help-0

[pulsar yarrow]

i mentioned (-2)^2 = 4 and -2^2 = -4 so it depends what your original question is and where your parenthesis is supposed to be placed

then it's 4

[vocal olive]

I have a question tho

[wary stream]

If you are taking an odd root of a negative number, the value will be negative. Even root of negative is a complex value

And parentheses matter because $$(-2)^2$$ and $$-2^2$$ results in two different values because $$(-2)^2 = (-2) \cdot (-2)$$ while $$-2^2 = -(2 \cdot 2)$$

[ocean seal]

dldh06

[vocal olive]

Should there be brackets here or no

[wary stream]

Yes

[vocal olive]

The root here is 3 right?

[wary stream]

3? Where?

[vocal olive]

Cuz the exponent is 2/3

[wary stream]

But you have a (-2^3)

Where the 3s will cancel

[vocal olive]

Oh

[sturdy field]

Need help on this pls 😢

[wary stream]

So you will be left with (-2)^2

[wary stream]

Look up resources

[pulsar yarrow]

with what specifically? I'm assuming direction of opening refers to its concavity so you'd probably be okay specifying that i guess

[wary stream]

Not that hard

[vocal olive]

Got it

[sturdy field]

Can u help me

[wary stream]

You have all the necessary info in the plot

If you don't know what the terms mean, look it up

Like do you know what the x intercept is?

Or vertex?

Y intercept?

[sturdy field]

Nah

[wary stream]

Then you are lacking the knowledge you need to solve that question, look up those terms

[tight birch]

how do i write this in set notatation?

[civic jungle]

How would you express that if you could express it the way you wanted?

[tight birch]

{x E R | x < -5 and x > +2 } ?

can i use the word "and" in set notations

or "or"

[civic jungle]

That's like, exactly the same as how one expresses it in set notation

Yeah there is nothing forbidding words in math

[vocal olive]

Help fren sed this and I'm confused
If the brackets weren't there it would be -4 = 4
I think it is 4i
Which is a complex number
Which we can do to the power of 3÷2 to get 8
The brackets have to be there

[wary stream]

$$\sqrt{-16} = 4i$$

[ocean seal]

dldh06

[wary stream]

Are you taking the square root?

[vocal olive]

Ic

[wary stream]

And this @vocal olive

[vocal olive]

https://media.discordapp.net/attachments/884884621689499688/902203752163971092/20211025_173525.jpg

My friend says this

[wary stream]

,rotate

[wary stream]

That is wrong

[vocal olive]

Why is that

[wary stream]

To cancel out the 2/3 exponent, you have to multiply by the reciprocal

Meaning $$-8 = 4^{\frac{3}{2}}$$

[ocean seal]

dldh06

[vocal olive]

Oh

But that's still wrong

[wary stream]

What's the full question?

[vocal olive]

(-8)^(2/3)

This is the problem

[wary stream]

So why is the an equals 4?

[vocal olive]

A proof

[wary stream]

$$a^{\frac{m}{n}} = \sqrt[n]{a^m}$$

[ocean seal]

dldh06

[vocal olive]

Ik

[wary stream]

So $$(-8)^{\frac{2}{3}} = \sqrt[3]{(-8)^2}$$

[ocean seal]

dldh06

[wary stream]

And what's (-8)^2?

[vocal olive]

64

[wary stream]

What's the cube root of 64?

[vocal olive]

4

[wary stream]

So then $$(-8)^{\frac{2}{3}} = 4$$

[ocean seal]

dldh06

[vocal olive]

Aight

[pulsar yarrow]

[vocal olive]

His problem was this

[wary stream]

Well, that's written incorrectly

[vale sapphire]

you have to be careful when putting exponents on the other side

especially when you see anything remotely even

[civic jungle]

\begin{align*}
(-5)^2 &= 25\
-5 &= 25^\frac12\end{align*}
Tada

[wary stream]

Also, that's not even a valid expression

[ocean seal]

Icy001

[vocal olive]

How would u do it correctly then

[vale sapphire]

because if you're not careful, you might end up going 3²=9=(-3)², thus √9=3=-3

woops

[wary stream]

.

[vale sapphire]

-3 is a square root of 9

the square root doesn't exist unless you're restricting yourself to positive numbers

[vocal olive]

Talking about the proof thing

(-8)^(2/3) = 4

[civic jungle]

-8 is not equal to 4^(3/2) though

[wary stream]

Literally what I said above

[wary stream]

.

[vocal olive]

(-8)=4^2/3?

[vale sapphire]

nope

you can't just do that with negative numbers involved

[vocal olive]

O

[vale sapphire]

in the same way that (-3)²=9 doesn't mean -3=√9

[vocal olive]

Ic ic

[vale sapphire]

√9 refers to one and only one number and that is 3

[vocal olive]

This has been over complicated

[civic jungle]

Yes

[vocal olive]

Imma just chill out and trust myself

[civic jungle]

The simple way to approach everything is do not write false statements, e.g. equals signs between two things that aren't true or which you aren't sure are true

Life will be good if you do that

[vale sapphire]

"the simple way to not make mistakes is not to make mistakes"

thanks, helped a lot

[vocal olive]

Nice

[civic jungle]

The thing is every equality he wrote down can be checked

with a computation

And crossed out if it turns out false

hence, it's possible to avoid writing false statements

[wary stream]

This depends, if the equation was $$x^2 = 9 \implies x = \pm 3$$ but if it was just $$x = \sqrt{9} \implies x = 3$$ and only 3

[ocean seal]

dldh06

[vale sapphire]

bottom line is, 3²=(-3)² is the heart of why you can't just take square roots willy-nilly

the terminology here admittedly very confusing

[vocal olive]

Ic

[vale sapphire]

3 and -3 are square roots of 9 (no definite article)

so technically there is no "the square root of 9".... except positive numbers are convenient so we say √9=3 and here come the sign errors

[wary stream]

As I stated, it depends on how the equation was originally given

[vale sapphire]

i mean yeah, if the equation is different the solution will be different

what i said is still true, you have to be careful when dealing with roots because you might stumble upon some good old (by which i mean awful) sign errors

[lucid cedar]

When are 2 events independent in probability?

[wary stream]

When they don't affect each other, I think

[lucid cedar]

can you give an example of what that might look like?

bc I cant think of anything that wouldn't be independent

[glass lichen]

It rains and you find 20 dollars on the ground

[cunning obsidian]

^

[lucid cedar]

how are those dependent?

[glass lichen]

Oh you asked about dependent

[lucid cedar]

ye

[cunning obsidian]

Ohh xd

[glass lichen]

It rains and you have an umbrella

[wary stream]

You said independent?

[lucid cedar]

alright that makes mroe sense

[lucid cedar]

yeah, bc I couldnt think of dependent ones

[cunning obsidian]

So an event is dependent if it is affected by the outcome of another event

[lucid cedar]

alright that makes sense

[cunning obsidian]

I think?

Idk I’m teaching myself maths idhdiffj my school is still teaching linear equations

[glass lichen]

Events are independent if P(A)P(B)=P(AnB)

Dependent else

[lucid cedar]

ah that makes even more sense

thanks

that explains it

[vale sapphire]

yeah, dependency (dependence?) is a tough question

and the intuitive sense of "don't affect each other" really only goes so far when dealing with the concept in practice

but it is the idea

[ripe mountain]

How do you find all the local maxima, local Minima, and saddle points for f(x,y) = sin(xy)

[analog summit]

We can't prove e or pi's irrational if we don't know the infinite series of them?

[vale sapphire]

yes we can

[analog summit]

How

[lucid cedar]

set the gradient equal to 0

[vale sapphire]

niven's proof for π, and there's probably some other thing like that for e

also there is no "the" infinite series for a number

there are convenient ones, but they are by no means unique

[grim delta]

you take the partials and find where they = 0, that gives you all the x and y values of the critical points

then you have to take second partial derivatives and use the 2nd derivative test to figure out what each point is (min/max/saddle)

[analog summit]

alright thx

[lucid cedar]

or you could just use the hessian test

that would be a bit faster

[grim delta]

it’s basically the same thing, you just write it in a matrix form

i tend to do that too but not everyone has lin algebra

[lucid cedar]

fair point

[ripe mountain]

So I have the x partial as ycos(yx) and the y partial as xcos(xy), wouldnt that give an infinite # of critical points

[lucid cedar]

yes, there are an infinite number

but theres a pattern to it

[grim delta]

^
cos/sin theta both have min and max values no matter what theta is

depending on what the amplitude (coefficient) is

[lucid cedar]

yeah, so basically you need to find where $xy=n\pi-\frac{\pi}{2}$

[ocean seal]

WasMachenWirDennDa

[lucid cedar]

because in those cases $\cos(xy)=0$

[ocean seal]

WasMachenWirDennDa

[lucid cedar]

and thus the gradient is 0, meaning it's an extremum

[ripe mountain]

n is just a random infinite constant I assign right

Like it goes to infinity

[lucid cedar]

n is any whole number

[ripe mountain]

Yeah

[lucid cedar]

this holds true for $n\in\mathbb{Z}$

[ocean seal]

WasMachenWirDennDa

[nimble stratus]

plz help

can't calculate this

[analog summit]

Euler's proof didn't use that but it is really complex...

[vale sapphire]

yeah, things be just kinda advanced sometimes

euler wasn't half a dumbass

[analog summit]

ik

[ripe mountain]

How do u use the 2nd derivative test

[grim delta]

it’s the determinant of the hessian matrix

basically $D=f_{xx}f_{yy} - f_{yx}f_{xy}$

[ocean seal]

Dogecode

[grim delta]

whether it’s a maximum minimum or saddle depends on what D equals at that point

[spice elk]

Hiya, i need help with how to find this : √(43.75 x 7)
i tried factorising 43.75 by removing decimal point and i got in total 5 x 5 x 5 x 5 x 7 x 7 which i wrote as 5^2 x 5^2 x 7^2
then i cancelled root with the squares and got 5 x 5 x 7=175
im confused how to go about adding the decimal point?

[grim delta]

and f_xx

[novel kettle]

Yoooo if the tide changes every 6 hours then if it's high tide at 6:30pm low tide will be at 12:30am or just 12am

[grim delta]

if D<0 it’s a saddle point no matter what
if D>0 and f_xx > 0 it’s a local minimum
and if D>0 and f_xx <0 it’s a local maximum

[spice elk]

i think 12:30

[novel kettle]

Ah ok thank you :D

[light sleet]

quick question

[vale sapphire]

do you have any idea yourself

[forest jacinth]

@nimble stratus
$22,5 = 9 \cdot 10^9 \cdot (\frac{16 \cdot 10^{-9}}{64} + \frac{q_2}{25} + \frac{12 \cdot 10^{-9}}{4})
\newline \frac{45}{2} = \frac{9}{4} + \frac{9 \cdot 10^9}{25} q_2 + 27 \newline \newline$
multiplying both sides by 4:
$90 = 9 + \frac{36 \cdot 10^9}{25} q_2 + 108 \newline
\frac{9 \cdot 10^9}{25} q_2 = -27 \newline
10^9 q_2 = - \frac{3 \cdot 25}{4} \newline
q_2 = -18,75 \cdot 10^{-9} C = -18,75 nC$

[ocean seal]

JarrGarde

[dreamy orbit]

Can someone help me out how to find the total?

[light sleet]

no, not really, i think -3 is on the > but then again < so idk

[vale sapphire]

what is a negative number

[forest jacinth]

This is probably some awful LaTeX-writing practice, but it will do. @nimble stratus Next time, when solving physics-related questions, try and solve for q_2 as an equation before plugging in values. It's a neat practice.

[light sleet]

-3

[vale sapphire]

i was asking in general

what are negative numbers

[light sleet]

something like less that zero and has less value than zero

these are integers tho so

[vale sapphire]

yeah, and what does that change?

a negative number is a number that's less than zero

[light sleet]

¯_(ツ)_/¯

i thought it had a diference

[sturdy field]

,help

[ocean seal]

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

[vale sapphire]

formally that's all a negative number is, but it's boring if you just put it plainly like that

[light sleet]

hmm ok

[spice elk]

any1 kno how to do this

[vale sapphire]

rule 2 please

[vale sapphire]

so then, is -3 less than or greater than 0 ?

[light sleet]

less

[vale sapphire]

correct

do you know which inequality symbol that is

[light sleet]

cool, i just needed some reminding

[wary stream]

In all honesty, pcode was here before za1nt

[vale sapphire]

okay fair

[stoic raft]

what is the actual solution to the problem here, f(x) isnt 15 on the given domain right?

[spice elk]

oh oki ill ask in a dif channel :D

[wary stream]

Do you know the difference between the 3?

[alpine sable]

hello guys

may i get help please 😅

a) Find the rate of change of the area with respect to the radius.

[light sleet]

No not really in this situation

[wary stream]

In general, do you know the definition of each

[light sleet]

for those equestions if I summed them together? Yeah

[wary stream]

What's the general definition for distribution?

[alpine sable]

i am sorry guys but i have a test tomorrow so i will ask too much pardon

[light sleet]

Distribution function, mathematical expression that describes the probability that a system will take on a specific value or set of values.

[light sleet]

hey uh try a different channel

[alpine sable]

and literally idk anything

[light sleet]

this one is occupied atm

[alpine sable]

yes okay , i am sorry

[light sleet]

Nah no problem

[wary stream]

Distributive property

Not function

[light sleet]

multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

[wary stream]

That sounds like a Google definition

[light sleet]

it is lol

look i wanna understand this as much s possible so i dont fail for my tests on friday

[light sleet]

[simple current]

do you know the definitions?

For example it seems like you've clearly memorized the distributive

[wary stream]

@oak chasm 100% apologies for the ping but I don't recall if it was you or not, but I remember that someone like you gave a really good analogy about distributive, commutative, and associative a while back. Can you assist with that so that person can understand the meaning of each?

[light sleet]

No, they didnt teach me in the way I'd understand

[simple current]

I see

[light sleet]

[simple current]

do you have examples of each? to understand what they are?

[light sleet]

Nope

[alpine sable]

What is 0/0

[simple current]

occupied and undefined

[alpine sable]

Wdym is occupied

[oak chasm]

@alpine sable Sorry, this channel is busy. Please read the rules and tips for getting help in #❓how-to-get-help.

[simple current]

this channel is occupied

[alpine sable]

Oh sry

[light sleet]

try calcuator

[oak chasm]

@novel kettle Sorry, this channel is busy.

[simple current]

same thing for you

[wary stream]

Hold on, I pinged Chai, who's currently here, because a while back, they gave a very good analogy that will help you

[novel kettle]

Ah ok soryyyy

[light sleet]

okk

[oak chasm]

@light sleet When people go to work and back, that's called their daily commute. Have you heard that term?

[light sleet]

uhhh no?

[oak chasm]

Well, when people travel on the roads, that's called a commute.

[light sleet]

Ohhh I see

[oak chasm]

So, commutative is like that.

You move something from one place to another.

Like a + b + c → a + c + b

The c moved.

It commuted.

That uses the commutative property.

[light sleet]

then where did they a go?

[oak chasm]

It stayed in the same place.

[light sleet]

hm Alright

[oak chasm]

a + b + c
a + c + b

Notice that the c moved, though.

a + b + c
a + c + b

[light sleet]

Yeah I understand Commuted now

[oak chasm]

Do you know what it means to associate with people?

[light sleet]

yes

[oak chasm]

It's like you do stuff with them.

[light sleet]

exactly

[oak chasm]

Well, in math, if you want to get two numbers to be doing something together, you can use parentheses.

(a + b) + c

(a + b) · c

And so on.

Does that make sense so far?

[light sleet]

Yeah I'm understanding a lot more

[oak chasm]

OK, the associative property says that if you have this:

(a + b) + c

You can change it to this:

a + (b + c)

It changes which numbers are associating with each other.

First, a and b are associating with each other.

Now b and c are.

You can do that with multiplication too.

(a × b) × c
a × (b × c)

Does that make sense?

[light sleet]

Yes It does

[oak chasm]

So, associative is about when you're allowed to change which numbers are associating right now.

Commutative is about when you're allowed to move numbers to new places, like a person moves to where they work in their morning commute.

So, what about distributive?

Well, have you heard of taking a bunch of things and distributing them to people?

[light sleet]

hmm Yeah ?

[oak chasm]

OK, so let's say you have:

a × (b + c + d)

You can distribute the a × part to the terms in the parentheses.

a × (b + c + d)
a × b + a × c + a × d

We took the a × and we distributed it to all the terms, so that they each got one.

Just like if you distribute a newspaper to people who pay for it, they each get a newspaper each day.

Does that make sense?

[light sleet]

Yes

[oak chasm]

So, the way to tell them apart is that associative is changing which numbers are associating together, so the parentheses move but nothing else changes.

Commutative moves exactly one number from one place to another. That's the only change you'll see.

Distributive distributes a bunch of copies of some multiplier to a bunch of terms.

So you'll see a bunch of new multiplications.

Does that make sense?

[light sleet]

Yes, yes it does

ty for ur help

[oak chasm]

You're welcome.

[ripe mountain]

i would need to do the same thing for f_yy too right?

[grim delta]

No that part only depends on what f_xx equals at the point

[ripe mountain]

umm im not sure what u mean by that

so i got f_x, f_y, f_xx, f_yy, and f_xy

and i got D based on what you said

with this

$D=f{xx}f{yy} - f{yx}f{xy}$

[ocean seal]

נעה

[nimble moss]

2

[light sleet]

ok

[light sleet]

what about this one

[nimble moss]

9

[light sleet]

ty

[blazing rose]

can anyone help me understand part b

i used up my 5 attempts for this hw assignment but i still just wanna know how to do it

[rapid nova]

you need to factorize the denominator

[grim delta]

yeah
if D<0 at the point it’s a saddle, if D>0 you have to check what fxx equals at the point to know whether it’s a max or a min

if fxx < 0 its a max and if fxx > 0 its a min

[blazing rose]

how

what can u factor x^2 + x +6 into

[ripe mountain]

so because it's asking for in general, and i've got trig functions, do i need to answer them all in terms of pi

[rapid nova]

are you allowed to use complex numbers?

[blazing rose]

i assumed not

[rapid nova]

I doubt there's another way

[blazing rose]

i used a calculator and it gave me

1 + (-x-6)/(x^2 + x + 6)

[rapid nova]

oh wait maybe you can do it with Bx+C

let me see

[blazing rose]

i did the Bx + C

check the answer

but itsstill wrong

[rapid nova]

sorry, I have no idea what answer other than yours can be expected

[blazing rose]

alright time to complain to my teacher then lmao

[alpine sable]

how can I quickly solve this without trying them one by one, ideally in less than 20 secs?

The question is ”Which one is a possible answer for x”

[rapid nova]

\begin{gather*}
5x^2 + 3x = 0 \
x (5x + 3) = 0 \
\left[
\begin{array}{l}
x = 0 \
5x + 3 = 0 \implies x = -\frac{3}{5}
\end{array}
\right.
\end{gather*}

[ocean seal]

rept1d

[jade birch]

0 being the trivial answer isn't given so you factor the x which gives you: x(5x+3)=0 from there 5x+3=0 must be the answer or x=-3/5

[alpine sable]

that’s a very good method, thx a lot

I was going to test them one by one, luckily it was the first answer, otherwise that question would have been a time killer

[twin badger]

Can someone help me

[alpine sable]

Try these, and think of the answers

Hey I need help

I’m gonna fail this class and if I don’t do this crossword thing

It’s geometry can anyone help?

[rapid nova]

[sterile vale]

Essentially when the y values are positive

The way the question is formulated, it's asking for strictly positive.

:) thats polite of you to say

[azure jungle]

determine the slope of the graph of f at point X0
need help

number 6

[ripe wasp]

I guess 7a) is $(-1)^3$

[ocean seal]

AlexNotLion

[alpine sable]

This must sound super simple but

Wouls this round to 4.01 or 4.02?

[limpid rock]

4.01 i think

[alpine sable]

ok

[devout summit]

Round to what number of decimal places?

[alpine sable]

second

@devout summit

[devout summit]

Ok...

[alpine sable]

also would this be correct?

[safe wyvern]

how do i calculate the growth in this graph?

[alpine sable]

Final - initial?

[safe wyvern]

pff idek im just doing this for a presentation to sound smart

[alpine sable]

If you want to find the growth by percentage unit then it is the highest- the lowest

English @alpine sable.

In #help-1.

Oh wait nvm.

I didn't read the heading.

translation in the question

Yeah, just saw that.

[safe wyvern]

ohh aight, tyvm

[azure jungle]

please ?

[steep briar]

Have you tried differentiating?

[azure jungle]

i didnt try anything, idk how to start the task

[steep briar]

What class is this for?

[azure jungle]

12

[steep briar]

Have they taught you derivatives?

[azure jungle]

yes

those are derivatives

[steep briar]

Alrighty, you know how to take a derivative of a polynomial? (power rule)

[azure jungle]

yes

[steep briar]

So when you plug in x0 to the derivative, by definition that gives you the slope at x0 (of the original function).

[azure jungle]

the only confusing part here is the x0
can i just derive it the usual way and then the f´(x) = x0 ?

for example a)

[steep briar]

Uh the form is f'(x0)=answer

[azure jungle]

wait but

it says in a) x0 = 2

[steep briar]

Yes, you're finding the general function f'(x) then plugging in x0 which is f'(x0). You're finding f'(x) at x0.

So f'(2).

[azure jungle]

i reaaallllyy don't follow... when i ignore the x0 and just derive the task
i get f´(x) = 3/2 x^2 - 2

when i theory it should be f´(x) = 2 ?

[steep briar]

No, you're not setting f'(x)=2. You're setting x=2

[azure jungle]

so i have to insert 2 in the x

[steep briar]

Like f(x)=x² at x=2 is 4, since f(2)=2²=4.

[azure jungle]

to make it f(2)

[steep briar]

Yes.

[azure jungle]

oooh

[steep briar]

f'(2), since f(2) outputs a constant no longer dependent on x (and so if it was let's say 8, the derivative of 8 is 0, not what you calculated above). That's why I said to calculate the general f'(x) and then plug in x=x0.

[azure jungle]

okay il try thanks

[steep briar]

To make sure, lemme know what you get.

[flat copper]

help

@steep briar could you help me with derivatives aswell

[steep briar]

Okay, I'll need a little bit to draw it.

[flat copper]

yup, thanks

[azure jungle]

i was working on a different task so far, now threw a look on the task we just talked about..
so its basically
2 = 1/3 x^3 - 2x | +2
4 = 1/3 x^3 - x | : 1/3
12 = x^3 - x
now what do i do ?

solve by factoring ?

x(x^2 - x) ?

[steep briar]

Huh you lost me there. Step 1. Differentiate f(x) w.r.t. x. Step 2. Plug in x=x0=2 to f'(x). f'(2) is the slope, and hense the answer.

[azure jungle]

HUH.. i thought i was on the right path

[steep briar]

It's a bit of a nasty derivative so I want to LaTex it, sorry for being slow.

[flat copper]

its all good

atleast u know how to do it i kept messing up

[azure jungle]

could you solve the task for me in steps ? maybe im going to recognize the pattern then... this aint homework,im willingly learning haha i want to crack it

[steep briar]

f'(x) is a function that tells you the slope at all x for a function f(x), that's the purpose of f'(x). Should be no need to factor.

[steep briar]

Alright

[alpine sable]

3.45<= y < 3.55?

[steep briar]

So you already got f'(x)=(3/2) x² -2, which I agree

Now plug in x=x0=2 to get f'(2)=(3/2)2²-2, and simplify.

That would be your slope at x=2 for f(x).

[azure jungle]

its -2x at the end

[steep briar]

No, f(x)=½x³-2x, therefore f'(x)=(3/2)x²-2.

[azure jungle]

ah ah yes... my bad, im all tangled up rn

[steep briar]

No problem

[azure jungle]

alright so i have been overthinking a simple equation

[steep briar]

Happens a lot.

[azure jungle]

thanks a lot ❤️

[steep briar]

Good luck,

Now to LaTex

[steep briar]

So far do you understand this? (I realize the H at the bottom isn't the answer to the given question, we'll talk about it).

gosh I keep forgetting to crop, rip.

[flat copper]

yeah i was somewhat around taht point

[steep briar]

So you know why in the bottom I have terms like 22*6, and 16*6, where the 6 comes from?

[flat copper]

yes like i know what the numbers that are given in the question are like dx dy etc

but i think i mixed up at a certain point

[steep briar]

Yeah so you know how to get the distance as a function of t?

[flat copper]

ya but im getting the wrong answer

[steep briar]

What's your function?

[flat copper]

i raged and deleted the whole LMAO

[steep briar]

rip lol

[flat copper]

but im pretty sure i just had a function misinput

[steep briar]

H(t)=√[(30+22*t)²+(0+16*t)²]

You got something like that?

[flat copper]

yeah but the 6 at the end was t

yeah that

did i really just mis calculate?

[steep briar]

Alrighty, so we agree the differentiating is tedious, the idea would be chain rule.

[flat copper]

just tried again

same wrong answer

what did u get?

[steep briar]

I also got the wrong answer (checked on Desmos), let's see how long until I get it right. Shame on me.

[flat copper]

lol alr

[strong karma]

Any help in this permutation and combination question ?

[flat copper]

@steep briar I have like 10 more mins to hand this in till its due if you think it gonna take longer just forget ab it haha

[azure jungle]

dont mind me castle, answer this when you can 🙂 do i have to do 1/2x^2 times the numbers in the bracket to get rid of the bracket ?

,rotate

[steep briar]

This should be it.

[flat copper]

ur a goat

luv u dawg

[steep briar]

Yeah you could distribute (that'll actually be the efficient technique)

[azure jungle]

1/2 x^2 or just x^2

i think its 1/2x^2 hahha

[steep briar]

½x², yeah.

[azure jungle]

tnx

[steep briar]

Yields the same answer but distributing all would be simpler.

I'll be heading to class, g'luck.

[azure jungle]

bye, have a nice day

[mellow tinsel]

For a matrix A, if (A^2)^3=I does A^2=I too?

[sick quail]

what's the derivative of tan (5-2x) ??
--> is that sec² (5-2x) . (-2) ??

[raw shard]

yes

[sick quail]

okay thx!

[tawny fable]

Anyone can help in room 2? 🙂

Questions - 1 🙂

[azure jungle]

uhhh

how does this go from -3√x to 3* 1/2√x ?

[dull onyx]

derivative

[azure jungle]

basically, i dont understand first to 3rd, step

[dull onyx]

(x)’=1

[raw shard]

you don’t understand the second step

[azure jungle]

yeah, we never use the second step in school

i literally only see it on the net

[dull onyx]

(sqrt(x))’= 1/2sqrt(x)

[hardy gulch]

[ \frac{d}{dx} \sqrt{x} = \frac{d}{dx} x^{\frac{1}{2}} = \frac{1}{2} x^{-\frac{1}{2}} = \frac{1}{2\sqrt{x}} ]

[ocean seal]

ricey

[dull onyx]

or that

[tawny fable]

Please help me in room number 1 😦

[azure jungle]

i still dont know what d and dx means, like i said, the teacher NEVER showed us this step.. we had x^n-1 and similar things but nothing with d/dx

[raw shard]

d/dx means the derivative with respect to x

[azure jungle]

aah

[dusty willow]

Is there any easy way to learn math vocab?

[hardy gulch]

do more math

[raw shard]

probably work with it

[dusty willow]

Like... I hate fields that utilize a lot of complicated vocabulary because I have problems learning the terms

[raw shard]

or just find it interesting enough to remember lol

[dusty willow]

And like... before analysis I didn't really have to learn a lot of vocabulary for math

But now I do

And it's terrifying

I can't even start a problem that requires me to utilize Cauchy's mean value theorem to prove something if I don't even know what the mean value theorem is

Or the triangle inequality

Or whatever

[azure jungle]

ye i have the same problem, i need to work on my math vocab

[dusty willow]

I had my tutor put together a vocab list for me because of this problem 😆

But it's not really helping

I just suck at memorizing shit

I'm good at solving stuff

[azure jungle]

mind sending me the pic ? might help me (:

[dusty willow]

But..

[raw shard]

could you try to do problems with them?

[dull onyx]

u should do more math then

cant memorise things if u dont use em

[dusty willow]

@azure jungle

[raw shard]

first page is already too much

[dusty willow]

Fair

Yeah

But it's a good reference

If I need to look up a word

[raw shard]

actually as i look into it more it’s not too bad

the math in there is all over the place

[dusty willow]

It is?

[azure jungle]

oh god, how old are you, im way under that xd not even close.... god i envy all the smart guys in here that do the helping, thanks fellas

[cosmic cedar]

Which is a permutation, combination, or combination of both?

[sinful ether]

help in room 8 please?

[alpine sable]

Don't beg for help in another help channel

[azure jungle]

e)
should be the last question about sums derivation

here is the answer:

[alpine sable]

Yeah. What's your question

[azure jungle]

why the hell is it 1/2 x^1/2
the derivative of root x is x^-1/2

[alpine sable]

yes

[dusty willow]

I'm 18

[alpine sable]

Thats what it says

[azure jungle]

and then the asnwer says: 1/2 times 1/2x^-1/2
i dont understand it

how is there suddenly 3 times 1/2

and why is there no - on the first x^1/2

[alpine sable]

The exponent gets pulled down and multiplied with the original factor, that's where the 1/2 * 1/2 comes from

and you subtract one from the exponent

[azure jungle]

but the exponent should be -1/2 not +

[alpine sable]

Making it -1/2

[alpine sable]

It is after you derive it

[azure jungle]

i derive the square root x

[alpine sable]

Yes

[azure jungle]

and get x^1/2

[alpine sable]

no

[azure jungle]

wym no

[alpine sable]

The derivative of sqrt(x) is 1/2 * x^(-1/2)

[raw shard]

remember power rule

[azure jungle]

whaaaat... im so falling appart....
then why is the derivative of this square root x not 1/2 * x^(-1/2)

[raw shard]

is it

[alpine sable]

negative exponents go in the denominator and are positive if that’s what is confusing

[raw shard]

it’s just multiplied by a constant

[alpine sable]

The constant gets preserved

a * x^b derived is a * b * x^(b - 1)

[glass lichen]

Differentiated wrt x*

[raw shard]

everything other than x is a constant, is you couldn’t tell

that’s kinda obvious here

[alpine sable]

As this is 10th grade level I left this out as to not make this confusing for them

[raw shard]

bruh

this is not 10th grade

what kind of school do you go to

not even close

[alpine sable]

I was in 10th grade last year and we had the exact same textbook

lol

[raw shard]

well your school is unique

[alpine sable]

?

Derivatives are normal 10th grade stuff here in germany

Atleast for G8

[raw shard]

oh

i’m in america

so

[alpine sable]

Well

[raw shard]

lol

[alpine sable]

Just to make sure

Did you think this was higher or lower than 10th grade?

[raw shard]

higher

[alpine sable]

Ok

[raw shard]

like 12th grade or college in america

[alpine sable]

this is usually 12th grade math in America

[azure jungle]

im in Biotechnological gymnasium grade 12 rn......

[raw shard]

something like that

[glass lichen]

Yeah this comes after grade 10 in most currs

[alpine sable]

I'm in 11th grade abd we started analytic geometry in 3D space rn, next topic after that being integrals

[azure jungle]

and believe me, i feel so damn stupid not being able to know this, math is like my worst enemy

[forest jacinth]

It's a learnable skill, don't get discouraged

[azure jungle]

yh, people that are helping me do it with ease and some of them are younger than me

its sad

[raw shard]

it takes practice but it gets easier over time

[forest jacinth]

It isn't, you just started at a later date

[azure jungle]

thanks i guess

[alpine sable]

I was trying to solve an exercise from a book but i got stuck in my calculation.
I'm trying to show that foundamental groups of a class of orientable 3-manifold is not left orderable where by this i mean that they admits a strict ordere invariant for left multiplication.
The groups are Seifert manifold built over a surface where the surface is $\mathbb{R}P^{2}.$

They admit the following presentation: $$\pi{1}(M)=\langle\gamma{1},...,\gamma{n},y,h;|$$
$$yhy^{-1}=h^{-1},\gamma{j}^{\alpha{j}}=h^{-\beta{j}},\gamma{j}h\gamma{j}^{-1}=h,y^{2}\gamma{1}\cdots\gamma{n}=1\rangle.$$

With some calculation I got to show that if $k>0,h>1$ the following holds: $h^{-k}<y^2<h^k$ and $h^{-k}<y^{-2}<h^{k}.$ In the book I was given the hint to show that $yhy^{-1}>1()$ and this in facts concludes as it is a contradiction with the assumption that $h>1$ given the first relation but I could not find a way to prove the key fact $()$. Any suggestion in what kind of relations I should look for?
Thanks in advance.

[ocean seal]

Stephen

[azure jungle]

Green = function ; red = number

So if i understood this correctly..
When its function times number, when deriving, i just have to write it like it is.. nothing changes.

When its number plus function, the number dissapears, just like with normal derivations.

[sweet badger]

Can anyone please help me finding the general claim for this problem?

[forest jacinth]

In this case yes, but I'd look up a table for derivatives if I were you, because f'(x) = f(x) is almost never true.

[azure jungle]

okay

[mighty sinew]

What does y represent

[raw shard]

wow that is a lot

[mighty sinew]

mech/civ engineers smh

[warm brook]

Maybe some context is good here so I know what I'm looking at

[forest jacinth]

Is this a matter of converting from polar to Cartesian form?

[warm brook]

Okay nevermind, I see what you're asking

I had no idea what y was

[mighty sinew]

the y on the pic has a + instead of - tho

[forest jacinth]

Not gonna lie, before this comment I wasn't able to find y on the picture.

[warm brook]

^

[bleak ridge]

Maybe it'd be better to forget the context then

[warm brook]

yea i regret asking

what is application i only know math

[mighty sinew]

so why is there a - sign

[forest jacinth]

is this really the biggest issue

[warm brook]

So I presume this is some elliptical crossection?
If it weren't elliptical, then R = b, and it's a little clear
the ellipse formed by this is (x/a)^2 + (y/b)^2 = 1
so if you take
y = bsqrt(1-x^2/a^2), you have
(y/b)=sqrt(1-x^2/a^2)
(y/b)^2 = 1 - x^2/a^2
(y/b)^2 + (x/a)^2 = 1

:)

It's just a point on boundary of the ellipse

Now, if the + sign is correct, I have no idea what it means because you have
(y/b)^2 - (x/a)^2 = 1 which is nonsensical in this context

[warm brook]

I believe because you're given x, it's just finding y in relation to the ellipse eq.

[mighty sinew]

hyperbolic arches sound dope

[warm brook]

Hell yeah

[mighty sinew]

when im not in a building that has one

[warm brook]

Architecture > engineering

no

don't be an econ kid

[mighty sinew]

lmao

plz no econ

i have an econ course this semester and i want to die

my mind is going bankrupt

[warm brook]

Econ is cool
Just sidestep all of the crypto and business bros, then you'll be in the best place

regarding business anyway

Also, afaik econ is just a math major with money so idk

[mighty sinew]

im sure econ majors take 4 analysis courses

[bleak ridge]

Econ 🤢

[warm brook]

I know my intro real analysis class had econ majors in it

which was the 3rd class in the undergrad analysis pathway at my uni

[mighty sinew]

hm here analysis i is intro

excluding diff/int calculus

[warm brook]

So we have foundations of analysis i and ii which is actually intro real analysis
the intro real analysis course is an intro to measure theory and functional analysis in addition to a more intensive view on topology

[vast bobcat]

could someone give me the original equation and the transformed equation please

[warm brook]

@vast bobcat I'm not going to give you the answer, but what have you tried

[vast bobcat]

oh wait i just realised

oops i thought the first point was at 2 not 1

[warm brook]

? when x = 0, y = 2

[vast bobcat]

is the equation y=2^x+1

[warm brook]

Close, when x = 1, what is 2^x + 1?

[vast bobcat]

1?

[warm brook]

2^(1)+1

[vast bobcat]

oh so 4

im so confused

is the coefficient 2?

[warm brook]

Yes, you're correct in that

What I'm just saying is that 2^1 + 1 = 3, but you want it to be 4

[vast bobcat]

oh so it's y=2^x+2?

[warm brook]

Again, that's close, but when x = 0, you see that 2^0 + 2 = 1 + 2 = 3

The trick with this is multiplication

So instead of adding, I'd recommend multiplying by something

[vast bobcat]

is it y=2*2^x?

[alpine sable]

ye

[vast bobcat]

oh

so if i transformed it

would it be y=1/2*2^x+2?

$$ y=1/2*2^x+2 $$

huh

$$ y=1/2*2^(x+2) $$

[alpine sable]

how do you reflect a graph about the x-axis ?

[alpine sable]

.

[vast bobcat]

oh wait

it's -2

y=-2*2^x+2 right

[slender marten]

dx/dt = x^2 for x >= 0 and dx/dt = -x^2 for x< 0. Find the solution each interval.

[wanton folio]

helllo

[azure jungle]

is 1/e a number or a function ?

[raw shard]

number

[azure jungle]

thanks

[golden ridge]

Hey I'm doing calc2 partial fraction integrals and I'm not sure what I should use for my second convenient value for x. I tried 1 but idk if this looks right

[azure jungle]

shouldnt the 1 fall off ? its a number

the last one, -1

aaaaah nvm, i just got it.... im tired and i've noticed im missing a lot of obvious stuff

the one is a derivative of the x...

[raw shard]

not sure how 1/2 turned to 1/e

[azure jungle]

hmmmmm

1/2 is wrong, the task says 1/e

mb :/

[raw shard]

@golden ridge you can post your question again to get it to the bottom of the channel

[golden ridge]

thanks, i was unsure if thats allowed

Hey I'm doing calc2 partial fraction integrals and I'm not sure what I should use for my second convenient value for x. I tried using 1, but this does not look correct

[raw shard]

@azure jungle if you’re gonna ask questions go to another channel please

@golden ridge maybe you could do it again? you have a value for b, and a denominator under b

not very sure if that would work though, probably not

[golden ridge]

yeah

my value for B looks very incorrect lol

[brittle path]

Can someone help me with this, what does b and c suppose mean.

[raw shard]

@brittle path channel is occupied

[brittle path]

oh sorry

[alpine sable]

Hi, a little group theory problem i got stuck all day and cant seem to be able to solve it. I have a group and i'm supposing that it is left orderable. If I know that $yhy^{-1}=h^{-1}$ and that $h^{-k}<y^{2}<h^k$ and $h^{-k}<y^{-2}<h^{k}$ with $h>1, k>0$ how can I show that $yhy^{-1}>1$? I've tried for a while to work it out with "bare hands calculation" but I think I'm missing something

[ocean seal]

Stephen

[vast bobcat]

i need help with ii please

[alpine sable]

A statement of the form "For every element x in D, p(x)" is meaningless when D is an empty set, right?

[empty ridge]

It is always true (find and x in D, for which it isn't)

[alpine sable]

what

really?

What the heck is going on in mathematician's mind

[empty ridge]

Can you find any counter example in D?

[alpine sable]

That's not what I would argue in real life, tbh

But anyways

thanks

So saying that statements of this form are true when p(x) is true for every x in D, is not quite true, is it?

Because obviously that condition doesn't make sense when D is an empty set

So the condition is really: there are no elements in D that do NOT satisfy p(x)

right?

[terse vale]

can someone show the steps in solving this

[alpine sable]

Well, that explains why the definition of one-to-one function makes sense

Not intuitive sense, but logical sense

In that regard

[empty ridge]

Oddly enought, for all x in D, ~p(x) (when D is the empty set)

In some sense, all elements of D doesn't satisfy p(x).

[alpine sable]

There are no elements in D

[empty ridge]

Exactly, and that's why "all those elements" have so many weird properties... they just "aren't"

[alpine sable]

Okay, thank u

[empty ridge]

Is the result of this a natural number? What have you tried so far?

[terse vale]

i tried taking out the +3 first

[midnight ether]

when math exercice is a sussy baka

how do i demonstrate wether this is true or folse

[terse vale]

4^x * 5^3 * 5^4x = 10^3 * 10^2x

[empty ridge]

Ok, you should try to "create a 10" on the left side. Do you have any ideas on how to do that? (note that 4 is 2^2)

[glass lichen]

what does it say in words?

[alpine sable]

For all real numbers x, there exists a real number y such that 3x^2 - 2xy^2 - 1 = 0

[midnight ether]

for what ever value x takes there be a y value that vvorks with the equation

[solar pebble]

discriminant

[glass lichen]

I didnt ask the peanut gallery btw

It was a leading question

[solar pebble]

a= 3, b = -2y^2, c = -1

[glass lichen]

No

Just solve for y

then conclude whether it's true or not

[solar pebble]

that works too i guess

[midnight ether]

y2=smthng

then i replace

[terse vale]

uh idk im doing it right

[midnight ether]

in y2 by that smthng

[terse vale]

so i got

[solar pebble]

what values of x is y^2>0

[empty ridge]

This is the way. Create more stuff on the left. The 5^(4x) = 5^(2x) * 5^(2x) for instance...

[midnight ether]

and tis?

[azure jungle]

can someone check out #help-2 been waiting for 20 minutes, and i gtg soon, would be nice to understand the last task, no pressure tho

[solar pebble]

Disprove by counterexample

[midnight ether]

by 1 and 0 right?

[solar pebble]

yeah, for all pairs of integers p and q, because they can be different, x and y can also be different

[empty ridge]

Is it working?

[solar pebble]

this is more a test of your understanding of logical operators

[midnight ether]

i dont get it bruv

[terse vale]

sry im still confused im gonna ask my teacher tmw

[solar pebble]

then read it?

[midnight ether]

i mean does it help?

[solar pebble]

if you read it

[empty ridge]

Ok, don't worry. If you want to keep thinking about it, the way to solve this is trying to simplify the expression on the left by producing 10's . For instance:
4^x * 5 ^ (4x + 3) = 2^(2x) * 5^(2x) * 5^(2x) * 5^3 = (10)^(2x) * 5^(2x) * 5^3 ...

[midnight ether]

how do i go from x+p=y+q to x=y and p=q

[solar pebble]

1+5=2+4

5≠4

1≠2

[midnight ether]

so its wong?

[solar pebble]

false

not wrong

[nimble grotto]

If I have two different blocks, lets say 3 of block A and 2 of blocks B. How would i get the permutations of how I can align them?
Is 3!x2! wrong?

[midnight ether]

what abou tis

[alpine sable]

me

[copper stone]

si tu poses a=x+p et b=y+q , tu as a=b donc la partie entiere de a est egale a la partie entiere de b

d’où p=q

donc x=y

[midnight ether]

Tyyy

Tysm

[copper stone]

tkt

[inner sage]

Can someone help me how I would go about solving these ?

I get how to determine the quadrant its in without the sin, cos, tan etc. but I dont get what I'm supposed to do with the sin and cos stuff

[copper stone]

you have to calculate it

this is for a)

sin 3pi/4 is √2/2

[inner sage]

So, what exactly did u calculate ?

[copper stone]

these are known angles

[inner sage]

you just plug that in the calculator ?

[copper stone]

you have to know 0, ½, √2/2, √3/2 and 1

[copper stone]

i mean you can in order to verify but you have to know the value

[inner sage]

so, what exaclty is √2/2 ? cuz its asking for like a bunch of things for me to find right ?

[copper stone]

√2/2 is the value of sin 3pi/4

[inner sage]

so, thats the value of the related acute angle? Also, does related acute angle basically just mean the angle ?

Like, sin3pi/4 is the acute angle

[copper stone]

no

the acute angle is between the terminal arm and the x-axis when the terminal arm is in quadrants 2 3 or 4

so its between 0 and π/2

for a) the acute angle is π/4

[inner sage]

So if the acute angle is pi/4, wouldnt that make it in quadrant 1 ?

[copper stone]

that’s the purpose

3pi/4 is in quadrant 2 so you want the angle in quadrant 1 which makes π/4

[inner sage]

Wait question, so is the terminal arm like the line that makes the radius ?

Ok wait i googled it, i got that

i think

[copper stone]

i see what your point is but you expressed it wrong since there is not just 1 radius

[inner sage]

Oh, ok yeah

[copper stone]

maybe this can help

[inner sage]

ohh ok

ok i get that

[olive basalt]

Does anyone know this?

[inner sage]

wait so, I was still a bit confused as to what I would be doing with sin

Like, how does sin help with solving this whole thing

[copper stone]

i dont see how sin is related either

the question could have been 3pi/4 and we would have done the same

so idk

[inner sage]

oh

[inner sage]

ok thanks tho loll

[wanton patio]

quick question, how do you type a matrix like this in Latex?

with parentheses and a line

[copper stone]

$\left(\begin{array}{ccc|c}2 & -1 & 1 & 11 \ 3 & 2 & 2 & 8 \ 4 & 4 & -4 & -20\end{array}\right)$

[ocean seal]

nisrine

[wanton patio]

thank you

[compact lynx]

Hi.

[copper stone]

it’s de morgans formula

let’s call $A=(p \wedge \neg q)$ so you have $A \vee (\neg p \wedge q)$

[ocean seal]

nisrine

[copper stone]

it’s not de morgan sorry it’s just distributivity

[wanton patio]

@copper stone i got an error, can i dm you a picture?

[copper stone]

yea?

yes that’s distributivity

that’s what they did on line 2

[compact lynx]

what

how is what is done distributivity though

[copper stone]

here we get
(A ∪ notP) ∩ (A ∪ q)

look at line 2 that’s exactly the same

just replace A by (p ∩ notq)

[compact lynx]

oh ur distributing the

entireity

ohhh

i see ty ty

[copper stone]

np

[late parcel]

Can someone help me

I need a full walk through

[alpine sable]

LMFAQO

i CNAT

[dreamy ridge]

can someone help me with this related rates question

i got

[raw shard]

can you post the whole question

[dreamy ridge]

uh

this si the whole question'

its a cone

i dont have the actual question because it was on a whiteboard and i didnt take a pic in time

[raw shard]

oh

i guess i can try

@late parcel what’s 6.1*10^9/100

[dreamy ridge]

i got $\frac{75}{\pi} (\frac{\pi}{750})^\frac{2}{3}$

[ocean seal]

dirtball

[supple timber]

Current population global is 7.1 Billion

[raw shard]

that doesn’t matter for the question

[bleak ridge]

,ask global population

[ocean seal]

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Requested by PapaBread#3820

[raw shard]

and that’s not even right

it’s like 7.9 now

[late parcel]

@raw shard im confused on ur thinking

[raw shard]

just answer my question

it will help

[late parcel]

And ya the human population is 7.9 nil

What’s your question?

[raw shard]

what’s 6.1*10^9/100

[late parcel]

I’ll type it in the calculator

One sec

[raw shard]

bruh

[late parcel]

What

[raw shard]

that’s not needed

[late parcel]

Ok then what do I do

[raw shard]

it’s just 10^9/10^2

do you know how to do that?

[late parcel]

What are you talking about

Idk

No

I do not

I do not know how to even attempt this question

[raw shard]

repost the question and i’ll explain

[raw shard]

wait this is a test

[late parcel]

It it’s not

[wicked gorge]

wait

did I do something wrong

[late parcel]

It’s the AP practice

Open note open friend

It’s 8:45 here, how would I have a test at home lol

8:45 pm at night @raw shard

[raw shard]

i don’t know what time is it for you lol

[late parcel]

Look at the top left

See it’s 8:46

I promise I’m not cheating

[raw shard]

ok

all you needed to say was open notes lol

anyways

[late parcel]

But if it wasn’t open note a lier could still say it was

Lol

[raw shard]

so the world population is growing at 1.35% per year

[late parcel]

But anyways

Correct

I follow up to there

[raw shard]

do you know how to get a percent of a number?

[late parcel]

Multiply by 100

[raw shard]

divide

1% of x is x/100

[late parcel]

Yes

[raw shard]

so first do 6.1*10^9/100

[late parcel]

Ok

[raw shard]

and then multiply that by 1.35

approximate and there’s your answer

[late parcel]

Doesn’t seem correct

[raw shard]

you put that in the exponent

you did 6.1*10^(9/100)

when i said that, i didn’t mean the exponent

[late parcel]

What

Like that

Then multiply that by 1.35

[raw shard]

(6.1*10^9)/100

if it was in the exponent, i would have put parentheses around the exponent

[late parcel]

That gives me this

[raw shard]

yeah

[late parcel]

Which one

[raw shard]

does that look like any of your options?

[late parcel]

No

[raw shard]

look at the power

[late parcel]

7

[raw shard]

so which do you think it is

multiply by 1.35 if you want

[late parcel]

I think C

Is that correct

[raw shard]

yes

[late parcel]

Thx

[raw shard]

no problem

[subtle cedar]

How do I solve how long each side of a triangle is if I know the perimeter

[raw shard]

if you know the angles that can help

[raw shard]

actually no

[subtle cedar]

Instructions: find the value of x for the triangle

[raw shard]

add all the sides together and set it equal to 24

[subtle cedar]

Well idk what x is

[raw shard]

i know

[subtle cedar]

?

Sorry I have so much homework my brain is fried rn

[raw shard]

add all the sides together, and set it equal to 24

solve for x

[subtle cedar]

Oh right

Thanks

[raw shard]

no problem

[subtle cedar]

So (x+4) + 4x + 10(x-1)

[snow nest]

=24 yeah