333,0.3266},{0.5333,0.8-a,0.0817},
{0.3266,0.0817,0.8-a}}

[ocean seal]

Results provided by WolframAlpha

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

Requested by EndTimes#8053

[tight locust]

lol i think it's the bot

actually go to the website, i think something's up with the API call

https://www.wolframalpha.com/input/?i=[[0.8-λ%2C0.5333%2C0.3266]%2C[0.5333%2C0.8-λ%2C0.0817]%2C+[0.3266%2C0.0817%2C0.8-λ]]

[thorn kindle]

please don't do this here

go to #bots

[alpine sable]

Can someone please explain when to use brackets, parenthesis, and infinity signs in this type of problem? I understand the math portion but I don't know when to add those things

[ionic jewel]

() means not inclusive, [] means inclusive, and you always use () with infinity or negative infinity

[glass lichen]

x has no lower bound, so it's anything less than 1 inclusive

[ionic jewel]

^

[alpine sable]

but how do you tell if its inclusive or not

[ionic jewel]

x is less than or equal to 1, so therefore it could be 1, so therefore it's inclusive of 1

so you get ..., 1]

[alpine sable]

so why is the infinity not inclsusive?

[ionic jewel]

infinity isn't a number so you always use exclusive

[alpine sable]

So a normal parenthesis will always be next to an infinity symbol? even if it's negative?

[ionic jewel]

yes

[glass lichen]

infinity isnt a number, so you can't equal infinity

hence exclusion

[alpine sable]

How can you tell if it's a negative infinity? that concept confuses the hell out of me

if its not a number how can it be negative

[glass lichen]

x<a -> (-inf,a)

[ionic jewel]

what happens when you keep making your numbers lower?

[glass lichen]

it just means you go towards -inf

[ionic jewel]

you keep decreasing forever

[alpine sable]

so if a is negative then infinity is negative?

[glass lichen]

no

negative infinity just means keep going down the negative side of the number line

like how positive infinity means go up the positive side of the number line

[alpine sable]

I got that but where in the final answer of the above problem determines if it's a negative or positive infinity

x is less then or equal to 1

[glass lichen]

the fact the inequality is x<=1

anything less than or equal to 1

less than

$-1\leq x \leq 1 \to [-1,1]$

[ocean seal]

moshill1

[alpine sable]

So what if it came out to x<=2?

[glass lichen]

you tell me

[alpine sable]

i dont know thats why i'm asking

[glass lichen]

$x\leq 2 \to (-\infty , 2]$

[ocean seal]

moshill1

[alpine sable]

I just dont get that because then couldnt the x coordinate be positive 1? thats not a negative number but it's less then 2

[glass lichen]

yes

it's all numbers less than or equal to 2

$1\in(-\infty , 2]$

[ocean seal]

moshill1

[ionic jewel]

ah yes bringing out the fancy math notation

i didn't learn the \in symbol until college

[alpine sable]

man this is so confusing, i dont get why this infinity is negative if it includes a positive number

[upbeat gorge]

Education has evolved rapidly for a long time now

[glass lichen]

the negative infinity just means the "lower bound" is negative infinity

[ionic jewel]

hey I'm not a boomer or anything

[upbeat gorge]

i never said that

[glass lichen]

$(-\infty , 2] = (-\infty , 0]\cup (0,2]$

[ocean seal]

moshill1

[alpine sable]

Okay i'm gonna try and do this next one and ill get your feedback on it

i got x <= 6

[upbeat gorge]

gj

Now express it in interval notation

[alpine sable]

so would it be (-inf,6]

okay so what would be a scenario that would make inf positive?

[ionic jewel]

$h(x) = \sqrt{x-6}$

[ocean seal]

bunny

[ionic jewel]

find the domain

[alpine sable]

x >= 6

[pearl wraith]

how how i convert square inches to square feet?

[ionic jewel]

yes, so what is the interval notation

[pearl wraith]

just divide by 12 right?

[ionic jewel]

144 square inches in a square foot

[pearl wraith]

oh so then i would take the square inches and divide them by 144 then

[ionic jewel]

if you want square feet sure

[alpine sable]

( inf , 6 ]

[pearl wraith]

so then this is incorrect

[ionic jewel]

also i gtg but for sacred assault the answer is ||[6,infinity)||

the smaller number is always on the left

[fickle dock]

Hey, I'm trying to solve this problem:

This is what I've tried so far to find the implicit derivative:

and in the end, ended up with this:

my question is, what do I do now?

I would assume I'd want the derivative to be 0, so I'd set y' to 0, but then I'd still have an equation with both x and y

[solar cradle]

The tangent lines should be at the points where the circle $$4x^{2} + 4y^{4} = 81$$ intersects the lemniscate

[ocean seal]

Billy Clintorus

[buoyant stump]

so, whats the chance of me doing something 12 times with a 1/3 of a chance for it to be different each time, and not getting it all 12 times

im not really too sure how to find it, its not homework or anything related im just curious

[elfin relic]

Yo how do I solve this

[solar cradle]

@buoyant stump Assuming I'm understanding your question correctly, it should just be (1/3)^12 which is about 1.88 x 10^{-6}

[alpine sable]

Does it matter which is u and dv in the integration by parts?

[manic quail]

Yes, it does.

[fickle dock]

@solar cradle thank you!! didn't notice that

[manic quail]

You get a different result, which isn't wrong, but it might not be helpful, if you choose the wrong u and dv, @alpine sable .

[alpine sable]

Then how should I pick the u and dv?

[manic quail]

if you try integrating $\int{\ln{x}dx}$ You must decide between setting $\ln{x}=u$ or $\ln{x}=dv$. One doesn't help you, the other one does.

[ocean seal]

veryhappyperson

[manic quail]

It always depends on the situation what you pick.

[alpine sable]

Thanks, any other specific situation I should know about like the lnx one?

[solar cradle]

@fickle dock no problem, happy to help! Do be careful, I just noticed I made a typo. It should be 4y^{2} not 4y^{4}.

[fickle dock]

yeah I just used the equation that I got and it seems to work, I just need to solve for x and y :)

[manic quail]

No, not really. As you do more integrals you get a hang of what to choose, @alpine sable .

[fickle dock]

on the graph it looks right tho

[alpine sable]

@manic quail alright, more practice for me then. Thank you

[elfin relic]

How to solve (it's been 15 minutes by the way) <@&286206848099549185>

[torpid estuary]

umm

i think ur supposed to ask

and wait 15 mins for an answer

not solve it for 15 mins then ask here then ping helpers 2 mins afterwards

[elfin relic]

I don't think I solved it, and I already waited 15 minutes and got no help

[torpid estuary]

oh sorry

but dont repost

also use an open help channel

not one in the middle of a convo

[elfin relic]

Alright sorry

[alpine sable]

This in use?

[mortal wraith]

does anyone know to to prove two quadrilaterals are congruent to each other?

[manic quail]

@alpine sable come question 6

[tight locust]

ok here's a question: is the function x^n sgn(x) smooth for n>=2?

[alpine sable]

,w is the function x^n sgn(x) smooth for n>=2?

[ocean seal]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by ⃟⃟#8027

[alpine sable]

Why isn't the total derivative of a function $\vec{f}:E \to \mathbb{R}^m$ unique?

[ocean seal]

fjd djf

[alpine sable]

Does it have to do with the fact that for a linear transformation A, A'(x) = A?

[latent thistle]

how do i calculate a line integral?

for a curve

thx ann for helping me on curve

need help with those 2

i understand how to do 1

<@&286206848099549185>

[untold warren]

need some quick help

assuming i is always a positive number are these 2 equations correct?

[untold warren]

<@&286206848099549185>

[coral pagoda]

Hold on.... i is never a positive number

I is the imaginary number

[untold warren]

not in this case

i is just a variable

its not supposed to be an imaginary number in my case

just think of i as x for now

[coral pagoda]

Are you dealing with summation?

[untold warren]

yeah I am eventually

this sort of stuff

[coral pagoda]

[quartz tusk]

Can anyone tell me how to find remainder of mixed fraction ?

They both looks right but surely they are not as there can be only one unique quotient and remainder

[tight locust]

quotient and remainder is a unique concept to integers

also

12/2 divided by 5

= 12/10

equals 1 + 2/10

i guess you could say that's the remainder

2

[vale wigeon]

@quartz tusk normally we don't speak of quotient and remainder when dividing two rational numbers. quotient and remainder are an integers-only thing

[quartz tusk]

@vale wigeon thanks

[cold mica]

i have an integrand of :
cos^4(theta)*sin(theta)

between 0 and pi and i have these 2 standard integrals given to me, i am not sure how i use them to solve it ? i don't think i can just multiply the two solutions together right?

[rocky cape]

YO.
How can I solve this equation ?
10x^2 - 7x - 12 = 0
We are allowed to use a graphics calculator in exams.
So the answer I got was : 3/2 and -4/5
So how can I work backwards from the answers ?

[latent thistle]

,w 10x^2 - 7x - 12 = 0

[ocean seal]

Results provided by WolframAlpha

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Requested by Elmo_AK47#8460

[latent thistle]

quadratic formuila

[rocky cape]

i got that thru graphics

How can I solve from answer backwards

[rocky cape]

oh ok

but what about just using the numbers from the answer

[latent thistle]

(x-(-4/5))(x-3/2)=0

@rocky cape solve for that

[rocky cape]

how

wdym

[thorn kindle]

=

[rocky cape]

hm

[latent thistle]

(x-a)(x-b)=0

a and b are x intercepts

[thorn kindle]

Ok.

[mystic sinew]

why are these 2 triangles similar

(the green one and the blue one)

[thorn kindle]

If their corresponding side lengths are multiples of each other

Similar triangles are those with their side lengths scaled up or down

Do what the problem says and you will see why they are similar

[mystic sinew]

reeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee, the corresponding side lengths are multiples of eachother for every single right angle triangle

we need to show that 2 of their angles are the same

right

and therefore all of them scale by the same thing between the triangles

[mystic sinew]

to find the perpendicular you need to show that these two triangles are similar tho

[thorn kindle]

Not for every right angle triangle

Only for similar

https://www.sparknotes.com/math/geometry2/congruence/section5/

[mystic sinew]

uh, I understand what you were trying to say but how do I prove that thye are similar ie that their angles are the same

^2 of their angles are the same

1s already there

[upbeat gorge]

The key is to show that each of the tiny triangles are similar to the big triangle

Through AA

[mystic sinew]

why is it that the other triangle is the same as the other in the other triangle

that is my question yes

[acoustic valve]

idk what the curvy thing means

[jade birch]

In mathematics, the intersection of two sets A and B, denoted by A ∩ B, is the set containing all elements of A that also belong to B (or equivalently, all elements of B that also belong to A).

[acoustic valve]

so B?

number letter number (A), number letter number (B)

so that they have the same proportions

actually yes im stupid i see now

wait no

double stupid

C

[zenith oyster]

I'm not sure how to even start this problem would anyone be able to help?

[tight locust]

solve for y

or just implicitly differentiate

[gleaming granite]

take the derivative using implicit differentiation then create an equation for the tangent line solve for the x and y intercepts and then sum them, substitute c in using definitions you gave for it before and if it ends up being c then it should be correct

[proud tendon]

??

[ionic jewel]

(x^2)/2+C

basic power rule, look up simple integrations rules

[thorn kindle]

Do a rayman sum

[ionic jewel]

reimann*

doesnt even work here

[white obsidian]

It's somewhere between. The proof is when your result works in the end. The "Ansatz" is more or less guessing at start - what pattern could match? With a bit experience you'll see what works, depending on the type of differential equation.

[cloud matrix]

why doesnt the value of det changes when we swap rows to columns

[white obsidian]

bc you just swap factors

[cloud matrix]

i mean

if we think of it as linear equations

oh cmon

[scarlet fox]

yo can someone help me out and tell me what should in the blank box

[white obsidian]

or write out both variants by hand, so you see the pattern

[cloud matrix]

3x + 5y

4x + 9y

if we swap rows and columns

3x + 4y

5x + 9y

[white obsidian]

so you get either (3 * 9) - (5 * 4) or (3 * 9 ) - (4 * 5). just swapped the sum within the factor.

[scarlet fox]

what's a set of 5 values for k? i tried like {7,12,17,22,27}

[white obsidian]

BUSY

[scarlet fox]

didn't seem to work

[cloud matrix]

but the determinant should be different since the equation is changed

[white obsidian]

*pardon i mean swapped the factor, not the sum, oc

[upper ember]

Thats not how it works

but this is a consequence of how determinants are

exactly

i am... wait no i typed something wrong

[stable pecan]

@cloud matrix , I would recommend you see 3Blue!Brown's Linear Algebra series to get an in-depth view of how determinants work

[cloud matrix]

I-

cannot do that immediately sir

[upper ember]

See the video about determinants only then

[cloud matrix]

Let me rephrase my doubt

[upper ember]

and see the whole series later

sure

[cloud matrix]

lets begin from scratch

[stable pecan]

I wasn't asking you to do it immediately. I was just suggesting you to watch it whenever you want

[cloud matrix]

yes, i will do that

but since i cant do that right now so it wont solve the problem im stuck with

anywho

what does a determinant tells about a pair of linear equations

[white obsidian]

it tells you the type of solutions

[cloud matrix]

yes seabird

so if we change the coefficients (swap) of the equations emselves, wouldnt its solution change?

oh wait

does determinant tells you about the number of solutions?

images/gifs/emotes arent loading for me

the articles you sent

im not qualified enough to understand that

?

[upper ember]

im as confused( if not more) as ramon rn

[cloud matrix]

you need to be banned

[upper ember]

its no mission for u, u can confuse me any time, well, anyone can

[cloud matrix]

if you actually tried to waste my timd

evrn more confusion

mope

not sure if ill follow

[cloud matrix]

im not sure what youre trying to do

[fading zephyr]

[cloud matrix]

thanks for all the assumptions you made

[fading zephyr]

what was the original question

[cloud matrix]

nothing

just move on

[fading zephyr]

doesn't seem they want help anymore, anyway

[gleaming granite]

ho lee sheet

this actually helped me visualize it hella well

[upper ember]

this is what 3b1b tells straightaway

[ionic jewel]

3b1b linalg is great

[gleaming granite]

what's 3b1b

[ionic jewel]

3 brown 1 blue

[upper ember]

3b1b=3 blue 1 brown

its a youtube channel

[ionic jewel]

this guy

[upper ember]

and i love it

[upper ember]

yup

[fading zephyr]

you really think so? i personally find his videos too heavily based on visualizing stuff, which makes things worse for me

[upper ember]

Visualizing is what makes it easy for me

[stable pecan]

It's my favorite yt channel.

[fading zephyr]

icic

[gleaming granite]

HE DOES

LMAOOOOOO

bruh

this wouldve been a life saver

[stable pecan]

I have never heard someone say that "visualising makes things more difficult" before

[upper ember]

I kinda realised after getting interested in maths that i have a good imagination

lmao

[upper ember]

it is one

why?

[fading zephyr]

because visualization can lull one into thinking concepts apply only to concrete scenarios

[upper ember]

that can happen, but u can also turn it around, maybe

So in conclusion,
Both, both is good.

[stable pecan]

I don't think so. Visualisation can also help one understand more abstract scenarios. 3B1B has a video on this too

[upper ember]

u are again beyond my understanding

shift back into a spectrum i can get

[upper ember]

Some people, dont understand, that this stuff is not trivial

lol

thats a lot? or less?

hmm

one week? doesnt sound so bad

Still not so bad

ohh

ok thats....getting into the territory of bad

i hope i will be able to relate to all this soon

Ohh

now im scared, i was gonna start with lang today, but now it seems that i might now be able to do it

am i supposed to know what all that is?

all in good time

yea, i realised that, coz if it was, i would have been so screwed

[vagrant sphinx]

Hey, trying to do probability on the chance that a person hits red on this colored dartboard, does the formula p = favorable outcome/sample space work for this?

[vale wigeon]

are we assuming the person's hits are uniformly distributed across the area of the dartboard?

[vagrant sphinx]

yes

[vale wigeon]

well okay then yeah just calculate the red area and the area of the whole dartboard

and then divide one by the other

[vagrant sphinx]

alright, awesome.

[onyx cargo]

Does it matter what direction vector I use to find my normal vector?

[fading zephyr]

you need two direction vectors to find the normal

you can use any two of them

[cloud matrix]

is this channel occupied

[fading zephyr]

the normal you get might point in the opposite direction, but it still works

[vagrant sphinx]

ok, how do I find the probability of hitting the bullseye hole thing.

with the same assumption as "We are assuming the person's hits are uniformly distributed across the area of the dartboard."

except not the dart board

but whatever this thing is called

[agile compass]

Area of the bullseye/area where you can hit

[vagrant sphinx]

oh wait right I forgot, the fact that it is a circle

doesnt matter

I can just do the same thing again

thanks

[formal zodiac]

$\int_\epsilon ^1 x^a dx =\Big|_{\epsilon}^1 \frac{x^{a+1}}{a+1} = \frac{1}{a+1} - \frac{\epsilon ^{a+1}}{a+1}$ it's this wrong? Textbook says it shoud be $$1 - \frac{\epsilon ^{a+1}}{a+1}$$ but why?

[ocean seal]

Cracknut

[vale wigeon]

are you sure your textbook says \textbf{that} and not $\frac{1 - \ep^{a+1}}{a+1}$?

[ocean seal]

Ann

[vale wigeon]

also the vertical thing with the 1 and epsilon should be on the right

[formal zodiac]

Вопрос при каких а интеграл существует, если что

[vale wigeon]

странно

так

давай-ка у вольфрама спросим

,w int[epsilon, 1] x^a dx

[ocean seal]

Results provided by WolframAlpha

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Requested by Ann#0413

[vale wigeon]

bruh

[formal zodiac]

Мне он тоже самое сказал (

[vale wigeon]

да там точно $\frac{1 - \ep^{a+1}}{a+1}$, при $\ep \to 0$ это дело должно стремиться к $\frac{1}{a+1}$, а не $1$, как в учебнике твоем написано

[ocean seal]

Ann

[formal zodiac]

Значит интеграл существует при всех а, кроме - 1, так?

[vale wigeon]

в смысле несобственный?

$\int_0^1 x^a\dd{x}$?

[ocean seal]

Ann

[formal zodiac]

Оригинально вопрос такой, да. Что значит несобственный?

[vale wigeon]

(пишется слитно)

неформально это интеграл от функции, которая плохо себя ведет в одном из концов промежутка (ну или в обоих, что уж там)

[formal zodiac]

Вроде бесконечности?

[vale wigeon]

сейчас полезу в вики за более точным определением

\

короче, вопрос был в том, при каких значениях a этот интеграл сходится

при a < -1 у тебя ε^{a+1} улетит в плюс бесконечность

так что сходимости не будет

[formal zodiac]

А, точно.

Thank you very much!

[vale wigeon]

yw

[sinful lintel]

Hello, I have a question about limits.
If I want to take the limit of a function on the boundary of its domain, would that limit be defined? Or would it not exist?

Example: Limit of sqrt(x) as x approaches 0.
As x approaches 0 from the right, sqrt(x) approaches 0.
But x cannot approach 0 from the left because that region is outside the domain of sqrt(x).
So does the limit exist?

[vale wigeon]

the limit does exist

when a point can only be approached from one side, the limit is equal to the corresponding one-sided limit

[sinful lintel]

Got it, thank you! Question answered

[rocky cape]

my limit also does not exist

i have infinite potential

[vale wigeon]

😒

[latent thistle]

based

[alpine sable]

[flat gust]

Make a table

Input (the terms) on one side

Output (the corresponding numbers to the input) on the other side

Find what is the pattern

[rocky cape]

Hey how can I solve this ?

2x-1 / 5 = -2x

[upbeat gorge]

Is this 2x-(1/5) or (2x-1)/5?

Either way multiply both sides by 5

[rocky cape]

2nd one

[upbeat gorge]

so yeah multiply both sides by 5

[rocky cape]

i used space between 1 and 5

[rocky cape]

oh why?

[upbeat gorge]

to get rid of the fraction

That way you can easily solve for x

[rocky cape]

so i always use the denominator number

[upbeat gorge]

For equations like these yes

[rocky cape]

5(2x-1)= -2x*5

[upbeat gorge]

as long as the denominator is a nonzero constant

[rocky cape]

What is that

[upbeat gorge]

You can cross-multiply without much issue

[rocky cape]

so 2x-1 = -2x*5 also works (cross )

[upbeat gorge]

so like 1, -3, $\pi$, $\sqrt{2}$, etc

[ocean seal]

CST

[upbeat gorge]

just not 0

since anything divided by 0 is either undefined or indeterminate and that’s problematic

[upbeat gorge]

Anyway isolate x and solve for it from here

[rocky cape]

ooh ok

yeah

[rocky cape]

oh alright.

x = 1/12

[upbeat gorge]

Ye

[rocky cape]

i see

thanks

for this

[alpine sable]

PLS ANSWER

[rocky cape]

3/8 = weight of all fruits individually

3/8 x 3 = 1.125

[alpine sable]

why 3/8

[rocky cape]

3/8 x 5 = 1.875

[alpine sable]

3/5 right

[rocky cape]

3 kg

3 kg divided by 8 fruits

[alpine sable]

why 8

[rocky cape]

Because that's all the fruits together

[alpine sable]

oh okay

[rocky cape]

ya

3 + 5 = 8

[alpine sable]

ok

[flat gust]

I hope you understand the process because when the test comes up you’ll be screwed.

It’s really important to know the process rather than the answer

[pastel jasper]

This might be more of a physics question, but my teacher used phi for an angle

but isn't it supposed to be theta?

or can both be used

[rich basin]

From a mathematical point of view there's rarely any semantics in simple labels like that, so you call an angle whatever you want, phi, theta, <CAB, "the actute angle", "cowboy bebop". I am not sure whether phi and theta have reserved meanings in physics though.

[rocky cape]

join the physics discord btw if u ever ask a more physics heavy question

[pastel jasper]

@rocky cape Already in it:) this server just seems more active and i felt like it was appropriate enough to ask here as well

@rich basin thanks

[rocky cape]

💯

yeah its far more active

[swift grail]

How am i supposed to obtain a straight line equation from the curve one in part c

[umbral sapphire]

.

[floral herald]

I have exams tomorrow but I can't seem to understand
Commission, Interest, Tax, Percent of Increase/Decrease

[thorny coral]

How do i do this?

[rich basin]

"half-way between" two numbers is just another way to say "average" of those numbers

[thorny coral]

So its 3.5/4.5?

[rich basin]

No

Do you know how to calculate an average?

[thorny coral]

You plus togther then divide by the number of numbers u added togther

[sand matrix]

help please! calculate the area of the triangle if every square is 10cm^2

[rich basin]

Yes, so $\frac{2}{3} + \frac{5}{6} = ?$

[ocean seal]

Roenbaeck

[rich basin]

@sand matrix Move to an unoccupied channel.

[sand matrix]

how do i know that

[rich basin]

Look at how long ago the last message was posted?

[sand matrix]

i have

thanks

[thorny coral]

9/6 so 1/ 1/ 2

[sand matrix]

1 1/2

[rich basin]

You need to divide 9/6 by 2 also.

[sand matrix]

hm

[thorny coral]

So then 4.5/3?

[sand matrix]

so 9/6 x 1/2 its 9/12?

9/12 RIGHT?

sorry caps

[thorny coral]

then 1 / 1 / 2?

[rich basin]

That's weird notation.

$\frac{9}{12} = \frac{3}{4}$

[sand matrix]

9/6/2 is just 9/6 x 1/2 which is 9/12 right

[ocean seal]

Roenbaeck

[thorny coral]

Ooh oke

thanks

[gusty oyster]

Hi, could anyone please help me
What happens to this equation when q approaches 1

$$(xp^\frac{q-1}{q} + (1-x)z^\frac{q-1}{q} ) ({p^\frac{-1}{q})$$

[ocean seal]

màe
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[gusty oyster]

I got 1/p

But I should get p

[rich basin]

$(xp^0 + (1-x)z^0 ) (p^{-1}) = (x + 1 - x)p^{-1} = \frac{1}{p}$

[gusty oyster]

Yes I got 1/p too but it should be p

[ocean seal]

Roenbaeck

[gusty oyster]

Maybe I should stick with 1/p then

Thank you!

[rich basin]

Well, what you wrote simplifies to that. You sure you wrote it correctly?

[gusty oyster]

Yep, I hope i took the 1st derivative correctly

[tame trellis]

This may be an easy question for me to ask but I don't know how to calculate odds yet

[rich basin]

What was the original expression?

[tame trellis]

What would be the chance of getting four 1% odds within 10 attempts?

This question is really making me struggle

[rich basin]

@tame trellis Read #❓how-to-get-help and move your question to an unoccupied channel.

[tame trellis]

Oh ok sorry

[rich basin]

No worries.

[gusty oyster]

$$ [x p^\frac{q-1}{q} + (1-x) z^\frac{q-1}{q}] ^\frac{q}{q-1}$$

[ocean seal]

màe

[gusty oyster]

I differentiated it w.r.t p

And got

$$ \frac{q}{q-1}[ x p^\frac{q-1}{q}]^\frac{1}{q} . [x \frac{q-1}{q} P^\frac{-1}{q}$$

[ocean seal]

màe

[rich basin]

,w d/dp f(p) = (x p^((q-1)/q) + (1-x) z^((q-1)/q))^(q/(q-1))

[ocean seal]

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Requested by Roenbaeck#4166

[gusty oyster]

Oh

Yes I got the same thing

[gusty oyster]

Forgot to add Z

[rich basin]

Hmm... but

,w x p^((q - 1)/q - 1) (x p^((q - 1)/q) + (1 - x) z^((q - 1)/q))^(q/(q - 1) - 1), q = 1

[ocean seal]

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[rich basin]

Are you supposed to do a limit?

[gusty oyster]

Yes

As q approaches to 1

[rich basin]

,w lim_(q->1) x p^((q - 1)/q - 1) (x p^((q - 1)/q) + (1 - x) z^((q - 1)/q))^(q/(q - 1) - 1)

[ocean seal]

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Requested by Roenbaeck#4166

[gusty oyster]

Huh

[rich basin]

That's nowhere close to just being p though.

[gusty oyster]

:(

Alright

Thank you so much!

[rich basin]

Did we actually achieve anything by this?

[gusty oyster]

Um, yes the answer should be x/p and not xp

[edgy cape]

Is there some sort of trick to correctly simplifying trig functions before integrating them because I manage to perfectly mess up each time i try

[ancient bear]

Just identities

Learn identities by heart (flashcards or something) and practice them a lot till your brain notices them automatically, that's p. much the only 'trick' there is

[edgy cape]

i know my identities but I tend to go off on a tangent trying to simplify the incorrect way and always fail to see the simpler method

[unborn hull]

Anyone here doing stats?

[zinc ridge]

@unborn hull 🙋‍♂️

[brazen shuttle]

hi

I got this and in book it says

we multiply everything with

$z^2 and get z' = 4x + 1$

[ocean seal]

dervaa_

[knotty trail]

Question 4

The answer is 2

But it makes no sense

Is it possible if someone showed me their working?

<@&286206848099549185>

[manic quail]

have you tried creating a sketch?

wait, now I get the confusion. $x=\pi$? xD

[ocean seal]

veryhappyperson

[manic quail]

,w plot y=cos(x+pi/4) and x=pi

[ocean seal]

Results provided by WolframAlpha

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Requested by veryhappyperson#1152

[rich basin]

It makes sense.

The answer is 2.

[manic quail]

Isn't that just integrating the cosine then?

[rich basin]

Note that the "area bounded by" means total area, regardless of it being below or above the x-axis.

[knotty trail]

So...

[rich basin]

Just integrating between 0 and pi won't work, since it will cause the area below to be negative.

[knotty trail]

Oh

So what do you do

[rich basin]

,w integrate abs(cos(x + pi/4)) between 0 and pi

[ocean seal]

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[manic quail]

I cannot read

[rich basin]

Either that, or you make two cases.

[knotty trail]

So you integrate from 0 to pi instead?

Or nah

You have to split

But after splitting I got this

[velvet pelican]

There should be 3 splits

[knotty trail]

Ph

Oh

But there's only two if I put up the graph

[rich basin]

,w plot cos(x + pi/4) = 0 between 0 and pi