help-13

[crimson sedge]

notice how there is the word then between the two ways the man moves

the distance in the second way of travelling would already have the previous distance accumalated on top of it

[cedar kiln]

@hasty pollen Has your question been resolved?

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[copper geyser]

Hi, does anyone know the fast method of completing the square:

f(x) = a(x+b)²+c

find a: 1st coefficient
find b: (2nd coefficient) / 2a

• the 2 is the square, so if its quartic it would be 4 x a
  find c: y-int (x=0) difference with normal c

My notes are a bit rough and hard to read, sorry, but i forgot how to get c again. I'm trying to complete the square of x^2 -2x-3

[cedar kiln]

@copper geyser Has your question been resolved?

[worldly chasm]

\begin{align*}
0 &= ax^2 + bx + c \
&= x^2 + \frac{b}{a} x + \frac{c}{a} \
&= x^2 + 2 \frac{b}{2a} + \frac{b^2}{4a^2} - \frac{b^2}{4a^2} + \frac{c}{a} \
&= {\qty(x + \frac{b}{2a})}^2 - \frac{b^2 - 4ac}{4a^2}
\end{align*}

[wraith dagger]

OmnipotentEntity

[worldly chasm]

@copper geyser

[copper geyser]

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[vast ermine]

help please

[steel crest]

circumscribe a circle

[spark mist]

Since angle h,I,j are the same

Since it was regular 10 sided polygon

[steel crest]

notice that polygon ABCDEFGHIJ is cylic

in particular
JADG is cyclic

[clear ember]

i would just use the inscribed angle theorem

[vast ermine]

what does that mean

[clear ember]

get a circle and "shove" that shape inside that circle

such that all the vertices touch the circumference of the circle

[vast ermine]

simplest way to do this in a test? (not in a test rn lol just preparing)

[clear ember]

by definition, all regular polygons with sides >= 3 can be inscribed in a circle

[clear ember]

this is pretty simple

[clear ember]

after u accept this

[vast ermine]

alright then

gona watch a vid on polygons first lol

.close

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[vast ermine]

.reopen

[cedar kiln]

✅

[vast ermine]

nvm cant find one

still stuck-

[clear ember]

stuck on what exactly

[vast ermine]

ok so i got this far

wait

[steel crest]

do you know cyclic quads?

[vast ermine]

no

[clear ember]

do you not want to inscribe this into a circle?

[clear ember]

^

@vast ermine

[vast ermine]

i can but idk how to ive never studied that

[clear ember]

so you're telling me for the green "center"

you wouldn't be able to find <IOH?

if someone asked you it

[fallen heath]

do you know formula for interior angle of a regular n-gon?

srry I meant to tag @vast ermine

Icecube, you know what the interior angle of a regular n-gon is?

[vast ermine]

uhh no never studied that

[vast ermine]

each angle or like all interior

[fallen heath]

each angle

that's basic sum of all interior angles divide by number of vertices, so either works

[vast ermine]

yes

[fallen heath]

what is sum of all interior angles of a 10-gon?

[vast ermine]

144x10

[fallen heath]

x = 144° - 90°, and BC || AD => y = 90° - (BAD) = 90° - (180° - ABC) = 144° - 90°

[vast ermine]

ok so

x=54

[fallen heath]

.... You're supposed to prove x = y

[vast ermine]

ik that

but i need to find out what x equals if i wanna do that-

[fallen heath]

x = 144° - 90° = y is sufficient ✓

[vast ermine]

y + something = 90

y + 36 = 90

90-36=54

x=y

thank you

.close

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[clear ember]

how did you get <GAB = 90?

[blazing zephyr]

GB is diameter

[clear ember]

"diameter" is only for a circle though

[blazing zephyr]

just inscribe a circle

[clear ember]

they just said they couldn't do that

[fallen heath]

ow draw BF || AG, GFBA is rectangle

[blazing zephyr]

and spam symmetry

[cedar kiln]

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[daring rune]

Did i do it right?

[still barn]

No, 1^inf is an indeterminant form.

[daring rune]

How would u do it

[fallen heath]

$\frac{L^{2026}}{2025} = \lim_{x \to 0} \left(1 + \frac{2025x}{2025^x}\right)^{\frac{1}{x}} = e^{2025}$

take log, simplify, done ✅

[wraith dagger]

Arya

[daring rune]

Alrighty thanks 👍

[fallen heath]

wdym thanks ;-; did you get how I concluded?

you understood both equalities?

[daring rune]

No i havent learned this yet ima go learn it now 💀

[fallen heath]

LEARN WHAAAAT =_= I only did algebraic manipulation for the first equality

[daring rune]

Taking logs with limits i didnt know u could dothat ;_;

[fallen heath]

that's for the second equality, and no, I did not take log

Used: a = e^{ln a}

(1 + y)^{1/x} = e^{ln(1+y) / x} = e^{y/x} = e^{2025}

You'll understand the steps as you write them down ._>

btw y = 2025x/2025^x

[daring rune]

Hold leme write em

Wut do u from here ;_;

[fallen heath]

do from where?

[daring rune]

At L^2026 how dou get to L^2026/2025

O wait nvm i get it

[fallen heath]

You'll get most parts just by rewriting in your notebook ._> Ask if you don't get sth

[daring rune]

How do u continue from here

[fallen heath]

Do you know $\lim_{y \to 0} \frac{\ln(1 + y)}{y} = 1$?

[wraith dagger]

Arya

[daring rune]

Nop

[fallen heath]

then derive it by yourself, so you'll know from now on

[daring rune]

Okie leme try

[fallen heath]

this is very vital to deal with 1^inf indeterminate forms

[daring rune]

Is this from the e limit?

[fallen heath]

did you derive it?

[daring rune]

Tryin

[fallen heath]

yes

[daring rune]

Like dis?

[fallen heath]

Amazing

yes

[daring rune]

Yippie

[fallen heath]

but the steps would be the other way around, from bottom to top :p

but anyways

identify the ln(1 + y) term

[daring rune]

OKIE

[fallen heath]

got it?

now it's doable?

[daring rune]

Hold on me trying

[fallen heath]

$= \lim_{x \to 0, y \to 0} e^{\frac{\ln(1 + y)}{y} \cdot \frac{2025x}{x\cdot 2025^x}}$

[wraith dagger]

Arya

[daring rune]

LETS GOOOI GOT IT

[fallen heath]

yep, so it's e^2025

Now, can you solve $\frac{L^{2026}}{2025} = e^{2025}$ ?

[wraith dagger]

Arya

[daring rune]

U figured it out so fast ;0;

🙌yes

[fallen heath]

you will too, I just hope no one taints you with L'hopital ;-;

practice n build on your basics!

[daring rune]

Wats wrong with Lhopital ;-;

[daring rune]

Thanks for guiding meee

[fallen heath]

$\lim_{x \to 0} \frac{\ln(1 + x)}{x} = \lim_{x \to 0} \frac{1}{1 + x} = 1$

[wraith dagger]

Arya

[fallen heath]

Using l'hopital ;-; does this look pretty to you?

honestly speaking I appreciate that you used the definition of "e" and derived the limit !!

[daring rune]

Less intuitive i think

[fallen heath]

that's using the basics -> what you already know -> and building up on that

[daring rune]

[daring rune]

U are great teacher

[fallen heath]

ty

[daring rune]

I should close it right?

[fallen heath]

.close

[daring rune]

.close

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[obsidian crest]

im confused whats wrong

[wraith dagger]

Arya

[obsidian crest]

wait why does it have brackets?

[sonic folio]

Bc u sub -3 into x

[kindred elm]

(-3)^2 = 9

[sonic folio]

Think -5 + (x)^2

If that makes it easier

[obsidian crest]

is that just what you do when its a x with an exponent?

[sonic folio]

Its just what u do with any x

[young portal]

Always put parenthesis when substituting values so that you won't get confused or get lost in the process

[obsidian crest]

oh ive never heard of that

[sonic folio]

Bc its trivial

[obsidian crest]

well idk no one ever told me

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[warm apex]

If there are total of 10 people in a round table, how many times can i :
a. Arrange them?
b. Arrange them but 3 people have to sit with each other
c. Arrange them but 4 people cannot sit with each other

[warm apex]

Permutations yes, formula is
P=(n-1)!

[teal wraith]

for a) should be 9!

for b) group 3 together

for c) total - exclusion

@warm apex did u try

[warm apex]

B.P=((10-2)-1)!
P=(8-1)!
P=7!

[teal wraith]

you're not including internal arrangement of the 3 people

[warm apex]

i havent for c, because it needs to have the total for "If to arrange them but 4 people CAN sit with each other" for it to be
9!-t

[warm apex]

yes thats the part im confused at

[teal wraith]

internal arrangement is just 3!

[warm apex]

at our lecture before, we had 2 before for a "Couple" situation. But then later on they stated 2!

so i was confused whether to include them requires a factorial or not

[warm apex]

but that clears it, ty

So 7!*3!

[teal wraith]

after a person is placed u don't subtract 1

since we alr placed the 8 people

[warm apex]

76543!²
(425)43!²
(2104)3!²
84036

oh ny gosh

[warm apex]

Oh

[teal wraith]

u can solve (c) now

9! Is total

and for exclusion

6!*4!

[warm apex]

i see

[teal wraith]

6!(9×8×7- 4×3×2)

[warm apex]

how about if
D. Combine 4people not wanting to sit together and 3people sitting together

[teal wraith]

this is a good question

[warm apex]

we know 4people not wanting to sit is
9!-4!(6×5) And
3people wanting to sit together is
3!(6×5×4)

hello? @teal wraith

i tried 9!×9!-4!(6×5)-3!(6×5×4)

does that work

<@&286206848099549185>

So far i have
9!-(9!-4!(7×6×5)-3!(6×5×4))
where i tried a-(b-c) makes
Arrangement of B making 4 people not wanting to sit together subtract 3 from wanting to sit together having 3 people left to sit wherever you want

[stark monolith]

for (C) if you want to arrange them in a way no two of the that 4 people should not sit together it's wrong

in fact you have subtracted all the way you can arrange the 4 people together in a row

if I get (C) right one way to solve it is to first arrange 6 others (5!) then choose 4 of the empty spaces between that 6 (c(6, 4)) and then arrange the 4 (4!)

are you there?

[warm apex]

yes

i was on a ride to home mb

[stark monolith]

Is it ok?

[warm apex]

yes

[warm apex]

Oh do we use combinations for this then?

[stark monolith]

C(6, 4)x4! = 6x5x4x3

it's true also

[warm apex]

we havent learned combinations unfortunately

[stark monolith]

ok so you have first arrange 6 people then you have 6 empty space between these 6 and you want to arrange 4 others in this 6 empty space

for first one you have 6 way to choose one empty space then you can't use this empty space so for next you have 5 way to put it and so on. 6x5x4x3 = 6!/2! = P(6, 4)

[warm apex]

oh hold on, the reason theres empty space is because of c.?

is it something like this? !!!/!/!/!/

[stark monolith]

I didn't get that exactly but if arrange those 6 !!! !!! there are 6 space between them

[stark monolith]

one way of doing that yes it is

[warm apex]

i see

[stark monolith]

if you have any doubt tell me

[warm apex]

i dont have doubts dw

[stark monolith]

now I think you can solve for (d) right?

[warm apex]

only just questions

or more like "i cant seem to understand it"

Can u try solving for it, like step by step

[stark monolith]

(C) right?

[warm apex]

i mean like in the equation form

yes

[stark monolith]

first you arrange the 6 people in a round table with 5!

[warm apex]

oh

[stark monolith]

then you have 6 space between them and you have to arrange other 6 in these space and each space should be filled with at most 1 of them (no two of them should be in the same space)

so you can sit first one with 6 way second 5 , other 4, and last one with 3 so 6x5x4x3 way to do the second part

and in total 5!6!/2!

maybe draw it gives you a better intuition

[warm apex]

nono i get why 6!/2!, i dont get why 5!×6! Though

6×5×4×3 can be arranged while 2×1 can not be arranged hence
6!/2!. ?

[stark monolith]

6!/2! it's just equal to 6x5x4x3 in way of multiplication of numbers

do you know P(n, k)?

[warm apex]

yes ig

[warm apex]

is P(6,4)

[stark monolith]

yes exactly

[warm apex]

yes

[stark monolith]

I don't know if I did a bad explanation in each part tell me

[warm apex]

Alright ill tell u if i dont understand something

lemme try d

so
b=7!x3!
c=P(6,4)?

[lilac flame]

For c can you not just get 9! and subtract that from the arrangement where 4 people sit together?

[stark monolith]

no for c 5!P(6, 4)

[warm apex]

Oh

[stark monolith]

no in this way you just removed all the way you arrange them in a row

[stark monolith]

you want to arrange them in a way that no two of that 4 sit together

[lilac flame]

Isnt 9! - (6!x4!) an option?

[stark monolith]

assume this way of arranging them xyyxxxyxyx

it's not a valid arrangment but you count it in your way

[warm apex]

i tried
9!/(5P(6,4)+b)

wait mo mb

im not getting it

[stark monolith]

for (d)?

[warm apex]

yes

[stark monolith]

can you explain your way to me?

[warm apex]

i only thought of
How many of b+c is inside of a

[stark monolith]

I dont get it

[warm apex]

exactly

it doesn't make sense as well for me

[lilac flame]

What's d asking for?

[stark monolith]

no I don't know what you said D:

[warm apex]

10 People
3 People in group
4 People not wanting to group

[lilac flame]

I assume its just total - exclusion

Why involve combinations?

[warm apex]

so like
9! Is arrangement of all
7!x3! Is for 3 people wanting to group

hold on i mistake

[stark monolith]

did you see my example?

[lilac flame]

Which one

I was doing something

[stark monolith]

assume this way of arranging them xyyxxxyxyx

it's not a valid arrangment but you count it in your way

[lilac flame]

No 2 people wanna sit with each other?

[stark monolith]

no 2 of that 4

[lilac flame]

Was that in the og question?

Wait i got it

Nvm

[stark monolith]

try it step by step

you know how to make no 4 people sitting together

so first sit those 6 in a way that satisfies the other conditions of the problem

[stark monolith]

wait you want to no 4 people group or no 2 of that 4 sit together?

[warm apex]

No 4 people group

yes, no 4 people group

[stark monolith]

for C the same?

[warm apex]

it is c.

b is for 3 people group

[lilac flame]

Welp

[stark monolith]

here you said 4 them not sit together

so if you wanna just not grouping them you just subtract those 4 grouping ways

by this 9! - 4!6! is correct

[warm apex]

Oh wait does
5!P(6,4) represent the
2 of 4 thing

[fallen heath]

!status

[cedar kiln]

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

[fallen heath]

where are we right now

[warm apex]

i think 2

[stark monolith]

It's for the ways no 2 of those 4 sit together

[fallen heath]

If there are total of 10 people in a round table, how many times can i :
a. Arrange them?
b. Arrange them but 3 people have to sit with each other
c. Arrange them but 4 people cannot sit with each other

this is the Q? which part are you stuck on

[warm apex]

AH

[lilac flame]

I think its just a basic exclusion question

[warm apex]

it make sense now

[stark monolith]

yeah it is D:

[warm apex]

Oh i added a D.

were currently D

Have : 10 People
3 want group
4 no want group

[lilac flame]

Just calculate ways where they do sit together and subtract that from all arrangements

[warm apex]

I cant visualize ittz

[lilac flame]

Imma let my boy romicro take it from here lmfao

[warm apex]

ight 👍

thenks for trying

[stark monolith]

the ways you group those 3 - the ways you group those 3 and grouping those 4

[warm apex]

(7!3!)-(7!3!)(9!-4!6!)

deez?

[stark monolith]

the answer is 7!3! - 3!4!4!

[warm apex]

wat

[stark monolith]

It's a negative number D:

https://cdn.discordapp.com/attachments/987845070910795776/1236402014477488158/Sib2.gif

[warm apex]

oh wait ur right

[warm apex]

how to?

[stark monolith]

you know how exactly 7!3! come from?

[warm apex]

yes

(10-3!)(3!)

[stark monolith]

infact you group 3 of them as g and you want to arrange 7 others and g arraound the circle (8 thing)

[warm apex]

holon u got a typo

[stark monolith]

what?

[warm apex]

what does 8 thing mean

Ok so i say Group the 3 which are not related to Grouping/Not-Grouping as 7!3!

Then the grouping of 3 could be written as 3!
And the not-grouping of 4 could be written as 4!4!.?

7!3! - 3!(4!)²?

[stark monolith]

you arrange those 3 in a box (g) now you want to arrange this box and 7 other (8 thing)

[warm apex]

oh

[stark monolith]

7!3! is just the same as I told you

3!4!4! is the ways you arrange 3 of them in a box (A) and arrange other 4 in a box (B) and arrange other 3 and A and B (5 thing) arround a circule

[warm apex]

sorry im not really understanding,

arrange 3 in BoxA and arrange 4 in BoxC and arrange 3 in BoxB
mash them together we get
aaabcbcbcb

[stark monolith]

[aaa][cccc]bbb

can you talk?

[warm apex]

yes

im just not understanding well

[stark monolith]

if I share a screen and explain it to you I think it's better

[warm apex]

alright

i could do with that

[stark monolith]

ok wait a moment I'll be back

call me if you want

[warm apex]

ight

i could only do chat is that ok

[stark monolith]

ok

[clear ember]

[warm apex]

tyvm

.close

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[gleaming ibex]

could somebody help me solve this limit?

[gleaming ibex]

n is a natural number greater than 0

[mental trail]

can you show the thing inside the limit is positive and smaller than something that goes to 0?

basically squeeze theorem

[gleaming ibex]

@mental trail

[mental trail]

yes

you posted the same thing

I gave you a hint

use the 't^(n+1)' inside the integral

to get rid of the 'x^n' denominator

and give it a bound

[gleaming ibex]

cant i use IBP?

integrating e^-t and t^n+1

could it work?

[mental trail]

that's not going to solve your integral

[gleaming ibex]

n is a natural number so the exponent is going to get to 0, isnt it?

[mental trail]

well after some point

but it's not worth the computations

[gleaming ibex]

well anyway what's the answer supposed to be then?

[mental trail]

if you follow my hint

to upper bound it by something that goes to 0

you could guess

[gleaming ibex]

is the answer 0?

[mental trail]

yes

[gleaming ibex]

oh ok thx

[mental trail]

but I'm guessing you're supposed to prove it

[gleaming ibex]

i think integration by parts is going to do it

because all the terms goes to 0

[mental trail]

I'm not advising that to you, but go for it if you want

[gleaming ibex]

so it just the integral of e^-t

well anyways tysm have a great day

.close

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[raw hollow]

The answer key says b but I got something completely different when I did the taylor expansion

[raw hollow]

I checked it a million times and couldn't find a mistake

What did I do wrong?

[mild spear]

Check second derivative again

[raw hollow]

I did 3-4 times before posting here

The only thing I found was the first cos is cos^2 which doesn't change anything since it's 1^2

[mild spear]

Second derivative should be -2/9(terms) instead of -2/3

[raw hollow]

oh wait I got it thx

I multiplied 1/3 and -2/3 and found -2/3 mb

thx for the help

[cedar kiln]

@raw hollow Has your question been resolved?

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[mint moth]

For part a, is my answer correct??

[mint moth]

.close

[cedar kiln]

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[cedar kiln]

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[magic axle]

<@&286206848099549185>

[lusty pawn]

!15m

[cedar kiln]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[magic axle]

this is my room bro

[lusty pawn]

you know the formula for area of a rectangle?

[magic axle]

err

[lusty pawn]

what do you mean?

[magic axle]

man

i must be r-worded or something

cant get banned for that word again

ha ha

[lusty pawn]

answer this

[odd verge]

How old are you?

[magic axle]

why...

[lusty pawn]

discord ToS

[magic axle]

oh

15

why?

[odd verge]

Np you're good.

Anyways do you know the formula for the area of a rectangle?

[magic axle]

nah

forget it now

thanks anywho

if u wanna give me one anweerrr thoooo

[cedar kiln]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[magic axle]

ik the rules bro

im just f~cking abt

[gleaming ibex]

84.37-x=26.14

x=84.37-26.14=(84-26)+(0,37-0,14)

=58+0.23=58.23

[magic axle]

thank you sexy PFP man

i dont owe u anything

💯

[gleaming ibex]

💀

[magic axle]

what is her name sir

my friend wants to know

[gleaming ibex]

if you look closely you can see my nickname right there pal

[magic axle]

my friend is called LIL fish

HMMMM

ima guess

[gleaming ibex]

aight go ahed

[magic axle]

ion know

[gleaming ibex]

just put the fries in the bag bro

close the thread

[magic axle]

NO

[gleaming ibex]

if you dont have to ask for anything else

[magic axle]

IT SHALL ALWAYS BE OPEN

[cedar kiln]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

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[exotic zenith]

is this not right?

[lusty pawn]

how did you get 1/225

one of the 15 gets cancelled when you substitute for dx in the integral

[exotic zenith]

oh i see

thanks

[lusty pawn]

close this if you're done

[cedar kiln]

@exotic zenith Has your question been resolved?

[cedar kiln]

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[proven sigil]

Hello I have a question

[cedar kiln]

No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/

[proven sigil]

I tried to solve a problem with height between floors (I can send a math problem but its in foreign language, so you need it to translate online)
And I wanted to solve that problem with law of sine and it gave me a wrong answer, but solving that problem with for example tangens works

could someone please help me with that?

[livid hound]

how'd you get the massive number
257.4

[proven sigil]

by law of sine

I knew yellow information and should get red one

and it gaves me wrong answer, because correct one should be 297

[livid hound]

can you do the translation

[proven sigil]

i wanted to send it but its is forbiden to send ai answers, or for translation is it okay?

[livid hound]

type it into Google translate

[proven sigil]

Determine the height between two floors if you know that the number of steps between the two floors is 18, the incline angle is
30 (degrees), and the length of one step is 28.6 cm. Provide the result in centimeters rounded to the nearest whole number.

Correct answer is 297

[livid hound]

because your diagram is wrong

[proven sigil]

how?

[livid hound]

length of the step indicates the horizontal component of the step

not the slanted distance between corners

so 18 * 28.6 isn't the hypotenuse of the triangle

[proven sigil]

well when I counted that task with tangens function it gave me good answer with this diagram that 297

[livid hound]

yes

because tan is related to the horizontal component

[proven sigil]

problem: is why not with law of sine? can you show me how it should look right (diagram)?

[livid hound]

your 18 * 28.6 should be the horizontal base

NOT the yellow hyp

[proven sigil]

could you please show me it in image?

[livid hound]

can you see the horizontal base of your triangle?

[proven sigil]

not really i know what you mean, i have problem with math in english

[livid hound]

the flat _ part at the bottom

[proven sigil]

im lost

[livid hound]

do you know what horizontal means?

[proven sigil]

can you show me it in a image?

[livid hound]

just a flat line like that,

[proven sigil]

yes

[livid hound]

that part of the triangle is where
your 18 * 28.6 will be

[proven sigil]

well then it doesnt make a sense because it should be a staircase

[livid hound]

the length is the horizontal component

and you have 18 of those

the part your feet steps on when you walk on stairs,
the length of those are 28.6cm

[proven sigil]

okay lets say you're right hwo would you go on nexT?

[livid hound]

draw your updated triangle

tan will immediately give you what you want
if you want to use the sine law, you'd need the angle opposite the base which is at the top (60°)

[livid hound]

label the total horizontal length at the base

you don't care that much about the diagonal

[proven sigil]

done

[cedar kiln]

@proven sigil Has your question been resolved?

[cedar kiln]

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[cedar kiln]

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[burnt sphinx]

what

[proud vigil]

i wouldn't say that third statement is equivalent.

since its the converse of the second.

[burnt sphinx]

It's not

It's not equivalent

[proud vigil]

okay, lets take an example.

suppose i go take a run whenever its noon.

would you be able to sufficeintly say, "if its noon, then i run"?

[burnt sphinx]

The first two

Are

The 3rd isn't

You asked if they are equivalent

[proud vigil]

in fact, no.

[burnt sphinx]

no

[twilit bison]

it's equivalent to the first one

[burnt sphinx]

The fish bite only when the moon is full ⟹ If the fish bite, then the moon is full

Those are equivalent

Bye

[proud vigil]

again, converse.

converses are not always true.

think about it like a cause and effect statement.

[proud vigil]

the reason why this is not 100% true is because there are other things that can cause me to not take a run when it is noon.

if i can, i will.

[burnt sphinx]

If the fish bite, then the moon is full

[proud vigil]

see how the opposite statement doesn't necessarily work out?

[burnt sphinx]

👍

[cedar kiln]

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[proud vigil]

👍

[cedar kiln]

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[crimson sedge]

Hii, is anyone able to explain this question and the topics around it?

im lowkey failing mathsss qwq

[proud vigil]

why don't you try expanding and simplifying the expression first?

[thick ravine]

^

solve the (n-2)^2 part then open brackets accounting for sign change with the "-"

then it all falls into place

[crimson sedge]

hmmm

wait i dont understand

how do i expand the brackets

[tulip dune]

Have you learnt opening binomials

[proud vigil]

do you know the formula for (a+b)^2?

[crimson sedge]

No qwq

[proud vigil]

ah.

well, i hope you know the distributive law?

and the FOIL method?

[crimson sedge]

I think so

idkk

[proud vigil]

okay.

[crimson sedge]

idk this

I know foil

[proud vigil]

recognize this?

[proud vigil]

👍

[crimson sedge]

ooh ya i do

[proud vigil]

so, imagine (a+b)^2=(a+b)(a+b)

can you expand the right hand side?

[crimson sedge]

leme try

Is it n^2 -4n +2

[proud vigil]

close, but not quite.

check your constant term.

[crimson sedge]

do i have to add the other values when i expand the brackets

[proud vigil]

wdym?

[crimson sedge]

Like it has (n-2)^

[thick ravine]

(a+b)^2 = this

[crimson sedge]

and the other stuff beside it

[thick ravine]

(a-b)^2

[proud vigil]

hm?

[crimson sedge]

ive never seen this :(

[thick ravine]

if u expand on this u get that

[proud vigil]

you can turn pings off for replies

[thick ravine]

remember it, pretty useful identity

[crimson sedge]

hmm oka

[thick ravine]

mb

[thick ravine]

now apply that identity to the equation

[proud vigil]

so, what we have done so far; $10+n^2-(n-2)^2=10+n^2-(n^2-4n+4)$

[wraith dagger]

;(

[thick ravine]

(n-2)^2

[crimson sedge]

ohh

I se

[proud vigil]

👍

[crimson sedge]

and then after i expand what do i do?

[proud vigil]

^

[thick ravine]

open the brackets accounting for signs

[proud vigil]

you can distribute the negative to the terms, then "add" everything together (i say add tentatively since you're not really adding, but subtracting)

[crimson sedge]

ohh so it becomes 4n + 6?

[proud vigil]

yep!

so, what forms do even numbers take?

[thick ravine]

lowkey if u learn how to use chatgpt it will help you a lot in maths

at this stage

[proud vigil]

would not recommend that.

[crimson sedge]

uhh i dunno

[crimson sedge]

it made me fail when i was cheating last year

[thick ravine]

right

i dont mean in exams

as a tutor

[thick ravine]

show a pic of what youve done so far

[crimson sedge]

oof i dont have my phone because my mum took it away for 4 months qnq

[proud vigil]

okay, give me an example of an even number.

[crimson sedge]

10000

[proud vigil]

another?

[crimson sedge]

72

[proud vigil]

what do they all have in common (i.e., what are they divisible by?)

[crimson sedge]

by

2

:3

[proud vigil]

👍

so, if an even number is in the form $n=\frac{a}{2}$, solve for a.

[crimson sedge]

s

[wraith dagger]

;(

[crimson sedge]

Huh

what does that even mea

[proud vigil]

aren't all even numbers divisible by 2?

[crimson sedge]

Yeah

[proud vigil]

lets propose that a is an even number itself.

therefore, when it is divided by 2, it produces another integer, right?

[crimson sedge]

Yaa

wait so is 2 the only number that when u divide by 2 it becomes a not even number

[proud vigil]

not necessarily.

6/2=3.

also, "not even" is an odd number.

[crimson sedge]

oh yeaa i forgot

[proud vigil]

so, continuing from the stement earlier

propose $n$ is an integer such that when performing the operation $\frac{a}{2}$, we have $\frac{a}{2}=n$. now, what would $a$ be?

[crimson sedge]

Yeah

[proud vigil]

stupid fucking keyboard can't register a shift key for half a millisecond

[crimson sedge]

😭

gosh

since when did even numbers get so confuse

A would be any number

[wraith dagger]

;(

[proud vigil]

well, not necessarily.

we have defined a to be an even number, right?

[crimson sedge]

Yeahh

[proud vigil]

so, if you solve for a in the equation given, what do you get? (i.e., isolate a in the given equation)

[crimson sedge]

N woul;d be an integer

[proud vigil]

[proud vigil]

isolate for a

[crimson sedge]

I dont understand the words ur saying im sorryy :(

[proud vigil]

solve the equation for a

[crimson sedge]

Umm

a / 2 - n

o

a = 2n

?

[thick ravine]

yes

2 times any number is even, isnt it?

[crimson sedge]

Yaa

[thick ravine]

so if you can show that a number is divisible by 2 without a remainder i.e it has 2 as one of its factors. you can say the number is not odd

meaning its even

in this context you want to show that an equation has 2 as its factor

[proud vigil]

nice!

so, try to factor out a 2 from this equation.

[thick ravine]

how do you do that? you take 2 as a common factor

[thick ravine]

did you simplify this equation?

[proud vigil]

she did

[crimson sedge]

4n + 6

[proud vigil]

^

[thick ravine]

can you show that 2 is a factor of that equation

?

[crimson sedge]

Uhh

[thick ravine]

i.e both of those terms are divisible by 2

[crimson sedge]

2(2n + 3)

[thick ravine]

yes

[proud vigil]

👍

[thick ravine]

you got it!

[crimson sedge]

YAYY

im definitely failing maths

[proud vigil]

nah

[thick ravine]

nah its normal bro i sucked at this thing when i was in school too

[proud vigil]

you could also prove this with induction if you would like but you probably haven't learned that

[crimson sedge]

i dont even

know

inductiobn

[proud vigil]

k

[crimson sedge]

Why are u guys so msart

smart

????

[proud vigil]

i just threw it out as a suggestion, since maybe i thought you knew it

[proud vigil]

[crimson sedge]

Do u guys know like any idea how to get smart at maths

[proud vigil]

practice and building intuition

[thick ravine]

chatgpt 🔥 🔥

[crimson sedge]

chat gpt

[crimson sedge]

Yeah but idk how

.solved

[cedar kiln]

Channel closed

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[crimson sedge]

.close

[proud vigil]

no.

[cedar kiln]

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[acoustic portal]

I'm reposting this question since I left it before

[acoustic portal]

last time I was doing it I had drawn EC and ED which was 3 cm but I do not really know where to go from there

I understand I most likely will need to draw out triangles

[tulip dune]

See ED = 3

From here you can calculate radius of small semicircle

By pythagoras

[acoustic portal]

But I am still very unsure where to go from here

yeah

EC and ED are both 3

but we don't have the length of the line from E to the midpoint of CD do we?

[tulip dune]

See this diagram

OO' = radius

Let it be z

O'D is also radius = z

[acoustic portal]

ohhhhh so then we can use pythagoras

[tulip dune]

Yeah

As OO'B will be 90° (angle between tangent and radius)

[acoustic portal]

yeah

[tulip dune]

Which will further eqals OO'C

Alternate angles

In triangle CO'O apply pythagoras theorem

[acoustic portal]

that makes sense

thank you

I think I should be able to do it from here

[tulip dune]

Ok if you need help further feel free to ask

[acoustic portal]

will do thank you

[acoustic portal]

sorry one more thing

I'm doing pythagoras for z^2 + z^2 = 9

[tulip dune]

Yes

z = 1.5 sqrt (2)

[acoustic portal]

yeah

so when I try to find the angle OO'D I get sinx = z/3 so 1.5root2 divided by 3

[tulip dune]

Observe what i say

In triangle OO'C

Angle O'OC = 45 as OO'C is right isoseles

Similarly with O'OC = 45

BOC = 90°

[acoustic portal]

sorry could you put this onto your diagram I'm misunderstanding

[tulip dune]

I think you got calc mistake

W8 lemme open it

Got it?

[acoustic portal]

yeah I see

[tulip dune]

Now can you get area of sector OCD

Remove the area of triangle COD from it and add the area of semicircle CODO'

I think you will get

[acoustic portal]

area of OCD I got as 9pi/4

[tulip dune]

Yeah great

Remove triangle ocd

[acoustic portal]

yeah I got the answer

[tulip dune]

Great

[acoustic portal]

well I found the area of the semi circle and then added that by finding the area of the segment using 1/2r^2(x - sinx) where x is pi/2

[tulip dune]

Great

[acoustic portal]

thank you so much

Have a great week

.close

[cedar kiln]

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[fickle cedar]

Help

[fickle cedar]

I cant solve this question

g(0) =0
f(x) = k(x-1)(x-a)
0<a<1
Integral 0 to 1 f(x)dx = 0

[dire geode]

how do you know g(0) = 0

and how do you know f(x) has the form k(x-1)(x-a) for 0<a<1

[fickle cedar]

Put x = 0

Integral |f(t)| can’t be 0

So g(0) =0

[dire geode]

oh yes

[cedar kiln]

@fickle cedar Has your question been resolved?

[cedar kiln]

@fickle cedar Has your question been resolved?

[cedar kiln]

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[heady spindle]

I don't understand the sets D and E

[dull oxide]

Hi @cerulean sail

[cedar kiln]

@heady spindle Has your question been resolved?

[heady spindle]

<@&286206848099549185>

[flint prawn]

:0

[cedar kiln]

@heady spindle Has your question been resolved?

[cedar kiln]

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[oblique prawn]

what does r hat mean

[oblique prawn]

like when u do $E=k\int\frac{\dd{q}}{r^2}\hat{r}$

[dire geode]

unit vector in r direction

[wraith dagger]

Jash

[oblique prawn]

what does it change when doing calculations

[dire geode]

5.5.2.1 http://www.physicsbootcamp.org/Motion-in-Polar-Coordinates.html

"doing calculations" is too vague

[oblique prawn]

like if ur given the bounds and the values of k how would u evaluate the integral

[dire geode]

yea still too vague

[cedar kiln]

@oblique prawn Has your question been resolved?

[cedar kiln]

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[cedar kiln]

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[earnest garden]

Someone yesterday told me to use u=n+1 but someone else said it would be better to use epsilon delta stuff but i was already asleep at that moment so hopefully someone can help me with the epsilon delta stuff

[proud vigil]

do you know what epsilon delta is, first of all

or at least how it is defined

[earnest garden]

well yes i did it for normal limits with functions

so i think it is:

All epsilon > 0 There exists a Delta > 0 s.t. |f(x)-L|<epsilon , all x 0<|x-a|<delta

And for infinite i think it is
All epsilon > 0 there exists a M>0 such that |f(x)-L| < epsilon for all x> M

[proud vigil]

👍

[earnest garden]

so they just told us about sequences yesterday so i dont really know how to use it here

[proud vigil]

😭

well, lets take the limit $\lim_{x\to\infty}\frac{1}{x}$

[wraith dagger]

;(

[proud vigil]

why don't you try that as an exercise first

[earnest garden]

sure

I am stuck at the last step fuckk

M=1/e > 0

oh wait

I think i got it

[earnest garden]

@proud vigil

[proud vigil]

aa one secon

[earnest garden]

okay no worries

[proud vigil]

👍

(i have a question of my own pending cause of a stupid hw assignment)

[earnest garden]

no worries ill just make some food rq take ur time

just ping me when u are ready ill just do some other excersises first

[proud vigil]

ok

well the proof looks good for a warmup

[cedar kiln]

@earnest garden Has your question been resolved?

[proud vigil]

@earnest garden ima be back soon

[earnest garden]

sure no worries

[proud vigil]

forget i said that, i will be back never cause i gotta work, sry 😔

[earnest garden]

Owh no worries bro gl

[cedar kiln]

@earnest garden Has your question been resolved?

[earnest garden]

<@&286206848099549185>

.close

[cedar kiln]

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[earnest garden]

Sn <= 1000 for all n. How is all n true? Doesnt all n mean an infinite amount of n?

[proud vigil]

recall that $S_n=\sum a_n$

[wraith dagger]

;(

[earnest garden]

Yes but only finite right

but all n is not finite?

[proud vigil]

but

$S_{\infty}=\sum_{n=1}^{\infty} a_n$

[earnest garden]

huh

[proud vigil]

oh what

[wraith dagger]

;(

[proud vigil]

why did that put a backslash there

anyways

[proud vigil]

^

[earnest garden]

S infinite is sommation n=1 infite an

Sn is sommation k=1 n an?

[proud vigil]

yes

[earnest garden]

Aaah okay ye than it does make sense

wait noooo

cuz here it says

sn <= 1000

and not s inifite

or is it s infinite since they say for all n?

[proud vigil]

yep

[earnest garden]

okay

thank you again 💀

so sommation of n=1 to infinite of an is also <= 1000?

so that means it must be convergent

[proud vigil]

yep

[proud vigil]

👍

[earnest garden]

thank you so much

.close

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[dusky coral]

is proving f(f(a))=f(f(b)) implies f(a)=f(b) enough to prove injectivity?

[twilit bison]

i don't think so

isn't f(x)=x^2 a counterexample?

[earnest garden]

ye

or |x|

[dusky coral]

aight, thanks

[dusky coral]

thats not injective

[dusky coral]

neither is this

[twilit bison]

that's the point

[dusky coral]

oh

right

my bad

thanks!

[earnest garden]

no worries

cuz f(a)=f(b) but not a=b

[dusky coral]

hmm ye

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[covert wasp]

anyone could help me but by using similar triangles?

[clear ember]

angle chase

actually tbh it's just geometric mean lol

you can complete that right triangle given to you by realizing that it is an integer multiple of a pythag triplet

(3,4,5) * 2 = (6,8,10)

and by geometric mean you have 6^2 = 8 * n where n is the base length of the smaller right triangle

and yeah you're done...

[covert wasp]

Ohh

ok thanks

. Close

.close

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[split raven]

Pls help, I'm confused on which is the given and also on how to answer

[clear ember]

lol it's one line

idk about the two column proof tbh

show that triangle FEH is congruent to HGF

and you're done

[split raven]

huh

[split raven]

what do u mean one line?

like one line of proof?

[fallen heath]

||FEH cong to FGH HGF gives FH = FH|| :p

[clear ember]

uh

angle F in the first triangle doesn't match

[fallen heath]

@split raven You are given a rectangle EFGH. For a rectangle, the opposite sides are parallel and equal and each vertex angle is 90°. Now you have to use these details about a rectangle to: a) show triangles EFH and HGE are congruent. b) Use that EFH and HGE are congruent to show FH = GE

[clear ember]

with the angle F in the second triangle

[fallen heath]

||still shows FH = FH||

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@split raven Has your question been resolved?

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[crimson sedge]

can someone help me with the last part?

d) ?

[cedar kiln]

@crimson sedge Has your question been resolved?

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@crimson sedge Has your question been resolved?

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[foggy mica]

Hello! just wanted to see if someone could verify my answers for this review I just took

[frigid dust]

3rd is wrong

[foggy mica]

ty syndra league of legends

is that it?

[frigid dust]

4th is wrong too

[frigid dust]

nah im just going one by one

[foggy mica]

[frigid dust]

1st and 2nd are good

[mental geyser]

The last one is wrong

[foggy mica]

oml

[mental geyser]

arctan(22/67.7)

I think(?)

[frigid dust]

5 is wrong

wait, i might be doing it wrong

one sec lol

[foggy mica]

i hate trig

[mental geyser]

nahhh trig makes everything so much easier you’ll learn to love it when you get to calculus 😋😋

[frigid dust]

,tex .sohcahtoa

[wraith dagger]

Bonk

[frigid dust]

you know this right?

[foggy mica]

yes

did i get stuff mixed up

[frigid dust]

6 is wrong

7 is wrong

[mental geyser]

Can you show your work so we can see what’s going on

[foggy mica]

i have terrible dyscalculia i think i might be cooked for this unit

[frigid dust]

8 is wrong

[mental geyser]

Nah bro don’t say that

You got this

[frigid dust]

what i find interesting is that you got 1 and 2 correct

but then the rest wrong

also

[frigid dust]

OMG CAIT FROM ARCANE 2???

[mental geyser]

💀

[foggy mica]

is the answer for number 3 16.9

[frigid dust]

,w 10/sin(53.8 degrees)

[wraith dagger]

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Requested by .bonk__

[frigid dust]

no