help-10

[dreamy jackal]

oohh so thats what its called

its transforming principal nth roots to radicals right?

[small thicket]

sure

[dreamy jackal]

like this? then do you simplify the fractions right?

[small thicket]

yea

where did the variables go tho

[dreamy jackal]

oh oops lemme work on it again

is it like this? im really unsure what to do with the variables

[small thicket]

distribute fractions and simplify

:)))))))))))))))))))))))))))))))))))))))))))))))))

[dreamy jackal]

wdym distribute 🥲

[small thicket]

yk how u did it for this

same thing for the variables

[dreamy jackal]

the variables here is wrong ??

[small thicket]

no?

just do

$(x^4)^\frac{4}{6}$

[warm shale]

Mothy

[small thicket]

multiply 4 by 4

giving u x^16/6

[dreamy jackal]

what about the 4^2y^8 if their exponents are different?

[small thicket]

it doesnt matter

just multiply the first thing (4^2) ^ of the fracton and (y^8) power of fraction

u can take them as seperate things iykwim

[dreamy jackal]

like this??

[small thicket]

huhuhuhuhuhu

should be tis

[dreamy jackal]

ohhh so thats what you mean by separate i thought its like putting parenthesis

[small thicket]

oh mb

[dreamy jackal]

like this???

[small thicket]

huh we cant do that

[dreamy jackal]

huh

[small thicket]

the denominator

[dreamy jackal]

wdym where is it

[obtuse pebble]

@dreamy jackal Has your question been resolved?

[dreamy jackal]

<@&286206848099549185> 🥲

[obtuse pebble]

@dreamy jackal Has your question been resolved?

[random depot]

raise each side to power of 6

then simplify each side of the equation

[obtuse pebble]

@dreamy jackal Has your question been resolved?

[dreamy jackal]

can u explain how to simplify each side?

[strange bough]

Bro 💀How

[flint sundial]

move the decimal point to the right

the divide

[obtuse pebble]

@dreamy jackal Has your question been resolved?

Channel closed

Closed by @dreamy jackal

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.

[warm shale]

bluepianist

[obtuse pebble]

@drifting merlin Has your question been resolved?

Channel closed

Closed due to the original message being deleted

Available help channel!

Send your question here to claim the channel.

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

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

[solemn crater]

if I have an equation similar to f(x) = 4x^4 - 16x^2, how can I go about finding the value of x that will give me a specific value for f(x).

ie. -16 = 4x^4 - 16x^2 (how do I get x by itself here)

[timid silo]

I'm not sure but i would try to write it with X=x² and then resolve the quadratic equation

[brittle blaze]

I would factor a 4x^2 out

[solemn crater]

I tried the factoring, which blew up in my face, but now that you say that, I think I was trying to factor our the wrong value. Ill try the substitution thing first, and if that doesnt work, I'll try the factoring again. Thanks guys!

[brittle blaze]

Wait i didn’t understand the question fully at first and now i do. Im not completely sure the factoring is the way to go

Let me think for a moment

[solemn crater]

yeah no problem. (For some more info, I need to draw the graph of a similar equation. I have a rough idea of what the graph looks like, and I know that the range. So I am trying to figure out what the x value would be for the range that I know.)

[timid silo]

You can divide everything by 4 first maybe

[solemn crater]

^ before factoring?

or whats the end goal with that?

[timid silo]

Just you equation with -16

-16 = 4x^4 - 16x^2 <=> -4=x^4 - 4x^2 <=> x^4 - 4x^2+4=0

[solemn crater]

so that does make sense, but I still need to isolate that x somehow. Would the quadratic equation be able to help with those higher degree suckers?

[timid silo]

Well you gotta try right

X²-4X+4=0 with X=x²

Then x=+-sqrt(X)

[solemn crater]

sounds good, I'll give that a go and see what happens. I can get excel to give me the answer immediately, but on paper this is a bit of a pain lol

[obtuse pebble]

@solemn crater Has your question been resolved?

Channel closed

Closed by @solemn crater

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.

[prisma juniper]

https://media.discordapp.net/attachments/409706781078454274/1019658393633435679/unknown.png

[prisma juniper]

can anyone explain the identity they use?

like i understand it's addition theorem but why doesn't it work with the unit circle diagram

https://cdn.discordapp.com/attachments/409706781078454274/1019658864943173683/unknown.png like this, how are the y co-ordinates here equal

[obtuse pebble]

@prisma juniper Has your question been resolved?

[prisma juniper]

<@&286206848099549185>

[obtuse pebble]

@prisma juniper Has your question been resolved?

[obtuse pebble]

@prisma juniper Has your question been resolved?

[prisma juniper]

<@&286206848099549185>

[brisk grove]

Which part of the solution you don't understand?

I don't see where 4/7pi appears

[obtuse pebble]

@prisma juniper Has your question been resolved?

[prisma juniper]

oh sorry, basically i was using the unit circle diagram

so i converted to a positive sin using -sin(x) = sin(-x) so i ended up with sin(-11pi/7)

and the angle -11pi/7 can be thought of as clockwise from the x-axis by pi + 4pi/7

which is where the 4pi/7 comes from

and i'm trying to understand how with that logic the sin(-11pi/7) = sin(3pi/7)

[wild swallow]

,w -11pi/7 + 2pi

[warm shale]

Results provided by WolframAlpha

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

Requested by 夢雪#2250

[wild swallow]

@prisma juniper

[wild swallow]

it is a full rotation around the unit circle

[frosty spoke]

The identity can be seen this way: $\sin(x + \pi) = \sin(x - \pi) = -\sin(\pi - x)$

[warm shale]

Saccharine

[prisma juniper]

bruh

how did i miss that

that was literally the exact thing i was looking for

thanks tho

.close

[obtuse pebble]

Channel closed

Closed by @prisma juniper

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.

[worthy arch]

damn you bill

[wooden cipher]

if f is 1-1 and monotonically increasing, you know a lot about fof

i was typing

let me finish

[wild swallow]

imagine f is a conveyor belt that only moves forwards

that's monotonously increasing

then you put a copy of the belt onto itself

are you still always moving forwards?

from definition D:

definition of monotonically increasing

if x < y then f(x) <= f(y)

unless you're one of the strict guys

in which case it's f(x) < f(y)

yeah

and then using monotonically increasing

its also the monotonically increasing

otherwise you'll mess up stuff

yep

good good

x^2 - 3 wasn't it

anyway

seems like you got it

im out

[stable rain]

whats ur

Q

i feel

if uve a new Q u shlda

just start a new thread

vxeR?

for all x in R?

is this another condition

or a separate question has this condition

i think

monotonically increasing f means

f' is >0 for all x in R

ditto decreasing g'

right

same

fill in with the same stuff

so then

we want to find if h is increasing or decreasing

essentially

h'

i think u use quotion rule on h

[river kindle]

Did you say that that g(x) and f(x) are both >0

[stable rain]

what happens when u use quotion on h

what the derivative of h in terms of f and g

[river kindle]

I mean just based on intuition it is h(x) monotonically increasing yeah?

[stable rain]

do this

[river kindle]

1/1 <1/0.5

If the denominator is getting smaller

[stable rain]

OH

ok actually

[river kindle]

The value is going up

[stable rain]

ive a better way to explain this

so

monotonically increasing f means that f is convex right

and monotinically decreasing g means g is concave

however

g is lower bounded

thus g is the constant function

a positive constant

thus f* constant is also convex -> monotonically increasing

wew

why didnt i see this earlier

[river kindle]

Yeah as long as they >0

[stable rain]

checks out? bee

wait did u

did i

nvm

so sad

[river kindle]

Bill what class is this? Out of curiosity

Calc 2?

Or high school

[river kindle]

I think I get what you’re saying

Okay ye

It’s def increasing

[stable rain]

didnt we already kinda conclude that lol

anw im outa here

i got ignored like 6x

feels dank man

[gilded needle]

that's kinda hard to read, do you have a screenshot?

ah i see

the second line, should i read it as: $f(x) = 1 - \phi^2(x) - e^{2x} + 2e^{x}\phi(x) \ \ \forall x \in \mathbb R$ ?

[warm shale]

Bungo

[gilded needle]

and in this context, does $\phi^2$ mean the (pointwise) square, or the composition of $\phi$ with itself?

[warm shale]

Bungo

[gilded needle]

ok that looks correct

what does fmax mean?

oh max value of f, got it

well there's no reason to expect f(0) = 1, is there?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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.

[buoyant zenith]

real quick question

can some explain why some of these are horizontal translations

and some of them are vertical translations

idk how to like identify what each look like inside a function

omg help is here

[trim locust]

Anything inside with x effects the x axis, anything outside effects the y axis. With green, because if bidmas, you do 2 abs(x) first, so the vertex is at y=0, then 3 is subtracted from the output, which lowers the y by three. You see this happening on purple as well, it’s raised 4 up, something else is happening here too as it’s been shifted by -2 in x axis. The way I like to think of this is, the vertex occurs when the abs(x) = 0, therefore the vertex will occur now when the x+2 = 0 therefore x =-2, which is why the graph is pushed that way on x

[buoyant zenith]

woah woah woah

[trim locust]

Does that make sense?

Is that what you were asking?

[buoyant zenith]

i sort of get it but keep in mind i cheated my way into alegbra 2 so i have idea what some of those terms mean

[trim locust]

What terms specifically

[buoyant zenith]

like about green and purple

could you re explain it

in simpler terms

i get the first sentencr

[trim locust]

Ok I’ll have a go

So

Abs(x) has the sharp point when y=0, because that’s the whole point of absolutes values

But the -3 after abs(x) means that your entire graph is shifted downwards

Imagine every value you get, take 3 from it

[buoyant zenith]

ok i understand that

[trim locust]

So that’s green

[buoyant zenith]

ok that too thats called a vertical translation right

[trim locust]

For reference I’ll be calling the sharp point thing on the abs x graph a vertex, as that’s how I was taught

So it’s easier for me to explain

[buoyant zenith]

alright no problem

[trim locust]

Purple:
For the graph y =abs(x), the vertex occurs when x= 0, when x < 0 the graph goes up again (because you take the absolute value) so in the case of abs(x+2) the vertex will still occur at the x position that makes x+2=0 which is x=-2, hence the shift to the left in the purple graph

Just like before, all values you get out, you need to add 4, this is why the graph is lifted up

[buoyant zenith]

got it

[trim locust]

The same goes for that quadratic

The black one, y=x^2 has its turning point at x=0, (x-8)^2 has it at x=8

Hence the shift to the right of the black curve

I hope that makes sense

[buoyant zenith]

yeah i got it

thanks

[trim locust]

Np

[buoyant zenith]

u saved my math homework

.close

[obtuse pebble]

Channel closed

Closed by @buoyant zenith

Use .reopen if this was a mistake.

[trim locust]

😂

[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

[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.

[eternal jewel]

How does this work sheet just go from $$\frac{2x+6}{\frac{1}{2}x^{2}-\frac{3}{2}x}$$ to $$\frac{4(x+3)}{x(x-3)}$$?

[warm shale]

Bolvarsdad

[eternal jewel]

I don't see it

[tidal hawk]

the denominator is (x^2 - 3x)/2

[tidal hawk]

so the numerator 2x+6 is divided by this

u can rewrite as (2x+6) • 2/ (x^2 - 3x)

factor out 2 from numerator and x from denom

that’s how u get to that form

[eternal jewel]

Nice, great explanation

Thank you

🙂

.close

[obtuse pebble]

Channel closed

Closed by @eternal jewel

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.

[pseudo hatch]

Why did they multiply 3x and 4 x both sides

[high lily]

you mean to the numerator and denominator?

[pseudo hatch]

Yeah

[high lily]

so they could apply the limit identity for
$$\lim_{k\to0}\frac{\sin(k)}{k}$$

[warm shale]

ℝamonov

[pseudo hatch]

Now I got this but how is it 4

[obtuse pebble]

@pseudo hatch Has your question been resolved?

[pseudo hatch]

.close

[obtuse pebble]

Channel closed

Closed by @pseudo hatch

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.

[pseudo hatch]

Can someone go through his they do 25

[zenith raft]

expanding the numerator seems like it would be ok to start with

[pseudo hatch]

Oh I got it thanks

.close

[obtuse pebble]

Channel closed

Closed by @pseudo hatch

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.

[clear cape]

how do i solve this?

[boreal condor]

u have to look at the graph

and correctly identify the where the types of discount occur

[clear cape]

so by looking at the graph i have to identify it

[boreal condor]

yes

there isnt any math u can do

[clear cape]

so

for jump it will (-6,0.5)?

[boreal condor]

what is the definition of a jump discountinuity

[clear cape]

when two sided limit doesn't exist

[boreal condor]

that's part of it

but the limit at as x approaches -6 exists right?

[clear cape]

yea

[boreal condor]

so then what type of discount is that?

[clear cape]

removable

?

[boreal condor]

yes

[obtuse pebble]

@clear cape Has your question been resolved?

[obtuse pebble]

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.

[dark orchid]

How to solve number 3?

[timid silo]

<@&286206848099549185>

[dark orchid]

@ruby fulcrum

Wait wrong one

<@&286206848099549185>

[obtuse pebble]

@dark orchid Has your question been resolved?

[dark orchid]

💀

<@&286206848099549185>

[dark orchid]

<@&286206848099549185>

<@&286206848099549185>

[dark orchid]

<@&286206848099549185>

This feels like a discord issue with loading messages

[cedar lichen]

!15m

[obtuse pebble]

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.

[cedar lichen]

once

[obtuse pebble]

@dark orchid Has your question been resolved?

[obtuse pebble]

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.

[split wraith]

I need help with an abstract algebra proof that involved showing/proving a that a given function is/is not a sub group of the group g.

G= {G, +}, H={log (n): n in Z, n>0}

[zenith raft]

what's G?

also hiiii

[split wraith]

:0

FRIEND!

G is just like a general group

in this case, it is the addition group

[zenith raft]

hmmm

[split wraith]

i know that some of the ways to prove is something is a subgroup is to see if it is

1. closed with respect to the opperation

2. closed with respect to the inverse

and maybe non-empty..?

le sigh i have 4 problems left...im never gonna get this done before 3 am

[zenith raft]

yesss you can do it

[split wraith]

I rly am trying XD

[zenith raft]

is this exactly how the problem was stated?

[split wraith]

ummmm hold on let me grab the photo

[zenith raft]

so G is the real numbers with addition 🙂

[split wraith]

yes (:

[zenith raft]

so you know the identity in H must be the same as the identity in G right?

[split wraith]

yeah, e has to be equal in both H and G

[zenith raft]

so 0 is the identity in H

what do the elements in H looks like?

[stable rain]

what topic is this

[split wraith]

um....well H is log(n) so its kinda like a curve thing

this is abstract algrbrea

[zenith raft]

can you write a few out?

[split wraith]

yeah i can write out a few log values out

[stable rain]

sounds fun

[split wraith]

its not

[zenith raft]

haha yes it is

[split wraith]

my calculator is dead....i cant rememeber any log values

[stable rain]

lol nice cry

is there a lot of calculations?

[zenith raft]

lol it's ok

,calc log(1)

[warm shale]

Result:

0

[zenith raft]

,calc log(2)

[warm shale]

Result:

0.69314718055995

[stable rain]

i thought complex analysis wouldnt hv any but it has so many series :c

[zenith raft]

,calc log(3)

[warm shale]

Result:

1.0986122886681

[zenith raft]

notice anything?

[split wraith]

well it passes 1

[zenith raft]

if log(2) is in H, what else needs to be in H for H to be a subgroup?

[split wraith]

well n can be anything above 0

if it cant be 0 and 0 is the identity element than does that mean its not a sub group?

[zenith raft]

well 0 is in H

log(1) = 0

so that's ok

what else do we need for H to be a subgroup?

[split wraith]

oh okay, i wish it wasnt lol, it would make this easier

[zenith raft]

haha

[split wraith]

we need the inverse, right?

[zenith raft]

yep

[split wraith]

so we would need the actual value of e

like the irrational number/function?

[zenith raft]

hmm I think it's easier than you are thinking

[split wraith]

you're probably right...

[zenith raft]

is -log(2) in H?

[split wraith]

no

[zenith raft]

then that's all you need, log(2) has no inverse

[split wraith]

maybe?

hold on, can we go over this a little more?

I am confused with the no inverse part

which sounds dumb..

[zenith raft]

ok so for H to be a subgroup it needs to be a group under + and be a subset of R

in order to be a group, one property it needs is that every element must have an inverse

log(2) is in H, but it's inverse (it's unique inverse in R) is -log(2) and that's not in H because -log(2) < 0

and log(n) >= 0 for any positive integer n

[split wraith]

wait is that what the problem said?

the problem said that n>0

it didnt say anything about log(n)</> 0 or anything

[zenith raft]

oh it didn't say that but it's true

log is an (strictly) increasing function

so if log(1) = 0

then log(n) > 0 for any n > 1

[split wraith]

makes sense

and since i cant put any numbers below 0 in it log cant be below 0

[zenith raft]

below 1*

[split wraith]

yeah XD

so, H is not a subgroup because log(n) cannot be be below 0 and therefore there are no inverses?

or something like that

[zenith raft]

sure that works

[split wraith]

since the values for -log(2) do not exist if n>0

cool, ill probably be back....unfortunately..

thank you layla, i owe you big time, this has to be like the 5 time youve helped me

[zenith raft]

haha of course ❤️

[split wraith]

.close

[obtuse pebble]

Channel closed

Closed by @split wraith

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.

[ruby skiff]

find the number of 4 digit natural numbers that can be formed that do not contain the digit 5?

[ruby skiff]

so it would be from 1-9

so there would be 9 possibilities right?

but if we exclude the 5 it would be 8

[wooden cipher]

youre forgetting about 0

[ruby skiff]

wait but is 0 not apart of whole numbers?

[wooden cipher]

for the first digit it is 8, for the other digits it is 9

[ruby skiff]

and not natural numbers/

[wooden cipher]

think about a number like 4063

it is a natural number

[ruby skiff]

oh

[wooden cipher]

which also does not contain 5

[ruby skiff]

wait the answer is somehow 5832

[wooden cipher]

sounds right

let me explain

[ruby skiff]

k

[wooden cipher]

for the first digit, you have 8 choices: 1-4 or 6-9
for the other digits you have 9 choices: 0-4 or 6-9
since the number is 4 digits you have 8x9x9x9

8x9x9x9=5832

[ruby skiff]

wait but how come the first one we exclude 0?

[wooden cipher]

(e.g.) 0123 is not considered a 4 digit number

it is considered a 3 digit number with a leading zero

[ruby skiff]

oh

but 0 is still considered a natural number right?

[ruby skiff]

wait one more question

[wooden cipher]

in some cases, some people consider it a natural number because the definition for a natural number is controversial

like some people say "natural numbers count objects so it starts at 1, instead 0 is a WHOLE number"

negative numbers fall under integers blah blah

most people just say positive integers for those greater than 0 and nonnegative integers for those greater than OR EQUAL to 0

reduces confusion

[ruby skiff]

k thx man

[wooden cipher]

yup np

[obtuse pebble]

@ruby skiff Has your question been resolved?

Channel closed

Closed by @ruby skiff

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.

[soft bloom]

ive tried writing the initial x and y velocity components in terms of the total velocity times cos and sin theta respectively to see if i could derive the time of flight but no luck

[obtuse pebble]

@soft bloom Has your question been resolved?

[soft bloom]

<@&286206848099549185>

[trim locust]

Ok so you’re gonna need suvat

What’s the displacement?

[soft bloom]

300 ft

What does suvat mean

[trim locust]

The equations for projectiles

So yeh
S = 300
U= 0
V= v
A= 800
T=t

That’s the horizontal axis, you see how I got those variables

Specifically u=0

[obtuse pebble]

@soft bloom Has your question been resolved?

[soft bloom]

No what is u

Is it the horizontal acceleration?

Or dy

Oh it’s initial velocity

How is it 0

[obtuse pebble]

@soft bloom Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[past solar]

Hello, Is there a way to know which number system they are using without trial and error?

[obtuse pebble]

@past solar Has your question been resolved?

[past solar]

<@&286206848099549185>

[worn ocean]

[past solar]

First time encountering these kinds of problem, Kind of stuck.

[past flame]

suppose estallarium used base B

then 291=1+9B+2B^2

where we can write B in our very cool decimal number system

do that for the rest

you get a qudratic equation for B

[worn ocean]

well its fairly easy honestly, if you imagine that whatever their base was, their addition at the end comes out to 0 in the final answer, so if u add all the unit digits, you get ur answer :D

[past flame]

tru

[worn ocean]

or u can do what @past flame is saying for better understanding of the base system instead of the problem directly

i'd suggest both

[past solar]

Hmmmm, Thanks, I will try it.

[past solar]

Wdym by this?

[worn ocean]

in any base, to get a 0 at the units digit, you need to have the sum be equal to the base itself

so if u add 1 + 3 + 1 + 4 + 3, u get 12 here

but the professor writes the last digit as 0 in his answer, right?

so it must mean that he's using base 12

[past solar]

OH OK.

[past flame]

well having the sum of units being a multiple of the base works just as well

[worn ocean]

ah yes but then u check tens and hundreds and so on ;-;

[past flame]

ye

[past solar]

Wait, Where did this equation come from?

[worn ocean]

the unit digits of the numbers

[worn ocean]

this case is special since they have a 9 in their system, so all the factors of 12 are eliminated instantly haha

[past solar]

OHH I GET IT NOW, THANKSSS.

.close

[obtuse pebble]

Channel closed

Closed by @past solar

Use .reopen if this was a mistake.

[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.

[wanton kraken]

Need help solving "Find for which values of x and y the expression A=(x+y-2)^2+(2x-y-1)^2+13 has the lowest value"

[wanton kraken]

I'm at system of linear equations

do I put it as
|(x+y-2)^2=0
|(2x-y-1)^2+13=0

I solved it for x and y

ignoring the +13

in the second line

but am I right?

x+y-2=0
2x-y-1=0

[neon anchor]

why the hell did you ignore the 13

[wanton kraken]

what do I do then

I just need a little guidance

[neon anchor]

first solve (2x-y-1)^2

[wanton kraken]

=0

right?

2x-y-1=0

-y=1-2x
y=2x-1

[neon anchor]

no

(2x-y-1)^2=-13

[wanton kraken]

hmm ok

squared trinomial

gimme a min

[neon anchor]

and your question is quite weird and confusing

lowest value of x and y

?

[wanton kraken]

it should be, this is a problem for excellent preparation

gimme a min

let me first

solve

ty

[neon anchor]

why did you even cut this equation into 2

dosent make sense at all

[wanton kraken]

because

and also

pls for the love of god

let me solve

then ping

so because

[neon anchor]

fine

[wanton kraken]

I solved problems of the sort: "Find for which values of x and y the equation is true: (x+2y)^2+(y+2)^2=0"

somehow I have to work with system of linear equations

so

x+2y=0
y+2=0

y=-2

x-4=0

x=4

before the type of problems

I'm currently (this one) solving

[neon anchor]

x+2y=y+2

according to your new equation

[wanton kraken]

Does it become 2x-y-1=-13 ?

or do I have to simplify it first?

[neon anchor]

you distribute the ^2 i suppose

[wanton kraken]

4x^2+y^2+1-4xy-4x+2y

is what I get

=-13

what do I do next?

[neon anchor]

i dont know what youre even looking for

neither ive seen this type of question before

[wanton kraken]

💀

<@&286206848099549185>

nvm solved it

.close

[obtuse pebble]

Channel closed

Closed by @wanton kraken

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.

[little knot]

I don't know the Formula name in english but how do i calcute 2ab in a² - 2ab + b²

[little knot]

is 2ab : 2 x a x b OR 2 x a + b

[drifting wraith]

2×a×b

[little knot]

Okay thankss

[proven zephyr]

and it's (a - b)^2

it's called expansions if im not wrong

[little knot]

yess thats the name i was trying to look for

tyty

[proven zephyr]

you're welcome

[little knot]

How do i apply the formula on the B ?

[inland solar]

Salut Maë. Developes les formules avec les identités remarquables

[little knot]

Salut, oui je sais qu'il faut utiliser les identités remarquables mais je ne sais pas faire sur les fractions

[inland solar]

Remplace 5a/2 par A et 4b/3 par B.

Tu auras alors (A-B)^2

[little knot]

Et je divise ou je laisse les fractions comme elles sont ?

[inland solar]

Developes et à la fin tu remets les fractions

[little knot]

D'accord mercii

[inland solar]

Je fais de mon côté. Donnes ta réponse quand tu as fini

Fini pour moi.

[little knot]

3 secondes, j'ai presque finis

J'ai eu: 6,25a² - 12,5² + 1,77b²

[inland solar]

Ou sont a et b?

[little knot]

J'ai fais 5/2² et 4/3²

[inland solar]

Il manque les carrés de a et b et ab au milieu

5a/2=A

4b/3=B

[little knot]

je refais

5a/2 = 2,5

[inland solar]

Tu as bien A^2-2AB+B^2

Garde sous forme de fraction, c'est plus facile

[little knot]

5a/2² = 25a/4

[inland solar]

5a/2 au carré donne 25a^2/4

[little knot]

Ahh et après je fais la même pour le b

[inland solar]

Pour B pareil

[little knot]

B= 16b²/9

[inland solar]

Yep

[little knot]

Ah le ² va au neuf non?

[inland solar]

Restes le -2AB

(a/b)^2=a^2/b^2

Le 3 est devenu 9

[little knot]

800ab² / 72

[stable rain]

woo cool langauge

[inland solar]

Non

Etape par étape pour -2AB

[little knot]

Poir -2AB j'ai fais 2 x 25a x 16b

Ce qui fait 800ab

[inland solar]

-2×5a/2×4b/3

Les 2 s'annulent

-5a×4b/3

Donc -20ab/3

Pourquoi as-tu viré les fractions ?

[little knot]

Non j'ai commencer par les numérateurs

Ah donc 40a/ 12b

[inland solar]

Y'a pas a faire de carrés dans -2AB.

[little knot]

là j'ai pas fais de carrés, J'ai fais 2 x 5a x 4b= 40
Puis 2 x 2 x 3 = 12

C'est bon ?

[inland solar]

Pourquoi tu multiplies le dénominateur par 2?

[little knot]

Faut annuler le 2 quand il y a plusieurs?

[inland solar]

Pour simplifier, oui

Quand il est en haut et en bas

[little knot]

tu as mis 4b ?

[inland solar]

4b/3, oui

Il est pas joli mon b? 😥

[little knot]

Il est originale 🤣

Du coup le résultat c'est 20ab/3

okay billy

[inland solar]

Burger, soda, cowboy

Can you let us , bill

Bye.

[little knot]

on peut faire le 1er aussi?

[inland solar]

Donc Maë, écris toute la solution.

[little knot]

la solution? genre le résultat

[inland solar]

Peux-tu la remettre la 1ère question, elle est perdue en haut maintenant.

[little knot]

20ab/3 = 6ab

[inland solar]

Oui le résultat.

Ouf!!!

[little knot]

c'était pas si compliqué ça va

[inland solar]

Je voyais plus ça

[little knot]

166²/9 ? il vient d'ou

ah

Si c'est compliqué enfait

[inland solar]

16b^2/9

Tu es fâché avec mon b, on dirait.

[little knot]

Il me porte a confusion 😂 mais j'arrive a le distinguer maintenant

et le résultat c'est..

[inland solar]

Y'a pas, faut juste développer, non?

[little knot]

21ab/10

ah oui

Ok j'ai pas besoin de faire tout ça

on peut passer au 1er

[inland solar]

Ok

Meme technique

[little knot]

(4x² - 8x + 4)

[inland solar]

Oui pour la première parenthèse

L'autre maintenant

[little knot]

• (9 - 12x + 4x)

[inland solar]

-8x pas -8x^2

[little knot]

je continue a développer ?

[inland solar]

Non

[little knot]

Non ou?

3²= 9
2x² = 4x²

[inland solar]

9-12x+4x^2

[little knot]

effectivement

là c'est bon normalement

[inland solar]

Maintenant assembles les 2 parenthèses

Je fais de mon côté

La réponse est courte.

[little knot]

11

11x

[inland solar]

Nope!

[little knot]

11x²

Je refais

1 ?

1x

[inland solar]

4x-5

[little knot]

Je peux voir ton calcul pour voir comment tu as trouver ça

[inland solar]

Je saute des étapes que je fais de tête.

[little knot]

J'avais oublier qu'il fallait annuler..

moi j'avais calculer les 2 parenthèses Developper

[inland solar]

Refais le à ton rythme

Montres, stp

Je veux voir où est ton erreur de logique

[little knot]

1. la première parenthèse déjà developper

2. la 2eme (aussi déjà developper)

[inland solar]

Ça c'est bon

Et après

[little knot]

0x - 1x = -1x

mais toi tu avais écris un autre résultat

[inland solar]

C'est quoi ça ????

[little knot]

Ben j'ai soustrais ça

[inland solar]

Oh je comprends

Ouhlala

[little knot]

fallait me dire qu'il fallait seulement assembler les parenthèses d'origine

[inland solar]

C'est pas ça.

Tu ne peux pas additionner carrés de x, x et constante comme ça.

[little knot]

Alors j'enlève juste le x

[inland solar]

Non

[little knot]

Je refais ton calcule

[inland solar]

J'essaye de trouver une analogie pour te faire comprendre.

Je vais le refaire sans griller d'étapes.

[little knot]

Comment tu as trouver (2x-2)² = 8x + 4 ?

(2x - 2)² = 0 ?

Ah je sais, la règles des signes

J'ai fais ça mais j'ai pas trouver 4x -5 ..

[inland solar]

Je pense pas avoir brûlé d'étape.

Le plus important, c'est que tu ne peux pas additionner des x^2 avec des x et avec des nombre.

J'ai rajouté une étape

[little knot]

Pourquoi 2x,

2x² = 4x ?

[inland solar]

Je regroupe les x^2 ensembles, puis les x puis les nombres. On mélange pas les torchons avec les serviettes.

[little knot]

et le 8x + 12x tu l'a annulé ?

[inland solar]

-8x+12x

[little knot]

ah oui donc = 0

[inland solar]

(-8+12)x

(12-8)x

[little knot]

J'ai tout compris maintenant

[inland solar]

4x

Faut regroupez x^2, x, et nombre.

[little knot]

Ils demandent une 2ème méthodes, je suppose que c'est (a+b) (a-b) = a² - b²

[inland solar]

Ouaip

[little knot]

j'avais essayer hier soir et ça m'a fait 4x² - 4x²

[inland solar]

Si tu te mélange pas tu obtiens 4x-5

[little knot]

Bon je recommence pour avoir 4x-5

[inland solar]

Je develope de mon côté sans sauter trop d'étapes.

Fait, 4x-5 pareil

[inland solar]

Du tout!!!

[little knot]

montre

[inland solar]

(2x+2) est a

(3-2x) est b

[little knot]

J'ai factoriser enfait

j'ai pas développer

Attend non puisque la formule c'est (a+b) (a-b) = a² - b²
Et (a+b) (a-b) c'est (2x-2)² - (3-2x)²

[inland solar]

Faut que tu arrêtes de mélanger les x^2 avec les x et les nombres.

[little knot]

Ok j'ai compris le calcule

[inland solar]

Faut pas mélanger les torchons avec les serviettes, jamais.

C'est ton erreur récurrente, dans notre discussion

[little knot]

Faut que je regroupe quoi encore

Les x ?

[inland solar]

Tu regroupes les x^2 avec les x^2, les x avec les x, et les nombres sans rien avec avec les nombres sans rien avec.

Quand tu lis , remplace x^2 par patates, les x par pomme.

[little knot]

D'accorddd Je vais faire ça, est-ce que tu sera disponible plus tard? je vais faire une pause mais j'ai besoin d'aide dans d'autre exercices

[inland solar]

Je suis en Corée, il est 1h13 du matin, je vais aller faire dodo.

[little knot]

Ah oui il est tard

Ben un autre jour alors, si tu veux tjr

[inland solar]

Pas de soucis, mp moi si je suis en ligne. Bonne journée, moi je vais pioncer.

[little knot]

Bonne nuit!

[obtuse pebble]

@little knot Has your question been resolved?

[obtuse pebble]

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.

[pearl aurora]

A group of 40 campers decided to buy a gift for the guide.
10 more campers joined the group, so each camper paid two shekels less
of the amount planned to be paid. In total, the amount of money collected was 20 shekels more
from the amount needed to buy the gift. How much money did each pay?

[pearl aurora]

How to solve this?

??

[devout sable]

Yes me too

[pearl aurora]

<@&286206848099549185>

[devout sable]

!15m

[obtuse pebble]

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.

[pearl aurora]

????

[devout sable]

What have you tried

[pearl aurora]

40 = x and 50 = x - 100

idk how to solve this

because this does not make sense

[devout sable]

Wait what

I saw different question earlier

[pearl aurora]

Yeah my mistake, I copied the wrong question

?

1 hour...

???????

[obtuse pebble]

@pearl aurora Has your question been resolved?

[pearl aurora]

??

[obtuse pebble]

@pearl aurora Has your question been resolved?

[pearl aurora]

2 hours

[obtuse pebble]

@pearl aurora Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[winter geyser]

Can someone help me with this?

From my linear algebra class, I know i'm supposed to come up with equations to create a system of equations

[normal turtle]

that means its min and max points are those coordinates right

[winter geyser]

yeah

[normal turtle]

so u know then the gradient is 0 when x = those numbers

[winter geyser]

but the linear algebra needs to be applied here, which is what I'm struggling with

[winter geyser]

yes

[normal turtle]

so u gotta use matrices?

[winter geyser]

yes

I did something weird and it seems wrong

let me show my work

[normal turtle]

okay go for it

[winter geyser]

I plugged the numbers and got 2 equations, then I took the derivative and plug again and got 2 more equations

but this feels wrong

i ended up with a quadratic equation 💀

we only have an online meeting once in a week, we basically have to teach ourselves linear algebra 😭

[normal turtle]

so youre using reduced echelon form?

[winter geyser]

yes

I know my work is chaotic

[normal turtle]

okay so for that you dont actually have to make it entirely the identity matrix

this is a trick i was taught

only make everything underneath the line of 1s in the identity matrix a 0

and then use simul and subbing in to work it out from there

[winter geyser]

okay I will try that now

but is this approach a good idea?

taking the derivative as well

[normal turtle]

no cause the derrivate finds the equation of a tangent to the line

so its a different equation

subbing in another number to original eq is better

[winter geyser]

Im only given two pairs

is that enough?

where do I find more pairs of numbers

[normal turtle]

hm yeah

sorry man im stumped ill see if i can think of anything

its like half 10 so im half asleep ahah

[winter geyser]

no worries man, thank you still! 🙏

[normal turtle]

dudeeee

[normal turtle]

when its the differential

u know its equal to 0

as its the turning points

points of inflection

[winter geyser]

Yeah

[normal turtle]

so

make it equal to 0

not 2

and stuff

wait

no

cazoz

wait yeah u cant do differential

cause its another equation

hm

could u plug in some random numbers and give it a go

[winter geyser]

I’m currently in the online tutoring center (apparently my college has that)

[winter geyser]

this is exactly what the guy just did

but he didnt finish it lol, just showed me that

im gonna do it and see if the website accepts the result

[normal turtle]

ahah fair enough okay

[normal turtle]

damn useful

[winter geyser]

yeah it was quick too, im gonna be there all the time now

:D

[normal turtle]

lucky you man i dont have shet ahah

[winter geyser]

gonna try this, brb

[normal turtle]

okay see how it goes

then show me im curious

[winter geyser]

that was it!

[normal turtle]

what making the differentials equal 0?

[winter geyser]

yeah i just set this up and solved the matrix

thanks a lot for the help!

[normal turtle]

damn nice well done

ahah i did nothing lol

but have a good day man

[winter geyser]

you were on the right path with it lol

you too man!

.close

[obtuse pebble]

Channel closed

Closed by @winter geyser

Use .reopen if this was a mistake.

[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.

[woven shoal]

supposedly this problem is a lot easier with Parsavels

[woven shoal]

the integration seems like a pain to brute force

how would you use parsevels

[wild swallow]

e^imt form an orthogonal basis

so the norm of g(t) is just the sum of the squares of the coefficients

taking modulus ofc cuz you have complex coeffs

[woven shoal]

so its just 1/2pi int 0 to 2 pi of g(t)^2?

im confused how parsevels comes into play here

[wild swallow]

that integral is the squared norm of g wrt the inner product

[woven shoal]

correct

[wild swallow]

to compute the norm of a vector

where you have an orthonormal basis

you take the sum for the squared coeffs

[woven shoal]

I know how to compute the norm however my instructor said to use parsevals, and that isnt parsevals right?

i mean id have to find the ak values

so basically take the integral with respect to e^ikt

• g(t)

then just square that right

whatever computes

basically that

then square the result

would be parsevals right?

[wild swallow]

you know the basis

it's just e^imt

[woven shoal]

correct

[wild swallow]

you can see that g is a linear combination of the basis

so you can see the coefficients

there's no need to compute integrals to get them

the coefficient of 1 is 2

the coefficient of e^-3it is 6

the coefficient of e^5it is -i

add the sum of squares* and you're done

(not actually sum of squares but sum of square absolute values)

[woven shoal]

so essentially it would be 4 + 36 -1

or am I totally misunderstanding

[wild swallow]

|-i|^2 = 1

[woven shoal]

+1 **

correct

[wild swallow]

you never subtract when calculating norms

that's it

[woven shoal]

so 41?

[wild swallow]

that's all there is to it

[woven shoal]

huh we were never taught that

[wild swallow]

well your formulas suggest otherwise

[woven shoal]

yeah, thats true I guess I just didnt understand it was that simple

that we were GIVEN the basis

[wild swallow]

i mean

how else did you think extracting the coefficients worked

you need to take an inner product with the basis in the first place

[woven shoal]

that makes sense

thanks for the help

[obtuse pebble]

@woven shoal Has your question been resolved?

[obtuse pebble]

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.

[plain stag]

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

[timid silo]

I did 10x8

Got 80 Multiplied it by 12 and got the answer is that correct?

[plain stag]

it's asking for the perimeter. Do you know what that is?

[timid silo]

Yes

[plain stag]

what is it?

because your work calculates something different

[timid silo]

Ohh I see I’m stupid the answer should be 48

[plain stag]

it should

48in because math teachers are anal about including units

[timid silo]

😭😭

Could u help me with this please I have no idea what I’m doing

[plain stag]

can you show the figure at the right?

[plain stag]

ok cool

[warm shale]

Steakanator

[timid silo]

Yes angle RTS

[plain stag]

can you draw the angle on that figure?

[timid silo]

Yea? Does it form a L

[plain stag]

it depends on the size of the angle

[timid silo]

Yea it forms an “

L*

[plain stag]

perhaps more important, do you know what this means?

[timid silo]

I don’t know what the thing in between the letters mean

[plain stag]

it means "perpendicular"

[timid silo]

Ohh alright

[plain stag]

for two line segments to be perpendicular, what must the angle between them measure?

[timid silo]

I don’t know tbh

[plain stag]

what is the defining characteristic of a right triangle?

[timid silo]

90 degrees?

[plain stag]

yes

two line segments are perpendicular when the angle between them measures 90 degrees

[timid silo]

Ohh ok

So what do I do?

[plain stag]

you have an expression for the size of the angle, and you know what it must be numerically

all that's left is to find x that makes them equal

[timid silo]

Can you just tell me the answer pls this is to stressful

[plain stag]

• When asking for help, do not insist on getting just the answer; we are here to help you learn, not do the work for you.

[timid silo]

Ok do you know a place to go where I can actually get the answers instead of wasting my time

[plain stag]

just getting the answers would be wasting your time

going through the problems and actually learning the techniques is never a waste

[timid silo]

It literally is tho I’m never gonna use any of this in the real world lol but ok💀

[plain stag]

ok then, good luck

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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.

[timid silo]

.reopen

[signal marten]

hello there pops

[signal marten]

f(x)= (x +1)
j(x) = x²- 1
g(x) = (x-1)
k(x) = 2x² + 3x + 1
l(x) = 2x² - x – 1

find : (j ○ f)(4)

[obtuse pebble]

@signal marten Has your question been resolved?

[amber meteor]

Ok so do you know how to factor $x^2-1$

[warm shale]

Absolute Chips

[amber meteor]

And doing long division

@signal marten