help-0

[upper pebble]

elimination method just sounds more evil

idk

[rapid pagoda]

true

[river hearth]

???

[jagged trout]

Horner Schema

[rapid pagoda]

3/2 would be the answer

[glass lichen]

factor theorem

[rapid pagoda]

simple division if uk nothing

[rapid pagoda]

it is a factor

[rich niche]

can someone help me prove that (10^(n-1)-1) is always divisible by 9, provided that n>1 and n belongs to natural numbers

[jagged trout]

first prove it for 2

[rapid pagoda]

you can take different assumptions

[wet fulcrum]

long division

[rich niche]

so like, proving for n=2,n=3

like this?

[rapid pagoda]

yep

[wet fulcrum]

if it leaves a remainder that cant be divided its not factor somple

[rapid pagoda]

show 3-4 assumptions

[glass lichen]

examples dont work for a proof

[rapid pagoda]

already did.. he isn't responding

[rich niche]

i was looking for something rigorous tbh

[glass lichen]

yeah, you use induction

[river hearth]

so wait is 1 the correct number to put off to the side here?

[rich niche]

if there is a way

[glass lichen]

Induction...

[rich niche]

so first like assuming its not true

[glass lichen]

that's contradiction....

[rapid pagoda]

you can use induction as well

[rich niche]

wait how does induction work

[rapid pagoda]

like @glass lichen said

[glass lichen]

show the base case is true
assume true for n=k
prove that n=k+1 is true under the assumption

[tropic pine]

/hcf

[rich niche]

so wait we have to assume that its true for k?

[tropic pine]

Heh

[glass lichen]

yes, you assume the inductive hypothesis is true

[jagged trout]

https://www.youtube.com/watch?v=5JGjELKJYD0

[rich niche]

i see thank you

[chilly monolith]

I am reading IGCSE, so a lot of these concepts are new vocabulary to me as I am ESL.

How do I find out if a number is irrational by inheritance? From what I get unless it goes by the power of 2 it's pretty much irrational

[gray isle]

a rational number can be expressed in the form p/q where p and q are integers (and q is't 0)

[chilly monolith]

Sorry, got somebody telling me something there for a sec. I get that part, but then that means d and c and a are irrationals, as they all use a decimal.

Is this correct? just to make sure I am understanding this, don't want to build off bad habits. (sorry if I am too insecure)

[gray isle]

as they all use a decimal.
is vague

[jagged trout]

A irrational number is a number which can not write as a fraction

[gray isle]

bad wording, and as is, is not good enough to justify whether something is rational or irratinal

[chilly monolith]

ahhh, so it's not just a decimal that does it, I see.

[gray isle]

e.g.
0.5 (has a decimal and is clearly rational, it can be represented as 1/2 and 1 and 2 are both integers)

[chilly monolith]

so because a c d use pi and square root of 2, that are irrationals, i can safely assume they're irrationals too?

[jagged trout]

Yep, because 0.5 = 1/2

[gray isle]

wait

the given values are irrational

however what they're asking for may be rational

you'd need to do the work (apply the appropriate formula, do some caluclations)

[chilly monolith]

Oh! I see now. I didn't get the task was to give a value, thanks

[gray isle]

the value will be part of the justification

[edgy path]

curious if im simplifying this correctly

[livid pier]

seems correct

[arctic wren]

I don't know cause the inverse of matrix isn't 1/matrix

[edgy path]

[glass lichen]

yeah you cant divide by a matrix

[edgy path]

I see

how would I go about simplifying this? pls helpu

[glass lichen]

$(AB)^{-1}=B^{-1}A^{-1}$ assuming both A and B are invertible

[ocean seal]

Mosh

[glass lichen]

easy to verify the truth in that since $B^{-1}A^{-1}(AB)=I$

[ocean seal]

Mosh

[edgy path]

so would it be $y\cdot(-XP)^{-1}$

[ocean seal]

Alkappa

[edgy path]

XP positive oops

[candid bolt]

Hey could I ask a question?

[glass lichen]

is y a matrix or a scalar?

[edgy path]

vector

[glass lichen]

then you cant move it around, it stays right multiplying

$=(XP)^{-1}y$

[ocean seal]

Mosh

[edgy path]

ah thanks :d

[glass lichen]

which "is what you got"

but proper

[edgy path]

i see i see :d

[candid bolt]

Could I ask a question?

[arctic wren]

But you can move the XP inverse matrixes to multiply the normal ones ? @glass lichen

[glass lichen]

$P^{-1}X^{-1}(P^T)^{-1}(X^T)^{-1}X^TP^Ty$ is what you get when expanding the inverse

[ocean seal]

Mosh

[glass lichen]

all the transposed matrices reduce to I's by associativity

[arctic wren]

But why the transposed matrixes go to the Right?

[glass lichen]

cause I expanded the inverse

[arctic wren]

And not stay on the left

[glass lichen]

and inverse is anti-commutative on products

probably a proper term but idk it, so anti-comm

[arctic wren]

Ooo i didn't know about that

[glass lichen]

$(AB)^{-1}=B^{-1}A^{-1}$

[ocean seal]

Mosh

[glass lichen]

easy to prove that via definition of inverse

[arctic wren]

Thanksss when i stuided matrixes on High School i didn't see that

[warped phoenix]

Determine whether $x−2$ is a factor of the polynomial $p(x)=2x^3−3x^2−5x+6$ using the Remainder Theorem.

[glass lichen]

just put dollar signs around what needs to be texit'd

[ocean seal]

TheMane3

[warped phoenix]

ok

so

i did synthetic division for this

and put -2 in the little square

[glass lichen]

use remainder theorem

not division

[warped phoenix]

but i thought synthetic division gives you a remainder

[glass lichen]

it does

but that isnt remainder theorem, like the question explicitly says to use

[warped phoenix]

what is that again

is it when p(x) / x - a = p(a) ?

or something like that

[glass lichen]

but if a polynomial p(x) is divided by mx-b, then p(b/m) will be the remainder

[warped phoenix]

so

p(2)

so at that point you literally just plug in 2 into the equation, and if you get 0 from solving, it's a factor?

[glass lichen]

yes

[warped phoenix]

ohhh

ok

[glass lichen]

p(a)=0 means x-a is a factor is factor theorem

[mellow canyon]

hey, can anyone explain some algebra to me?
it's in trig but algebraic
so we have the degree - radian formula
theta degrees / 180 = theta radians / pi
so if we plug 3pi/4 into this
we get something like this

(3pi/4)/pi = theta degrees / 180
3pi/4 * 1/pi = theta degrees / 180
how did they make this jump? where did you factor out the division by pi?

[glass lichen]

division is the same as multiplying by the reciprocal

[acoustic abyss]

anyonee

help?

i got 7 is it correct?

[warped phoenix]

plug it into a calculator and check if it is

[mellow canyon]

really?

[warped phoenix]

you're just replacing each variable with what the instructions tell you the variable stands for, and then doing the proper operations

[mellow canyon]

how does that work out

[glass lichen]

$\frac{a}{b}=a\cdot\frac{1}{b}$

[ocean seal]

Mosh

[mellow canyon]

oh, I always thought hat when you divide by b, it's assumed that it's already 1/b

since a * 1 = a

but I guess that does'nt work out does it

[glass lichen]

/b and *1/b is equivalent

[mellow canyon]

that makes sense I guess. I was explaining my original reasoning above. I guess I should have been thinking about B as more in a vacuum. thanks!

[slim grove]

Could anyone help me with question 3b?

[granite mountain]

Multiply by 3

Than delta

There should be two answers

[acoustic abyss]

halp plz

[warped phoenix]

channel in use

[slim grove]

When I did part of it I was getting a negative square root, would that mean no real solutions or am I doing something wrong?

[acoustic abyss]

oh sorry

[granite mountain]

Let me put it on paper, 2 secs

[strong citrus]

It doesn't have real solutions

[granite mountain]

Yea, delta is negative

[strong citrus]

Are you getting a -2/3 under the sqrt

Did I do it correctly?

[glass lichen]

,w solve 3x^2+2x+7/3=0

[ocean seal]

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[glass lichen]

yes

[strong citrus]

Why is the answer looking a bit different?

[glass lichen]

yours isnt rationalized

$-\frac{1}{3}\pm\sqrt{\frac{2}{3}}i=-\frac{1}{3}\pm\frac{\sqrt{6}}{3}i$

[ocean seal]

Mosh

[slim grove]

Ohh I think I understand it now, thanks everyone!

[arctic wren]

This limit is -1/4 but mine is 0, what i'm doing wron?

[gray isle]

you're making some wrong/unjustified/assertions/leaps in the last two lines

[arctic wren]

I'm not seeing it

[gray isle]

how are you getting 0 for the limit on the left

[gray isle]

ok, however by splitting it the way you did, the second limit doesn't exist

[arctic wren]

Ok

I'll try again

[gray isle]

consider analysing the whole expression

$-\lim_{x \to 0}\frac{\sin(x)}{(\cos(x)+1)2x}$

[ocean seal]

ℝamonov

[wild lagoon]

is this right the 80 th percentile of this data set
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is 8 or is it using the dataset {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}?

[arctic wren]

@gray isle thank you, i get it now

[modern saffron]

why is C0 equal to 0

[charred flint]

@modern saffron c0 is coefficient of the term with no x

and here it's 0

[visual moon]

Find the curl and divergence f arrow on top(alpha,beta)=<5*alphasinbeta, 4 *alphacosbeta)

what am i supposed to put for the k value?,nothing?

i got 4cosbi-5acosb

and 5sinb-4asinb

[charred flint]

what's a k value?

[timid wind]

ok.

[visual moon]

for the curl, shouldnt there be i,j,k?

there is no thirs value so i left k out which im unsure of which is the right thing

[charred flint]

oh k as in the vector

in 2d you don't need to include the vector

[visual moon]

ahhh

right

thanks,looks like its right then

[alpine sable]

A basketball player, about to “dunk” the ball, jumps 76 cm vertically. How much time does the player spend (a) in the top 15 cm of this jump and (b) in the bottom 15 cm? Does this help explain why such players seem to hang in the air at the tops of their jumps?

For this, we have to calculate 0.76 m = y'(0)t_1 - gt_1^2 / 2?

I found some answers online in my book that instead calculate 0.15 for the top of the jump, which I don't understand

You're not solving anything

It's very useful to have a periodic function, and its graphical interpretation using triangles

[timid canyon]

how come we can't use the pumping lemma to prove regularity of a language?

[charred flint]

good alt

[tawny venture]

Hello I am a student from Spain I would like to know if you could help me solve this:
1.Consider sets X.
A. Type the ratio R of X to Y, defined by (x, y)> y, where X €
B. Type the domain and range of R.
C. R, is it a function? Explain
D. Write the R array.

Try translating the problem, sorry for my bad English.

[river fractal]

If two people are playing chess, and one is a mind reader, and the other is a man who can see into the future: who wins and why?

[worn urchin]

Depends who is ultimately the better chess player as it would be a fair match-up. I do think the mind reader would have an advantage because if the man who could see into the future was thinking about what happens, then the mind reader would be able to access that

[ionic jewel]

define see into the future

assuming they could see every possible outcome it would simply be whichever side wins in chess

its not a solved game, but both players would play optimally so it would be the same outcome every time

[warped phoenix]

How do I do this?

I know how to do synthetic division and get the remainder

but i messed up that even i think

because in all the options the remainder is 6, but I got -133.5

[ionic jewel]

l o n g d i v i s i o n

[arctic wren]

Someone can help me in this equantion, my answer isnt equal to the answer in the book?
Since $y = A \sin(x) + B$
Find A and B to make the following equation true:
$y^{''} + y^{'} - 2y = \sin(x)$

[ocean seal]

Guilhotina

[ionic jewel]

,w y'' + y' - 2y = sin(x)

[ocean seal]

Results provided by WolframAlpha

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Requested by 兔子#6562

[ionic jewel]

idk how to solve the DE and wolfram doesnt seem to answer the question

wait a second

you can just take the derivative

[arctic wren]

Yes... A is -3/10 and B is -1/10

[ionic jewel]

y'' = -Asin(x), y' = Acos(x)

-Asin(x) + Acos(x) + 2Asin(x) + 2B = sin(x)

[worn urchin]

In a regression estimating the impact of years of education on a person’s income, if there are no measures of ability in the regression, then
A. the error term will simply pick up the effect of ability, and the coefficient estimate on years of education will be unbiased.
B. we would expect the coefficient on years of education to be biased upward as it picks up the impact of higher ability and ability and years of education are positively correlated.
C. we would expect the coefficient on years of education to be biased downward because we are leaving out of the regression the positive impact of ability.

[ionic jewel]

Asin(x) + Acos(x) + 2B - sin(x) = 0

[arctic wren]

,w sin(x)*(-3A-1) + Acos(x) - 2B = 0

[ionic jewel]

is this your soln or the books?

[arctic wren]

Book

[ionic jewel]

what was yours?

wolfram says B = A/2

[arctic wren]

A=-1/3 B -cosx/6

[ionic jewel]

hmph

idk then

unless this is a standard DE form no clue

[ionic jewel]

not you again

[upper pebble]

use Google

[alpine sable]

Problem: A cylindrical toilet must hold 2 gallons of liquid shit for Nikocado Avocados mukbang aftershow. Find the dimensions of the container which will minimize the amount of material needed.

[sleek elbow]

the point of sin is to get the opposite side of an angle divided by the hypothenuse in a right triangle @cobalt breach

[stiff moth]

Anyone have an idea on an irl example of air pressure as a function of time ,, i dont really understand the relation so am trying to connect it to real life which may possibly help

[charred flint]

a plane rising has its external air pressure change

[glass lichen]

if you can relate vertical height to time, then you can relate pressure to time

[clever folio]

Would the pressure of the air inside a tire over time count?

[ashen wave]

Can anyone help me with this

[charred flint]

sure mehstruslehpy

[clever folio]

Seems like an ex most people might be vaguely familiar with is all.

[clever folio]

Try to graph y=|x-2| first. What happens at x=2? What happens if you look at x=anything to the right or left (along the x-axis) of 2?

[ashen wave]

wait what? I thought -2 was the y-int?

[clever folio]

I'm just trying to point out at x=2 you have y=0

[stiff moth]

how so

[glass lichen]

pressure is a function of height

[ashen wave]

how did you know x=2?

[charred flint]

there's 0 air pressure in space

so the air pressure has to go from something to nothing as you rise

[stiff moth]

so a planes pressure would decrease as it rises bc its getting closer to space?

[charred flint]

yup

[clever folio]

I looked at y=|x-2| and asked myself what happens if x=2, since |x-2| has a 2 in it.

[stiff moth]

ahh that makes sense ty!!

[glass lichen]

$f(x)=\abs{x}\implies \abs{x-2}=f(x-2)$ so it's the parent function shifted 2 units to the right

[ocean seal]

Mosh

[clever folio]

^mosh has a very nice general way of looking at it too.

[ashen wave]

oh okay that makes sense! So every time there are those lines surrounding the x and another number you substitute the x to that value?

[glass lichen]

No

[clever folio]

Not exactly

[ashen wave]

oh

[glass lichen]

|x| is a function

,w graph y=abs(x)

[ocean seal]

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Requested by moshill1#9771

[clever folio]

I just did the equivalent of asking myself "what if x=this thing".

Generally to graph a function it's not a bad idea to pick a few x values to see what corresponding y values that function produces.

As you pick x values and draw then into your diagram you'll see the shape of the function slowly become more visible.

It doesn't hurt to pick random values that seem interesting.

[ashen wave]

alright I think I get what your saying im going to answer a few more practice problems and if dont understand something could I ask you?

[clever folio]

I think you can just post here and ppl will respond?

[ashen wave]

oh right okay

thank you!

[clever folio]

Don't forget

[ashen wave]

?

[clever folio]

To figure out how to shade your inequality too!

[ashen wave]

oh yes I know xd

thank you lol

[clever folio]

No problem.

[arctic wren]

@ionic jewel i think this is the way to resolve the equation https://www.mathsisfun.com/calculus/differential-equations-first-order-linear.html

[warped phoenix]

$\frac{1}{x}+\frac{1}{x+3}=\frac{1}{2}$

[ocean seal]

TheMane3

[warped phoenix]

How do i solve this?

[wintry kernel]

get the variables out of the denominators

[warped phoenix]

how 😦

[vague coral]

what do you do when you have two fractions with differents denominators ?

[warped phoenix]

you find the lcm

:0

[vague coral]

do it

[warped phoenix]

the lcm of x and x+3...

dont you multiply the denominators to find the lcm?\

[vague coral]

yes

[warped phoenix]

so x^2 + 3x?

[vague coral]

no

wait yes

x(x+3) = x^2 + 3x

[warped phoenix]

..now what

do i multiply both fractions by x^2 + 3x

[vague coral]

you will get :
$$\frac{2x+3}{x^2 +3} = \frac{1}{2}$$

[ocean seal]

Herels

[vague coral]

now think

[warped phoenix]

MY BRAIN IS HAVING A STROKE RN 😭

[vague coral]

never heard of this ? :
$$ \frac{a}{b} = \frac{c}{d} \implies ad = bc$$ ?

[ocean seal]

Herels

[worn urchin]

Can someone help me in #help-3

[warped phoenix]

ig not..

wait but

its 1/x + 1/x+3 = 1/2

so a/b + c/d = e/f

[vague coral]

basic algebra tho..

what are you doing

[warped phoenix]

idk

um

what do i do with the lcm

do i multiply it with the 1/x ?

[vague coral]

$\frac{1}{x} + \frac{1}{x+3} = \frac{2x+3}{x^2 + 3x} = \frac{1}{2}$

[glass lichen]

no

[warped phoenix]

so 2x + 3 / x^2 + 3x is the lcm

[ocean seal]

Herels

[vague coral]

no

I just calculated 1/x + 1/x+3

[wintry kernel]

The first thing you should do when faced with variables in the denominators is to move them up, by multiplying by the lcm

[vague coral]

^ that's the idea (i just don't know how to explain it in english)

[placid venture]

loga^b = bloga right?

So why is

100(ln2)^2 different from 200(ln2)

100(ln2)^2=48.04
200(ln2)=138.6

[clever folio]

log(a^b) and (loga)^b are different. Are you mixing them up?

[placid venture]

just realized this channel was already in use

my bad

[placid venture]

didn't realize they were different

[clever folio]

Yeah you have to be sort of careful with how you compose them. One you plug in a^b into a log the other you do log to the bth power.

I think that is where you are getting it mixed up.

[placid venture]

which one's the one where the rule applies?

[clever folio]

Well 100ln(2^2)=200ln2 for ex

[placid venture]

ohh ok

thanks!!!

[clever folio]

No problem

[placid venture]

again sorry about interrupting the chat

[warped phoenix]

np

[warped phoenix]

i found the lcm

but what am i multiplying it with?

[clever folio]

I probably wouldn't think too hard about multiplying by x^2+3x I'd probably see that the x, x+3 and the 2 are all in the denominators then mul by 2x(x+3)

Then a bunch of stuff cancels in such a way that you can rewrite the whole thing as a quadratic equation.

I mean, it's the multiplying by the same thing (almost)

Just in a way that might be more convnient.

[warped phoenix]

oh..so you multiply all the denominators together to get 2x(x+3)?

[clever folio]

Yah the idea is to cancel out each denominator

It's the same thing you are being told to do already

I'm mainly just explaining how I think of it and why I do it in that particular form.

[warped phoenix]

$\frac{2x\left(x+3\right)}{1}\cdot \frac{1}{x}+\frac{1}{x+3}=\frac{1}{2}$

[ocean seal]

TheMane3

[warped phoenix]

so this is what im doing?

and it cancels out 1/x and 1/x+3

[clever folio]

No multiply both sides

[warped phoenix]

ohh

[clever folio]

Multiply the whole thing too not just the 1/x

On the left

[warped phoenix]

so that'd leave me with

$2x^2+6x=0$

[ocean seal]

TheMane3

[warped phoenix]

?

[clever folio]

This is different from 2x(x+3)[1/x +1/(x+3)]

The parens are important

I'm saying multiply both sides. So 2x(x+3)[1/x + 1/(x+3)]=2x(x+3)(1/2)

[warped phoenix]

$\frac{2x\left(x+3\right)}{x}+\frac{2x\left(x+3\right)}{x+3}=\frac{2x\left(x+3\right)}{2}$ ?

[clever folio]

Why x+1?

[warped phoenix]

oh

sorry

[ocean seal]

TheMane3

[clever folio]

Yah. Now see how lots of stuff cancels and you don't have any more fractions after you cancel all that junk?

[gritty gull]

bro what does the upside down exponent mean

[clever folio]

Upside down?

Like a subscript?

[gritty gull]

its a exponent at the bottom

[clever folio]

It's a subscript

[gritty gull]

like tiny 2 then C then 4

oh thats what its called

is it the same as a regular exponent

[clever folio]

That's 2 choose 4. It's for combinations

[warped phoenix]

@clever folio 5x+9=0?

after cancelling stuff out

[gritty gull]

5 has to be negative

so

maybee

wait

maybe

[warped phoenix]

cuz im left with 2x + 6 + 2x + x + 3 = 0

[clever folio]

Pretty sure you'll get a quadratic

[gritty gull]

x = -9/5

oh

[warped phoenix]

😦

$\frac{2x\left(x+3\right)}{x}+\frac{2x\left(x+3\right)}{x+3}=\frac{2x\left(x+3\right)}{2}$

[ocean seal]

TheMane3

[clever folio]

https://www.mathsisfun.com/combinatorics/combinations-permutations.html

Sounds like this too me

[warped phoenix]

For the first term, I cancel the x outside the parens, the second term, i cancel the x+3, and the last term, I cancel the 2

OH WAIT

one sec

[warped phoenix]

i think i got it $x^2+7x+6=0$

oh wtf

[ocean seal]

TheMane3

[warped phoenix]

there lol

😄

wait..

i get x = -1 and x = -6

that's neither of the answer chocies :/

[clever folio]

I think you made an algebra mistake

[warped phoenix]

😭

[clever folio]

I got something different from x^2+7x+6?

I could have messed it up too of course.

[warped phoenix]

well

after canceling stuff out

i get $2x+6+2x+x^2+3x$

And then I add like terms, giving me x^2 + 7x + 6 -0

[ocean seal]

TheMane3

[clever folio]

After simplifying you would get 2(x+3)+2x=4x+6=x^2+3x. Subtract 4x and 6 from both sides and you get x^2-x-6=0 right?

Unless I'm having a bad algebra moment lol.

[warped phoenix]

omg

ur right

i thought they were all on the same side of the equation

🤦‍♂️

i forgot that they werent, ig thats what happens when i dont write all my steps out lol

[clever folio]

Yeah you def have to be very careful with algebra to avoid these kinds of mistakes.

[warped phoenix]

$x^2-x-6=0$

?

[ocean seal]

TheMane3

[warped phoenix]

now i think i got it

i hope

[clever folio]

Yah, so solve that like normal and then reject any erroneous solutions using your very original equation.

[warped phoenix]

x = 3

is the answer

😄

got it..so ill keep that rule in mind

that if there's an equation in which all the numerators are one, you can multiply the denominators together and then multiply that on both sides

solve the quadratic, and then solve for x

and bada bing bada boom

[clever folio]

It's not so much that the numerators are one but that the denominators have a bunch of ugly stuff like variables and junk in them that you can get rid of by multiplying the product of all the denominators by

[tired estuary]

the integral of x^-1 = the integral of 1/x?

[clever folio]

The most efficient way is to take the lcm of all the denominators of course.

[warped phoenix]

so the lcm was that 2x(x-3)

thing

[tired estuary]

cuz the integral of 1/x should be ln|x|dx

[clever folio]

Yah

[warped phoenix]

can you give me a practice problem/what to search to find a practice problem to try it on my own? I doubt all my test questions are going to have a numerator of 1

[clever folio]

No dx

Also for indefinite integrals don't forget +C

[tired estuary]

oww yeh

but why no dx?

[clever folio]

Well you can try just picking new numbers maybe instead of 1/x try 2/(3x) or 7/(5x+9) or whatever. Do tou have a textbook, because that's usually where I'd start for practice probs.

[ocean seal]

Red Cell

poolparty

Red Cell

[warped phoenix]

$x^3^4^0^2^4-x-int=dx$

[clever folio]

There's probably a fancy deeper reason but I usually just think of the dx in the integral as part of the notation for the integral operator.

[ocean seal]

TheMane3
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[clever folio]

Ignoring u-sub tricks and junk

[warped phoenix]

there, i fixed it @cobalt breach

[ocean seal]

poolparty

[clever folio]

$\int f(x) dx$

[ocean seal]

mehstruslehpy

[tired estuary]

yeh me too

but the dx stands for your distance

between x2 and x1

[ocean seal]

Red Cell

[tired estuary]

your minimal distance

[ocean seal]

Red Cell

[glass lichen]

sintheta

[ocean seal]

Red Cell

Red Cell

[glass lichen]

#bots if you're going to spam the bot

[tired estuary]

@clever folio

[ocean seal]

Red Cell

[glacial hedge]

could someone verify the answer of this surface integral, I got 0 but am sceptical using Stokes theorem

[ocean seal]

Red Cell

[clever folio]

I mean it's sort of analogous to delta x in the reimann sum defn (idk how to spell it). But explanations of it are sort of outside the scope of a calc 1-3 course (and outside the scope of my experience lol)

[glacial hedge]

Could you stop spamming please

[clever folio]

Besides as like a linear approx or something?

[ocean seal]

Red Cell

[tired estuary]

owww yeh i don t like the leibniz notation

dy/dx = f'

[glacial hedge]

wdym leibniz notation is great

[tired estuary]

dy= f'(dx)

[clever folio]

I'd think of it more in terms of antiderivatives i guess lol.

[tired estuary]

that dx is so confusing tbh

limits, differentials, integrals

partial differentials

[glacial hedge]

once you get used to leibniz notation, it becomes very usefull

[tired estuary]

and continuity

[glacial hedge]

Basically everything past calculus including calculus too... unless ur doing modern algebra or something like that

[tired estuary]

yeh i like to see those complex letters in differentialmathematics

but it becomes rlly confusing in integrals

cuz the dx stands suddenly alone

and gets another meaning

[glacial hedge]

Real analysis, complex analysis, partial differential equations, differential equations, linear algebra, topology, differential geometry, modern algebra.....

[glacial hedge]

well u better get used to it in integrals..... thats the only notation used for integrals because the non leibniz way doesnt make sense for multiple variables

U dont need to worry about this stuff for a looonggg time

[tired estuary]

oww

[clever folio]

It works nicely from an intuitive point of view at least for basic calc ode and (basic) physics?

[warped phoenix]

@clever folio if you're not busy, what about something like $\frac{2}{3x}+\frac{7x}{2x+9}=\frac{1}{4}$ Would I still multiply the denominators with each other?

[ocean seal]

TheMane3

[glacial hedge]

bruh my question got burried

[clever folio]

Yah I'd do the same trick but this time using 3x(2x+9)4 and see where that led me.

[ocean seal]

Red Cell

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

[clever folio]

I haven't touched vector calc in so long that I didn't think I'd have anything helpful to say lol.

[ocean seal]

Red Cell

[warped phoenix]

if you dont have any questions and you're only here to test out the bot please do it in #bots

[warped phoenix]

what determines what you should be combining in the denominator?

channel in use

the channel is in use

you clearly havent read #❓how-to-get-help

[pseudo field]

would you like me to help?

[warped phoenix]

the channel is occupied, move elsewhere @cobalt breach

[pseudo field]

nevermind, seems the other guy is back

[warped phoenix]

oh ty for the offer ❤️

but yeah mehstruslepy, i combined the denominators and got 6x+36

but you got 3x(2x+9)4

[pseudo field]

1 + lnx if i remember correctly

[clever folio]

I'm not sure how you got that. You don't have to multiply it out btw.

[warped phoenix]

oh so what did you do then?

with the denominators

[clever folio]

Have you tried working it out by parameterizing it? I thought there were ways to do these things that way?

[warped phoenix]

dude the channel is in use

[glacial hedge]

yes, but thats a terrible way to do it, plus probably pretty hard to solve the resulting integral. But stokes theorem makes it much easier, and this homework is called stokes theorem

[clever folio]

Just multiply both sides of the equation by the product of all the denominators to clear out all the fractions. I don't multiply out the product of the denominators themselves which is why I had 3x(2x+9)4 rather than multiplying that prod out.

[clever folio]

Yah it's also written basically in the perfect form for stokes lol. It's still worth a shot to try things the slow harder way sometimes. Checking a result two different ways can give you confidence that you got the write answer which it sounds like your issue is you don't trust what you got via stokes thm?

Maybe there's an easier way to check it lol?

[glacial hedge]

well idk i just like its weird... i get weird vibes when an integral boils down to like sin(2x) from 0 to 2pi

[clever folio]

Seems too easy lol.

I remember the difficulty of surface integrals being highly dependent on picking convenient parameterizations that would reduce to certain easy known cases for surface integrals.

Maybe you can check it on wolfram alpha too?

[glacial hedge]

How do u check that on wolfram alpha?

do i have to parametrize the surface 😦

[clever folio]

Idk just a guess lmao

[clever folio]

It's just the only other way I personally recall on how to work out surface integrals without using stokes thm.

Or some other slick theorem

[glacial hedge]

u mean the deez nutz theorem?

[clever folio]

Whatever thms you have lmao.

[pseudo field]

uhh i think 147 metres? but don't count on my physics

[glacial hedge]

$y=v_i*t-4.9t^2$

[pseudo field]

i've only done math lol

[glacial hedge]

shit wrong equation

[pseudo field]

lol

[glacial hedge]

$y=y_0 v_i*t-4.9t^2$

damn wrong again

[pseudo field]

lol

[glacial hedge]

$y=y_0 +v_i*t-4.9t^2$

[ocean seal]

Elonmosqito96

[glacial hedge]

plug in y as 0 and plug in t=5 ans v_i = 0 then solve for y0

[pseudo field]

yea so I think i was wrong, sorry

14

does the ' mean a power?

why though, if you're 12 then you should just relax

you don't need to do an online test for calculas at 12

but nevertheless

if those symbols are power signs, then 21x^2 -4x + 4

[strong furnace]

<@&268886789983436800>

spam and then this

[tall wing]

thank you

banned

[rich basin]

I was wondering why did i get this answer wrong

I did something under the lines of finding the derivative of both of them

and them making them equal

so it is like ln(10) 10^x = ln(5) * 5^x

and then i did ln(5)/ln(10) = 5^x/10^x

and then i did ln(5)/ln(10) = (5/10)^x

This is the final equation i had

replace the log(10)/ log(5) with base e log

i evaluated it to -0.516697

But it is the wrong answer

[pseudo field]

well

i dont think you need to do all of that

[clever folio]

Did they tell you to round it that way?

I'm wondering if this is an online hw where your last digit is rounded wrong is why.

[rich basin]

The answer for this is (0,1)

[pseudo field]

yeah im just dumb ignore me

[rich basin]

So why is it that my answer is wrong

I don't see anything i've done wrong

[clever folio]

That's odd I was thinking they meant like what x-value are the slopes the same? Lmao.

[rich basin]

I think that is synonymous to the question asking for when they are parralel

Because it is a necessary condition for a tangent to be parallel to each other to have the same slope

[clever folio]

Yes of course

My point is more I was expecting them to want the x-value and not like the point along the graph. I don't think they have tangent lines with equal slopes at (0,1)?

Like if you graph f(x)=10^x and g(x)=5^x they both def pass thru (0,1) but have diff slopes at that pt.

*or at least the tangents at that pt have diff slopes.

Like this I mean

[rich basin]

@clever folio So what do you think the answer would be

[clever folio]

I was thinking your answer made sense. Maybe we are both wrong or maybe the answer they had was wrong?

[rich basin]

Yeah, the answer could be wrong. I guess i would assume the answer is wrong

[rich basin]

that is 30t

[tulip tiger]

Thx

[sinful monolith]

i dont get this question

[glacial hedge]

meaning

What is the average of the 1st set

and what is the average of the second set

then what is the average of those 2 averages?

[sinful monolith]

i use the median right

[glacial hedge]

*median

sorry

so median of a is 3.5

and median of b is 4

[sinful monolith]

oh so 3.5+4

[glacial hedge]

so 7.5/2

divided by 2

[sinful monolith]

why do i have to / 2 may i ask

[ionic jewel]

the average

[glacial hedge]

because average

yeah go get em bunny

[ionic jewel]

the average of n numbers is adding them all together then dividing by n

in this case there are two numbers

[sinful monolith]

i see

[ionic jewel]

so you add em all then divide by 2

[ionic jewel]

yeah i stole your helping job 😔

[sinful monolith]

3.75

[sinful monolith]

for this do i have to make the hours into min then calculate it?

[arctic wren]

@sinful monolith no, the problem is asking kilometer per hour, so you have the kilometer and the hours, just divide one by another

[sinful monolith]

its 3hours and 20min tho

[arctic wren]

Yes, in this case you have to transform the 20 minutes in hours

[sinful monolith]

so 1/6?

1/3*

[arctic wren]

Yes

[sinful monolith]

so 190/3 and 1/3

[arctic wren]

Yes , it will be $\frac{190}{3+\frac{1}{3}}$

[ocean seal]

Guilhotina

[sinful monolith]

i see

[rustic mango]

wha?

[gray isle]

what seems to be your issue with this question?

[rustic mango]

i dont understand how to do it

is it as simple as -4/5?

[gray isle]

What are you doing to get -4/5

[rustic mango]

putting g'(3)/h'(3)

[gray isle]

No

[rustic mango]

okay

[gray isle]

you have a quotient of two functions

use an appropriate rule to differentiate that

[sinful monolith]

and how many two digit numbers do not contain the digit 9

[gray isle]

note that you'll need to use all the values given in the right column

[warped phoenix]

how do ik if this is increasing or decreasing?

aka the end behavior?

[ancient creek]

when its derivative > 0, it is increasing

[warped phoenix]

whats a derivative

[ancient creek]

The "instantaneous" rate of change of a function

[warped phoenix]

is it an algebra 2 thing

[ancient creek]

Oh... no, derivatives are from calculus

[warped phoenix]

oh LOL yeah i think im supposed to figure it out a different way then..

[gray isle]

you should have a decent idea of what a log graph looks like

[warped phoenix]

i do

[warped phoenix]

something like this right?

since it's (x-1) the x intercept is 1

[gray isle]

like that, yes (that is what a log curve could look like)

But x int isn't 1

for your question

[warped phoenix]

oh..?

[gray isle]

how did you jump from
(x-1) is present to "x int is 1"

[warped phoenix]

because a log graph is normally on the origin right? and since it's x-1, that's a horizontal shift/transformation by 1 unit to the right

so the x-intercept is 1

[gray isle]

No

y = log(x) doesn't pass through the origin

[warped phoenix]

ohhhhhhh

where does it

[gray isle]

log(what) gives 0

[warped phoenix]

0?

[gray isle]

No

,w log(0)

[warped phoenix]

😦

[lethal stump]

think about the index law

a^0 = what?

[warped phoenix]

1?

[lethal stump]

yea so rearrange it and you'll see

👍

[valid bone]

Is this channel in use

[arctic wren]

How can i make logs with textix?

[warped phoenix]

wdym rearrange?

[north sail]

What is n+n+n+n

[upper pebble]

4n

[north sail]

Thanks

[upper pebble]

np

[north sail]

How about b+b+b+b+b+b+b

[upper pebble]

7b

it's just n 4 times and b 7 times

[north sail]

That so easy

[upper pebble]

[alpine sable]

Hi

[upper pebble]

hi

[alpine sable]

why math so hars

hard

[warped gyro]

Hi everyone, this is a question from my textbook (which also includes a solution). I've never before used phasors before, and after a couple web searches I kind of understand the concept behind them, but I still don't get how to apply them to this problem. Can anyone help?

[alpine sable]

WOw

this is hard

[north sail]

I like math but i dont love it

[upper pebble]

from my experience, new math tends to look more difficult than it really is

[north sail]

I forgot how to divide

[alpine sable]

same

[alpine sable]

true

[alpine sable]

divide is ez

[north sail]

I just a calculator

[alpine sable]

what grade math u learning?

[warped gyro]

So far, I understand about phasors:

• phasors are like tiny clocks
• the hands of the block are the arrows
• you can "add the arrows" or something to make linear combinations of sine/cosine functions easy (but the problem is I don't get how to do this part)

[upper pebble]

also practicing is important

[warped gyro]

Can anyone help me with this? or should I repost to another channel

[alpine sable]

that math i havent learned b4

[warped gyro]

if you guys are busy

[alpine sable]

but i will try to ask my teacher

[arctic wren]

@warped gyro probably #get-advanced-access math will help you more

[north sail]

Everything hurts

[alpine sable]

]

[warped gyro]

so it turns out I don't know what category this is

because I'm actually learning this for physics

not math

but I know that this is a part of math too

[alpine sable]

O

@warped gyro

u good at physics?

[warped gyro]

good is relative

[alpine sable]

can u teach me physics?

haha

[upper pebble]

[north sail]

Im gonna not do my homework

[atomic saddle]

That's not good

[north sail]

Yes i know

50 more minutes

[rotund fox]

what is this pi looking thing called

[upper pebble]

i mean the largest symbol there is uppercase pi

[rotund fox]

i found it now thanks

[alpine sable]

Hi is the channel free

[upper pebble]

looks like it

[alpine sable]

Ik x is 3

But idk steps

Ah noone s there

[gray isle]

consider 25 = 5^2

[upper pebble]

wasn't this problem asked about yesterday

[alpine sable]

yeh

[upper pebble]

there's just one step i don't understand

[alpine sable]

k

[undone dock]

What don't you understand? The reason or why it's true

[north sail]

4n + 1 is 5n right?

[alpine sable]

da whole thingy

[alpine sable]

[alpine sable]

it will be 4n+1 only

[upper pebble]

how do we go from subtracting from 5^2x - 1 to multiplying by (5 - 1)

[upper pebble]

no, 4n + 1n would be 5n, 4n + 1 is just 4n + 1

i'm assuming it's an exponent rule that either i'm unfamiliar with or don't remember

[undone dock]

$\frac{5^{2x-1}}{5}=5^{2x-2}$ so $5^{2x-1}$ is a multiple of $5^{2x-2}$

[ocean seal]

K.

[upper pebble]

oh, i see

thanks

[dark granite]

yes, as long as x>0 is an integer.

[alpine sable]

Capital Pi

[fervent fiber]

Can someone explain me the meaning of this equation please

[upper pebble]

i wish i could

[fervent fiber]

Oh

[tough hatch]

product

of all those terms

similar to the summation sign

this is the product sign

i.e.

[rotund fox]

thank you

[fervent fiber]

<@&286206848099549185>

[tough hatch]

maybe give us more context? i.e. the entire problem

[fervent fiber]

Ok just a sec

[rapid fog]

quick hint pls?

[tough hatch]

channel is occupied, u may post on another #questions- channel

[tough hatch]

so what are alpha, beta and gamma equal to?

[fervent fiber]

I haven’t calculated that yet

There’s no need to find them

I can use the relation btwn coefficients and roots

Ok wait I’ll find out

[silver wave]

Aren't roots like the numbers?

[fervent fiber]

One is -1 others are complex

[tough hatch]

..

.......

.......................

[fervent fiber]

Oh I thought u were telling me to find them lol

[tough hatch]

............................................................................

[fervent fiber]

?

What do you wanna know

[rotund fox]

they are like the two points when y is 0 i think

[fervent fiber]

Yeah

[tough hatch]

..........................................................................................................................................................................................

[rotund fox]

well depends on your question

[fervent fiber]

A root is a number on which the value of your function is 0

[fervent fiber]

So someone gonna help me with this?

I just wanna know what that summation expression will be like

Ok np

[rapid fog]

sry, and nvm, i just got it

[fervent fiber]

That’s because here there will be fixed values of the variables

[red ledge]

It says that we need 2 points to compute the slope, but why not 1 point?

[rotund fox]

rip dhaval314 and his question

[fervent fiber]

Yeah

[red ledge]

I have a hard time understanding the concept of function and its notation

I have quesitons

[tough hatch]

wdym

@red ledge But on another #questions- channel, for good measure

[fervent fiber]

The reason for why k=1 isn’t given

[tough hatch]

it doesn't say that y=... satisfy the equation

the word was satisfies

so it's a single solution of the respective equation

the problem therefore is the need for the summation

and what that makes sense for

@fervent fiber

[midnight pendant]

can you have a square number that can be represented by two different sums of square numbers?
idk im asking
like
10² = 8² + 6²
can you have
10² = a² + b²
where a and b arent 8 and 6

[clever folio]

3^2+4^2=25 and 0^2+5^2=25?

Like that?

@midnight pendant

Sort of trivial though. But anytime a^2+b^2=c^2 you know c^2+0^2=c^2 also.

So i guess it would be more interesting to find a case where none of the term are zero lol.

[arctic wren]

A can be 6 and B can be 8

[clever folio]

Lol, that's also a nice sort of trivial answer.

[arctic wren]

Jokes aside, probably with complex numbers you can have something like that

[midnight pendant]

isnt there another set of numbers when squared and added is equal to a 100

[arctic wren]

[midnight pendant]

no 0 allowed lol

[clever folio]

Cheater cheater lol

[midnight pendant]

(this isnt for a test btw, just general knowledge_

[arctic wren]

I think in complex number , yes

[clever folio]

That was not in the original q!

[midnight pendant]

very sad

but im not cheating

[midnight pendant]

hmmm

wokay

[jagged imp]

there's only 6 and 8 if we're talking positive whole numbers

[clever folio]

I don't mean it like that, I mean in the changing the q way

[midnight pendant]

im in 10th so i dont know exactly what complex numbers are

[midnight pendant]

oh lol

[arctic wren]

Yes

[clever folio]

No worries I realize using 0 is super unsatisfying.

[arctic wren]

$\sqrt{-1}= i$

[ocean seal]

Guilhotina

[jagged imp]

i mean if you're fine with nonintegers you don't even have to go to complex numbers right

like you could use square roots

[midnight pendant]

this ik, perhaps the ony thing ik

about complex numbers that is

[arctic wren]

Yes

[midnight pendant]

yes yes, makes complete sense

[ocean seal]

Guilhotina

[midnight pendant]

$\sqrt{-1}=i$

[ocean seal]

Vin Sanji

[fervent fiber]

Yeah thanks got it

[glacial hedge]

How do I do this problem? How do i parametrize this thing?

[harsh swallow]

$\oint_{C} \vec{F} \vec{dl} = 0$ what is the field called when this is true

[ocean seal]

Katharine

[harsh swallow]

nvm i found it

conservative

[ionic jewel]

be careful with this

write it as $i^2 = -1$

[ocean seal]

bunny

[harsh swallow]

@ionic jewel I'm intrigued why do you say this?

[ionic jewel]

$\sqrt{-1} = \pm i$

[midnight pendant]

yea why lol

[ocean seal]

bunny

[ionic jewel]

if you define i the other way you could say

[harsh swallow]

ah right

[ionic jewel]

$i = \sqrt{-1} = -i \implies 1 = -1$

[ocean seal]

bunny

[ionic jewel]

like principal root and all but you just define i the other way to be right

[harsh swallow]

fun problem

-i * i

😄

some number

,w that

XD

someone asked what number - number was

so wolfram alpha that

to find the answer

[upper pebble]

[ionic jewel]

-i * i = 1

[harsh swallow]

i know

but in the sense that +-i

[upper pebble]

nice sylveon pfp

[ionic jewel]

thanks

everyone told me "that's not Sylveon that's a duck" but i knew someone would see it

[acoustic abyss]

heyy help?

Using v = u + at, find t when

u = 10, a = 2.5 and v = 3

[tough hatch]

how do u find t without substituting first?

[ionic jewel]

try plugging in the numbers

[tough hatch]

i.e. how do u isolate t

@acoustic abyss

[acoustic abyss]

u sent it to the other side right?

[upper pebble]

name is bunny but pfp is a duck

[tough hatch]

how exactly

[upper pebble]

that's even better

[tough hatch]

what would be ur new equation?

[acoustic abyss]

umm

[tough hatch]

from v=u+at

[acoustic abyss]

t =( v/a ) - u

[acoustic abyss]

i think its wrong

[tough hatch]

addition goes away first

since at goes first in u+at

[acoustic abyss]

alr so what will it be

[acoustic abyss]

oh yea

(v/u) - a = t

[tough hatch]

?

[acoustic abyss]

not sure

plz help with the equation

dont tell the answer

[tough hatch]

inverse of addition is subtraction

[acoustic abyss]

alr so how?

[acoustic abyss]

ohh

[tough hatch]

what do u do to transfer u to the other side?

[acoustic abyss]

yea a bit

t = (a/u) - v

[tough hatch]

no

[tough hatch]

answer this first

stop guessing

[acoustic abyss]

t/a = a-u

[acoustic abyss]

ok

[acoustic abyss]

by - (minus)

[tough hatch]

ok, so what is ur new equation?

[acoustic abyss]

the sign will change right

ok one sec

[tough hatch]

what do u subtract from both sides?

[acoustic abyss]

v = at- u

[acoustic abyss]

v

[tough hatch]

no.

[acoustic abyss]

30

[tough hatch]

ok i will now assume u are trolling

[acoustic abyss]

nope

ok i rlly need help

[tough hatch]

due to the random answers

which probably implies u aren't serious about this

[acoustic abyss]

no i said 30 cause that the (t)

[acoustic abyss]

huh

[warped phoenix]

(Im really sorry to interrupt but im about to take my semifinal and i just wanted to verify one tiny last thing, "to find the asymptote of a function, you set the denominator equal to 0, and then solve, right?")

[tough hatch]

???

[acoustic abyss]

in my equation we have to substitute t with 30

[tough hatch]

@warped phoenix u may wait for some1 to answer ur question on #help-1

[ionic jewel]

yes, but if the numerator is 0 at the same point it's a hole instead

so you gotta watch out for that

sorry superficial just answered his rq

[warped phoenix]

(got it, ty!!!!)

srry again

[tough hatch]

np

[tough hatch]

but aren't u solving for t?

[acoustic abyss]

(U) sorry

[upper pebble]

looks like you found t!

aw

[tough hatch]

still

[acoustic abyss]

ok plz help im so confused

[tough hatch]

u said u=10 up there

now u want u=30

[acoustic abyss]

(V) = 30

[tough hatch]

a=30

[acoustic abyss]

the quation is

[tough hatch]

so v=30, not v=3?

[acoustic abyss]

U = 10

A = 2.5

[tough hatch]

see, u can just post the original question

[acoustic abyss]

V = 30

[tough hatch]

instead of having to type it out

[acoustic abyss]

i just copy pasted

yea sorry

[tough hatch]

(incompletely, yeah)

ok then

so

[acoustic abyss]

30 = 10 + 2.5 * t

[tough hatch]

we want u to be on the LHS (lefthand side of the equation), with v

[acoustic abyss]

yea

[tough hatch]

or if u want u can substitute first, like u did

[acoustic abyss]

i have to find t

[acoustic abyss]

yep

[tough hatch]

now what do u do to get 30 and 10 together on the other side?

note that the outermost operation on the RHS is addition

[acoustic abyss]

yea

[tough hatch]

so what inverse operation do u need to apply

[acoustic abyss]

so it becomes (-)

[tough hatch]

to both sides

subtraction

[acoustic abyss]

yea subtraction

[acoustic abyss]

.

[tough hatch]

😦

[acoustic abyss]

i meant subtraction

[tough hatch]

ok good

[acoustic abyss]

yea

[tough hatch]

it's better to say the actual words that you mean

[acoustic abyss]

yea sorry

ill note that

[tough hatch]

to minimize confusion

so what do u subtract from both sides?

of

[acoustic abyss]

so minus 30 from both sides?

[tough hatch]

u want t to be alone on one side