help-39

[boreal raptor]

from 0, 0

you can see that A

is 4 units to the left

and 2 units down

which means its x is -4 and y is -2

[pale skiff]

WAIT OK I GET IT NOW

i was looking at the line and not the letter

so thats how u find coordinates?

[boreal raptor]

ye

[pale skiff]

what about wherethe line intercepts? what is that

[boreal raptor]

u

don't really need it

in this example

r u just asking?

[pale skiff]

what do i need it for?

[boreal raptor]

it is when x = 0 or when y = 0

[pale skiff]

yeaa

[boreal raptor]

uh

lots of different examples

[pale skiff]

yeah my finals are like in a week and i still dont know what to use it for

[boreal raptor]

what grade r u

[pale skiff]

8

[boreal raptor]

https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:linear-equations-graphs

[pale skiff]

if the question is cause of how dumb i am i failed like all my math tests

[boreal raptor]

see if u can do these questions

[boreal raptor]

it's fine

[pale skiff]

its showing me a donation thing

oh nevermind

[boreal raptor]

i got 30% on my math test before
then i worked hard and the next one i got 96%

watch the videos

[tacit wolf]

i feel like this was a lie for a sec

[boreal raptor]

if u don't understand the questions

[boreal raptor]

want proof?

[tacit wolf]

same with me

[tacit wolf]

what is the topic of the test

[boreal raptor]

u can read it

the second one was

yearly

mm lemme blur out some stuff

[pale skiff]

the videos?

i didnt know it was substitution at first

but after i got a question wrong i could do it just fine

[pale skiff]

if i fumble hard enough on functions and relations i might actually get a 30% byeyey

[pale skiff]

i could do this cause it was substitution and i think im okay with 1 and 2 linear variables

[tacit wolf]

I see

Improvement is key

[pale skiff]

icl i cant see it but congrats dude

[boreal raptor]

mhm
rly goes to show how much u can improve

[pale skiff]

okay back to this,

A = (-4, -2) B = (1, 4) right?
if i put it into the formula its
-2-4/-4-1 right?

[tacit wolf]

yeah

[tacit wolf]

what grade are u on?

[boreal raptor]

10th (doing 12th math)

[pale skiff]

ok great now is the perfect time to mention i dont know the step after this

[boreal raptor]

yep

but make sure

put the brackets around

(-2-4)/(-4-1)

then calculate it

what does it become

[pale skiff]

oh okay, what r the brackets for?

[pale skiff]

nevermind i just had to calculate it

[pale skiff]

-6/-5 right?

i can turn it into a positive?

[boreal raptor]

because if you don't put the brackets, division comes first

you're essentially saying

-2-(4/-4)-1

[boreal raptor]

yep

[boreal raptor]

yep

[boreal raptor]

in text ofc

[pale skiff]

OH

[boreal raptor]

but if u write it as a fraction

yk

u put -2-4 on top

[pale skiff]

yeah it doesnt matter right

[boreal raptor]

the -4-1 on bottom

yeah

if u write division sign

it does

if u write fraction

it doesn't

[pale skiff]

okay so i turn it into a mixed fraction?

wait its called mixed right

[tacit wolf]

nice

[pale skiff]

yay the first statement is right

[tacit wolf]

pecahan campuran (indonesian translations)

[boreal raptor]

if u want

[pale skiff]

theres still a 2nd number oh my godddddddddddddd

[boreal raptor]

wait nooo

don't

for gradient

[pale skiff]

why

[tacit wolf]

$m_1 = \frac{-2-4}{-4-1}$

[boreal raptor]

it's ugly

as mixed

[jolly parrot]

Newt

[boreal raptor]

just leave it as improper fraction

easier to deal with numbers n stuff

[pale skiff]

can i just turn it into a mixed one to confirm the first staement of AB = 1 1/5?

[boreal raptor]

generally, we change to mixed if a coordinate is afraction

[boreal raptor]

ohhhh

[tacit wolf]

agree but yeah

[boreal raptor]

yea

sry

[pale skiff]

u dont have to apolgoize im lost too

[boreal raptor]

didn't realise the question was weird

[boreal raptor]

nono

u do convert

but

weird cuz normally gradient

isn't mixed

ur right

[pale skiff]

M = (6, -2) N = (2, 4) right?

[tacit wolf]

the first statement is correct

[pale skiff]

okay tyty

[tacit wolf]

yes

[pale skiff]

(-2-4)/(6-2) then right?

[boreal raptor]

yes

[tacit wolf]

yeah

[pale skiff]

okay so -6/4 = -2 1/4?

is the 3rd statement wrong or can i simplify it further to reach -1 1/2?

[tacit wolf]

-6/4 is not 2 1/4

$(-1) \times \frac{6}{4}$ think like this

[jolly parrot]

Newt

[tacit wolf]

u simplify the 6/4

and then times by - 1

[pale skiff]

oh wait i didnt do the mixed right

-1 2/4 and i can simplify the fractions to make it -1 1/2?

[tacit wolf]

yeah

[pale skiff]

omg yay i finally did one question

is tehere any way for me to learn relations and functions with a website?

[tacit wolf]

Indonesian source or international source?

international khan academy are the best though

[pale skiff]

okok ill use this

thank u flatus and newt

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[compact ridge]

do you know what log a + log b is?

[crude root]

yea

= log ab

[compact ridge]

cool so $\log_2 (x^2 + 2x) = \frac{1}{4}$ right

[jolly parrot]

southlander!

[compact ridge]

now raise 2 to the power of both sides

[worthy lance]

Have in mind that x>0

[crude root]

yes dont worry

[compact ridge]

very good point

it's a nasty quadratic so you might as well use Desmos

[crude root]

ye LOL

thats what i had in mind but there's gotta be some workaround

[worthy lance]

Or complete the square

[compact ridge]

quadratic formula also works

[crude root]

.clsoe

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[hearty gate]

Question: A study shows that 35% of the fish caught in a local lake had high levels of mercury. Suppose that 10 fish were caught in this lake. Find; to the nearest tenth of a percent, the probability that at least 8 of the 10 fish caught did not contain high levels of mercury?

[hearty gate]

how do you answer this im confused

[compact ridge]

binomial probability

do you know the binomial formula?

[hearty gate]

yeah

[compact ridge]

yeah you just add the probabilities for 0, 1, 2 and it helps if you use probability = 0.35

[hearty gate]

8,9,10 probability combined is 0.5

if 1-0.5 then thats 99.5 but the study shows 35% contained mercury though

ah

[compact ridge]

sorry I keep editing

but

[hearty gate]

0,1,2?

[compact ridge]

,w 0.35^0 0.65^10 + (10 choose 1) * 0.35 * 0.65^9 + (10 choose 2) * 0.35^2 * 0.65^8

[compact ridge]

yeah, so if 8, 9, 10 fish did not contain high levels of mercury
that means 2, 1, 0 fish did contain high levels of mercury

[hearty gate]

how about the ones in between?

[compact ridge]

yeah I did all 3 then added them all up

[jolly parrot]

Results provided by WolframAlpha

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

Requested by sooouth.

[hearty gate]

I don't quite understand

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[compact ridge]

you need to go and watch a YT video or something that explains then

[pearl pond]

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[polar crypt]

10x^2 - 18x^3 + 14x^4 factorise

[midnight haven]

Firstly, take out common the HCF.

[polar crypt]

what i dont understand is

my teacher said use the following formula for 3 terms

like write in accending orded

and then multiply the first and last coefficent

then factorize that umber so it can be somehow related to the middle number or someting like that

thats why im kinda confysed on these questions

[polar crypt]

on

ok

[midnight haven]

Do you know how to factor this?
x^2 - 5x + 6?

[polar crypt]

no

i cant do 3 term

s

i can do 2 or 4 terms easily

[pearl pond]

@polar crypt Has your question been resolved?

[polar crypt]

ik im pathetic

[solar patio]

Ok so the formula is
X²-5x+6
a+b=-5
a*b=6
Then you type it like that
(x+a)(x+b)

Only when ax² a=1

Otherwise you do
ax²+bx+c
X1,2=(-b±√(b²-4ac))/(2a)

[pearl pond]

@polar crypt Has your question been resolved?

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[unkempt yacht]

what have you tried?

[crimson valve]

i substituted the 0

[leaden marsh]

Just observe what happens to |x-2| when you get close to 0

Try to dissolve the modulus into a + or -

[crimson valve]

i mean the ifnal result should be 2/0

it should be +infinity why is - infinity?

[leaden marsh]

You wanna try again
Or should I tell?

[crimson valve]

please tell

[foggy mason]

for values greater than 0 but close to 0, the absolute value changes depending of the sign of x-2

x-2 is negative for x<2

[leaden marsh]

Alright

Notice that when x gets very close to
x-2 is less than 0
And the modulus then multiplies a - to it to convert it to a positive

So u can say |x-2| = -(x-2)

In this case

From the bottom, take x common

And then simplify

So you get

$\lim_{x->0^{+}}\frac{-(x-2)}{x(x-2)}$

[crimson valve]

sorry i didnt understand this : |x-2| = -(x-2)

[jolly parrot]

@leaden marsh

[crimson valve]

?

sorry i didnt get that

[leaden marsh]

Ummm see
For values close to 0
Take 0 for example

If u put 0 in |x-2|
You get |-2| = 2

So here you can say that the modulus function actually multiplied -1 with the -2 to give you the answer 2

Do you know piecewise functions ?

[crimson valve]

oh no.

[crimson valve]

so it should be 2/0 right?

[leaden marsh]

Um no

Wait

[leaden marsh]

See
Piecewise functions are basically the breakdown of a function
Mostly discontinuous ones

Like |x| is same as
x if x>=0
-x if x < 0

Basically it means that return x if x>= 0 and -x if x < 0

This is the definition of modulus(x)

You knew this?

[crimson valve]

ohhhh

and x-2 is less than 0

[leaden marsh]

So similarly try breaking |x-2|

[crimson valve]

x-2<0

so it becomes -(x-2)?

right?

[leaden marsh]

Exactly

That means x<2

Which is pretty much true in our case

So just put -(x-2) in place of |x-2|

[leaden marsh]

And u get this

[crimson valve]

why should i also do it at denominator?

[leaden marsh]

No, at denominator I did basic maths

You had x² - 2x

Just take an x common

You get x(x-2)

[crimson valve]

but at the end i have to substitue the 0?

[leaden marsh]

Yeah
So from this
From the numerator and denominator (x-2) cancels

You get -1/x

Put 0 in that and you get -1/0 which -> - infinity

[crimson valve]

wait a sec

why is -1? 😭

[leaden marsh]

What

[crimson valve]

at the numerator

-(0-2)

[leaden marsh]

In the numerator you had
-1 * (x-2)
And x*(x-2) in the denominator

[leaden marsh]

No
See in solving limits, put the value only after you have simplified the function to its maximum

[crimson valve]

ooooo

because i need to simplify the (x-2)

okok

[leaden marsh]

Yeah

[crimson valve]

ok last question

i have to do this process when i have limit of a number with (-/+)

as in this case 0+

[leaden marsh]

Exactly

Here listen

And try to understand

When it is said x -> 0+

It means that x is something very close to 0 but greater than 0
So like if you put even 0.0000000000000001
You can later approximate it to -1/0 to get -infinity

But

Apart from question
If you were asked x -> 0-

It means that x is something very close to 0 but less than 0

Less than 0 means a negative sign
Like -0.000000000001

If you put it in the final function
You have -1/-0.0000000000001

So minus minus cancels out
So you get 1/0.00000000001 which now you can approximate to 1/0 which gives u + infinity

And you can clearly see this if you plot the graph of it

Always come to the conclusion of +ve or -ve infinity after maximum simplification

Understood?

[crimson valve]

okkkk

thank youuuuuuuu❤️

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[velvet ferry]

how to get the greatest common divisor of 2022^2023 and 2025^2024 without prime factorization pls help

[proper dove]

Just do prime factorisation

[velvet ferry]

i cant 😭 its told so in the task, can it be done with euler's formula?

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[bitter herald]

Why does it happen that the Fourier series of a continuous-time function is aperiodic in frequency, but the Fourier series of a discrete-time function IS periodic in frequency

[bitter herald]

I can't seem to conceptualise this well

Ah, is it because in discrete-time the frequency is inherently defined modulo 2pi, hence the periodicity?

But is it modulo 2pi, or modulo N, the fundemental period?

[pearl pond]

@bitter herald Has your question been resolved?

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@bitter herald Has your question been resolved?

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[stiff mauve]

i can follow this until the last step

how is f''(x) = 0

[pearl pond]

@stiff mauve Has your question been resolved?

[sharp vigil]

if f'(x) is constant on some interval then f''(x) must be 0 on that interval

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@stiff mauve Has your question been resolved?

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[rose sentinel]

54 b

[rose sentinel]

Not really sure how to determine n

Just made this

Idk how to solve for a bound

Don’t think I ever have before

[plush bramble]

Do you know how to find the antiderivative of 1/x^4

[rose sentinel]

I’ll take it from here 💀

Yeah I see thanks

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[modest wave]

im confused

,, i changed 9^{x-2} = 3^y -> \log(9x-2) = log(3^y)

[jolly parrot]

learning maths need help

[modest wave]

wait itll be easier if i send a photo

then idk what to do from there

[dusty pilot]

what are you trying to do?

solve for y?

[modest wave]

this

and honestly i have no idea anymore

i just learned logs

[dusty pilot]

ahh ok

[modest wave]

and now its telling me to do simultaneous equations with them

[dusty pilot]

the first one solve for y for example

[modest wave]

i mean i just got the 2 bases the same

[rugged niche]

First equation: consider 9 = 3² and use logarithm with base 3.

[dusty pilot]

saying y = log_3(2(x-2))

[modest wave]

,, 3^{2x-4} = 3^y

[jolly parrot]

learning maths need help

[modest wave]

which is then y=2x-4

[rugged niche]

yes.

Second equation: rearrange to an equation with just one logarithm on one side and use 3^x on both sides.

[worthy lance]

No

Rewrite 1 as log_3(3)

And use log properties

To add the right side

U will get log_3(2x) = log_3(3y)

2x=3y

There u have your second equation

[modest wave]

and then i do simultaenous equations with the two

ahhh so the goal is to bring it down to x and y

[worthy lance]

Yes

[modest wave]

i thought i had to do it with the logs

i was so confused

now it makes sense

thanks guys

[worthy lance]

U can, but why

[modest wave]

im not sure, it's my first time seeing this kinda thing lol

but this is a nice way to do it

thank you 🙂

[worthy lance]

!done

[pearl pond]

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[modest wave]

.close

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[opaque vector]

need help with part b, alr created an expression for Volume in terms of r being (rS)/2 - (pi)(r^3)/2 but im confused about what to do afterwards wehn proving h=r, cant rly take a photo of my work with a phone ban policy rn so mb

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[sweet ridge]

How was the green highlighted part derived?

[sweet ridge]

Or to be more specific, what is P(uk)?

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[river lodge]

for the cos2x part

how can i determine which one i use

[merry carbon]

For now, do you know the identity for sin(2x)?

If you write it out, what do you think you'd want the denominator to be to get tan(x) out of it?

[river lodge]

yes

[river lodge]

cos

since sin/cos is tan

oh so u can eliminate one of them

and the first one wont work

so ur left with the second?

so its basically trial and error

[merry carbon]

Second one is the best one

[river lodge]

alr alr

thanks

[pearl pond]

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[pearl pond]

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[rose sentinel]

55

[compact ridge]

!status

[pearl pond]

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

[karmic kestrel]

^

[rose sentinel]

I dunno how to approach

How do I find the exact value of that series

[compact ridge]

have you tried any of the other problems in this section?

[rose sentinel]

It’s not geometric

[compact ridge]

you don't need to

[rose sentinel]

All up to this one

[rose sentinel]

I tried integrating already

[chrome plank]

keep summing 1/n^3 until the difference is less than the accuracy you want

[rose sentinel]

I integrated with bounds n to infinity equal 0.01

I got like 7.1

Or so

Think I just have to integrate?

Dunno if they want me to do all that

[karmic kestrel]

Partial sums

then estimate the remainder

[compact ridge]

no, don't integrate

[rose sentinel]

Why

[compact ridge]

let me think sorry

[karmic kestrel]

Use partial sums, you know it's convergent as its a p-series with p=3>1

[compact ridge]

ah yes the picture you are given for 54a is very useful

it's a decreasing function of course

so you just need to find $a$ such that $\int_a^{\infty} 1/x^3 \ dx < 0.01$

then the sum of the rectangles. the right Riemann sum has to be less than the integral

[karmic kestrel]

Compute partial sums up to N s.t. the remainder R_N = Sum_n=N+1 ^ inf 1/n^3 < 0.01

[jolly parrot]

southlander!

[compact ridge]

jesus, can you LaTeX this

[karmic kestrel]

Yes sorry m.b.

[rose sentinel]

I did

And I got 7.1 ish

Sqrt50

[karmic kestrel]

$R_N = \Sigma_{n=N+1}^\inf \quad \frac{1}{n^3} < 0.01$

[jolly parrot]

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

[karmic kestrel]

it does not like me at all

[rose sentinel]

uh

Anyways

Is my answer right

So does that mean 8 is the upper index

[karmic kestrel]

7.01 is fine for N

[rose sentinel]

n is an integer tho

[karmic kestrel]

then yes

8 is the upper index

[rose sentinel]

Okay awesome sauce

Thanks

[karmic kestrel]

calculate partial sum

[rose sentinel]

I don wanna do allat

Do I gotta

Oh I do

I see

Yikes

[karmic kestrel]

$S_8 = \Sigma_{n=1}^8 \frac{1}{n^3}$

sum to 8

[rose sentinel]

,w \Sigma_{n=1} \frac{1}{n^3}

[jolly parrot]

TLB

[rose sentinel]

Wah

[jolly parrot]

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Requested by 12nathan12

[rose sentinel]

😔

[karmic kestrel]

Hold on I'll write it out by hand so you can see

[compact ridge]

yes so to be safe you need to round that up then add 1

,w sum 1/n^3 from n = 1 to n = 9

[jolly parrot]

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Requested by sooouth.

[rose sentinel]

This?

[compact ridge]

,calc 19148110939/16003008000

[jolly parrot]

Result:

1.1965319856742

[compact ridge]

,w sum 1/n^3 from n = 1 to infinity

[jolly parrot]

Results provided by WolframAlpha

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Requested by sooouth.

[rose sentinel]

Looks right to me

Awesome

Thanks

.close

[pearl pond]

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[compact ridge]

to be safe you need to add on +1/729 to this

,calc 19148110939/16003008000 - 1/729

[jolly parrot]

Result:

1.1951602435617

[compact ridge]

like it happens to work up to n = 8 for this specific question

[rose sentinel]

I did didn’t I?

I had 8

[compact ridge]

no you need up to n = 9

[pearl pond]

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[bitter herald]

Is there a way to do (5) without explicitly computing the integral?

[bitter herald]

For (4) I assume it is direct enough to equate it to $2\pi x(0)$

[jolly parrot]

Aero

[bitter herald]

For clarification: [x(t) \xrightarrow{\mathscr{F}} X(j\omega)]

[jolly parrot]

Aero

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[bitter herald]

<@&286206848099549185>

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[marble mirage]

ello, I want to know if I drew the right free body diagram for this question

[marble mirage]

N = normal force
W = weight
Fapp = applied force
f = friction

[midnight haven]

Sakto clark

[marble mirage]

sino kang imaw ka

[pearl pond]

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[vocal veldt]

Please help me I’m struggling in this question for a prolonged period of time 🙏

[vocal veldt]

And btw it is about compound angle formula

[pearl pond]

@vocal veldt Has your question been resolved?

[vocal veldt]

Ok nvm it is sine formula

.close

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[tiny jay]

help can someone break this down for me

[unkempt yacht]

i assume $\mathbb P_n$ is the set of all polynomials deg $\le n$?

[unkempt yacht]

just use the subspace axioms

[tiny jay]

can you walk me through with one example

[unkempt yacht]

do you know what are the subspace axioms?

[tiny jay]

ya isnt it the 3 properties

that 0 is member of the vect space

and u v can do addition and can multiply to a member of the vect space? 😭

[unkempt yacht]

the set U is a subspace of a vector space V iff it satisfies these properties

• additive identity: there exists u in U for which 0 + u = u
• closure under addition: for u, v in U, u + v must also be in U
• closure under scalar multiplication: for a in F and v in U, av must also be in U

F here is the field V is a vector space of

example, you can easily verify the set $${(x, y, z) \in\mathbb F^3 : x+y+z=0}$$ is a subspace of $\mathbb F^3$

[tiny jay]

how can i verify

[unkempt yacht]

prove the 3 axioms hold

of course addition and scalar mult are defined as usual unless otherwise specified

[tiny jay]

do i plug in random values for x y and z that make up 0?

[unkempt yacht]

uh no?

first, can you tell me is there an element, call it 0, for which u + 0 = u?

[tiny jay]

sorry i wasnt exposed to many examples 😭

[tiny jay]

i dont understand what u mean

doesnt any value work?

[unkempt yacht]

any value of u yes

pick an arbitrary u, is there such an element 0 for which u + 0 = u?

clarification, 0 is not a number here, it is the neutral vector

[tiny jay]

yeah? when x y z are all 0?

i srs dunno

[unkempt yacht]

good, so 0 = (0, 0, 0)

thats one axiom down

for closure under addition, pick arbitrary vectors u, v in the set. prove u+v is also in the set

same deal with closure under scalar multiplication

[tiny jay]

so x y z + x y z equals 2x 2y 2z and since x y z is =0 it means its also in the set?

help im so lost

[pearl pond]

@tiny jay Has your question been resolved?

[pearl pond]

@tiny jay Has your question been resolved?

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@tiny jay Has your question been resolved?

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[willow siren]

Hey! I've got a question regarding the L1 norm unit ball. In particular, I'm strugling to find the orthogonal projection of a point onto the unit ball.
My question guided me to define each entry of the projection as y_i=sign(x_i)max(|x_i|-u,0) where x_i is the point I want to get the orthogonal projection of.
I know that I can prove this is indeed to projection by showing <x-y,z-y> <= 0 for any z in the unit ball, but I can't figure out how to

[willow siren]

This is the question in latex

This is what I have so far pretty much. But I think I'm doing something wrong because no matter what I can't seem to upper-bound it.

Any hint would be appreciated! 🙂

[pearl pond]

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[plain ember]

calculate area of ABCD using vectors

[plain ember]

.close

[pearl pond]

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[plain ember]

find two matrices A, B such that both A*B and B*A are possible but the matrices are of different sizes

[shrewd rune]

Open new channel for question

[plain ember]

.close

[pearl pond]

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[midnight haven]

Can someone help 💀 whyd i get -100 if i do the square root og that would be 10i but this is quadratic equation 😭

[midnight haven]

Or is it supposed to be in this

[dapper kraken]

whats the original question?

[midnight haven]

If someone can uh tell me if it's right that's great

[midnight haven]

Its

(X-10)²=-25

[dapper kraken]

this isnt correct, its close though

try tk recheck your work

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[dusky isle]

need help with this question, i don't get how to graph it

[snow sail]

whatd your differentiation show

maybe it helps to write f( x(y), y)?

[pearl pond]

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[sudden badger]

hi!

I have a question about inequalities like these, with quotiens and absolute value

After seperating and solving both cases, and getting the set for both cases

Do I find the final answer intersecting the sets or with union

[nocturne plover]

it depends

:D

it depends on whether you have extra conditions

if you just have the 2 inequalities

$\frac{1}{2} x - 1 \leq 2$ and $1 - \frac{1}{2} x \leq 2$

[jolly parrot]

Katharine

[nocturne plover]

then it's intersection

but if you take into account the fact that the switch happens when x = 2

and so when x > 2 it's the first one

and when x < 2 it's the second

then you would union

as the sets would be smaller

the second one is this

i hope that makes sense

You can also think about it this way

In the first case all you're doing is splitting the inequality up into two inequalities without caring about any limitations on x and so you want to find the values for x that solve both inequalities. This is precisely the intersection

In the second case you split it up into two but in this case it is based on the condition of when the term inside is positive or not

And when you solve the inequalities they have the added requirement of the inside being above or equal to 0

This causes it to require the union due to the extra limitation on x

[pearl pond]

@sudden badger Has your question been resolved?

[sudden badger]

ohhhh

yeah that makes sense

thanks!

.solved

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[pearl pond]

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[exotic gale]

Can someone help me with this question? Thank you!

[hard kite]

hmm, so x/(10^936) + x/(10^(2 * 936)) + x/(10^(3 * 936)) + ... = 1/937

where x is the number that repeats

[exotic gale]

how did you get this equation

[hard kite]

just like 0.142857 + 0.000000142857 + 0.000000000000142857 + ... = 1/7

[exotic gale]

oh thanks for clarifying

[hard kite]

then you could probabilly factor out x there and solve it then use something like modular arithimetic or something to get the last 3 digits

[exotic gale]

oh ok

so i can factor it into: x(1/(10^936)+(1/(10*(2936))+(1/(10(3936)) + ... = 1/937

[hard kite]

yeah

notice it's a geometric series

you don't even need to factor actually, that one would also be a geometric series, just a different initial term

but either work

[exotic gale]

oh ok

so now do i mod both sides by x?

[hard kite]

first evaluate the geometric series

notice each term is 10^936 times smaller than the previous

[exotic gale]

so the common ratio is 10^936

[hard kite]

no

it's getting divided by 10^936 not multiplied

you could say it's getting multiplied by 1/10^936

or 10^(-936)

[exotic gale]

1/(10^936) is the common ratio sorry

ok

so now do i find the sum of all the 936 terms

[hard kite]

it's an infinite sum, not a sum with 936 terms

the expansion goes forever

[exotic gale]

so what do i do now

[hard kite]

do you really understand this?

[exotic gale]

it's a geom sequence

[hard kite]

but do you understand why that would be equal to 1/937?

and why it's getting 10^936 times smaller

[exotic gale]

yes i understand it, but it's hard to convey through words

[hard kite]

you can just use the formula for infinite geometric series

why would it be zero

[exotic gale]

i mean (x/(10^936-1))

[hard kite]

yeah

[ivory swallow]

there's an easier way to do this if you don't mind me butting in. but feel free to finish up

[hard kite]

please do

[exotic gale]

after i finish, please do

[hard kite]

you can just substitute it in the initial equation and solve for x

and find the last 3 digits

[exotic gale]

ok

are the last 3 digits 062

or did i make a mistake

[hard kite]

,w ((10^936 - 1)/937) mod 1000

[jolly parrot]

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[exotic gale]

bruh that was the original answer i had

but i didn't have confidence in it

[exotic gale]

can you explain

[ivory swallow]

sure

the hardest part is just finding one modular inverse

start with:

(10^936 - 1)/937 mod 1000

then:

-1 * 937^-1

-1 * (-63)^-1

63^-1

all you need is 63^-1 mod 1000

does that make sense so far?

[exotic gale]

how do you know to start with this?

[ivory swallow]

this is turning the repetend into an integer

[exotic gale]

oh that makes sense

[ivory swallow]

10^936/937 - 1/937

[exotic gale]

ok pls continue

[ivory swallow]

do my steps make sense?

(10^936 - 1)/937 mod 1000
-1 * 937^-1 mod 1000
-1 * (-63)^-1 mod 1000
63^-1 mod 1000

[exotic gale]

for the most part, yes

thanks for sharing

[ivory swallow]

so all that's left to do is compute one modular inverse

[exotic gale]

are you in college?

or uni

[ivory swallow]

we know that 3x7 = 21, so the last digit is 7

yes i am

[exotic gale]

oh nice

[exotic gale]

then how are we supposed to calculate the other 2 units

.close

[pearl pond]

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[ivory swallow]

euclidean algo

[pearl pond]

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[drowsy plank]

how coeff of t^2 =t^3 in (1-(1-t)^18)

[dense jasper]

Multiply both sides by $t$

[jolly parrot]

Civil Service Pigeon

[drowsy plank]

why

if i solve without sustituting 1+x=t then?

[dense jasper]

??

1-(1-t)^18 = a_0 t + a_1 t^2 + a_2 t^3 + …

[drowsy plank]

by usind gp i calculate the lhs as 1-x^18/(1+x)

[pearl pond]

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[pearl pond]

@drowsy plank Has your question been resolved?

[pearl pond]

@drowsy plank Has your question been resolved?

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@drowsy plank Has your question been resolved?

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[split badger]

pls how do i solve this

[elfin pecan]

i’m struggling i feel like there’s gotta be an easier way

[split badger]

like is there maybe a trick to this? or should i just try to find fxy and plug things in?

im not allowed calculators on a real test, so i dont know how i would appraoch this

[molten matrix]

Is it answer is c?

I dont thi k so

[split badger]

yeah

the first image is from the solutions

[dusty flame]

I think u applied the generalized product rule wrong

@split badger

[split badger]

oh i did

im going to try to fix it

[elfin pecan]

is this how you did it?

u’v + uv’. where u was x and v was cos*ln

[dusty flame]

Yes

Take partial y next

[dusty flame]

I used another formula

I see uvw where u = x, v = cosx^2 and w = ln(xy)

[split badger]

thats so much easier

[split badger]

can i assume here that fxy=fyx?

or would i only be able to do that when theyre product of continuous functions?

oh i guess not

[split badger]

i think i give up

ill accept my fate

[split badger]

i dont see what i did wrong here

[dusty flame]

?

@split badger u did correct

Now u have to find fyx

[dusty flame]

U forgot 1/y

[split badger]

oh

ill rewrite it to be more neat

one second how did you get the squared on 2x^2sin(x^2) for fyx?

oh i see now

[elfin pecan]

this is what i have now

[split badger]

now ill just plug everything in

[elfin pecan]

that was a lot easier than i expected

thank you for your help

i really appreciate

i was stuck on this question for an hour 😔

hope you have a good day

[split badger]

:))

.close

[pearl pond]

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[split badger]

.reopen

[pearl pond]

✅

[split badger]

i was wondering if i can just consider fyx and fxy equal

then i would do 2023-2022=1

or would i not be allowed to do that because ln is not a continuous function?

[pearl pond]

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[torpid schooner]

hi i just wanna make sure is $\frac{1}{cos^3x}$ the same as \sec^3x

[jolly parrot]

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

[broken fossil]

yes it is

[torpid schooner]

ok thank

.close

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[torpid schooner]

Yes

I agree

Buy me nitro

@quaint dawn

Buy me nitro

[spiral pivot]

! occupied

[pearl pond]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[torpid schooner]

Yea

[versed mica]

🤔

[torpid schooner]

I really like this channel

This is my favorite

.reopen

[pearl pond]

✅

[torpid schooner]

Ignore the work shown under the problem. My work is the engineering paper, am I currently doing this correct?

[versed mica]

bro

[torpid schooner]

Help me with my problem

Then I’ll click ip grab

[worthy lance]

<@&268886789983436800>

[inland lantern]

<@&268886789983436800>

I missed

[versed mica]

buddy is gone

say bye mr sandal

[torpid schooner]

https://tenor.com/view/xqc-bozopack-ripbozo-koopa-xqc-l-gif-25325903

[versed mica]

yo you wrote 1/u^3 and changed the bounds to be for u and then you converted back to theta without changing the bounds and didn’t even take the anti derivative

[torpid schooner]

oh

bruh

[versed mica]

bruh

[grim kelp]

XD

bro

[versed mica]

☠️

[torpid schooner]

?

[grim kelp]

why cant i

[torpid schooner]

#help-12

use it

[grim kelp]

ty

[torpid schooner]

It would be written like this right?

Or am I still tripping

[versed mica]

ya that’s good but again, when you change back to theta why are you not changing the bounds back

like the whole point of changing the bounds was so you could integrate it in terms of u

[torpid schooner]

Right but didn’t I do this on the top right? Sorry if it wasn’t clear

[versed mica]

what there is nothing on the top right

[versed mica]

oh this

yea you changed the bounds there

but

[versed mica]

here you have the vertical bar with bounds for u but anti derivative in terms of theta

[torpid schooner]

Oh

I substitute in the other stuff

Instead

Right

Am I dumb

LOL

I think I know what u mean

BRB

Ok I got the right answer now

Thank u

Idk why I put cos again

[versed mica]

yep

[torpid schooner]

.close

[pearl pond]

Channel closed

Closed by @torpid schooner

Use .reopen if this was a mistake.

[torpid schooner]

i heard when u go more in depth into math

u learn to prove like

prove why equations are true

is that true

prove why this and that are true

instead of

stuff

idk

[versed mica]

you prove things yes

less computational

[torpid schooner]

that sounds rough

[versed mica]

indeed

[plush bramble]

https://www.math.purdue.edu/~price79/SU14/proofsintro.pdf

They give a few examples of what it's like

[torpid schooner]

terrible

probably

[pearl pond]

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[midnight flicker]

what graphic?

[summer imp]

What do you think?

[midnight flicker]

it will be sin x

graphic

and it will be go under

idk

what you think?

[summer imp]

Let's say sin(x) is positive. Then |sin(x)| = sin(x).
What does y look like?

[midnight flicker]

sin x not equals 0

[summer imp]

Yeah positive sort of implies that but what does the formula for y look like in that case?

[midnight flicker]

it has to be function graph

[autumn fossil]

What is sin(x) / |sin(x)| if sin(x) is positive?

[midnight flicker]

just need to draw function graph

[summer imp]

We're just trying to have you see what it should look like

[midnight flicker]

idk how it looks

[summer imp]

It's a really simple graph

I told you that |sin(x)| = sin(x) if sin(x) is positive.

Then what is y?

[midnight flicker]

i dont understand i’m bad at math

[summer imp]

$y = \frac{\sin(x)}{|\sin(x)|} = \frac{\sin(x)}{\sin(x)}$

[autumn fossil]

What is sin(1) / |sin(1)|?

[jolly parrot]

Azyrashacorki

[midnight flicker]

soo

1

?

[summer imp]

Yeah

So when sin(x) is positive, y = 1

[midnight flicker]

omg

[summer imp]

When sin(x) is negative, then |sin(x)| = - sin(x)

What does the formula for y look like in that case?

[midnight flicker]

thank you

it’s goes y=-1

[summer imp]

Yep

So now when sin(x) is positive, the function is 1, when sin(x) is negative, the function is -1

To graph it you just need to know when sin(x) is positive / negative

[midnight flicker]

when negative?

[summer imp]

sin(x) < 0, think of the unit circle

[midnight flicker]

oh

got it

ty

[pearl pond]

@midnight flicker Has your question been resolved?

[pearl pond]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[exotic gale]

i believe the answer is 23, but i don't know for a fact

[exotic gale]

.close

[pearl pond]

Channel closed

Closed by @exotic gale

Use .reopen if this was a mistake.

[pearl pond]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[flint wyvern]

so this was my question and answer

[flint wyvern]

i just used my function from part A

this is Part B

is everything look correct here

<@&286206848099549185>

[compact ridge]

your function in part a is wrong

[flint wyvern]

someone told me i did it right

[compact ridge]

total money = money/room * number of rooms

[flint wyvern]

hold on

[flint wyvern]

this is my part A work

[flint wyvern]

im confused

what do i ned to fix

[compact ridge]

wait

[warm copper]

It's correct

I literally told him so earlier lol

[flint wyvern]

yeah

[flint wyvern]

was there something wrong

[compact ridge]

how is it correct?

[flint wyvern]

im following a vid my teacher sent and going off it

[warm copper]

g(x)=rooms=x/3 ie a room takes 3 hours to clean from reciprocals

I can elaborate further if you don't understand

I think you might have misread the question

[compact ridge]

ah right, g(x) = x/3 means the person renovates 1/3 of a room each hour

ahhhh I see sorry

[flint wyvern]

yeah i think i see why you thought it was wrong

does part B look good though

[compact ridge]

so money/room * rooms/hour = money/hour

got it

dimensional analysis is super useful

[flint wyvern]

damn reallyy

[compact ridge]

wait

[compact ridge]

sorry part b is also correct

[flint wyvern]

oh okay ty i was boutta get a heart attack

😭

[compact ridge]

yes x is the number of hours he works

[flint wyvern]

yessirr

[flint wyvern]

everythings on notepad so i understand why its difficult to read 😭

not the efficient way

[compact ridge]

yeah the way it works is hours = 40, you sub the output into the number of rooms

the number of rooms gets subbed into your f(x) which tells us the money, where x = number of hours

damn compound functions

[compact ridge]

this question messed with my brain a lot

it's not about you

wait

[flint wyvern]

lol same took a while to get for me

[compact ridge]

isn't the final result still in terms of money per hour

[flint wyvern]

MANNN

hold up

my teacher had a similar question and this is exactly what she did

[compact ridge]

ah jesus I know you're correct but

ah but you're not multiplying you're subbing in

that's why my reasoning is wrong

[flint wyvern]

the 40h yeah

[compact ridge]

yeah it's hours -> rooms -> money as I said before

[warm copper]

I'm actually going crazy I literally checked this question earlier and now I feel like I did it wrong

[warm copper]

(I didn't sleep and it's 8am that might be the issue)

[flint wyvern]

okay yeah

[flint wyvern]

yup basically that

so i should be correct right

still gotta do part C so i need start that

[compact ridge]

also it's bad practice to use the same variable for two different things

that's why I got so confused

[warm copper]

Wait why do we plug in g(x) into f(x) can someone explain my own logic 5 minutes ago

Like I'm hella confused now

[flint wyvern]

LMAOOOO

[compact ridge]

g(x) gives you the number of rooms, if you know the number of hours
h(x) gives you the money, if you know the number of rooms

[flint wyvern]

i get that yea nah it took a while for me to get this

[warm copper]

Yeah but why should we consider the income as exponential and not constant

Just divide by 3😭🙏

I'm getting brainrot

Like if it takes 3 hours for something and you get 27x²-75 per that activity wouldn't you just divide by 3 to get the hourly income

[compact ridge]

my thoughts exactly but nope, this question is about composite functions

okay I finally understood it

[warm copper]

So bassically one of those weird topical questions that don't actually pop up in exams got it

I feel like it's not clear enough it could be either

Also I just realized

He LOSES money for decorating less than 2 rooms

[flint wyvern]

yup

[warm copper]

Weird ass question 😭