help-23

[brave wolf]

and that's row number 4, column number 2

(if we start numbering from 0, otherwise just sub 1 from the input)

$f(n, s) = \frac{(n-1)!}{(s-1)!(n-s)!}$

[flat frigate]

MæthIsAlwaysRight

[brave wolf]

this would be that function

[misty abyss]

2 3 is not even in pascals triangle it gives 21

[brave wolf]

Could you give some example input - output pairs

[solid shell]

That math was a translation of the code you had, not saying whether it was right at all

[misty abyss]

i didnt have the 2n in there it was
(n+s)! / (n!s!)

[brave wolf]

but you set
s := s + n

[solid shell]

You had s += n

Which is where that came from

Every s became (n+s)

[misty abyss]

oh i forgot to remove that that was a try at correcting the numbers

i want like
f(n, s) is the number in the s th number in the n th row

[brave wolf]

what should f(4, 2) be?

[misty abyss]

3

[brave wolf]

$f(n, s) = \frac{(n-1)!}{(s-1)!(n-s)!}$

[flat frigate]

MæthIsAlwaysRight

[brave wolf]

this could work I think

[misty abyss]

im not sure on the +-1 on the inputs im first trying to get the correlation right
not sure where to index from

[brave wolf]

,calc 3! / 1! / 2!

[flat frigate]

Result:

3

[brave wolf]

this should be the indexing you want

(now it starts counting from 1)

so e.g. f(5, 3) should give 6

[misty abyss]

it works thx

.close

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[stiff bobcat]

stop spamming.

[safe radish]

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[heavy pawn]

Can someone explain to me why in this Stoke's Theorem problem, when I change the capping surface to be the flat rectangle I get an answer of -2, when the correct solution (and solution you get if you dont change the capping surface) is +2? (The image contains my work, but I can share the soltuion aswell if necessary)

[plucky elk]

Yea just show it

[heavy pawn]

soln

they are using a slightly different method to me as this is from a seperate school

[plucky elk]

What does "change capping surface" mean?

[heavy pawn]

like, using a different surface S which has the same boundary curve C to simplfiy the calculations

[plucky elk]

I fail to see why you think they should have the same value double integral when the boundaries dS and dS' are different

[safe radish]

@heavy pawn Has your question been resolved?

[heavy pawn]

Based on this

[plucky elk]

You changed C. The surfaces in the image here did not

[plucky elk]

Yours is in the xy-plane

[plucky elk]

The one in the question is not

z=x^2 is most certainly not in the xy plane

[heavy pawn]

yes thank you

I mixed up D and C, because D is the projection onto the xy plane (atleast in my course) so the D is the same, but the C is the surrounding curve

thank you for the help

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[cursive slate]

Hello help me with 4 questions

[junior raven]

,rotate

[cursive slate]

I lost my notes

[junior raven]

seems like the answers arw there

whats your question?

[cursive slate]

Ye but I gotta show work

How do I solve for the premiere

Perimeter

[craggy falcon]

perimeter of what?

[cursive slate]

For question66

[junior raven]

the ratio of the perimeters is 3/4

[cursive slate]

Yes

[junior raven]

12 x (3/4) is the working

[cursive slate]

Interesting

Thank you for question 66

Now for my next question

Do I do the same for Weston 67

Question

[junior raven]

the ratio of the side lengths is 2/5

find the ratio of the area

[cursive slate]

How 😔

[junior raven]

how do i find area from side lengths?

how would the ratio of side lengths be connected to the ratio of areas

[cursive slate]

Similar shapes?

Idk

[cursive slate]

Come back

[junior raven]

the ratio of area is the square of the ratio of side lengths

[cursive slate]

Wait pausse

I understand snow

It now

Okay nvm

[cursive slate]

I don’t understand man

[junior raven]

what do you understand by similarity

[cursive slate]

That they are similar

[junior raven]

okay

that means nothing

[cursive slate]

Okay thank you

[junior raven]

what does it mean

when things are similar

in math

[cursive slate]

They have the same shape and are alike

[junior raven]

somewhat there

it means all the sides are connected by a ratio

[cursive slate]

Sighs

Thank you

[junior raven]

the area of shapes are connected by the squares of the side lengths

so the ratio of areas is the square of the ratio of side lengths

[junior raven]

the ratio of area is 4/25

[cursive slate]

Why 25

[junior raven]

becayse

(2/5) squared

[cursive slate]

Oh yeeeeeee

That’s the one I’m supposed to be squaring

So do I like mutilplebit by 40

Pls come back

[cursive slate]

Come back

😢

[junior raven]

the ratio is 4/25

the smaller area is 40

find the larger area

[cursive slate]

Oh greater intelligent being please grace me with a hint

🙏

[junior raven]

what multiplied by 4/25 gives 40

[cursive slate]

I see

250

[junior raven]

yes

[cursive slate]

So are you okay with helping me with other questions

Put a thumbs up if yes put a thumbs down if no

Okay thank you 😊

.close

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[junior raven]

if you need help just ask

[safe radish]

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[viral bloom]

Among the Z complexes such that | z + 1 + i | = 1, determine the maximum modulus z

[safe radish]

@viral bloom Has your question been resolved?

[viral bloom]

<@&286206848099549185>

[devout scroll]

so basically you have z is on a circle around (-1,-i) with radius 1

use that

[viral bloom]

I'll try, thanks

[viral bloom]

I understood what you meant, I think I managed to make the circle, but I don't know how to get the maximum z module with this information.

[devout scroll]

so you want the point on the circle farthest from the origin

[viral bloom]

would it be like that?

[devout scroll]

no

the circle is arounf -1-i

[viral bloom]

I can't imagine that, srry

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[gaunt coyote]

im just confused on why this method works

[thin bridge]

remainder theorem

[gaunt coyote]

f(x) divided by x-b=f(b)? i dont see the application here

like i dont see the connection

[thin bridge]

remainder is given be f(b)

and you know the remainder is 4

so you're looking for values of b where
f(b) = 4

i.e. what values when plugged into the function gives 4

[gaunt coyote]

oh ok

[gaunt coyote]

wait so can u restate the remainder theorem in this form then

[thin bridge]

remainder when f(x) divided by x-b=f(b)?
and f(b) = 4

[gaunt coyote]

ohhh nvm i get it

[gaunt coyote]

im making a concept sheet for my final exam tmr, how would i best word this?

If f(x) is divided by x-c, f(c) is the remainder (plug in numbers where f(c) is the remainder in the polynomial)

this is what i have currently

[thin bridge]

yeh

could copy a definition directly from online

make sure to also mention polynomial f(x)

[gaunt coyote]

If a polynomial f(x) is divided by x-c, f(c) is the remainder (plug in numbers where f(c)= the remainder in the polynomial)

is that better?

also another general question @thin bridge hope u dont mind

how does a 3 or 4 level fraction work?

like ive seen stuff like tan=sin/cos

but wouldnt that be four different things

[thin bridge]

wdym

[gaunt coyote]

like tan=sin/cos and sin(30)=1/2 and cos(30)=√3/2

or wait

so how would 1/2/√3/2 work?

or would you just multiple the recipricol of the second fraction?

[thin bridge]

you pay close attention to the order of operations

and represent that by making fraction lines as long as required and using sufficient parentheses

[gaunt coyote]

could you give me an example?

[thin bridge]

and you can apply reciprocal rule to that

[gaunt coyote]

and then u multiply the recipricol of the bottom one over the top one?

[thin bridge]

yes

[gaunt coyote]

ah ok

[thin bridge]

or multiply numerator and denom of main fraction by 2

[gaunt coyote]

main fraction?

[thin bridge]

(or use the special ratio for tan(30°) at the start)

[gaunt coyote]

oh yeah i just used those numbers cuz it was the first example i thoguht of

[thin bridge]

the fraction with the longest line, that indicates the division of the two lesser fractions

[gaunt coyote]

so u times both by 2 to clear the lesser fractions first i see

[gaunt coyote]

also, the teacher might throw some more advanced curveball questions at us tmr, any tips on just general problem solving

[gaunt coyote]

alr

[thin bridge]

practice, understand the basic principles

[gaunt coyote]

ok

u mind if i freind u if i have any more questions?

[thin bridge]

just ask in the server

[gaunt coyote]

alralr

[thin bridge]

plenty of people other than me capable of helping

[gaunt coyote]

thx man appreciate it

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[zinc pier]

In 10th grade; what do you learn?

[red delta]

Depends on region and school.

[zinc pier]

Idk

Just generally

[dapper star]

elementary algebra

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@zinc pier Has your question been resolved?

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[blissful flicker]

Why are only these two matrices the answers to this question? According to me, all are correct.

[safe radish]

@blissful flicker Has your question been resolved?

[rigid lagoon]

<@&286206848099549185>

[stoic dune]

You're correct. Any 3×3 matrix can represent a linear transformation on R³. Just multiply the input by that matrix.

,w row reduce {{1,2,3},{4,5,6},{7,8,9}}

[flat frigate]

Results provided by WolframAlpha

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

Requested by kaynex

[stoic dune]

Their answer is wrong for the question asked, but it would have been right if they were only looking for invertible linear transformations.

@blissful flicker

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@blissful flicker Has your question been resolved?

[dire trellis]

Matrices??

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[nimble jungle]

1. ABCD is a parallelogram. DE is the perpendicular to AB from D. Length of DE is 3 cm less than the length of AB. Area of ABCD parallelogram is 40 cm^2. By taking the legth of AB as x cm build up a quadratic equation using x and by solving it find the length of AB.

[nimble jungle]

.close

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[nimble jungle]

.reopen

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✅

[nimble jungle]

sorry i ddint know

[nimble jungle]

? can someone help me with this

[nimble jungle]

i dont understand how to create a perpendicular to AB from D

[unkempt blade]

maybe something like this

perpendicular has to be 90 degree

so I think this is only way

[nimble jungle]

isn't it a parallelogram tho? if its a parallelogram, how do i draw the perpendicular line?

[unkempt blade]

I think this one is better

[nimble jungle]

how do i build a quadratic expression using x and how to solve it to find the length of AB?

[unkempt blade]

are those all the keypoints?

[nimble jungle]

yup they've only said the ones that i've mentioned in the question

[unkempt blade]

alr I found solution but why dont u try

[nimble jungle]

i did but its just messing up with my head more, i tried that question for like half an hour now and looked for a solution in dc

[unkempt blade]

can u continue from here?

this will give you quadratic equation

x^2 - 3x - 40 = 0

[nimble jungle]

okey

[unkempt blade]

x = -5 and x = 8

answer = 8

vieta's theorem

[nimble jungle]

i haven't studied about vieta's theorem yet

[unkempt blade]

but do it yourself with discriminant

yeah vietas theorem is very good for quadratic equations u can solve 40% of quadratic equations without even thinking and writing with vieta

[nimble jungle]

would it be acceptable for exams tho?

[unkempt blade]

yea

just write by vieta's theorem:

x1 = something and x2 = something

or just do it with vieta's theorem

but it doesnt always work tho

[nimble jungle]

is there any other way to solve x^2 - 3x - 40 = 0

[unkempt blade]

yes

[nimble jungle]

do i have to expand them?

[unkempt blade]

using simple quadratic equation formulas

[unkempt blade]

naa

just write

D = b^2 - 4ac

b =- 3 a = 1 c = -40

D = 9 + 160 = 169

then

x1 = -b + √D
--------
2

and x2 = -b + √D
---------
2

u know everything here

b = -3

-(-3) = 3

3 + 13

divided by 2

= 8

x1 = 8

x2= -(-3) - 13
---------
2

x = -10 / 2

x=-5

but in geometry we can't accept negative numbers as edge can't be negative

so AB = 8

[nimble jungle]

so like (x-5)(x+8) ?

[unkempt blade]

ye

but thats vieta

but when u are dealing with vieta u just need to know how to solve with it

and u can do it in your head like I did before

but as I said it doesnt always work

[nimble jungle]

uhh isn't it (x-8)(x+5)
bcz when i multiply them as (x-5)(x+8)
it goes as x(x+8)-5(x+8)
which gives x^2+8x-5x-40 instead of a minus before 8x and a plus before 5x

[unkempt blade]

why are you even doing that?

[nimble jungle]

to check if the quadratic equation i got is correcct

[unkempt blade]

U dont need that

u got that quadratic equation from 40 = x*(x-3)

by vietas theorem u can just write

x^2 - bx + c = a(x-x1)(x-x2)

So in our case

x^2-3x-40 = 1*(x+5)(x-8)

[nimble jungle]

so when u actually said this, is x 8 and x-3 = 5?

in cms

[unkempt blade]

yes

[nimble jungle]

so thats the answer? the final answer

[unkempt blade]

but question is just asking for length of X = AB = 8

final answer is 8 I said that a long time ago

[nimble jungle]

oh right sorry

thank uu

[unkempt blade]

np

[nimble jungle]

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[lean otter]

When setting up a proportion are these the same thing or no?

[peak estuary]

those equations are equivalent, yes

[lean otter]

Is there a way that is better for some reason? Assuming 8 and 10 are shirts and 520 and x are related to money?

Or a way people usually do it

[peak estuary]

well I personally would always for example want both sides to have units shirt/money or money/shirt for example

but its really up to you

[lean otter]

Thanks

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[formal ocean]

How do I solve this question?

[split moss]

Hi

@formal ocean

[formal ocean]

Hello !

[lean otter]

i got like 3b x (3b^2)^1/4

i dont think you can simplify even more

[formal ocean]

Thank you but it told me this :p

[lean otter]

what did it say

[formal ocean]

It doesn’t give me feedback it just says I’m wrong 😪

[lean otter]

but b isnt given

[formal ocean]

We’re not supposed to get the exact value I don’t think

Just simplify as much as possible

But I don’t know how to simplify 243

I know that 3^4 is 81

And 4^4 is 256

[plucky elk]

,calc 3^5

[flat frigate]

Result:

243

[formal ocean]

I guess this was the answer

I don’t understand how it got there though

[formal ocean]

This was close

[formal ocean]

Can u show your work by any chance ?

Because I think you got it right but the website just wanted it a certain way

[safe radish]

@formal ocean Has your question been resolved?

[formal ocean]

No

[formal ocean]

No I don’t know how to solve it but I got the answer for it

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@formal ocean Has your question been resolved?

[formal ocean]

https://tenor.com/view/kurt-angle-stare-100-yard-stare-meme-gif-251436459491629941

[formal ocean]

I need help man I got a final tmrw

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[finite igloo]

,rotate

[vast birch]

Hello

If AD=DB and if DB=BF and if BF=FE, what is AEG?

They are all the same just add one more x

Idk

Im only in 7th grade im sorry-

SCRRRR,, x

💋

<@&286206848099549185> HELP PLZZZ

I WANNA KNOW TOO

[gleaming hawk]

If AD = DB then D is the midpoint correct?

[vast birch]

Yess

[gleaming hawk]

if AB = BC
And DB = BF
What does that make F?

Another midpoint

So BF = FC

Same can be proven for E

Can you proceed from here?

[vast birch]

Its okay just calm ur nerves and think hvnny

Because its a straight line correct

[gleaming hawk]

Prove that E is midpoint

If that's done

Then we can conclude that BE is an perpendicular bisector

Making angle AEG = 90

Can you proceed from here?

[vast birch]

We are here if u need support x

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[candid ocean]

idk i tried doing

log_2(x)^(1/3) = log_8x

so 2^log_8x = x^(1/3)

but idk where that gets me

[deep rapids]

make the log part same

log8 x can be written as log(2)^3 x

[candid ocean]

how do i dooo thatt

[deep rapids]

now u need to use the property when the base has a power wm

[vapid glen]

have you learned the rule log_b(a) = log_c(a)/log_c(b)

[candid ocean]

ermmm

im not sure bc i dont remember that

[vapid glen]

that's ok I like your steps, you could do it that way too

[candid ocean]

ya but im stuck tho

[deep rapids]

if ur base has a power it comes out as 1/n

[vapid glen]

I'd be careful about your parenthesis log_2(x^(1/3)) the 1/3 should be inside the log not outside btw

[candid ocean]

ya sorry its just hard to type it out LOL

[vapid glen]

instead of making these powers of 2, maybe try making them powers of 8

[candid ocean]

oh

ahh

[deep rapids]

re write log_8x as log (2)^3 x

now log has a property that the power gets outside of log as 1/n

so eqn becomes 1/3 log_2x

https://www.mathdoubts.com/log-base-power-rule-proof/

used this

[candid ocean]

o

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[orchid lotus]

Hi Can someone explain this to me? I understand its coming from a power/taylor series

[orchid lotus]

I am hoping to get pointed in the right direction

[severe pond]

do you know the infinite sum for e^x

also what’s this for

[orchid lotus]

(-1)^n * x^(2n+1) al divided by (2n+1)!

?

[severe pond]

you’re thinking of sinx

[orchid lotus]

x^n / n!

i have a calc 2 exam thurs i am cooked

[severe pond]

lol

[orchid lotus]

no i do not

[severe pond]

well since -3 and x are both raised to the power of n you can write it as (-3x)^n

[orchid lotus]

oh bruh

i always miss these things

always

[severe pond]

$e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!}$

[flat frigate]

knief

[orchid lotus]

yea i know of i t

[severe pond]

but instead of x we have -3x

[orchid lotus]

but i need to memorize a list of

mac series

[severe pond]

so what does the given sum become

[orchid lotus]

it converges on (-inf,inf)

[orchid lotus]

e^-3x

[severe pond]

yep

so you’re just verifying e^-3x is a solution

[orchid lotus]

i pluggin it in for y?

and finding the first 2 deriv

[severe pond]

yes

[orchid lotus]

thats irritating but wow ok

i just need to memerize these

thanks

[severe pond]

you’re welcome

[orchid lotus]

.close

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[orchid lotus]

wait

.reopen

[safe radish]

✅

[orchid lotus]

the deriv of e^-3x = -3*e^-3x

right?

[severe pond]

yes

[orchid lotus]

so i got 0=0

which shoes it does satisfy?

[severe pond]

yes

[orchid lotus]

usually theres a good answer but this time it was just

so i was like Huh

thanks again

.close

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[proven notch]

Can somebody check if my answer is right? I got...
ED=20
EF=16.84
DF=14.11
∠E=44
∠F=80
∠D=56

[stray holly]

What method did you use?

[proven notch]

law of sines.

Here is my work

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[rotund merlin]

The second one

[rotund merlin]

I tried everything but doesn’t work

When I submit

It could be a typo idk

Just says simplify it

[queen ingot]

a^6 can come out

to become "a"

one "a" remains inside

[rotund merlin]

So isn’t it “a * 6th-root(15ab)”

Im pretty sure it is

I’m pretty confident with that answer

Even though the computer keeps saying it’s wrong

I think it’s just a problem with the software

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[spare zenith]

what is dy/dx

pls help

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[karmic finch]

can you help me?

[karmic finch]

The ratio of girls to boys in a certain school is 5:4. On the opening day, 1/3 of the boys and 1/5 of the girls were absent. If 8 less students had been absent, 3/4 of the students would have been present. Determine the number of students in the school that day.

please help

[devout scroll]

let the number of boys is b, and nmber of girls, g, than you have a few linear eqns that you can solve

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[karmic finch]

I solved it

[karmic finch]

answer is 864 = total number of students

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[junior raven]

is theta not a constant?

[torpid fable]

theta is a function of h

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[twilit grove]

Desmos

[noble kiln]

Put polar mode in settings

And then just type it

[ancient socket]

unfortunately desmos doesn't support when r is non-linear

maybe you can write r as sqrt(sin(theta)) instead

so that r becomes linear

[modern bloom]

Thx

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[ancient socket]

don't forget to account for the +- !

[modern bloom]

👌👌

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[atomic geyser]

how to convert fraction into mixed fraction

[bronze gust]

Do division with remainders

Eg.) we have the fraction $\frac{10}{4}$

[flat frigate]

denzio321

[icy lance]

Dont. Its immoral

[bronze gust]

Dang

What's immoral

I mean I guess the the practical solution would be just to use a calculator lmao

@icy lance is that what you mean 😭

[icy lance]

mixed numbers are a sin

[bronze gust]

Oh

Yea tbh I agree

But like

Bro asked the question so

[icy lance]

we gotta stop the cycle somewhere

save the next generation

let em fail

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@atomic geyser Has your question been resolved?

[bronze gust]

Dang man

[icy lance]

https://tenor.com/view/elmo-flames-burning-fire-gif-5342919

(ill allow it this once)

[bronze gust]

10/4=2R2

So $\frac{10}{4}=2\frac{2}{4}=2\frac{1}{2}$

[flat frigate]

denzio321

[bronze gust]

You put the quotient at the side to represent the whole component

And the remainder at the numerator of the fractional part

Because it's the part that cannot be expressed as a whole

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[real jacinth]

what does this mean?

[real jacinth]

what should be my representation

[lament blaze]

you have 2 numbers with digits AB and BA

A+B=6
10A + B < 3(10B + A)

[real jacinth]

what do you mean by < 3 (10B+A)

do you mean equals

[versed wave]

let $\overline{ab}$ be the two digit number you want to find

[versed wave]

(the overhead bar tells that this does NOT mean "a times b")

[versed wave]

thus $\overline{ab} = 10a + b$

[versed wave]

@real jacinth are you following so far?

[real jacinth]

yes

[versed wave]

okay

now reverse it

the reversed number is $10b + a$

[versed wave]

but this number is larger than the original number, times 3

thus $10b + a > 3(10a + b)$

[versed wave]

can you now simplify this expression for me?

[real jacinth]

i dont get what you mean by >

[versed wave]

do you know what the symbol > means?

[real jacinth]

greater than

[versed wave]

yeah

the reverse number is 10b + a

this number is greater than the original number times 3

[versed wave]

you write it as this

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[burnt grail]

how do i do question 2

[burnt grail]

i’m not sure how i would continue this

[desert pasture]

Notice that you can split it to $2\frac{1}{n}- \frac{1}{n+1}$

[flat frigate]

ƒ(Why am. I here)=I don't Know

[desert pasture]

Each term is $2( \frac{1}{n} - \frac{1}{n+1})$

[flat frigate]

ƒ(Why am. I here)=I don't Know

[desert pasture]

can you see why

[burnt grail]

nope

ur talking abt this after the last line right?

[desert pasture]

notice tha nth term is 1/ the sum of the first n natural numbers

yes

[burnt grail]

yes

[desert pasture]

so...

so what is the general formula for the nth term

[burnt grail]

well

isn’t Tn = f(n)?

[desert pasture]

uh

what

What is the general formula for the nth term

[burnt grail]

idk

there’s one for AP and one for GP

[desert pasture]

okay, so I have $\frac{1}{1+2+ \dots + n}$

[flat frigate]

ƒ(Why am. I here)=I don't Know

[desert pasture]

right

how can I re-write the denominator

[burnt grail]

im not sure

[queen ingot]

the denominator is the triangle sum

T(n)=n(n+1)/2

[burnt grail]

oh

so it’s 2k/k+1 + 1/n(n+1)/2 +1?

idk how to do latex

[queen ingot]

2k/(k+1) + 1/((k+1)(k+2)/2)

[burnt grail]

imagine the n is k

[queen ingot]

k+1

wait you put +1

[burnt grail]

this?

[queen ingot]

ok

yeah

[burnt grail]

should i multiply by 2 to get rid of that denominator

like n(n+1)/2

.close

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[drifting stratus]

Question: A 138 kg block is dragged up an inclined plane by a winch at constant velocity, as shown in the figure below. The coefficient of kinetic friction between the block and the inclined plane is 0.41. Given that the total work equals 8700 J, determine the minimum force of the winch.

[drifting stratus]

I've been stuck on this exercise for a while, no matter the force I find using the free-body diagram, I never get the 8700 J of work. Could it be that I misunderstood the problem?"

This was my original thought process

[covert yoke]

Your work due to gravity is constant and equal to mgy = 138kg * 9.8 m/s^2 * 28.2m = 38100J

This is larger than your target work of 8700J. Can you double check that the problem is communicated correctly?

Your work in this problem will be larger due to the force of friction

[drifting stratus]

yeah thats was my exact issue. So teachers fault? I need to contact her

I'm on my finals, she is kinda busy

[covert yoke]

I wouldn't say it's her fault as she likely did not design this problem

She probably just selected it from the book or something.

I would alert her about the issue, and ask how you should handle it though.

[drifting stratus]

She designed the exercise. The original one has the power topic. Its from another uni

[drifting stratus]

Thanks, gonna do that

[covert yoke]

Whoopsy then

Maybe she used g = 1 on accident.

[drifting stratus]

yeah like, even from the reality aspect

8700j is close to 2 hp

2hp winch will never drag 140kg to a 29m hill

[covert yoke]

Different units

[drifting stratus]

I'm gonna try to contact her

thanks for the help, I was going crazy over this last night

[covert yoke]

8700W is like 12 horsepower

8700J is incompatible units with horsepower.

[drifting stratus]

.close

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[fleet sun]

what's the difference between defining function as 3-tuple and defining it as fucntional relation? I've been told that 3-tuple definition is much more convenient and general as it prevents every function to be trivially surjective, but I don't really get what else makes first definition more 'general'
for context: 3-tuple definition is f := (X, Y, G), G is functional relation

[fleet sun]

help please

[mint citrus]

If we define a function as only its graph, we can only see the range of the function, that is the values it achieves somewhere over its domain

If we define $f\colon X \to Y$ by a triple $(X, Y, G(f))$ instead, we can specify a codomain

[flat frigate]

robin goodfellow

[mint citrus]

that's pretty much the whole difference

[fleet sun]

thanks!

[mint citrus]

all good! hope it helped

[fleet sun]

.close

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[latent moth]

quiz question , here the m in (0 , 4m , 0) stands for meters or milli?

[latent moth]

also to find the distance between point P and the wire on x-axis , i use (0 , 0 , 0) point , yeah?

<@&286206848099549185> (srry for the ping )

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[oak storm]

Hello, I know that $\frac{\pi^2}{6} = \sum_{n=1}^\infty \frac{1}{n^2}$, so how would I find $\sum_{n=1}^\infty \frac{1}{n^4}$,

[flat frigate]

Fred Durst

[oak storm]

<@&286206848099549185>

[edgy isle]

https://math.stackexchange.com/a/1006510

there's also a general formula for any even integer

[oak storm]

Amazing, thank you

[tulip pendant]

@oak storm keep on rollin baby

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[spice void]

im slightly confused how would you prove that y is even here so that i can ues the well ordering principle

i just need a hint

proving x is even is easy proving y is even is kinda hard

cause like isolating for y^2 gives you y^2 = 1/2 L^2

<@&286206848099549185>

[plucky elk]

!15m

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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.

[spice void]

oh sorry about that i didnt know that rule

bro can you help me tho pleaseeee

<@&286206848099549185>

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[plucky elk]

do you have to use well-ordering?

can you use fundamental theorem of arithmetic?

3 is odd

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[spice void]

you can use both i think

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[eager crypt]

the answer said that the amplitude was -2, how is this possible?

[eager crypt]

for the cosine function

The answer key said the function was y=-2cosx + 2

[plucky elk]

amplitude is 2. there's a typo

https://www.mathsisfun.com/algebra/amplitude-period-frequency-phase-shift.html

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[polar knot]

check again

your working

[polar knot]

i mean its right, but the amplitude is the abs val of a

so |-2| = 2

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[warm finch]

How to prove using the Peano axioms that a(b+c) = ab + ac ? I have previously proven that 0 * anything = 0, and that addition and multiplication commutes

[frank horizon]

should probably use induction

[shadow compass]

yes induction is ideal for that

[warm finch]

I'll try that

Base case : 0(b+c) = 0 and 0b + 0c = 0+0=0

(Sa)(b+c) = a (b+c) + b+c = ab + ac + b + c = ab + b + ac + c . Since we have (Sa)b = ab + b and (Sa)c = ac + c, we get (Sa) b + (Sa) c

I think this is it

thank you all

.close

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[normal quartz]

i have no idea what BC is-

[normal quartz]

its a circle theorems question

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[left gyro]

do you recognize this?

[empty gyro]

!status

[safe radish]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[left gyro]

not really

its saying f(a) is the same thing as its limit

that wouldnt be happening if it had a removable discontinuity, f(a) would be different

[empty gyro]

What gives you this feeling?

[left gyro]

I figured the same, I can stay

at x=a, this is the definition of continuity

differentiable is not the same as continuous

[empty gyro]

I think you meant "differentiable implies continuous"

Your reasoning for iii is correct. Your reasoning for ii is very odd. Tbh I'm a little puzzled on your struggle here given how well you answered iii

sorta

ii is correct, yes

but the function doesn't imply continuity

The function is given to be continuous at x=a, which makes ii true simply by the definition of continuous

jump discontinuity is a good example, the limit may not exist.

Or hole discontinuity, the limit and f(a) may simply be different

so yeah, c is correct

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[spiral saddle]

Let $m$ and $n$ denote the greatest and least positive three-digit multiples of $7$, respectively. What is the value of $m + n$ ?

[flat frigate]

938c2cc0dcc05f2b68c4287040cfcf71

[safe radish]

@spiral saddle Has your question been resolved?

[mortal sandal]

what would you multiply by 7 to get 100

[spiral saddle]

,calc 7*14

[flat frigate]

Result:

98

[spiral saddle]

14 I guess

[mortal sandal]

ok well the idea was 100/7 but sure

however you found it 14 is close

Except 7*14 isn't a 3 digit integer

[spiral saddle]

,calc 15*7

[flat frigate]

Result:

105

[spiral saddle]

,calc 100/7

[flat frigate]

Result:

14.285714285714

[spiral saddle]

least positive three digit multiple of 7

thats 105?

because 15×7 is multiple of 7 and least positive three digit number

, calc 999/7

[flat frigate]

Result:

142.71428571429

[spiral saddle]

,calc 142 * 7

[flat frigate]

Result:

994

[spiral saddle]

,calc 143 * 7

[flat frigate]

Result:

1001

[spiral saddle]

m = 994

n = 105

,calc 994 + 142

[flat frigate]

Result:

1136

[spiral saddle]

,calc 142 * 7

[flat frigate]

Result:

994

[spiral saddle]

,calc 100/7

[flat frigate]

Result:

14.285714285714

[spiral saddle]

,calc 14*7

[flat frigate]

Result:

98

[spiral saddle]

,calc 15*7

[flat frigate]

Result:

105

[spiral saddle]

,calc 999/7

[flat frigate]

Result:

142.71428571429

[spiral saddle]

,calc 142 * 7

[flat frigate]

Result:

994

[spiral saddle]

,calc 143 * 7

[flat frigate]

Result:

1001

[spiral saddle]

994 = 142 x 7

105 = 15 x 7

,calc 105 + 994

[flat frigate]

Result:

1099

[spiral saddle]

ty

.solved

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[loud ore]

How do I split vector of higher dimension in to numbers of occurrence of -1 in the vector plus 1 parts where -1 exists? I.e for vector V= (1,2,4,-1,7,2,6,8,-1, 7) -> V1 = (1,2,4) , V2 = (7,2,6,8) , V3 = (7)

I wanted to implement a math function that does exactly this. How do I go about this ?

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[hasty wagon]

.close

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[restive niche]

!status

[safe radish]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[autumn kite]

actually my teacher had solved it

the answer was given as 1/2

but i was curious and checked it on desmos

it gave me this result

so area under curve is 0

so answer should be 0 according to this

[restive niche]

the issue with all of these is that the sequence $f_n(x) = \frac{nx^{n-1}}{1+x^2}$ does not converge uniformly , so switching the limit and integral actually isnt allowed

[flat frigate]

Asteroid destroyer 6969

[restive niche]

you cant apply the dominated convergence theorem here either to switch the integral and limit

[autumn kite]

Ohh

So you first solve the integral then solve it like a limits problem

[restive niche]

unless you have reason to be switching the limit and integral, this will be your only choice

but im not sure how you will solve the integral inside either tbh

[autumn kite]

i had sent you three screenshots, so those are correct ryt?

nvm

[restive niche]

i can never tell you if they are correct if you dont tell me what justification you used to switch the limit and integral

[autumn kite]

no justification was used

[restive niche]

well i hope you know you cant always switch the limit and integral, as you have seen here. you need to use (in most cases) the dominated convergence theorem to justify the switching

[autumn kite]

so we take n as a constant, then solve the integral , then put in the limits.

[restive niche]

but im not sure it is so easy to solve the integral taking n constant

[autumn kite]

i saw a few solutions of it

in math stack exchange

but it had denominator as x+1

not x^2 + 1

[restive niche]

indeed the problem is different. taking x+1 is solved easily with t substitution as you can see

again note how none of the solutions switch the limit and integral

[autumn kite]

Yeah

so i gotta learn the theorem properly so that i know when i can put the limit inside and when i cannot

[restive niche]

why does your teacher not know about this though?

[autumn kite]

ig he missed it

like its JEE advanced/mains level

[restive niche]

hmm well if he is switching the limit and integral he should be giving justification as to why

[crystal spindle]

The answer is 1/2, right? I guess some inequality scaling may work

[restive niche]

ah okay well most questions you see will let you switch the limit and integral

[autumn kite]

ig he wouldnt have thought that it would be out of syllabus

[restive niche]

certainly you wont need to worry about this for jee

[autumn kite]

Ahh

one more thing

how do you identify this?

[restive niche]

do you know the definition of uniform convergence?

[autumn kite]

ah no

ig lets leave it here

Thank You broski

mad help

.close

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[restive niche]

probably

[restive niche]

.close

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[crystal spindle]

I'm working on your problem, and have made some progress@autumn kite

Wait me a minute

[restive niche]

it is 1/2, by method 3 (M-III) which uses DCT properly

unless im missing something

[crystal spindle]

The inequality method worked

Let me write it down and send to you

[autumn kite]

ah alright

after you send it i have another doubt

[restive niche]

actually both the MSE solutions can be adapted

[autumn kite]

nvm

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[fringe dock]

can someone explain coprime in this context

[junior raven]

coprime means they share no factors other than 1

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[gritty agate]

help

[gritty agate]

someone help me solve this

[lean otter]

but you already solved it?

[gritty agate]

k

thx

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[indigo birch]

Two capillary tubes AB and BC are joined end to end at B, AB is 16cm long and of diameter 4mm whereas BC is 4cm long and of diameter 2mm. The composite tube is held horizontally with A connected to a vessel of water giving a constant head of 3cm and C is open to the air. Calculate the pressure difference between B and C. (In centimeters of a column of water)

I tried to solve this by solving for the pressure difference between A and B, which is rho * g* h which is 1 * 980 * 3 = 2940 Ba
Then I recalled the equation of continuity
a1V1 = a2V2 a1 = pi * 0.2 ^2 a2 = pi * 0.1^2 V1 = pi/8 * 2940 * 0.2^4/(η * 16) V2 = pi/8 * p * 0.1^4/(η4)
We want to find p/(rho g) to find the column of water

However when solving for p ( i got 47040) which corresponds to 48 cm of water, but the answer is 2.4 cm How did I go wrong by a factor of 20?
Here is the solution online (which I didn't understand)
https://youtu.be/K7SCruah6ds?si=cMvtRLFyX8eOxQeC

[indigo birch]

here is an image for reference, note that the numbers are different
also i tried my method for this one too, and again my answer is off by a factor of 20

<@&286206848099549185>

[ionic tide]

What is the question ?

[ionic tide]

?

[indigo birch]

Here

[ionic tide]

Hmm show me how to caculte the pressure

Did you write on book ?

[indigo birch]

which pressure difference

[ionic tide]

Between B and C

[indigo birch]

a1V1 = a2V2

and from poiseuille's formula

one sec

[ionic tide]

Sorry

I dont know the n at 8n x 16 or 8n x 4

[indigo birch]

thats called eta

the coefficient of viscosity

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@indigo birch Has your question been resolved?

[indigo birch]

<@&286206848099549185>

[lean otter]

Hello, how can I help you?

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[forest sequoia]

Hey, can someone explain me what equals E[z^X] please?

[forest sequoia]

With E the expected value

[digital leaf]

Sum of [z^k * P(X = k)] for k integer ≥ 0

By the "Changement de Variable" theorem over discrete variables in french

Note that the fact |z|<1 guarantees your expectancy is less than infty
The latter would be dominated by sum of z^k for k≥0 since a probability is always less (or equal) to 1

and this sum is finite (and equal to 1/(1-z) as you know)

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@forest sequoia Has your question been resolved?

[forest sequoia]

Okaay thank you very much!!

[forest sequoia]

Yes of course ^^

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[rich dawn]

how do i even approach a question like this

[edgy isle]

that question seems incomplete

[plucky elk]

you cut off the question

[rich dawn]

sorry your right

G(1) <= 0

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[narrow ridge]

what does this mean

[narrow ridge]

could someone rewrite it ike

like

[flat frigate]

wasu

[pale lily]

thats already the form its in is it not

your just not given the bounds

[narrow ridge]

what are the bounds

i dont really understand the G = {things}

[pale lily]

G is just what your integrating over

[queen ingot]

What shape is G?

[narrow ridge]

circle

[queen ingot]

Yes

[pale lily]

you should use polar

convert the integral to polar form

[narrow ridge]

from MSE

i dont understand how they change the

integral

[gusty trench]

the jacobian part or the bounds?

[pale lily]

bro thats just not knowing polar than

[narrow ridge]

i can do gaussian integral

i understand it

the _G part confuses me

[gusty trench]

then this is the exact same thing except they just send R to infinity in the gaussian

[queen ingot]

You have to parameterize G

[gusty trench]

the gaussian integral, after squaring it, integrates over the plane which is the same as integrating over a circle G with infinite radius

this is the same concept but G is a finite circle

[queen ingot]

r and theta in those bounds will cover that circle

[narrow ridge]

oh

ohhh ok

.close

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[frail cobalt]

hi can you please help me with this?