help-10

[obtuse pebble]

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[royal basin]

no need to thank me when i've provided exactly no help lmao

[obtuse pebble]

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[manic wolf]

is this possible to solve/is it logical The spring pendulum is made so that a spring with a coefficient of elasticity of 0,25 N/cm can be suspended from the ceiling with the upper end attached to the ceiling and a weight of mass 100 g can be suspended from the lower end. If a spring with a coefficient of elasticity k is stretched by s, its elastic energy is We=1/2 ks^2 How much energy must the pendulum give off to stay in the equilibrium position after a long time?

[pine sail]

@manic wolf

[manic wolf]

yea

[pine sail]

Is anything about the initial condition known?

[manic wolf]

wdym

[pine sail]

There's no extension in the spring initially? And you're dropping the mass from there?

[manic wolf]

you have a spring you attach it to the ceiling hand a weight on it and place it so that it somehow stretches 8cm of its original position even tho it weights 100g

[manic wolf]

no you place the weight on the end of the spring

the thing I dont get is how can it stretch 8cm of spring with the mass of 100g

[pine sail]

Do you have an actual question?

I mean, the image or anything.

[manic wolf]

yea

not in english tho

https://www.imagetotext.info/

you can get text from here and translate for yourself

[pine sail]

I've already done that haha.

No worries.

[manic wolf]

oh

anyway you got a conclusion?

[pine sail]

Anyways, what I think is this,
The spring is streched by 8cm. So there's some energy stored.
However it is streched by a length more than required to attain equilibrium. And so, the extension should be reduced for that. With that there will also be a change in energy. This new energy is less than the old once, hence there's this amount that the spring must release.

Which is your question.

Do you have any objections thus far?

[manic wolf]

ok that makes sense

[robust sleet]

ohhh stretch length is given

[pine sail]

I think so.

[pine sail]

Do you know how much extension is required for equilibrium?

[manic wolf]

4cm?

Wait your a genius

all you do i plug that in and get the answer no ?

energy = 1/2 * 25N * (4/100)^2

cus 0.25N/cm = 25N/m and 4cm = 0.04m

[pine sail]

Correct.

[manic wolf]

and I get 2/100 of a joule which is 20 milijoules

thats good right ?

[pine sail]

The number should be a 2, yes.

[manic wolf]

Tysm appreciate it

[pine sail]

But!

This isn't the answer.

[manic wolf]

it is ?

[pine sail]

As you knew, it was streched at a length of 8cm.

There's some energy corresponding to that.

And then there's the energy you figured now.

The question asks how much of that old energy corresponding to 8cm extension should be released to get a 4cm extension.

[manic wolf]

well 0.02joules ?

[pine sail]

I don't think so.

[manic wolf]

I checked the answers and A is correct so it must be

[pine sail]

Then our interpretation of the question was probably wrong.

[manic wolf]

I just didnt get the question

I didnt realise you could stretch it 8cm and release it

[pine sail]

Just so you know, the answer could be C if the other interpretation holds.

[manic wolf]

and then it would have to lose energy to get to the 4cm at which its stable

[pine sail]

Yes, precisely.

And I thought this lost energy is what you are finding.

[manic wolf]

and whats the other interoretation

Well I am no?

[pine sail]

That you're looking for the lost energy.

[manic wolf]

Oh wait

you mean from the original ?

[pine sail]

Yes.

From the original.

[manic wolf]

ohh yea nah its not asking for that

ik what u mean

[pine sail]

I see, okay.

[manic wolf]

tysm anyway

appreciate it, have a good one

[pine sail]

Likewise.

[manic wolf]

.close

[obtuse pebble]

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[rancid cliff]

https://cdn.discordapp.com/attachments/1100882893137518723/1124362898337173605/20230630_123608.jpg

[rancid cliff]

guys, I need to find the area between f(x), g(x) and the y axis. f and g are defined in the pic I sent

but look what I got in the last line, ln(0) ????

it's in spanish so I can translate the text if you want.

[brittle tusk]

Is it $f(x) = \frac{16}{x+5}$ and $g(x) = x + 5$?

[warm shale]

trustinjudeau

[rancid cliff]

yup

here u can see the image in a better quality
https://media.discordapp.net/attachments/1100882893137518723/1124362898337173605/20230630_123608.jpg

[brittle tusk]

Let's see here...

Okay, you should see that we have a triangle here first of all

[rancid cliff]

triangle???

Im supposed to solve this via integrals

[brittle tusk]

Well, you considered it with your integral

I would argue that using the shapes can be easier, but we can do that also

In fact, I think your integral is wrong

[rancid cliff]

if u can make me that favor I would appreciate it yeah

[brittle tusk]

You have $\int_{-5}^{-1} ...$

[warm shale]

trustinjudeau

[brittle tusk]

But the reciprocal graph there is not defined for x=-5

[rancid cliff]

yeah :/

[brittle tusk]

That's why I think the only way is to use the triangle

[rancid cliff]

wow :/ okay lets try it

cause im supposed to use ints

Ill ask the proffesor

[brittle tusk]

The triangle is not necessary, actually, you can also just do 2 separate integrals

[rancid cliff]

so first the triangle and then substract that little area in the top right?

[brittle tusk]

First, you will need to integrate the line from its x-intercept up to where it intersects the reciprocal function

That is the same as the triangle

Then, you will need to subtract the area underneath the reciprocal function between the intersection and 0

[brittle tusk]

Oh, wrong triangle

Let me show you

Please allow me one moment

[rancid cliff]

absolutely

[brittle tusk]

Here is the situation

Now, let me draw the two separate integrals we need to do on here

[flat anvil]

It’s going to diverge

U can bound the area below by int from -5 to -1 of -C (C a positive constant) - 1/(x+5) which diverges

[brittle tusk]

This yellow bit is the first bit

Then the remaining blank bit is the second bit

This kind of red bit

We need to find both these areas and add them

[rancid cliff]

but the yellow starts from 5

[brittle tusk]

Yep!

That's not an issue. We're not considering the reciprocal graph

The question just wants the area bounded by that line, the curve and the y-axis

Which includes that bit

[rancid cliff]

[brittle tusk]

So the yellow bit, you hopefully can see that the limits on your integral will be -5 and the x-coordinate where the line intersects your reciprocal graph

and then the red bit will be that coordinate again and 0

Right?

[rancid cliff]

yes

they intersect in -1

[rancid cliff]

correct

I tried to do that with ints and got in troublenwith the first part

[brittle tusk]

Brilliant. If you carry out, then
$\int_{-5}^{-1}g(x)dx + \int_{-1}^{0}f(x)dx$

[rancid cliff]

so we try to do it with the triangle (the first part) and then thebother part with the int?

[warm shale]

trustinjudeau

[brittle tusk]

You were trying to integrate the reciprocal graph from -5 to -1.

But the yellow area is the area below our linear graph

[rancid cliff]

oh wait

my ints are wrong.

[brittle tusk]

Yep.

[rancid cliff]

[brittle tusk]

You simply swapped f and g

[rancid cliff]

okay 😄

🫤🙄

[brittle tusk]

wait, no, it was more wrong than this

[rancid cliff]

yeah

I considered f as the top where it wasnt

something like that

[brittle tusk]

Yep

Anyway, do you now see the way forward?

[rancid cliff]

Yup 😉

thanks a lot Trustin

I mean

ur not trusting judeau but

thanks anyways

🤣

[brittle tusk]

Good stuff

[rancid cliff]

have a good one!!!

[brittle tusk]

🧙‍♂️

[rancid cliff]

🙂

.close

[obtuse pebble]

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[slow fulcrum]

Find all solutions $x$ to the equation
$$(x^4-11x^3+24x^2)-(4x^2-44x+96)=0.$$

[warm shale]

dabbbingpotato

[slow fulcrum]

I factored both $x^4 - 11x^3 + 24x^2$ and $4x^2 - 44x + 96$

[warm shale]

dabbbingpotato

[slow fulcrum]

Into $(x^2 - 8x)(x^2+3x) - (4)(x-8)(x+3)$

[warm shale]

dabbbingpotato

[slow fulcrum]

and then I set them equal to each other

and then I divided both sides by (x-8) and (x+3)

to get $x^2 = 4$

[warm shale]

dabbbingpotato

[slow fulcrum]

so x = -2 or 2

but both sides could also be 0

so x could be 8

or -3

so the solutions are 2, -2, 8, -3

but it says its wrong

what did i do wrong

[rich plume]

,w roots of x^4-11x^3+24x^2-4x^2+44x-96=0

[warm shale]

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[rich plume]

Your factorization is wrong

the factorization of (x^4-11x^2+24x^2) into (x^2-8x)(x^2+3x) is wrong

[slow fulcrum]

oh yeah thanks

.close

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[lilac path]

You see a righttriangle what is your first idea?

[merry cave]

its pythag ik

i jus dont know how to set the equation

like number wise

[lilac path]

D is the point where ac intersect the circle

So AC-AD=DC

[merry cave]

but how do i know the numbers

jus 5 squared - 8 squared?

[lilac path]

Use pythagoras

a²+b²=c²

[obtuse pebble]

@merry cave Has your question been resolved?

[merry cave]

close

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[ionic hawk]

IM LOST ON HOW STEP 8 HAPPENED

[warm canopy]

they've gone from (6) to (8) using (7)

[ionic hawk]

what substitution did they use

[warm canopy]

the one in (7)

[ionic hawk]

but in step 8 it says they used 6 and 8 for eqn

[warm canopy]

well they obviously didnt use 8 to get 8

just ignore the writing on the right and use (7) on (6)

[ionic hawk]

i see thank you

.clsoe

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[azure anchor]

integrate. not sure what to do here. don't easily recognize any IBP or trig sub or even u-sub.

[kind hawk]

it might help to add and subtract something in the numerator

[azure anchor]

something that doesn't change it like +1 -1 or something?

dx of denominator is 2x+1. but not sure how to use that.

[kind hawk]

x is 1/2 * (2x)

you might move the 1/2 in front of the integral

and then +1-1 looks promising

[azure anchor]

so, when i went to try u-sub, i got 1/2du = x + 1/2dx

if i continued with u-sub, it seems similar to what you're suggesting

but how do i handle the + 1/2 on the x side of du

would it be a subtraction?

[kind hawk]

+1/2 - 1/2

[azure anchor]

so lets say i move that to the u side

1/2du - 1/2 = xdx?

[kind hawk]

pull the integral into two parts

[azure anchor]

sorry im having a hard time visualizing

[kind hawk]

$\int \frac{2x+1}{x^2+x+1} \dd{x} - \int \frac{1}{x^2+x+1} \dd{x}$

[warm shale]

denascite

[azure anchor]

so, im trying to understand the logic of getting to this point. 2x+1 is the dx of denom... but how do we equate 2x + 1 - 1 = x?

[kind hawk]

.

$\int \frac{x}{x^2+x+1} \dd x = \frac12 \left(\int \frac{2x+1}{x^2+x+1} \dd x - \int \frac{1}{x^2+x+1} \dd x \right)$

[warm shale]

denascite

[azure anchor]

so this is kinda like a u-sub right? but instead of getting an integral in terms of u, we simply used that derivative to find a way to split?

because otherwise we wouldn't be able to decompose into partials with only one factor in the denominator

hmmm i think im starting to see it

[kind hawk]

I mean so far is just some rearranging

[kind hawk]

well I havent done any u-sub yet

you can now u-sub the first integral

but for the second you'll have to do something else

[azure anchor]

would completing the square work for the second? partial fraction after that?

[kind hawk]

completing the square yes

partial fractions no

[azure anchor]

ohhh it would be trig

[kind hawk]

it has no (real) roots

[azure anchor]

let me try and chug through the first part

feel like my trig sub is a little off somehow... think it needs to be the root of 3/4 right?

[obtuse pebble]

@azure anchor Has your question been resolved?

[azure anchor]

.close

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[timid silo]

How do u do these

Also what kinda math is even this

[proud coyote]

rubbish drawing

(pythagoras)

[warm canopy]

The distance formula is pythagoras

[proud coyote]

imo its important to know why it works not just use it

[timid silo]

How do I solve it tho

[proud coyote]

what is length of this line

[timid silo]

(4,4)?

I mean 9,4

[proud coyote]

no like what length is this red line

[timid silo]

Idk

How do I find that

[proud coyote]

ok

first

what is the coordinate of the bottom corner

[timid silo]

3,-4

[proud coyote]

bottom right😭

[timid silo]

I dunno

0?

[proud coyote]

it's the same x coordinate as the top corner

right?

bc its in a straight line with it

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

I guess

Yes

[proud coyote]

so using the same logic whats the y coordinate of the bottom right

[proud coyote]

best diagram ive ever drawn

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

4

-4

@timid silo so what now

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[brisk matrix]

is there any nice way to rewrite (\dv{x}g) given [g(x) = \int_0^x f(x,y), dy]

[warm shale]

maximofs

[hybrid gull]

What if you try letting some function F be the (partial) antiderivative wrt y?

g(x) = F(x, x) - F(x, 0)

[lethal sand]

yes, this is just liebniz's integral rule

that's probably the nicest way you can express the derivative of g(x)

[brisk matrix]

ah i'd seen that before as well

thank you both

[hybrid gull]

I guess a "final answer" could be written as:

$g'(x) = \frac{\partial F}{\partial x} (x, x) - \frac{\partial F}{\partial x} (x, 0)$

[warm shale]

shenny17

[brisk matrix]

it then simplifies to [f(x,x) + \int_0^xf_x(x,t),dt]

[warm shale]

maximofs

[brisk matrix]

was trying to use this to solve a gre question and just forgot how to take the derivative of that haha

[hybrid gull]

Well F would be the integral wrt y, not x, right?

[brisk matrix]

it's a dummy variable

doesn't really matter

[hybrid gull]

Ah

[brisk matrix]

thanks again waler and shen

.close

[obtuse pebble]

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[hybrid gull]

🫡

[obtuse pebble]

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[brisk matrix]

rank 2^(1/2), 3^(1/3), and 6^(1/6) in increasing order

[brisk matrix]

i tried using x^(1/x) but didn't really help

is there a nice way to do this one

[sage geode]

Just rewrite all of them as 6th roots

[brisk matrix]

omg

thank you bean

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[sage geode]

The question wasn't about the sequence x^(1/x)

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[torpid echo]

i dont understand this step

[torpid echo]

when I do $R_1 \rightarrow xR_1$
i need to multiply the determinant by $\frac{1} {x}$

why dont we need to multiply by $\frac{1} {x}$ here?

[gilded needle]

adding any multiple of a row to another row does not change the determinant

that's one of the fundamental determinant properties

[warm shale]

LILY

[torpid echo]

but x is just a variable, its not a multiple of any row here is it

[gilded needle]

x stands for some number

so xR1 is a multiple of R1 by some number x

[torpid echo]

ah ok i get it

i was just confused because in another example they did R1-> xR1 and multiplied the whole thing by 1/x

thats a different property

[gilded needle]

yep

multiplying a row by x causes the determinant to be multiplied by x, so you multiply by 1/x to compensate for that

[torpid echo]

yea i get it now

thanks

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[obtuse pebble]

@tight mango Has your question been resolved?

[whole dock]

$({\f {4\cdot 27^{\f 14}}{3^{\f 12}\cdot2^{\f 13}}})^{\f 13} \times \f {16^{\f 19}}{3\cdot3^{\f 1{12}}}$

[warm shale]

coldtee

[whole dock]

Yeah

It actually helps a lot

You can try simplifying it

From here

You can write 27 as 3^3 and similiarly other

Numbers

[rich plume]

Yeah you can do that

The main thing is to write all terms as powers of primes

,w simplify cbrt((4*(27)^(1/4))/(sqrt(3)cbrt(2)))((16^(1/9))/(3*3^(1/12))

[warm shale]

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[rich plume]

Your simplification must be incorrect

oh nvm

if you could show your process

[whole dock]

Basically make the bases same and add or subtract them

So make it 3^(13/12) yeah

[rich plume]

Yes

NICE

No

An irrational is one which can't be expressed as a fraction

and its digits do not repeat

Yes

22/7 is not the exact value of pi

it is an approximation

No

pi*r^2/r^2 is just pi

which is irrational

No fraction is there since the denominator cancels few terms 0of numerator

By experimentally finding the perimeter of a circle and dividing by radius

EXPERIMENTALLY*

Using thread or smth

what

could you send that symbol?

Oh you mean tao?

I'm not too sure but tao is actually just 2*pi

The symbol is not official i guess

https://tauday.com/

Read more here

welcome

[obtuse pebble]

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[cloud igloo]

This correct?

[lone dirge]

I don't understand what you wrote there

is it $\binom{5}{3} (3x/2)^3 \cdot 1^2$?

[warm shale]

Cain

[lone dirge]

So the coefficient is $\binom{5}{3} (3/2)^3$

[warm shale]

Cain

[lone dirge]

I assume that this is what you wrote there with $r=3$.. So yeah, that's correct

[warm shale]

Cain

[lone dirge]

,w \binom{5}{3} (3/2)^3

[warm shale]

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[lone dirge]

on the other hand:

,w expand ((2+3x)/2)^5

[warm shale]

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[lone dirge]

There you go @cloud igloo

[obtuse pebble]

@cloud igloo Has your question been resolved?

[obtuse pebble]

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[sullen tusk]

hey guys, i got huge understanding problems right now how to prove that the derivative of an odd function is an even function

my starting point was odd function: f(-x) = -f(x)
and declaring g(x) = -x

Next started the chainrule

(f(g(x)))' = f'(g(x)) * g'(x)
= f'(-x) * (-1)
= -f'(-x)

thats the same as f'(x) no?

[sage geode]

Okay, so the derivative of f(-x) is -f'(-x), right?

[sullen tusk]

Yes

[sage geode]

And the derivative of -f(x) would be -f'(x)

Because f(-x) and -f(x) are equal, their derivatives shall be equal as well

So we have -f'(-x) = -f'(x)

Multiplying both sides by -1 yields f'(-x) = f'(x)

Hence f' is even

[sullen tusk]

give me a minute, i need to reproduce that

So basically i am getting the derivative of each side
odd function is f(-x) = -f(x), and g(x) = -x
now i am going for first derivative
(f(g(x))' = f'(g(x)) * g'(x)
= f'(-x) * (-1)
= -f'(-x)

Then going for the second one (-f(x))

(-f(x))' = -f'(x) * 1
= -f'(x)

then i compare both and get -f'(x) = -f'(-x) which is the same as f'(x) = f'(-x) so its even ?

[sage geode]

Yes, two typoes in the final line though

f'(-x) and not f(-x)

[sullen tusk]

fixed,

[sage geode]

Right

[sullen tusk]

so the procedure to prove that the derivative of even gets odd should be working the same right?

[sage geode]

Yes

[sullen tusk]

f(x) = f(-x)
g(x) = -(x)

first:
(f(x))' = f'(x) * 1
f'(x)

second:
(f(g(x)))' = f'(g(x)) * g'(x)
= f'(-x) * (-1)
and get -f'(-x)

f'(x) = -f'(-x)
-f'(x) = f'(-x)

which is the definition of uneven functions. Correct?

[sage geode]

That is correct, yes

[sullen tusk]

Finally i understood it. big thanks man! i was really confused on this simple thing

.close

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[cobalt mortar]

How to do this question?

[cobalt mortar]

Considering that the pdf will be 1/2

And likelihood function = 1/32

[pseudo swift]

you're sure about that ?

"for any theta, the likelihood is 1/32"

[cobalt mortar]

As the pdf = 1/2

Won't depend on theta

So won't the likelihood be 1/32 considering 5 samples are there

[pseudo swift]

yeah pdf = 1/2 between theta -1 and theta +1

otherwise it's 0

[cobalt mortar]

Oh yeah yeah

[pseudo swift]

what if you have a sample that's not even in there

[cobalt mortar]

I see i see

So how will we proceed in this now?

[pseudo swift]

well just compute the likelihood for each of the proposed thetas

you'll see what happens

[cobalt mortar]

Ahh right

So we get the range

Theta > 0.7

And theta < 1.04

[pseudo swift]

yeah

[cobalt mortar]

Thank you so much!

.close

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[timid silo]

so from my understanding

afer I add the sigma notation and whatever

I have one part that is the width of the rectangles, and another that is the height

thw width would be (b-a )/ n i thihnk

hence pi / n

not sure how to find the height

I'm leaning towards C

[boreal patio]

you are correct about the height.

try to think there is finite n. lets say n= 3. Divide the interval [0,pi] into 3.... So one option could be to divide it into 3 intervals of length pi/3.

For the height you have to consider the function you are given, in this case sin(x). And you have to chose a point a on each of these intervals so that sin(a) will represent the height of these rectangles. one option could be to chose the edge points of your smaller intervals.

now if the intervals are [0,pi/3], [pi/3,2pi/3], [2pi/3,pi]
then you can choose 1pi/3, 2pi/3 and 3pi/3

[timid silo]

c was wrong

[boreal patio]

so if you put i as the variable that will go throught your edge points you get i*pi/3, and the answer b

[timid silo]

oh I see

what would the answer be if the function was sin2x

would it be 2ipi/n

[boreal patio]

if the interval is the same yes

[timid silo]

what if the interval was

2pi to pi

[obtuse pebble]

@timid silo Has your question been resolved?

[boreal patio]

try to get a general formula for any interval

so if i have interval [a,b] then i-th point is a + i(b-a)/n*

the width of each such interval is just (b-a)/n

[obtuse pebble]

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[echo thistle]

how did this happen

its a silly question but im kinda lost in the sauce

i got 2 equations and 3 unknown variables

right ?

[timid silo]

yes

[native crag]

Yeah, they have paramterised it all by setting a_3 = t

[echo thistle]

so like i set a_3 equal to t

and then work ?

so i assume that a3 is something which is t

since i dont know it

[native crag]

Yeah. You could, say, eliminate a_1 by an operation on A(1) and A(2) to isolate a_2 in terms of a_3=t.

[echo thistle]

i seee

[echo thistle]

can i do that in every situation like this ?

say i got 3 equations and 4 unknown variables

i can assume a_4=t and a_3=t ?

wait no

a_4=t a_3=v something like this ?

[native crag]

No, what's important here is that the defining constants form linearly independent vectors, which means one isn't just some linear combination of the others. Also, you mean 2 equations in 4 unknowns, but then yes if the defining equations form linearly independent vectors via their coefficients, you could parametrise with two parameters.

3 equations in 4 unknowns would still only require one parameter.

It might be helpful to think about this geometrically. In an n-dimensional space, each linear equation in n variables imposes a geometric condition. It demands that the points all lie on a hyperplane (a space one dimension smaller, so if n=3 this is a usual plane, if n=2 it is a line, etc). Then assuming that these hyperplanes aren't just essentially `linear copies' of each other (for example, parallel lines) , intersecting n of them determines a unique point (think of the intersection of three `general' planes in 3-dimensional space, or two `general' lines in two dimensional space). If you only had two planes in 3-dimensional space, they would generically intersect in a line. t is then the parameter which describes this line. In higher dimensions weird stuff happens, and for example two hyperplanes in 4-dimensional space generically intersect in a usual plane. In this case, you would need two parameters.

[echo thistle]

thank you so much friend

[obtuse pebble]

@echo thistle Has your question been resolved?

[obtuse pebble]

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[candid yarrow]

These channels are for asking questions you want help on

You could go to #chill or #discussion instead for chilling or discussion

,calc 12.3 * 2

[warm shale]

Result:

24.6

[candid yarrow]

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[unkempt bramble]

Lol

[obtuse pebble]

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[plain jungle]

i just completed 12th, what's an interesting math topic which i can learn

[zenith raft]

graph theory

[plain jungle]

anything else?

[teal turret]

Don’t you need some intro LA and some calc for that?

[zenith raft]

no

[sacred root]

Number theory

[plain jungle]

hmm

anything related to calc

except multivariable calc

cuz i've done that

[zenith raft]

real analysis

[plain jungle]

more?

i need related to calculus

[sacred root]

Complex analysis

[teal turret]

Or something unrelated: cryptography perhaps

[sacred root]

There's smth called contour integral or smth like that in complex analysis

[plain jungle]

kk thnx a lot

[sacred root]

Sounds sick tho contour

More like bonjour

[plain jungle]

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[lyric totem]

,w derivative x(2x+1)^4

[warm shale]

Results provided by WolframAlpha

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

Requested by dopediscorduser#4906

[lyric totem]

[\frac{d}{dx}(x(2x+1)^4)]
[1(2x+1)^4+x * 4(2x+1)^3 * 2]
[(2x+1)^4+8x(2x+1)^3]

[warm shale]

dopediscorduser

[lyric totem]

Am I making a mistake?

[high lily]

seems ok so far

[lyric totem]

Why does wolfram give a different answer?

[high lily]

factor out the common factor to simplify

[lyric totem]

Or is that just what I have but distributed?

[teal turret]

Did u end up figuring out that other problem

[lyric totem]

No I never finished it, I should tho

[teal turret]

Ah

[lyric totem]

thanks

.close

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[twin peak]

can someone help me understand direction in parametric curves

[obtuse pebble]

@twin peak Has your question been resolved?

[glass dagger]

can you give an example of something you don't understand?

[obtuse pebble]

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[limpid widget]

52627276. wut why

[obtuse pebble]

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[high lily]

it helps to draw in the centre and draw lines to A and C

which part of what i said don't you understand

i said nothing about any of that

you shouldn't see any triangles

after drawing what i recommended

can you show me what you've drawn

yes

for conenience less call the centre O

OA and OC will be radii

properties of tangents will get you two angles in quadrilateral OADC
the measure if arcAC is the same as the central angle it subtends

from there D can be determined from angle sums

properties of tangents

[obtuse pebble]

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[mellow stag]

I need help finding the derivitive of

[mellow stag]

I don't know how to solve for dy/dx from here

[agile thorn]

do you want the derivative of y or smth else

[mellow stag]

Yes, I want the derivitive of y

[next reef]

which is what you have been given.

[agile thorn]

then youve gotta solve the differential equation

[mellow stag]

Im looking for the second derivative

This is the original question

[agile thorn]

substitute 2x/cos(y) for dy/dx

then use the fact that cos^2(y)=1-sin^2(y)=1-x^4 in order to write everything in terms of x

[mellow stag]

What do you mean? Aren't they the same?

[agile thorn]

replace dy/dx with 2x/cosy

[agile thorn]

in this expression

[mellow stag]

Ohhhhhhhhh

I see now

[agile thorn]

so you're gonna be left with d^2y/dx^2 in terms of x and y

[agile thorn]

then do this

[mellow stag]

Ok

I got it now

Thank you so much!

[agile thorn]

np

[mellow stag]

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[next lantern]

how can i solve this?

i was initally thinking taking the norm of the cross product of PQ and PR but that wouldnt work

[royal basin]

find angle QPR

then the area is the product of |PQ|, |PR| and sin(QPR)

[next lantern]

right

for angle QPR i can use the one formula with inverse cos right

[royal basin]

sure but actually knowing cos(QPR) suffices

[next lantern]

why is that?

[royal basin]

you can find sin(QPR) from that

[next lantern]

we have this slide relating sin and cos but i dont really understand it

[royal basin]

it's just sin^2 + cos^2 = 1 no?

[next lantern]

well i know that relation

is that the one they are mentioning?

im just not sure where they are relating them here if that makes sense

[royal basin]

... ok i can't make heads or tails of your slide either sorry

[next lantern]

ok

i will see if theres something online

glad its not just me lost on the slides lol

.close

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[shadow lava]

do you prefer writing logs with brackets for arguments or without brackets for arguments?

[forest sinew]

@wild swallow

[proud moon]

With brackets

[forest sinew]

ping for a free log question since u seemed passionate

[shadow lava]

I tend to always write with brackets, by habit
forgot to do it for the original up top..
but wondering if that will bite me in Calculus 2? to use extra brackets or to avoid them

[forest sinew]

please dont bite

[shadow lava]

it's also extra clear that the exponent is only over the variable, when I use brackets

i always use brackets for trig functions too

sinx^2 = sin^2(x), or sin(x^2)?

[restive acorn]

When writing myself i always use the parentheses for functions

[shadow lava]

the confused part of me feels that people should be executed on the spot for not using argument brackets
but i also gotta get comfortable around them when I don't see argument brackets, as it happens a lot

[proud moon]

Honestly just write with the brackets. It’s just easier to see it

Especially when the questions gets harder

[kind hawk]

it really depends. 2, 3 or more symbols inside the argument -> brackets

but stuff like ln2? nah

[proud moon]

I usually only write it if it has a X after it or a variable following it

[shadow lava]

alright

that makes sense

[restive acorn]

Its important to preserve clarity as much as possible in math work, so i feel it would be better to have a universal bracket rule

[kind hawk]

well of course you have to for stuff like ln(2) x

[proud moon]

Kinda true

[restive acorn]

But hopefully texts that dont abide by that make it clear

[warm shale]

janniku

[shadow lava]

I'm kinda surprised to see math fallacy here, no bracket for 3x^2 and 2y^2

bad Professor Leonard, that's a no no

[proud moon]

Wait btw @shadow lava are you in IB

[shadow lava]

what's IB?

Irritable Bowel syndrome?

[proud moon]

Nevermind. It’s a program

[restive acorn]

International Baccalaureate

[forest sinew]

Irritable Bowel program

[shadow lava]

I run my own school

[proud moon]

Ah ic lol

[shadow lava]

Monday - Friday

[restive acorn]

Its like an international level AP style program

[shadow lava]

with weekends off

[proud moon]

Results are coming in like 6 days and I’m scared lol

[restive acorn]

For those familiar with AP in usa

[proud moon]

Might get my offer rescinded

[shadow lava]

it's relatively new, right?

[proud moon]

Cause like I bombed

[restive acorn]

Good luck hope you do well

[proud moon]

Nah it’s pretty old

[proud moon]

Thank you

[restive acorn]

Its more common now

[shadow lava]

oh, i dunno why I'm just hearing about it now

[restive acorn]

Its actually old

[forest sinew]

I B -> I Bombed

[robust sleet]

Bombed

[proud moon]

Ong. I answered like half the questions on math paper 3

Cause I didn’t know how to do the other ones

[restive acorn]

They had IB when i applied to college 15 years ago or so, and one ofy teachers said she used to teach IB programs

[proud moon]

Predicted at a 6/7 in HL tho 💀

[shadow lava]

AP -> Actually Passed

IB -> I Bombed

[forest sinew]

all i remember is IB kids being anxious

[proud moon]

Lol. IB very easy to make uni tho

[restive acorn]

Ive never met anyone thats actually taken IB anything

Even as a tutor

[forest sinew]

IB means you have anxiety problems

[proud moon]

Cause I made several T20 and 1 T10 American uni and several T10 LAC

[forest sinew]

AP means youre salty you didnt get transfer credit

[shadow lava]

what country is this for?

[restive acorn]

I got a ton of ap credit xD

[shadow lava]

you trying to get into Harvard?

[proud moon]

America

[proud moon]

Nah I already enrolled lol

[restive acorn]

IB is an international program standard

Supposedly

[shadow lava]

that's what I heard too, but that it's newer

[proud moon]

It is. It’s also the worst program in existence

[shadow lava]

maybe for certified IB teachers, (Irritable Bowel teachers), that's what's "newer"

[proud moon]

Like I got 3 weeks to write 2 12 page lab reports and 1 history essay

[restive acorn]

Yea it being found outside of elite private schools is probably whats newer

[proud moon]

With 25 percent of my final mark

[proud moon]

True. But my school doesn’t offer AP so I had to take it

AP is just better

[restive acorn]

AP is def really good lol

[proud moon]

Yeah

[restive acorn]

I had like 43 credits going into college

[proud moon]

Lol crazy

[restive acorn]

I took a lot of them though

[shadow lava]

https://tenor.com/view/ib-ibdp-stressed-school-high-school-gif-25672922

[proud moon]

Yeah. You must’ve done rlly well in Hs

[proud moon]

Lol true. In my cohort of around 60 students, 20 dropped out

[restive acorn]

I was lucky enough to have decent teachers for the subjects too

[proud moon]

Yo nice

Anyways I gtg to hang out with friends rn

[restive acorn]

So i didnt have to study like crazy to do ok

Yeah have fun good luck

[teal turret]

Which APs u took

[restive acorn]

I took

Calc ab/bc
Physics (calculus based mechanics i forget what they call it now)
Bio
Govt
World history
French

And then studied on my own for
Human geography

Got 4s or 5s on those

[teal turret]

Yeah it’s physics C for E and M with calc

[teal turret]

Niceee

[restive acorn]

Now they have algebra based physics too

[teal turret]

Yea I took both of them

1 is basic mechanics and 2 is a large variety of topics

[shadow lava]

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[dreamy gale]

I don't understand why we can substitute an arbitrary value into any coordinate x, y, z and solve for the other two.

I know sort of why we're doing it, since we can't solve for three variables with just two equations

but if the solution to a system of planes is a line, wouldn't there be places where this line wouldnt pass?

wait a sec I think i've been thinking of this wrong, the line isn't strictly along an x axis or something so it'd eventually hit every value in each coordinate

but not every point in space ofc

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[shadow lava]

#help-11 message
@native inlet ln(x)^4 and ln^4(x) are not the same thing?

[shadow lava]

according to Desmos they are the same thing..

[candid yarrow]

it says (ln^4)x is not supported

[shadow lava]

but i tried with ln^2

[candid yarrow]

ln^2 works but not ln^4

[shadow lava]

why?

i mean, just syntax wise, not Desmos calculator issue

why are these not the same thing? just written differently

[candid yarrow]

desmos only lets you do ln^2 and not anything else, I assume

[shadow lava]

that's not what i mean

@native inlet said these are different

but are they?

[daring rock]

I've seen it written that way, like the first one

But it's not the typical way to write it

very bad notation in my opinion

[shadow lava]

these are both identical, right?

just making sure i understand

first one is bad notation

but means the same thing

[daring rock]

the first one is ambiguous and could be interpreted to mean other things

[shadow lava]

interpreted to mean other things like what?

it's like sin^2(x) and sin(x)^2, both mean the same thing afaik

so long as the exponent is not inside the argument

[daring rock]

In a broader sense a superscript on a function usually means iteration

like f^2(x) = f(f(x))

not f(x)*f(x)

[shadow lava]

omg lol..
who in their right mind started OK'ing this notation

what a mess

[daring rock]

but yeah for some reason we write exponents on trig functions like that, no idea why

and some people started doing it on logs I guess, I've only seen that once or twice

so yes if your book uses that notation, it probably just means the same thing as ln(x)^y

[shadow lava]

f(xy)^2 does not mean f(x^2 y^2) correct?

but (xy)^2 does mean (x^2 y^2)

[daring rock]

f(xy)^2 = f(xy)*f(xy). But I'd still use parentheses to make it clearer, and write (f(xy))^2

[shadow lava]

the first example the brackets are an argument
the second example the brackets are grouping

[daring rock]

but that's just me

yes, f(xy)^2 means f(xy)*f(xy)

not f(x^2y^2)

[shadow lava]

that's what I thought.. brackets are different depending on context

do you think we should be using different brackets for function arguments? to be extra clear what they mean?

or are there times when you want the brackets for argument and grouping to look the same?

[daring rock]

meh

If I'm ever not sure that what I'm writing is clear, I just use more brackets

[shadow lava]

like we could use f{} for arguments since we never see {} outside of set notation

sin{x}

[daring rock]

I suppose that would be clearer, but I don't think it's really an issue tbh

[shadow lava]

𝓼𝓲𝓷(𝔁)

or write all functions in script

i think VSCode does this with certain fonts

it can be helpful

[daring rock]

Haha, latex actually does the opposite

It un-italicizes sin cos, etc

$f(x) = \sin(x)$

[warm shale]

tatpoj

[shadow lava]

i could see this as confusion for those starting out. "wait you said (xy)^2 is (x^2y^2) but now you are saying f(xy)^2 is f(xy)f(xy)" ...

[daring rock]

I just think of it like functions come first in the order of operations

[shadow lava]

BEDMAS?

[daring rock]

BFEDMAS, I guess lol

[shadow lava]

but it's really FBEDMAS?

wait, FB or BF?

lol

[daring rock]

Uhh BF I guess, you still want to simplify the argument first

but honestly it doesn't really matter lol

[shadow lava]

oh right, if it's f(x^3)^2 and (f(x^3)^2)^4 you still wanna do brackets first
so it becomes f(x^3)^6

always start with outside first, I think?

[shadow lava]

is that a good rule to follow with math? or depends

[daring rock]

I think you're overestimating how big of a problem this kind of ambiguity is going to be

[shadow lava]

lol

[daring rock]

Generally what is meant is clear from context

[shadow lava]

yeah it was just kinda on my mind

due to the comment above

but if they are the same it's all good

[daring rock]

yeah, I still like good notation as much as the next guy lol

[shadow lava]

yep

otherwise we get memes like this one

the only way to solve this question is to execute the teacher

https://tenor.com/view/kill-gif-21102518

but according to bedmas it's brackets first, so 1+2

6 / 2(3)

and the DM in bedmas are in whatever order comes first

so it would be 6/2

3(3)

9

final answer

BUT.. if it was written as a fraction instead of the division symbol it would be a different answer

since fractions have invisible brackets surrounding both the numerator and denominator

to jail them in so to speak

[native inlet]

no I said to also know that form

[shadow lava]

OK

[native inlet]

at least that’s what I meant

[shadow lava]

in fraction form this answer would be 1

[fierce vale]

according to bedmas? i thought that's always true

[shadow lava]

it is

this is 16

they even wrote a NYT article about it https://www.nytimes.com/2019/08/02/science/math-equation-pedmas-bemdas-bedmas.html

I think ppl are confusing division symbol for fraction bar

they are not equal, afaik? yet we are allowed to divide both sides of an equation this way

dividing by fraction, rather than dividing by division symbol

do they even teach this in school? that both are not the same

[magic dagger]

Hi

8 / 2 (2 + 2) = 8 / 2 (4) = 8 / 8 = 1

[magic dagger]

if it was (8/2)(2+2) then it would be 16

[high lily]

it's ambiguous

[magic dagger]

so depends if it was $(8/2)(2+2)$ or $8/2(2+2)$

[warm shale]

WPawnToE4

[warm shale]

ℝamonov

[shadow lava]

sadly, I had a question like that on Calculus 1 Final

the entire class was confused, the professor wasn't even aware it was ambiguous

https://tenor.com/view/fml-theoffice-michael-gif-5219520

[fierce vale]

what does that have to do with calc xd ?

[shadow lava]

ambiguous notation i mean

to do with the way a trig function was written double exponents no brackets whatsoever for argument

[fierce vale]

oh ok

did u tell him about it after the exam?

[shadow lava]

during the exam

she wrote the correct meaning on the board

she said it's common notation but total bs, full class was confused

kinda like the example above with ambiguity, depending on which calculator you use you will get a different answer for the exact same question

https://tenor.com/view/math-is-hard-addition-wrong-answer-fail-mathematics-gif-24427575

[fierce vale]

yeah it depends if the calculator uses implied multiplication or not

[shadow lava]

.close

[obtuse pebble]

Channel closed

Closed by @shadow lava

Use .reopen if this was a mistake.

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[wide star]

is there a formula or somthing to find ln(x)?

[waxen helm]

taylor series is one way

[tardy epoch]

$\log(x) = \int_1^x \frac{dt}{t}$

[warm shale]

rie.mann

[waxen helm]

tbh that's a really general question

[wide star]

ah

see

I need one that uses only the basic operations if possible

• • • / ^ √

[blazing lark]

ln(x) is log base e (x)

[hidden garnet]

doubt that's gonna work

[blazing lark]

Do u know what a logarithm is?

[wide star]

sorta

I know what they do

[south oracle]

Log x
Do you mean ln x or log(10, x)

[blazing lark]

Can u post the problem you are trying to do

[wide star]

no

I can not sadly

[tardy epoch]

$\sum_{n=1}^\y \frac{(-1)^n(x-1)^n}{n}$

[warm shale]

rie.mann

[tardy epoch]

+, *, / only

[wide star]

hmmm I could try that

[hidden garnet]

damn this was creative, nice one

[blazing lark]

Bro definitely just did a Taylor expansion in his head

[obtuse pebble]

@wide star Has your question been resolved?

[wide star]

what if it diverges to infinity?

[tardy epoch]

What value of x does that happen

[wide star]

not one that you want to know about

[tardy epoch]

Can't answer questions that aren't defined

The correct answer was to use log properties derived from the integral to get to the domain where the summation does converge

[violet kindle]

Can i ask why?

[grizzled shore]

You sorta need a definition for the number e first

It doesn’t make sense to ask what is ln of something when you don’t know what e is

[wide star]

because that's what is already defined with the number that I am finding the natural logarithm of

[violet kindle]

Ok wait

So you want to find the ln of one number?

[wide star]

yes

[violet kindle]

Using just those basic operations?

[wide star]

yea

[grizzled shore]

Can you show the problem

[violet kindle]

Does this formula have to be applied to any other numbers?

[wide star]

I would pefer that it is

[tardy epoch]

Just look in their history to find out

[wide star]

but thats not needed for now at least

[violet kindle]

Ok

[tardy epoch]

Since they're unwilling to answer

[violet kindle]

😭

[wide star]

???

[violet kindle]

You're asking a very strange problem with vague constraints that we dont know whats for

Im just kinda confused

I mean if youre only looking for the ln of one number, just put in that number

Uses no operations

I just dont know what the actual problem is

[wide star]

my number ain't on calculators

[violet kindle]

What

?

I'm confused

[wide star]

its not a real or complex number

[violet kindle]

Wait

Its not real OR complex?

What is it then?

[wide star]

i guess you can call it hypercomplex

[violet kindle]

How do you define that

[wide star]

its not relevant what the number is

I just need somthing to plug it into

[violet kindle]

I'm even more confused now

[wide star]

I just need a way to find ln(x) for this number that doesn't diverge to infinity

[violet kindle]

This number that is not real or complex?

[wide star]

(unless the answer is infinity?)

[wide star]

yes

[violet kindle]

I dont even know how that would be defined

Either youre on some gigabrain shit i cant understand or this problem is flawed in some way

[wide star]

I would assume its both

[violet kindle]

😭

Sure

I wouldnt know cause i dont understand what youre asking for

[wide star]

Im looking for a forumla to solve ln(x)

[violet kindle]

Taylor series wont work?

[wide star]

is that this?

that diverges to infinity

[violet kindle]

What?

Diverges to infinity for what

[tardy epoch]

This

[wide star]

my number

[south oracle]

if you're seeing something like ln5 or ln3 or something in your calculator or something yes it's a real number by a high chance

Or idk I misunderstood what you're doing

[tardy epoch]

This is the current state.

[violet kindle]

And you cant tell us what your number is

[wide star]

If i do then yall I just going to ask even more quesntions or just call it dumb

[tardy epoch]

Guessing questions is a waste of time for helpers

[wide star]

I asked if there were any other ways to solve ln(x)

[violet kindle]

Ok well either we ask questions to solve your problem or the problem is just dumb

[wide star]

too most people the quetion is dumb

[tardy epoch]

You were given two insufficient answers. It's reasonable to ask why and then you became cagey to wakebloom

[tardy epoch]

.

[violet kindle]

Well idk if were most people

This is a math server after all

[wide star]

fine i'll say it

the number is 1/0

[south oracle]

The number is not defined

[violet kindle]

😭

[south oracle]

You cannot define anything divided by 0

[tardy epoch]

Guessing you didn't look far enough into their history

[wide star]

see this is why I didn't want to say it

[violet kindle]

Why do you want to take the natural log of 1/0

[violet kindle]

Lmaooo

[wide star]

ran into it more than once with the weird things im doing

[violet kindle]

Idk what you could possibly be doing that requires you to evaluate ln(1/0)

It doesnt exist

[south oracle]

Do you want to listen to why it's left undefined or something
I aslo can't find any correlations with the previous question you asked, could you elaborate more

[wide star]

defining 1/0 and finding its properties

[tardy epoch]

They've been told many times

[violet kindle]

1/0 is undefined

[rocky goblet]

it's not actually 1/0 in a meaningful way, they've just come up with some weird operation and called it "/"

[violet kindle]

Oh wait @tardy epoch when you said history you meant SERVER history i thought you meant question history

[wide star]

but the number being 1/0 is only relevant in that it means i can't use a calculator

[violet kindle]

This has gone on elsewhere?

[south oracle]

Okay let's say 1/0 is defined