help-27

[finite briar]

💀

sorry

well its bromine

[hollow ice]

what do you think that A does?

in paint

[finite briar]

i didnt see it 💀 i just drew it up will note from next time

thanks

the name, if u know

3-methyl,bromomethyl-5-methylhexanol

[hollow ice]

methyls should be grouped and thats bromomethyl and not bromoethyl

[finite briar]

is my new guess

[finite briar]

so 3-bromomethyl-3,5-dimethylhexanol?

[hollow ice]

yea

[finite briar]

i see, thank u

[hollow ice]

hex-1-ol i think

[finite briar]

isnt hexan-1-ol

just hexanol

[hollow ice]

idk

I hate organic and havent touched it in almost 7 years

[finite briar]

💀

[final osprey]

idt locant is important for alcohol here

[finite briar]

this one is a question from my notes but i seem to have written ethane-1,2-dial forgetting the double bond

so i think this shud simply be

ethene-1,2-dial or ethenedial

[final osprey]

that isnt aldehdye

[finite briar]

OH WAIT

this is wrong

okay yeah

i know what went wrong

this is bs

sorry 🙏

thank u

.close

[devout snow]

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[restive river]

Why are they using 3ab^2 here from pascal's triangle for x^2.?

[timber pebble]

you dont need to think of it as directly from the triangle

just write out the 3 factors

(2-cx) (2-cx) (2-cx)

we need two cx and by necessity one 2

3 ways to exclude a cx

does that help?

[restive river]

I dont understand what you mean

Am i supposed to only expand 2 brackets?

[timber pebble]

no, we are imagining picking out pieces of the distribution

so you select one term from each factor

we must select exactly two cx

or we wont get x squared

does that make sense?

[restive river]

I think I understand

I need to write out the whole equation but onlu pick out the part that has an x^2

[timber pebble]

you dont have to write it all out

[restive river]

which expands to 6c^2x^2

[timber pebble]

we can kind of imagine how the distribution will happen

[restive river]

How

[timber pebble]

because eventually every term hits every other

[restive river]

ohh because its only to the power of 3

[timber pebble]

right?

i mean imagine it were just this

(2-cx) (2-cx)

we want all the x terms

[restive river]

im genuinly so lost on what you mean with the 2 brackets

[timber pebble]

imagine which parts of the distribution will donate x terms

[restive river]

do i expand them

[timber pebble]

no

[restive river]

or what exactly do i do with them

[timber pebble]

select one term from each factor

to create the power you want

[restive river]

okay

[timber pebble]

since in distribution all the terms you select will be multiplied

[restive river]

can i pick two (-cx)

[timber pebble]

so if you want only x terms

you only pick one x term

(2-cx) (2-cx)

we can either pick one from the first factor

or one from the second

this tells us that the coefficient on the x term in the expansion will be 2 (times stuff)

i hope that makes some kind of sense

maybe it is easier to just say how to read the triangle

[restive river]

Ive not gone on to the factiorial notation or binomail expansion yet maybe im missing something

Because I dont understand how you would just pick

and what you would even do with the pick

[timber pebble]

lets do an easier one

is that okay

[restive river]

yeah

ill do it

[timber pebble]

(1+x)(1+x)

there are 4 terms in the expansion right

[restive river]

yeah

[timber pebble]

1 + x + x + xx

[restive river]

yeah

[timber pebble]

this comes from pairing up terms in the factors

and taking their product

then adding everything up

[restive river]

youve just expanded the brackets?

[timber pebble]

yea

you heard FOIL before

describes the four pairs you get

[restive river]

its a way of expanding brackets

[timber pebble]

instead of expanding everything

we can just select the pairs we know will give us relevant terms

[restive river]

ohhh sure

[timber pebble]

we know there are 4 pairs

[restive river]

i can understand that

[timber pebble]

only some give x^1

[restive river]

if we want the x^2 we pick the pair that gives us that

[timber pebble]

so we stare at(x+1)(x+1)

imagine taking x from the first and 1 frm the second

or visa versa

we dont expand everything

[restive river]

okay

[timber pebble]

we just pick the pairs

how about (x+1)(x+1)(x+1)

can you pick out the x coefficient?

now we want triplets

[restive river]

is it 3x

[timber pebble]

yea

we take x 1 1

or 1 x 1 ...

[restive river]

wait

[timber pebble]

you can try picking up factors

[restive river]

are we picking out in pairs of 3

do we need to take something from everything

[timber pebble]

(1+x)(2+x)(3+x)

[timber pebble]

yea

one term from each factor

[restive river]

ahhh i see

[timber pebble]

whats the x coefficient here?

actually

do x squared

[restive river]

3x or 6x or 2x

[timber pebble]

yea

[restive river]

3x^2, 2x^2 and x^2

[timber pebble]

,w distribute (1+x)(2+x)(3+x)

[woven radish]

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[timber pebble]

you counted 11

theres 11

make sense?

[restive river]

ahhhhhh

i think i understand

[timber pebble]

[restive river]

you pick them out and then add them like they would be added in the equation without doing all the extra

[timber pebble]

yea

just do the terms you want

[restive river]

alright lemme try the og again

[timber pebble]

okay

[restive river]

alright i see you would get 2(3)C^2X^2

I understand thank you

[timber pebble]

np

[restive river]

is there a name for this btw?

Just so I can put it in my notes

[timber pebble]

im not sure

i mean really, were working out entries of the triangle

or counting out the actual binomial coeficient

but this will work even outside of binomials

sorry not sure

[restive river]

its fine thanks again

.close

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[devout snow]

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[light pecan]

does anyone have any tips for teaching the intro to differential calculus? mate of mine is in year 11 and starting soon and would love to help him

[pseudo basin]

start with some simple functions and their derivatives

work your way through all the rules and make sure your friend understands it all

[light pecan]

this is before he knows what a derivative is

[pseudo basin]

and practice plenty

[pseudo basin]

well you did say intro to differential calculus

[light pecan]

i meant like beginning beginning

infinitesimal change

[pseudo basin]

ig send him to khanacademy

[light pecan]

fair enough

do you remember how your first 'lesson' was

[stone stump]

we had a function which gave us the distance that some runner runs in some time. then we were asked the average speed in some time spans which got shorther and shorter

[light pecan]

thats a cool idea

[stone stump]

I assume this and variations is fairly standard

[light pecan]

i remember something like that

anyway ill have a look

thought i should ask around

.close

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[devout snow]

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[iron kindle]

whats your question

[viral lynx]

(2x - 3)(e^2x-1) = 6x - 9

(2x - 3)(e^2x-1) = 3(2x - 3)

e^(2x-1) = 3 and 2x - 3 = 0

x = (ln(3) + 1)/2 and x = 3/2

[iron kindle]

BRACKETS

[pure flower]

oh it's him again

[viral lynx]

Where?

[iron kindle]

e^2x-1

[viral lynx]

Ah

[iron kindle]

e^(2x-1)

[viral lynx]

So x1 is obviously 3/2

(ln(3) + 1)/2

ln(3)/2 + 1/2

ln(sqrt(3)) + ln(sqrt(e))

ln(sqrt(3) * sqrt(e))

ln(sqrt(3e)) ?

Is that allowed?

[iron kindle]

yes

$\sqrt{a}\cdot\sqrt{b}=\sqrt{ab}$ if $a,b\geq 0$

[woven radish]

Bonk

[viral lynx]

Awesome

So c is just 3e?

[iron kindle]

yup

[pseudo basin]

??

[iron kindle]

and x1?

[viral lynx]

3/2

[iron kindle]

yup

[viral lynx]

Noiceeee

[iron kindle]

so what exactly was the problem?

haha

[viral lynx]

I wasnt sure how to do it really

But you guided me haha

Thank you!!

❤️

[iron kindle]

i didnt do shit lol

haha

[viral lynx]

You did 😂

.close

[devout snow]

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[viral lynx]

Bonk is so humble 😝

[iron kindle]

look back

what did i do

lol

[viral lynx]

Im teasingggg

[pure flower]

oh he was here a few days back

[viral lynx]

Im here every day...

[pure flower]

and it seems to always be the case that whenever he's here we just stay in chat and watch him type for 5 minutes

until he goes 'oh i got it'

lmao

[viral lynx]

You dont have to wait...

You can go do other things

[twin spoke]

yeah

but that's good

[iron kindle]

1. youre wrong
2. maybe your instructions were just shit
3. you dont have to help and stay

[pure flower]

chill guys im not being intimidating i love the guy

i didnt even say anything 😭

[iron kindle]

trueeee

[pure flower]

😭 so rude

listen

if you're someone who thinks figuring it out yourself in 5 minutes is anything but exemplary, something's wrong with you

and i don't think that so

chill out

[iron kindle]

you are the one that started lol

if you dont have anything useful to add, just keep it to yourself next time

[pure flower]

*okay but i didnt mean it rudely * 😭

i get it though

[iron kindle]

???

[pure flower]

nono i was gonna help i just got something else to do immediately after typing that

parents

[devout snow]

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[tired oak]

AK is 13 and i need arc AB

[distant helm]

arc AB can be calculated through angle AOB

[tired oak]

but is there any angle?

they didnt give any angles

[distant helm]

connect O and K, you can see OK divides the quadrilateral into 2 congruent right triangles

[tired oak]

damnnn

ur so smart

[distant helm]

:b

[tired oak]

so degree k and degree o are both 90

.close

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[tired oak]

so it wants major arc ab, i got 47.13 using 3.142 as pi but the answer is 44.54

[distant helm]

lemme see

AOK is a right triangle and we already know OA = 10 and AK = 13
so tan(AOK) = 13/10

[odd prism]

ude 22/7

[lethal pollen]

His approximation works for the accuracy they want

He probably just made an error somewhere

[distant helm]

i wouldnt do approximation midway, i will always find exact value then approximate in the end

i also got 44.54 smh

u should recheck what u did wrong

[lethal pollen]

Yea me too

Even with 3.1412

[devout snow]

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[distant laurel]

Can somebody help me solve this

[keen fulcrum]

Hihi, I really need help on how to solve the median of a trapezoid 😿

[lethal pollen]

Read #❓how-to-get-help

[distant laurel]

is this correct?

[winter torrent]

sure that looks right

[distant laurel]

whahh really?? I've seen staring at it for a long time and keep thinking it looks wrong thank god 🥲🥲

[winter torrent]

it's kinda janky because of all the +1 and -1 going on but the logic seems right

[distant laurel]

alright tyyy

[devout snow]

@distant laurel Has your question been resolved?

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[thorny ferry]

how would i get the first derivative of this if a is a constant

[thorny ferry]

it was written exactly like this so i wasnt sure of if it was arcsin(x/a) + sqareroot a^2+x^2/x or arcsin(x/a + sqareroot a^2+x^2/x)

are these derived separately as in arcsin formula + quotient rule? or the whole thing being (u) for arcsin

[dense jay]

i would confidently say its the first case

separate terms

[pure flower]

if they're both the argument for arcsin then your instructor needs to get a sense of how brackets are used

[devout snow]

@thorny ferry Has your question been resolved?

[thorny ferry]

actually ill close and just ask for when im done

.close

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[thorny ferry]

is this correct?

[thorny ferry]

finding the first dervative

[pure flower]

whats the second term

i cant read it

[thorny ferry]

-a^2/x^2squareroot a^2-x^2

[devout snow]

@thorny ferry Has your question been resolved?

[thorny ferry]

<@&286206848099549185>

[devout snow]

@thorny ferry Has your question been resolved?

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[devout snow]

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[granite anvil]

how do i do this right

I thought this was just sec^2(x) from pi/4

so then the integral would js be tanx

[blissful igloo]

tan(theta) = u

[granite anvil]

why do you have to use u sub tho

oh wait

[blissful igloo]

because ehy not

[granite anvil]

no

i was saying tanxsecx = secx 💀💀💀

[blissful igloo]

try

[granite anvil]

yeah

one sec

[restive river]

have u solved this problem

[granite anvil]

im working on it

rn i have integral of u^2

i gotta find the boundaries and solve

i got 1/3

[restive river]

final answer is 1/3??

[granite anvil]

ye

[restive river]

no

[granite anvil]

thats what the ms says

[restive river]

oh no

yes tanQ = t

we should replace like this

[granite anvil]

wdym

[restive river]

as u know if tanQ = t, dQ = dt*(cosq)^2

right?

[granite anvil]

i said U = tanx

[restive river]

dQ=dt*(cosQ)^2

[granite anvil]

du = sec^2x dx

[restive river]

no

if tanQ = t

[granite anvil]

the integrand is (tanxsecx)^2

[restive river]

yes

to solve this problem

the most important is subtitution

[winter patrol]

you did fine

[restive river]

so let tanx = t

right?

let derivate right and left term

[granite anvil]

yeah i thought so too

[restive river]

we can get dx = dt*(cosx)^2

[granite anvil]

i dont think thats right

[restive river]

right?

[granite anvil]

shouldn't it be dt/dx = sec^2(t)

[restive river]

yes

they are equal

[winter patrol]

sec^2(x), not t

[restive river]

bcz secx = 1/cosx

[granite anvil]

oh right

[granite anvil]

im so confused

[winter patrol]

you did fine

[granite anvil]

how is sec^2x = cos^2x

[restive river]

if u solve like this, no matter

[granite anvil]

yeah ima js close

[restive river]

where are u located in

[granite anvil]

why

[winter patrol]

Arin's just doing / placing stuff in an unconventional way/location

[restive river]

i am Chicago

in

[restive river]

i wanna where u are in

i can give u lots of advice

[granite anvil]

.close

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[restive river]

.close

[devout snow]

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[restive river]

hi can someone help me with a and b

[restive river]

!status

[devout snow]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[restive river]

1

[lone ravine]

There is a (-1)^n. So this calls for which criteria?

[restive river]

no there isn’t

it’s a -2^n

[pseudo basin]

(-1)^n * 2^n

[restive river]

ohh

that falls under alternating

and for b?

[grand warren]

find an equivalent

[restive river]

wdym

[grand warren]

find an equivalent of the general term in +inf

you saw things like $a(n) ~ b(n) \iff \frac{a(n)}{b(n)} \to 1$ ?

[restive river]

no

[woven radish]

tm

[grand warren]

fck i doesn’t appear

i would say $3n^6 -1 \approx 3n^6$ for $n \to +\infty$, $5n^8 +1 \approx 5n^8$, and then you can conclude

[woven radish]

tm

[restive river]

i have to use the ratio test for the first one

where would i go from here?

@grand warren

[grand warren]

Where did the square root go?

[restive river]

cancelled it

sqrt(n) and sqrt(1)

[grand warren]

yeah okay it makes sqrt(1+1/n)

so you have $\frac{u_{n+1}}{u_n}=\frac{-2 \sqrt{1+1/n}}{5}$

[woven radish]

tm

[grand warren]

if im not wrong you forgot a 2

[restive river]

indeed

[restive river]

huh

what happened to the 5^n+1/5^n+2

[grand warren]

i simplified it into 1/5 ?

$5^{n+1-n-2}=5^{-1}$

[woven radish]

tm

[restive river]

u can do that?

man im so cooked

okay so the answer is -2/5

[grand warren]

$\frac{5^{n+1}}{5^{n+2}}=5^{n+1-(n+2)}=1/5$

[woven radish]

tm

[grand warren]

😭 np

[grand warren]

yes the limit

so using D’Alembert rule, what can you say about the convergence of the series

[restive river]

converges

[grand warren]

can u explain why

[restive river]

-2/5 is less than 1

[grand warren]

yeah exactly

[restive river]

and for b r u saying to use limit comparison

[grand warren]

no

you sure you didn’t saw things like $f \approx g \iff f/g \to 1$ ?

[woven radish]

tm

[restive river]

oh i have

like 1/1.00001

[grand warren]

what’s that lol?

[restive river]

,w 1/1.000001

[woven radish]

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[restive river]

nvm

okay but what does that have to do with this

[grand warren]

what’s the limit of $\frac{3n^6-1}{3n^6}$

[woven radish]

tm

[restive river]

1

[grand warren]

yeah

so we can say $3n^6-1 \approx 3n^6$ for $n \to \infty$

[woven radish]

tm

[grand warren]

do the same with the denominator, find an equivalent

Then, make the quotient of the two equivalents

and you’ll have the answer

[restive river]

but the radical

[grand warren]

using the theorem of comparison

You will have that the general term of the series will be equivalent to $\sqrt{\frac{3n^6}{5n^8}}$

[woven radish]

tm

[grand warren]

you can simplify this

[restive river]

n^3/n^4

[woven radish]

tm

[grand warren]

yeah, simplify more 😭

[restive river]

1/n

[grand warren]

exactly

[restive river]

and that diverges

[grand warren]

yess

so using comparison theorem, your series diverges

[restive river]

im so cooked for this midterm

i mean its in 2 weeks

but this stuff doesn’t make sense to me

[grand warren]

Try to learn the methods to show that a series converges or diverges and it will go by itself

[restive river]

you’re really good at explaining things you should become a teacher

[grand warren]

it’s my objective 🙂‍↕️

thank you 🙏🏼

[restive river]

oh lol

what kind

[grand warren]

in university

in canada maybe it seems cool lol

[restive river]

ah i see well i hope it all goes well

[restive river]

their housing crisis is tragic

[grand warren]

thank you, i hope you will be the major in series test 🙏🏼

[grand warren]

i don’t want to teach in france that’s why i want to leave 😢

[restive river]

that’s fair

housing crisises are also pretty unavoidable

ig america is one of them that isn’t in one but u pay over 100 for groceries every week 😭

[grand warren]

uh 😭😭 what do you buy to pay 100

[restive river]

literally like a loaf of bread and eggs

[grand warren]

💀💀💀

[restive river]

inflation has gotten so bad here ever since trump went to office

[grand warren]

well, i saw university teacher are rlly good paid lol

[restive river]

yeah they do

high school teachers are a different story

and below

mostly underpaid

[grand warren]

yeah in france too 😅

they have a very low salary for what they’re doing

[restive river]

yeah it’s quite sad considering they’re the building blocks of a nation

[grand warren]

ye 😢 with all the taxes idk if they have more than 2k / month lol

[restive river]

right

anyways thanks a lot for the help wish you the best!

[grand warren]

np you welcome 😁

[restive river]

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[lofty verge]

I wrote always but the correct answer is sometimes

here is my reasoning

If b=4, and a<8, then a is also <64
If b=-4, and a<-8, then a is also <64

so can anyone provide a counterexample?

this is like transitive property isnt it cus a<x and x<y so a<y

[pseudo basin]

what is the domain of discourse?

[lofty verge]

what is that?

this is a competitive algebra 1 test

[tired oyster]

maybe 2b<=4b^2 must always be true for a<2b and a<4b^2

try a fraction

[lofty verge]

ahh yep

1/2

[topaz axle]

it's always true, maybe it's not in complex numbers

ah i see

[shell plover]

One example is a=1/3 and b=1/4
And for it , the equation is not true

[lofty verge]

i guess that makes sense since fractions can only get smaller when squared

where i was just assuming squaring makes a number bigger

thanks all!

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[shell plover]

:)

[raven leaf]

I know this is closed

But you can't order complex numbers

that's to say you can't say $1 > i, 1 < i or 1 = i$

[woven radish]

Xetrov

[shell plover]

Yes

[devout snow]

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[verbal mesa]

any tips for proving this one?

[sand dove]

one implication is easy

the other way around

if H1 U H2 is a subgroup of G and neither H1 nor H2 is a subset of the other

then I can find h1 in H1 but not in H2, and h2 in H2 but not in H1

now try to reach a contradiction

[verbal mesa]

okay

true

so by contradiction is easier?

[sand dove]

here contradiction is the easiest

[verbal mesa]

okay

i got it

thank you

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[restive river]

u can solve this problem by total area of squares...

so let the biggest square 's length is x!

x-4=x-h so h=4

do u understand

[devout snow]

@wintry musk Has your question been resolved?

[wintry musk]

whered u get 4

[devout snow]

@wintry musk Has your question been resolved?

[lunar harbor]

By considering this segment,

We know that this side must be x-1

Similarly, by considering this segment,

We know that this must be x-2

keep repeating this logic

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[cosmic lodge]

Want to check if my applied numerical methods hw is right.

For the QR algorithm. Show that if $A$ is symmetric, then so is every $A_k$.

I did

Base case:

$A_1 = Q^{-1}AQ=Q^{-1}A^TQ=A_1^T$

Inductive hyp: $A_k=A^T_k

Inductive step:
$$A_{k+1}=R_kQ_k$$
$$A_{k+1}=Q_k^{-1}AQ_k$$
$$A_{k+1}=Q_k{-1}A^TQ_k$$
$$A_{k+1}=A_{k+1}^T$$

Ik the intended answer but does that work?

[cosmic lodge]

The intended answer would be using the definition of Q being orthonormal, then transposing A_{k+1} to show its equal to itself i think

Hm some errors on the typesetting still

[woven radish]

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

[cosmic lodge]

My reasoning is just that they have the same QR factorization

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[ivory umbra]

need help solving this question step by step, this is for unit 2 of MCV4U, derivatives

[lunar vault]

Let x be the horizontal distance from the bow of the boat to the dock.
Let y be the vertical distance from the bow of the boat to the pulley.
Let z be the length of the rope from the bow of the boat to the pulley.
y=1m
dt/dz=−1 m/s
We want to find how fast the boat is approaching the dock, which is dt/dx, when x=5 m
x^2 +1^2 = z^2

d/dt (x^2 + 1) = d/dt (z^2)
chain rule
2x * (dx/dt) + 0 = 2z * (dz/dt)
x * (dx/dt) = z * (dz/dt)

from there just substitute

[ivory umbra]

final answer that I got is -5/2 sqrt6 = -1.02m/s

is that correct?

[lunar vault]

idk i didnt finish it

but u take abs anyway

and leave it in fraction form

[ivory umbra]

oh okok

sounds good

[devout snow]

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[devout snow]

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[grand haven]

does A show rotational symmetry? if so, what is the angle of symmetry

[grand haven]

what would the angle of symmetry be for this one?

[faint zinc]

I can help, but we can't just give answers. Can you explain your analysis?

[grand haven]

for which one

[faint zinc]

And then perhaps I can guide you to the conclusion?

Whichever one you want to work on first

[grand haven]

idk how to do it so i cant really analyze it

[faint zinc]

So do you know what rotational symmetry is?

[grand haven]

yes

[faint zinc]

Can you explain it to me?

[grand haven]

figure can be mapped onto itself by being rotated less than 360 degrees so that it and the original shape are indistinguishable

[faint zinc]

That is exactly correct

Ok so let's take the first one

https://cdn.discordapp.com/attachments/903486480075354182/1354242894420246640/IMG_2918.jpg?ex=67e4947a&is=67e342fa&hm=6dd34df183ea136d0756a9ff3dda6eb17e0ceb3accb875eb68167167af52e5ae&

Can this be rotated and mapped back onto itself?

[grand haven]

thats the problem i dont know

[faint zinc]

Ok, so if it can be mapped back onto itself then both of the distinguishing features would map back to themselves right?

The nuts and the fin shaped holes

[grand haven]

the book says yes but i dont know how to see it. my teacher only did simple ones and assigns the hard ones he didnt teach for hw

[faint zinc]

How many nuts are there? What about the fins?

[grand haven]

4 nuts 7 fins

[faint zinc]

Ok, so do 4 and 7 share common factors?

[grand haven]

1

[faint zinc]

Yes, so this means that you have to spin it around 360° to get everything lined back up again

If it were 2 it would be 180°. In general if there are multiple features then you take the gcd and find 360°/n where n is the gcd

[grand haven]

GCD?

[faint zinc]

Greatest common denominator

[grand haven]

for b i got you cant and for c i got yes, 72 degrees

wait if its 360 degrees wouldnt A not have it?

[faint zinc]

That checks out

A doesn't, no

[grand haven]

Dam

the book says it does

[faint zinc]

The book is mistaken, unfortunately

Generally, the person who writes the problems is not the person who writes the answers. And it's easy to miscount 7 as 8

And if it's 8 then it has 90° rotational symmetry

[grand haven]

i see

[grand haven]

can we do this one now

[faint zinc]

Sure, this one is easier

[grand haven]

i think its 360

[faint zinc]

Why is that?

Would it be possible to rotate it so the arrows map onto themselves?

[grand haven]

it doesnt look the same when i rotate it the other ways

[grand haven]

i dont think so

[faint zinc]

It doesn't?

[grand haven]

yeah it doesnt

[faint zinc]

Ok, so, if you've actually manipulated this image the perhaps you know better than I do

But I would have thought it was

Which part is different?

[grand haven]

lemme try to use a photo editor to rotate it

maybe im off

[faint zinc]

Looks pretty much the same to me

Maybe there's some very minor spacing differences

[grand haven]

but its not exact

[faint zinc]

Ok, in this case I would answer in this manner:

[grand haven]

i think ima go with its 270 degrees clockwise

when i put it on the paper they look the same

[faint zinc]

"Although, this logo seems to have 120° rotational symmetry. Because of minor spacing differences, it is not actually rotationally symmetric."

Not 270°

[grand haven]

howd you get 120?

[faint zinc]

360/3

[grand haven]

how do you rotate it 120 degrees with just using ur eyes and hands

[faint zinc]

I just looked at it and imagined it?

[grand haven]

how?

i only know how to do 90,180,270,360

and thats by rotating the paper

[faint zinc]

Some people have difficulty with visualizing things in their head

But 120° is 1/3 of a revolution

[grand haven]

so for ones like those you just divide by the number of arrows and stuff?

[faint zinc]

Yeah

The same way you got to 72°

For 7c

[grand haven]

i see

this shell does not show rotational symmetry because you have to rotate it 360 degrees

what about 11 and 12? we didnt learn anything the directions say so ima just do what we’ve been doing the past few @faint zinc

for 11 i got yes, 90 degrees

for 12 i got yes, always symmetrical

or, would 11 be 120 and 12 be 45

because of the arrows thing we did

[devout snow]

@grand haven Has your question been resolved?

[grand haven]

<@&286206848099549185>

confused on whether its 90 and always OR 120 and 45

[devout snow]

@grand haven Has your question been resolved?

[faint zinc]

This one

Sorry about the delay, I had to go AFK

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[restive river]

what does -(-x)*|(-x)^3| become im so confused

[restive river]

someone save me pls 😭

[ripe flax]

theres an absolute value in the -x^3 right

hence everything there becomes positive

so it turns to x^3

[restive river]

it doesnt i think

[ripe flax]

its an absolute value aint it

[restive river]

bc look at this answer from my quiz

[winter patrol]

abs val doesn't mean remove minus sign

[restive river]

so what happens how do i deal with it

[ripe flax]

its either the magnitude which is positive, or the modulus which is positive again

from what i learnt its like how far u travel from 0 to there using the number line

so yeah distance has to be positive

[winter patrol]

from abs value laws |-x^3| = |-1| * |x^3| = |x^3|

also why were you just focussing on the numertor component

[restive river]

okay wait so what would (-(-x)|(-x)^3|)/((-x)^2+2 be

[restive river]

little by little for my struggling brain

[winter patrol]

the x/x, or in that example the a/a, -a/(-a) cancels

which reduces the clutter

[restive river]

ik but wb this example this is what im on rn

[winter patrol]

is that +2 on the end supposed to be part of the denominator?

[restive river]

yes

i wish i could draw it out but idk how to use the bot lol

[winter patrol]

using sufficient parentheses is good enough for me

or you could use something like desmos to mathematically type it

or draw it in paint

$\frac{-(-x) |(-x)^3|}{(-x)^2+2}$

that?

[restive river]

wait no theres an extra ^3 in that image

its outside of the parenthesis

[winter patrol]

sry

[woven radish]

ℝαμOmeganato5

[restive river]

yes!!

okay what happens here 😭

[winter patrol]

dw about the abs value bars for now,
would you be able to simplify the other components with ()

$\frac{\blue{-(-x)} |\violet{(-x)^3}|}{\red{(-x)^2+2}}$

[woven radish]

ℝαμOmeganato5

[winter patrol]

first simplify each colour

[restive river]

mhm mhm i got that far

but its this silly business w/ the absolute value thats messing with me

[winter patrol]

what do you have atm

[restive river]

(x|-x^3|)/(x^2+2)

[winter patrol]

apply
$$|ab| = |a||b|$$
note: $-x^3 = -1 \cdot x^3$

[woven radish]

ℝαμOmeganato5

[restive river]

okayyyy so id have x|-1||x^3| on the numerator right

[winter patrol]

yes, and simplify that further

[winter patrol]

you can't assume that x is positive

[ripe flax]

x can be negative

but after putting the absolute value

anything in there becomes positive regardless of what x is

like |x^3| where x=-3

it becomes |-27| but it evaluates to 27

[restive river]

im not sure how

[winter patrol]

|-1| = ?

[ripe flax]

take vectors for instance, AB = -27i, the magnitude AKA |AB| = 27

[ripe flax]

1

[winter patrol]

NOT U

[restive river]

OH

okay wait so it would just turn into x|x^3| right

[winter patrol]

yes

[restive river]

and you cant simplify further right?

[winter patrol]

just to be clear, are you saying that |-x^3| = x^3 or something else

[ripe flax]

yes

[winter patrol]

ok, like i said that's wrong then

with x=-3, you'll get 27 on the left side but -27 on the right side

[ripe flax]

do u mean i have to examine 2 cases

like if x is positive and x is negative

[winter patrol]

if you want to express that without abs values, you'd need cases

which is tedious, makes it look more complicated
so just leave it as is (unless you need to do it for another goal)

[restive river]

why doesnt it turn into -x-|x^3|

[winter patrol]

why do you think it should turn into -x-|x^3|

what laws are you applying

[restive river]

(-1)x (-1)|x^3|

[winter patrol]

not what you typed,
regardless still wrong

multiplication doesn't distribute over multiplication

$2 \times (3 \times 4) \redneq 2\times 3 \times 2 \times 4$

[woven radish]

ℝαμOmeganato5

[devout snow]

@restive river Has your question been resolved?

[restive river]

OH wait that makes sense ty!!!

[devout snow]

Channel closed

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[restive river]

.reopen

[devout snow]

✅

[restive river]

ok we're back

😔

😔how would i find the symmetry of this

[severe bolt]

Symmetry by x = y?

[restive river]

ermmm i dont know 🌹

symmetry over y axis or origin

[severe bolt]

Do u want to draw it?

Or to calcul it

[restive river]

calculate it

graphing isnt allowed

[severe bolt]

Your educational level is higher than mine

I just noticed

[restive river]

its only precalc so youre probably still ahead of me

[severe bolt]

Do u remember

$f(x) = f(-x)$

[woven radish]

╰ 𝕃 𝕌 ℂ 𝕀 𝔽 𝔼 ℝ ╮

[restive river]

mhm

[severe bolt]

Do u?

[restive river]

yeah

[severe bolt]

That's it

[restive river]

theres more to it

its |y| =

[severe bolt]

If f(x) = f(-x) that means the function is symmetric by y axis

[restive river]

its not f(x) =
its |f(x)|

[severe bolt]

|f(-x)| = |f(x)|

[severe bolt]

I think u have to deal with that

[restive river]

Now im confused again 🥀

[restive river]

okay yeah how]

[severe bolt]

I showed u ur way

[restive river]

😭 you showed me the part that i already know

how do i deal with the absolute value

[severe bolt]

Can't u cancel it?

x² + 2 >0

[restive river]

i have no idea

[severe bolt]

For ]-inf;0]: x <0

y remains itself

For [0; +inf[: x > 0

U need to multiply by -

So y could be positive

That's justly symmetric...

[restive river]

symmetric over what

origin or y axis?

[severe bolt]

Y

I found out that | | doesnt change the symmetrically

if f(x) = f(-x)
Then |f(x)| = |f(-x)|

[restive river]

its not symmetric over origin or y axis

[severe bolt]

Yes, f(-x) = - - x |-x³| / (-x)² + 2 = x |x³| / x² + 2

That's why not symmetric

[devout snow]

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[restive river]

hi guess whos back >.<

[restive river]

is there an easy way to do this

[graceful cosmos]

Not really haha

Graph it

Graphing it isn't too hard with transformations in mind

[restive river]

we arent allowed graphing calculators

😭

[graceful cosmos]

I wasn't suggesting using a calculator

[restive river]

fml

LMAO

which points should i focus on?

or like how do i do it in the fewest possible points

[graceful cosmos]

|x - 4| is like |x|, but shifted right by 4

[restive river]

my prof didnt graph it but i cant make sense of what he did

[graceful cosmos]

Ah that's a cool way to do it

|u| = u, if u is positive
|u| = -u, if u is negative

So they check the signs for
x < 0,
0 < x < 4, and
x > 4

[restive river]

OH so i just have to plug in a few numbers?

i actually dont understand absolute values theyre killing me

[neat oar]

that is just playing with the inequality

[graceful cosmos]

So as an example, if 0 < x < 4
x is positive, so |x| = x
x - 4 is negative, so |x - 4| = -(x - 4)

[neat oar]

not random plug in number

[graceful cosmos]

So |x - 4| - |x| = -(x - 4) - (x)

[restive river]

i wish i understood LMAO

ty though!!

[graceful cosmos]

Alright good luck!

[restive river]

💚

wait wait

how is -infinty,0 possible for a one to one function

@graceful cosmos

[neat oar]

why not

[graceful cosmos]

Like, how is such a domain possible? I don't see why not

[neat oar]

one to one function mean theres only one input corresponding to one output ONLY

-infinity just mean no limit, can go to as small as you want

[restive river]

i mean its not one to one it fails the horizontal line test

[neat oar]

in that region it satisfy the test

should be

[restive river]

it doesnt

[neat oar]

hmm what

[graceful cosmos]

Then their answer is wrong!

[restive river]

😭 😭 😭 😭 😭 😭 this is my professor dawg im so cooked

[graceful cosmos]

Do you see the largest domain that would give a one-to-one function?

[restive river]

yeah it should be 0,4

right?

[neat oar]

yeah i think should be opposite

[graceful cosmos]

Yeah that looks like it to me

[neat oar]

[0,4] is the correct interval if u want it to be one to one function

[restive river]

oki ty at least i know im not insane

[graceful cosmos]

,w graph |x - 4|, |x|, |x - 4| - |x| between -10 and 10

[woven radish]

Results provided by WolframAlpha

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

Requested by kaynex

[fallen oak]

Not trying to budge in yalls session but have either of you taken college stat recently/ enought to know what i should be doing?

[restive river]

Nope 🥀

[graceful cosmos]

#❓how-to-get-help

[restive river]

im taking it next semester

[fallen oak]

its terrible

[graceful cosmos]

This is my "graph it" strat. Yellow and blue should be easy graphs to make, but green might be trickier to see

[restive river]

tyy

[winter torrent]

you can also just kinda think about "well what happens if x is really big" because then x-4 is positive and so is x

so your thing becomes (x - 4) - x

[restive river]

that kinda makes sense but i think the problem is that i fundamentally dont understand absolute values 😭

who decided to add if/else statements to algebra

[devout snow]

@restive river Has your question been resolved?

[devout snow]

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[fading hollow]

Part b please

Is the solution (4-p)/3 or (1+p)/6

[devout snow]

@fading hollow Has your question been resolved?

[fading hollow]

<@&286206848099549185>

. close

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.close

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[tall summit]

i know im suppose to complete the square.... but this is a technique i never used since forever.....

[devout snow]

@tall summit Has your question been resolved?

[tall summit]

.close

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[normal bolt]

I want to undertand these questions fundamentally. I don't want their answers but to understand concept behind then fundamentally so i can apply to any question. If anyone could explain this stuff?

Q. Find the domain and range of the following real functions:
(i) f(x) = - |x|
(ii) f(x) = √(9 - x^2)

Definitions ⏬

A function which has either R or one of its subsets as its range is called
a real valued function. Further, if its domain is also either R or a subset of R, it is
called a real function

A relation f from a set A to a set B is said to be a function if every
element of set A has one and only one image in set B.

In other words, a function f is a relation from a non-empty set A to a non-empty set B such that the domain of f is A and no two distinct ordered pairs in f have the same first element.

If f is a function from A to B and (a, b) ∈ f, then f (a) = b, where b is called the
image of a under f and a is called the preimage of b under f.

[lime plaza]

Uh so domain is what all values we can enter for x so f(x) is defined

Range will be the outputs which you get for entering values from domain

Use that to solve?

[normal bolt]

let me try tosolve

[lime plaza]

Is that a whole root over 9-x^2

[normal bolt]

indeed

[lime plaza]

Ok

Put brackets then

Ok solve then

[normal bolt]

(i)
domain = set of all real numbers
range = set of all real numbers

(ii)
domain = set of all real numbers
range = set of all real numbers

[lime plaza]

uh no

So for (i) domain is set of all real numbers ok

But now ur range is wrong

[normal bolt]

y

[lime plaza]

Choose 3 numbers

From domain

choose a -ve choose 0 and choose positive

[normal bolt]

7, - 2 , 15

[lime plaza]

Put x= that

And see what you get

[normal bolt]

7 , 2 and 15

[lime plaza]

uh u sure?

f(x)= -|x|

[normal bolt]

modulus function change every value to positive

doesn't matter if there is - sign before

[lime plaza]

f(x)= - |x|

[normal bolt]

-7, -2, -15, but i dont think -ve sign matters since it is a modulus function

[lime plaza]

That's where you are wrong

It doesn't matter inside modulus

The negative sign is outside the modulus

So if I tell you x= -3

What is |x|

[normal bolt]

3

[lime plaza]

ok but now

there is a - |x|

So we know |x|=3

Just put -ve before that

[normal bolt]

-3

[lime plaza]

Yes

[normal bolt]

why does it happens?

[lime plaza]

Negative becomes positive only inside the modulus

Modulus is defined that way

[lime plaza]

So what is range of modulus

But always try 0

To check if 0 is included or not

[normal bolt]

range = {-7, -2, -15}

[lime plaza]

no

Like for any number you enter

You get negative values right?

[normal bolt]

yes

[lime plaza]

for f(x)= - x

Ok so now try 0

what do u get

[normal bolt]

0

[lime plaza]

ok so 0 is included

now are you getting any positive values

[normal bolt]

no

[lime plaza]

for any number

Ok so positive can never be the output

[normal bolt]

yup

[lime plaza]

So all negative numbers and 0 is the output do you agree?

[normal bolt]

but the domain is set of all real numbers

[lime plaza]

Yes

Enter any number you can think of

[normal bolt]

it should be integers rather

[lime plaza]

enter a real number then

Just check the range

[normal bolt]

f(9) = -9

[lime plaza]

It will never be positive

Ok now f(x)= - x

Yep

see

so it's always negative

[normal bolt]

but for 0 it is 0

not -0

[lime plaza]

Yes

That means

0 is also included

In output

0 is neither positve nor negative

That is why always check zero

To check range choose a -ve number choose a +ve number and choose 0

[normal bolt]

but in real numbers we are only talking abut -ve nums. Here 0 is not -ve not +ve

[lime plaza]

Huh

We get 0 as output

DOMAIN is real numbers

We are trying to find range

So enter different values of domain and see what we will NOT get

[normal bolt]

range will include 0 and all negative nums?

[lime plaza]

That's it

Do you know how to write it?

[normal bolt]

no