help-0

[ocean seal]

Arya

[lethal galleon]

oh

i got it

[little drum]

so not all of a, b, c, d, e can be > 3

[lethal galleon]

how do we prove p^2 = 1 (mod 6)

(p-1)(p+1) divisible by 6

oh got it

[little drum]

any prime p > 3 is of the form 6k + {1, 5} => p² is 6k' + 1

[lethal galleon]

oh now i got it

tysm

so this problem doesn't have any sol?

[little drum]

Also, a, b, c, d, e ≥ 2 => f² ≥ 24 => f ≥ 5, and so f² = 1 (mod 6)

No it probably does. You just got a way to look at the problem differently

[lethal galleon]

oh ok

so if i coutinue with this and use mod 6

there is at least 1 prime which is <= 3

case 2: a or b or c or e is divisible by 3
without loss of generality, suppose a = 3
9 + b^2 + c^2 + d^3 + e^2 = f^2

[little drum]

=> LHS = 1 + 1 + 1 + d^3 + 1 = 4 + d^3 (mod 8)
RHS = 1 (mod 8) 
=> d^3 = 5 (mod 8) or d = 5(mod 8) and d is prime => d = {5, 13}(mod 24)```

[lethal galleon]

is this a new way

[little drum]

idts bash is good ._. I'll see if something clicks in a while

[lethal galleon]

alr ty for your help

[little drum]

uhh

I just checked and idts there's finite soln to this thing. Are you sure you weren't given additional restrictions?

[lethal galleon]

yes

[little drum]

!original

[lone heart]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[little drum]

Send a pic

[lethal galleon]

its different language but ok

"tìm sáu số nguyên tố" its vietnamese and it means "find prime numbers"

"thỏa mãn" means "satisfy"

i replacd p1, p2, p3, p4, p5, p6 with a, b, c, d, e, f

[little drum]

here's a small list

[clever nimbus]

it feels like this kind of problem would have some clever solution

[little drum]

hmm, perhaps I'd do better to arrange so that it doesn't permute

[clever nimbus]

that we are missing

[lethal galleon]

maybe

or my teacher typo

idk yet

but im doing it anyway

[lethal galleon]

wait how do u calculate them

[clever nimbus]

hes using a script i believe

brute force

[lethal galleon]

can u show me all the sol

or if its a script is it finite

like can u count the number of solutions

[lethal galleon]

that i can only see f = {23; 47; 173}

[little drum]

we also had f = {29, 43, 19, 61, etc. ...}

[lethal galleon]

is there finite amount of value of f

[little drum]

idts, only searched for (a, b, c, d, e) in [2, 50)

[lethal galleon]

can u search in [2, 100] that would be slower like 13 times but for checking

and have a<=b<=c<=e
bcause if (a1, b1, c1, d1, e1, f1) is a solution we can shuffle (a1, b1, c1, e1) and have 24 solutions which is similar

[little drum]

(2, 2, 11, 31, 3, 173)
(2, 2, 13, 7, 3, 23)
(2, 2, 43, 7, 3, 47)
(2, 3, 11, 31, 2, 173)
(2, 3, 13, 7, 2, 23)
(2, 3, 43, 7, 2, 47)
(3, 3, 11, 5, 5, 17)
(3, 3, 11, 29, 11, 157)
(3, 3, 11, 101, 89, 1019)
(3, 3, 13, 5, 7, 19)
(3, 3, 19, 5, 5, 23)
(3, 3, 23, 5, 13, 29)
(3, 3, 37, 5, 13, 41)
(3, 3, 41, 5, 5, 43)
(3, 3, 53, 5, 23, 59)
(3, 3, 89, 101, 11, 1019)
(3, 3, 103, 197, 17, 2767)
(3, 3, 107, 5, 17, 109)
(3, 3, 109, 29, 31, 193)```

[lethal galleon]

odd

my problems usually dont have this much solution

[little drum]

no lol, my rusty laptop was taking too long generating the 967 solutions for e ≤ 100

So I only uploaded the first 20

Bruh =_= isn't it asking for any six prime numbers

You're only supposed to find one such list

[lethal galleon]

yea

i doubt my teacher typoed

[little drum]

🤦 Just plug a = 2, b = 2, c = 3, d = 5, and solve for e, f smh

[lethal galleon]

maybe hes trying to type d^2 instead of d^3

[little drum]

doesn't matter. you're only to find one such solution probably

[lethal galleon]

^3 in the middle of ^2 is weird

yea

no normally i have to find all the answer

[clever nimbus]

i genuinely cant think of an approach to find a general solution

[lethal galleon]

this evening i have a lesson so maybe ill ask my teacher about this problem

[clever nimbus]

probably the best approach yeah

[lethal galleon]

yea

ty all for spending time to help me

.close

[lone heart]

Channel closed

Closed by @lethal galleon

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.

[zinc haven]

hello i'd like my proof checked please

[paper mango]

Yes but can be simplified

[zinc haven]

i think i need not consider Tv = 0?

[paper mango]

ys, since

which means

[zinc haven]

yes, makes sense

thank you

.close

[lone heart]

Channel closed

Closed by @zinc haven

Use .reopen if this was a mistake.

[paper mango]

np 🦩

[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.

[sudden mesa]

polease help

[sudden mesa]

The tower of a particular network is designed to service 12 km in radius, if the tower is located at -2,5 on a coordinate plane then

a. what is the standard equation of the outer boundary of the region serviced by the tower
b. if you are located at (3,1) and your friend is at (8,-4), will you and your friend receive a service from the tower

zz..

[serene scarab]

how much is 1 unit distance in the coordinate plane

[sudden mesa]

12km

but i think i have to square 12

[serene scarab]

thats the radius of the service of the tower isnt it?

im asking how much is 1 unit distance in km

like 0,1 to 0,2

[green jacinth]

<@&286206848099549185>

[serene scarab]

This channel is occupied please open your own channel

[solemn seal]

Make one in a avalible help channel

[sudden mesa]

idk men 1k meters

[north rover]

!15m

[lone heart]

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

[north rover]

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[green jacinth]

I am new could u plz explain

[serene scarab]

i mean we can proceed using that assumption

[north rover]

look at the above message

[serene scarab]

so what have you tried?

[solemn seal]

Hi : D

[green jacinth]

How can i get my own

[solemn seal]

Click on #❓how-to-get-help

Then follow instructions

[sudden mesa]

none 💔

[green jacinth]

Thx

[north rover]

i think it tells you in the bot message

[serene scarab]

okay so you can start with writing the equation of a circle centered at -2,5, radius 12

[green jacinth]

Bot message??

[north rover]

.

[green jacinth]

Okkk

[sudden mesa]

so its (x+2)^2 + (y-5)^2 = 12^2

[serene scarab]

this essentially is the boundary as mentioned in the question if youre out of this boundary you wont get service

[serene scarab]

12^2

[sudden mesa]

oh ye

that for letter a.. and b

[serene scarab]

ok so now you have the equation of the boundary do you agree?

[sudden mesa]

yes

[serene scarab]

and do you know how we judge whether a point lies inside or outside a circle

[sudden mesa]

nope..

[serene scarab]

okay lets take a simple example, a circle centered at origin with radius 2, well come back to the question in just a moment

what would be its equation

[sudden mesa]

x^2 + y^2 = 2^2

centered at origin right..

[serene scarab]

2^2

yes thats correct

[sudden mesa]

oh god i keep forgetting

[serene scarab]

and lets take two points: i) 0,0 ii) 3,0

[sudden mesa]

yes

[serene scarab]

we know that i) lies inside the circle and ii) lies outside the circle

now plug those inside the equation of the circle

ill do one 0^2 - 0^2 - 4

for 0,0

this gives a positive or negative value?

[alpine sable]

Guys

[sudden mesa]

what i dont get u

[alpine sable]

I have a question related to a.pm

[serene scarab]

bro

[sudden mesa]

negative

what

😭

[alpine sable]

Arithmetic Progression

[serene scarab]

go to another channel

[serene scarab]

yes

[alpine sable]

Which one

[serene scarab]

!occupied

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[serene scarab]

if you do the same for 3,0 will you get a negative or positive value

[sudden mesa]

positive..

hhuh

[serene scarab]

yes

correct

now just check for another point inside the circle, say 1,0 what value are you getting

[sudden mesa]

positv

pls what

[serene scarab]

1^2 + 0^2 - 4

[sudden mesa]

oh

[serene scarab]

my point is if you plug in any point which is inside the circle you will get a negative value and any point which is outside the circle you will get a positive value

now, coming back to your quesiton if you plug in the two points, the two friends will recieve service only if both of them lie inside the circle

so the value should be negative when you plug in the points in the equation of the circle

[sudden mesa]

ohh

[serene scarab]

!done

[lone heart]

If you are done with this channel, please mark your problem as solved by typing .close

[serene scarab]

if you have a question about something you can ask

[lone heart]

@sudden mesa 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.

[tiny oak]

pls someone help me with math

[tiny oak]

dms

[ripe parcel]

?

[tiny oak]

;-;

[ripe parcel]

here

[lone heart]

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

@tiny oak Has your question been resolved?

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.

[wicked jolt]

In a day a machine makes 5900 lamps, in a control it shows that 26 of them are broken. About how many are broken if it instead was 2000 lamps

[lunar robin]

,w 26/5900 times 2000

[ocean seal]

Results provided by WolframAlpha

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

Requested by nyxzore

[lone heart]

@wicked jolt Has your question been resolved?

Channel closed

Closed by @wicked jolt

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.

[warped topaz]

x^2 - 10x + 25 factorizes to (x-5)^2

A(x - 5) + B

Ax - 5A + B

Chartbit ❤️

Ax and 5x so A = 5

-5A + B and we have -1 so -5A + B = -1

sub A=5 into -5A + B = -1

-5(5) + B = -1

B = 24

A/(x - 5) + B/(x - 5)^2

5/(x - 5) - 24/(x - 5)^2

[jagged cobalt]

(+24/...)

[warped topaz]

Its not ^2? 🤔

I thought there was a rule for perfect squares like this

Where 1 is /(x-n) and the other is /(x-n)^2

[pseudo ice]

(you changed the sign from + to - is what @jagged cobalt is saying)

[warped topaz]

Oh 😭

5/(x - 5) + 24/(x - 5)^2

[frigid orchid]

try factorizing the denominator

[pseudo ice]

@frigid orchid it would help if you read what has been done before commenting...

[warped topaz]

5/(x - 5) Integrates to 5ln(x - 5)

-24/(x - 5)^2

-24/(u)^2

[frigid orchid]

it wouldn't, because i don't know integration myself very well

[pseudo ice]

Signs again

[warped topaz]

24/u^2

24u^-2

integrates to
-24u^-1

-24/u

-24/(x-5)

I got it right 😅

Idk where I made my mistake(s) before hehe

But thank you everyone for guiding me through it!!

[pseudo ice]

The 52, maybe you got it mixed up with differentiating?

[warped topaz]

I think soooo 😅

Thank you everyone for your help!!

❤️

.close

[lone heart]

Channel closed

Closed by @warped topaz

Use .reopen if this was a mistake.

[steep wing]

Hello

I need help with this

[jagged cobalt]

#❓how-to-get-help

[warped topaz]

This channels about to close

Id use https://discord.com/channels/268882317391429632/903481105888452609

[steep wing]

Ok

[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.

[chrome marlin]

hllo

[chrome marlin]

.help

[lone heart]

Commands:

• clopen: .close, .reopen
• consensus: .poll
• factoids: .tag
• help: .help
• version: .version

Type .help <command name> for more info on a command.

[chrome marlin]

okay

i need help can someone check my answer

are all ym answers correct?

[safe meadow]

Number 1 is wrong I think

A I mean

Number b is wrong too

[chrome marlin]

why

how did u

[safe meadow]

I think all of your answer is wrong except number d

Hint : find CBE first

Then find AEB and CEB

Then the question become easier

@chrome marlin I think your answer is right

I thought e was the center point

Yeah ur answer is right

[lone heart]

@chrome marlin Has your question been resolved?

[safe meadow]

After further checking the only part that you are wrong from question 1 is question f and g

[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.

[dapper cedar]

Hi my Math teacher isn’t giving my any answers to what went wrong so basically I did “- 1/10 + 1/5 “ and so my result was “- 1/30” but it was wrong so I’m confused what I did wrong

[dapper cedar]

Im just trying to understand what went wrong for next time

[tardy stag]

hmm -1/10 + 1/15 does in fact equal -1/30

[little drum]

perhaps your teacher wasn't ready to believe your genius

[dapper cedar]

Oh? That’s weird it was supposed to be addition so the sign with the biggest number is the sign that’s kept in the answer right? Sorry English isn’t my first language so this might be confusing😭

Im guessing it supposed to be “+1/30” but now I have no idea

[tardy stag]

no, it should be -1/30 like you said

1/15 is smaller than 1/10

[dapper cedar]

Oh right well that’s weird

[tardy stag]

well yeah that intermediate work doesn't make much sense

-1/10 would be -3/30

and 1/15 would be 2/30

[dapper cedar]

My bad I did write 5/30

Then for the subtraction I wrote 1/30

So basically I was right?

[tardy stag]

it might be that your teacher didn't understand what you were doing and didn't want to give credit for an answer whose work made no sense

[dapper cedar]

That could be true and it would be really annoying but too bad he won’t help me at all so I had to ask here to see what went wrong-

Well thank you for your help anyways

💗

[tardy stag]

yeah the not-helping part is bad, but it's somewhat common to give credit for work, in both directions

[dapper cedar]

Oh icc I guess I should try motivating my response then

[lone heart]

@dapper cedar Has your question been resolved?

Channel closed

Closed by @dapper cedar

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.

[viscid portal]

$[(-2+5)^4 * 3^6] : 3^3 : (-7+4)^4 + (-3)^3$

[ocean seal]

Simon James B

[viscid portal]

$(3^4 * 3^6)/ 3^3 / (-4)^4 + (-3)^3$

[ocean seal]

Simon James B

[coral flower]

-4?

[woven kestrel]

!status

[lone heart]

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

[viscid portal]

2

$(3^4 * 3^6)/ 3^3 / (-3)^4 + (-3)^3$

[ocean seal]

Simon James B

[woven kestrel]

first off

divide 3^10 with 3^3

then what you get, divide by 3^4 (cause (-3)^4 = 3^4)

[viscid portal]

well

we would get 3^10/3^3/(3)^4 -(3)^3

[woven kestrel]

PEMDAS

[coral flower]

the parenthesis/brackers are wrong look at the question , should be like this

[woven kestrel]

are they?

i don't think they are

[coral flower]

$$\frac{\frac{[(-2+5)^4 * 3^6]}{3^3}}{(-7+4)^4 + (-3)^3}$$

[woven kestrel]

the (-3)^3 is at the end

[ocean seal]

JustToPro

[woven kestrel]

no

[viscid portal]

this one is right

[woven kestrel]

His question was: $[(-2+5)^4 * 3^6] : 3^3 : (-7+4)^4 + (-3)^3$

[ocean seal]

alex <3

[woven kestrel]

Which isnt equal to this.

If it were equal, it would have to be $[(-2+5)^4 * 3^6] : 3^3 : [(-7+4)^4 + (-3)^3]$

[ocean seal]

alex <3

[coral flower]

it be easier if u compare 2 ratios at a time
$$\frac{(-2+5)^4 * 3^6}{3^3}$$ and $$\frac{3^3}{(-7+4)^4 + (-3)^3}$$

[coral flower]

.
OP said that one is right

[woven kestrel]

well then he made a mistake in writing it

Cause $[(-2+5)^4 * 3^6] : 3^3 : (-7+4)^4 + (-3)^3$ isn't equal to $[(-2+5)^4 * 3^6] : 3^3 : [(-7+4)^4 + (-3)^3]$

[ocean seal]

alex <3

JustToPro

[viscid portal]

i wrote the problem correctly

[woven kestrel]

But $[(-2+5)^4 * 3^6] : 3^3 : (-7+4)^4 + (-3)^3$ isn't equal to $[(-2+5)^4 * 3^6] : 3^3 : [(-7+4)^4 + (-3)^3]$

[ocean seal]

alex <3

[coral flower]

in a ratio question , the left thing would be read as the right thing

[woven kestrel]

is it a ratio question though?

[coral flower]

1+2x : 4x+2

[viscid portal]

we are supposed to get 0

[woven kestrel]

he might have used : as "dividing"

[viscid portal]

: means dividing in my country

[coral flower]

damn

can u ss the problem :d

[woven kestrel]

then there needs to be

a parantheses

if its a ratio of 3 things

[viscid portal]

it's shown the same as i stated first

[woven kestrel]

Unless it's the ratio + (-3)^3

$$\frac{\frac{[(-2+5)^4 * 3^6]}{3^3}}{(-7+4)^4} + (-3)^3$$

[ocean seal]

alex <3

[woven kestrel]

Might be like this.

This is the only thing I see.

Since there are no parantheses

[coral flower]

if its a ratio question , its the way i wrote

[viscid portal]

problem 8B

[woven kestrel]

: is division

to him

[coral flower]

,rccw

[viscid portal]

8B

[coral flower]

in ratio , ":" is usually written as division

[woven kestrel]

but this isn't ratio

Even if it was ratio, it would have to be $[(-7+4)^4 + (-3)^3]$

[coral flower]

yeah maybe not , my bad

[ocean seal]

alex <3

[woven kestrel]

With a parantheses

[viscid portal]

maybe you understand better if i say $[(-2+5)^4 * 3^6] / 3^3 / (-7+4)^4 + (-3)^3$

[ocean seal]

Simon James B

[woven kestrel]

see?

no parantheses

(-3)^3 is standing alone

meanwhile the rest is division

[viscid portal]

-3)^3 is not part of the fraction

[woven kestrel]

so it's 3^7/3^4 + (-3^3)

which is 3^3 - 3^3

which is 0

[woven kestrel]

as i said

[viscid portal]

the fraction is the big [] with 3^3 and the ()

[woven kestrel]

yes

[viscid portal]

i am supposed to get 0

[woven kestrel]

so i'm correct

[viscid portal]

but i got stuck somewhere

let me do it again

$[(-2+5)^4 * 3^6] : 3^3 : (-7+4)^4 + (-3)^3$

[woven kestrel]

you need to divide from left to right

[ocean seal]

Simon James B

[viscid portal]

$(3^4 * 3^6)/ 3^3 / (-3)^4 + (-3)^3 \newline 3^{10}/3^3 / (3^4) + (-3)^3$

[ocean seal]

Simon James B

[woven kestrel]

now divide 3^10/3^3/3^4

[viscid portal]

3^7/3^4 + (-3)^3

3^3 - 3^3

0

[woven kestrel]

yes

[viscid portal]

i don't understand where i got it wrong at all

[woven kestrel]

probably the division part

[viscid portal]

most likely

tysm

.close

[lone heart]

Channel closed

Closed by @viscid portal

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.

[void canyon]

A ramp into a building forms a 6° angle with the ground. If the ramp is 8 feet long, how far away from the building is the entry point of the ramp? Round the solution to the nearest hundredth.

5.33 feet
6.05 feet
7.04 feet
7.96 feet

(if i don't pass this exam my parents are gonna beat my ass 🙏)

[broken pivot]

You need to do your exams on your own.

[void canyon]

mf you're in a math HELP server

i need said HELP

[lone heart]

@void canyon 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.

[delicate spruce]

l

[delicate spruce]

my teacher wants to me show that i understand logarithms in my log

Log 5 (125) =

wait i confuse

nvm

.close

[lone heart]

Channel closed

Closed by @delicate spruce

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.

[modern sinew]

Hi

[modern sinew]

Using the Triangle Proportional Theorem

The angle at top Is B btw

Anyways

Is it r AC
— = —
BD BE

[lone heart]

@modern sinew Has your question been resolved?

[modern sinew]

<@&286206848099549185>

[modern sinew]

<@&286206848099549185>

Send help

Theres no answers

[river fern]

did you get those values right?

because 18/15 is not equal to 35/24

question feels wrong as far as my knowledge allows

[dense portal]

the values are wrong

[lone heart]

@modern sinew 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.

[alpine sable]

Someone help me pls?

[twin nimbus]

!show

[lone heart]

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

[alpine sable]

I don’t understand it

Can someone explain?

[twin nimbus]

So you're instructed to choose two students at random from those who study drama

Do you know what parts of the diagram correspond to that?

[alpine sable]

So the D circle

[twin nimbus]

Ok, how many people total are in this circle?

[alpine sable]

22

[twin nimbus]

How many people in that circle also study music?

[alpine sable]

5

[twin nimbus]

Excellent

[alpine sable]

5/22?

[twin nimbus]

Not quite but close!

If we pick one person in drama the probability that they study music is 5/22

But we're asked for 2 people

So let's say we pick one person and they do study music, that's 5/22

[alpine sable]

Am I suppose to draw a tree diagram?

[twin nimbus]

We set this person aside

There are now 21 people left and we choose another

What is the probability that this person also studies music?

[alpine sable]

2/21?

I’m confused now

1/21?

[twin nimbus]

So we removed our person who studies music

There were 5 of them before

So now there are how many?

[alpine sable]

3

Oh 4

4/21

And multiply both, right?

[twin nimbus]

Yup!

[alpine sable]

OMG THANK YOU!!

.close

[lone heart]

Channel closed

Closed by @tight raptor

Use .reopen if this was a mistake.

[twin nimbus]

Have a bouba day

[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.

[sharp marsh]

Im confused on what im supposed to do

[sharp marsh]

I got tan theta - theta + C
or
t/sqrt1-t^2 - arcsin(t) + C

i dont understand what the question is asking me to do

so the explanation doesnt make sense

[hushed locust]

the fact that you got different answers is a definite sign that something went wrong

[sharp marsh]

because in part a they do

in part b:

they write it in terms of t in the first part

thats why im distinguishing my answers

[hushed locust]

yes, but even with the different methods you should get the same final number

[sharp marsh]

okay this isnt my final answer

i know its not

im just confused on what im supposed to do next

[river fern]

maybe you missed the ^2 on the t in the numerator?

[hushed locust]

in part a) you translate back in terms of t and use the given limits, and in part b) you stay in terms of theta and turn the given limits into limits in theta

[sharp marsh]

so plug in t = 1/2

then plug in t = 0 and subtract it from that

[hushed locust]

that's what you would do for part a), yes

[sharp marsh]

okay but how does 1/2 = pi / 6

i do arcsin(1/2)?

thats the only thing that comes to mind

[hushed locust]

you are trying to translate the limit
t = 1/2
to a limit
theta = ?

[sharp marsh]

right

[hushed locust]

so you use the definition you gave for theta

[sharp marsh]

this just means "in order to get 1/2 in theta we did arcsin(1/2) to obtain pi/6"

thats how i interpreted it

.close

[lone heart]

Channel closed

Closed by @sharp marsh

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.

[latent cosmos]

ok cant reopen the chat I had

[latent cosmos]

Someone explained it as...

$\frac{1}{\sqrt{ u }}=u^{-\frac{1}{2}}$

[ocean seal]

Ousel

[latent cosmos]

And I though I got it, but dont think I do. Why is the numerator getting the +1 from the power rule?

[hushed locust]

they are dividing by 1/2

which is the same as multiplying by 2

[latent cosmos]

so p+1 means divide by 2?

(in the denominator)

makes sense now I think, just wanna be sure. 😅

[hushed locust]

the power rule says "add 1 to the power and divide by the new power"

so p + 1 = -1/2 + 1 = 1/2

so the integral is [ \int u^{-\frac 12} \odif u = \frac{u^{\frac 12}}{1/2} +C = 2u^{\frac 12}+C ]

[ocean seal]

cloud

[latent cosmos]

ok, gotcha. This is why I hate school breaks. 😅

[lone heart]

@latent cosmos 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.

[spare bluff]

How do you do this

[steady jungle]

prove that in a non multiple pythagorian triple the difference between b and c cannot be 16. I don’t even know where to start 😭

[alpine sable]

new channel, please

this one is occupied

[steady jungle]

Mb

Sorry

[alpine sable]

all good

[spare bluff]

Know how to do this?

[alpine sable]

it's in inches so i wouldnt know

sorry

[spare bluff]

The concept tho

[spare bluff]

An inch is 2.54 cm

Or just use 1 inch as a meter since it ends up being whole number

.close

[lone heart]

Channel closed

Closed by @spare bluff

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 mulch]

Can someome help me with 1 exercise of ecuation systems?

[fossil laurel]

what did you try so far?

and whats the first step?

[junior mulch]

Triao and error

And commom factoe

[fossil laurel]

possible, but not very efficient or elegant

[junior mulch]

Factor

[fossil laurel]

you solve the first one for x

right?

[junior mulch]

Correct

[fossil laurel]

then go ahead

[junior mulch]

Ok let me work some

I'll tell you on a momento

Moment

Wait i just get something else

This is what I tried

I guess it doesn't have any solution?

[oblique pine]

In other words -> Inconsisent

[junior mulch]

Yes, thank you very much

Now i'm missing like 30 exercises more 👍

[lone heart]

@junior mulch Has your question been resolved?

Channel closed

Closed by @junior mulch

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.

[mortal ridge]

i got kevin has to invest more money

but answerkey says lui

<@&286206848099549185> please sirs

[lone heart]

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

[exotic belfry]

thats wrong.

[exotic belfry]

thats right.

[mortal ridge]

can i explain what i did

and u tell me where i went wrong

[exotic belfry]

show

[mortal ridge]

i used this formula to calculate future value

so far all good?

[exotic belfry]

no.

[mortal ridge]

oh so i used to wrong formula

its 1 of these

[exotic belfry]

no, you used the right formula, but in the wrong direction.

[mortal ridge]

what do u mean in the wrong direction

i did that to calculate the future value, then i calculated interest, kevin had more interest so he had to pay more

[exotic belfry]

you have the future value (10000) given, and you want the present value.

[mortal ridge]

thats so confusing

so they want to have 10000$

in the future

so thats our future value ig

so we caluculate both of there present values and subtract it from 10000, whoevers number is bigger needs to pay more?

[exotic belfry]

A = 10000, i = 5%, what is P?

[mortal ridge]

10000

wait no

P?

P is 10000no?

OHHH

10000=P(1+0.05)^20

and solve for p?

[exotic belfry]

this

[mortal ridge]

u asked what is P

P is principle

we dont have that

if 10000 is the future value

[mortal ridge]

so we need to use this to find it

no?

[exotic belfry]

ok, if A = 10000 and if i = 5% and if n = 20 what is the value of P?

[mortal ridge]

3773

thats what i got

[exotic belfry]

and now for i = 4.8?

[mortal ridge]

but its also compounded monthly so i need to divide i by 12 and multiply n by 12

right

[exotic belfry]

yes.

[mortal ridge]

3831

thats what i got

for lui

@exotic belfry right?

[exotic belfry]

i didnt calculate the exact values, but the value for lui hast to be > the value for kevin, so it seems to be ok.

[mortal ridge]

alright brother i understood it but this question is much different

[exotic belfry]

its jsut the same question.

[mortal ridge]

am i still making the future value 25000 and solving for p?

[exotic belfry]

yes.

[mortal ridge]

alr bet

[low cradle]

skibiti

[mortal ridge]

@exotic belfry i need u again man

i got the right answer by not the right value

i got franco invested more correct but not by how much

[exotic belfry]

and your question is?

[mortal ridge]

what is the value of how much more franco invested earlier than david

[exotic belfry]

!nosols

[lone heart]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[mortal ridge]

brother this is exam review

[exotic belfry]

you can show what you did.

[mortal ridge]

im not asking for the exact value, i cn ask anyone who did the review, i want the process

[exotic belfry]

you have the right formula, and ....

[exotic belfry]

.... you know how to coompounf monthly.

[mortal ridge]

theres my work

i have the answerkey and it said franco had a greater investment at the start but by 204.20$

im getting by 477$

[exotic belfry]

what is 1.069^30?

[mortal ridge]

7.402

[exotic belfry]

i get 3377.60

[mortal ridge]

thats exactly what i got too bro

look at the working

[exotic belfry]

come one, dont attack me, i didnt say its wrong.

[mortal ridge]

not attacking u man

i appreciate u

[exotic belfry]

what is 6.9/12?

[mortal ridge]

thats 6.9% no?

we need to divide it by 0.069

[exotic belfry]

???? what is 6.9 /12 ?

[mortal ridge]

now ur attacking me bro

its 0.575

[exotic belfry]

and you are calculating this:

[mortal ridge]

thats correct

[exotic belfry]

no, 0.006 is not 0.00575.

[mortal ridge]

its rounded

[exotic belfry]

thats the point.

[mortal ridge]

that little rounding

fucked my whole answer up?

[exotic belfry]

yes, that little rounding.

[mortal ridge]

wow

didnt even know

[exotic belfry]

calculate with the not rounded values.

[mortal ridge]

got it

preciate u man

dyk annuities?

bc i gota learn it before my exam tmr ngl

[lone heart]

@mortal ridge Has your question been resolved?

Channel closed

Closed by @mortal ridge

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.

[umbral lotus]

im thinking about the question: how many binary strings of length n have exactly 2 descents (i.e. exactly two instances of the pattern 10), i did some really weird calculations and got this formula, but I don't know if its correct or not, and would like some input on how to approach counting this (since i am not sure if what i am doing is right)

[umbral lotus]

my approach was to first look at a subproblem where we have exactly 1 descent, from which I got (n-1)(n)(n+1)/6, and then I used this to count for two descents by splitting the whole string into different sections that would have a descent in them

[lone heart]

@umbral lotus Has your question been resolved?

[umbral lotus]

i also have tried a bit of regular expressions but im not sure how to work it out

[lone heart]

@umbral lotus Has your question been resolved?

Channel closed

Closed by @umbral lotus

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.

[left scarab]

How can I solve this?

[left scarab]

should I be trying to find the roots of that function, or is there another way to solve it?

[young solstice]

you can evaluate the equation at the endpoints of each interval (e.g. 2 & 3 for the first interval). from there, if the sign changes, then you know that the function must have passed through 0, which indicates that a root exists in the interval

this is by the intermediate value theorem btw

[left scarab]

so like
2(2) cos (2*2) - (2 - 2)^2 = -2.61246

2(3) cos (2*3) - (3 - 2)^2 = 4.76102

[young solstice]

yes that's good

also if this is a written response you might have to state that the function is continuous over the given interval

[left scarab]

ohhhh f(a) < K < f(b)

so -2.6 < 0 < 4.76

[left scarab]

do i need to prove that it is continous? im not sure how i would do that numerically if so

[young solstice]

you can just state it probably. it should be continuous for all real numbers so it's not super relevant

[young solstice]

also slight nitpicking but the bounds should be inclusive (use <= instead)

[left scarab]

ohh i got led astray by this

are there some cases where it is written with < vs <=

[young solstice]

actually you may be right

I was just assuming that it would inclusive though since the interval is inclusive, so those values are included with its a mapping from a to f(a) and b to f(b)

[left scarab]

ohhh right i see what you mean

thank you for your help!

[young solstice]

np

[lone heart]

@left scarab Has your question been resolved?

Channel closed

Closed by @left scarab

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.

[strong swan]

Find an equation of the graph that consists of all points
(x, y)
having the given distance from the origin.
The distance from the origin is three times the distance from
(0, 8).

[oak chasm]

!status

[lone heart]

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

[lunar birch]

@oak chasm

[strong swan]

probably 1, im not sure how to start

[lunar birch]

I need help

Wait

Wrong channel

Mb bro

[strong swan]

nw

[lunar birch]

I thought this was mine

[oak chasm]

OK, so they want you to do all points at a certain distance from the origin (which is (0, 0)).

They say that certain distance is 3 times the distance from the origin to (0, 8).

How far is (0, 8) from the origin?

[strong swan]

8

[oak chasm]

OK, now they want it at 3 times that distance, so how far do they want it?

[strong swan]

24 units

[oak chasm]

OK, now what shape do you get when you draw all points a certain distance from a point?

[strong swan]

a circle

[oak chasm]

OK, what's the formula for a circle?

[strong swan]

y = sqrt(r^2 - x^2)

[oak chasm]

Well, that'll only do half a circle.

,w plot y = sqrt(5^2 - x^2)

[ocean seal]

Results provided by WolframAlpha

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

Requested by chai.t.rex

[oak chasm]

sqrt is actually the principal square root, which gives the nonnegative value.

A better equation is ((x - h)^2 + (y - k)^2 = r^2).

[ocean seal]

Chai T. Rex

[oak chasm]

(h, k) is the center and r is the radius.

[strong swan]

(h, k) is the origin (0, 0) so it's x^2 + y^2 = r^2

but that simplifies to what I said earlier

[oak chasm]

Not quite.

y^2 has two values.

Like let's take x = 0.

Then y^2 = 24^2, right?

,calc 24^2

[ocean seal]

Result:

576

[strong swan]

hmmm i see

but that's still a point on the graph

(0, 24)

[oak chasm]

Right, but here's the thing. y^2 = 576.

One way is 24^2 = 576.

Another way is (-24)^2 = 576.

Both y values work.

[strong swan]

so y = sqrt(576)

yeah

[oak chasm]

But when you do sqrt, it only gives one of those values.

It only gives 24, the nonnegative one.

It can't give -24.

So, you leave out half the circle.

[strong swan]

so I guess that's where I'm stuck, I'm not sure what to do next

it has to be one equation so I can't add a second that would just be the first equation multiplied by -1

[oak chasm]

Well, x^2 + y^2 = 24^2 is one equation.

[strong swan]

Oh I just have to stop there?

[oak chasm]

That's what I'd recommend.

[strong swan]

I'm thinking strictly in terms of y

[oak chasm]

If they need y = something, then y = plus or minus sqrt(...).

But if they don't require that, use the standard form with x^2 + y^2 = 24^2.

[strong swan]

That solution was wrong according to the homework, but I still have attempts left

[oak chasm]

Does doing the squaring work?

[strong swan]

no

[oak chasm]

Like x^2 + y^2 = 576.

Can you show a picture of the question?

[strong swan]

sorry, HDR makes my screenshots weird

[oak chasm]

Do they have a (\pm) symbol you can use?

[ocean seal]

Chai T. Rex

[strong swan]

no

[oak chasm]

OK, does changing 24^2 to 576 work?

[strong swan]

No

I think it might be saying that the distance from (x, y) to the origin needs to be 3x the distance from (x, y) to (0, 8)

[oak chasm]

Hmm.

OK, what's the distance formula from the origin and the distance formula from (0, 8)?

[strong swan]

sqrt(x^2 + y^2) for the origin

from (0, 8) I think it'd be sqrt(x^2 + (y - 8)^2)

[oak chasm]

OK, so what would an equation that fits the question be?

[strong swan]

,help

[ocean seal]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[strong swan]

,tex $\sqrt{x^2 + y^2} = 3 \cdot \sqrt{x^2 + (y - 8)^2}$

[oak chasm]

\sqrt{x^2 + y^2}

\cdot for multiplication.

Needs the curly braces, like {} instead of ().

Ahh, they want you to put $ on both ends (no space between the $ and the thing it touches).

[ocean seal]

NickTrain111

[strong swan]

ok final answer lol

[oak chasm]

OK, now square both sides and then simplify.

Or submit that.

[strong swan]

,tex $x^2 + y^2 = 9 \cdot(x^2 + (y - 8)^2)$

[ocean seal]

NickTrain111

[strong swan]

,tex $x^2 + y^2 = 9 \cdot(x^2 + y^2 -16y + 64)$

[ocean seal]

NickTrain111

[strong swan]

,tex $x^2 + y^2 = 9x^2 + 9y^2 -144y + 576$

[ocean seal]

NickTrain111

[strong swan]

,tex $-8y^2 + 144y = 8x^2 + 576$

[ocean seal]

NickTrain111

[oak chasm]

OK, now you can divide by 8, I think.

[strong swan]

,tex $-y^2 + 18y = x^2 + 72$

[ocean seal]

NickTrain111

[strong swan]

,tex $-y^2 + 18y - 72 = x^2$

[ocean seal]

NickTrain111

[oak chasm]

I'd go with the more circle standard form, like x^2 + y^2 - 18y = 72, but it probably doesn't matter.

Does your answer work?

,w plot -y^2 + 18y - 72 = x^2

[ocean seal]

Results provided by WolframAlpha

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

Requested by chai.t.rex

[oak chasm]

Not quite a circle.

,w factor y^2 - 18y + 72

[ocean seal]

Results provided by WolframAlpha

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

Requested by chai.t.rex

[strong swan]

I got 2 attempts left so I'll try that one first

gotta divide by -1 first

[oak chasm]

,w plot (y - 6)(y - 12) = -x^2

[ocean seal]

Results provided by WolframAlpha

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

Requested by chai.t.rex

[strong swan]

,tex $(y - 6)(y - 12) = -x^2$

[ocean seal]

NickTrain111

[strong swan]

This worked ^

[oak chasm]

OK 🙂

If you surround your LaTeX with $, you don't need the ,tex in front.

$x^2$

[ocean seal]

Chai T. Rex

[strong swan]

ohh ok, thanks, that's the first time i've used it

[oak chasm]

No problem.

[strong swan]

You've been very helpful and I appreciate you working it out with me, thanks a million!

[oak chasm]

You're welcome.

[strong swan]

.close

[lone heart]

Channel closed

Closed by @strong swan

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.

[amber isle]

how do i do 88

[amber isle]

idk how to resolve the bottom

or the top tbh

i just dk

[zinc haven]

are you asked to prove the identity or?

[mortal magnet]

theres a lot of steps but thats an identity

[paper mango]

hm start by using the third angle formulas

[amber isle]

yes

[mortal magnet]

(if you dont know the third angle formulas, you could spam sin(x + y) and cos(x + y) a few times to break apart sin(3x) and cos(3x) completely)

[amber isle]

ok i wasnt sure whether to use sum to product or third angle

ima try third angle 1s

[paper mango]

sin(3x) = 3sin(x) - 4sin(x)³
cos(3x) = 4cos(x)³ - 3cos(x)

as remember note

which means at the top you'd then have

3sin(x) - 4sin(x)³ + 4cos(x)³ - 3cos(x)

can be grouped by the 3's and 4's

then probably trinomial

oyoyoy

yeah and then the denominator should be a factor

[amber isle]

hrmmm ok

[zinc haven]

oyoyoyoyoy

[paper mango]

If you're stuck you can use this
||3sin(x) - 4sin(x)³ + 4cos(x)³ - 3cos(x) = 3(sin(x)-cos(x)) + 4(cos(x)³ - sin(x)³) = 3(sin(x)-cos(x)) - 4(sin(x)-cos(x))(cos(x)²+sin(x)cos(x)+sin(x)²)||

[amber isle]

r yall doing this bc poyyo

[paper mango]

:D

[amber isle]

lol

[amber isle]

how did you get from step two to three

where did the minus sign come from

[paper mango]

cos(x)³ - sin(x)³ is similar to a³ - b³ right

and a³ - b³ = (a-b)(a²+ab+b²)

[amber isle]

ohh ok

[paper mango]

trinomial

[amber isle]

lemme try that rq

[paper mango]

the great thing is that after using the trinomial

both terms have sin(x)-cos(x) as a factor

and sin(x)-cos(x) is the denominator

which means, begone denominator!

[amber isle]

confused, idt both have the same factor

3sinx-3cosx has sinx-cosx as a factor, but the other term has cosx-sinx as a factor

[little drum]

5 = -(-5)

[amber isle]

hmmm ok

other term has a factor of cosx-sinx aka -(sinx-cosx)

aight so i have (cosx-sinx) (cos^2x +cosxsinx+sin^2x) but idk where to put my 4 and -3

-3 because that turns into 3sinx-3cosx from before

and 4 from the breakup on sin3x and cos3x

@paper mango

so from 4cos^3x - 4sin^3x + 3sinx-3cosx i split it into
4(cosx-sinx)(cos^2x + cosxsinx + sin^2x) + (-3)(cosx-sinx)

so itd be (cosx-sinx)(4)(cos^2x + cosxsinx + sin^2x -3) and idk how the 3 and four fit in

[paper mango]

ys 1 sec

[paper mango]

yeah so far good

notice what I mentioned before

[amber isle]

yea but idk how to properly handle the other stuff after canceling out

[paper mango]

after canceling what are you left with

I had 3(sin(x)-cos(x)) - 4(sin(x)-cos(x))(cos(x)²+sin(x)cos(x)+sin(x)²) at the top so after canceling it would be

[amber isle]

4(cos^2x + cosxsinx+ sin^2x - 3)?

[paper mango]

3 - 4(cos(x)²+sin(x)cos(x)+sin(x)²)

[amber isle]

ohhhhh that makes more sense

[paper mango]

why's the 3 inside there

[paper mango]

:D

[amber isle]

wasnt sure where to put it

[paper mango]

now notice

cos(x)² + sin(x)² = 1

3 - 4(cos(x)²+sin(x)cos(x)+sin(x)²) = 3 - 4(1+sin(x)cos(x))

3 - 4(1+sin(x)cos(x)) = -1 - 4sin(x)cos(x)

wait I must have gotten a - wrong somewhere

since it's correct otherwise

[amber isle]

i think its -3 and +4

[paper mango]

yes yes

just looking where I missed the -

or I'll leave the task for you

left as an exercise for the reader

🐧

[amber isle]

you just distributed wrong i think

wtv tho it works

tyvm

[paper mango]

np! :]

[amber isle]

.close

[lone heart]

Channel closed

Closed by @amber isle

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.

[onyx granite]

1. d) pls

i said the range for the reciprocal is x cannot = -3 and y cannot equal 0

[onyx granite]

however the answer key says x cannot = 3 and y is greater than or equal to 0

[onyx granite]

yes that question

[paper mango]

dym cannot be x = -3

because x = 3 is in the domain

[little drum]

d) y = (x + 3)² correct?

[onyx granite]

the domain i put was x cannot equal -3

answer key says cannot equal positive 3

[little drum]

?

[onyx granite]

how does that work

yes

thats correct

[little drum]

Reciprocal is 1/(x + 3)² yes?

[onyx granite]

yes

[little drum]

can it output non-positive values?

[onyx granite]

yes i believe so

x equals all real numbers except for restrictions

[little drum]

Huh? for what x do you suggest, 1/(x+3)² is negative or 0?

[paper mango]

convince us :D

[onyx granite]

if you use a negative value for x, it outputs a y value

except for -3

[little drum]

I'm asking you

[winter light]

What's the result when you put, say, -5?

[little drum]

Does there exist any x in real number R that makes (x + 3)² negative?

[onyx granite]

1/4

[winter light]

Is it negative?

[onyx granite]

arya im trying to answer u but gimme a sec

[onyx granite]

the question is asking me the range and domain of the reciprocal

[little drum]

But your question is "why the answer key says y is greater than or equal to 0". Am I wrong in my interpretation?

[onyx granite]

yes you are right

[little drum]

So answer me then

Does there exist any x in real number R that makes (x + 3)² negative?

[paper mango]

let's solve it without the answer sheet

and only compare afterwards

[little drum]

is my english that bad.

[onyx granite]

no theree are no negative numbers that make (x+3) negative

[little drum]

In fact, there are no number that make (x + 3)² negative

for the simple fact that no matter what (x + 3) is, squaring it will only give a positive output

That is why, (x + 3)² can only be ≥ 0

[onyx granite]

i was only taught to test values, is there any other way to figure out domain & range?

[little drum]

And so, the reciprocal 1/(x + 3)² > 0

does that answer your question?

[onyx granite]

so, no matter what value is used, y will be more than 0

y > 0, because 1/(x+3)^2 cannot equal negative

[little drum]

y = (x + 3)² takes in any value of x, adds 3 to it, but despite whatever value (x + 3) becomes, its square can only be ≥0. Is that clear?

[paper mango]

yes, for domain you check invalidities

[onyx granite]

yes

[paper mango]

y = (x+3)² is defined for all x e R

the reciprocal however

1/(x+3)²

[little drum]

Good.

[paper mango]

is undefined if the denominator is 0

[little drum]

So you understand that y ≥ 0, and so, 1/y > 0 are the respective range

[onyx granite]

and the only way it can be undefined is if x = -3?

[little drum]

yes, the reciprocal will be

[onyx granite]

yes i understan

how can y also = 0

what value would make y = 0 aswell?

[little drum]

y can be 0 at x = -3

[onyx granite]

ohh okay okay

i didnt take that into account

[little drum]

y = (x + 3)² = 0 => (x + 3)² = 0 => (x + 3) = 0 => (x + 3) - 3 = -3 => x = -3

Also, your answer key has wrong domain for the reciprocal for this question

[onyx granite]

yes, i believe so too

because 3 is permitted as an x value

[little drum]

the correct domain is $\bR \setminus {-3}$

[onyx granite]

the \ is to mean cannot = -3?

[little drum]

yes the \ implies the element {-3} is excluded from R

[onyx granite]

so for future reference, for y range i should test values such as -1, 0, and 1

in the x value

[winter light]

You don't have to test values, because there's an infinite number

You have to study the sign of the function, or understand in some other way (e.g. sometimes completing the square might be the way) what is the range

[onyx granite]

hmm okay

thank you Arya, Alberto, and lunatic

i think this helped

.close

[lone heart]

Channel closed

Closed by @onyx granite

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.

[fringe rune]

why is my range wrong?