help-0

[shrewd ruin]

can i just divide each number by 3?

and would taht be the answer?

[trim sorrel]

Yea

[shrewd ruin]

ok

thanks for everything

.close

[lone heart]

Channel closed

Closed by @shrewd ruin

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 show that x + 1/x >= 2, for all positive real x?

[alpine sable]

What is your math level/experience?

i got it

ok

[alpine sable]

umm im in highschool

do you know how to differentiate?

no why?

it would make a nice proof. but it seems you got it

[slender gull]

You can use AM/GM inequality.

[alpine sable]

i havent learnt that yet

i just saw this and was curious

[mortal trellis]

you can just do it by rearranging (which is how am/gm is proved)

[slender gull]

For 2 numbers, atleast.

[alpine sable]

so, you are saying (x + 1/x)/2 > 1

so, (x + 1/x) > 2

by am gm

[slender gull]

=

[alpine sable]

oh yes mb

i realised what i did earlier was not rigorous

I might try to split it into two proofs when 0<= x <=1, and x >1

[slender gull]

Unnecessary.

When 0< x < 1 then 1/x is > 1 and vice versa.

[trim sorrel]

Yeah there's symmetry there i believe

But it could be nice to do it anyway

If it makes it clearer

[mortal trellis]

it doesnt tho

it just makes two cases out of nothing

[trim sorrel]

Sometimes it's nice to see that yourself if it's not obvious from the outset

[alpine sable]

(x^2+1)/x >= 2
is equivalent to saying that (x^2+1) >= 2x (since x is positive real)
which is (x^2 - 2x + 1) >= 0 which holds true for all positive real x

[mortal trellis]

but why is that true

you need one more step

[alpine sable]

(x-1)^2

[mortal trellis]

yes

and thats it

[alpine sable]

is that a valid proof?

[slender gull]

It is.

[mortal trellis]

well assuming you can use that squares are >= 0

[alpine sable]

can you elaborate on that one a little more?

[mortal trellis]

which you hopefully can

[alpine sable]

I just saw the symmetry

[trim sorrel]

When 0 <= x <= 1, 1/x >= 1. Set y = 1/x, so 1/y = x, and you have a symmetric problem

[alpine sable]

i understand this point. but i cant seem to string together an argument from this

[trim sorrel]

x + 1/x = 1/y + y

[alpine sable]

x >= 2 - 1/x. As x gets larger, the 1/x gets smaller. So you have large numbers being greater than 2

[trim sorrel]

Same problem with a new variable

[alpine sable]

then for 0<=x<1. 1/x = 2 - x. If x gets closer to zero, you also have large numbers being greater than 2

[trim sorrel]

Needs to be rigorized but yeah

[alpine sable]

yeah

[trim sorrel]

Essentially

[alpine sable]

just intution

[trim sorrel]

Right

[alpine sable]

i'm sorry but i am unable to see how that helps

[trim sorrel]

Let's say you have proved that x + 1/x >= 2 when x >= 1.

And you wanna prove it for 0 <= x < 1

Set y = 1/x; therefore y > 1

Then x + 1/x = 1/y + y

You have already proved that y + 1/y >= 2 when y > 1

So you're done

[alpine sable]

how is it, how can i be sure that 1/x >= 2-x?

[trim sorrel]

Just assume you've proven it for x > 1

All we're doing rn is showing symmetry

[alpine sable]

wait give me some time to digest that

[trim sorrel]

Sure

What r u struggling with?

[trim sorrel]

Up here we proved that x + 1/x >= 2 when x > 1

[mortal trellis]

we didnt

we proved the general case

[trim sorrel]

For all x?

Oh

I didnt read too carefully my b

[mortal trellis]

you split it into cases for nothing and are now just confusing everyone

[alpine sable]

trying to get into the mindset that came up with this approach

[trim sorrel]

I mean im just tryna help them figure out why the cases are the same

[alpine sable]

i'm trying to understand this approach because splitting it into cases was my first thought but i just couldnt get through with it

[trim sorrel]

Right

I was just trying to help them figure out why some of the casework would be redundant

No need for rudeness😭

[alpine sable]

reduntant how?

[trim sorrel]

Ok let's say you were halfway through doing the casework, and you've already proven that x + 1/x >= 2 for x >= 1

[trim sorrel]

This argument will tell you why you have essentially already proven it when 0 <= x < 1

[alpine sable]

ahh

i think i understand what you were saying now

[trim sorrel]

Nice

[alpine sable]

and if i have (x+ 1/x) <= -2 for all neg real x is equivalent of saying
(y + 1/y) >= 2 for all y such that y= -x.
(y+ 1/y)>= 2 for all positive real y

and we know that thats true

right?

[trim sorrel]

Yea looks good

[alpine sable]

alright one more question

when i define the set Q, Q= {p/q : p,q is an element of Z, q neq 0 and p,q are coprime}

is the " p,q are coprime" part redundant?

[mortal trellis]

its unnecessary cause the set would be the same without it

[trim sorrel]

Yea ^ no duplicate elements in sets

But its easier to work with simplified fractions so i think ppl just include it cause its nicer

[alpine sable]

okay thank you so so much Denascite, Wakebloom and RankCheese

np

y'all are the best:))

.close

[lone heart]

Channel closed

Closed by @vivid walrus

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.

[junior warren]

in 4, it states OQ as OM + MQ,

would i also be able to say MQ=OM+OQ?

[trim sorrel]

No, MQ = OQ - OM

[junior warren]

oh right

q-m

[trim sorrel]

Subtracting OM from both sides up there

[junior warren]

so just for instance

when i was doing this earlier

using mq=om+oq was wrong

[limpid spade]

lp

[trim sorrel]

What is the problem

[lone heart]

@junior warren Has your question been resolved?

[junior warren]

it is just to find point Q

which is the same process as this i believe

[trim sorrel]

Yeah but you didnt provide any information on what O, M, or whatever n is

I don't know what you mean

[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.

[fathom field]

for ii)

this is what I have up to now

[lone heart]

@fathom field Has your question been resolved?

[naive valley]

in the inner integral, wouldn't y go from x to 1, instead of 1-x to 1?

your region is after all 0 < x < y < 1

[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.

[winter seal]

beepboop

[winter seal]

I've been stuck on this stupid HOMEQORK QUESTION

For HOURS

I have to integrate this by using by part integration

And I can't figure out wtf my u is

I think its 2x

and that my dv is sinxcosx

but I'm literally just

[plain flame]

you probably know the antiderivative for 2x

but not really for sinxcosx

so you should pick dv as 2x

[winter seal]

but why

because it's not next to the dx

so I figured that

[trim sorrel]

Why does it have to be?

[plain flame]

or alternatively

recognise a trig identity

sin(x)cos(x) = ...

[trim sorrel]

^

[winter seal]

okay let me try rto redo

[trim sorrel]

2sin(x)cos(x) = something simpler

[winter seal]

so

all I'd have to do

is just

integrate

sinxcosx

I could use the produc tri oh wait

that would work if we were taking the derivative

Oh wait we are

okay so I could use the product rule for this right?

[trim sorrel]

Are you doing integration by parts

[winter seal]

Yeah

So so far my u=sinxcosx

and my dv= 2x

[trim sorrel]

Yea

[winter seal]

my v=x^2

[trim sorrel]

Product rule to get du

[winter seal]

Right

okay perfect lemme do that out rlly quick

[trim sorrel]

Yea

Dont just assume dv is the thing next to the dx

You can interchange things

[winter seal]

okay I didn't do that

I always look for patterns in math

especially when I'm doing multiple problems

with the same concept

[trim sorrel]

Thats a good practice but dont rely entirely on one pattern

Especially if that pattern is predicated on some other person writing the problems

They can be out to trick u

[winter seal]

oooo okayokay

Ill redo and try to be unstuck

[trim sorrel]

It should work with that u and dv

[winter seal]

Okay so

I used the product rule and got

cos^2x-sin^2x

and I checked to see if it was right and it's not

like am I missing an identity

the only thing that comes to mind are the pythagorean identities

[trim sorrel]

derivative of sin x cos x?

Looks right

[plain flame]

sin(x) cos(x) = 1/2 sin(2x)

[trim sorrel]

You just have to do integration by part now

Yeah

The integration by parts would work as well

[winter seal]

but I double checked and it's not

[trim sorrel]

What

The derivative of sin x cos x?

[winter seal]

cos^2x-sin^2x

eyah

it's cos2x

I'm confused as to how tf they got that

[trim sorrel]

They’re equal

[winter seal]

okay but how did they simplify it to that

[plain flame]

,w sin(x) cos(x) = 1/2 sin(2x)

[ocean seal]

Results provided by WolframAlpha

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

Requested by heavy0201#0

[winter seal]

Am I allowed to post stuff like

[trim sorrel]

Double angle identities

[winter seal]

from symvolab

symbolab?

[trim sorrel]

Probably idk

[winter seal]

OHHHHHHHHHHHHHHHHHHHHHHHHHH

[trim sorrel]

Don’t worry about it

They’re equal

[winter seal]

I SEE IT

Okayokay

so either way it doesn't matter?

I'll just stick to what I got then

[trim sorrel]

Proceed with integration by parts or heavy’s method

[winter seal]

I do integration by parts!

Okay lemme continue

Can I do usubstitution??

[trim sorrel]

What do u have rn

[winter seal]

I want to use u=x^2

[trim sorrel]

It might be best to use heavy’s method

[winter seal]

ignore that u substitution

no but for this section I HAVE to use integration by parts to solve it

oh wait

do u mean the double angle identity???

[trim sorrel]

Maybe yeah

[winter seal]

ohhh okay let me try that

Math is so upsetting sometimes

especially trig

[trim sorrel]

Idk i’m a bit distracted but that will probably work

[winter seal]

I feel like there are so many ways to get to so many places

im even more lost nos

[trim sorrel]

Try using this at the very beginning

Skip the first integration by parts step

[winter seal]

hmm okay

[lone heart]

@winter seal Has your question been resolved?

Channel closed

Closed by @winter seal

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 need help wish 2.91+42.81

[lone heart]

Show your work, and if possible, explain where you are stuck.

[alpine sable]

I cant show my work

[heady pollen]

what did you try?

[alpine sable]

I first wrote the 2.91 and 42.81 up and down and did it from there

so .91 + .81= 1.72

and 2 + 42 + 1.72= 43.72?

I mean 45.72

[heady pollen]

👍

[alpine sable]

YES

my next problem is 89.56 + pi

first three digits of pi is 3.14

so 89.56 + 3.14 is 92.70?

[heady pollen]

yes, but note that 89.56 + pi = 92.70 is not true

we are approximating here

$\approx$

[ocean seal]

martin3125

[alpine sable]

ok

[lone heart]

@alpine sable 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.

[slim quiver]

all of you remember what this was? I don't remember what the ']' and the '<' meant

[alpine sable]

Looks like an interval with weird notation

If I say "open and closed intervals", does that ring any bells?

Also it would probably help if you gave more context

[slim quiver]

yeysyeysysy

yes

[alpine sable]

Welp there you go

[slim quiver]

It is in espanish but basically it says to point out the variation of:

[alpine sable]

No hablo español pero those are probably intervals indeed

@slim quiver You can .close this channel now

[ancient saddle]

Look at the range of values of sine over the second quadrant, write that as an inequality. Then operate in such a way that you get the expression L

[slim quiver]

.close

[lone heart]

Channel closed

Closed by @slim quiver

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.

[lean grail]

hello can anybody help with a math homework in dm call

[lean grail]

add me

[shy dove]

you'd get more help if you asked your question here directly

[lean grail]

oh

its mutiple questions tho

[proven leaf]

[lean grail]

ok

.close

[lone heart]

Channel closed

Closed by @lean grail

Use .reopen if this was a mistake.

[lean grail]

i come back later

[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.

[misty pumice]

can someone exlpain this to me

im trying to teach someone but i dont get it myself

something I dont know here?

[gray isle]

ideally get them here instead of playing telephone
but for A, set the expressions equal to each other then solve the equation
B is cursed with those boxes and should be skipped

[gray isle]

ideally get them here instead of playing telephone

[misty pumice]

what?

[gray isle]

if you intend to help someone, then get them on here as well if possible so there's no miscommunication

[misty pumice]

well its a kid...

[gray isle]

oh. ok then

for a) sub in the numerical value of n to get the nth term

for b) set the pattern equal to the desired value then solve for n

[misty pumice]

thanks mate...

[lone heart]

@misty pumice Has your question been resolved?

Channel closed

Closed by @misty pumice

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.

[barren mirage]

Hi!

[barren mirage]

The question was asked to be answered in interval notation

I can send my work but the answer I got was (-∞, 27/2]

[median oar]

Send your work

[rocky grove]

@barren mirage

[barren mirage]

did it go through?

[alpine sable]

looks like it contains all values

[rocky grove]

Hmm

[gray isle]

seems alright, what was your issue with it

[barren mirage]

I got marked as wrong because it said the bracket after 27/2, shoulve been a ().

also i took the bracket from my notes and im a little confused to what it means

i didn't entirely understand it

[gray isle]

well you were right

whoever said that is wtong

argue for your marks back

[barren mirage]

oh lol 😭

[gray isle]

square bracket for inclusion
parentheses for exclusion

the first inequality uses the
... or equal to sign
logically from your work 27/2 is included

[barren mirage]

the equal to on an inequality affects it then right?

so it should be brackets

[gray isle]

yes

[barren mirage]

ok thank you !

[gray isle]

substituting in 27/2,
6 is indeed less than or equal to 6

[barren mirage]

.close

[lone heart]

Channel closed

Closed by @barren mirage

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.

[celest hinge]

i have a science question that i need help with, what steps do i need to do

[celest hinge]

im pretty sure im combining them but not 100% sure

nvm im supposed to figure out the total amount of atoms

[lone heart]

@celest hinge Has your question been resolved?

[celest hinge]

<@&286206848099549185>

[rocky grove]

Total amount of atoms

Hmm

Wasn't it something multiplied by Avogadro's number?

Number of element particles * avogadro's number iirc

[celest hinge]

dont recall using avagardros number

[rocky grove]

Hmm

[trim sorrel]

Idts, that's when youre dealing with grams i believe?

I think its simpler than that

Well first of all idk if this is the right server

But Al (NO_3)_3 means you have one Al, and 3 NO_3

[rocky grove]

Oh yeah I remember now

[celest hinge]

i think i might need to like even them out

[rocky grove]

Molar mass

[celest hinge]

make ai 3 as well

alr well thanks anyway

.close

[lone heart]

Channel closed

Closed by @celest hinge

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.

[karmic coyote]

oh

oops

[next osprey]

hey bud

lol

[karmic coyote]

sorry

[next osprey]

youre good

[karmic coyote]

lol

[proven leaf]

that was just unlucky 😭

[next osprey]

help pls

[proven leaf]

can you show your work? :)

[next osprey]

i guessed lol

[karmic coyote]

😭

[proven leaf]

do you understand function notation? :)

[next osprey]

im assumed i just plug in f(x) into the bottom

[proven leaf]

ok so do you understand that if we have $f(x)=2x^2+4$, that $f(3)=2\cdot3^2+4=22$

[ocean seal]

XxMrFancyu2xX

[proven leaf]

f(x) is just y, but written differently

it does NOT imply multiplication

I've seen all too many people make that mistake

[next osprey]

yes

i know that

[proven leaf]

ok good good that's something

I've had to correct so many people on that

alright I digress

so we can plug variables in the same way we can numbers so $f(x+h)$ is just $2(x+h)^2+4$ :)

[ocean seal]

XxMrFancyu2xX

[next osprey]

the f is just gone?

and -f(x) too

[proven leaf]

the f is a function

[next osprey]

i though it woudlbe looked liked f((2x^2+4)+h) - f(2x^2+4)/h

oh ok

[proven leaf]

nope whatever we put in for x inside the function we put in the x in the definition

so $f(x+h)=2(x+h)^2+4$

[ocean seal]

XxMrFancyu2xX

[proven leaf]

those are the same thing

[next osprey]

what about that x^2 in the top?

would it not x^2 in the inside too?

[proven leaf]

you mean just the f(x)?

[next osprey]

wait i see it

ok what about the far right side

-f(x)

[proven leaf]

$f(x)=2x^2+4$

[ocean seal]

XxMrFancyu2xX

[proven leaf]

those are the same thing just substitute in :)

[next osprey]

si=o

so

2(x+h)^2 +4 -2x^2+4 / h

[proven leaf]

be careful actually the minus is getting wrapper around the entire second part

so we have $2(x+h)^2+4-2x^2-4$ rather than $2(x+h)^2+4-2x^2+4$

[ocean seal]

XxMrFancyu2xX

[proven leaf]

see the difference?

[next osprey]

yEA

[proven leaf]

you have a stroke? 😅 but now it's just algebra I skills :)

$\frac{2(x+h)^2+4-2x^2-4}{h}$

[ocean seal]

XxMrFancyu2xX

[next osprey]

yea lmao

im right there

do i distribute the 2

[proven leaf]

$(a+b)^2\neq a^2+b^2$

[ocean seal]

XxMrFancyu2xX

[next osprey]

i meant outside 2

left side

[proven leaf]

exponents first! :)

[next osprey]

hmm

so x+h *x+h

then foil

[trim sorrel]

Out of curiosity, which class is this for?

Precalc?

[trim sorrel]

Yeah

[next osprey]

preparing for a calc 1 placement exam

[trim sorrel]

Ah interesting

I like this question

[proven leaf]

ikr derivative, good introduction without the limit

[trim sorrel]

Right exactly

[next osprey]

i took a test expecting more calculus problems like derviatives

and integral

[trim sorrel]

Well

[next osprey]

nonething like that

[trim sorrel]

This is almost a calculus problem

[next osprey]

yea

test was lots of alegbra

[proven leaf]

gotta be good at algebra to be good at calc

hey @sour dove i see you sneaking 👀

(sorry for ping btw)

[next osprey]

im at 2(x^2+2xh+h^2)+4-2x^2-4

[sour dove]

I gotta make sure you're learnin' these lovely students right

[proven leaf]

learning? 😅

[sour dove]

yeah you know. For example "That'll learn em' to mess with me"

[next osprey]

...

[sour dove]

anywho, this looks good so far

[proven leaf]

he's a little confused but he's got the spirit? are you sure it's not teach 😅

[sour dove]

oh you're not from the south are you? In the southern US "learn" is used as "teach" sometimes with more rural communitites

[sour dove]

what's next after that?

[next osprey]

4 cancels out

[proven leaf]

ah! imma New Englander myself

not used to those southernisms

[next osprey]

then distribute

has h^2 on top

[sour dove]

stick with me kid, you'll be saying y'all frequently in no time

[sour dove]

good!

[next osprey]

theres a h at the bottom

so the h^2 turns into h

and bam

[proven leaf]

I already do 😭

[sour dove]

not quite. You need to pull out a factor of h at the top to be able to cancel

distribute out the 2, simplify, then you'll see 🙂

[next osprey]

i distributed so i did

2x^2+4xh+2h^2-2x^2/

over h

[proven leaf]

do you notice anything about those 2x^2's

[next osprey]

2xx^2 cancels out

so 4xh+2h^2/h

leads to 4x+2h

[proven leaf]

now we can divide out h :)

[next osprey]

final answer

bam

[proven leaf]

no point in guessing if you can do the algebra

[next osprey]

yup got it

thank you guys its always the first steps for me but then i get into it

.close

[lone heart]

Channel closed

Closed by @next osprey

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.

[next osprey]

i though it would be log based

[trim sorrel]

You can do it without logs

[next osprey]

hmm how

[trim sorrel]

If you know 2^x, what's 2^(-2x)?

[next osprey]

-6?

6

[trim sorrel]

Not quite

Remember exponent rules

a^(bc) = (a^b)^c

[next osprey]

they're being added

is it any different

[trim sorrel]

Hm

What

[next osprey]

lost

[trim sorrel]

2^(-2x) = 2^(-2 * x)

And you know 2^x

[next osprey]

so

(2^x)^-2

?

[trim sorrel]

Yup

Now what's that

[next osprey]

1/9

[trim sorrel]

Yess

[next osprey]

bc neg exponsent

[trim sorrel]

Ok now you have 2^(-2x), so whats 2^(-2x + 6)

Using exp rules

[next osprey]

1/9)^6

?

[trim sorrel]

Not quite

a^(b+c) = a^b * a^c

[next osprey]

3^-2 * 3^6?

1/9 not 3

[trim sorrel]

Huh

[next osprey]

...

[trim sorrel]

I dont think so

[next osprey]

don't know

[trim sorrel]

Umm

[next osprey]

lost me there

[trim sorrel]

2^(-2x + 6) = 2^(-2x) * 2^6

Right?

[trim sorrel]

Using this

[next osprey]

hmmm i see it

ok

[trim sorrel]

I think you can take it from here

[next osprey]

so 1/9 *64?

[trim sorrel]

[next osprey]

ok got it

.close

[lone heart]

Channel closed

Closed by @next osprey

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.

[static minnow]

.close

[lone heart]

Channel closed

Closed by @static minnow

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.

[next osprey]

no idea even on how to start

hi again lol

[gray isle]

consider the permissible values of each term/component

if you were asked for the domain of
$$\sqrt{x+7}$$
would you be able to do it?

[ocean seal]

ℝamonov

[next osprey]

no

[gray isle]

do you know what domain is?

[next osprey]

like the max x value on a graph?

[gray isle]

no

[next osprey]

hmm

i know its x value in graphs

[gray isle]

i'd recommend looking up the definition first for a clearer idea

[next osprey]

ohhh i remember from my calc class now

theres 3 rules

no 0 in a denom

no neg in sqr root

and i think neg in a log

it what helps make the graph

all the x values that can make a y

so hypothically if it was 1 and it keeps working it could pos infinity i think

[gray isle]

so hypothically if it was 1 and it keeps working it could pos infinity i think
wdym by "it"

[next osprey]

like we keep getting positvie outputs

[gray isle]

first, second and third

[next osprey]

if we plugged in 1 and get an output then 1 can be a domain

but 1 would not equal positive infinity i jusr realized

[gray isle]

if we plugged in 1 and get an output then 1 can be a domain
1 would be in the domain

[next osprey]

yes

[gray isle]

looking back at
$$\sqrt{\red{x+7}}$$
what are the set of values where the $\red{x+7}$ isn't negative

[ocean seal]

ℝamonov

[next osprey]

all the way to -7

[gray isle]

from which direction

[next osprey]

left

[gray isle]

no

you're inlcuding stuff like -8
are you saying that -8 + 7 = -1 isn't negative?

[next osprey]

wdym by which direction

-7+7 =0

thats the max

ohh i miread

so from -7 to the right

[gray isle]

yes, you want $x + 7 \geq 0$ leading to $x \geq -7$

[ocean seal]

ℝamonov

[gray isle]

similarly, what would be the domain for
$$\sqrt{8-x}$$

[ocean seal]

ℝamonov

[next osprey]

8 and left

[gray isle]

yes,
$$8-x \geq0 \implies x\leq 8$$

[ocean seal]

ℝamonov

[next osprey]

how would i know im looking at the domain of each one

[gray isle]

well for the domain of f(x), you'd need the values of x that satisfy both those conditions

[next osprey]

oh ok

[gray isle]

as violating either one would result in having a negative under one of the roots

[next osprey]

so from -7 to 8

got it

do you know how to read graphs its my final questin

.close

[lone heart]

Channel closed

Closed by @next osprey

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.

[light ether]

Is this what proj is for? I'm trying to figure out how to get the movement along the plane caused by the red vector

[vale wigeon]

yes, green is the projection of red onto the plane

[light ether]

I don't have the plane, unfortunately

Only its normal

[vale wigeon]

almost same difference.

when projecting one vector onto another, you decompose the projected vector into two components: one parallel to the projected-onto vector, and the other perpendicular to the projected-onto vector

[light ether]

So I'd rather subtract the projection from the vector I have if I can

[vale wigeon]

it's the second one you want in this case

[light ether]

yup okay so that works

Wait oh I can just get the other one?

I'd have to subtract the projected vector from the original, right?

[tardy stag]

that'll work yeah

[vale wigeon]

yes

[light ether]

Is there a way to get it straight from the projection or is that the only way to do it

Like, is there some inverse of proj that gives me that other component instead

if I dot them in the opposite order?

ah whatever I'll figure it out

.close

[lone heart]

Channel closed

Closed by @light ether

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.

[still wadi]

Can anyone confirm is the answer is C or not

[tacit arch]

Just use a calculator

[crimson carbon]

Ye

But itll be faster to use some online calc like mathway, symbolab, wolfram, etc.

[proud shoal]

Yes it is C because collect the like terms and add/subtract in this case 5x + 2x = 7x

[lone heart]

@still wadi Has your question been resolved?

Channel closed

Closed by @still wadi

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.

[crimson totem]

Need help with all of these questions

[raw jetty]

are these olympiad questions?

[crimson totem]

JEE Mains

according to fiitjee

I dont know myself

[raw jetty]

ok, just wanted to know (i cant help you cause im dumb)

[crimson totem]

man thats a massive skill issue

[raw jetty]

exactly

[lone heart]

@crimson totem 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.

[foggy knot]

could anyone explain why they just put this around parenthesis instead of just ln(2) + ln(-x)

cuz wouldnt you have to multiply everything by ln?

[lament forge]

we're not "multiplying by ln"

ln isn't a number, it's a function

[foggy knot]

whoops

I mean cancelling e

[lament forge]

...cancelling e where?

[foggy knot]

by bringing down the natural log

[lament forge]

...i'm not sure what you're talking about
what would be the result of the step you're talking about...?

[foggy knot]

so when I see that

I think

put everything to ln

and should get

-y = -ln(x) + ln(2)

[lament forge]

you can't apply ln to "everything"

you would apply it to both sides of the equation

so ln(e^-y) = ln(-e^x + 2)

[foggy knot]

is it the sane as the thing with e where you have to put everything to the power of e on each side

[lament forge]

i don't know what you mean by that

[foggy knot]

so

if I had

ln|x| + 2 = ln|y| + 3

I wouldnt do

e^lnx + e^2 = e^lny +ln3

I would do

e^(lnx+2) = e^(lny+3)

[lament forge]

yes
...that's always how it works

the only reason it would be valid to apply an operation to random parts of one side of the equation instead of the whole thing is if applying it to parts of that side is the same as applying it to the whole thing

so if a+b = c, that implies 2(a+b) = 2c, and 2(a+b) = 2a+2b, so you get 2a+2b = 2c

[foggy knot]

I see ok

thanks for the help

.close

[lone heart]

Channel closed

Closed by @foggy knot

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.

[cinder sundial]

So C is real number and a derivative of a number would be 0

[vale wigeon]

the derivative of a constant function is 0, yes.

[cinder sundial]

In this case, k is also a number

That mean g’(x) should be just 0

[gray isle]

no

[cinder sundial]

Since k after being derivative is 0

[vale wigeon]

the derivative of a product ≠ the product of the derivatives

[gray isle]

derivitive of a product isn't the same as the product of the derivatives

[proud shoal]

The derivative alters the value of f(x) so its not equivalent (incorrect)

[cinder sundial]

I’m trying to digest the context

[gray isle]

are you famiiar with the product rule?

(for derivatives)

[cinder sundial]

I’m actually learning about it

And that’s why I’m asking the question

It got me confused

[gray isle]

the constant multiple rule you have above is a special case of the product rule

[wanton valley]

Well think of it in terms of the tangent line to the function g(x). The derivative is the slope of that tangent line. If you look at g(x) = x then the slope is always 1 if you multiply by lets say k. So f(x) s x and g(x) = kf(x) and you derive both the it cant be 0 because the slope is never 0 of the tangent line

[gray isle]

can you try applying the product rule here?

[wanton valley]

So there might be something you're missing

What you're missing is the product role

[cinder sundial]

That is the product of the derivatives

[wanton valley]

Thats a product of derivatives

[cinder sundial]

But what is the derivative of a product

[proud shoal]

Product of derivatives is not equal to the derivative of a product

[gray isle]

yes it is, which as implied, is NOT what you're supposed to do

[proud shoal]

Its two different things

[vale wigeon]

$[f(x) \cdot g(x)]' \neq f'(x) \cdot g'(x)$

[ocean seal]

Ann (glomed)

[cinder sundial]

How do I write it in paper

[wanton valley]

But the derivative of product of functions is different.

[cinder sundial]

Thank you

[gray isle]

are you famiiar with the product rule?
I’m actually learning about it
do you have notes on it
or have you tried looking it up

[cinder sundial]

Let me see

I’m overwhelmed by the torrent of formulas on my book

[foggy knot]

so just do (f')(g) + (g')(f)

[cinder sundial]

Is it a more simple way to comprehend it

[foggy knot]

then take the derivative of the outcome from the equation above

[gray isle]

might be easier to just search online, but there should be a clear section on product rule

[cinder sundial]

For sure

I think I should just complete the learning process of product rule

Then the question will be solved by itself

Those are too much for me right now

[tacit arch]

Just do problems

[foggy knot]

product rule is just a function times another different function

[proud shoal]

The derivation of the quotient rule is also a branch of the product rule so learn that too

[foggy knot]

or well

can it be the same?

im forgetting lol

[proud shoal]

But yeah as riemann said do problems to get a feel for the rules

[tacit arch]

Or find a derivation of the product rule using limit definition and ask questions about it

Being overwhelmed is solved by focusing one ONE thing at a time

[foggy knot]

I think a big thing is to make sure to see the difference between chain rule and product rule also

it can fuck with people

[gray isle]

its also a recommended exercise to obtain (deliberately not using derive due to potential confusion of people using derive to mean differentiate)
the product rule from first principles

[proud shoal]

Utilising a visual diagram could aid as well

[foggy knot]

im seeing the problem again it just dont look like u know what product rule is bruh

gl

[lone heart]

@cinder sundial Has your question been resolved?

Channel closed

Closed by @cinder sundial

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]

not sure how to do these questions

[vapid shuttle]

the x-intercepts are when the function crosses the x-axis

(if it does)

what is the y-value along the x-axis?

[alpine sable]

i know what it means but unsure how to find the x-intercept

[vapid shuttle]

^

[alpine sable]

y value is -4?

[vapid shuttle]

On the x-axis??

[alpine sable]

y-intercept or value?

[vapid shuttle]

what is the value of y, for all points on the x-axis

,w plot y=x

[ocean seal]

Results provided by WolframAlpha

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

Requested by austinu#0

[vapid shuttle]

see the x-axis?

[alpine sable]

yes

[vapid shuttle]

what y-value does it sit at

[alpine sable]

0

[vapid shuttle]

mhm

so any x-intercept

must have y=0

agree?

[alpine sable]

yeah

[vapid shuttle]

so take these

and set y=0

and then solve for the x-values that satisfy the equations that are formed

[alpine sable]

0=xsquared -6x +9 -4

divide by x? or square?

[vapid shuttle]

I wouldn't expand out

are you doing question (a)?

[alpine sable]

yes

[vapid shuttle]

$0=(x-3)^2-4$

[ocean seal]

austinu

[alpine sable]

2=x-3

[vapid shuttle]

add four to both sides

$4=(x-3)^2$

[alpine sable]

5=x

[ocean seal]

austinu

[vapid shuttle]

take the square root of both sides

[alpine sable]

hpwever when i checked the answer it said 1 was also an x intercept

[vapid shuttle]

$\sqrt{4}=|x-3|$

[alpine sable]

i knew one was 5

[ocean seal]

austinu

[vapid shuttle]

that is because you forgot the absolute value signs

$\sqrt{x^2}=|x|\neq x$

[ocean seal]

austinu

[alpine sable]

idk what that is

havent learnt that

[vapid shuttle]

then learn it

[alpine sable]

shouldnt need it for this question

[unique arrow]

when you square root a number it’s plus and minus of the root

[vapid shuttle]

you do

(that is the same thing as setting the absolute value to the other side)

[alpine sable]

i will just skip it then, idk why my teacher would give questions on something we havent learn

[proud shoal]

and you cannot have a negative number from a square root (excluding imaginary)

[vapid shuttle]

I'm sure you have learned it. It also is a very short topic

nothing really to learn

[alpine sable]

can you rxplain it a bit further

[vapid shuttle]

absolute value just makes something positive

so

|-5|

=5

|5|

[proud shoal]

absolute value is the distance from 0

[vapid shuttle]

=5

[proud shoal]

so -5 or 5, the distance is 5 either way

[vapid shuttle]

mhm

[alpine sable]

yeah my teacher tripping then

[unique arrow]

so when you square root the 4 you get +2 and -2

then you just solve from there

[vapid shuttle]

Let's come back to this and work through it together

[alpine sable]

oh plus minus you mean

thats makes more sense thanks

[proud shoal]

yeah but you never get a neg number

so it always has tobe positive

[crimson carbon]

Note that abs f(x) = pm sqrt f(x)^2

[alpine sable]

-2 squared is also 4

-2 + 3 =1, 2+3=5

thanks, very helpful

[vapid shuttle]

$4=(x-3)^2$ $\newline$ $\sqrt{4}=|x-3|$ $\newline$ $2=|x-3|$ $\newline$ The right hand side can equal 2, when the thing inside the absolute value is either 2, or -2, since it will just take the positive version of whatever is inside. So we get, $\newline$ $x-3=2$ and $\newline$ $x-3=-2$ and then you can solve

[ocean seal]

austinu

[alpine sable]

do i do it differently when there is a number infront of the x

for example, d)

[vapid shuttle]

set y=0

solve for x

nothing different

I'd divide the equation through by 2

after adding 10 to both sides

to make it easier

but, the method is the same

[proud shoal]

if you know null factor law, split into different factors

[alpine sable]

ah ok thhanks

[proud shoal]

and then solve each one for 0

[vapid shuttle]

you just need to figure out the process for each

[vapid shuttle]

I'd read through this @alpine sable to help your understanding. I tried to lay out the steps and logic behind it, so hopefully this helps ^

[alpine sable]

i understand it now, thank you though

[lone heart]

@alpine sable 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.

[austere compass]

"A liquid consists of a mixture of four liquids with different densities. When the mixture is left in a test tube, four layers form after some time. By measuring the heights h_i, i = 1, ..., 4 of the layers using a ruler, one can estimate the proportions of the respective liquids. However, due to measurement inaccuracies, these estimations are flawed. Suppose the heights h_1 = 4.3 cm, h_2 = 3.5 cm, h_3 = 1.4 cm, and h_4 = 0.7 cm are measured with an error margin of 0.1 cm each. Provide an estimation and an error margin for the proportion of the third liquid."

This is supposed to be solved using multidimensional analysis, but idk how I could do that... I mean my first thought of were just simple calculations like (h_3)/(h_1+h_2+h_3+h_4) (which was also suggested by a helper here) but that has nothing to do with my subject (analysis 2) sooo ya

[lone heart]

@austere compass Has your question been resolved?

[austere compass]

<@&286206848099549185>

[lone heart]

@austere compass 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.

[kind path]

Hello, why is x bound in this interval?

[rose sigil]

i don't get what the question is

[kind path]

precisely, why is Ix-x0I < R for series which converge on the interval of convergence?

[mortal trellis]

well it makes no sense to talk about other x

cause for other x it doesnt converge

[kind path]

please elaborate

[mortal trellis]

f(x) doesnt make sense if x is not in the interval of convergence

cause it doesnt converge

[kind path]

I think i understand, thanks

[lone heart]

@kind path 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.

[frosty leaf]

a bacteria duplicates every hour, after 4 hours how many bacteras there will be?

[frosty leaf]

can geometric serie formula be used here?

is 8 the correct answer or 16?

[hasty hill]

what is the initial number of bacteria?

[frosty leaf]

1

[hasty hill]

8

no wait

it will be 16

[frosty leaf]

so geometric series formula does not apply for these kind of questions?

[tiny cipher]

it's a geometric sequence here but you're not adding its terms

[sand pawn]

it's a sum of 2^x

where 'x' is the hour

'a' is 1 or initial number
'r' is 2, is the rate of multiplication
'n' is 5, is the iteration

[gray isle]

you only want the general expression for the nth term in a geo sequence here

[tiny cipher]

yes

there's no sum

[sand pawn]

$n-th term = ar^(n-1)$

[ocean seal]

overlordprincekhan

$n-th term = ar^(n-1)$

[frosty leaf]

that gives 15

[sand pawn]

yep

[tiny cipher]

but that's not what you're looking for here

you're just looking for powers of 2

[sand pawn]

the question states how many bacteria, not how many bacteria will be produced during 4th iteration

[tiny cipher]

what

initially there is one, when it duplicates you have a total of 2

then 4, 8 and 16

[sand pawn]

it should be 31

[tiny cipher]

okay but that still isn't correct

[sand pawn]

how?

[tiny cipher]

"a bacteria duplicates" means the total number gets doubled

there's no sum

[sand pawn]

read the question properly

just reading the first half won't help

[tiny cipher]

"after 4 hours how many bacterias there will be ?" means you're looking for a_4 where a_0 = 1 and a_{n+1} = 2 a_n

[sand pawn]

it asks for Σa_n

[tiny cipher]

how ?

[sand pawn]

how many means total amount, not the produce of 4th iteration

[tiny cipher]

a_n is the total amount though

[sand pawn]

wait wait, we all might be wrong

[lone heart]

@frosty leaf 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.

[opaque radish]

for a question like (3x-2)^7 how do u find the coefficient of x^4

[gray isle]

binomial theorem

[opaque radish]

do u let r = 3

[gray isle]

depending on what you're looking at, use whatever value that results in getting x^4

[opaque radish]

likw (7Cr) * (3)^7-r *(-2)^r

for coefficient

and let r = 3

[gray isle]

don't just focus on the coefficient component of the binom

look at the entire thing

and also don't use x for multiplication

[ornate ginkgo]

Arent you missing an x in 3

[opaque radish]

im just looking for coefficient

[gray isle]

don't just focus on the coefficient component of the binom
look at the entire thing

that'll tell you for certian whether the value you're using actually gives you what you want

[opaque radish]

i split the (3x)^7-r into (3)^7-r * (x)^7-r

[opaque radish]

wdym

[gray isle]

whiuch part of what i said don't you understand

[opaque radish]

by look at whole thing u mean coefficint and power

right

[gray isle]

yes

[opaque radish]

oh ye so when r = 3 7-3 means power of 4

[gray isle]

as you didn't seem sure whether you should be using r=3

[opaque radish]

i thought it was just power ur looking for minus 1

[gray isle]

yes, and if using r=3 gives you the term with x^4,
then that is indeed the r value you should use

[opaque radish]

alright thanks

cya

.close

[lone heart]

Channel closed

Closed by @opaque radish

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]

The opposite angular points of a square are (3, 4) and
(1, –1), the other two vertices are?

[median oar]

What have you tried

[alpine sable]

applied midpoint

found the center

i can proceed with distance formula

but its lenghty

need a shorter way for it

[slow sentinel]

I think this is the shortest way

[alpine sable]

nothing other ?

[slow sentinel]

What are your steps after finding the distance?

[alpine sable]

uh wait

4x+10y−23=0

x = (23 -10y)/4

after equating the distances

[slow sentinel]

Which equation is this?

[alpine sable]

let a point coordinates be x,y

then
3,4 to x,y = 1,-1 to x,y

[slow sentinel]

Ohh okok

How about

You find the slope of the line passing through (3,4) and (1,-1). That will be the slope of one of the diagonals

And since we need to find the vertices of a square, the other diagonal will be perpendicular to this one

[alpine sable]

5/2 of the diagonal

-2/5 of the other

[slow sentinel]

Yes correct

[alpine sable]

did it too

[slow sentinel]

Now you know the slope and it passes through the midpoint of (3,4)(1,-1)

[alpine sable]

yes

midpoint is 2,3/2

did it

[slow sentinel]

So you can calculate the equation of this diagonal

[alpine sable]

then?

[slow sentinel]

And you know the distance

[alpine sable]

mhm

[slow sentinel]

Between centre and a point

So you just calc the points on the line that are the same distance away

[alpine sable]

yeah

i did the same thing

but

[slow sentinel]

Thats the fastest way i know