help-10

[fathom flicker]

I don't actually mean alphabetically I just don't have a better way of writing the elements

perhaps I should do a_1, a_2, .... a_n

something like that?

I'll restart using the new way of writing them

so f(x1) = {a1, a2, ..... a_n}

f(x2)={b1, b2, ...... b_m}

if f(x1)=f(x2) this implies that f(x1) is a subset of f(x2)

which implies that all a_1, a_2, .... a_n are elements of f(x2)

also, if f(x1)=f(x2) this implies that f(x2) is a subset of f(x1)

which implies that all b_1, b_2, ..... b_m are elements of f(x1)

so, since all the elements of f(x1) are in f(x2), and all the elements of f(x2) are in f(x1), then f(x1) and f(x2) are composed of the same elements

Let's rename these elements since we can now refer to them as the same things

They will now be called e1, e2, ..... e_n

This implies that there are no instances of 2 in x1 where there are not 2 also in x2. Because this would create an element e_m in x1 that would not be in x2 and that can't be.

and the same can be said about x2.

so, since x1 and x2 are only composed of 1s and 2s, wherever there are not 2's in x1, there must be 1s and since wherever there are not 2's in x1 there are not 2's in x2, this implies that wherever x1 has 1's x2 has 1's

and since x1 and x2 have 2's and 1's in the same place, and are composed entirely of 2's and 1's, then x1=x2

so f(x1)=f(x2) implies x1=x2

and f(x) then is injective

Could someone check my "proof" for showing that f(x) from this image is injective? I have typed it out above starting at the bolded message.

[kind hawk]

for starters, nothing says that f(x1) has to be finite

[kind hawk]

then here you start with the assumption f(x1)=f(x2) and then need 2 lines to conclude that the sets have the same elements?

equal sets means same elements. this is the kind of stuff that makes proofs longer unnecessarily

[fathom flicker]

alright, I don't know why I didn't just write that instantly

[kind hawk]

the rest is fine

[fathom flicker]

oh good

that's suprising

thank you for looking it over, sorry it was a bit overly complicated at the beginning

[kind hawk]

thats normal

early on you dont know what is clear and what you have to explain

which makes proofs cluttered and unreadable sometimes

you get better at that with practice

[fathom flicker]

Hopefully! Thanks again

working on surjective now

Would it be satisfactory to say that

So we are trying to prove that for all y in the image of f there exists an x s.t f(x)=y

any output of our function is a listing of some natural numbers, or is empty

if it is empty this output can be given by the input 0.111111......

if it is just some set of natural numbers

then we can construct an x, s.t for the d_-n is = 2 for any every n in our listing of naturals from our output set

[kind hawk]

not listing, set

but yes

[fathom flicker]

okay cool

alright ty Denascite I appreciate your feedback

.close

[obtuse pebble]

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[toxic mulch]

I can't figure out how they got 168,69

while I get -11.31

Do you happen to know what am doing wrong?

[obtuse pebble]

@toxic mulch Has your question been resolved?

[toxic mulch]

<@&286206848099549185>

[ionic geyser]

168.69 + 11.31 = 180

[toxic mulch]

hmmm

[toxic mulch]

how do I know when to subtract the angle I got from 180

usually tan^-1 (b/a) gives out the correct angle

[ionic geyser]

I'm not familiar with complex numbers, but I know it has axes
if the result is like this you might be looking at the wrong angle

[toxic mulch]

https://tenor.com/view/eureka-john-barrymore-the-invisible-woman-i-have-an-idea-a-ha-gif-18790999

[toxic mulch]

Thanks for your time and effort!

.close

[obtuse pebble]

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[timid silo]

Does this look right?

[midnight topaz]

no

cos76 x cos31 is not cos(76+31)

[timid silo]

So then what do u have

[midnight topaz]

nvm

its right

@timid silo

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[golden shore]

u can take AE as x and Be as 28-x

CE as Y and DE as 15-Y

and find area of kite in four pieces and subtract from area of circle

[timid silo]

Wait a second...

You don't need to

[onyx mantle]

im so sorry but ty for help but i dont understand anything

[timid silo]

There's a shortcut

Look at all 4 pieces

[onyx mantle]

idk why they put me in the top class but i am

soo ahahah

[timid silo]

And for each, create a copy

[golden shore]

like?

[timid silo]

You know how 2 congruent equilateral triangles make a rectangle?

Do that for all of them

[onyx mantle]

sureee

[timid silo]

And the solution should pop out

[golden shore]

ohk yeah

[timid silo]

Is that sarcastic? Do you understand what I said?

[onyx mantle]

ill just say bismillah

[onyx mantle]

no i msorry my english is not evry gpopd

[golden shore]

thats much easier

[timid silo]

Inshallah you'll pass this class

[onyx mantle]

inshallah

im only in yr 9 so i got time

[golden shore]

even i am in 9th

[timid silo]

Do you see what I mean by "2 copies of an right-angled triangle make a rectangle?"

[onyx mantle]

i question my self everyday on why they [put me in the higehst class 3 flipping years in row

[onyx mantle]

yes

[timid silo]

Equilateral triangle smh my head I meant right-angled

[timid silo]

Well if you so that for all 4 right-angled triangles in the diagram, what do you get?

[onyx mantle]

2 recta ngles?

[timid silo]

2?

Oh

[onyx mantle]

idk

[timid silo]

That's not what I meant but that works too

[onyx mantle]

oph lol mb

[timid silo]

I meant like... Double all 4 triangles

But yeah since it is symmetric you can also merge the left and right ones

[onyx mantle]

uhh lolol

so if i merge into rectangles

it

idik

[timid silo]

Just look back at the diagram

[onyx mantle]

yar

[timid silo]

If you merge then into 2 rectangles, what's the larger shape?

[onyx mantle]

AE?

[timid silo]

That's a segment, not a shape

[onyx mantle]

oh

the top one

the

symetrical first one

im sorry

[rich plume]

Chord CD is bisected by AB
Use intersecting chords find the lengths AE and BE
Now find r using the formula 4r^2=x^2+y^2+z^2+w^2 where x,y,z,w are parts of intersected chords (here CE, ED, EB, AE)
Now flip triangle AEC about CA and coincide the segment AC with AD. Do similar with BEC to get a rectangle. Now you got sufficient quantities to find required area

[onyx mantle]

for making this difficuly

[onyx mantle]

see now how am i gonna remeber all that and 20 other formulas

im def failing frfr

[rich plume]

It is just to make the question easier and that's my approach, there may be an easier one

[timid silo]

Again this is much more complicated than necessary

[onyx mantle]

eh dw bat it what ever happens in the test stays in the test and my parentd wotn know

i just hope over 70 since my avg is 90 form last yr

[timid silo]

If you take the triangles on the right and put them on the left, you get this shape

Do you see how?

[onyx mantle]

yes

hmmm

yar

yes

[timid silo]

And what are the lengths of this new rectangle?

[onyx mantle]

wdym lengths

[timid silo]

Like, the sizes of the sides

The width and length

[onyx mantle]

oh

[timid silo]

Or width and height

[onyx mantle]

holdo n

[timid silo]

Or whatever you call it

[onyx mantle]

number or no number

flip and i thoiyghth i was smart

im so sorry

[timid silo]

Number

[onyx mantle]

28+15?

[golden shore]

um won't it change from 28 and 15?

[timid silo]

15 is the length of CE

Look at the diagram again

Wait no

[onyx mantle]

what abt pi x 14 squared - half x 28 x 15

[timid silo]

CD*

[onyx mantle]

yar\

[onyx mantle]

whicxh would be 406?

[rich plume]

The given fact that AB is diameter makes it a lot easier. My bad we don't need those formulas

[onyx mantle]

cm squared

oh ok

[timid silo]

Oh, yes! You figured out it was meant to be half of 28*15, excellent

[onyx mantle]

oh nice

im not as dumb lol

thank you 1!!

ebertone for the help

[timid silo]

The moment where I realised this was easy was when I noticed the white area was half of the area I just highlighted, which we can easily calculate

@onyx mantle You can now .close this channel

[onyx mantle]

.close

[obtuse pebble]

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@queen dagger Has your question been resolved?

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[static patio]

can I use the same skolem function in two separate clauses?

[mighty geyser]

sounds like mathematical logic?

perhaps provide more context?

[static patio]

https://en.wikipedia.org/wiki/Skolem_normal_form

[static patio]

exactly

[mighty geyser]

only if it refers to the same free variable bound to the same quantifier

[static patio]

suppose i have these 2 formulas in a single theory

both need skolemization, do i need to create skolem function with different name, or i can use the same name?

[timid silo]

U sure?

[midnight topaz]

yaa i got the same answer

[static patio]

.close

[obtuse pebble]

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[wraith spear]

Hi, could anyone please help me with a measurement question that I feel should be easy but I'm doubting myself. Thank you

[candid yarrow]

[wraith spear]

Thank yoiu

[rich plume]

Better send a screenshot

[wraith spear]

ok, i'll try

[rich plume]

do you know any formula about volume of spherical cap?

or hemispherical (in this case)

[wraith spear]

do i approach it using an area scale factor k^2?

[rich plume]

probably not

use pythagoras I guess

[candid yarrow]

only area is needed

[wraith spear]

ooooh so find radius by using pythag?

[rich plume]

oh my b

[wraith spear]

nah, sorry, i'm still lost. I only know one side of the RA triangle

what's my hypotenuse?

[bold bane]

It's a hemi"sphere" so the radius is 10 cm.

[wraith spear]

and the radius of the water?

[wraith spear]

oooooh!!!! THANK YOU!!!

I was trying to find the hypotenuse that'd be buried in the water

so i have 8 and unknown as my legs and 10 as my hypotenuse. Easy peasy!! Thank you!!

How do I exit the chat? Super thank you for the help. I was thinking to find 1/5 of the area

.close

[obtuse pebble]

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[formal falcon]

$\int{(\frac{\sec x - \tan x}{2})^2 dx}$

[formal falcon]

Is there an easy way to get this

[warm shale]

Noir

[hot sonnet]

I think you can just expand the square

Then use some known derivatives to get the integral

Like derivative of tanx is sec²x

[obtuse pebble]

@formal falcon Has your question been resolved?

[formal falcon]

secx^2 - 2secx tanx + tanx^2

so, it's ?

$\frac{\tan{x}-2\sec{x}+\tan{x}-x}{4}$

[warm shale]

Noir

[hot sonnet]

Yes 👍🏽

[formal falcon]

I hate the result is √3π-π²/12

[formal falcon]

Thank youu

.close

[obtuse pebble]

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[timid silo]

how can I see that this is a odd function?

[timid silo]

I know odd function means f(-x)=-f(x)

when I graph it, it obviously becomes clear

but for example f(x)=(e^x-e^2x) is not odd, so how can I know?

[candid yarrow]

evaluate f(-x) and see if it is f(x) or -f(x)

[trim portal]

f(x) = e^x - e^(-x)
f(-x) = e^(-x) - e^(-(-x)) now just simplify it and see

[timid silo]

it becomes (e^-x)-e^x

[trim portal]

yeah, now try to evaluate -f(x)

it should be same

[timid silo]

not sure hot to evaluate that

oh wait

oh nicee

thanks

.close

[obtuse pebble]

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[empty scarab]

hello

fg(1) f(x)=4/(x-3) g(x)=(x-2)/x

[empty scarab]

what is this ?

[grizzled shore]

What is fg(1)?

[empty scarab]

no like

wait no

fg(a)=1 f(x)=4/(x-3) g(x)=(x-2)/x

how can I solve for a

?

[grizzled shore]

Is that f o g (x)?

Or f(g(x))?

[empty scarab]

just fg(a)=1

composite function

and I'm stuck

[grizzled shore]

Can you show the entire question

[empty scarab]

SOLVE fg(a)=1

f(x)=4/(x-3)

g(x)=(x-2)/x

[grizzled shore]

Do you know how composite functions work

[empty scarab]

well

our teacher didn't really do a good revision

but from what the book says

you apply function g closest to the bracket

then you apply the other function

for example fg(2) apply 2 to g then to f

to find the answer

fg(a) 1 I need to make g function a part of f function

?

f(x)=4/(x-3)

g(x)=(x-2)/x

g(a)=(a-2)/a

then put this to x in f function f(x)=4/(x-3)

right?

[grizzled shore]

You apply g to 2*

Not 2 to g

You apply f to (g to 2)

So you know what g is, g = (x-2)/x

So wherever you see x in f(x)

Replace it with what g is

[empty scarab]

put that

yes

but the equation becomes quite difficult to simplify

[grizzled shore]

So what would f(g(x)) be?

[grizzled shore]

You kinda have to try

[empty scarab]

i'll try wait

i think

-1/3?

I'm not so sure.

[grizzled shore]

Show your work

[empty scarab]

uh ok

4/((x-2)/x -3

4/((x-2-3x))/x

4/((-2-2x))/x

now do that thing where you multiply numerator denominator

[grizzled shore]

Write it on paper

[empty scarab]

Ok

I did the math and it's correct

[grizzled shore]

👍

[obtuse pebble]

@empty scarab Has your question been resolved?

[obtuse pebble]

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[late flare]

I did $cos\left(xy\right)\cdot y:+xy':+sin\left(x+y\right)\cdot \left(1+y'\right)$

[warm shale]

Sprites

[late flare]

but i think am getting the wrong answer

actually i think i did it correct

but how do i separate the y' values alone

so i take them as a common factor

.close

[obtuse pebble]

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[obsidian halo]

any idea how to do this

[trim surge]

so do you know that area = side*(perpendicular line)?

@obsidian halo

if you know then just calculate the ratio of APQC and ABC and you get the answer

cuz people here forbids me from revealing even a minor step in the solution, and this question is so easy that I can't say anything without revealing everything

or I'll send answer in DMS

[obsidian halo]

ok i ma try frist

ty guys ik how to fix this

.close

[obtuse pebble]

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[autumn adder]

Who forbids you to do so

We just tell you not to give out solutions that can be copied as homework

[obtuse pebble]

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[trim surge]

Once, a guy give me like 1/100 of the solution, not even anywhere close to the final answer and people already ping him .nosols, that shuts him off and no one else help me for the next 4 hours (I afk after 4 hours so it automatically close)

[trim surge]

.close

[obtuse pebble]

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[storm mountain]

can someone help me with quadratic sequences

[brisk grove]

Just ask

This is what this channel is for

[proper totem]

can someone help me with quadratic sequences im stuck T_T

[storm mountain]

how does the formula for quadratic sequences work

Tn = an2 + bn + c

[wintry fable]

you put numbers in n and you get the value for Tn

[storm mountain]

that isnt helpful

[proper totem]

wtf

sorry for my friend

hes a little cranky

O_o

[wintry fable]

wdym by work

bruh

your question wasnt specific enough

[storm mountain]

and what is n

how do u use it

[wintry fable]

generally you put natural numbers in n

and you get the value of Tn

[storm mountain]

can u give me an example of the formulaTn = an2 + bn + c filled out

[wintry fable]

huh?

generally

bro

ive never seen someone

put an imaginary number

in sequences

[storm mountain]

yeh

[wintry fable]

bro its a sequence

ffs

read the question

yeah delete yo message

[storm mountain]

yeah get yo ass outa here fr

[wintry fable]

frfr

[proper totem]

LMFAO

DAMN

[storm mountain]

mb cuh

[proper totem]

💀

[storm mountain]

can we move on

we is finna do ours meth hw

math*

broski rlly left us smh

[wintry fable]

a

[storm mountain]

nvm

hey hwacc

bro is talking to his demons ☠️

[wintry fable]

i have schizo

[storm mountain]

mb cuh

u might wanna gets that shitz checked out

bro is really good at math 💀

bro is top one

https://tenor.com/view/screams-vanishing-gif-23313762

mb guys i rlly needa do this work

[proper totem]

mb for my friend

hes a little sleeepy

and he gets cranky

at this time

its 11:20

[storm mountain]

if we cant finish this ima finna move to reddit 💀

wait

what does a b and c mean

hey bestie

slay girl

[proper totem]

ssssllllllllllllllllllllaaaaaaaaaaaaayyyyyyyyyyyyyyyy

dssssssssss

soy viientpo
papi

[storm mountain]

hey papi

https://tenor.com/view/forehead-gif-11013302

dis u

[proper totem]

look at that ;forehead;

[languid pelican]

Please refrain from posting anything that is not related to the question in hand

[storm mountain]

this is very related tho

[languid pelican]

What is the question in hand?

[storm mountain]

how do you justify your general statement in algebraic sequence

[languid pelican]

By general statement, you mean general sequence to be shown algebraically or?

[storm mountain]

yes

[proper totem]

YES

[languid pelican]

Depends on the question.

Different will have different ways or representations

[storm mountain]

ok

[languid pelican]

If you're done with the question then you can close the channel to make it available for others

[storm mountain]

can u give me an example of a representation

[languid pelican]

Ok, let's take the natural numbers

You can represent it as Sigma(n, i=1) i

Whole numbers will be Sigma(n,i=0) i

[storm mountain]

if my general statement is tn=4n^2+6n-8

than how can i justify my general statement

[languid pelican]

Clarify what you mean by 'justify'

[proper totem]

verifying

use a prediction and another example to verify that the rule works

[languid pelican]

What you've provided here is a general term of a sequence.

There is nothing to justify here.
It would've been the case if you were given the sequence instead and told to prove the term

[storm mountain]

oops

wrong chat

[proper totem]

we have to find the sequence

[storm mountain]

oops wrong thing again

[proper totem]

and we already did

[storm mountain]

man i hate doing meth

math*

i love meth

[proper totem]

*math

he meant math

hes a little

[languid pelican]

The channel is being occupied for no reason.

Someone can use the resources instead.

[proper totem]

uhm

tired

[proper totem]

we're trying to figure out a math question

[languid pelican]

I suggest you give the close command and enjoy rest of your day

[proper totem]

wym by that

[storm mountain]

is u blind

there are 4 available channels cuh

4

f

o

u

r

5

mb

if someone needed it

they would use it no

[proper totem]

四个

[storm mountain]

https://tenor.com/view/ban-gif-26566142

.close

[obtuse pebble]

Channel closed

Closed by @storm mountain

Use .reopen if this was a mistake.

[storm mountain]

.reopen

[proper totem]

.reopen

[obtuse pebble]

✅

[storm mountain]

ima go back to my csgo game

cya cuhs

https://tenor.com/view/milk-nomilk-milk-emergency-empty-gif-25023694

.close

[obtuse pebble]

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[tawny kite]

Question 9

[royal basin]

!status

[obtuse pebble]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[tawny kite]

3

[royal basin]

and where did you get it from that your answer is wrong?

[tawny kite]

oh

my bad

its right

I have another question

[tardy epoch]

the previous interaction was short enough where you can just ask here

[tawny kite]

The work i did was like 2 days ago? I'm going to try it again, I dont think I'll get it tho

but I want to try it again first

[tardy epoch]

i see. does the big black circle dot represent dot product?

[tawny kite]

The other question I had, I ended up solving it. Its so weird cause when i tried it 2 days ago i could not do it

[tardy epoch]

and that 1 is just the scalar 1 and not the vector of ones = (1,1,1)

because if so, your $u^2$ should be $u \cdot u$ and not the component-wise squaring

[warm shale]

riemann

[obtuse pebble]

@tawny kite Has your question been resolved?

[tawny kite]

update

am I allowed to do the step on the right? Replace 23 with 3?

[tardy epoch]

yes

do the same for the 5

5 = 0 mod 5

what happened from the top equation to the bottom one

[tawny kite]

ohhh wait

noo

omg my bad

i subtracted the wrong part

since b cant be -4 in modulo 5, i changed it to 1

[obtuse pebble]

@tawny kite Has your question been resolved?

[tardy epoch]

looks right. you can plug b back into the equation to verify

[tawny kite]

Thank you soo much 🙂

I'm entering my 2nd year of undergrad, deciding between applied and pure

what are your thoughts on the two

[timid silo]

Using what technique

[obtuse pebble]

@tawny kite Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[zinc nimbus]

So there are two ships, one is double as fast as the other and i have to find out p through the location of A and P all the Values in the picture are available or easy to calculate. But I have to write an equation to find out p. How does this equation look like? What we know in the question is x is smaller than 30° (it's on earth). The two ships have to meet at the same time in T

[obtuse pebble]

@zinc nimbus Has your question been resolved?

[obtuse pebble]

@zinc nimbus Has your question been resolved?

[obtuse pebble]

@zinc nimbus Has your question been resolved?

[obtuse pebble]

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[daring yew]

Hi all, i was here yesterday with these same questions

Ive asked so many people and everyone has different opinions

And i dont know what to put for my answers on 66 and 67

I guess I just want to hear more explanations since im still confused

[dim kraken]

do you the meaning of mutually exclusive events? forget the formal definition, if two events are mutually exclusive then when one event occurs the other one cannot occur

look at b

with ONE roll of a number cube, rolling a 5, rolling a 3

[daring yew]

thats not possible to get both

I dont understand how 67 isnt all of them

And why 66 isnt just A and D

[dim kraken]

is the right answer just one?

the fact that you're swimming today and then you do the same tomorrow is somehow influenced by the previous action

$P(A|B) \neq P(A)$

exactly that

[warm shale]

daffyduck

[dim kraken]

most likely you're going to swim tomorrow again

why? you did that yesterday, the event has already occurred

might as well do the same tomorrow

even if it's a small chance

seems like my answer is pretty reasonable, but i do hate those questions

[daring yew]

The other ones are but these ones seem to be choose all that apply

[dim kraken]

mmh

my professor would probably get mad at me and say

choose the simpler answer

[obtuse pebble]

@daring yew Has your question been resolved?

[obtuse pebble]

@daring yew Has your question been resolved?

[obtuse pebble]

@daring yew Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[formal cosmos]

help

[formal cosmos]

i got 0

i dont want to do this again

[fast flower]

okay, let me solve it

wait for minute

[formal cosmos]

yayy thank u

[fast flower]

hang on

To solve this problem, we use the formula to calculate the total initial capital value including interest when compounding interest:
Value of initial capital = initial capital * (1 + interest) ^ number of deposit periods
In there:
initial capital is $900 for both Bo and Levi
Bo's interest rate is 8.5% continuously
Levi's interest rate is 8.875% compounded annually
Deposit period is 7 years
First, we calculate the amount Bo has 7 years after depositing with continuously compounded interest:
The annual interest rate is equivalent to the continuous interest rate, so we will find the largest t such that 1 + 8.5%/t^t * 7t = e^(8.5%x7). Calculate t = 96.0336.
Bo's initial capital value after 7 years:
V = 900x(1+8.5%/96.0336)^(96.0336x7) = $2184.08
Next, we calculate how much Levi has after 7 years on deposit at compounded annual interest:
Levi's initial capital value after 7 years:
V = 900x(1+8.875%)^7 = 1938.84 dollars
So after 7 years, Levi will have 2184.08 - 1938.84 = $245.24 more than Bo in his account.

@formal cosmos

but I'm not sure if it's true

[formal cosmos]

op

thank u

ill see lol

it wasnt 🫠

it was 0

lmaoooo

thx thoo

[obtuse pebble]

@formal cosmos Has your question been resolved?

[timid silo]

what is 0?

you're right

[timid silo]

Did you use chatGPT for this answer?

[obtuse pebble]

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[formal cosmos]

Nah

I got 0 myself

But I got the previous ones wrong

[obtuse pebble]

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[formal cosmos]

Okay can I have help with algebra two

[formal cosmos]

Same type of problem

[tardy epoch]

[formal cosmos]

Let me send an image lol

Ya da

[timid silo]

isn't that the exact same problem you asked before

[formal cosmos]

Wait

Sht mb LOL

One sec

There we go lmao

Wait

[timid silo]

Do you know the formula for compound interest?

[formal cosmos]

Mhm

[timid silo]

how many quaraters are in a year?
how many months are in a year

[timid silo]

You solve this problem the exact same way you did the previous.
Just plug the values into the formula and compare the two numebrs you get

[formal cosmos]

4 and twelveeee

[formal cosmos]

Ya

Okay imma do it and come back if I don’t get it right lmao

5240?

🤩two!!

Im going to try to put 5240 in

No it was not correct 🫠

Can someone please help?

[formal cosmos]

🥲

help

[hot hazel]

can you show your attempt?

im not sure where youd be getting $5240 from

[formal cosmos]

yea hold up

My work is a bit messy 😅

The decimals are to replace the fraction below it

And then you subtract the two answers

[hot hazel]

the compounding rule given in the question is different from what you have

[formal cosmos]

oh.

[timid silo]

?

[hot hazel]

you seem to be writing as though they were compounded quarterly and monthly

[formal cosmos]

🫠 are they not?

[hot hazel]

reread the qeustion?

oh wait

i was looking at the original image

my bad

lmao

apologies let me reread

[formal cosmos]

lmao all good

[hot hazel]

im still not sure where you got $5240 from

i ran that computation and got a different number

[formal cosmos]

op

what did u get?

[hot hazel]

a number between $1000 and $1200

[formal cosmos]

oh lmao

im a bit off

huh

uhhhh let me try again

[hot hazel]

again your formula seems to be correct

just presumably something went wrong when plugging it into a calculator

[formal cosmos]

Okay okay

1926413

[hot hazel]

thats uh... a bit high

[formal cosmos]

🫠🔫

I’m so doneeee

I took the test for this already so it’s just left my brain lmao

[hot hazel]

are you sure youre plugging it into the calculator as written?

[formal cosmos]

Yea

[hot hazel]

,calc 9200 * (1 + 0.0325/4)^(4 * 19) - 9200 * (1 + 0.02875/12)^(12 * 19)

[warm shale]

Result:

1141.0571807707

[hot hazel]

because this gives a different value from what you're listing

[formal cosmos]

Ight

[hot hazel]

not sure what the discrepancy is

to find computational errors, it can help to do individual steps first and see whether they make sense

like computing one of the returns first

,calc 9200 * (1 + 0.0325/4)^(4 * 19)

[warm shale]

Result:

17016.924306225

[hot hazel]

this value seems reasonable for example, about a 3% interest rate approximately doubling after about 20 years

if you do a lot of problems you have intuition for what results "make sense"

like if you got $10 000 here thatd be clearly too low, if you got $500 000 that'd be way too high

[formal cosmos]

Mm

[hot hazel]

and if you get a negative number you did something really wrong

,calc 9200 * (1 + 0.02875/12)^(12 * 19)

[warm shale]

Result:

15875.867125455

[hot hazel]

this value makes sense as well

its a bit lower since the interest rate is a bit lower, even though its compounded more frequently

and then we just find the difference

,calc 17016.924306225 - 15875.867125455

[warm shale]

Result:

1141.05718077

[formal cosmos]

Yaaay I gots it

Thank you very much wise person 🙏

.close

[obtuse pebble]

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[formal cosmos]

Thank uuuu :]

[obtuse pebble]

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[mint whale]

I'm wondering how this = 0?

[mint whale]

also it's a lambda*x in exponent

[ruby path]

$\lim_{x \to \infty} \frac{-x}{e^{\lambda x}}$

Does this make it any clearer?

[elfin burrow]

no negative in the denominator

[warm shale]

NEONPerseus

[elfin burrow]

Is lambda > 0?

[mint whale]

ohhh so I can just use l'hopital and it'll converge to 0

[elfin burrow]

yes

[mint whale]

thanks 🙂

.close

[obtuse pebble]

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[viscid escarp]

I need help with this question

[leaden ginkgo]

!status

[obtuse pebble]

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[viscid escarp]

1

1. I don't know here to begin

[ivory trout]

are you familiar with similar triangles?

[viscid escarp]

No not really

I am only in 6th grade

This is my tuition homework.

[ivory trout]

well personally I'd use similar triangles identities but it looks like you haven't done them yet

perhaps there's a simpler way to solve this

you might rewrite the area of that triangle in terms of x

and then solve for it

[viscid escarp]

<@&286206848099549185>

[gleaming ridge]

do you know pythagoras theorem and similarity

[viscid escarp]

I know Pythagoras

[gleaming ridge]

it doesn't look like grade 6 homework ngl

[viscid escarp]

I know, my tuition makes them much harder

[gleaming ridge]

I think I have a value guess

[viscid escarp]

?

[gleaming ridge]

you see that the square creates two smaller triangles

[viscid escarp]

Yes

[gleaming ridge]

use the fact that the sum of areas of the triangles and the square is equal to the area of the bigger triangle

[viscid escarp]

Oh

Ok

I get it

[viscid escarp]

Wait

Nevermind

How do I find the area of the smaller triangles

@gleaming ridge

[gleaming ridge]

you see the points

[viscid escarp]

Yes

[gleaming ridge]

do you what formula for area of a triangle

[viscid escarp]

1/2bh

Yes

I know it

[gleaming ridge]

find length AD and CE

[viscid escarp]

That is the problem

I don't know how

[gleaming ridge]

AD = AB - BD

[viscid escarp]

Yes

So How do I find BD

[gleaming ridge]

wdym it's already given as x right?

[viscid escarp]

Oh

3-x = AE

[gleaming ridge]

AE????

[viscid escarp]

Wait my mistake

AD

[gleaming ridge]

alright what is CE then?

[viscid escarp]

BC-BE

Is equal to CE

So

What do I do

[gleaming ridge]

wdym you already know BC and BE?

BE is a side of the square

[viscid escarp]

Yes

So How do I calculate it

Like

What should I do

[gleaming ridge]

are you kidding me

[viscid escarp]

I am only in year 6

I don't know

[gleaming ridge]

Then maybe tell your tuition to give easier problems

[viscid escarp]

Sorry

[gleaming ridge]

you'll calculate EC in the same way you did AD

[viscid escarp]

Ok

So EC = BC-BE

AD= BA-BD

[gleaming ridge]

Then as seen here area(ABC) = area(AOD) + area(COE) + area(ODBE)

ODBE is a square so all sides are equal

that should be enough, if you can't go through call for some other helper cause I have to go for work

[viscid escarp]

Ok

<@&286206848099549185>

[clever pier]

Okay, find the length of AD and then find the length of CE.
Calculate the length of AO and CO in terms of x.
Now you know CO+AO=5 so you can add them and get the value of x.

Or you can do it the way numbpy told. That also works.

Yeah their method is much easier so I'd recommend to go with what numbpy told, @viscid escarp

[obtuse pebble]

@viscid escarp Has your question been resolved?

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[obtuse pebble]

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[weak meadow]

There exists an x such that the following is true:

[weak meadow]

I am supposed to find a^2 and not sure how to start

[timid silo]

is that supposed to be a binomial or like a vector?

[weak meadow]

Its a matrix

[spice citrus]

Look at the determinant of the matrix

When can the product of a matrix and nonzero vector ever be the zero vector

[obtuse pebble]

@weak meadow Has your question been resolved?

[weak meadow]

how do I see that I should use the determinant?

[obtuse pebble]

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[tender kindle]

Can anyone help me read this graph?

[tender kindle]

the blue line is f(x) = 3/(x-1)
the green one is g(x) = 2/(x+1)

the task asks me to find f(x) < g(x)

the solution i found by doing the math is (-infinity, -5) U (-1, 1)

i can see the former part in the graph but not the latter

or is (-1, 1) the part highlighted in red?

ok yeah i used the graph program to check

.close

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[burnt cipher]

Hey guys

[burnt cipher]

what have i done wrong here?

[ruby path]

You can't change the power of x

[burnt cipher]

in the frame is an identity, might be using it wrong as well

[ruby path]

It needs to be x^2

[burnt cipher]

i can do that only to the free number? (a)

[ruby path]

Yes

[burnt cipher]

thanks for the help @ruby path

.close

[obtuse pebble]

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[humble maple]

Hey, how would i resume this?

[timid silo]

how is

[royal basin]

3e^(-x) * e^x is not 3e

also "let e^x = x" is bad

[timid silo]

e^x multiplied by e^(-x) e

yeah what ann said

[humble maple]

Why is that bad?

[royal basin]

you're trying to do a substitution, yes?

the new variable should not be the same name as the old

[humble maple]

Yes yes my fault I ended up using W instead

I managed it in the end @royal basin

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[boreal sleet]

To remove these brackets do i have to do that long formula

Or for example i can just delete the zero on the left bracket so am left with x^2

A^2-2AB+B^2

[timber island]

no

u can solve the interior and proceed

[proud coyote]

$(x-0)^2 = x^2$

[warm shale]

Poelymole

[proud coyote]

if thats what ur asking

[timber island]

yeah

[boreal sleet]

I get a different answer tho

[knotty gulch]

no

[boreal sleet]

Answer sheet

[knotty gulch]

that’s not how square roots work

[proud coyote]

you cant do that

combine the x^2 and x^2/4 into 1 number

then square root

[timber island]

Uhm this is wrong

[timber island]

yes exactly

[proud coyote]

its like a square, you cant just square each term bc there might be middle terms

[knotty gulch]

hey that’s mean, we don’t do that here

[timber island]

$\sqrt{a+b} \neq \sqrt{a}+\sqrt{b}$

[warm shale]

ItzKraken2

[timber island]

oop, sorry

[proud coyote]

ie $(x+y)^2 = x^2 + y^2 + 2ab \neq x^2 + y^2$

[warm shale]

Poelymole

[boreal sleet]

Ok thanks i just mixed up because in integration i can do that

[proud coyote]

yeah sqrt is indices rather than calculus

[boreal sleet]

Thanks again

.close

[obtuse pebble]

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[hollow grail]

how was this coverted to that

[normal oracle]

divide numerator and denominator by sqrt(1+x)

[proud coyote]

difference of 2 squares

[obtuse pebble]

@hollow grail Has your question been resolved?

[obtuse pebble]

Channel closed

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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>.
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[burnt cipher]

my answer in the book and symbolab shows me different answers , can anyone help me out here?

[fierce lagoon]

What answers do they show

You can have different answers for antiderivatives (they usually differ by a constant)

[burnt cipher]

@fierce lagoon

[normal oracle]

that is correct

what's the other?

[burnt cipher]

these are both answers

in the frame

[normal oracle]

oh

i just read the last thing

[burnt cipher]

thats the answer from the book

[fierce lagoon]

The first box is correct

That's what I got

[normal oracle]

i got the second one

so ig both are correct

[burnt cipher]

what did u use?

to get the second one

[normal oracle]

it depends what method u use to solve it

oh

[burnt cipher]

as in calculator , or did u do it yourself and got it

[normal oracle]

first you write sinx as 1/2(sinx+cosx) + 1/2(sinx-cosx) and separate like this

wait writing here is awful

i'll paint

[fierce lagoon]

Lemme see how they got the second one, because the first one is what I got from symboblab to check

[normal oracle]

like this

and apply linearity (idk if the word is correct in english

[fierce lagoon]

Yeah

Integral linearity is correct

[normal oracle]

then use subtitution

for the first one

u = sinx-cosx etc..

i guess u can finish that part

u will get 1/u

and solve

[burnt cipher]

im still trying to figure out what is Integral linearity and how u made it happen on the 1st pic

[normal oracle]

you can also solve it with trigonometric identities but i think that's longer

[burnt cipher]

im not sure we even used Integral linearity in class yet

[candid yarrow]

it just means you can take the addition outside of the integral

[fierce lagoon]

Lemme try to type this out

I think I know what lord did

[normal oracle]

yeah, i just asked about the word in english itself, that might have confused u

[fierce lagoon]

Your terminology is correct

[burnt cipher]

well this doesnt explain how he added that 1\2 and cos(x) to the mix

which as where im stuck at

[normal oracle]

here

i said

[candid yarrow]

why is there a c in there

[normal oracle]

it's a trigonometric identity conviniently used on this exact problem

let me see

oh that's a typo

parenthesis that didnt close

dyslexia problems xd

[burnt cipher]

i have never seen this identity leap before lol, do u have some sheet u can send for identities , because mine does not have it

[normal oracle]

no, it's just right away identity

just add both things u'll see

it's the same

you can use other identities to make the integral easier to solve but I think they are larger

[burnt cipher]

i see it, but i never seen that method

its not even identity really

[fierce lagoon]

$$\begin{align*}
I &= \int\frac{\sin(x)}{\sin(x) - \cos(x)}\dd x \
&= \int\parens{1 + \frac{\cos(x)}{\sin(x) - \cos(x)}} \dd x \
2I &= \int\parens{1 + \frac{\cos(x) + \sin(x)}{\sin(x) - \cos(x)}} \dd x\
I & = \frac12 \int\parens{1 + \frac{\cos(x) + \sin(x)}{\sin(x) - \cos(x)}} \dd x
\end{align*}$$

[warm shale]

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

[burnt cipher]

just like 2=2-1+1 kind of thing

[fierce lagoon]

Took way too long to type on mobile 💀

[normal oracle]

that also works lol

[burnt cipher]

dang nice

thanks!

[normal oracle]

but u got compile error

so must be wrong

[fierce lagoon]

Yeah well

[normal oracle]

kidding xd

[fierce lagoon]

Being on mobile sucks ass sometimes

[normal oracle]

at least u can type latex, not like me i have to use paint xd

[candid yarrow]

paint can be faster

[fierce lagoon]

Latex is neater though

[fierce lagoon]

@burnt cipher do you know how I got from the first step to the second though

That's probably the one thing that'll confuse you

[normal oracle]

there are some paint - to - math conversors, maybe i should use them

[fierce lagoon]

I didn't really show steps in between those two

[normal oracle]

1 = (sinx-cosx)/(sinx-cosx)

remember u can always play with the number one in a lot of the integral problems

they solve a lot of headaches

[fierce lagoon]

And the number 0

Like algebraically manipulating 1 and 0 opens up a bunch of doors

[normal oracle]

yes

[burnt cipher]

nah i just did the whole thing thanks

thanks guys! @normal oracle @fierce lagoon @candid yarrow

.close

[obtuse pebble]

Channel closed

Closed by @burnt cipher

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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.

[edgy needle]

Hi

[edgy needle]

For this question

I did AO is shared/common

But the answer is AAS

Can i still do this?

I got SAS btw

[rich plume]

You just need to prove them congurent

[edgy needle]

Did i do that with the common

Idk if they r actually common

[rich plume]

Wait

That isn't SAS

[edgy needle]

Noooooooooooooooooooooooo

Y

[rich plume]

That is SSA which is not a valid criteria

[edgy needle]

Why is it not

What.....

[rich plume]

Because the angle can take any value

[edgy needle]

Um what

They say that the angle is the same

[rich plume]

I'm talking about congruency criteria

You used SSA

[edgy needle]

What is congruency criteria?

Ya

[rich plume]

Like SSS, SAS, ASA