help-27

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[unborn stratus]

My backyard is a rectangle with area 480 square feet and its length and width are both an integer number of feet. If the perimeter of the backyard is less than 120, how many different dimensions could the backyard have?

[unborn stratus]

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[gaunt olive]

I NEED HELP PLS

[gaunt olive]

wassup

I need help here

@spare zealot

<@&286206848099549185>

[lunar oar]

looks like you got the right answer

what do you need help with?

[gaunt olive]

YEA

parts with the question marks

Can u speak French?

@lunar oar

[lunar oar]

a tiny bit

[gaunt olive]

cus som terms Idk in English

fine I’ll try my best in English

[mild saddle]

i can speak french

[gaunt olive]

Ah daccord

J’ai fait l’arc de sécante dans ma calculatrice de -17/8

Pour vérifier si c’est dans [pi, 3pi/2]

mais ce n’était pas dedans

@mild saddle

@lunar oar wow lool just abandoned me

I need u BACK

PLSS’SPLSLSLLSS

@lunar oar

[lunar oar]

oui d'accord

[gaunt olive]

Ok lorsque j’ai fait l’arc de sécante de -17/8

[lunar oar]

je suis desole but my french is not going to be enough for math

[gaunt olive]

OK

So I’ll speak English

I did sec-1 on my calculator

To verify if -17/8 is in [pi,3pi/2]

it ain’t IN IT

HOW?

[lunar oar]

Basically the calculator will give you the value for arcsec for values of theta between 0 and pi i believe

[gaunt olive]

O

So….

[lunar oar]

but you can take that value and add pi to it

and it will work

[gaunt olive]

ah thx

ur the best

goodbye

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[zenith fable]

whats (n!)^(1/n)

[zenith fable]

i am not sure how to approach this

.close

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[cold hornet]

are the values of k

-6

and 2?

[restive river]

Yeah

[cold hornet]

and

for this question

what would i do

[restive river]

I’m in high school and have no idea about Riemann sums sp cant help with this one

[cold hornet]

alright thanks but wait were you trolling saying yeah

or you for real

[restive river]

No that wasnt trolling

[cold hornet]

ah okay i appreciate thanks for confirming the answer

[restive river]

Because I know like when it is continouous the limit from both sides should be equal to k(k+4)

And lim sin(t)/t for t->0 is 1 so the limits for the upper one is 12

[cold hornet]

alright thanks

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[uncut cobalt]

A physicist found that a force of 0.68 N was measured between two charged spheres. The distance between the spheres was 1.0 m. Calculate the force between the two spheres when the distance was decreased to 0.50 m.

[uncut cobalt]

Can someone tell me how to work this

[nova ibex]

I believe (I haven’t took physics in years ) you’d use coloumbs law?

Try setting up simultaneous equations

[uncut cobalt]

Is that the newtons/ coulomb thing

the physics lesson im on has so many different formulas im shiteing myself just figuring out what to use

[restive river]

$F_el=k\times\frac{Q_1*Q_2}{r^2}$

i think

bru hwat

[nova ibex]

Missed a q

😂

But yeah

I think you can also use the inverse square law

[woven radish]

Prime Minister

[nova ibex]

Since everything is the same

[uncut cobalt]

would r be distance

in this equation

[restive river]

yeah

[uncut cobalt]

oh okay thx gimme a momment i think i might have this

[restive river]

You have $F_1=0.68N$ i think you can find it if you divide by parts

[woven radish]

Prime Minister

[uncut cobalt]

okay the force is .68 when its 1

so .5^2

so .25

[restive river]

$\frac{F_1}{F_2}=\frac{k\times\frac{Q_1Q_2}{r_1^2}}{k\times\frac{Q_1Q_2}{r_2^2}}$

[uncut cobalt]

.68 divided by .25

[woven radish]

Prime Minister

[uncut cobalt]

or wait

no would it just be 1/4 of .68

[restive river]

ks q1s q2s cancel out and you can solve for F2

[uncut cobalt]

I dont know the qs just r and the first f

[restive river]

yeah the ks and qs cancel out

[uncut cobalt]

I can do that with this equation?

[restive river]

s o youre left with $\frac{F_1}{F_2}=\frac{r_1^2}{r_2^2}$

[woven radish]

Prime Minister

[uncut cobalt]

yeah

and we know f1

.68

equals 1/.5

so then

[restive river]

you know both f1, r1 and r2 so youre just solving for f2

[uncut cobalt]

so would the awnser be .37

for f2

unless my r2 is wrong

[restive river]

0.5m squared

[uncut cobalt]

oh yeah .25

forgor

1/.25

equals

.68/ ?

so then

[restive river]

1/0.25 is 4

[uncut cobalt]

ye

[restive river]

so you have $F_1=4F_2$

[woven radish]

Prime Minister

[uncut cobalt]

and f1 is .68

[restive river]

wait but the objects are getting closer how is the force smaller

[uncut cobalt]

oh yeah

[restive river]

[uncut cobalt]

what i do then

is it changed to a multiply

instead of divide

2.72

[restive river]

$\frac{F_2}{F_1}=\frac{r_2^2}{r_1^2}$

[woven radish]

Prime Minister

[restive river]

sp

$F_2=\frac{r_2^2}{r_1^2}F_1$

[woven radish]

Prime Minister

[uncut cobalt]

just mutiply .68 by 4 right

2.72 should be correct awnser i think

for f2

[restive river]

$F_2=0.25*0.68=0.17N$

[woven radish]

Prime Minister

[restive river]

that or i fucked something up horribly

still no what

[uncut cobalt]

hell if i know tbh

[restive river]

man i fucking hate maths

[uncut cobalt]

physics is confusiong

this discord server is my saveing grace actually explains it in a understandable way most of the time

[restive river]

$\frac{F_2}{F_1}=\frac{r_2^2}{r_1^2}=(\frac{r_2}{r_1})^2$

[woven radish]

Prime Minister

[restive river]

not with me brace tight

[uncut cobalt]

Alrighty

[restive river]

i think i just cant do math

[restive river]

youre left up with a ratio of the forces with respect to the square of their distances

if you get your numbers right unlike me the F2 should be bigger than the F1 since theyre moving closer

[restive river]

and since the distance was decreased by 2 the force should be 4 times stronger

[uncut cobalt]

Yeah multiply it by 4

[restive river]

where did i go wrong

[uncut cobalt]

Id tell you if i knew

I mean 2.7 was the right awnser

Didnt know you had to square the distance

Thanks anyways

[restive river]

God wait

[uncut cobalt]

?

[restive river]

i think it becomes $\frac{F_1}{F_2}=\frac{r_2^2}{r_1^2}$

[woven radish]

Prime Minister

[restive river]

then $F_2=\frac{F_1*r^2_1}{r^2_2}=\frac{0.68}{0.25}$

[woven radish]

Prime Minister

[restive river]

which means that $F_2=2.72N$

[woven radish]

Prime Minister

[restive river]

i did it letsgoo

[uncut cobalt]

Maths

[restive river]

yeah its painful

[uncut cobalt]

Math is something simple disguised as something hard really

Cause in the end all it was was squareing .5 and divided .68 by it

[devout snow]

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[devout snow]

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[restive river]

just out of curiosity how "long" is real analysis? like in terms of content compared to calculus?

[frozen aurora]

might be a better idea to ask in #discussion or #math-discussion

[restive river]

it shows no access to me

[frozen aurora]

oh, you have perma-studying

then no luck

maybe someone will answer here

[restive river]

hv u not done RA

[frozen aurora]

no

[restive river]

oh i see

over here RA and Proof based LA are first sem

[frozen aurora]

i know some from youtube and stuff but i never actually formally learnt it; i'm not in a math major (yet)

[heavy current]

afaik, it depends on what you mean by "real analysis"

do you mean "rigorous calculus"?

or like lebesgue integration and co.

[restive river]

idk like
if you took a course in single variable calculus right and then followed by that you took a course in real analysis, how many hours would you spend on that ra course

[heavy current]

well

i only did differential calculus in high school

but my uni is the same as yours

RA and proof based LA in 1st year, if you mean "rigorous calculus" by RA

i definitely spend a LOT more time in RA than i did in calculus

[restive river]

where do you do uni

[heavy current]

university

[restive river]

yes

where do you do university

if ur comfortable sharing

[heavy current]

uhh, i dont really wanna dox myself lol

[restive river]

i see

[heavy current]

tbh though, i'm kinda bad at math lol

if you are good with proof-writing to start, it helps a lot

[restive river]

is this what your first year looks like approximate

it's in french but i think you can decipher what they mean

[heavy current]

what is "Enjeux mondiaux"

[restive river]

that's just some stupid extra in global issues

ignore that bit

[heavy current]

ok lol

it's not the same as mine

but some parts are

i dont have a discrete math course

or algebraic structures for that matter

[restive river]

but ig you have some cs and maybe physics

[heavy current]

i do have physics

but personally, i have put 10x less effort into physics and done 10x better so idk lol

[restive river]

bro's a show off

[heavy current]

nah

[restive river]

bro is feynman

[heavy current]

when i say 10x the mark

i dont mean the mark is like 100

i say 10x the mark, because my math grades are not good lol

[restive river]

oh

nah i'm sure you're good

thanks

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[heavy current]

gl with your studies

[devout snow]

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[floral cradle]

where do I start for this

[frigid jetty]

Advise you to write given

And drawing if it's necessary

[floral cradle]

I did and found force friction as 15696 but idk where to go from there. Never did a question like this so I'm not sure which formula I'm using.

[devout snow]

@floral cradle Has your question been resolved?

[devout snow]

@floral cradle Has your question been resolved?

[versed hare]

anyone please help me with this question-Consider that a, b, c, d are positive real numbers satisfying (a + c)(b + d) = ac + bd.
Find the smallest possible value of S=a/b+b/c+c/d+d/a

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[low tundra]

Can someone please help me with this

[restive river]

try u sub

[low tundra]

What should I sub here

Hold on

[restive river]

do u know how u sub works?

[low tundra]

Yeah I do

Shojkd I take sin x as t

Or x^2 as t

[restive river]

try taking the denominator, see what it goes to

[low tundra]

Okay

Ok so it isn't making sense to me

Can you like show me how to substitute to the denominator

[eager nova]

You put a variable and substitute it

[low tundra]

Yes

[eager nova]

u = denominator

[low tundra]

Oh ok

[restive river]

yeah you definitely dont know how u sub works

that's no worries

you will learn

[low tundra]

Uhm I know how to like substitute a single term

Not the entire denominator but yes

I will learn

[restive river]

yes you will!:)

[low tundra]

Ok so now I take the denominator as u, what do I do next

Omg ok

I think I figured it

Omg

I togally forgot how substitution works but I got it now

Thanks a lot guys

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[devout snow]

@random gale Has your question been resolved?

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[pastel glacier]

Are there any good online tools or software to create and calculate probability diagrams?

I would like to calculate things similar to this...
Task 1: Score 3 total points with 50% chance at 3 points, 30% chance at 2 points, 10% chance at 1 points.
Task 2: Score 2 total points with 50% chance at 1 point.
etc. (with the points being cumulative between tries)

And calculate something along the lines of "What is the odds of being able to succeed at all tasks back to back in 8 total tries".

I've done it by hand when it is a lot amount of tries, but it becomes impossible for me to figure out over higher number of tries.

Thank you so much for your help, and let me know if it is clear/unclear! 🙂

[harsh wigeon]

Yeah

Python

Just write some code and display the results after running it a couple thousand times

[pastel glacier]

I would only need to run it once, but I was hoping a tool existed so I didn't have to write a program to calculate probability diagrams

[devout snow]

@pastel glacier Has your question been resolved?

[devout snow]

@pastel glacier Has your question been resolved?

[devout snow]

@pastel glacier Has your question been resolved?

[pastel glacier]

Finished making a script that calculates all the branches \o/

.close

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[rain marten]

Is this quadratic inequality?

[fervent sundial]

yes

[rain marten]

How to do these inequalities

Fuck

I forgot

x(x+7) < 44

x^2 + 7x < 44

[fervent sundial]

x^2 +7x - 44 < 0

(x+11)(x-4) < 0

then draw a number line and plot x = -11 and x = 4

[rain marten]

Got it that’s all

[fervent sundial]

and check regions (-inf, -11), (-11, 4), and (4, inf)

[rain marten]

Check for?

[fervent sundial]

check whether the values of x in that region satisfy this

[rain marten]

Okay 👍

[fervent sundial]

this is a "word problem" so x can't be negative nor can a rectangle be like a linee, but ig you were curious on how to solve quadratic inequalities in general so yeah

[rain marten]

Ye thanks alot

[fervent sundial]

[rain marten]

.close

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[wintry coral]

I've done the first part of this question (prove that both of these power series have infinite radius of convergence) and computed p'(x) and q'(x)

I've also proven the identities 2p'(x)=q(x) and p(x)-q(x)=2xq'(x)

the last bit evades me

no rearrangement I make seems to get me any closer

[devout snow]

@wintry coral Has your question been resolved?

[devout snow]

@wintry coral Has your question been resolved?

[devout snow]

@wintry coral Has your question been resolved?

[devout snow]

@wintry coral Has your question been resolved?

[devout snow]

@wintry coral Has your question been resolved?

[supple knot]

Show your work for the previous parts

[wintry coral]

ratio test for p(x) and q(x)

[wintry coral]

not necessary to solve the second part whatsoever

but i have this for the first part of b)

$p'(x)=\sum\limits_{k=0}^\infty{\frac{kx^{k-1}}{2k!}},q'(x)=\sum\limits_{k=0}^\infty{\frac{kx^{k-1}}{(2k+1)!}}$

[woven radish]

george clooney real account

[dire forge]

This took me a little thinking but I see what to do now. Hint: Start by differentiating p^2 = 1 + xq^2.

If the derivatives of both sides are equal, then p^2 and 1 + xq^2 can only differ by a constant.

Finally, plug in x=0 to show that they are actually equal.

[devout snow]

@wintry coral Has your question been resolved?

[wintry coral]

ah tysm

[devout snow]

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[grim mountain]

a^lnb -b^lna

[grim mountain]

Dont get me wrong

I know the answer but i forgot its property

[sturdy yew]

0 r8

[grim mountain]

a^ln_b -a^ln_b

[grim mountain]

You switch a and b

[sturdy yew]

yea

thats t

[grim mountain]

What’s the property name again

[sturdy yew]

idk base change property?

[grim mountain]

Like How would you define it

[sturdy yew]

u want the proof of that property?

[grim mountain]

Base of a, logaritm exponent to Base of b

Yeah

[sturdy yew]

i think u can take lna on both ssides and try simplifying fromthere

[grim mountain]

How you mean

[sturdy yew]

when u take lna on both sides, the powers come out

and then u shud be able to simplify it from there

[grim mountain]

Can you write that up

So i can see what you mean

[sturdy yew]

kind of messy but i think it shud help

[grim mountain]

I thought they changed their bases..

But maybe not

Hmm

.close

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[restive river]

help with 5 6 7

[devout snow]

Please don't occupy multiple help channels.

[devout snow]

It is suggested that you limit yourself to one question per help channel, opening a new one once your original question is answered and your original channel has been closed. This is to make your channel easier to follow for potential helpers and can bring attention to the fact that your question has changed.

[restive river]

<@&286206848099549185>

Y

<@&286206848099549185>

[low nexus]

are you familar with laws of sines and cosines

[restive river]

not rlly

[graceful flax]

use the law of sine and cosines

[restive river]

idk what that is

[graceful flax]

angle r is 75 btw

[restive river]

ty

yk how to do 6?

[graceful flax]

yeahh

[devout snow]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[restive river]

can u help me plz

[graceful flax]

from figure ∠Q = ∠X = 55⁰, ∠S = ∠Z = 50⁰
sum of angle of triangle is 180⁰,
∠Q + ∠S + ∠R = 180⁰

∠R = 180 - 55 - 50

∠R = 75⁰

this is how you get angle r

and btw have yuo tried solving for xy

[restive river]

for which problem

[devout snow]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[graceful flax]

6th

obv

[restive river]

nah

[graceful flax]

try man

[restive river]

is it 55

[graceful flax]

hmm wait\

[restive river]

yea?

how that tell me what XY istho

[graceful flax]

xy is 6cm

becasue the traingle is congruent

[restive river]

ohh i see

[graceful flax]

how did you get 55

?/

[restive river]

for number 7 i got 55

mb

[graceful flax]

ok wiar 75 plus 50 -180 is the answer for 7th

[restive river]

it was js asking the angle for x

and since q and r are correspong

[graceful flax]

yeah angle x is 55

good job

[restive river]

i got 5

Alr ty

think we can do sum more

[graceful flax]

how many

[restive river]

12?

if u got the time

[graceful flax]

sorry man i got a ton of thesis tow rite

to write 8

[restive river]

Could we do maybe js 2

[mighty galleon]

Number 2?

[restive river]

i did those

this is a difrrent page

accidentally put 2 pages

i tried doing it as u can see opn the left prolly wrong though

[mighty galleon]

There is no question 2 here

[restive river]

i ment 2 questions because he wasnt availble to help with all 10

[mighty galleon]

Ok, give me a second to look at them

[restive river]

ok thank ytou

[mighty galleon]

For question 3, how did you get x = 15?

[restive river]

i thought it added uyp to 90

so i ddi 75 plus 15

[mighty galleon]

No

[restive river]

oh

[mighty galleon]

I would look at this triangle like this. 2 sides are equal so it is isosceles which means 2 angles are also equal, with this triangle it's easy to tell but typically it is the angles that are not in the corner of the two equal sides

So the angle that has 75 is equal to the angle that has x

[restive river]

so x is 75?

[mighty galleon]

Yes

[restive river]

okay i see

[mighty galleon]

And the sum of all the angles of a triangle is 180 so you can solve for the last angle, which isn't exactly y but will help solve for y

[restive river]

the last angle would be 30

yew?

[mighty galleon]

Yes

[restive river]

so y would be 60

[mighty galleon]

Yes

[restive river]

yessir

ok number 4

idk where to start

[mighty galleon]

So the middle triangle has all equal sides and all angles are equal which means they are locked at 60 degrees each

Equilateral triangle

[restive river]

okok

only for the middle tho

[mighty galleon]

A straight line always equals 180 obvs. So solve for x

[mighty galleon]

Yes

[restive river]

where the straight line

the bottom line?

with 40

[mighty galleon]

Yes, you have two out of the 3 angles

[restive river]

X+40+180?

[mighty galleon]

Not quite

x + 60 + 40 = 180

[restive river]

ohhh i see

i ment equals 180

im just a clumsy typer

[mighty galleon]

Yeah, fat/fast fingers will do that. It's hard to type as fast as you think

[restive river]

x+80

X+80

[mighty galleon]

I'm going to assume equals and yes

[restive river]

x=80

so with x as 80

y would be80 as well?

[mighty galleon]

Not quite, that arrow is I am assuming meaning parallel to the other line that has an arrow

And if they're intersecting the same line then they'll have the same angle(s)

[restive river]

i see

so y is50

[mighty galleon]

No

[restive river]

but i thought they the same

[mighty galleon]

No

[restive river]

and they gotta add up to 180

oh

[mighty galleon]

The bottom line

You're gonna get the other non-wanted angle of that triangle

[restive river]

which are trhose

[mighty galleon]

Which is x + y + ? = 180

[restive river]

and x is 80

so y is 100?

[mighty galleon]

No, none of those angles are obtuse

[restive river]

there paraellel?

[restive river]

ohhhh

those arrows

[mighty galleon]

The two yellow angles are equal since the two parallel lines intersect the same straight line

[restive river]

so y is 60

[mighty galleon]

Yes

[restive river]

there we go

[mighty galleon]

They're funky looking arrows

[restive river]

tahyea lol

for 6

i mean 5

i see the line so that equalds 180

the straight line

[mighty galleon]

Yep so the missing angle is?

[restive river]

x

[mighty galleon]

No

[restive river]

y?

[mighty galleon]

No

On the straight line

[restive river]

i think im looking at the wring ine

im looking at the one going from the right of x to y

[mighty galleon]

Look at the line that has 60 and 70 on it first

[restive river]

ok i see

theres 2 missing yea?

[mighty galleon]

This line

[restive river]

yea

is missing the top and the bottom one

[mighty galleon]

No

The one inbetween 60 and 70

[restive river]

ohh its missing the one across from y

i see

[mighty galleon]

Those two you can't solve for using straight line = 180

[mighty galleon]

What is that missing angle

[restive river]

50?

[mighty galleon]

Yes

So now you can solve for x and y

[restive river]

so y is 50

[mighty galleon]

Not quite

[restive river]

60

my bad

[mighty galleon]

Yeah

And x = ?

[restive river]

70?

[mighty galleon]

No

[restive river]

ooh no

60

[mighty galleon]

Yes

[restive river]

there we go

for 6 i think x is 40

[mighty galleon]

There is another way to tell from the beginning and it's called the bowtie theorem, if it looks like a bowtie you can just about assume the inner two angles pointing towards eachother are equal

[restive river]

ohhh

that a good mathod ngl

method

[mighty galleon]

Yes x = 40

[restive river]

idk abt y

[mighty galleon]

You are given 1 angle and the other (not the angle y) can be solved for using straight line = 180

[restive river]

y is 160>

?

[mighty galleon]

Yes, but the other angle above y

[restive river]

thats 160?

or they both are

[mighty galleon]

No

[restive river]

but y is 160 is correct

[mighty galleon]

No

[restive river]

oh

[mighty galleon]

The yellow angle = 180

[restive river]

y is 70

[mighty galleon]

Yep

[restive river]

there we go

[mighty galleon]

I'm going to repost the page picture quickly so I don't have to keep scrolling up and down

[restive river]

ok

for 7

i think x is 5

[mighty galleon]

Yep

[restive river]

and so is y

[mighty galleon]

No

3y + 3x = 9x = 45

Or 9x = 45
3y + 3x = 45

You solved for x which was 5

3y + 3(5) = 45

[restive river]

y is 20

[mighty galleon]

No

[restive river]

25

[mighty galleon]

3y + 15 = 45

Use algebra and solve for y

[restive river]

10

[mighty galleon]

Yes

[restive river]

ok there we go

for 8

is see that rhe angle is 38

[mighty galleon]

This one is tedious

[restive river]

looks scary

[mighty galleon]

Very

[restive river]

(10x+6y)=38?

ad

[mighty galleon]

Yes

[restive river]

(20x+4y)=52

[mighty galleon]

Yes

[restive river]

do i add those 2 together

[mighty galleon]

No

[restive river]

oh i just solve?

[mighty galleon]

Yes-ish

Technically you would solve for either y in terms of x (y = 52/4 + 20x/4) or you can plug and chug/use basic multiplication

[restive river]

idek

[mighty galleon]

For instance 6 times what equals a number that has 8 in its ones place?

[restive river]

5

[mighty galleon]

6 * 5 = 30

[restive river]

yea

[mighty galleon]

6 * ? = _8

[restive river]

5

[mighty galleon]

No

That has a 0 in the ones place

[restive river]

6 times what =38

[mighty galleon]

There is also 10x in that equation

10x + 6y = 38

10 times a (whole) number can't have an 8 in the ones place, but 6 can

[restive river]

oh i seee

6 times 3

[mighty galleon]

Yep

10x + 18 = 38 whats x

[restive river]

1

2

[mighty galleon]

Yes

Plug them into the other equation to see if it works

[restive river]

ok

both x and y

or just x

[mighty galleon]

Both

[restive river]

ok

yea it =52

so x is 2 and y is 3

[mighty galleon]

Yes

[restive river]

ok 15

o dont see what i do

i see is isocolies so they both are equal

the equationa

[mighty galleon]

Yes, set up the equation

[restive river]

3x+15-=4x+12

X=3

for 16 it looks equal angular so they are all equal

[mighty galleon]

Set up the equation

[restive river]

8x-22+6x

i got 11

that right?

[mighty galleon]

Not plus

8x - 22 = 6x

But yes 11

So I'm assuming you meant = and hit + again

@restive river

[restive river]

yea

[mighty galleon]

You good from here?

@restive river

[restive river]

almost but stuck on 17

are those also all equal

[mighty galleon]

Wdym are they all equal? The sides are equal since it's an isosceles triangle

And they are on the equal sides

The angles are there to show/hint it is isosceles

[restive river]

so i just make the equation again

[mighty galleon]

Yes

[restive river]

okok

im confused on 18

because there is=no agle to combinde

i mean equation

[mighty galleon]

The triangle is equilateral so all the angles are equal, and there is only way for the angles to all be equal on a triangle. They're always 60 degrees on equilateral triangles

[devout snow]

@restive river Has your question been resolved?

[restive river]

s0 x is 30

[mighty galleon]

Yep

[restive river]

ok thank you

6y.close

[mighty galleon]

Just use .close

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[devout snow]

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[bright juniper]

A guy walked 18 km wich is his dayly walks 60% how much dose he have to walk

[faint zinc]

!status

[devout snow]

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

[bright juniper]

Idk where to start

He has 40% of the way to go right

Oh i did it the answer is 30 right

[faint zinc]

yeah the answer is 30

you divide 18 by 0.6

[bright juniper]

.close

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[static pollen]

how is the RHS derived?

[static pollen]

.close

[devout snow]

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[mellow scroll]

how do i do part i)

,close

.close

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[late girder]

could anyone explain why the answer isnt infinity/infinity so like not defined 🫣

[restive river]

inf/inf is not undefined it is an indeterminant form of a limit

which means its value can't be determined unless some manipulation is done

[late girder]

oh wait right

ty!

.close

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[thorn bramble]

Find the sum of all 4-digit numbers whose digits are different from each other and do not contain the digit 0.

[thorn bramble]

<@&286206848099549185>

[dry geyser]

I suppose if we add the last digits of our numbers, we add 1 n times, 2 n times, 3 n times and so on. Same for all other digits. Now we need to find n

The question likely then becomes: How many 4-digit numbers with different digits and not containing 0 can we create that have the last digit 1/2/3/…

Any idea on how that number could be calculated?

[forest nimbus]

Sequence equation maybe but tweaked for the conditions

[thorn bramble]

<@&286206848099549185> there is such a hint

[forest nimbus]

Well first thing is that out of 1000 there are 900 numbers without a 0

1-9 x 10
Then do it again for the hundreds

Wait no im dumb

Lol

900 i mean

[graceful flax]

do you know the answer

[forest nimbus]

Not in the fucking slightest lol, we are at the gathering clues stage

I mean if you know the equation then thatd be nive

Nice

[graceful flax]

no like do you know the answer

is there solution based

text or smth

[forest nimbus]

Well its math, so its likely solution based

Sorry i dont quite get what you mean

[graceful flax]

the total number of such 4-digit numbers = 9 * 9 * 8 * 7 = 4536.

The sum of the digits (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) = 45.
As there are 4536 numbers, the sum of the units place = 45 * 4536.

For the tens place
The digits will occupy the tens place as the same number of times as they do in the units place so obv the sum of the tens place = 45 * 4536 * 10 (as each digit in the tens place represents a value ten times greater).

the sum of the hundreds place = 45 * 4536 * 100.
For the thousands place:
Again, the sum of the thousands place = 45 * 4536 * 1000.

calculate the total sum:
Sum = Sum of units place + Sum of tens place + Sum of hundreds place + Sum of thousands place

@forest nimbus

does this make sense

[forest nimbus]

Woah

[graceful flax]

i have a speech to text makes it easier ig

[forest nimbus]

WOAHHHHHH

Holy shit that was crazy lol

[graceful flax]

for big sentences i use it

[graceful flax]

?

[forest nimbus]

Howd you get this?

Like why specifically 998*7

9*8

[graceful flax]

There are 9 options (1-9) for the first digit, 9 options (excluding the first digit and 0) for the second digit, 8 options for the third digit, and 7 options for the fourth digit

so then the total number is this

ig

i was not sure that is why

[forest nimbus]

Why only 8 options for 3rd digit?

Its not 9?

[forest nimbus]

Wait fuck we overlooked something

[restive river]

it should be 9.8.7.6
Since numbers are non-repeating?
Number of ways to arrange 9 numbers in 4 places = $ 9 \choose 4$
$$= \frac{9!}{4!}$$

[woven radish]

Snöwdinger

[forest nimbus]

Digits are different from each other

[graceful flax]

oh yeah hmmm

[restive river]

[graceful flax]

There are 9 choices for the thousands place (since it cannot be 0), 9 choices for the hundreds place (as it cannot be the same as the thousands place), 8 choices for the tens place (as it cannot be the same as the thousands or hundreds place), and 7 choices for the units place (as it cannot be the same as the thousands, hundreds, or tens place).

[forest nimbus]

27360

[graceful flax]

9 * 9 * 8 * 7 = 4,536.

i think this is right

[forest nimbus]

Its not because it will repeat

[graceful flax]

we can use the formula for the sum of an arithmetic series: S = (n/2)(first term + last term)

[graceful flax]

howw

[forest nimbus]

How will it not?

[graceful flax]

bruhh lol

[forest nimbus]

Bro 9 options for tens and ones that means you included the multiples of 11

[graceful flax]

the fourth digit can be chosen in 7 ways (from 0 to 9 excluding the digits already used as the first, second, and third digits) that is why the total number of such 4-digit numbers is 9 * 9 * 8 * 7 = 4536.

hm

[restive river]

Repetition and 0 is not allowed in this permutation ._.
number of ways to arrange numbers in first digit = 9
' '' second digit =8
' '' 3rd =7
' '' 4th digit =6
?

[forest nimbus]

Mhmm

[dense lynx]

to answer this question, all one needs to do is count how many times each digit appears in each location, and sum that

[graceful flax]

Assuming positive 4-digit numbers with no repetition, and without digit 0 amd then for each number formed we have 9 choices for the first digit, 8 choices for the second digit, 7 choices for the third digit, and 6 choices for the fourth digit. Therefore, we can form 987*6 = 3024 such 4-digit numbers. The smallest such number is 1234, and the largest is 9876. The average of 1234 + 9876 = 11110/2 = 5555. This is also the average of all the numbers
Therefore, the sum of all the 4-digit numbers not containing 0, and without repetition of digits is 5555 * 3024 = 16,798,320.

[forest nimbus]

What would that look like?

[dense lynx]

it would look like this

… sort of

[forest nimbus]

Jesus christ how did you type so fast

Also you changed it bleh

Noice equations, very useful

[graceful flax]

so am i right

or is there something i am missing

[forest nimbus]

How would it not repeat the digits tho, like if you have 9 single digit number options, thatd mean it would take up every number spot

[graceful flax]

huh sorry i didnt underdtand

[forest nimbus]

There are only 9 number options right cause we dont have a 0?

So lets say 1234+1235+1236+1237+1238+1239

We have to start at 1234

So then why is the ones digit 9 options

Then after that wed have to add it to 1243+1245+1246

[thorn bramble]

16798320

[forest nimbus]

Howdya getit

[thorn bramble]

i didnot the answer was written

[forest nimbus]

Chad

[graceful flax]

that is my answeeer

[forest nimbus]

Bro why do we have 9 digit options in the ones

Its literally impossible

From the start

We only have like 6 options

[forest nimbus]

..

Nvm im dumb

Aight fair enough

Just realized the mistake

[devout snow]

@thorn bramble Has your question been resolved?

[dry geyser]

This is really just the formula we need. It’s based off of the reasoning I gave earlier

[dry geyser]

The solution is correct but I’m not sure the reasoning is complete… WHY can we simply take the average?

[dense lynx]

i'm not sure how much rigor we'd need here but you'd expect each digit to be distributed evenly/symmetrically as nothing's weighted here

[devout snow]

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[ebon yoke]

I need help solving this kind of problem

[dense lynx]

there's roughly two ways you could go about solving this problem...

the easier way would be to consider the following:

the arcs WU (23x - 5) and WU (37x + 5) make up the entire circle, right?

[ebon yoke]

yes, making it = to 360

so, should I just do the whole circle first? then answer the tangent?

[dense lynx]

yes that's the more straight-forward method

[ebon yoke]

I was thinking that it was supposed to be something else thanks

is it also possible to add those 3 and make it equal to 450?

or no?

nvm

thanks!!

.close

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[red spire]

hi I need to transform/convert the term:
((b → a) ↔ c) =
((b → a) → c) ∧ (c → (b → a)) =
(¬(¬b ∨ a) ∨ c) ∧ (¬c ∨ (¬b ∨ a)) =
((b ∧ ¬a) ∨ c) ∧ (¬c ∨ ¬b ∨ a) =
(b ∧ ¬a) ∨ c∧ ¬c ∨ (¬b ∨ a) =
(b ∧ ¬a) ∨ 0 ∨ (¬b ∨ a) =
(b ∧ ¬a) ∨ (¬b ∨ a) =
(b ∧ ¬a) ∨ ¬b ∨ a =
¬b ∨ ¬a ∨ a =
¬b ∨ True = True

somewhere in here is a mistake, my assumption is at line 5, after this step (line 4): "((b ∧ ¬a) ∨ c) ∧ (¬c ∨ ¬b ∨ a) ="

so first question, is this the mistake? "(b ∧ ¬a) ∨ c∧ ¬c ∨ (¬b ∨ a) =", can I convert it from line 3 to 4 like that?

[red spire]

my new approach:

((b → a) ↔ c) =
((b → a) → c) ∧ (c → (b → a)) =
(¬(¬b ∨ a) ∨ c) ∧ (¬c ∨ (¬b ∨ a)) =
((b ∧ ¬a) ∨ c) ∧ (¬c ∨ ¬b ∨ a) =
(b ∧ ¬a) ∨ c ∧ ¬c ∨ (¬b ∨ a) =
(b ∧ ¬a) ∨ 0 ∨ (¬b ∨ a) =
(¬a ∧ b) v a v ¬b v 0 =
a v b v ¬b v 0 =
a v 1 v 0 =
a v True v False =
a v True =
True

[drifting yarrow]

if you are unsure whether you are mistaken in that line, have you tried writing out the truth tables and confirming they are logically equivalent?

[red spire]

it´s not, so i made another mistake

there is false and true in the truth table

.close

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[mighty copper]

how were they able to calculate the lim equalling L

[mighty copper]

?

this is the proof for monotonic sequence theorem though

[pulsar sand]

You usually pick L to use in your proof by using other methods from Calculus etc

[supple knot]

Show the whole statement

[supple knot]

Yea that's just the eps-N definition of a sequence converging to L

[mighty copper]

is there a proof for that?

[supple knot]

There usually aren't proofs for definitions

[full sand]

The theorem here only gives you the fact that the sequence has a limit, it doesn't tell you a nice expression for the limit. In general you may not have a nice expression for the limit other then L=lim_{n->inf} a_n

In general, most real numbers do not have nice expressions for them (there are uncountable real numbers, but countably many mathematical expressions that equal some real number, since each mathematical expression must be written as a finite sequence of characters), and each real number is the limit of some increasing sequence of rational numbers lower than them (so the sequence satisfies this theorem)

[devout snow]

@mighty copper Has your question been resolved?

[devout snow]

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[bright juniper]

I got a rombus the perimeter is 8 and the radius of the inscribed circle is 0,5 i need to find the big angle of the rombus

[hasty saffron]

What did you try

[bright juniper]

Idk where to start

@hasty saffron

[hasty saffron]

By big angle you mean the larger angle of the rhombus right?

[bright juniper]

Yes

[hasty saffron]

My brain is fried

[bright juniper]

The sides would be 2sqrt2 right

[hasty saffron]

In a rhombus all sides are equal

So if side is x, perimeter =4x

[bright juniper]

Oh i mixd up area and perimeter

[tired oyster]

would the rhombus side not be 1

0.5 x 2

[bright juniper]

Its 2

[hasty saffron]

8/4 is the side isn't it

[tired oyster]

would the diameter of the inscribed circle not be the side of the rhombus?

[bright juniper]

Ik the sides there all 2 now how do i find the angle

[bright juniper]

No

Perimeter is 8 rombuses sides are equal

So the 1 side is 2

[brisk totem]

probably not

[tired oyster]

okeh apologies

[bright juniper]

How dk i find the big angle now tho?

[tired oyster]

oh sorry i was basing my assumptions on the drawing HAHHAHAHA

[brisk totem]

as far as i see pythagoras a bunch of times should work

[bright juniper]

Finding a angle??

[brisk totem]

i mean a square is a rhombus
but it doesn't work in general

i mean if you can bash the side lengths then ye just take the sin or cos

but if you don't have trig at your disposal im not sure

[bright juniper]

Ik a bit of trig

So what do k do?

[brisk totem]

you should know that if a line is tangent to a circle, then drawing a line from the centre of circle to the tangent point creates right angles

then have fun constructing equations using pythagoras

[tired oyster]

yeah thats gonna take a while

[bright juniper]

Like this?

[brisk totem]

yes

[bright juniper]

How does that make a triangle?

[brisk totem]

it doesn't, it just gives you right angles
so with those right angles you might have a hunch as to which right angle triangles to construct

[bright juniper]

I don’t have a hunch idk

Do j connect it to the corner?

[brisk totem]

seems like a good starting point

[bright juniper]

Idk can’t do it

[brisk totem]

the problem with me telling you which triangles to use is it immediately ruins the problem turning it into thoughtless algebra

and finding hints to give is hard

but i think just connecting the centre of the circle to each corner should be a decent hint

[bright juniper]

So if i find the triangles the problem would be easier?

[brisk totem]

should be

[bright juniper]

Is this the triangle?

[brisk totem]

that's one of them, you need a few more

[bright juniper]

?

@brisk totem

[brisk totem]

eh, ye that's most of them lol

due to symmetry you only need a quarter of that

[bright juniper]

Wait can i just not find 1 hypotnus and use sin?

[brisk totem]

you can, which was my whole point

[bright juniper]

Ok so radius is 0,5 and the side would be 1 right?

[brisk totem]

i have no idea where you're getting that from, but no

[bright juniper]

its 2 but

I need pyth to find the hypotnus right

One side i 0,5

How do i find the hypotnus

?

[brisk totem]

huh, interesting

i got the answer but it feels like you need a calculator because that's not the most common value

but i guess if you can use a calculator it's easy enough

[bright juniper]

So how do i find it

[brisk totem]

pythagoras works, but easier is to use similar triangles

[bright juniper]

Is the hypotnus sqrt5/2?

[brisk totem]

i didn't actually calculate it (which is why similar triangles is easier) but it doesn't feel right

what's your final answer for the angle?

[bright juniper]

Yea that wrong

How would the hypotnus be with similar triangles 0,5/x equals 0,5/x ??

And the other side would be 1

And ill find hypotnus from that?

[brisk totem]

lemme give you this annotated diagram of a quarter of the rhombus+circle

the big triangle is formed by 2 smaller right angle triangles

show that the smaller right angle triangles are similar

[bright juniper]

Is the radius in both triangles?

[brisk totem]

sure is

[bright juniper]

Mhhh

Is the bottom side 1?

[brisk totem]

no, and justification needed

[bright juniper]

Is it not 2 radiuses?

[brisk totem]

no
if you draw the diagram to scale the answer is a much clearer no

[bright juniper]

Oh i see it its not

[brisk totem]

none of the side lengths besides the 0.5 are nice numbers, so you can throw those guesses out of the window

[bright juniper]

The other side is 2-x no?

[brisk totem]

yes

[bright juniper]

0,5/2-x equals

The frist bit is right?

[brisk totem]

i'm not sure what you mean by "the first bit"

[bright juniper]

0,5/2-x

[brisk totem]

that's an expression and not a statement

but it is a ratio of 2 sides of one of the triangles so i'd say you're on the right track

[bright juniper]

Equals hypotnus/bottom side

??

[brisk totem]

0.5 is not the hypotnus in either triangle

[bright juniper]

2-x/0,5??

[brisk totem]

i'm not sure what you're trying to do

because you're just giving me expressions without explaining what you want to do with it

and 2-x is also not the hypotnus of either triangle

[bright juniper]

Naa i just don’t get how to do it

[brisk totem]

ok, i told you to show that the smaller triangles are similar to each other

now show that they're also similar to the big triangle

[bright juniper]

Wym show how do i show that

[brisk totem]

have you learned how to prove triangles are similar and what kinds of conditions you can use for those

[bright juniper]

Are th angle equal?

[brisk totem]

yes

and i'm asking you to convince yourself that the angles are equal so all 3 triangles are similar to each other

if you just get told what's equal and what's not you won't be able to do similar problems and will have to come back to ask every time

[bright juniper]

Ok now what do i do?

[brisk totem]

start solving the problem using properties of similar triangles

specifically if two triangles are similar then the ratios between corresponding sides is constant

[bright juniper]

0,5/x equals x-2/x??

Yhats wrong

My best guss is 0,5/x equals 2-x/x idk

[brisk totem]

nope, one of those pairs aren't corresponding sides

i'd recommend labelling each vertex and listing which triangles are similar..but it probably gets more confusing

i guess just label each side "short", "long", and "diagonal" and see which sides correspond to each other

[bright juniper]

Wi h one is not corresponding?

[brisk totem]

actually neither, the entire equality doesn't make sense

at this point i think it might be easier for you to go back to bruteforcing with pythagoras..but this really should be easier if you can correctly identify which sides correspond to each other in the 2 smaller triangles

here's one with labelled vertices, please show which 3 triangles are similar

[devout snow]

@bright juniper Has your question been resolved?

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[opal falcon]

3 * -4 is -12?

[restive river]

yes

[opal falcon]

.close

[devout snow]

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[opal falcon]

Is this correct?

Solve this if x=3.

[devout snow]

@opal falcon Has your question been resolved?

[opal falcon]

<@&286206848099549185>

<@&286206848099549185>

[devout snow]

@opal falcon Has your question been resolved?

[hexed gust]

yes its correct

[devout snow]

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[digital fox]

im having trouble with this

[digital fox]

i need the 3rd and 6th reason

[warm lance]

Number three is because of the right angle IHJ.

[digital fox]

right angle IHJ?

[warm lance]

Yes.

Number 6 is SAS I think.

[digital fox]

.close

[devout snow]

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[placid trail]

Would somebody be able to explain how this smooth(er)step function by ken perlin actually works, or point me in the right direction?
I know that when you pass in t to the function, it returns a value that is closer to 0 or 1 depending on if t is less than or more than 0.5, but I do not understand at all how we get to 6*t*t*t*t*t - 15*t*t*t*t + 10*t*t*t and i would like to understand instead of just mindlessly using it.

function Fade(t) {
    return 6*t*t*t*t*t - 15*t*t*t*t + 10*t*t*t;
}