help-0

[alpine sable]

youre either using the formula wrong

or the book is wrong

the formula is correct

[smoky tangle]

hmm

wait

let me do it

again

so

(6/7) / 2 is 12/7 right?

[alpine sable]

no

[smoky tangle]

wait

wha

how

if you do the reciprocal

which is 6x2 / 7

[alpine sable]

you cant divide a positive number by 2 and the result is a bigger number

[smoky tangle]

wdym

ohhhhh

[alpine sable]

6/7 is smaller than 12/7

[smoky tangle]

yes

so its

6/14

right

[alpine sable]

this would be correct if you said 6/(7/2)

[smoky tangle]

oh ok

but the answer is 6/14

right

[alpine sable]

yeah

[smoky tangle]

ok so

[alpine sable]

you can simplify the equation bfore you solve it

[smoky tangle]

okay

[alpine sable]

are you going to use formula or square completion?

[smoky tangle]

square

(x - (3/7))^2 +/- (3/7)^2 + 2/49

here

which one do i put

plus or i

(Minus*

plus right

[alpine sable]

minus

[smoky tangle]

oh

ok

[alpine sable]

because the original sign was minus

right?

[smoky tangle]

ah ok

yeah

wait so if it was plus

(x + 3/7) ^2

then the other 3/7 would also be +

[alpine sable]

if it was a plus, and you put a minus, then they cancel out

thats why we keep them the same

[smoky tangle]

oh ok

so its always minus

no matter what

[alpine sable]

if the original is minus

then you put a minus

if positive than positive

[smoky tangle]

oh ok

[alpine sable]

-4 = -2 -2

+4 = +2 +2

[smoky tangle]

ah ok

[alpine sable]

if you put like +2 -2 then thats 0

[smoky tangle]

ok thanks

so

after simplifying

and stuff

(x - (3/7))^2 = 1/7

right?

ill do the rt if this is correct

@alpine sable rlly sry for ping but its like 11pm here i got to sleep soon or something idk

[alpine sable]

lets see

[smoky tangle]

ye

[alpine sable]

can you re send the original equation

its too far to scroll

x^2 - 6/7x +2/49 was it?

[smoky tangle]

uh ok

part f

[alpine sable]

(x^2 - 3/7x-3/7x) =-2/49

now we need to add

21/49

so

[smoky tangle]

wait

[alpine sable]

(x-3/7)^2= 19/49

[smoky tangle]

can i send a pic of my working

[alpine sable]

do that

[smoky tangle]

can you correct me

wai t

i got the first value of x

yooo lets go i got the answer

the values

[alpine sable]

x-3/7= +-sqrt19 /7
x= (3+/-sqrt19)/7

[smoky tangle]

i got the values of x in the question

[smoky tangle]

ill do part h

[smoky tangle]

(its correct)

[alpine sable]

show me the values

[smoky tangle]

x = 0.8, x = 0.05

[alpine sable]

is this exact or approximate?

[smoky tangle]

exact

for the first value its about 0.81ish

[icy token]

should be sqrt(7)/7

[smoky tangle]

im doing the other part now

[keen plinth]

👀

[icy token]

\frac{3 \pm \sqrt(7)}{7}

[keen plinth]

$\frac{3 \pm \sqrt7}{7}$

[ocean seal]

夢雪

[icy token]

ahh so that's the LaTeX bot

[keen plinth]

tis

[alpine sable]

weird

i got 3+- sqrt 19

[keen plinth]

i didnt write this just for the record

that was @icy token

[smoky tangle]

wait

[icy token]

$\frac{-b \pm \sqrt{b^2 - 4ac}{2a}$

[ocean seal]

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

[smoky tangle]

ill send my working

[icy token]

like this?

hmmm

[smoky tangle]

should i send it?

[icy token]

ah I missed a brac

$\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

[ocean seal]

Rαιη

[keen plinth]

i agree

it should be 7

[icy token]

$\frac{6/7 \pm \sqrt{36/49 - 8/49}}{2}$

[keen plinth]

not 19

[ocean seal]

Rαιη

[smoky tangle]

gusy

i got my question answered

[icy token]

$\frac{3}{7} \pm \frac{\sqrt{28/49}}{2}

oh missed the dollar sign

$\frac{3}{7} \pm \frac{\sqrt{28/49}}{2}$

[ocean seal]

Rαιη

[icy token]

factor out the 7 from 28/49, and you'll get 4/7

[keen plinth]

$x^2 - \frac67 x + \frac2{49} = \left(x - \frac37\right)^2 - \frac7{49}$

[ocean seal]

夢雪

[smoky tangle]

.cloe

wait actually

i have 2 more questions

can someone help

Here

ill ask i a new channel

.close

[lone heart]

Channel closed

Closed by @smoky tangle

Use .reopen if this was a mistake.

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.

[native venture]

so the question was that the sum of all 6 trig ratios is 7 and we need to find the value of sin theta . cos theta

[half epoch]

Oh god, this sort of problem is better left to the computers, do you HAVE to do this? 😄

[native venture]

yes 😅

[storm river]

where r u getting stuck then

[native venture]

and then when i looked it up then max and min values of sin theta . cos theta should be between -1/2 and 1/2

[storm river]

yup

[native venture]

i don't have the answer unfortunately

[native venture]

so the value i'm getting for the same is not between the range

[icy token]

Would it not be nicer to sub a = sin\theta, b = cos\theta, 7 = 7(a^2 + b^2)

it'll be so much nicer too look at for me

[native venture]

i just wanted to solve the equation without having to write sin theta . cos theta again and again

[icy token]

Use a and b

[native venture]

do you want me to rewrite the whole thing in terms of a and b?

[icy token]

I'll do this Q, hang on...

[keen plinth]

oof

[icy token]

ugly question

[keen plinth]

clear denoms

[native venture]

..

[keen plinth]

sinθcosθ = 11 - 4sqrt7

[wary stream]

Lmao

,w sin(theta) + cos(theta) +1/sin(theta) + 1/cos(theta) + sin(theta) /cos(theta) + cos(theta) /sin(theta) = 7 solve for theta

[keen plinth]

no chance

[ocean seal]

Results provided by WolframAlpha

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

Requested by dldh06#2659

[keen plinth]

denote sinθ and cosθ by s and c respectively

then multiplying through by sc

you get

[wary stream]

Alright, bit nicer when I put the = 7, which I forgot

[native venture]

it should be between -1/2 and 1/2

[keen plinth]

it is

[wary stream]

,w 11 - 4sqrt(7)

[ocean seal]

Results provided by WolframAlpha

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

Requested by dldh06#2659

[native venture]

ohh my bad then

[keen plinth]

so you get

s^2c + sc^2 + s + c + s^2 + c^2 = 7sc

which is (s + c)sc + s + c + 1 = 7sc

[native venture]

yea i got the answer

[keen plinth]

which is (s + c)(sc + 1) = 7sc - 1

squaring both sides gives

(s^2 + 2sc + c^2)(sc + 1)^2 = (7sc - 1)^2

let sc = z

[native venture]

i should have just evaluated 11 - 4 sqrt 7 in a calc

[wary stream]

Even though the OP posted their work, still don't do the work for them

[native venture]

i thought it is not within the range

[keen plinth]

it becomes (1 + 2z)(z + 1)^2 = (7z - 1)^2

solve for z in the resulting cubic

[wary stream]

They can figure it out, using hints

[keen plinth]

you get z = 0, 11 +- 4sqrt7

[native venture]

yeaa i did that above

[keen plinth]

sry my bad

[native venture]

thanks for the help

.close

[lone heart]

Channel closed

Closed by @native venture

Use .reopen if this was a mistake.

[wary stream]

Guess your primary issue was, you didn't realize 11 - 4sqrt(7) was in between -1/2 and 1/2

[lone heart]

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.

[ivory remnant]

This may seem really stupid, but I'm genuinely confused as to why they change 10x to -10x and +38 to -38 here, can someone explain this?

[wind cloak]

They didn't

[icy token]

Rearranging equation

[wind cloak]

What they did is

subtracted 38 on both sides

[icy token]

so like-terms goes to one side

[wind cloak]

and subtracted 10x on both sides

[ivory remnant]

Huh

When did they -10x

[icy token]

Think of the equal sign as a balance

[wind cloak]

I assume you're thorough with the basics of algebra

[ivory remnant]

I am

[icy token]

and what happened was that they removed some weight of equal mass from both sides

[wind cloak]

So they are just trying to isolate x

[ivory remnant]

I know

I understand that much

but why subtraction?

[wind cloak]

They subtracted 10x on the RHS

[wind cloak]

So that all the x terms are on the LHS

How else will you remove that 10x on the RHS?

[ivory remnant]

I know they are combining like terms by putting them on one side

[wind cloak]

Then what's the issue :(

[icy token]

Whatever you do to LHS, you do to the RHS

[wind cloak]

out

your own channel

[bronze atlas]

sorry

[wind cloak]

sorry if that came as harsh @bronze atlas xd

didn't mean for it to sound rude

[bronze atlas]

np 🙂 carry on

[ivory remnant]

My question is when combining like terms do you have to swap the sign?

[wind cloak]

no lol

[ivory remnant]

Because i dont remember seeing that before

[wind cloak]

they're just abiding by rules of algebra

they subtracted 10 x on the RHS which is why they subtracted 10x on the LHS

[ivory remnant]

Alr i think i understand now

ty

<3

.close

[lone heart]

Channel closed

Closed by @ivory remnant

Use .reopen if this was a mistake.

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.

[grizzled echo]

Hi

[grizzled echo]

Can someone tell me how do I put that in a graph, using only numbers

[icy token]

y = -x + 2

[lone heart]

@grizzled echo Has your question been resolved?

[icy token]

you tagged the wrong person

[tacit arch]

plug in a few points and find a pattern. x = 0, 1, 2, 3 should be enough

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

[alpine sable]

I dont understand how to do the graphing portion.

[marsh rapids]

find the set of x values that aren't in the domain of g. This is the boundary of the domain, which you can plot

[alpine sable]

How do I find the x values?

[marsh rapids]

should have said (x, y) pairs actually since it's a function of 2 values

finding the domain is the same process as with 1D functions

[alpine sable]

Can I get an example please?

[marsh rapids]

f(x, y) = y/x

domain is the whole plane except for the line x = 0 because it's not defined for x = 0

[alpine sable]

.close

[lone heart]

Channel closed

Closed by @sacred carbon

Use .reopen if this was a mistake.

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.

[alpine sable]

How do I calculate the two complex roots in the equation: x^3 = -8 ?

[mortal trellis]

find one root, then multiply with the roots of unity

[alpine sable]

I can find -2 ofc. Then what?

[mortal trellis]

find roots of unity

specifically the third roots of unity

exp(2pi k i /3) for k=1,2,3

[alpine sable]

thats the only way to solve it?

[mortal trellis]

well you could guess? that would be a different way

you can do it by converting to polar form and comparing angles

[lone heart]

@alpine sable Has your question been resolved?

Channel closed

Closed by @karmic isle

Use .reopen if this was a mistake.

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.

[cursive glade]

can someone talk me through this solution im lost af

[tacit arch]

what's the first line you don't understand

[cursive glade]

like i accept thats the general form and then im lost from there

this

where has that come from

[tacit arch]

integral of an odd function over a symmetric domain

[cursive glade]

what even is

an odd or even function

[tacit arch]

https://www.mathsisfun.com/algebra/functions-odd-even.html

[wary stream]

The symmetry of the function

[cursive glade]

ah ok

so do I just need to remember this as a formula for FS coeffs for an odd function or what

or is there a way i can work it out easy from the general coeff

just cuz i dont remember this being in lectures now its used in a solution

[tacit arch]

you should work it out, but you should also be familiar with odd and even functions and how to identify them easily

[cursive glade]

work it out from the general formula for coeff of FS?

i can follow the rest of the solution through

just not sure where how where this was whipped out from

[lone heart]

@cursive glade Has your question been resolved?

[cursive glade]

<@&286206848099549185> FS

[lone heart]

@cursive glade Has your question been resolved?

[tacit arch]

you just plug in 0 for n on the left hand side

what is this vector when n=0

[cursive glade]

no i get that

i just dont know where the an and bn came from

[tacit arch]

that's just the definition of the fourier coefficients written in vector form

if you don't like vectors, just write that equation in two equations

[cursive glade]

oh

so it is

idk wtf is wrong with me

thank you

.close

[lone heart]

Channel closed

Closed by @cursive glade

Use .reopen if this was a mistake.

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.

[potent rain]

https://i.imgur.com/MH802oT.png
graph the equation y= -2x^2

[potent rain]

I think it's bugged?

(-2, -8)

(-1, -2)

it keeps saying it's wrong, what the heck

[tacit arch]

how is your graph produced

[potent rain]

it's on pearson for my homework

I just plot 2 points

I did (-2, -8)

and (-1, -2)

[tacit arch]

where's the question

[potent rain]

https://i.imgur.com/ggNmJ42.png

here are my options

[potent rain]

https://i.imgur.com/0SDRVy7.png

[tacit arch]

you realize your graph is wrong?

[potent rain]

how

[tacit arch]

plot x = 1

[potent rain]

weird

1 gets me y = -2

x =2 , y = -8

hmmm

just looks like a vertical line now

nvm

so it's the other way now

https://i.imgur.com/vtVh8Z8.png

[tacit arch]

2 points are not enough to plot a parabola

https://www.youtube.com/watch?v=ZJDM4TE6I30

[potent rain]

oh

so I'm supposed to know what kind of graph it is

darn

so I guess y=-2x^2 is a parabolic formula or whatever

or "3 point quadratic"

[lone heart]

@potent rain Has your question been resolved?

Channel closed

Closed by @potent rain

Use .reopen if this was a mistake.

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.

[vagrant flax]

Hello someone please help me how to do part C

thankyou

<@&286206848099549185>

woops i solved it

.close

[lone heart]

Channel closed

Closed by @vagrant flax

Use .reopen if this was a mistake.

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.

[digital steeple]

Im retackling mathematics starting from basic algebra and calculus to cover any gaps (context so im sure i understand everything explained to its core).

Im currently studying right triangle analysis and one of the questions im trying to find online but i guess its not clearly explained is this, what exactly does the sine and cosine of an angle explain in ratio?

What is this ratio explaining?

[wanton nova]

sin is opposite / hypothenuse

[digital steeple]

That i understand, but what is that ratio usable on?

What does it explain in context?

I get its the ratio of opposite towards hypothenuse, but what about it?

[wanton nova]

if you know a angle and a side, you can find everythuing

[digital steeple]

only 1 angle and 1 side?

[wanton nova]

yes

[digital steeple]

okay lets take it a step back cause im clearly noticing some of my gaps in basic geometry here

I know i can find pretty much everything if i got 2 sides, or 1 side and 2 angles

but i dont recall any instance of 1 angle - 1 side

i do assume a 2nd angle the 90o angle of a right triangle

[wanton nova]

yes

[digital steeple]

yes to what please?

And even then, what does that ratio explain?

Where can i use it?

I get i can probably find something using it, but i dont understand what i can find by "using" it

[wanton nova]

find bc here

[digital steeple]

is 30 an angle of B?

[wanton nova]

yes

30 degrees

[digital steeple]

i dont understand how to solve it

[wanton nova]

to find bc

what trig functuion do we us

e

[digital steeple]

i would find bc using the pythagorean theorem

but i dont know BA

[wanton nova]

yeah

[digital steeple]

i guess BA would be half of AC

i base that cause C is 60 degrees

[wanton nova]

its not

[digital steeple]

cool, so im wrong, keep going sorry to interrupt

[wanton nova]

so

we use sin here

sin B

what's the ratio?

[digital steeple]

Sin(30) = 15/BC

[wanton nova]

=

not =>

[digital steeple]

you are right pardon

[wanton nova]

good

now

you need to know sin30 degrees

,rotate

[wanton nova]

meaning you have to memorise this

[digital steeple]

is it too stupid that i solve it on a triangle with hypotenuses of 1 each time?

i always fail to memorize it properly thats why

What i am describing is this:

I add a mirrored side on the right triangle's bottom face - smaller angle and create a triangle which has all sides equal

Since all sides are equal (and hypotenuse is 1) so (all angles are equal) we know half of that is 1/2 (for right side)

based on that i solve Sin(30) for 1/2

[wanton nova]

[digital steeple]

Yea sorry if this seems bewildering but i have issue memorizing any information i dont understand to its very core, and since i know how to solve any sin - cos - tan using geometry i usually dont memorize and solve for it each time

Okay so anyway i can solve for that and get Sin(30) and substitute it for 1/2, so

1/2 = 15/BC

BC = 30

[wanton nova]

ok and what exactly do you need help with if you know how to solve it

[digital steeple]

i still dont understand the ratio usability besides using it as a placeholder to solve an equation

its a ratio, but what is its usability as a ratio

[wanton nova]

i just showed you

[wanton nova]

yeah that's basically it

[digital steeple]

Huh

Okay so what does the tangent explain as a function?

The ratio of opposite - adjacent, but where is that usable on then?

[wanton nova]

same thing

[digital steeple]

Ugh so its just a matter of me getting a bit more comfortable with it to link its usability to that

it doesnt have any deeper meaning

its just that

okay i see

.close

[lone heart]

Channel closed

Closed by @digital steeple

Use .reopen if this was a mistake.

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.

[split glade]

If x^2-13x+42=(x+A)(x+B), then find the value of 3A-B

[split glade]

I factored the first prat

part

and got

x=7, and x=6

but now what do I do?

[placid zinc]

You factored and got
(x - 7)(x - 6)

[split glade]

\yes

[placid zinc]

A and B are -7 and -6

[split glade]

oh

[placid zinc]

You can swap them though, haha. A can be -6 and B can be -7. Not enough info to determine them exactly

[split glade]

ok I figured it out. It could be -11 or -15

thanks for the help!

.close

[lone heart]

Channel closed

Closed by @split glade

Use .reopen if this was a mistake.

[lone heart]

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.

[remote heron]

what have u tried

[warm verge]

Btw it’s asking “determine the resulting polynomial”

[warm verge]

Everything at this point

I’m so burnt out

[remote heron]

did you FOIL?

which idk thats what they called it when i was in school

but i am basically dust now

[warm verge]

Idk what FOIL stands for

[remote heron]

oh i guess you cant foil since its not just two terms each

it just means distribute

[warm verge]

No

[remote heron]

i guess we go back a little bit

do you get what $f(x) \cdot g(x)$ is asking for?

[ocean seal]

jan Niku

[remote heron]

what operation is it asking you to do

[warm verge]

Polynomial

[remote heron]

right but add? divide?

what do you do to f and g

[warm verge]

Here is an example of that helps

[cunning raven]

box method 💀

[remote heron]

sure, yea

so the distribution is whats tripping you up?

the multiplication, i mean

[cunning raven]

this method is better imo https://d20khd7ddkh5ls.cloudfront.net/binomial_by_trinomial.png

[remote heron]

yea this is more or less FOIL

just with more terms

[cunning raven]

your school is so wack making you do box

[remote heron]

box is fine

you shouldnt use something if it's not helping you though

well maybe more say

you should try a lot of things to find what helps you most

[cunning raven]

yeah

[cunning raven]

btw "simplify" here just means combining like terms

[warm verge]

So umm does anyone got the answers lmao (I’m sorry if that sounds rude I’m just so burnt out I’ve been working on this for so long)

[cunning raven]

can you send your work so far

[warm verge]

You can see I kinda gave up once I started doing the box method

Sorry for my wack ass handwriting too

[cunning raven]

Ok let's work on this step by step (Ignoring box 💀 )
$(-3x - 3)(-7x^2 + 3x +2)$

[ocean seal]

Salt

[cunning raven]

what do you get when you multiply $-3x$ by $-7x^2$

[ocean seal]

Salt

[warm verge]

49?

[cunning raven]

you got the coefficient right, but what about the x variable?

$x \cdot x^2 =?$

[ocean seal]

Salt

[warm verge]

Ohhh so do I have to multiply 3 and 7x2

[cunning raven]

@warm verge answer this question first

[warm verge]

Ok

[cunning raven]

dw once we get past the first term the rest will be a breeze

[warm verge]

Thanks man

Ok I’m ngl i’m lost in this too 😭 I suck at math

[cunning raven]

no worries, do you know the exponent laws?

[warm verge]

Not really lol

[wise tinsel]

you can add the exponents if its multiplication

[cunning raven]

you need the same base as well

so in this case
$x \cdot x^2 = x^3$

[ocean seal]

Salt

[warm verge]

Ohh it’s the other x that makes it x3

[cunning raven]

now you might be wondering, what if I am multiplying, let's say
$x^2$ by y?

[ocean seal]

Salt

[wise tinsel]

yes because the x is also x^1

[cunning raven]

you can't really use exponent law of adding if the base is not the same

[warm verge]

Ah

[cunning raven]

so for this example, the answer is

$x^2 \cdot y = x^{2}y$

[ocean seal]

Salt

[warm verge]

Ok

[cunning raven]

alright I think we have enough basic knowldege to continue with the larger problem now

$(-3x - 3)(-7x^2 + 3x +2)$

[ocean seal]

Salt

[cunning raven]

so what is $-3x \cdot -7x^2$?

[ocean seal]

Salt

[warm verge]

12x?

[cunning raven]

can you tell me why it's actually supposed to be $21x^3$?

[ocean seal]

Salt

[warm verge]

Ohhh

Multiply

That’s right

[cunning raven]

shoot mb I said that this was correct coefficient while it is not
the coefficient is actually 21
this is jsut an edit to my previous message

[warm verge]

Ok

[cunning raven]

so, can you tell me why $-3x \cdot -7x^2 = 21x^3$?

[ocean seal]

Salt

[warm verge]

Wait for which question

This one or the one you got wrong

[cunning raven]

just this

[warm verge]

Oh ok

[cunning raven]

why is the answer 21x^3

[warm verge]

Well when you multiply 3 and 7 you get 21 and you ad the 2 x with another x which gets you 3x

[cunning raven]

exactly

$(-3x - 3)(-7x^2 + 3x +2)$

[ocean seal]

Salt

[cunning raven]

now what is -3x * 3x

[warm verge]

9x1

Not 9 times 1

9x1

Idk how to make the 1 smaller

[cunning raven]

use ^ to show exponent

[wise tinsel]

hey wait where did you get 1

[warm verge]

Oh ok

[cunning raven]

also you don't need to write the 1

when you type 9x

[warm verge]

Ok

[cunning raven]

it literally means 9x^1

also you forgot the negative

the answer is -9x

[warm verge]

Ah

[cunning raven]

ok moving on

what is -3x * 2

[warm verge]

-6x

[cunning raven]

correct

what about -3 * 7x^2

[warm verge]

21x^2

2 because there’s no other x

[cunning raven]

right but you are wrong on 1 part

do you see where that is

[warm verge]

Ohh the negative

[cunning raven]

Correct!

the answer is -21x^2

[warm verge]

Yes

[cunning raven]

ok so do you see the pattern with the questions I am asking

[warm verge]

Yes

[warm verge]

So that’s the method to use to get the answer?

Better than the box method I’m sure

[cunning raven]

so if we really expand this, what we are doing is essentially

$(-3x \cdot -7x^2) + (-3x \cdot 3x) + (-3x \cdot 2)

• (-3 \cdot -7x^2) + (-3 \cdot 3x) + (-3 \cdot 2)$

[ocean seal]

Salt

[cunning raven]

this is the distributive/foil method

[warm verge]

Ok

[cunning raven]

now, you just find the answers to the brackets.

the last 4 questions I've asked you are the questions of the first 4 brackets

[warm verge]

Alright

[cunning raven]

what is $(-3x \cdot -7x^2) \$
what is $(-3x \cdot 3x) \$
what is $(-3x \cdot 2) \$
what is $(-3 \cdot -7x^2) \$

[ocean seal]

Salt

[cunning raven]

the last 4 questions I've asked you

[warm verge]

Ok

[cunning raven]

This is essentially what you want to do for distributive method
$(-3x \cdot -7x^2) + (-3x \cdot 3x) + (-3x \cdot 2)

• (-3 \cdot -7x^2) + (-3 \cdot 3x) + (-3 \cdot 2)$

[ocean seal]

Salt

[cunning raven]

now we simplify this further/solve the brackets

$(21x^3)+ (-9x^2) + (-6x)

• (21x^2) + (-9x) + (6)$

[ocean seal]

Salt

[cunning raven]

=
$21x^3 - 9x^2 - 6x

• 21x^2 - 9x + 6$

[ocean seal]

Salt

[warm verge]

Ahhhh

[cunning raven]

and now you just combine like terms

and you reach the answer

[warm verge]

Alright

[cunning raven]

foil/distributive is kinda complicated at first but as you practice it becomes easier and easier to do with your head

[warm verge]

Thank you guys so much for all your help

[cunning raven]

this works no matter how big the polynomials get
But it takes longer and longer to do as the polynomials get larger and larger as well

what I did is essentially this image but expanded the first step
https://d20khd7ddkh5ls.cloudfront.net/binomial_by_trinomial.png

what the box method is doing is also essentially this ^ but imo the formatting is confusing af for box method

box method is basically making you write down the answers for each 'bracket' if you understand what I am saying

[cunning raven]

by 'bracket' I mean this

[lone heart]

@warm verge Has your question been resolved?

Channel closed

Closed by @warm verge

Use .reopen if this was a mistake.

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.

[alpine sable]

Can you please help me gain a better understanding of finding f and g in this graph?

I am focusing on question 83 at the moment

[nocturne wing]

U can separate it into f(-3)+g(-3)

[alpine sable]

I looked into photomath and it says the solution was 5. But I don't really understand how it got to 5. Plus it says to use the graph to solve for f and g too?

[nocturne wing]

Okay so basically ur solving for f(x) and g(x) when x is -3

So you look at what y is at -3 on the graph

f(x) just means y for the function named f

F*

[alpine sable]

Which is 0? Like (-3, 0)?

[nocturne wing]

For which one

F or g

[alpine sable]

For G

[nocturne wing]

G is the darker colored one

So if u look at the vertical line at x=-3, function g passes through 1

So g(-3) is just 1

[alpine sable]

Ohhh because the y intercept is 1, so that's saying that f is 1?

Sorry I meant g

Not f

[nocturne wing]

No but ur on the right track

The y intercept would be g(x) at x=0

But you have to look where y is at x=-3, 3 units to the left of that

Its a coincidence that they are the same

[alpine sable]

In the graph, it also shows that y=g(x) points at -3 so I see what you're saying

[nocturne wing]

So what is g(-3)?

[alpine sable]

So my g would be x=-3 as well?

[nocturne wing]

Well yeah x is at -3 but what you want to know is what y value you have at that point

[alpine sable]

Ohhh, the value would be at 0

[nocturne wing]

Its like the y intercept but ur looking at a different line

[alpine sable]

Because y=g(x) lies at -3, 0, so that's what I think

[nocturne wing]

At -3, g(x) is 1

Not zero

It doesnt get to zero until -4

[alpine sable]

Ohhh are you talking about the y intercept and not the x-axis? Because the y int is at 1?

[nocturne wing]

Not quite

Here lemme draw something

[alpine sable]

Alright, I appreciate your patience :)

[nocturne wing]

thats the line we are looking at

imagine finding the y intercept but instead of the line at x=0, we are looking at the line at x=-3

[alpine sable]

Mhm, I'm following that

[nocturne wing]

and since y = 1 at that point, g(-3) = 1

you can basically always replace g(x) with y, cuz all it means is the output of function g when u plug in an x value

so ur looking for the y value

get it?

[alpine sable]

Hmm. I don't get how y equals 1 on that line the you drew. Unless it's because of that graph line going through at 1?

[nocturne wing]

we are looking at line g, the darker of the two functions we have

dont worry about the axis lines or the f function

[alpine sable]

Oh okay!

[nocturne wing]

ok so now that uve got how to find the y values, see if you can find f(-3)

which would be the lighter line

[alpine sable]

Which would be at 2, right?

[nocturne wing]

that would be the y intercept

remember we are looking at -3 tho

[alpine sable]

ohhh

[nocturne wing]

i get how its kinda confusing tho cuz the last one had the same numbers for both

[alpine sable]

If I'm looking at -3 for the f(x) graph, wouldn't I be looking at (-3, 4)?

[nocturne wing]

yep!

so f(-3) = 4

now we have f(-3) and g(-3)

so we can get the answer pretty easily

(f+g) (-3) is literally the same as just f(-3) + g(-3)

you can split it up

[alpine sable]

Ohhh

[nocturne wing]

and the same can be done with other things like subtraction

so you have a one and a four, and that gives you the five from photomath

get it?

[alpine sable]

ohhh!!

I see the pattern, okay

so we were just actually looking for the y intercepts this whole time, right?

[nocturne wing]

y intercept is only for x=0

we are looking at y values at different x's, so pretty similar method but different notation

[alpine sable]

Ohhh, y values and not y intercepts. Okay!

[nocturne wing]

👍

when you say y intercept, that means the place a function crosses the y axis

[alpine sable]

That makes a lot of sense. I think I can carry it here from now on! Thank you a lot

[nocturne wing]

good luck :)

[alpine sable]

Thanks! Have a great day/night :)

.close

[lone heart]

Channel closed

Closed by @kind parrot

Use .reopen if this was a mistake.

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.

[alpine sable]

1. Rewrite the following problem using the commutative property of addition.
   2x + 3y

[alpine sable]

Wondering if someone could answer this so I can get an idea on how to do the rest of them

[wary stream]

No, we're not here to give you answers

Do you know what commutative property of addition is?

[alpine sable]

I just need help with this one so I can get the others

I can't find ANYTHING about it online

Not really

I was really lost in class today

[wary stream]

Are you sure about that?

[alpine sable]

Yeah

[wary stream]

Because all I looked up was "commutative property of addition" and got tons of results

[alpine sable]

Nothing that makes sense to me

[wary stream]

Literally this

[alpine sable]

my brain hurts looking at that

what is that supposed to mean

[wary stream]

Literally switch the position

What's confusing about that?

[alpine sable]

so like 3y + 2x?

[alpine sable]

o

So 2x + (3y + 4z)

would be like (4z+3y) + 2x

[wary stream]

Yes

[alpine sable]

Ahh okay thanks

I think I got it now

.close

[lone heart]

Channel closed

Closed by @grand oar

Use .reopen if this was a mistake.

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.

[placid zinc]

(v²)(v⁶) = v⁸

Not v¹²

[thin urchin]

oh duh

thanks

nvm i got it

.close

[lone heart]

Channel closed

Closed by @thin urchin

Use .reopen if this was a mistake.

[lone heart]

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.

Channel closed

Closed due to the original message being deleted

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.

Channel closed

Closed due to the original message being deleted

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.

[alpine sable]

this is probably kind of trivial butwhatever

[alpine sable]

how do i prove that a group is isomorphic to itself?

i think ive got the general idea down but idrk how to start the proof

[worn fox]

Well what map are you going to use for the isomorphism?

[alpine sable]

wait how would i pick one in this case?

[worn fox]

What's the obvious map from a group to itself?

The most simple map

[alpine sable]

one that assigns each element to itself?

[worn fox]

Yes, the identity map

[alpine sable]

oh right

[worn fox]

Convince yourself the identity map is bijective and a group homomorphism and you're done

[alpine sable]

oh it was this simple

thanks lol

.close

[lone heart]

Channel closed

Closed by @fierce oracle

Use .reopen if this was a mistake.

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.

[hard raptor]

does anyone know how to do this?

[wary stream]

Find the coordinates of vertices, add 4 to the x, and -3 to the y

Let's do point A, what are the coordinates of point A?

[hard raptor]

(2,0)

[wary stream]

So x + 4, means add 4 to the x coordinate

[hard raptor]

So 4 to the right?

[wary stream]

And y - 3 means subtract 3 from the y coordinate

[hard raptor]

(2,-3)

[wary stream]

Not quite

[wary stream]

These are the coordinates, so what's x coordinate plus 4?

[hard raptor]

6

[wary stream]

And y coordinate minus 3?

[hard raptor]

0-3=-3

[wary stream]

So what are the new coordinates?

[hard raptor]

(6,-3)

[wary stream]

Yes

[hard raptor]

ok

[wary stream]

Apply that same logic to the other three points

[hard raptor]

Then for B

It’s the same thing

[wary stream]

What do you mean by same thing?

[hard raptor]

Add 4 to the X

And -3 to the y

[wary stream]

Yes

[hard raptor]

ok thank you

so that means

B is (2,-1)?

and then C is (-3,-2)

And then D is (7,-3)?

[wary stream]

Not quite

[wary stream]

Not quite

[hard raptor]

What’s B then?

[hard raptor]

And then D

[wary stream]

Wait, hang on

[hard raptor]

Ok thank you

[wary stream]

What shape is the original, the blue one or green one?

[hard raptor]

The blue one

[wary stream]

What's the coordinates of B?

[lone heart]

@hard raptor Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

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.

[past bloom]

anyone know how to draw beat graph?

[past bloom]

this is not in my syllabus but i wish to learn bout it

is there any formula or i must add the amplitude of every point manually

[vernal holly]

Have you heard of a "sine wave?"

I mean, I'm sure you have; that's what the equations are at the bottom of that image

@past bloom

[past bloom]

yes ofc

[past bloom]

my question is how to i combine the sine and cosine wave to form beats

[vernal holly]

"beats?" Like heart beats? Like the last example?

You could add, multiply, divide, subtract, really anything. Try it out and see

[past bloom]

beats graph on (c)

[vernal holly]

They have multiplication

All you really need to know is how the inside of the sin/cos affects it,

Start moving it around

[past bloom]

.close

[lone heart]

Channel closed

Closed by @past bloom

Use .reopen if this was a mistake.

[lone heart]

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.

[pliant mortar]

can someone ehell

help

idk what to do

[alpine sable]

Fractions?

[pliant mortar]

i have no idea

it’s

grade 10 math

[alpine sable]

can you show the whole problem?

[pliant mortar]

it’s

[pliant mortar]

and ended up with 15

[alpine sable]

,rotate

[ocean seal]

Couldn't find an attached image in the last 10 messages.

Aug 25, 2022, 4:10 AM

[alpine sable]

I think you need to add them together

[pliant mortar]

wdym

like

😅😅i wasn’t here when we learned it

[alpine sable]

you probably know fractions right?

[alpine sable]

add the numbers

[wary stream]

You need to post the entire question

[wary stream]

Then maybe you should learn it?

[pliant mortar]

yeah??

Molly gave 5 of her jolly ranchers to Kevin. She then sold 1/3 of those left and ended up with 15

[alpine sable]

you cannot solve the question if you don't know how to add fractions

[pliant mortar]

it’s not my hw

[alpine sable]

what?

[pliant mortar]

it’s my older sisters

but i’m helping her

[alpine sable]

oh

so the hw is for Grade 10?

[pliant mortar]

yes

[alpine sable]

ask your sisters if they know how to add fractions

[pliant mortar]

she is walking our pup

that’s why she wanted me to help

[alpine sable]

oh

then ask her later

[pliant mortar]

do you know what i put for the thing for now then

[alpine sable]

can you elaborate that question?

[lone heart]

@pliant mortar Has your question been resolved?

[lone heart]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[lone heart]

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.

[paper terrace]

is there a reason to not simplify the 10 and the 4 to a 5 and a 2?

[paper terrace]

the answer is a derivative btw idk if that matters

[chrome plank]

Sure simplify it

[paper terrace]

ok

that's the answer in the answer key

idky it isnt simplified then cuz the answer to the next problem is simplified

is there ever a reason to not simplify

[chrome plank]

Eh they probably forgor, but it's the same thing and it can be simplified

Notice that everything is factored both in the nominator and in the denominator

[paper terrace]

yeah i just wasnt sure if it was fucky cuz it's a derivative

thx you

.close

[lone heart]

Channel closed

Closed by @paper terrace

Use .reopen if this was a mistake.

[chrome plank]

Derivative or not, it makes no difference

[lone heart]

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.

[fluid schooner]

i need help

[fluid schooner]

If Jillian jogs 2.6 miles at 6mi/hr, how long does it take her?

The equation is time = distance / speed

[gilded citrus]

what do you need help with

[fluid schooner]

@gilded citrus

[gilded citrus]

distance and speed are given

plug the values into the formula

[fluid schooner]

yeah so

2.6 miles / 6mi/hr

[gilded citrus]

yes

[fluid schooner]

which is

0.43?

but how is rhat the answer

like what is the units

[gilded citrus]

miles / (miles/hour) -> hour

0.43 hours

could convert that to minutes if you like

[fluid schooner]

OHHHHHH

what’s 0.43 hours converted😭😭

to minutes

[gilded citrus]

1 hour is 60 minutes

0.43 hours is

,calc 0.43 * 60

[ocean seal]

Result:

25.8

[gilded citrus]

that

[fluid schooner]

OHHHHHH

OMG

I FET IT

.close

[lone heart]

Channel closed

Closed by @fluid schooner

Use .reopen if this was a mistake.

[lone heart]

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.

[rancid widget]

what am I doing wrong here? the answer is supposed to be x>=10/8, however I'm getting -10/8...I understand that if I add 3 to both sides at the beginning this would result in 10/8, but what am I doing wrong here when it should be viable to subtract 2 and 5 from both sides?

[gilded citrus]

-8x <= -10
10 <= 8x
10/8 <= x

[ornate condor]

adding and subtracting will not change the inequality, multiplying by a positive number will not as well, only when u multiply by a negative number

[rancid widget]

oh fuck, divide both sides by -8, I was making it 8 as if it was add/subtract

[rancid widget]

is the -8x<=-10 to 10<=8x required?

what if you do
-8x<=-10
x>=-10/-8
wouldn't that be valid?

[gilded citrus]

same thing

[rancid widget]

x>=-10/-8 is the same as 10/8 <= x?

[golden falcon]

no

oh, nope

it is

just cancel out the minus in numerator and denominator

[rancid widget]

ahh that makes sense, thanks 🙂

.close

[lone heart]

Channel closed

Closed by @rancid widget

Use .reopen if this was a mistake.

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.

[hard veldt]

I am not really understanding what I'm doing wrong

First I convert the given equation to slop intercept form and I got y = 7/5x - 7

Then I tried to use y- y1 = m( x - x1) and I got that

[hard veldt]

Like I put everything in and got

Y + 1 = 7/5(x - 5/12)
Then
Y + 1 = 7/5x - 7/5 times 5/12

Wait it's definitely the fraction I messed up on I think

The 5s would cancel out the. 7 times 12

Which is 84

Then i subtracted 1

Would It be 84 over 12

[solemn juniper]

Not 7 times 12

7 divided by 12

[hard veldt]

Hm

Oooo wait yea that makes sense idk why I'm cross multiplying both

Would y = 7/5x - -5/12

Look right

[solemn juniper]

You have two - on the right hand side

[hard veldt]

I can't really write fractions

It's negative 5 over 12

Would I just make the entire thing positive

[solemn juniper]

Does it make sense to make it positive?

[hard veldt]

Or no cause it's only 1 side of the fraction

No not really

[solemn juniper]

Look again at what you have after the first distribution

y+1 = 7/5x - 7/12

[hard veldt]

Yea

Then I subtracted 1

[solemn juniper]

Now be a little more careful with your signs

[hard veldt]

And made it negative 5 over 12

[solemn juniper]

-7/12 - 1 = ?

[hard veldt]

I am being so slow

It's going over my head my god

[solemn juniper]

Do you see the issue?

[hard veldt]

I think so

So it would be 19 over 12

[solemn juniper]

Negative, yes

[hard veldt]

Ohhh alr so yea I just can't multiply or add or subtract 🗿

Thank you

[solemn juniper]

[hard veldt]

.close

[lone heart]

Channel closed

Closed by @hard veldt

Use .reopen if this was a mistake.

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.

[fiery quest]

Can someone give me pointers on how to approach this question

And just like tips in general on how to come up with sequences that satisfy certain properties

i dont know where to start

Except maybe them telling us that f is bounded means that you should use bolzano weierstrass somewhere lol

[ornate condor]

as c is a cluster point of S, then there exists as sequence of {xn} that converges to c as the for every delta>0 u choose, u can find a N such that n>N implies that xn lies in the deleted neighbourhood of c

[fiery quest]

does this work?

also the img needs to be opened cus i took it on my phone so its large i think

[ornate condor]

wait sry mines a bit off, it should be for subsequence

[fiery quest]

Ok i just realuijused me saying that was so dodgy

XD

let me compress the image

[ornate condor]

lol..

there

[fiery quest]

ok ty

[alpine sable]

firstly i think we can take the case c = 0 and f(c) = 0, then i think what you can do is throw away all the negative values of f(x), this might mean that there are no values of f(x) up close, in which case throw away all the positive values of x and take negative only. so WLOG i'll take only positive values

now since we need to use the bounded part I'll take some finite ball around x = 0 in the input neighbourhood, say with radius = 1

wait i dont think this works nvm

[ornate condor]

@fiery quest first, when u said the neighbourhood of c is non-empty, i think u should say every neighbourhood of radius r>0 is non-empty

[fiery quest]

o yep i was just being a bit lazy there

[alpine sable]

now we can define the sequence $y_n := \lim_{n \to \infty} {\sup{f(x_n)}$

[ocean seal]

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

[alpine sable]

which will always exist as it is a monotonically decreasing function, and sup always exists because $f(x_n)$ is bounded for $|x_n| < 1$ in some radius ball

[ocean seal]

jet printer

[alpine sable]

wait no i got confused

[ornate condor]

wait sry, @fiery quest u shown that {f(xn)} has a convergent subsequence, but didnt show that it always converges

[fiery quest]

oh the question was to show the existence of a sequence so that its limit is c and f(sequence) also converges

So the sequence i found that satisfies that is a_nk

[alpine sable]

i meant $y_n = \sup{f(x_m) | m > n}$

[ocean seal]

jet printer

[alpine sable]

so now y_n is monotonically decreasing and sup exists because its bounded etc.

[ornate condor]

oh yea mb, yea i guess u finished it

[alpine sable]

normally sup needn't actually be achieved, i.e sup isnt max, but if any y_n is not a function value, i.e some f(x_j), then that would mean there would be a sequence of function values converging to the sup value

in the other case y_n exists and converges to some value (due to its monotonic decreasing in bounded) and is a function value at every point, so we also have a sequence of function values

[alpine sable]

doesnt bolzano also require the set of function values to be closed as well as bounded?

sorry i meant @fiery quest

[fiery quest]

this is our definition

[alpine sable]

guess i dont remember it very well

[fiery quest]

i think ur thinking of sequential compactness

that needs closed and bounded

[alpine sable]

yeah i remembered that

[fiery quest]

and its an equivalent theorem

[alpine sable]

i know that, i was saying that i couldnt remember that this was an alternative way of saying it