help-10

[obtuse pebble]

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.

[clear mauve]

What am I doing wrong?

[fallen spoke]

What's the problem

[clear mauve]

To solve the simultaneous equations

[fallen spoke]

Calc assumed?

[clear mauve]

The second image is the equation that I need to solve

The first image is my workings

[clear mauve]

?

[fallen spoke]

Can you use calculator

[clear mauve]

Nope

[fallen spoke]

Easy

[clear mauve]

🥲

[forest yacht]

i didn't see any mistakes actually

[fallen spoke]

Use a calculator to verify the answe

[clear mauve]

How??

[fallen spoke]

Classpad

[clear mauve]

Huh?

I am confused lol

[fallen spoke]

Omg you must be old

[clear mauve]

I m legit 15 🥲

[blazing sentinel]

plug in the answers?

[clear mauve]

Or the opposite 😂

[clear mauve]

Alr

[fallen spoke]

Get on a voice call

[clear mauve]

Alr

[fallen spoke]

4x-y equals -4

[clear mauve]

Yes

[fallen spoke]

X-2y=28

[clear mauve]

How did you get this one?

😆

Ale

Alr

Y=12

X = 4

And how do I verify if it's good or not?

Is desmos going to work?

.close

[obtuse pebble]

Channel closed

Closed by @clear mauve

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[rain coral]

I don’t know what to do next

I think I might have went wrong somewhere

[atomic hornet]

?

[rain coral]

sin^2 + cos^2=1

oh

[atomic hornet]

sin^2(2x) = 1 - cos^2(2x)

yeah

[rain coral]

ohhh

[atomic hornet]

it happens

[rain coral]

I have to change the 2x as well

lol

it just happens way too much for me =.=

[atomic hornet]

lol

[rain coral]

but apart from that

there isn’t like big mistakes?

[random ocean]

isnt it cos2x-1)/2

[rain coral]

is it?

I can’t remember

[atomic hornet]

also why would you not just let u=cos(2x)

[rain coral]

wait

ah yes

why not

then I can solve it normally

with quadratic

[atomic hornet]

mhm

[rain coral]

I went through my notes it’s 1+cos2x/2

[random ocean]

what did u do here?

cos u into u isnt cos squared u

[random ocean]

yes right that

[rain coral]

yea that’s a mistake as well

imma redo it

thx

[obtuse pebble]

@rain coral Has your question been resolved?

Channel closed

Closed by @rain coral

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[lone vault]

can someone show me their method?

[royal basin]

given that this question begins with "Hence" and is labeled as (ii), you need to show us part (i)

[random ocean]

did u try? what're u getting?

i got like -72

[royal basin]

aha

and you have found that these expansions go up to x^2, yes?

meaning all higher terms in them will be x^3 or higher

so you can replace (1-x)^6 and (1+2x)^6 with their expansions from part (i) and it won't affect the x^2 term

which you can then find via explicit expansion

[lone vault]

coeffeicent of x^2 right from the 2 brackets

[clear mauve]

You'd use the binomial theorem right?

[lone vault]

yes

[clear mauve]

I have an explanation in one of the books I use

@lone vault

[lone vault]

ok thanks

[random ocean]

@atomic hornet do u have the answers? of your sheet?

if yes can u verify

[atomic hornet]

wrong person?

[obtuse pebble]

@lone vault Has your question been resolved?

Channel closed

Closed by @lone vault

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[knotty linden]

Let $f(x) = \lfloor x \lfloor x \rfloor \rfloor$ for $x \ge 0.$

(a) Find all $x \ge 0$ such that $f(x) = 1.$

(b) Find all $x \ge 0$ such that $f(x) = 3.$

(c) Find all $x \ge 0$ such that $f(x) = 5.$

(d) Find the number of possible values of $f(x)$ for $0 \le x \le 10.$

[warm shale]

Starlight

[random ocean]

try hitting values and you'll get to the answers

atleast thats how i solved first 3

[warm canopy]

for (a), we're looking for when $\lfloor x\lfloor x\rfloor \rfloor = 1$, and you know this happens when $1 \leq x \lfloor x \rfloor < 2$

[knotty linden]

$f(x) = \lfloor x \lfloor x \rfloor \rfloor$ for $f(x)$ to be $1$ we know that $x\lfloor x \rfloor$ must be from $[1,2)$. After plugging in some values between $[1,2)$ it is evident that all of these solutions do in fact work. So our solution for $x$ is $[1,2)$!

[warm shale]

ΣAC

Starlight

[knotty linden]

This is a valid way of solving (a) right?

[warm canopy]

you would need to convince yourself that there are no values of x outside of [1,2) that also work

[knotty linden]

hmm how would we do that?

[warm canopy]

well if 0 < x < 1, what is xfloor(x)?

[knotty linden]

0 right?

[warm canopy]

yep

so that rules out anything less than 1

and then think about xfloor(x) when x >= 2

in particular, what it must be greater than

[knotty linden]

It has to be greater than 4 right?

[warm canopy]

yep nice!

so we ruled out everything outside of [1,2)

and everything inside works

🙂

[knotty linden]

Nice 🙂

For $f(x)$ to be $3$ we know that $x\lfloor x \rfloor$ must be from $[3,4)$

[warm canopy]

similar arguments for b and c, just a bit more subtle

[warm shale]

Starlight

[knotty linden]

Wait would there be a value that even works for this case?

[warm canopy]

indeed, but you may run into an issue now based on what we just did

right bc for x in [1,2) xfloor(x) was between 1 and 2, and when x>=2 we jumped up to being bigger t han or equal to 4

[knotty linden]

So there are no valid answers for x right?

[warm canopy]

it seems not!

[knotty linden]

Alright now for c we already know that For $f(x)$ to be $5$ we know that $x\lfloor x \rfloor$ must be from $[5,6)$ and taking what u said with $a$.... typing noises

[warm shale]

Starlight

[warm canopy]

okay so first thing to do might be to find when xfloor(x)=5

[knotty linden]

Just from plugging in numbers we can see that $[2.5,3)$ is the correct range....

[warm shale]

Starlight

[warm canopy]

right yeah lol

you got some nice intuition

[knotty linden]

Thanks 😛 - Now we just have to prove that the numbers on either side of this range doesn't work right?

[warm canopy]

below the range we have covered!

[knotty linden]

right lol so it's just above

[warm canopy]

now convince yourself that if x>=3, then xfloor(x) >= 6

which i think will be very easy for ya haha

sory

=9

[knotty linden]

Ya xD it jumps to 9 doesn't it?

[warm canopy]

you got it

[knotty linden]

yay! now for (d) dun dun dunnnnn

[warm canopy]

yeesh

[knotty linden]

I'm not incredibly sure how to begin......

A hint comes along with it: Hint(s):
Divide into cases, based on the value of $\lfloor x \rfloor.$

[warm shale]

Starlight

[warm canopy]

yeah you may see a pattern if you do this

so you wanna look at [0,1),[1,2),[2,3),...

we've done some of the work

but maybe do one or two more intervals and see if you spot a pattern

[knotty linden]

Well from [0,1) we have 0
1 to 2 we have [1,2)
2 to 3 we have [4,6)
3 to 4 we have [9,12)
4 to 5 we have [16,20)
So it's always the first number ^2 +
and then + the first number for the upper bound right?

[warm canopy]

hang on, your notation a little confusing

do you mean for example that for $x \in [4,5), f(x)$ takes on values 16,17,18,19

[warm shale]

ΣAC

[knotty linden]

Yes

[warm canopy]

okay

good

so we are just counting now

1 value for x in [0,1)

1 value for x in [1,2)

2 values for x in [2,3)

3 values for x in [3,4)...

[knotty linden]

4 for 4 - 5
et et
9 for 9 - 10 correct?

[warm canopy]

yep!

[knotty linden]

So it's just 1+ (1+-----9) which is 1+45 so 46?

[warm canopy]

we didnt quite go up to 10

[knotty linden]

What are you talking about?

Thanks 😛

[warm canopy]

lmao

here the graph so you can see what you were doing actually looked like

[knotty linden]

Huh, interesting

cool anyway tysm and have a nice day

[warm canopy]

and you!

[knotty linden]

.close

[obtuse pebble]

Channel closed

Closed by @knotty linden

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[cunning citrus]

hiw do I do this
if an exterior angle of a regular convex polygon is 30degrees, find its number of sides

[random ocean]

exterior angle = 30 so sides = 360/30=12

number of sides^

[warm canopy]

For this reason we encourage those who help with answering questions to teach how to arrive at the answer, rather than giving the answer upfront.

[fierce lagoon]

The

[cunning citrus]

but isn't a the sum of the interior angles

[cunning citrus]

OH YEAH I DIDNT SEE THAT thanks I get it

[random ocean]

np

[cunning citrus]

.close

[obtuse pebble]

Channel closed

Closed by @cunning citrus

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[obtuse pebble]

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.

[timid silo]

35?

[glass sundial]

nope

i got 2 answers

should be 3 answers

[timid silo]

i mean

there are 2 questions

in ur pixture

[glass sundial]

oh yea 35

i have a question

[timid silo]

(i)x<-5
(ii)-5<=x<1
(iii)x>=1

case by case

[glass sundial]

for example |x+10|>4*|x+3|
its same as x+10>4*|-x-3|

[obtuse pebble]

@glass sundial Has your question been resolved?

[glass sundial]

<@&286206848099549185>

[kindred oasis]

No

[glass sundial]

ok then how to slove me question

[glass sundial]

.

[kindred oasis]

You divide it into two inequalities at first, then solve each of them case by case like they explained here

[glass sundial]

i got this for

=

could you explain?

[kindred oasis]

Why is x-1 now 1-x here?

[kindred oasis]

Actually the mistake is here, it should be 1-x but it's instead x-1

[kindred oasis]

Do you need me to explain how to solve the inequality?

[glass sundial]

i slove it

but i didnt know why they placed the x-1 for 1-x

could you slove it on a paper so i can understand everything?

[kindred oasis]

You should try to solve it first

[kindred oasis]

I don't even know where that comes from, the x-1 is not in the original expression. Are those inequalities from the same problem?

[glass sundial]

ye

slove this in your way let me see how

[kindred oasis]

At least give it a try, then if you made mistakes I can't correct them and explain.

[glass sundial]

i sloved it

solved

but i but 1-x how the app gave me

and the answers was right

[kindred oasis]

This is the original problem, here there's |1-x|, not |x-1|, that's why the app gives you the correct answer with |1-x|

[kindred oasis]

I have no idea where the |x-1| comes from

[kindred oasis]

What do you mean here with "they"? Who is they?

Is that a solution you've been given?

[glass sundial]

the app

[kindred oasis]

This is what you input in the app

[kindred oasis]

And this is what it gives you?

Which app are you using

[glass sundial]

camera amth

math

could you solve it

and let me see how the corrcet way

[kindred oasis]

I can't solve it ATM, i don't have a piece of paper and a pen with me. That app isn't helpful at all. If you just need the solution try using an app like Photomath, you get the steps there too

If you want to understand how to solve it just try to solve it, stop whenever you don't understand what you're doing, send a picture of your work and ask

[glass sundial]

i dont know how to start

[kindred oasis]

https://youtu.be/4FWtnwg1y3s
Watch this, then try to solve it. It takes ages to explain that via messages

It's even in the rules of help channels, show your work and explain were you're stuck. We can't explain things from scratch as it takes a lot of time, so we don't. We're glad to help when you're stuck on a problem and need help to go on though.

[timid silo]

They wrote both (x-1) and (1-x) because of the modulus (absolute value) that the expression was in. It is the non-negative value no matter the sign so that means if you had the expression under the “| |” brackets the sign of it wouldn’t change. For example if you had both +2 and -2 under the brackets sign that means that it would be both equal to 2. If you had a question like if x=-2 and y=+2 does |x|=|y| then the answer would be yes, because both |-2| and |+2| equal +2. In the expression you have |x-1| which means that both +(x-1) and -(x-1) would have the absolute value of a positive number under the modulus (the “|..|” brackets). So if you have x+5<3|x-1| you would have x-3|x-1|<-5 then you would have to take into matter the absolute value of the expression x-1 under the modulus which would mean you would have two ways: both +(x-1) and -(x-1), furthermore making the expressions x-3[+(x-1)]<-5 and x-3[-(x-1)]<-5. The first expression is if x-1 equals to something that equals to 0 or greater and the second which is -(x-1) which equals to something below zero because the expression has a negative sign outside of the brackets.

I don’t know if I can explain it more in detail, it would be best if you searched modulus (absolute value) of an expression, because it is very important for solving these kinds of equations and it’s truly fascinating in a way.

[obtuse pebble]

@glass sundial Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[obtuse pebble]

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.

[restive comet]

!15m

[obtuse pebble]

@restive comet Has your question been resolved?

[warm canopy]

?

[tardy epoch]

just close

[warm canopy]

.close

[obtuse pebble]

Channel closed

Closed by @warm canopy

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[obtuse pebble]

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.

[royal mirage]

hey

[royal mirage]

i was wondering if i was correct on this.

this is what i have achieved thru desmos graphing calcualtor and i believe it is right but can someone please verify

can someone please help me 🙏

[warm canopy]

if it was a good representation, the lowest point of the function would be 3 agree?

[royal mirage]

yes

and on the graph im pretty sure it is three

if i am correct let me recheck.

yes sir, it is 3.

[warm canopy]

check again

[royal mirage]

will do

yes sir.

[warm canopy]

you are telling me that those low spikes you're looking at, are at 3?

i urge you to look more carefully

[royal mirage]

each spike represents the revolution of one rope

that is why there are so many spikes i believe

ohhhh

[warm canopy]

okay but does this spike have y coordinate 3?

[royal mirage]

OHHHHHH

sorryyy

[warm canopy]

there you go

[royal mirage]

tysm bruh

it doesnt go underground 🤦‍♂️ 😂

sorry

thanks man

[warm canopy]

exactly

youre welcome

[royal mirage]

may i be aided on this problem too.

i believe it is C

could someone check these two for me please

[obtuse pebble]

@royal mirage Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[uneven palm]

\

[pine sail]

How familiar are you with arithmetic progressions and stuff?

[uneven palm]

idk my teacher didn't teach anything

[oblique sage]

Okay so then if g(n) is g(n-1)+6, and g(1) is -19, then g(1) is g(0)+6, so g(0) + 6 is -19?

[pine sail]

How about linear functions? Straight line? And stuff?

[uneven palm]

yeah

[uneven palm]

uhh yeah?

[oblique sage]

So then g(0) is g(-1)+ 6, so then g(-1) +12 = -19

Then g(-2) + 18 = -19

So it goes (-2, -37) then (-1, -31), (0,-25)

Then (1,-19)

[uneven palm]

oh so basically adding 6 each time?

[pine sail]

yeah

[oblique sage]

Okay so wait then that means it’s a function that keeps increasing by 6

[pine sail]

now do y = mx + b

[oblique sage]

I’m learning with you Kihei 😭

[uneven palm]

what 😭

[pine sail]

fr?

[uneven palm]

oh

OHH

SO ITS LITERALLY

[oblique sage]

Yeah I haven’t learned like series stuff.

[uneven palm]

y = 6x - 25

?

[oblique sage]

No it would be -19 because at 0 y is -19

[pine sail]

No it isn't lol

[uneven palm]

i thought that's (1, -19)

as provided

[pine sail]

It's -19 at 1 yeah

[oblique sage]

Oh wait yeah

[spring portal]

huh

[oblique sage]

Nevermind ur right

6x-25 👍🏻

[uneven palm]

alright bet

[oblique sage]

I feel smart I just did a big brain 👍🏻

[spring portal]

no

[uneven palm]

wait but like isnt that not explicit formula?

thats slope intercept form lmao

[obtuse pebble]

@uneven palm Has your question been resolved?

Channel closed

Closed by @uneven palm

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[mellow pulsar]

pls help its subtraction remember that. is it 0?

[mellow pulsar]

i was so confused until i saw the subtraction but then i was even more confused

[prime anvil]

you still use x = rcos(theta) and y = r(sin(theta)

note that cos^2 - sin^2 = cos(2theta)

that's one of the trig identity

[mellow pulsar]

im a little confused

am i looking for the x and y? or am i looking for an equation?

[prime anvil]

you're looking for an equation

relating r and theta

that's what the polar form of an equation is

[mellow pulsar]

hmmm

so whats the first step

x=r(x/6) y=r(y/6)

[prime anvil]

this

that's what you do when you transform into polar coordinates

[mellow pulsar]

but its not addition so how is it even a triangle

[prime anvil]

what do you mean

[mellow pulsar]

im sorry im so dumb lmaoo

im so lost

[prime anvil]

just know that one of trig identity is

$\cos(2x) = \cos^2(x) - \sin^2(x)$

[warm shale]

Azzurala

[prime anvil]

as opposed to what you're probably referring to

which is

$1 = \cos^2(x) + \sin^2(x)$

[warm shale]

Azzurala

[mellow pulsar]

okay

so how do i plug in what i know to that

[prime anvil]

you have this polar transofmr

[mellow pulsar]

so cos(2x)=36 right

[prime anvil]

just plug this into the original relation

no

there should be an r and a theta

no r or thetas are being cancelled here

[mellow pulsar]

r=6radical(sec(2theta))

????

[prime anvil]

hm

let me do it myself

that seems correct

$r^2 (\cos^2(\theta) - \sin^2(\theta) = 36 \
r^2 \cos(2\theta) = 36 \
r = \sqrt{\frac{36}{\cos(2\theta)}} = 6 \sqrt{\sec(2\theta)$

[warm shale]

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

[prime anvil]

there we go

yea

[mellow pulsar]

heck yeah

thank you

[prime anvil]

r can't be negative (well it could, but you usually include that in the trig function's phase itself when you plot it out on the xy-plane)

[mellow pulsar]

tysm

[prime anvil]

[mellow pulsar]

.close

[obtuse pebble]

Channel closed

Closed by @mellow pulsar

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[lone vault]

How do i factorise

[obtuse pebble]

Please don't occupy multiple help channels.

[lone vault]

4x^3 + 3x + 2

[sage geode]

Try finding its roots and then apply Vieta's theorem

[lone vault]

i hv no clue abt that theorem

[sage geode]

It says that ax^2 + bx + c = a(x - x1)(x - x2) as long as x1 and x2 are roots of ax^2 + bx + c expression

a, b and c being coefficients

[grizzled shore]

That’s a cubic

[sage geode]

Oh

Eh Vieta's theorem for cubics then lol

[warm canopy]

Vieta not really useful here

[sage geode]

Yeah, unless you are able to find just one root

[warm canopy]

You can check for rational roots and if you find one, divide by its factor

[grizzled shore]

Could you just use ferro’s method to solve depressed cubics

I wasn’t taught this in school but I’ve come across this before on the internet

[obtuse pebble]

@lone vault Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[paper oyster]

How do I solve these in a way that will not falsely say that these solutions are extraneous

or falsey say they are true

[kindred oasis]

Wdym "falsely say that a solution is true"?

[paper oyster]

likw

like

[kindred oasis]

Is there any particular one you're not sure about?

[paper oyster]

i mean the fact that some of them seem true but i got them wrong kinda

and all of them im confused on

[kindred oasis]

The first one seems pretty straightforward right?

√25=5

[paper oyster]

i think im missing a method or something but the video that taught me was so bad

[paper oyster]

yes i acciedntally selected the ones i thought were extraneous

but thats what confused me b/c i got it mostly right

because i didnt even answer the question correctly

but why wouldnt √6-6

equal 0

[kindred oasis]

Doesn't the X next to it mean it's false?

[paper oyster]

yes

why is it that √6-6

does not =0

[kindred oasis]

Yes, it's false that 6 is an extraneous solution, since 6 is a true solution

[paper oyster]

what

√6-6 is 0

and 0=0

right ?

[kindred oasis]

Yes

But

The question asks whether 6 is an extraneous solution right?

[paper oyster]

oh my god

im so supid

thank you holy shit

.close

[obtuse pebble]

Channel closed

Closed by @paper oyster

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[kindred oasis]

Np

[obtuse pebble]

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.

[bleak valley]

If a question asks me to "draw the graph of the functions from x = -1 to x =8" and gives me a linear equation below it (y = mx + b), are they asking me to draw a line that starts from the point (-1, ...) and ends at (8, ...)? I don't really get what they're asking me to do.

[high lily]

yes, that's pretty much what they want

[bleak valley]

oh, okay. thank you!

.close

[obtuse pebble]

Channel closed

Closed by @bleak valley

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[obtuse pebble]

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.

[finite flame]

Hey

[finite flame]

So I think it should involve some kind of limits

[royal basin]

some kind of series-manipulation shenanigans, more like.

[haughty coyote]

Manipulations are the way to go yes

[timid silo]

$\frac{n^2}{n!}=\frac{n*n}{n!}=\frac{n}{(n-1)!} = \frac{(n-1+1)}{(n-1)!}$

[haughty coyote]

Exactly

[warm shale]

Normal Cat

[timid silo]

start with this

[finite flame]

Wait, ig

We should involve logs in it

I just dk how

[timid silo]

I didn't require logs tho

[haughty coyote]

No. Use the series that defines e

[finite flame]

Uhh what is that?

[timid silo]

$e = \sum_{i=0}^{\infty} \frac{1}{i!}$

[warm shale]

Normal Cat

[finite flame]

Ohh

Well then we get 1/(n-2)! +1/(n-1)! And as n goes infinity it should be e+e=2e?

[finite flame]

But how did we get this?

[timid silo]

can u be a bit more formal

[finite flame]

I’m lazy today

Have to complete last 4-5 questions

Sry tho

[timid silo]

well

e is defined to satisfy

$\frac{de^x}{dx}=e^x$

as $e^0$ has to be $1$

that gives u enough info to calculate a maclaurian expansion of $e^x$
that is

$e^x=\sum_{i=0}^{\infty} \frac{x^i}{i!}$

Sub $x=1$

[warm shale]

Normal Cat

[timid silo]

that will give u this

[finite flame]

Ohh

Thanks

@timid silo

Pi=e

.close

[obtuse pebble]

Channel closed

Closed by @finite flame

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[timid silo]

[finite flame]

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[fluid meadow]

Could I get some help on question 20

I simplified down the expression but I don’t really see how it helps

[obtuse pebble]

@fluid meadow Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[vital maple]

Um yea usually I would say wat I think I have to do but this one I have no idea

[timid silo]

write point B=(x,y)=(x,x). Then try and find the distance from A to B and equate it to 5

[vital maple]

Oh thats where I went wrong

A=(-1,0) and b=(x,y) i put that into the distance of two points equation

But I I forgot x=y so when I was doing it I had a x and y so I couldn't solve

Ty I know what to do now

.close

[obtuse pebble]

Channel closed

Closed by @vital maple

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[obtuse pebble]

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.

[somber sierra]

Find the domain, f(x) = x^2 + 2x -4

[somber sierra]

Why is it all real numbers?

[cedar lichen]

What do you think it should be?

[random ocean]

write it as (x+1)^2 -5

range would be [-5,inf)

domain is

[somber sierra]

what’s the domain?

[random ocean]

R

[somber sierra]

why?

[random ocean]

usually domain is given if not then take it as R

[somber sierra]

How can I explain that?

[kind hawk]

informally, the domain are all numbers that you can plug into the function which make sense such that you eg don't divide by 0 or don't take the sqrt of a negative number

[high lily]

polynomial, there aren't any locations where its undefined

[cedar lichen]

The domain of 1/x isn't R, even though I haven't specified a domain

Also, please don't just give answers

[random ocean]

for a polynomial

[somber sierra]

I know the answer and understand why but I don’t how to put into words

[random ocean]

quadratic equation's domain is taken as R

[cedar lichen]

But why? Just because? To do a little trolling? Rather than just memorize a bunch of facts, its better to actually understand the content and why such things are true

[kind hawk]

well it depends on the level at which you have to argue. but it's probably fine to say that the domain is R because the expression x^2+2x-4 is defined for all x in R

[somber sierra]

Yeah I got it

Thanks!

.close

[obtuse pebble]

Channel closed

Closed by @somber sierra

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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 hawk]

I'm not exactly sure what you mean?

[random ocean]

weird ques

[kind hawk]

how would -834 be defined otherwise?

[timid silo]

what is x+(-x)=0 if the concept of x+(-x)=0 never existed ?

[kind hawk]

I mean you don't have to necessarily notice that x+(-x)=0 to "use" negative numbers I guess

[timid silo]

good point. loaded question

seriously ?

[kind hawk]

this question is in your worksheet?

with that phrasing?

[timid silo]

unless your teacher went nuts

you won't find this question anywhere

but it's fun to think about tho

[sage iron]

never say never
someone asked this exact same question yesterday

[timid silo]

I think they're just trolling or something

[random ocean]

bro's trolling

[kind hawk]

is the point that at higher levels of math you define a-b=a+(-b) with the additive inverse of b? and at lower levels of math you would do it the other way, i.e you define a+(-b)=a-b ? because you already "know" what subtraction is?

[timid silo]

he wasn't serious when he asked the question, but this doesn't mean the question is useless

it makes you think about the definition of the inverse

[sage iron]

#discussion message

[timid silo]

someone who asks this question (seriously) is unlikely to have gotten to this point

[kind hawk]

well that's a slightly different question about the number 0 in particular

[sage iron]

they edited it I’m pretty sure

because I remember this exact phrasing

[kind hawk]

ah ok. either way a very weird question

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[obtuse pebble]

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.

[random ocean]

...when they are parallel

[cunning ingot]

.close

[obtuse pebble]

Channel closed

Closed by @cunning ingot

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[fervent cairn]

How do I solve a compound inequality if there is less then negative number

[timid silo]

show the inequality

[timid silo]

you'll just move 4 to the right hand side, as you'd do normally

the inequality symbol won't change

[fervent cairn]

Ok thanks

.close

[obtuse pebble]

Channel closed

Closed by @fervent cairn

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[fervent cairn]

4(x+2)>18 how can I find the number to subtract when there parentheses

[obtuse pebble]

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.

[versed cave]

What's the question? "Evaluate [...] if [variable]" means to substitute the given values into the expression

Maybe that weird thing is that 0 in the exponent

$n^0 = 1$ [assuming n is not 0]

[warm shale]

Nonna

[versed cave]

@timid silo ?

[timid silo]

sorry im back

[timid silo]

yeah thats what i was thinking

[versed cave]

Ok

[timid silo]

i got the answer thanks

[versed cave]

nice

[timid silo]

.close

[obtuse pebble]

Channel closed

Closed by @amber sluice

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[fervent cairn]

Solve the inequality -1 _< 3(x+2)-1 _< x + 3

[fervent cairn]

The greater then is the less then or equal to I can’t put it into text

[distant moth]

Solve the left and the middle part alone, then solve the middle part and the right part alone, then take the intersection of their answers

[fervent cairn]

What’s the middle part

[distant moth]

3(x+2)-1

[fervent cairn]

Ah ok

Thanks I get it now

.close

[obtuse pebble]

Channel closed

Closed by @fervent cairn

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

Channel closed

Closed due to the original message being deleted

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[desert salmon]

Hi! I have a question regarding combinatorics. The problem is as follows:

4 six - sided dice are thrown at the same time. The numbers are recorded, and the order of the numbers don’t matter. How many ways can the dice be rolled such that at least 3 of the dice have different, distinct numbers?

[desert salmon]

If you can just walk me through your logic I would appreciate it a lot.

[obtuse pebble]

@desert salmon Has your question been resolved?

[long peak]

Nvm not sure that's right

[obtuse pebble]

@desert salmon Has your question been resolved?

[sage iron]

maybe split it into separate cases

[scarlet gale]

Yeah, what are the two main cases?

[obtuse pebble]

@desert salmon Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[obtuse pebble]

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.

[quasi needle]

Hello

[quasi needle]

I just wanna check what this notation means, please :)
(This has been used to describe an experiment divided into 5 groups, each with 10 subjects)
Yij: i stands for the elements/subjects from 1 to 10, j stands for the groups from 1 to 5 that each subject has been put into

And what exactly is the ~? Is that saying it's "distributed according to"? Where I presume N stands for a normal distribution with:

[warm shale]

Stellar

[obtuse pebble]

@quasi needle Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[tardy epoch]

Yes distributed as

But not that std dev

std dev is just sigma

[obtuse pebble]

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.

[hidden dragon]

Esteban's entry in a robotics competition moved 40 feet in 7 seconds. He wants to find how
fast it will go in 200 seconds, rounded to the nearest tenth. Esteban should divide 40 by 7,
and multiply the quotient by 200. Why is it better for him to round the decimal after multiplying,
rather than after dividing?

[hidden dragon]

help

[harsh remnant]

Common sense: To find a more exact answer

[obtuse pebble]

@hidden dragon Has your question been resolved?

[drifting wraith]

you want to round when it's largest

cuz you introduce an error bounded by 0.05

so it's relatively smaller

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[obtuse pebble]

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.

[pseudo chasm]

I've been stuck here for quite a while, can anyone help me find x and explain it to me?

[pseudo chasm]

Anyone?

[high lily]

what have you tried?

[pseudo chasm]

using x to express different angles

get angles throughout the whole circle

[high lily]

show don't tell

[pseudo chasm]

ah its on a notebook

and dont have discord on phone

[high lily]

take a pic, transfer to comp using cloud, cable transfer or otherwise

[pseudo chasm]

DID IT HOLY

it was easy as fuck

AOE = 20

and then x = BOE /2

the answer was right before my eyes yet i was blind to it

ty love ❤️

.close

[obtuse pebble]

Channel closed

Closed by @pseudo chasm

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[fickle swan]

right so

[fickle swan]

just a quick one

If x = asinθ, where a > 0 and θ is acute, simplify a^2 - x^2

[timid silo]

hint : square both sides

and use $sin^2(\theta)=1-cos^2(\theta)$

[warm shale]

Normal Zeta

[fickle swan]

wait

wouldnt the answer just be a^2(1-sin^2(θ))

[timid silo]

a^2(cos^2(theta)) i think

[fickle swan]

oh right

yeah

it can still be simplified

thanks man

[timid silo]

simplifying $a^2 cos^2(\theta)$ ?

[warm shale]

Normal Zeta

[fickle swan]

nono

a^2(1-sin^2(θ))

^this

[timid silo]

oh

ya

[fickle swan]

lmaoo

sorry

thanks for ur time man

:)

aight

[timid silo]

nah its ok dw

[fickle swan]

imma close this rn

have a great day!

.close

[obtuse pebble]

Channel closed

Closed by @fickle swan

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[fleet pendant]

I have tried the formula

A = P(1 + R/T)

It came out like this:

A = 9600(1 + 1x0.06)

A = 9600 + 0.06

Which makes no sense

wait

10176/9600 = 1.06

whatever

wasnt the answer

.close

[obtuse pebble]

Channel closed

Closed by @fleet pendant

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[timid silo]

Needs someone help in iii part of this question

Resultant will be zero?? bcz force A and C will be cancelled out.....

Right?

.close

[obtuse pebble]

Channel closed

Closed by @frigid ermine

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[wanton dagger]

So S=a/(1-r) when |r|<1

Here r=3

[royal basin]

nope

r is 1/3, not 3

[wanton dagger]

I mean 1/3

Yah

Ok cool

Ok I got it thanks

.close

[obtuse pebble]

Channel closed

Closed by @wanton dagger

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[wanton dagger]

For part a), am I to use the formula Sn=a(r^n-1)/(r-1) ?

[tardy epoch]

You should know the difference between arithmetic and geometric sequences and series

[wanton dagger]

Ok

Then would it be Sn=n/2 (2a+(n-1) * d) ?

[random ocean]

ye

this one is for b part Sn=a(r^n-1)/(r-1)

[wanton dagger]

Ye I realised that

Ok thanks

.close

[obtuse pebble]

Channel closed

Closed by @wanton dagger

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[mint bronze]

I'll just give you a brief sketch

Find the roots using the quadratic formula and simplify them

Evaluated I(t) with your roots

[random ocean]

ohh

[mint bronze]

Then differentiate I(t) with respect to t

Find max

Show it is a max

[random ocean]

alright ill try give me 5 mins

[mint bronze]

Sorry for not giving more info

I actually need to go rn

[random ocean]

okay np

[random ocean]

okay i got the answer, thanks

.close

[obtuse pebble]

Channel closed

Closed by @random ocean

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[odd arch]

Why is this solution wrong?

[random ocean]

3rd step

[royal basin]

$\log\paren{n \cdot (2/3)^{n-1}} \neq n \log\paren{(2/3)^{n-1}}$

[warm shale]

Ann

[royal basin]

likewise for the right

[gilded needle]

you don't really need logs here, there's a common factor of (2/3)^(n-1) on both sides of the first equation

[odd arch]

Thanks everyone!

.close

[obtuse pebble]

Channel closed

Closed by @odd arch

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[obtuse pebble]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

Channel closed

Closed due to the original message being deleted

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[polar parrot]

i found the first term being 15 and the common difference -8, but I cant find the value of N given that the n-th term of the sequence is -89 please help

https://cdn.discordapp.com/attachments/490557019623915520/1003247788655640658/unknown.png

[high lily]

what have you tried

[polar parrot]

not able to understand

I did q1a and found u1 being 15

and common difference -8

[high lily]

do you know the expression for the nth term in an arithmetic sequence?

[polar parrot]

a+(n-1)d right

a = 15, d = -8 so
15+(n-1)-8

would that work

thats whaht i was trying

[high lily]

the full equation would be
$$a_n = a_1 + (n-1)d$$

[warm shale]

ℝamonov

[high lily]

you are given the nth term a_n = -89

[polar parrot]

What does it mean by "given that the nth term of the sequence is -89"

a89 ?

[high lily]

a_n represents the nth term in the sequence

you are told that its -89

[polar parrot]

then would it be 15+(-89-1)-8

[high lily]

no

a_n = -89
NOT n=-89

[polar parrot]

ohh

[high lily]

and also *-8 is not the same as -8

the nth term is -89
NOT n is -89
n is what you're trying to find

[polar parrot]

if a_n = 89
would 15+(n-1)-8 = 89 ?

[high lily]

no

and also *-8 is not the same as -8

[polar parrot]

oh, what would d then be

[high lily]

by writing

15+(n-1)-8
you're expressing -8 being subtracted from (n-1) NOT multiplied

and also a_n is being given as minus 89 NOT 89

[polar parrot]

so would d be different

[high lily]

d is -8

[polar parrot]

or would i include multiplication beofre it

[high lily]

you would insert the appropriate symbols/notation so that the multiplication is still represented

[polar parrot]

15+(n-1)*-8 = -89?

[high lily]

yes

[polar parrot]

so will it be 15-8(n-1) - 89

[high lily]

no

equations don't become expressions

what's

so will it be 15-8(n-1) - 89
supposed to be and what does it represent

[polar parrot]

solving this ^

or would it be 15n-8 = -89

[high lily]

it looks like you just thanos snapped the = sign

now you also thanos snapped the -89

[polar parrot]

oh there sorry

[high lily]

among other things

no

wheres 15n coming from

are you doing this on paper?

[polar parrot]

nope

mind

[polar parrot]

/

[high lily]

write stuff down

[polar parrot]

15x-8 then ?

[high lily]

don't do stuff in your head especially if you're struggling

wheres x coming from

[polar parrot]

i mean multiplying 15 and -8

[high lily]

use \* for multiplication
and still no
where's multiplication between 15 and -8 coming from

like really, write stuff down

[polar parrot]

kk

[high lily]

take things one small step at a time if needed

the last correct thing you had was

15+(n-1)*-8 = -89

[polar parrot]

so now to continue this

i would not multiply 15 and -8?

because i was doing that before

[high lily]

there's nothing indicating multiplication between the 15 and the -8

[polar parrot]

then would i do 15+-8

[high lily]

no

there's nothing indicating you should do that either

consider the order of operations and simplify normally

this is pretty much a linear equation of one variable
and you should've have encountered plenty of these before doing sequences (and series)

[polar parrot]

yeah i havent really revised in a while which is why i am getting confused

[high lily]

knowing basic algebra is essential

you could first subtract 15 from both sides of the equation

[fickle swan]

dude whats happening here

finding n?

[polar parrot]

so 15-8(n-1)-15 ?

[high lily]

no

[polar parrot]

= -89-15

oh

[fickle swan]

yes

[high lily]

write the whole thing one one chunk

[fickle swan]

wait no

[high lily]

instead of separating it

[polar parrot]

15-8(n-1)-15 = -89-15

[high lily]

yes, that would be valid

simplify that a bit

[polar parrot]

-8(n-1) = -104 ?

[high lily]

yes

would you be able to solve the rest on your own?

[polar parrot]

would i take -104 to the left now

or would i divide

[high lily]

ideally you'd do division

[polar parrot]

so divide by 8

[high lily]

getting everything to one side doesn't work towards isolating n

[polar parrot]

-8*

[high lily]

you can divide both sides by the same amount

dividing both sides by -8 would be the most eifficient here

[polar parrot]

Ok

then

n-1 = -104/-8 which is 13

so n = 13+1 = 14?

[high lily]

yes

[polar parrot]

ok tysm

[high lily]

if you're struggling with algebra, i highly recommend doing a review on something like khan

[polar parrot]

i also had a doubt on a geometric sequence question

I found the common ratio being (-2/3)

first term being -243

and sum of infinity being 145.8, but then im getting confused with how to find the sum of the first 6 terms

[high lily]

apply formula for sum of geometric series (non-infinite)

[polar parrot]

Sn = a1(1−rn)1−r ?

so s6 ?

[high lily]

that's missing some symbols

notation is messed up too

[polar parrot]

lemme write better

S6 = a1(1-r^n)/1-r

[high lily]

missing parentheses for denominator

once you sub in n=6,
the n on the right side would also be replaced with 6

you also know your a and r

[polar parrot]

yes

so S6 = -243(1-(-2/3)^6 / 1-(-2/3)

[high lily]

missing parentheses for denominator.

S_6 = -243(1-(-2/3)^6**)** /( 1-(-2/3))

also missing closing parentheses for the numeartor

[polar parrot]

oh yes

[polar parrot]

how would i further simplify this then

[high lily]

algerbra

[polar parrot]

so first for the top

would it be -243x665/729

and bottom would be 5/3 ?

1-(-2/3) = 5/3 ?

[obtuse pebble]

@polar parrot Has your question been resolved?

[polar parrot]

@high lily ^

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

[obtuse pebble]

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 forge]

Does anyone that knows mathematica know how I can make it such that for example U4*U4 dagger =1,etc.

[obtuse pebble]

@tiny forge Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[brave portal]

Plz solve it's domain

[sweet crystal]

First simplify it

[brave portal]

Hello sir i am facing some prblm to simplify it

[idle gust]

factozirze x^2-1

[brave portal]

@idle gust your profile🤣 🤣 😂

[sweet crystal]

x^2 - 1 = (x + 1) (x - 1)

[idle gust]

but remember that your function wont be defined at x=1

[brave portal]

@idle gust for only x=1

-1 too

[idle gust]

there are multiple points

[brave portal]

So i think denominator fx x belongs to R-(-1, 1)

Plz help me😩 😭

@sweet crystal hello bhaiya plz help me😭🙏

@idle gust where did you go😭

[idle gust]

simplify the fraction like varun said, you have to see when the inside of the square root is negative since that will be not defined too

[obtuse pebble]

@brave portal Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Please take a minute to participate in [our survey](#changelog message) if you haven't already!

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.

[spiral bluff]

I don't know how to do question a. Please help me if you find it.

[weary pier]

well have you heard of gaussian elimination?

[spiral bluff]

Yes

[weary pier]

describe it

[proven zephyr]

wanted to rotate the first pic

sad

ima just go

[spiral bluff]

I have done it 3-4 times with different starts

But they end up with different values of XYZ

[weary pier]

yeah i see at least one error

hmmmm how to approach this

once you have values for XYZ, you can check them against the equations represented by the three rows in the original matrix

[wicked crown]

I can try the first one I should be able to solve it, let me try real quick

[weary pier]

if that checks out, you've found XYZ that work

[spiral bluff]

Yes but now I have to work the bracket process first

[weary pier]

you're not supposed to do it for them, you're supposed to help them with the issue they have

[weary pier]

wdym

[wicked crown]

yeah sure but I need to remember it first

lmao

its been 6 months since I last did it

[weary pier]

if they don't match, there'll be some step you did wrong

[wicked crown]

actually this should be v simple

[spiral bluff]

You have to use stuff like this

[wicked crown]

you only need to concentrate a lot

[weary pier]

and you can find it by trying to check your XYZ against some matrix in the middle

[wicked crown]

and just subtract and divide or mult or add the rows with each other so that you get the final form

[weary pier]

if they match against the matrix in the mdidle, the error is above; if they don't, an error is below

[wicked crown]

its really just a matter of practice

[spiral bluff]

Okay I will try it again

[wicked crown]

what exactly confuses you ?

like at which point are u unsure whether or not you are doing the right thing ?

[spiral bluff]

I cannot get the 0 and 1 on the left-hand corner

Like every time it's different numbers

[wicked crown]

but you understand the principle of these operations right ?

[spiral bluff]

Yes

[wicked crown]

ok thats good

then probably you are just sometimes calculating the wrong values

wait a second

[weary pier]

i wouldn't say it's just practice

if you're allowed to work on a computer, you could make a spreadsheet do some of the work for you, and the mistakes that computers make are also infuriating but in a new and different manner :P

[wicked crown]

for me it was

I mean idk I remember that I understood the principle very quickly and easily

maybe I am missing something

but its just basic arithmetik operations

to find the desired form

@weary pier can you check ?

I havent done it in a long time

no

ah

[weary pier]

...at the fourth equals sign, why did you turn the -3 into a -1 instead of a 0

[wicked crown]

3,3 has to be a 1 too

[spiral bluff]

Simplify them

[weary pier]

i don't follow, won't you need to bring it to 0 later anyway to get the bottom left half of the matrix all 0s?