help-10

[leaden ibex]

Didn't we already have this question?

I told him the same thing

[vapid hamlet]

$\sqrt{1+\frac{4}{9}x^2+\frac{4}{9}y^2}=\sqrt{\frac{4}{9}\cdot\frac{9}{4}+\frac{4}{9}x^2+\frac{4}{9}y^2}$

[warm shale]

Zanarcane

[ionic cedar]

thank you

[ionic cedar]

I ran into further issues. I wouldn't consider this a helpful thing to say

Got the rest. Thank you @vapid hamlet

.close

[obtuse pebble]

Channel closed

Closed by @ionic cedar

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.

[opal ivy]

Looking for help regarding generating a turing machine

[opal ivy]

Im trying to describe a turing machine that accepts the language www|w∈{a,b}*

i understand how turing machine works but just having a hard time trying to break this down into steps

the language pretty much is just taking some word/string that is any number of a's and b's, then making sure it repeats 3 times, but again just having some trouble

[obtuse pebble]

@opal ivy Has your question been resolved?

[obtuse pebble]

@opal ivy Has your question been resolved?

[opal ivy]

.close

[obtuse pebble]

Channel closed

Closed by @opal ivy

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.

[obtuse pebble]

@blazing meteor 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.

[sudden otter]

I know that the given angle and the opposite one have to equal 90 degrees but I dont know how to do that in this form. I also dont really know what to do after that 😅 (plz ping)

[delicate bay]

@sudden otter I believe you can use soh cah toa for this

[sudden otter]

yes but how

I haven't done this type of problem before

[delicate bay]

so you are already given one side of the triangle

which side

?

[sudden otter]

the hypotenuse

[delicate bay]

and which of the three soh cah toas use hyp?

and also opposite because that is what the question is asking

[sudden otter]

CAH?

[delicate bay]

yes, cah does use hyp!

but we also need opp

because that is what the question asks

[sudden otter]

so can we just do x/34.5?

or something like that. because we dont know the other side.

[delicate bay]

yes

and we already know the angle too

so we just put it all together

what would the eq look like?'

[sudden otter]

how?

[delicate bay]

we have sin(pi/8)=x/34.5

does that make sense?

[sudden otter]

ah right

that makes sense

[delicate bay]

so we need to solve for x

how can we isolate the variable?

(with algebra)

[sudden otter]

multiply both sides by 34.5

[delicate bay]

yes

now u just need to type it all in your calc

making sure it is in radians and not degrees

[sudden otter]

something like this?

[delicate bay]

the left side doesn't look right

it should just be x

wait, i think i get what you have

thats fine

[sudden otter]

yeah ok I was confused

um

then?

[delicate bay]

just type the RHS into your calc

[sudden otter]

RHS?

[delicate bay]

right hand side

[sudden otter]

ah

I got 13.2025

cool its right!

[delicate bay]

looks good

great!

[sudden otter]

then for the second one its the same thing just a different property

[delicate bay]

yes

[sudden otter]

thanks for explaining it to me step by step it helps

[delicate bay]

np, happy to help

[sudden otter]

I can do the other one on my own

.close

[obtuse pebble]

Channel closed

Closed by @sudden otter

Use .reopen if this was a mistake.

[sudden otter]

.reopen

[obtuse pebble]

✅

[sudden otter]

@delicate bay oh sorry I forgot the reason I asked in the first place XD

I dont know how to find the other angle

But both of them should be equal to 90

[delicate bay]

which angle should be equal to 90?

[sudden otter]

the known and the acute

repost

[delicate bay]

that doesn't make sense because a triangle's three angles must equal 180.

[sudden otter]

yeah but we know one is 90. so the other 2 must be 90 together.

Sorry if I didnt word that right.

[delicate bay]

true, so for the third question you can do pi/2 - pi/8

[sudden otter]

How do you know its pi/2?

[delicate bay]

because 90 degrees is equal to pi/2 (in radians)

[sudden otter]

oh right

[delicate bay]

it is easier to visualize with the unit circle or graph. would you like me to show u?

[sudden otter]

forgetting my unit circles

[delicate bay]

no worries

[sudden otter]

so thats 3pi/8

[delicate bay]

yes

[sudden otter]

cool thanks again!

[delicate bay]

for the third question

np!

[sudden otter]

.close

[obtuse pebble]

Channel closed

Closed by @sudden otter

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[fiery yew]

Is my math correct?

[fiery yew]

I simplified the expression on the top left.

[obtuse pebble]

@fiery yew Has your question been resolved?

[fiery yew]

<@&286206848099549185> Is anyone available?

[delicate bay]

@fiery yew which is the question and which is your final answer?

[fiery yew]

My question is \frac{\frac{1}{x}-\frac{2}{3}}{\frac{1}{x}+\frac{3}{4}} simplifies to

$\frac{\frac{1}{x}-\frac{2}{3}}{\frac{1}{x}+\frac{3}{4}}$

[warm shale]

Kenshin H.

[fiery yew]

$\frac{\frac{1}{x}-\frac{2}{3}}{\frac{1}{x}+\frac{3}{4}}=\frac{4(3x-2)}{3(4+3x)}$

[warm shale]

Kenshin H.

[fiery yew]

Now it's better

[delicate bay]

One sec. I’ll look

Yeah that looks fine

@fiery yew

[fiery yew]

Thanks!

.close

[obtuse pebble]

Channel closed

Closed by @fiery yew

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.

[glad compass]

stuck on this problem

discrete mathematics if anyone can help with that

<@&286206848099549185>

[short spruce]

• After 15 minutes, feel free to ping @Helpers.

[glad compass]

my bad

[keen cave]

Do you know what does symbols mean?

[glad compass]

i believe its a variable placement

honestly one of the hardest questions I have ever seen

its a logic symbol

sorry

quantifiers sorry

[obtuse pebble]

@glad compass Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

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.

[timid silo]

for a derivative function, if i have

[timid silo]

function 2x^2 -3x for x < or equals 0 and 5x^2 -3x >0, for acumulation point x0 = 0 which one do I choose?

[obtuse pebble]

@timid silo Has your question been resolved?

Channel closed

Closed by @round agate

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.

[fast horizon]

How would I solve this using the Law of Sines?

[fast horizon]

what is truly confusing me is determining if there should be no, one, or two triangles

[pine sail]

There should be A triangle.

Atleast try drawing something.

[fast horizon]

h = 17sin55
h = 13.93

h < c < a
(13.93 < 15 < 17)

[pine sail]

Now what is your original question?

What do you have to figure out?

[fast horizon]

solve triangle ABC

[pine sail]

Solve what?

For the sides...
Angles...

?

[fast horizon]

both

[pine sail]

Yes both.

Got it.

What does the sine rule say?

[fast horizon]

we didnt go too in depth on that, but i know sinA/a = a/sinA

[pine sail]

Sure.

$$\frac{a}{\sin(A)}=\frac{b}{\sin(B)}=\frac{c}{\sin(C)}$$

[warm shale]

What the hell am I doing here?

[pine sail]

Just put values now.

You have the third ratio.

Right?

[fast horizon]

$$\frac{17}{\sin(A)}=\frac{b}{\sin(B)}=\frac{15}{\sin(55)}$$

[warm shale]

itsimod

[pine sail]

Correct.

Now leave the middle one for a bit.

$$\frac{17}{\sin(A)}=\frac{15}{\sin(55)}$$

[warm shale]

What the hell am I doing here?

[fast horizon]

A = 68.13 degrees

[pine sail]

Now you know B too, right?

[fast horizon]

180 - (68.13 + 55)

[pine sail]

Correct.

[fast horizon]

B = 56.87

[pine sail]

Now use this again.

To ultimately figure b.

[fast horizon]

b = 15.34

$$\frac{17}{\sin(68.13)}=\frac{15.34}{\sin(56.87)}=\frac{15}{\sin(55)}$$

[warm shale]

itsimod

[pine sail]

Sounds about correct.

That was it right?

Your question?

[fast horizon]

sort of

the question makes you solve for two triangles

[pine sail]

Based on this, see I can't say anything.

[fast horizon]

here is the answer key for this question

im confused on how to know when it is a two-triangle, one-triangle, or no-triangle question

[pine sail]

It means,

Because the height is less than the other sides.

An obtuse triangle is also possible.

[fast horizon]

yeah im confused on that

[pine sail]

What about it?

[fast horizon]

my teacher explained it like this

one sec

[obtuse pebble]

@fast horizon Has your question been resolved?

Channel closed

Closed by @fast horizon

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.

[vale quartz]

How can I prove the equality in the second statement?

[void pelican]

that's a riemann sum

it's the definition of an integral

[vale quartz]

so proof by definition?

[void pelican]

there's not even a proof

but sure

[vale quartz]

Seems kinda iffy to me because I've heard of integration being defined in other ways

[void pelican]

maybe you need to show how it is a riemann integral?

hmm

is this for a real analysis class?

[vale quartz]

Nah, numerical analysis. Here's the actual question

Approximate the integral of f(x) on [a,b] by a piecewise constant interpolation. Use a uniform grid with n subintervals (pieces) and the left end point of each subinterval as the interpolation node. What happens when n goes to infinity? Will the results change if you use the right end point of each subinterval instead?

[void pelican]

hmm idk then

maybe ask in #numerical-analysis

[vale quartz]

Aight

Since this isn't an analysis course, I'm just gonna assume that saying the words "this is a riemann sum" is good enough

[void pelican]

eh maybe there's something more

ask in that channel to stay safe

[vale quartz]

will do, thanks

.close

[obtuse pebble]

Channel closed

Closed by @vale quartz

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.

[misty valve]

Not sure how to approach this one

This lesson I learned how to find critical numbers

[compact shadow]

Just draw a line

I mean like segment Connecting those two points

You will see that is an example

[misty valve]

Ok from 0 to 2 right?

[compact shadow]

Yeah

(0,10) to (2,2)

[misty valve]

Ok so next would be to get the equation for the line

So 4 is the slope I think

So (y-10)=-4(x-0)

[compact shadow]

-4

[misty valve]

Oh

[compact shadow]

Good

[misty valve]

Y= -4x +10

[compact shadow]

Yeah

[misty valve]

So derivative is -4

Which is less than 1 but how do I know if it's for all x? X isn't part of the derivative

[compact shadow]

?

f’(x)=-4 for any 0<x<2

[misty valve]

So the answer would be yes right?

[compact shadow]

Yeah

[misty valve]

Thanks

.close

[obtuse pebble]

Channel closed

Closed by @misty valve

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[zinc cliff]

need help with this Bad Buoy exponential
i have to draw it as a graph but my y int i got must be wrong because its not letting me put it in (its some long decimal garbage)

[zinc cliff]

bc like. if i find the y int by putting 0 in for the x then that means my y int is equal to 3^-4 but of course it comes out weird

wait nvm lol i got it

.close

[obtuse pebble]

Channel closed

Closed by @zinc cliff

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.

[sudden otter]

I asked for help on a similar problem but the guy didnt explain himself very well.

[tacit hornet]

$\csc \theta =\frac{1}{\sin\theta}$

$\cos^2 \theta=1-\sin^2 \theta$

[warm shale]

◥▶_◀◤

[tacit hornet]

Rest all can be derived from sin and cos

[sudden otter]

okie thank you

.close

[obtuse pebble]

Channel closed

Closed by @sudden otter

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.

[chrome smelt]

how would i go about solving this

i know log base a of x multiplied by log base a of y is log base a of x+y

[plain stag]

Other way around

[nocturne minnow]

Not exactly correct

[chrome smelt]

wait wdym

[obsidian isle]

log_1(x) = y
x=1^y

This makes me deeply uncomfortable

[chrome smelt]

im so lost

wait

[obsidian isle]

Knowing that there is no y in C that satisfies this equation for non one x

We need a new field extension of C that satisfies this relation

Like infinite numbers but with distinctions between different infinities

[chrome smelt]

log base a of xy = log base a of x + log base a of y*

[obsidian isle]

Does that make sense?

[chrome smelt]

whats C

[obsidian isle]

Complex numbers

Nvm i think this is a bit beyond you right now.

[chrome smelt]

lol

fasho

i know we learn that a bit later

log base 5 of 7k

i just need to break that down

[obsidian isle]

Ok let help you out

Log rules are the exact same as exponent rules

Because logarithms are an inverse of exponentiation

[chrome smelt]

yea

[obsidian isle]

So let
log_5(7k) = x

Then we have:

[copper latch]

$b \log_n x = \ log_n x^b$

[warm shale]

Deep.

[obsidian isle]

7k = 5^x

[chrome smelt]

yea

[nocturne minnow]

?

[copper latch]

Umm didn’t mean to ping you

But wanted to add another property

Oohh shit

It is already there

My bad

[chrome smelt]

@obsidian isle

if u can explain how this works

i think ill be able to figure it out

[nocturne minnow]

Apply the log properties

[nocturne minnow]

Isn't that rule 3 from my diagram?

[chrome smelt]

im confused

[nocturne minnow]

See if this helps
https://youtube.com/watch?time_continue=9&v=OIz-5MyJA3g&feature=emb_title

[chrome smelt]

aight

log_5(7)

• log_5(k)

7log_5

• klog_5

[obsidian isle]

Let 7 = 5^p and k = 5^q. Then:
log_5(5^p × 5^q) =
log_5(5^(p+q)) =
p+q =
log_5(7) + log_5(k)

[chrome smelt]

oh

ok i get it

thanks

bro lol

@obsidian isle @nocturne minnow u guys were right that was easy

idk why i didnt see it

[obsidian isle]

Yeah it really is. It is important to see that the log laws are really just exponent laws

Then it all clicks

[chrome smelt]

yea

its basically like saying

a^(3+k)

break it down

a^3 + a^k

i mean

yea i think?

[nocturne minnow]

Was that video helpful?

[chrome smelt]

it was @nocturne minnow

[obsidian isle]

a^3 × a^k

[chrome smelt]

yea

x

thats what i meant

i just looked back at the exponent laws thing i have

and realized

[obsidian isle]

And if you want to go a step further, try wrapping your head around this

Logarithms decrease the order of the operation by one

It turns multiplication into addition and exponentiation into multiplication

Are you familiar with the concept of the degree of an operator?

[chrome smelt]

i am not

im just now learning log properties

@obsidian isle u think i can learn log properties, integrals and lagrange

within a week

[obsidian isle]

Multiplication is repeated addition, right? 3×4 = 3+3+3+3

[chrome smelt]

and the area underneath the curve

yea

[obsidian isle]

And exponentiation is repeated multiplication: 3^4 = 3×3×3×3

[nocturne minnow]

Within a week? That's a tough task to do if that's all new stuff for you

[obsidian isle]

Yeah shouldnt be too hard

Go for it

[nocturne minnow]

FYI, area under a curve and integrals are related

[chrome smelt]

yea

do u think i can make a groupchat with u guys and send questions there?

[nocturne minnow]

No, I don't suggest doing that

[chrome smelt]

aight

[nocturne minnow]

If you have more questions, just post it and someone will be by to help you out

[chrome smelt]

alr bet

is it - because 7k is on the denominator

[obtuse pebble]

@chrome smelt Has your question been resolved?

Channel closed

Closed by @chrome smelt

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.

[sudden otter]

Ok so I tried making the top section into one triangle and doing a SAS then finding the area.

Then I tried to make the bottom section into the same thing (and assumed the missing angle was 100)

idk what I did wrong?

[obtuse pebble]

@sudden otter Has your question been resolved?

Channel closed

Closed by @sudden otter

Use .reopen if this was a mistake.

[sudden otter]

.reopen

[obtuse pebble]

✅

[sudden otter]

<@&286206848099549185>

[tacit hornet]

@sudden otter u can easily find one of the diagonals and then use Herons formula to find area of both triangle

[obtuse pebble]

@sudden otter 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.

[dim root]

I have 6 items and for every item i get, only a few specific ones may follow.
If i have item 1 then i can only get item 1, 2, or 3.
If i have item 2, i can only get item 1, 2, 3, 4
If i have item 3, i can only get item 1, 2, 3, 4, 5
If i have item 4, i can only get item 2, 3, 4, 5
If i have item 5, i can only get item 3, 4, 5
How many possibilities are there of different item combinations

[dim root]

If my question is unclear, sorry i will try to further explain

[obtuse pebble]

@dim root Has your question been resolved?

[cinder wind]

If u draw a grid out with 6x6 then highlight those numbers specifically, would it answer ur question

I’m outside rn but I’m assuming it’s x/36

[dim root]

i got around 2000

do you think thats far off?

[cinder wind]

Nah it could be right

[dim root]

cheers! thats about the method i did as well

[cinder wind]

It’s a weird question ngl 😂

[dim root]

well, if you knew what it was for it would make sense

[cinder wind]

It quite tricky

True

[dim root]

its practical

.close

[obtuse pebble]

Channel closed

Closed by @dim root

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.

[timid silo]

hi can i please get help on proving this is a subspace?

i understand it needs to meet closure under addition, scalar multiplication and zero vector but im so confused how to do it

<@&286206848099549185> please help me 😦

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

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.

[timid silo]

I don’t know what I’m doing wrong ?

[timid silo]

She’s saying it’s wrong but I rechecked

d^3 is the issue but why- it seems right

[silent adder]

i think you forgot to write c in your final answer

[timid silo]

Oh ok I see it now , so 16c to the 9th or?

[silent adder]

$$-16 c^9 d^3$$

[warm shale]

Bunnies_

[timid silo]

Ok yeah thank you 🙏 .

[obtuse pebble]

@timid silo Has your question been resolved?

Channel closed

Closed by @upper sphinx

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.

[drowsy girder]

And whats the question

[austere gulch]

find first 5 term

[novel knoll]

So start with finding u_2?

[austere gulch]

yea its 5

how to find third

[short zodiac]

Using u_2

It's recursion bro

Are you familiar with it?

[austere gulch]

not quite

[short zodiac]

Read a Little bit about it

[austere gulch]

ooo

sub the previous term into the u

[novel knoll]

It says in the formula that u_3=2 * u_2-1?

[austere gulch]

yea i get it already thks

.close

[obtuse pebble]

Channel closed

Closed by @austere gulch

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.

[rough parrot]

Can any one help

I think thats true

<@&286206848099549185>

[obtuse pebble]

@rough parrot 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.

[wispy shadow]

how does one express in pure math notation "$a^2+b^2$ is greater than 0 for all a and b"?

[warm shale]

madlor

[wispy shadow]

$a^2+b^2 < 0 \forall a,b$

[warm shale]

madlor

[wispy shadow]

is it this simple?

[somber vapor]

I think so

You could also say >0,[ a,b€ C]

But I think yours is prettier

[wispy shadow]

found a hole in the statement btw

for a=b=0 it is equal to 0

loll

also breaks for complex numbers oof

.close

[obtuse pebble]

Channel closed

Closed by @wispy shadow

Use .reopen if this was a mistake.

[wispy shadow]

familiarize urself with how the server works

this channel is technically vacant but still listed as occupied

[wise granite]

Ah, my bad

[wispy shadow]

no worries

[wise granite]

But where can I get help?

[floral sonnet]

turn the adult ticket price and child ticket price into variables, then solve the system of equations

[wise granite]

I tried doing that, it didn't work out 😭

[wispy shadow]

#❓how-to-get-help <- probably worth reading

[wise granite]

Ok thanks

[wispy shadow]

glgl

[floral sonnet]

what’s the result

[wise granite]

I don't remember, I already erased it. But the result were both of the variables still there

If that makes sense

[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.

[wispy shadow]

what do you know about probability distributions clavite?

you're gonna have to put in some effort here

are you familiar with what probability is?

yes

reminder:

i am happy to help you find the solution, its not complicated

no worries, do you have some intuition as to what probability means?

chance of something happening or whatever

a probability distribution is in a sense a table of possible outcomes

it is the collection of possible things that can happen, and how likely they are to happen

with this understanding of what a probability distribution is, can you decipher what they are really asking here yet?

ohhh

F

so are you officially out of time?

anyways since its a probability distribution, something has to occur

so all the probabilities must sum up to 1

thats how u determine the probability when x=4

[obtuse pebble]

@timid silo Has your question been resolved?

[short spruce]

<@&268886789983436800>

[ocean topaz]

.close

[obtuse pebble]

Channel closed

Closed by @ocean topaz

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.

[dry ginkgo]

need help with 5bii

[dry ginkgo]

if someone could show me how to do the 1st one then ill try to do the rest

i found 4 for the first one but not sure if im right

[obtuse pebble]

@dry ginkgo Has your question been resolved?

[obtuse pebble]

@dry ginkgo Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

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.

[left needle]

is this incorrect, i think it is but the solution says its correct

[left needle]

also here, is the second interval just a set {1.3}

[unreal wharf]

It's correct

[left needle]

how, its union, it should be <10,22>

[unreal wharf]

Oh wait lol I noticed wrong one
I thought it was [11, 21) U (12, 22)

Yes it shall be (10, 22)

[left needle]

tnx

[unreal wharf]

Yes it shall stay the same

[0.3, inf) has {1.3} element in it

[left needle]

yes but does <1.3] mean just {1.3}

[unreal wharf]

Idk lol we use (a, b] notation of an interval

(1.3] doesn't make sense

[left needle]

yea, us too idk what this is

[unreal wharf]

Either they mean (1, 3] or {1.3}

Ig the mistake was done during typing

[left needle]

also, would you know how to prove if a^3>b^3, then a>b, its logical i dont know how to prove it

[left needle]

probably

actually wait

[unreal wharf]

If a³>b³
Then a³-b³>0
a³-b³ = (a²+b²+ab)(a-b)
So (a-b)(a²+b²+ab)>0

Which is only possible if
a-b>0 and (a²+b²+ab)> 0 .... (i)
or a-b<0 and (a²+b²+ab) <0.... (ii)

[left needle]

2nd line, for eg. a=-5 b=-2, -2ab=-20, -ab=-10, so -2ab is not >=-ab

[unreal wharf]

Oh wait I took the wrong case
Do RMS≥GM

But wait it can't be done like that too because for that a>0, b>0

[left needle]

why does it have to be >0

it can be negative

any real number

[unreal wharf]

Because assume a<0 and b>0
Then for GM you shall write (ab)^1/2

So we can't use that approach

[left needle]

also, sorry for jumping around
shouldnt this be (a<=0 and b>=0) or (a>=0 and b<=0)

[unreal wharf]

For which part?

[left needle]

is my solution correct

the results say (a>=0 and b<0) or (a<=0 and b>0)

[unreal wharf]

Yes

[left needle]

but b can be 0 too

[left needle]

thanks

now about the previous one could i just explain like this, if we "exponent"(idk how to say in english) both sides of an inequality, the validity remains because the sign doesnt "flip" since the exponent is an odd number and a bigger number multiplied by itself 3 times is still bigger than the smaller number multiplied by itself 3 times

[unreal wharf]

Ok hmm a²+b² + ab must be greater than 0

@left needle

The reason is

a² + b² + ab = 1/2 ( 2a² + 2b² + 2ab)

1/2 ( a² + b² + 2ab + a² + b²)

It becomes 1/2 { (a+b)² + a² + b²}

(a+b)²>0 , a²>0 , b²>0

Implying 1/2 { (a+b)² + a² + b²) > 0
=> a² + b² + ab> 0

[unreal wharf]

So only case (i) possible that

a-b>0

=> a>b

Convinced?

@left needle

[left needle]

im reading 1 sec

oh thats cool

thanks

[unreal wharf]

[left needle]

wait, one more :D

[unreal wharf]

[left needle]

it says prove the statement for every number a -1<a<0 the thing "works"

[unreal wharf]

Oh

[left needle]

the thing on the bottom is the intersection

[unreal wharf]

Ah nice

Let me try xD

[unreal wharf]

Yes so you got a belongs to (-1, 1/2)

So you gonna say that that -1<a<0 ?

[left needle]

nvm

wait

im stupid

i thought my interval was [-1,1/2>

and i had to prove for [1/2,0>

...

sorry

[unreal wharf]

(-1, 1/2) = (-1, 0) U [0, 1/2)
So if something gets valid over LHS then it shall automatically be valid over RHS too

[unreal wharf]

Np haha

I was thinking if we could go through the interval

[left needle]

i just say that <-1,0> is a subset of <-1,1/2>

[unreal wharf]

Yes

[left needle]

thank you for your help

😘

[unreal wharf]

There can be one more way

Imma send let's see

@left needle

[left needle]

the thing is we didnt "learn" roots yet in highschool, we did in primary school but we dont really use them and we didnt learn to write it in exponential form

ik its weird

but we did learn exponents..

its new thing in my country the school system changed everything is messed up

[unreal wharf]

It's fine
You shall learn about these eventually
I just gave an additional answer

[left needle]

i mean i know what it is just saying

thank you

<3

[obtuse pebble]

@left needle Has your question been resolved?

[obtuse pebble]

Channel closed

Closed due to timeout

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.

[sharp heath]

I have a grade 12 mathematics exploration paper I need to write and essentially what I'm doing is calculating air resistance's and spin's effect on a soccer ball.
I know I'm gonna seem lazy but I'm wondering where to start?
Or rather a couple more specific questions:
1.What are all the forces I should consider for air resistance?
2.How hard would it be to investigate turbulent vs laminar flow of air?
3.How might I involve differential equations in this?

[obtuse pebble]

@sharp heath Has your question been resolved?

[sharp heath]

no answer sadger

.close

[obtuse pebble]

Channel closed

Closed by @sharp heath

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.

[inland spoke]

hi

[inland spoke]

Where did the x go in the first step?

[short spruce]

what

[swift marsh]

Log laws

The x went nowhere

The power of x inside the log is ln(x), which they factored out

[short spruce]

there are multiple x's and none of them disappeared

the question makes no sense

[swift marsh]

He thinks they got rid of (or changed) the x that’s raised to ln(x)

[inland spoke]

wait

oh I dropped the ln(x) and kept it on the inside of the ln but it should be on the outside right?

oh i get it now

also shouldn't it be natural log of absolute value

not natural log

[short spruce]

huh

[unreal wharf]

[inland spoke]

we used log differentiation, which requires ln of the absolute value

not just ln ( )

but why is it ln ( ) in this case

[short spruce]

?

[inland spoke]

bro what did I do 😭

in log differentiation, we normally do ln I x I but in this case we did ln ( x ), I'm asking why

[obtuse pebble]

@inland spoke 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.

[scenic kestrel]

Question 2: I have no idea how to get the revenue function

[scenic kestrel]

I would guess that maybe you need to find R= px but that doesn’t really make sense and I think I’m missing a detail

[obtuse pebble]

@scenic kestrel Has your question been resolved?

[scenic kestrel]

<@&286206848099549185>

[obtuse pebble]

@scenic kestrel Has your question been resolved?

[scenic kestrel]

please @ me if you have any advice for me

[scenic kestrel]

.close

[obtuse pebble]

Channel closed

Closed by @scenic kestrel

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.

[primal hatch]

Can anyone explain how to verify identity #8? I’ve tried different methods like replacing the functions in terms of sine and cosine and using Pythagorean identities but I get stuck

[tacit hornet]

The result is incorrect

$\frac{\csc \theta +\cot^2 \theta}{\csc\theta}=\sin\theta+\cos^2\theta}$

[warm shale]

◥▶_◀◤

$\frac{\csc \theta +\cot^2 \theta}{\csc\theta}=\sin\theta+\cos^2\theta}$
```Compilation error:```! Extra }, or forgotten $.
l.57 ...heta}{\csc\theta}=\sin\theta+\cos^2\theta}
                                                  $
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.

Preview: Tightpage -1310720 -1310720 1310720 1310720
[1{/usr/local/texlive/2020/texmf-var/fonts/map/pdftex/updmap/pdftex.map}]```

[primal hatch]

thats actually what I've been getting but the worksheet said otherwise

.close

[obtuse pebble]

Channel closed

Closed by @primal 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.

[fluid dove]

Hi! I am stumped by this question:
Show that we can color the elements of the set $S={1,2,...,2007}$ with 4 colors such that any subset of S with 10 elements, whose elements form an arithmetic sequence, is not all one color.
I tried to use expected value, as this is in the Expected Value section of my textbook, but I don't know where to start.

[warm shale]

LukeyThePookie

[fluid dove]

Oops idk how to use sets in latex

please ping if you say something!

[obtuse pebble]

@fluid dove Has your question been resolved?

[obtuse pebble]

@fluid dove Has your question been resolved?

[compact shadow]

I think I have found a way

Express any integer from 1 to 2007 using 4-adic

Then we color it by the 4 digit

Like 491 is 13223 using 4-adic expression , we color it with color 2 because it’s 4-digit is 2

13 is 31 in 4-adic (13=1+(3)4)

Whose 4-digit is 3 so we color 13 with color 3

38 is 212 in 4-adic whose 4-digit is 1 we color it with color 1, 3 is 3 in 4-Adic so we color 3 with color 0

Anyway, any number whose 4-adic express is …k_2k_1k_0, we color it with color k_1

This satisfies the condition I think:

Because any ten numbers of the same color a

$x_{1}=…k_{3}^{1}k_{2}^{1}ak_{0}^{1}$,…, $x_{10}=…k_{3}^{10}k_{2}^{10}ak_{0}^{10}$

[warm shale]

Cogwheels of the mind

[compact shadow]

Then any 1<=i<=8

$k_{0}^{i}+k_{0}^{i+2} \equiv 2k_{0}^{i+1} \mod 16$

[warm shale]

Cogwheels of the mind

[fluid dove]

sorry, so how does this start?

im so sorry im not very good at this

[compact shadow]

So $k_{0}^{i}+k_{0}^{i+2} =2k_{0}^{i+1}$

[warm shale]

Cogwheels of the mind

[compact shadow]

The last sentence

[compact shadow]

This

[fluid dove]

do you mean 4-adic expression as in base 4? or something like that?

[compact shadow]

Yeah

[fluid dove]

oh ok

[compact shadow]

But I found a mistake

I am trying to fix it

[fluid dove]

oh ok

[fluid dove]

wait but i still don't get why this works, what if we have the sequence 1, 5, 9, 13, ..., then since they are all the same mod 4, wouldn't they all be the same color?

[compact shadow]

Yeah it doesn’t work

Sorry I need to think further

I just want to keep the idea of mod and p-adic in mind, might give me something in the end. Am trying again

[fluid dove]

ahok

[fluid dove]

wait

i got it

[compact shadow]

How?

[fluid dove]

I just found the total number of subsets, which turned out to be 222777

Then, the probability of a subset being the same color is 4*(1/4)^10

which is 262144

so the expected number of same color sets is 222777/262144 for some random coloring

this is less than 1, so therefore, some coloring have no colorings that are the same

wow

[compact shadow]

You mean number of all subsets containing 10 elements forming an arithmetic sequence?

[fluid dove]

yeah

[compact shadow]

It doesn’t sound very valid to me though 😂 but it’s your question

[fluid dove]

well if there wasn't a coloring

the expected value would be greater than 1

right

[compact shadow]

I mean I got it, just don’t feel proving by probability theory is very valid😂

[fluid dove]

i guess so

but i dont see any other way to prove it

[compact shadow]

Yeah…

[fluid dove]

lemme check the official sol

[timid silo]

maybe it could be rephrased in a combinatorial way?

[compact shadow]

Yeah. We should try it

Oh

4^2007>(222777)4^(2007-10+1)

Because 4^9>222777

Number of all colorings is 4^2007, number of all colorings that at least one arithmetic sequence of ten elements is colored with the same color <=4(222777)4^(2007-10)

Let A_k be the set of all colorings such that the k-th subset is colored with the same color, |A_1 union A_2 union … union A_222777|<=|A_1|+…+|A_222777|=4(222777)4^(2007-10)

[obtuse pebble]

@fluid dove 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.

[shrewd shore]

I have data set of approx. 2500 observations. Skewness of the data is 0.395 and kurtosis 35.895. With this information could one tell if there is conformity to normal distribution?

[shrewd shore]

I tried making bell curve in excel based on the data but results were, not that good

[thick fog]

Unless I am misunderstanding the meaning of conformity here, but you are asking if something that has a kurtosis of nearly 36 is close to normal?

[shrewd shore]

Yes, i guess? kurtosis is not only way to measure or assess normality right? so I understand its really high, normally it is like 3 (?)

so if kurtosis is that high, is there possibility of normal distribution or is it just straight out of window?

[thick fog]

It is hopeless

I really don't even have words for how hopeless that is. It's like asking if a coin that flipped 50 heads in a row is fair at alpha = 5%.

[shrewd shore]

hahahahah, thats kind of sad. so assuming the kurtosis is calculated correctly you can tell straight away no further testing on the data is required to tell it does not follow normal distribution

i dont study math really so new concepts to me

[thick fog]

Most statistical tests that test for normality use the third and fourth moments

[shrewd shore]

with a quick look thats out of my league

i have one of the bell curves i tried making but not sure if i failed, do u mind taking a look at it? maybe u can tell something of it, if it looks the way it should?

[thick fog]

The Jarque-Berrta test shows non normality if your test statistic is like 0.005 with your sample size, and the further away from 0 the worse it gets. Your test statistic is in the thousands.

maybe closer to 0.05, I don't have the inclination to actually figure that out

[shrewd shore]

this i think i made trying to perform kolmogorov-smirnov test

should it look like that?

[thick fog]

That doesn't look like anything to me.

[shrewd shore]

okey, altho it gives me hope if its hopeless, maybe thats how it should look like with my data

[thick fog]

I don't even know how to do this off the top of my head anymore, but my usual technique is to just have some code fit the data to one of 20 something distributions and rank them all using the Akaike information criterion. Since I just use computers for everything now, I'm not very helpful on how to practically do this "by hand".

[shrewd shore]

fair enough, i dont have time to learn all that from 0 before deadline on this assignment, unfortunately. i might just stick with "data set does not follow normal distribution" based on kurtosis alone (?) and the tests i tried performing

just for clarification, it is possible to tell only by the kurtosis value of the set that it does not follow normal dist?

[thick fog]

That's what I do

It's not very handwavy because if I wanted to formalize it the statistical tests I would have chosen are a function of the kurtosis anyway. I usually do the tests if the kurtosis is like, 5.

[shrewd shore]

i see. good thing the assignment states "efforts on this part will affect score" - and let me tell you, being beginner in any kind of mathematics i really put effort and tried hahah

even if its miserable

well, thanks anyway

was very insighful

!close

.close

[obtuse pebble]

Channel closed

Closed by @shrewd shore

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.

[mellow beacon]

This is what I did

[obtuse pebble]

@mellow beacon 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.

[static patio]

Where is a mistake ?

.close

[obtuse pebble]

Channel closed

Closed by @static patio

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.

[obsidian isle]

This one

[timid silo]

you can try #linear-algebra

[obtuse pebble]

Channel closed

Closed by @vital palm

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]

what does the plus inside the box sign mean? The answer is apparently d but i dont know how to arrive there

[obsidian isle]

Sorry I don't speak Arabic

[timid silo]

it says: If x + y =.... for all real x and y, then all real x, y applies:

d) neither of them between a and c applies

[obsidian isle]

Ok that little symbol is an operation defined on x and y that returns that operation

Maybe it would be more clear if I wrote it as a multivariate function

$f(x,y) = \sqrt{x^2+4xy+4y^2} - 2y + x$

[warm shale]

EndTimes

[obsidian isle]

Yes?

Or no?

[timid silo]

sounds clearer yeah

dont know how to solve this though

[obsidian isle]

Now look at the first problem

It tells you that f(x,y) = 2x

[timid silo]

yeah

[obsidian isle]

Is that always true?

Does 2x always equal that expression on the right hand side

[timid silo]

maybe?

if i simpy the expression it is 2x

[obsidian isle]

This is a multiple choice question?

[timid silo]

yes

[obsidian isle]

Does f(x,y) always equal 2x?

well let's see

(x-2y)^2 = x^2 - 4xy + 4y^2
Is that the same as what we have under the square root?

[timid silo]

no

[obsidian isle]

Ok

Now let's look at b

What is f(-x,y)?

[timid silo]

i am not familiar with multi variable functions

[obsidian isle]

It's ok

Just let x = -x

Then you get:
sqrt(x^2-4xy+4y^2) - 2y - x

Does that also always equal 2x?

[timid silo]

no

[obsidian isle]

Now finally let y = -y

Then you get
sqrt(x^2-4xy+4y^2) + 2y + x

Does that always equal 2x?

(x-2y)^2 is x^2 - 4xy + 4y^2
Does that match whats inside the square root?

[timid silo]

no

[obsidian isle]

Are you sure?

We have

[timid silo]

inside root is x^2 + 4xy + 4y^2

[obsidian isle]

But for this part we have to let y = -y

[timid silo]

then yeah we get x^2 - 4xy + 4y^2

both b and c

a is x^2 + 4xy + 4y^2

[obsidian isle]

But what do you get on the left side in part b?

If you move everything not on the square root to the left side of the equation

[timid silo]

(-x,y) + 2y - x ?

[obsidian isle]

Not quite

In part b we let x = -x:
2x = sqrt(x^2 - 4xy + 4y^2) - 2y - x
3x + 2y = sqrt(x^2-4xy+4y^2)

Is this always true?

[timid silo]

wdym always true?

[obsidian isle]

For all x and y values

[timid silo]

how am i supposed to know

[obsidian isle]

Square both sides

[timid silo]

ok then sqrt(3x + 2y) = fourth rt(x^2-4xy+4y^2)?

[obsidian isle]

No

[timid silo]

oh no

[obsidian isle]

Squaring means the opposite haha

[timid silo]

(3x + 2y) ^2 = x^2-4xy+4y^2

[obsidian isle]

Expand the left hand side

[timid silo]

9x^2 + 12xy + 4y^2 = x^2-4xy+4y^2

[obsidian isle]

Is this true for all values of x and y?

Basically does the left side exactly match the right side?

[timid silo]

x^2 + 12xy = 0

[obsidian isle]

If x=1 and y=1 then we get 13

Does 13 = 0?

[timid silo]

no

[obsidian isle]

So b is incorrect

Now let's look at c

We let y = -y, so we get:
2x = sqrt(x^2 - 4xy + 4y^2) + 2y + x

[timid silo]

a) is correct right?

because sqrt(x^2+4xy+4y^2) - 2y + x = 2x

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

[obsidian isle]

Oh wait yeah that's right

Nice job

a is correct

[timid silo]

so c) sqrt (x^2-4xy+4y^2) + 2y + x = (x-2y) + 2y + x = 2x

a) and c) both gives 2x but the answer is apparently d)

[obsidian isle]

Actually that doesn't make sense

Let's check

,w 2x = sqrt(x^2+4xy+4y^2)-2y+x

[warm shale]

Results provided by WolframAlpha

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

Requested by EndTimes#8053

[timid silo]

a) and c) gives solutions for some real x and y but not '''all''', maybe thats why a and c dont work?

[obsidian isle]

Here is what we are missing

Tell me this

What is $\sqrt{x^2}$

[warm shale]

EndTimes

[timid silo]

x

[obsidian isle]

NO

Thats the thing

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

[warm shale]

EndTimes

[obsidian isle]

Sqrt((-5)^2) = sqrt(25) = 5

Which is not -5

@timid silo does this make sense

[timid silo]

kind of

so lets say we have a f(x) = sqrt x^2 then what is the domain?

[obsidian isle]

All real numbers

sqrt(x^2) has a domain of all real numbers and a range of all real numbers >= 0

Because the square root of a number is always positive

[timid silo]

basically fx = |x|

[obsidian isle]

Yes

So it doesnt always give back the original number

[timid silo]

so all values of y have 2 x values

even though it is not 2nd degree

[obsidian isle]

Yes

Horizontal line test

It will cross the curve twice

Please do not confuse $\sqrt{x^2}$ and $(\sqrt{x})^2$ however

[warm shale]

EndTimes

[timid silo]

so is y=|x| a second degree equation ?

[obsidian isle]

It's not a polynomial

So there's no degree of it

[timid silo]

i solve both like this x^2*1/2 = x

[obsidian isle]

sqrt(x^2) is |x| for all real x
(sqrt(x))^2 is x for all x >= 0

[obsidian isle]

That rule only works when x is positive

[timid silo]

is there any intuitive understanding on why they are called roots?

i dont like the graphic portion of algebra

[obsidian isle]

Not really, we just say that roots are solutions to polynomials

[timid silo]

so back to the original problem, neither a, b nor c works because x and/or y are inside the root and negative values cannot be inside right?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

Channel closed

Closed by @manic shadow

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.

[cerulean plaza]

does the solution to this make sense so far?

[obtuse pebble]

@cerulean plaza Has your question been resolved?

[cerulean plaza]

<@&286206848099549185>

[obtuse pebble]

@cerulean plaza Has your question been resolved?

[swift marsh]

Assuming you’re trying to work out the derivative and g(tanx) is g multiplied by tanx, I think the only mistake is right towards the end, I think it should be fg(k) not fg(0) since the derivative of kx wrt x is k

[obtuse pebble]

@cerulean plaza Has your question been resolved?

Channel closed

Closed by @cerulean plaza

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]

When defining a n-touple as a function : (a,b,....,w) = x: {1,.....,n} --> u with x(1) = a ,x(2) = b ... x(n) = w. And on a set Y, (Y)^n is the set of all n-touple with x: N_<=n --> Y. How can one define (N^2)^3 (N as natural numbers). I guess one could say for N^2 = {x:{1,2} -->N} is that correct and how would you expand to (N^2)^3.

[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.

[fickle bramble]

Is the set notation of the statement "H does not include D" H\D or D∉H? Or are both wrong? Help please

[fickle bramble]

Or is it H⊄D?

or D⊄H?

[gloomy valve]

$\notin$ is a relation between elements and sets, not between a set and a set.

[warm shale]

nvx

[fickle bramble]

Okay how about the not a subset?

symbol*

Should I use the difference symbol instead? or the "not a subset" one?

[timid silo]

It's D⊄H

The subset relation is also referred to as the inclusion relation.

[fickle bramble]

Oh okayy.. Thank you so much for that. It was very confusing for me

.close

[obtuse pebble]

Channel closed

Closed by @fickle bramble

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[grizzled kelp]

@dusky light I'm sorry, I'm not sure, if I'm allowed to ping or not, but could you just walk me through your thought process, when it comes to solving those roots

[dusky light]

sup

so

(x)^2 +/- 2(x)(y)+(y)^2

idk what to tell you

rerepresent the integer with x^2+y^2

[grizzled kelp]

I know, but it's really difficult go the other way

[dusky light]

for example in 6-2sqrt5

[grizzled kelp]

I thought you had like a little process in your head, but I guess it's just practice

[dusky light]

you see that 2sqrt5

5 is a PRIME

[grizzled kelp]

okay

[dusky light]

and 2 cant be used at all

so you should think that we write it is 2sqrt5 *1

(sqrt5)^2+1^2=6

so yay

i forgor the 2nd example

[grizzled kelp]

9+2sqrt14

[dusky light]

here

you see sqrt14=sqrt2 sqrt7

well

isnt it just obvious now

🤨

[grizzled kelp]

yes yes, I think I get it now

mkay

[dusky light]

oh sometimes you split the 4 btw

2*(2x)*y

👍

[grizzled kelp]

okay, yeah I got it right

thank you hwai

[dusky light]

np

[grizzled kelp]

I'll need to work on these, but it's a start

.close

[obtuse pebble]

Channel closed

Closed by @grizzled kelp

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.

[nova wagon]

how can I solve this equation? Using arcsin doesnt work I think because then I'd have arcsin(0,81x)... which doesn't solve the issue
0=0,81x+sin(x)

[warm tulip]

can u give the whole question

[nova wagon]

its in german. I have to find the point with the biggest difference between two equations. So I decided to combine the two, then use f'(x) to figure out the highest point.

[warm tulip]

actually arcsin0.81x should work

[nova wagon]

but how do I solve it when x is involved

[warm tulip]

wait

[rugged kite]

yeah that's a shit equation, good luck finding an analytical solution

for the record the solution to cos(x)=x doesn't have a closed form expression

[nova wagon]

well I would guess that this is just not what they intended me to do

but otherwise I really have no idea how to do this

[timid silo]

Your best bet is to apply the newton-raphson method to f(x)=0,81x+sin(x) to find a good approximation of x

As it was pointed out it's unlikely that there is a closed form solution

the sine function is transcendental

[nova wagon]

hmm sad

[timid silo]

Yep weird equation

[nova wagon]

its -1.0981 and 1.0981 (got it from geogebra)

very sad, hoped i couldve solved it somehow

welp thanks all

.close