help-10

[robust sleet]

what grade is this

[warped flume]

Year 12

[robust sleet]

how do the other integrals look like

[warped flume]

My teacher just takes stuff from bits and pieces

So there’s no relationship between questions

[solar trellis]

.

[warped shell]

expand the bottom as taylor series lol

[warped flume]

it either ends with u and cos x or u with sinx

[robust sleet]

I'll give u 100 bucks your teacher can't solve it either

[solar trellis]

get the integral in one variable

[warped flume]

He probably can

He has 2 degrees in maths

One from oxford

One from cambridge

Yet hes a teacher

His explanation was teaching is a meaningful thing to do in life

[tardy epoch]

are his degrees in integrals?

[warped flume]

Never asked

[warped shell]

then you get wallis integrals

[tardy epoch]

like a bachelors degree in integration by parts and substitution

[robust sleet]

tbh in no exam at hs nor university will they ask such integral

answer is 3 lines long

[warped flume]

Ik,but solving it is an accomplishment

[solar trellis]

why do you think the integral is so hard?

looks can be deceiving

[robust sleet]

solve it yourself without using an online integral calculator lol

[solar trellis]

can't be bothered tbh, unless i can work it along with someone online

[warped flume]

…

[solar trellis]

also i'm not guaranteeing i can solve it

[warped flume]

<@&286206848099549185>

[tardy epoch]

yup i hate it

[warped flume]

i've seem this before

[solar trellis]

yea it's messy

but it's essentially just sub u = integrand then partial fractions

[tardy epoch]

links to different problem

[gilded needle]

ugh integrating sqrt(tan(x)) is a bear, that's a double or triple starred problem from spivak if I recall

i gave it as an extra credit hw question once

no one got it

[warped flume]

easy to say

hard to execute

[solar trellis]

computationally yes, mathematically no

[robust sleet]

https://gyazo.com/0ed9c153bf4568b14316b996d6d8cc14

[warped flume]

is that the answer

[robust sleet]

thats like one third

[warped flume]

jesus

[robust sleet]

one third or one quarter of the answer

[tardy epoch]

do you get this for u=cos(x) ?

[warped flume]

i'll try

[robust sleet]

0.4076421048449653... is answer

[tardy epoch]

it's not really an answer, but at least wolfie can numerically estimate it

dammit

[warped flume]

how do u get rt u(1-u^2)

for the numerator

cause theres still a sinx

[tardy epoch]

du = -sin(x) dx

[warped flume]

for the numerator

the power of sinx is 3

1-u^2 is only sin^2x

[tardy epoch]

sqrt(a^3) = a * sqrt(a)

[warped flume]

I am confused

Sin^2 is u-1

Sin is root u-1

Which makes it so messy

[tardy epoch]

yea doesn't seem fruitful

[solar trellis]

.

[tardy epoch]

^

cos(pi/2 - x) * sin(pi/2 - x) = cos(x) * sin(x)

someone ping me if this gets solved

[warped flume]

i'll ask my teacher tmr

[solar trellis]

lame

[obtuse pebble]

@warped flume Has your question been resolved?

[obtuse pebble]

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[lusty peak]

I have no clue how to express this into partial fraction

Can somebody please help me

[warm canopy]

,rccw

[pallid flame]

factor bottom

what do u get

[lusty peak]

(x^2+6) (x^2+4)

is that right

[pallid flame]

yes

[lusty peak]

you sure

[pallid flame]

A and B are representative of polynomials

[lusty peak]

because in the book there is like 5 term

but I dont know how they get that

[pallid flame]

you can convert it to that

[lusty peak]

sorry for being annoying

[pallid flame]

i will use that one instead then

[warm canopy]

There are certain rules on what the numerators should look like depending on the degrees of the numerator and denominator of your original fraction

[lusty peak]

so if you get x^4

you use that form

[pallid flame]

x^4 + 5x^2 + 2x = A(x^4 + 10x^2 + 24) + (Bx + C)(x^2 + 6) + (Dx + E)(x^2 + 4)

[lusty peak]

how did they get A = 1

[pallid flame]

x^4 + 5x^2 + 2x = Ax^4 + 10Ax^2 + 24A + Bx^3 + Cx^2 + 6Bx + 6C + Dx^3 + Ex^2 + 4Dx + 4E

1x^4 + 0x^3 + 5x^2 + 2x + 0 = Ax^4 + (B + D)x^3 + (10A + C + E)x^2 + (6B + 4D)x + (24A + 6C + 4E)

[lusty peak]

so do i just equate the coffecients

[pallid flame]

yes

[lusty peak]

damn

i get it now

thank you so much

[pallid flame]

no problem

[lusty peak]

you actually a saviour

thank you

.close

[obtuse pebble]

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[deep ravine]

let’s say these two are my only grades for french class

[deep ravine]

would this be my final grade?

[tardy epoch]

depends on how they're weighted

[obtuse pebble]

@deep ravine Has your question been resolved?

[deep ravine]

what are the ways for it to be weighted?

[tardy epoch]

1/3, 1/3, 1/3

exams are usually weighted more than homework

homework is usually weighted more than participation

[deep ravine]

hmm none of these grades are exams

but a grade worth 10 points must be exactly ten times less relevant than a grade worth 100 points, right?

[civic zealot]

depends on how they're weighted.

If classwork is worth 10% of your grade, homework worth 75%, and Review worth 15%
Then you'd have an A (I think)

If your grade is just point totals, then yes, you have 94/110 possible points.

[obtuse pebble]

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[opaque flicker]

hiya could i please have help with this question as i do not know how to do it, thanks 🙂

feel free to ping

i am completely and utterly stuck, cannot even understand what to do at the beggining of the question

<@&286206848099549185>

[dense imp]

@opaque flicker start off by factoring each denominator, then you can see what is the simplest factor you need to multiply each fraction by to get a common denominator (so you can combine the two terms into a single fraction)

$\frac{5}{2(x-3)}-\frac{x+2}{(x-3)(x-1)}$

[warm shale]

Sooshon

[opaque flicker]

kk

[dense imp]

ok so each has a factor of x-3, you need to have 2 and (x-1) as factors in each denominator, so multiply the left term by (x-1)/(x-1) and the right term by 2/2

[opaque flicker]

this is harder then i thought haha

[dense imp]

$\frac{5(x-1)}{2(x-1)(x-3)}-\frac{2(x+2)}{2(x-3)(x-1)}$

[warm shale]

Sooshon

[opaque flicker]

ohhhhh i see now

then you can combine the fractions...

[dense imp]

yep

[opaque flicker]

also

would it be ok if i cold have a bit more help with a different question?

[dense imp]

feel free to post it here, yes

you're good on this 1st question?

[opaque flicker]

yes i think i am

for some reason my windows snipping tool wont work

just one second

[dense imp]

Windows Key+Shift+S

[opaque flicker]

yeah it worked earlier but for some reason it wont work now

here we go

i sort of know what a parabola is, its the curvy graph thing

but i dont quite understand what they want me to do with it

maybe create a perfect square??, but i wouldnt know how to create one with 8 as it cant have a square root

@dense imp

sorry for ping

[dense imp]

well, if you just consider $x^2-8x+C$ what C would you need there to be able to factor it as a perfect square?

[warm shale]

Sooshon

[dense imp]

if you ask that you can see it's just half of -8 and squared so 16

so you could write the original equation as $x^2-8x+19=x^2-8x+16+3=(x^2-8x+16)+3=(x-4)^2+3$

[warm shale]

Sooshon

[opaque flicker]

o... why would it be like that, maybe i should do some more revision on perfect squared before this?

[dense imp]

perhaps

[opaque flicker]

but i can see why it would be like this

[dense imp]

if it's a perfect square quadratic (formula of a parabola) then yeah the C term will always be half of the coefficient in front of the x and squared

[opaque flicker]

why do we half the 8 over here and then square it, why not just square the 8?

[dense imp]

well try to factor $x^2-8x+64$ does that factor as a perfect square?

[warm shale]

Sooshon

[opaque flicker]

ahhhh I see, im guessing this is just knowledge i need to memeorise

[dense imp]

think about what happens when you FOIL $(x-4)^2$

[warm shale]

Sooshon

[dense imp]

$(x-4)^2=x^2-4x-4x+16$ so basically you get repeats of -4x

[warm shale]

Sooshon

[dense imp]

so it has to do with that

FOIL = first, outside, inside, last, you're familiar with that right?

[opaque flicker]

yes i use that 🙂

[opaque flicker]

ahhhh i see

[dense imp]

so you see how you get -4x terms twice (because the two terms are symmetric, so the inside and outside terms are actually always the same)

some other examples of perfect squares:

[opaque flicker]

yeah i see that now

[dense imp]

$x^2-10x+25=(x-5)^2$

[warm shale]

Sooshon

[dense imp]

$x^2+10x+25=(x+5)^2$

[warm shale]

Sooshon

[dense imp]

$x^2-20x+100=(x-10)^2$

[warm shale]

Sooshon

[opaque flicker]

i see it now, i hadnt learnt this equation type yet in class

thank you so much!

[dense imp]

sure, use .close to close the channel if youre done

[opaque flicker]

.close

[obtuse pebble]

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[noble kindle]

Im thinking letting $G = { A \in M_{2x2} (\mathbb{R}) }$

[warm shale]

Kurama

[noble kindle]

And $H = { A \in G : tr A = 0 }$

[warm shale]

Kurama

[noble kindle]

Both under regular matrix multiplicaiton

so G is a subset of H

[kind hawk]

G is not a group tho

if anything you need GL_n(R)

either way little bit complicated

[noble kindle]

wait why is G not a group

[kind hawk]

well not under matrix multiplication

0 matrix is in G

can you find a subset of the nonzero rational numbers which is closed under multiplication but not a group

[noble kindle]

So $G = \mathbb{Q} - {0}$?

[warm shale]

Kurama

[kind hawk]

yes

G is a group with the normal multiplication

[noble kindle]

Does $\mathbb{Z} - {0}$ work?

[warm shale]

Kurama

[twin sapphire]

take a simple group

[noble kindle]

Cause that still should be closed under multiplication. but it doesnt have inverse?

so its not even a group...

[kind hawk]

yes

[twin sapphire]

yeah that works

you could also have taken (Z,+) and N as the closed subset

[kind hawk]

oh true forgot about that

but afaik you need an infinite group. for a subset of a finite group being closed is afaik enough

[noble kindle]

hmm yeah, that is simple.

[twin sapphire]

also for any group

you can take the subset with just the neutral element

[kind hawk]

but that is a group

[twin sapphire]

oh yeah nvm

[noble kindle]

wdym neutral

element

[twin sapphire]

1

[noble kindle]

im dont understand

[kind hawk]

what kind of group theory do you learn without neutral elements

[noble kindle]

lol ive never heard that term before

[twin sapphire]

its the element e such that for any x in your group e . x = x . e = x

with . being the law

[noble kindle]

ohh

our textbook calls it the identity

lool, yeah ok

thanks guys\

.close

[obtuse pebble]

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[twin sapphire]

#help-16 message here is something similar

[vernal bobcat]

.close

[obtuse pebble]

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[fierce cedar]

can someone help me walk through this?

[fierce cedar]

can someone help walk me through this?*

[burnt scroll]

how many seconds are in 16 years

how would you solve that

[fierce cedar]

it said we have to do dimensional analysis but i’m having trouble where to startt

start

[long sinew]

Well, first think about how many seconds are in a minute

How many minutes in an hour

How many hours in a day

How many days in a year

[obtuse pebble]

@fierce cedar Has your question been resolved?

[obtuse pebble]

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[fierce cedar]

60 seconds in a minute, 24 hours in a day, 365 days in a year

[obtuse pebble]

@fierce cedar Has your question been resolved?

[strong vale]

So 60 seconds in a minute

How many minutes in a day?

[fierce cedar]

1440? i looked it up

[high lily]

don't look it up. try and do the conversion yourself

when doing unit conversions, you're pretty much multiplying by 1.
note that since 1 minute = 60 seconds,
60 seconds / (1 minute) = 1 minute / (60 seconds) = 1,
and you can do the multiplication depending on what you want to convert to and from
same idea for the other units/conversions

also note that they want you to use 365.25 days/year instead of 365days/year

[astral ivy]

this is so lit

I understand now

[obtuse pebble]

@fierce cedar Has your question been resolved?

[obtuse pebble]

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[wanton dagger]

Where am I wrong at

[urban patrol]

Don't you just

Slope is negative 2

No it's not

Nbm

[wanton dagger]

It’s not right

[urban patrol]

Shouldn't it be 5/2

for the x value

Since m=2

[wanton dagger]

Let me see

[urban patrol]

12.5-20+3 is what I did in my head

If x is 5/2

-4.5

-9/2

[wanton dagger]

Yh also what I got

[urban patrol]

do you have an answer key

[wanton dagger]

Yes

4x-2y-19=0

[urban patrol]

Oh what the equation is

I see okay

-9/2=7(5/2)+b

-9/2=35/2

[urban patrol]

Okay cool

[wanton dagger]

Thanks

.close

[obtuse pebble]

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[whole warren]

why doesnt the graph point up by only down

[whole warren]

for example the 1/cos 90 is just infinity

so how would you know if it is negative or positive

[obsidian isle]

You don't. It has a different limit from both sides

[obtuse pebble]

@whole warren Has your question been resolved?

[obtuse pebble]

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[surreal pewter]

Need some help with finding the area for this shape. Just the answer not an explanation or anything. Thanks

[fading musk]

make a dot under B

1 square

[surreal pewter]

?

[fading musk]

let the dot be z.
CB=sqrt(CZ²+ZB²)

have you learnt pythagoreans theorem

[surreal pewter]

Yeah

Hold on though

[fading musk]

make a triangle

CZB, where z is one unit under B

[surreal pewter]

I’m not looking for an explanation or any kind of equation

I just need a flat answer

This is a missing I have due in 40 min

And it’s the last day for missings

Squared?

[nocturne minnow]

Don't do the work for people

[fading musk]

okay sorry

let him do it

[surreal pewter]

This is a lot more confusing than I thought

[nocturne minnow]

Let them do it on their own

[fading musk]

use pyth. theorem

make a triangle

[surreal pewter]

The triangle is made with coordinates

I’m only looking for the area

[fading musk]

You need to find the length of the sides

[nocturne minnow]

Do you know the distance formula?

[fading musk]

by pythagoreans theorem, since it is a right angled triangle you can do it

[surreal pewter]

Yeah but I forgot how to plug CA and AB to it

[nocturne minnow]

Distance formula is an application of Pythagorean theorem

[surreal pewter]

Uh

[fading musk]

yes

[surreal pewter]

I learned this last semester I forgot it all

[nocturne minnow]

Recall that it's $d = \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2}$

[warm shale]

dldh06

[nocturne minnow]

Google is not hard to use

[surreal pewter]

That’s the problem though it really doesn’t have all the answers

[fading musk]

you just need the formula

and do it by yourself

[surreal pewter]

I

Do

Not

Know

[fading musk]

understand the formula

[surreal pewter]

How

[nocturne minnow]

I told you, you need distance formula, you said you forgot it, you can Google formulas

[surreal pewter]

This IS the formula

[fading musk]

x2 is the x coordinate of the finishing point

yes

now plug the coordinates in

[surreal pewter]

I don’t know how to plug it

With my numbers

Because I forgot

[fading musk]

find the coordinates of the dot

[nocturne minnow]

https://www.youtube.com/watch?v=CWUr6Jo6tag&ab_channel=TheOrganicChemistryTutor

Simple

Googled that too

[fading musk]

this guy explains everythint

[surreal pewter]

I’m going to fail

[fading musk]

better than giving answers

the point of learning is doing it by yourself

[surreal pewter]

I’m not here to learn though

[fading musk]

okay stop arguing do it now

[nocturne minnow]

You use utilize resources first

[nocturne minnow]

Too bad, because the purpose of the server is to teach, not give out answers

[surreal pewter]

I already go to school this is just tutoring I guess

Which isn’t a bad thing

[fading musk]

my bad, I should not give answer

[surreal pewter]

But I just thought I could grab the answers and pass rq

I have 30 minutes I’m really not gonna make it now

[fading musk]

believe in yourself

[nocturne minnow]

If you want answers, this is not the server for you

Instead of all this bickering, you should watch that video and learn how to apply the distance formula

[fiery olive]

The answer is : ||learn||

[fading musk]

we are not being mean to you, just telling you you should do your work by yourself

[surreal pewter]

I never said that

I just forgot everything

It’s old

[fading musk]

then try to learn it back

[surreal pewter]

might Fr just not do the work now

[fiery olive]

Ok bye

[nocturne minnow]

Hence Google things you forgot

[surreal pewter]

It’s due in 30 minutes

I’m malding

[fiery olive]

Do you think people are here to give you answers

[surreal pewter]

No

They already said that

[fading musk]

then do it now

[fiery olive]

Then do it?

[surreal pewter]

I’m typing and putting together the formula at the same time

[fading musk]

what's the point of arguing? it does nothing, you miss your assignment and learnt nothing, you really should do now

[surreal pewter]

I’m not arguing

[fading musk]

okay then do it

[surreal pewter]

I don’t have a point to argue

I.. already am..???

This kinda sucks though, it’s just old people telling me everything my teachers tell me again and again

I didn’t really actually expect to just be given answers but I thought at least the teaching methods might differ

[nocturne minnow]

Old how? A lot of people here are in high school

[surreal pewter]

But I’m not old like the rest of these people

Even if they’re in high school they’re probably 18+ when it comes to helpers or whatever

[nocturne minnow]

I gave you a formula, you said you forgot how to use it. I sent a video because a 5 minute video would explain in faster then text between two people

[nocturne minnow]

Anyone can be a helper, meaning that helpers are also in high school

[surreal pewter]

I’m just at school right now basically

They give you a video, formula then they just tell you to do it

.close

[obtuse pebble]

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[junior zephyr]

Hi

[junior zephyr]

A biased coin having heads 58% of the time and tails 42% of the time is tossed indefinitely. I want to know if this inequality is true,
P (n heads and 1 tail) <= P (at least n +1 heads and 1 tail)

[junior zephyr]

Also this must be in order, that is, first n tosses must be heads and last tail..

[noble kindle]

For P(n heads and 1 tail) I think u an define a random variable with geometric distribution , say X

For the second probability, again the geometric distribution

Where success is defined as getting a tail

[junior zephyr]

How to know which one will always be bigger than other

[noble kindle]

I think, for P(n heads and 1 tail), it would look like this

HHH...(n times)T

you know P(H) = 0.58

[junior zephyr]

X = p^k (1-p)

[noble kindle]

so you have $0.58^n \times 0.42$

[warm shale]

Kurama

[junior zephyr]

yes

[noble kindle]

the other side you have $0.58^{n+1} \times 0.42$

[warm shale]

Kurama

[noble kindle]

which equals $0.58^n \times 0.58 \times 0.42$

[warm shale]

Kurama

[noble kindle]

so you have $0.58^n \times 0.42 \le 0.58^n \times 0.58 \times 0.42$

[warm shale]

Kurama

[noble kindle]

i mean, does this seem true?

[junior zephyr]

Also( sum n till inf ) $0.58^{n+2} \times 0.42$

[junior zephyr]

Basically in the same X, comparing P(X=n ) with P(X >= n)

Why is my texit thing not showing up

[noble kindle]

i think for the first one, u are missing $ sign

at the end

[warm shale]

heyloo

[junior zephyr]

$0.58^n \times 0.42 \le {1 - 0.58^{n+1}}$

[junior zephyr]

So is the sum of the sequence bigger than n always bigger than value at n?

[noble kindle]

wdym

[noble kindle]

you have this right?

now, compare to see if this inequality is true for some numbers

[junior zephyr]

Its this inequality not the previous one..

[warm shale]

heyloo

[noble kindle]

theyre not the same

the rhs

[junior zephyr]

Will this always hold true for all n?

[noble kindle]

im not sure what that is, but P(at least n+1 heads and 1 tail) is like HHH...(n+1 times)T

[noble kindle]

put in some numbers

n = 1, n = 2, n =3

[junior zephyr]

Works for n = 1

[noble kindle]

what about n = 2

[junior zephyr]

Yes

Rhs keeps getting bigger and lhs smsller

[noble kindle]

yeah, thats a pretty good indication it will be true

[junior zephyr]

Thanks

[obtuse pebble]

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@bleak steppe Has your question been resolved?

[obtuse pebble]

@bleak steppe Has your question been resolved?

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[open solar]

help please

[royal basin]

have you made a diagram?

[open solar]

that's what i'm struggling with

[royal basin]

start by drawing a triangle ABC

[open solar]

im struggling w D,E and F

I don't know the shape of ABC because I don't know where DEF would go

[royal basin]

just draw them wherever and mark the edges that are meant to be equal

your diagram does not have to be to scale

[open solar]

could you draw the diagram? im pretty sure mine isn't correct

[royal basin]

i don't have paper on me atm

[open solar]

ah could you try instruct me then

<@&286206848099549185>

[obtuse pebble]

@open solar Has your question been resolved?

[kindred spoke]

Hi, I can help you draw the diagram

[open solar]

really? thank you

[kindred spoke]

Wait, lemme draw the diagram in paint, I cannot send the pic of the paper

@open solar

They asked you to prove that the center of the circle in the diagram, is in the line bisecting angle DEF

[open solar]

how do I prove it? you can see it in the diagram but I don't know how to explain it

[kindred spoke]

Try identifying isosceles triangle, I think they were meant to be used

angle BDE = angle DBE, angle EFC = angle ECF

Also, angle DBE + angle ECF + angle DAF = 180 degrees

Try to exploit these two facts

and create more conclusions

[obtuse pebble]

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[open solar]

.reopen

[obtuse pebble]

✅

[open solar]

is it a cyclic quadrilateral?

[kindred spoke]

lemme see

[silver flint]

I believe a cyclic quadrilateral is when ALL corners of a quadrilateral are touching the circumference of the circle.

[kindred spoke]

nah

[kindred spoke]

Well obviously

[silver flint]

i mean he/she/they asked if it was one so i explained what 1 was

[kindred spoke]

IF DAF + DEF = 180 degrees, it's a cyclic quadrilateral as you all know

[silver flint]

it is not

that is a cyclic qudrilaterial.
Notice that all the corners are touching the edge of the cirlce

[kindred spoke]

Yes that's what I said

[open solar]

oh oops sorry

[silver flint]

that is not

[kindred spoke]

the quadrilateral is not cyclic unfortunately

[silver flint]

yea

[kindred spoke]

I think I know the way to solve it @open solar

Basically, we need to prove that the angle bisector of DEF must pass through the center of the circle. But this means it has to be the bisector of angle A too, and I am saying this because it seems to be true

Now, the incircle is the circle made by the interesection of angle bisectors being the center

So, the only thing you have to do prove this conjecture:
Prove that if the angle bisector of A passes through the center of incircle, it has to be the bisector of angle DEF too.

It seems to be simple, let me also try it

[open solar]

thank you so much!

it's quite late so I'll probably write up an official solution tmrw morning

[kindred spoke]

Okay!

Basically, try to get as many angles as possible, since the question seems to deal with bisectors

[kindred spoke]

and then, after hunting for all those angles, try to prove this little statement

wait I wrote the reverse sorry

@open solar Can I close this thread?

.close

[obtuse pebble]

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[quick knot]

need to find the radius :^ pls

[shell wind]

Hi, Can I see your work

[quick knot]

work?

what do you mean? In the book? Or...

[shell wind]

Work as in what you have tried yet

[quick knot]

I didn't write anything yet, I just don't know how to solve it at all

[shell wind]

Ok, If I say length OC is x then what is the length of OJ

Also I am assuming O is the center

[quick knot]

Yep. O is the center

[quick knot]

17 - OC = OJ ?

[shell wind]

yes

[compact shadow]

x+y=17,x^2+25=y^2+144

[shell wind]

Do you know that the perpendicular from the center to the chord divides it in two equal lenths

[compact shadow]

You will obtain a linear function of x, solve it then

[quick knot]

Yes, I know it

[shell wind]

so we can find BC and FJ

[quick knot]

then CB = 5 and FJ = 12

[shell wind]

yep, now use Pythagorean theorem in triangles BCO and OJK
note OB=OK as they are radii

[turbid wing]

BCO and OCA*

[shell wind]

What is the difference OCA is congruent with OCB

[turbid wing]

OCJ is not a triangle I meant

its a straight line

[shell wind]

typo

[turbid wing]

ah np

[quick knot]

hmmm, I guess radius = ... 13? probably

[turbid wing]

I haven't calculated. lemme confirm too

[shell wind]

yes

[turbid wing]

13.47

approx

[shell wind]

check your calculation

[quick knot]

so I am right! )

Thank you very much!

oh, may I ask one more question? I have another math problem 😄

[turbid wing]

thats 3^x?

[graceful trellis]

2

[quick knot]

Yes

[turbid wing]

okay

solving wait

[turbid wing]

can't be solved

there should be another equation in terms of x and y

[quick knot]

Oh, okay

[turbid wing]

where did you take this question from?

[quick knot]

From my teacher

She gave it to us in class and surprisingly the answer was 6, but I didn't understand why

[turbid wing]

uh and the answer is 12 not 13

[turbid wing]

not possible at all

you can get the question confirmed from her

[quick knot]

r sure?

[turbid wing]

yes absolutely

should I send the solution pic?

[quick knot]

Yes pls 😛

😋

[turbid wing]

wait

[quick knot]

I'll ask her then, just to confirm

[turbid wing]

yeah okay

[quick knot]

Oh, okay. Thanks

so be 12 the right answer

i guess I can close the channel?

[turbid wing]

yes 12 is right

[turbid wing]

yup

[quick knot]

thanks again^^

.close

[obtuse pebble]

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[shell wind]

They were asked the radius not distance from center

[obtuse pebble]

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[turbid wing]

uh am dumb!

[shell wind]

close this channel, if you are not using it

[obtuse pebble]

@turbid wing Has your question been resolved?

[turbid wing]

.close

[obtuse pebble]

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[static patio]

converges or diverges ?

[eternal bloom]

converges

[static patio]

which test should i use ?

[eternal bloom]

test for absolute convergence and use ratio test

[static patio]

and if it converges absolutely then it converges without abs ?

[eternal bloom]

yep

[static patio]

ok thx

im going to try it

[compact shadow]

Stirling’s approximation or directly use alternating test

[static patio]

i ended up with limit in form n^n/(n+1)^n, what to do with it ?

[static patio]

thx, i will check it

[eternal bloom]

write it as 1/(1+1/n)^n, and use the fact that (1+1/n)^n goes to e

[static patio]

thanks, works

[obtuse pebble]

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[clear cloak]

Hi

[clear cloak]

In getting a derivative of a function

Applying the powerrule to a constant results in 0 right?

So The Sqrt(3) must also be 0?

,rotate

[shell wind]

Derivative of a Constant is 0, Power rule is only for algebraic equation

[clear cloak]

Okay

So here th Sqrt of 3 stays?

[shell wind]

Yes

[clear cloak]

Ok so

1x^1 = 1 and then 1Sqrt(3) = Sqrt(3)?

So it’s Sqrt(3)+3/2Sqrt(x)?

[shell wind]

the sqrt(3) remains as it is

[clear cloak]

Ok thank you!

[obtuse pebble]

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[timid silo]

This is going to be pretty easy but i just wanna be sure if the limit is 0

[prisma python]

It's 4

[timid silo]

Cancel the t's then multiply zero and 4

Wait what

How

[prisma python]

What do you get after cancelling ts

[royal basin]

why multiply 0 and 4?

[timid silo]

Wait will it be an exponent

Idk im pretty new to calculus sorry guys

[royal basin]

what exponent lol it'll just be 4

don't overthink it

[timid silo]

Im getting my head boggled on basic calc

Im reviewing for a short quiz tomorrow and this is the reviewer so thanks guys

[prisma python]

When you apply limit to a constant it remains the same also I don't know where you got that 'multiply by zero' concept. When you're applying limit of 0 you simply replace the variables in this case ts with 0 and compute the result.

[timid silo]

For this one im quite sure its 3/8

Please tell me im right

Because you simplify the difference of two squares first correct?

[timid silo]

Im new to the concept of limits so i got confused on that part

[prisma python]

Umm I don't have a paper to solve this right now but applying Lhopital gives me something else ... If my mental math is not wrong.

Sec

[timid silo]

I used simple factoring and rationalization

[prisma python]

I might be wrong give me a sec.

[timid silo]

Let me try

Idk what Lhospital would result i havent tried that

[compact shadow]

=(v^2+2v+4)/(v+2)(v^2+4)

[prisma python]

Yea it's 3/8

[shell wind]

With LHospital we get 3/8

[haughty coyote]

I do think that's 3/8

[compact shadow]

Just plug in v=2

[timid silo]

Oh ok thank you

[haughty coyote]

,w lim as x -> 2 (x^3 - 8) / (x^4 - 16)

[warm shale]

Results provided by WolframAlpha

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

Requested by themateo713#5303

[shell wind]

Do they teach LHospital in American High school?

[timid silo]

I find my weakness in calc is forgetting basic algebra

Btw thanks tho i appreciate the help

[prisma python]

I'm sure they teach that everywhere

[timid silo]

.close

[prisma python]

It's essential

[obtuse pebble]

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[shell wind]

Teach as in the proof

[prisma python]

Probably not the proof

[eternal bloom]

factor the numerator and denominator and cancel the common factors. remember that when taking a limit, you don't look at what's happening at the point itself, only around the point.
"limit of f at a = L means for every epsilon > 0, there is delta > 0 such that for any x in the domain, if 0 < |x-a| < delta, then |f(x) - L| < epsilon."
the 0 < |x-a| means you don't look at what happens at the point itself. that's the idea being tested here, and that's why you can cancel the t in the first one, and cancel the factors of t-2 in the second

[obtuse pebble]

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[somber notch]

Let a,b,c, d be a positive integer

[somber notch]

I'm trying to figure out how many different ways I can add together values of a, b, and c to be become d.

[stable aurora]

Hi does anybody have the pdf link of the answer-sheet of this book? “Set Theory with Applications Book by Shwu-Yeng T. Lin and YOU FENG LIN”

[somber notch]

mel_hzt2019 I think we both took this room at once 🙂

Could you grab another one, please? I think by chance I ended up assigned to this one.

Let a,b,c, d be a positive integer

I'm trying to figure out how many different ways I can add together values of a, b, and c to be become d.

For context, I'm trying to do a complexity analysis for a leetcode problem I'm doing.

[compact shadow]

What?either a+b+c equals d or doesn’t

If it does then one way, if it doesn’t then 0

Or they are variables?

a,b,c are variables d is constant or a,b,c,d all of them are variables?

[timid silo]

This helped a lot in my understanding thank you

[somber notch]

(x1)a + (x2)b + (x3)c = d

How many difference combinations of x1, x2, x3 can this be true

Assume d is larger than a, b, c

all variables here are positive integers

[compact shadow]

Then I guess you have to count…

If it has one integer solution (x_0,y_0,z_0)

Then any other solution is of the form

x=x_0+ub/gcd(a,b)-vc/gcd(a,c)
y=y_0+wc/gcd(b,c)-ua/gcd(b,a)
z=z_0+va/gcd(c,a)-wb/gcd(c,b)

For integers u,v,w

I guess you have to count how many u,v,w can make your x,y,z positive… like a range

[nocturne token]

This sounds like an integer partition problem. How many ways can you write the positive integer n as the sum of exactly three positive integers.

[compact shadow]

He has coefficients

a,b,c

Not 1,1,1

[obtuse pebble]

@somber notch Has your question been resolved?

[nocturne token]

Hrm, so then it becomes how many ways can you write a positive integer n as the sum of positive multiples of a, b, and c. That's going to be bounded above by the number of ways you can write n as a sum of 3 positive integers, which is bounded above by the number of ways you can write n as the sum of 1, 2, or 3 positive integers.

That last one is the nearest integer to $\frac{(n+3)^2}{12}$

[warm shale]

Fyriole

[compact shadow]

You will end up with some inequality, u>=Mv+m, v>=Nw+n, w>=Ou+o for some M,N,O,m,n,0. Together you will have three inequality of u,v,w themselves respectively, it will give you boundaries of them

[obtuse pebble]

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[timid silo]

${(x,y,-x,w)}$

[warm shale]

mahmooz

[timid silo]

how do i go about finding a basis for this set

this is what i came up with ${(1,0,-1,0),(0,1,0,0),(0,0,0,1)}$ but im not really sure

[warm shale]

mahmooz

[dawn meteor]

yup, looks good

why are you unsure?

[timid silo]

cuz i used logic i didnt use rules

[dawn meteor]

ah ok

I'm not sure of a formal way to do it either, so I'll let someone else answer

[timid silo]

alright ty 😄

[obtuse pebble]

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[steel socket]

hello can someone help me find a formula of integration for this integral?

[obtuse pebble]

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[obtuse pebble]

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[keen lodge]

i need help with this question the answer is y=2x+30 but idk how to do this

[fierce lagoon]

Draw a line of best fit

Like manually sketch one

[keen lodge]

alright

[fierce lagoon]

Or

actually nvm

This other way will be easier

Find the slope between two arbitrary points

[keen lodge]

and thats it?

[fierce lagoon]

Well that's just solves for your m

For y = mx + b

What did you get for m

[keen lodge]

wait one sec im almosy done

i got 10

[fierce lagoon]

That's wrong

Show me your work

[keen lodge]

wait one second i think i did it wrong sorry

okok i got 20

i accidentallly did X1-Y1

wait nvm

i figured it out

thank u thooooo

[obtuse pebble]

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[glass trail]

Hello can someone explain how we got to this

[glass trail]

Where did the (k-1)! And (n-k)! Go?

[fierce lagoon]

$\frac{k!}{(k-1)!} = k$

[warm shale]

Umbraleviathan

[fierce lagoon]

@glass trail you understand why?

[glass trail]

Yeah thanks

[fierce lagoon]

Basically they disappear because they get cancelled out by higher-order factorials

[obtuse pebble]

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[unreal prawn]

is this correct?

[unreal prawn]

thanks in advance

[teal prawn]

first one is correct

at 8n = 4, re-check your working

[unreal prawn]

what is wrong about it?

[teal prawn]

nothing....

[unreal prawn]

i meant

the 8n = 4

@teal prawn

[teal prawn]

yeah

do you see why n = 2 isnt correct?

8 × 2 = 4??

[unreal prawn]

thats x btw

why is it 8x2?

[teal prawn]

it isnt

but you wrote x = 2

[unreal prawn]

yeahg

[teal prawn]

8x = 4
x = 4/8 = 1/2 ≠ 2

[unreal prawn]

so what is x equal to

1/2?

[teal prawn]

yes

[unreal prawn]

careless mistake by me

i divided 8/4

not 4/8

@teal prawn could you help me check some mean mode median answers

[unreal prawn]

also for this question out of 5 marks how many do you reckon i get

i got 1 value and the working is there

is this all correct?

.close

[obtuse pebble]

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[haughty thistle]

Hi, the other day I decided to find the surface area of a mobius strip. I wanted to find a general formula, but i wanted to ask the question, is the surface area just infinity, or is it the surface area from point n to point n(sorry, im not that good at topology). Thanks. From what I've measured, the equation may be the thickness of the strip times 4pi times the radius, im not sure though.

[royal basin]

well the thing is

topology doesnt care about areas

many different surfaces homeomorphic to each other may be called möbius strips, and their sizes and shapes will be different

if you have a particular surface you're working with that just happens to be shaped like one, you can calculate its area

[haughty thistle]

ok thanks

.close

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[soft wind]

hi , this is the question i need help with :

[soft wind]

anyone here to help

??

<@&286206848099549185>

anyone heree

[haughty thistle]

sorry, i dont use these types of currency, waht does p stand for?

what

[soft wind]

p ?

[haughty thistle]

it says a carton costs 70p, what does p stand for?

[soft wind]

ahhh

£0.70

p is pence

[haughty thistle]

oh sorry

[soft wind]

no its ok

[haughty thistle]

imma calculate it now

yeah i got it

wait no

im pretty sure i did the wrong thing, but my current answer is 5.1+1/3

no

5.13333333333333333333

and so on

[soft wind]

how did u do it ?

whats ur method

[haughty thistle]

First, i calculated (2/5x10)+(1/3x10)

which was 7+1/3

and multiplied it by 0.7

[soft wind]

ohhh

[haughty thistle]

so the answer was 5.133333333... pounds

[soft wind]

thank u so much

[haughty thistle]

np

write .close to close

unless you have another question

[soft wind]

oh okay

thanks again

[haughty thistle]

np

[soft wind]

.close

[obtuse pebble]

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[obtuse pebble]

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[glossy magnet]

How do I work out the point C which is exactly 1 unit from point A and B

[glossy magnet]

Basically I need to get from one point to another (0 to 2 units apart max)

But I need to get there with 2 straight lines of 1 unit

How do I find the coords of that point?

[dense imp]

You can set up two equations using pythagorean theorem / distance formula between your unknown points and each of the known points and you’d then solve the system of 2 equations

[glossy magnet]

Oh simultaneous equations?

Yeah I guess that makes sense

[brave bramble]

You'll put a circle around each point. If two circles intersect, they'll intersect in two different places.

[obtuse pebble]

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[fluid wolf]

how do i determine whether or not this matrix is diagonizable?

[brave bramble]

,w eigenvalues of {{2,1,1},{1,2,1},{1,1,2}}

[warm shale]

Results provided by WolframAlpha

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Requested by Kaynex#7520

[kind hawk]

shortcut, it's symmetric. long story: calculate all eigenvalues and eigenspaces

[fluid wolf]

what will be indication based from the eigenvalues and eigenspaces to tell that the matrix is diagonizable if i were to infer from those eigenvalues and eigenspaces instead of concluding that matrix is symmetric

[kind hawk]

if the algebraic multiplicity of each eigenvalue is equal to the geometric multiplicity

so if an eigenvalue lambda has an exponent e in the char polynomial, then the eigenspace also needs to have the dimension e

here the eigenspace corresponding to the eigenvalue 1 needs to have dimension 2

because 1 is a double root of the char polynomial

[fluid wolf]

oh so since the eigenvectors are [-1,1,0] and [-1,0,1] then eigenspace for 1 has dimension 2

[kind hawk]

not "the" eigenvectors. but yes. since there are eigenvectors which are linearly independent the dimension is 2

[fluid wolf]

if i want to make the diagonal matrix of this, will matrix P be affected depending which order i put the eigenvalues as?

[kind hawk]

well P is the matrix of eigenvectors

so clearly it matters how you put them in

D will only be affected in the order of the eigenvalues on the diagonal

order corresponds to the order of the columns in P

[obtuse pebble]

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[obtuse pebble]

@high flint Has your question been resolved?

[high flint]

<@&286206848099549185> any ideas? (sorry for ping)

[obtuse pebble]

@high flint Has your question been resolved?

[obtuse pebble]

@high flint Has your question been resolved?

[obtuse pebble]

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[cloud radish]

Looking for a formula or methodology to find the shortest unique way to represent the numbers(n) 0 to 10,000 using: a single digit(x) from 0 to 9; and the operations +,-,*,/,^,(,)

Example is test n=x*x-(x+x)if n is 100 or less.

Discrete answers
n=0,x=0;n=-1,x=1;n=0,x=2;n=3,x=3;n=8,x=4;n=15,x=5;n=24,x=6;n=35,x=7;n=48,x=8;n=63,x=9

x=0,2 because n=0 in both cases, also 0=0 is unique.
x=1 fails because the answer is negative.
x=2 could be 0=2^2-(2+2) or 0=2-2/2-2/2 both of which have nine symbols, but 0=2+2-2^2 has seven.
The test formula has nine symbols.
x=3 fails because 3=3 has one symbol.
x=4 fails because 8=4+4 has three symbols.
x=5 fails because 15=5+5+5 has five symbols.
x=6 could be true as 24=6*(6-6/6-6/6)has twelve symbols, but fails because 24=6+6+6+6 has seven symbols as does 66-6-6.
x=7,8,9 fails because 35=77-7-7 has seven symbols as does 48=88-8-8 has seven symbols and 63=99-9-9.
While the failures noted do not prove the shortest unique formula for n=, they are shorter than n=xx-(x+x).
In base ten this formula would be x^2-2x=xx-(x+x)

[cloud radish]

Looks like a lot of * got deleted on post.

The shortest unique way to represent the numbers(n) 0 to 100 using: a single digit(x) from 0 to 9; and the operations +,-,,/,^,(,) Example is test n=x[times]x-(x+x):n=0,x=0;n=-1,x=1;n=0,x=2;n=3,x=3;n=8,x=4;n=15,x=5;n=24,x=6;n=35,x=7;n=48,x=8;n=63,x=9
x=0,2 because n=0 in both cases, also 0=0 is unique.
x=1 fails because the answer is negative.
x=2 could be 0=2^2-(2+2) or 0=2-2/2-2/2 both of which have nine symbols, but 0=2+2-2^2 has seven.
The test formula has nine symbols.
x=3 fails because 3=3 has one symbol.
x=4 fails because 8=4+4 has three symbols.
x=5 fails because 15=5+5+5 has five symbols.
x=6 could be true as 24=6x(6-6/6-6/6)has twelve symbols, but fails because 24=6+6+6+6 has seven symbols as does 6x6-6-6.
x=7,8,9 fails because 35=7x7-7-7 has seven symbols as does 48=8x8-8-8 has seven symbols and 63=9x9-9-9.
While the failures noted do not prove the shortest unique formula for n=, they are shorter than n=xx-(x+x).
In base ten this formula would be x^2-2x=x*x-(x+x)

[obtuse pebble]

@cloud radish Has your question been resolved?

[cloud radish]

<@&286206848099549185> going once

[obtuse pebble]

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[obtuse pebble]

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[wanton dagger]

How can I factor this?

[royal basin]

factor out (3x-2)^4

[wanton dagger]

How?

I feel confused on that

This is what I did

[royal basin]

"How do I do this?" [goes ahead and does it]

[burnt scroll]

Where’d the x go @wanton dagger

[near saffron]

spectral theorem guarantees it by the fact that it is symmetric

[wanton dagger]

Oops

[wanton dagger]

Forgot

[near saffron]

oh wait

this was an old question

mb

[wanton dagger]

Ok thanks

.close

[obtuse pebble]

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[void swift]

Hii im still stucked on the same question,

[void swift]

Correction its 2x - 1

i need to rearrange the first set of expression to satisfy the form, 4(Ax + B)/sqrt 4x + 3

[grand breach]

what is the question

[void swift]

@grand breach

Wait no

Not this

This

[grand breach]

hmm

i think this require calculus

[void swift]

Yes

I have solved it with product rule

[void swift]

Here is my answer

[grand breach]

is the answer wrong there?

[void swift]

But i need to transform it into 4(Ax + B)/ sqrt 4x + 3 form

[grand breach]

hmm lemme do it

[void swift]

Correct answer is 18x + 11/sqrt 4x + 3

But how should i change this into

Wait

Wait nvm

Nevermind

[grand breach]

MAn

[void swift]

It didnt say it needs integers

It just need constants

but

wait what

nvm

okay so

the answer is 18x + 11/ 2 sqrt 4x + 3

but its asking me to rearrange to the form 4(Ax + B)/sqrt 4x + 3

how should i deal with the 2 in the denominator

wait

Okay i think I got the answer

Is this correct

[grand breach]

,r

[void swift]

huh

[grand breach]

,rotate

[grand breach]

k

[void swift]

wdym

.close

[obtuse pebble]

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[royal forge]

Hello! Could someone please help me choose which approach is more appropriate to this problem? If I define X as the random variable that denotes how many defective products there are in a batch, then I have 2 potential approaches to the problem.

The first one is that I model it as a binomial, where I get the parameters by noting that since the average is 3 per 100, then np = 3, so 100p = 3 and p = 3/100.

The second one is to model it as a Poisson random variable, with lambda 3. It seems to satisfy all the assumptions.

Which would you say is more appropriate and why? Thank you!

[royal forge]

Here is the continuation of the problem. I am heavily leaning towards modeling it as Poisson random variable since it asks for probabilities of an extended interval, whereas the binomial is only specifically defined for n=100. Is this correct? I'm only really caught up on whether it would be appropriate to model it as Poisson

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[obtuse pebble]

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[deft nymph]

Is it true that lim x->y (g(f(x))) = g(lim x->inf (f(x)))?

[deft nymph]

so for example with lim x->y ln(x/(x+1)), since the only thing that limit affects is the fraction, and ln just takes that value, can't we just move the logarithm before the limit and only care about limit of x/(x+1)?

.close

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[obtuse pebble]

Please don't occupy multiple help channels.

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