help-23

[safe radish]

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[hidden spruce]

hey, can someone help me to solve the polynomial congruence of 2x^3 + x^2 - 26x +2 = 0 mod 11025

[dusty crescent]

I would start by prime factorising 11025. Then perhaps you can use hensels lemma.

[hidden spruce]

i did that, but when i solve for 2x^3 + x^2 - 2x + 2 = 0 mod 3, the solutions do not give f'(x) coprime to 3

[dusty crescent]

perhaps you can brute force mod 9 then?

[hidden spruce]

yeah

lemme try

when i do for mod 9, i do not need to verifie if the gcd of (9,f'(x_1)) = 1 right?

the solution for mod 9 is 8

then the general solution is 9n + 8

[dusty crescent]

I don't see why that would be needed if you have already found solutions mod 9.

[hidden spruce]

ok

i'm doing for 5 right now

[safe radish]

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[safe radish]

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[sacred wadi]

i i have x²arctan(1/(1+x)) -1 is not in the domain I am looking for vertical asymptote
I make the limit tends to -1 it gives Arctan(1/0) I have to make an array of sign la ,
?
but I need to make a sign array for X²arctan(1/(1+x)) or only for arctan

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[mental eagle]

no idea whats this

[frigid spruce]

ur answer

[mental eagle]

wdym ?

[frigid spruce]

is

[safe radish]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[frigid spruce]

first find the sum of 50 terms and then subtract the sum of 31 terms from it

[mental eagle]

1

[main mural]

what's the difference between any two terms?

[mental eagle]

4

[main mural]

yep

so d=4

[mental eagle]

alright

[main mural]

the first term is a=3

[mental eagle]

so sum 2 is 7

[main mural]

what?

[mental eagle]

nvm

continue

[main mural]

use the first thing

[mental eagle]

so 3

?

[main mural]

what 3

[mental eagle]

wait no 4

[main mural]

what 4

[mental eagle]

since first sum of arithmetic

.close

[safe radish]

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[indigo tundra]

.

[gaunt raptor]

Lol

[indigo tundra]

IVE NEVER EVEN HEARD OF THESE

[cursive nacelle]

I don't think u need to memorize those things

[indigo tundra]

I think C

[cursive nacelle]

this feels like a visualization problem lol

I also think C

[marsh walrus]

hollow cone frustrum aka cone of shame

[cursive nacelle]

Doggy cone

[indigo tundra]

Guys I got it right

[cursive nacelle]

lets go

what class is this?

[indigo tundra]

Geometry

Highschool

[cursive nacelle]

hmm

[indigo tundra]

/integrated math 2

Anwyays ty

.close

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[indigo tundra]

.reopen

[safe radish]

✅

[indigo tundra]

ITS B RIGHT

[marsh walrus]

youd do better finding a way to think about these than asking for every problem

[indigo tundra]

Plz

[celest ember]

It's not that hard to imagine, if you're still having problems take a paper or something and rotate it yourself

[indigo tundra]

Does that mean I'm right

(I don't know what a rotation about a line does)

[celest ember]

Yes it's B

[indigo tundra]

Ez

[pallid saffron]

ok so

imagine that line is a stick

[indigo tundra]

Does it automatically mean a 360

[jolly bridge]

no

i mean

[pallid saffron]

if it does not say an angle i would say it does

[jolly bridge]

if the degree is not mentioned yeah

[indigo tundra]

OK

So cool

[indigo tundra]

Plz teach me how to integrate

[jolly bridge]

you mean integration?

[cursive nacelle]

visualize it like it is rotating around the line

[indigo tundra]

yes teach integral calculus rn

The symbol looks so cool

[jolly bridge]

thats a jump from what you are doing rn , i would suggest you check lectures about it online ( khan acadmy or some) and practice , then ask doubts with your teacher , or here

[indigo tundra]

I made my friend call me the antiderivative

[cursive nacelle]

man it looks like a worm

[celest ember]

Bro what grade are you in

[indigo tundra]

IT LOOKS COOL

[pallid saffron]

do you know how to derivate?

[jolly bridge]

snake

[indigo tundra]

10th

[jolly bridge]

yeah wait a year

[indigo tundra]

No

[celest ember]

Do you know what limits are?

[pallid saffron]

thats very basic knowledge, without that u cant integrate

[indigo tundra]

😔

[cursive nacelle]

we are going to backtrack into foil rule

[indigo tundra]

no

[tall bough]

Bruh

[indigo tundra]

teach limits rn🙏

[tall bough]

Do u know what foil is

[indigo tundra]

LOL HIS NAME

[cursive nacelle]

do u know what a polynomial is?

[indigo tundra]

Don't u wrap sandwiches with this or something

[pallid saffron]

wait do you know functions and their graphs

[indigo tundra]

yes

[tall bough]

What is it

[celest ember]

Wtf is foil bruh?

[jolly bridge]

bros asking the right questions

[indigo tundra]

maybe

[cursive nacelle]

a way to expand (a+b)(c+d)

[indigo tundra]

easy

Learned in like algebra 1 level

[celest ember]

Why do you call it foil

[tall bough]

Nerd

[indigo tundra]

I just use the distributive property twice

[pallid saffron]

do you know what to do if i say "trace the graph of the function f(x) = ln(x+3)

[indigo tundra]

No

Long noodles(x+3)

[cursive nacelle]

cause u get the terms by multiplying First, Inside, Outside, Last. It's not a rule just a way to remember how to do it, u probably do the same anyways just never gave it a name

[cursive nacelle]

that is what foil is basically

[celest ember]

"long noodles"

[pallid saffron]

if i say that ln(x) is the inverted function of e^x

[jolly bridge]

long noodle

[celest ember]

I see

[jolly bridge]

new name given

[indigo tundra]

That's me

(I don't know wat e is)

[cursive nacelle]

bruv

[indigo tundra]

Teach limits rn plz

[pallid saffron]

e is a number equal to 2,7....

[celest ember]

Do you know what functions are?

[cursive nacelle]

go on Khan Academy and start learning if ur actually interested

[indigo tundra]

yes

[celest ember]

Are you sure?

[indigo tundra]

But ill get there like 5 months from now fr since I'm gonna do linear algebra before calc 1

So far away

[cursive nacelle]

wait have u done precalc?

[indigo tundra]

No im finishing integ math 2

rn

[cursive nacelle]

well u will learn limits and derivatives in precalc

the basics of it

[indigo tundra]

oh

i think I saw it at the last unit

On precslc

Ez

Omg guys wanna see the roadmap I made

[cursive nacelle]

idk exactly how it works in the US but I think that is right

[indigo tundra]

It's pretty cool right

[cursive nacelle]

good luck

type .close if u have no more problems though

so someone else can use this

[indigo tundra]

There are other channels😔

.close

[safe radish]

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[timber moss]

$f(t)=c_0e^{-\lambda t}\$
you are given an initial point where at t = 0, $c_0e^{-\lambda (0)} = 820\$
and one other point where at t = 20, $c_0e^{-\lambda (20)} = 200$

[flat frigate]

Triaxyz

[timber moss]

point (0,820) allows you to find $c_0$ while point (20,200) lets you find \lambda

[flat frigate]

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

[timber moss]

using these two values you then set your equation equal to 20 bacteria; $20 = c_0e^{-\lambda t}$ and solve for t

[flat frigate]

Triaxyz

[stone hawk]

I do not understand

[timber moss]

@stone hawk are you familiar with this equation

[stone hawk]

yes somewhat. the only one i do not know how to use tho

[timber moss]

it just shows exponential decay, which is what is being modeled in this problem

to understand how it works you need to know your properties of exponents and logarithms

[stone hawk]

ah okay

oh okay. I will work on it then. thank you for your assistance

.close

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[wary veldt]

does the rational root theorem work for quadratics?

[solar hazel]

yea

[wary veldt]

can a second person confirm or disprove?

[main mural]

it does

[wary veldt]

thank you

[solar hazel]

can a third person confirm

[wary veldt]

.close

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[fresh vessel]

I have completed the differentiation, no clue how to get that final answer

[hasty falcon]

1/3 - 1 is not -1/3

answer is perfectly fine..just recheck your calculations and simplify the resulting expression

[fresh vessel]

I have to redo it..😭😭

Fixed?

How does this simplify

If the power was like 2 or 3 i would expand and then simplify but what do i do here

[safe radish]

@fresh vessel Has your question been resolved?

[safe radish]

@fresh vessel Has your question been resolved?

[safe radish]

@fresh vessel Has your question been resolved?

[modest spear]

Its -2/3 btw 😭. Redo it and you ll get there eventually

[safe radish]

@fresh vessel Has your question been resolved?

[junior smelt]

Maybe start by trying to factor out a $(1 + x)^{-2/3}$, and that should hopefully give insight on how to go...

[flat frigate]

@junior smelt

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[thin shoal]

could someone help me work this out

[timber moss]

partition the top piece as a right triangle and add the two areas together

or you can use trapezoid formula if you wish

[thin shoal]

whats the trapezoid formula?

[lean otter]

average of the parallel sides * the height

[fresh jetty]

Is the answer 171mm

[timber moss]

I got 126 using this and my method

[thin shoal]

ok im gonna try it

tysm i got it correct

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@thin shoal Has your question been resolved?

[thin shoal]

yes

[safe radish]

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[frigid marlin]

{σ ∈ Sn : σ(1) = j ∧ σ(j) = 1}

[frigid marlin]

Hi guys this set means

a function

i mean its a permutation, but a permutation is a function, right?

and it says that j = 1 and σ (1) =1

for example (1 1)

this permutation would be a function

[safe radish]

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[jolly stirrup]

Does the hypotenus on a unit circle always equal positive 1?

[plucky elk]

The radius of a unit circle always equals 1

The length of the hypotenuse of a triangle is always >=0

[safe radish]

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[harsh olive]

Find the Cartesian equation of:

$x = t + \frac{1}{1+t}, y = 1 + t + \frac{1}{t}$

[flat frigate]

BOHO

[harsh olive]

i dont like parametrics 😭

anyways i dont think t can be made the subject

so i probably need to add the two equations or smth?

[final bay]

Try to write the RHS as one fraction maybe?

[harsh olive]

alr

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

[flat frigate]

BOHO

[final bay]

And y?

hmph this doesn’t work

bruh

[harsh olive]

$y = \frac{t^2+t+1}{t}$

[flat frigate]

BOHO

[final bay]

Now consider x-y maybe?

We might be cooking something

[harsh olive]

$x - y = /frac{t^2+t+1}{t(t+1}$

oops

$x - y = \frac{t^2+t+1}{t(t+1}$

[flat frigate]

BOHO

[final bay]

yeah i think you can try to solve from here

[harsh olive]

can i simplify the RHS further?

or do i get it in the form of x and y ?

[final bay]

look at x then look at y then look at x-y

[final bay]

Also this is y-x not x-y

[harsh olive]

oh

for x-y it would be -t^2 - t - 1 on numerator right

[final bay]

Yea

I got an answer it’s very messy

[harsh olive]

i did x/y and i got t/t+1

dunno if that helps

[final bay]

Do you want to see what I did

Or do you want to try solve

[harsh olive]

yea sure

[final bay]

The answer is the 4th lowest line

the other stuff is just me testing stuff

like I cancelled xy somewhere which was possible because x and y can never be 0

the algebra gets messy if ur lost lmk I’ll tell you what I did

[harsh olive]

im lost here

how did you get to the denominator?

[safe radish]

@harsh olive Has your question been resolved?

[safe radish]

@harsh olive Has your question been resolved?

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[fresh vessel]

Is this true?

[final halo]

Yes

[fresh vessel]

.close

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[fresh vessel]

Is this true?

[cunning heron]

yes ,you coud add a + - sign

to be more accurate

[fresh vessel]

Ok

.close

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[floral willow]

need help with this one

i have no clue on this one

.close

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[lean otter]

hey, quick question if the graph of a quadratic equation does not intersect in x point then does that mean that all the zeroes obtained will be imaginary numbers?

[mortal sandal]

If it doesn't have any x-intercepts

[lean otter]

yeah

[mortal sandal]

Then yes, all zeroes will be complex

[lean otter]

Oh ok

thanks

.close

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[mortal sandal]

Np

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[lyric apex]

Hi! I need to some help with explaining a theorem in linear algebra that i don't quite understand.
"The subspace of a vector space needs to contain the Zero vector" What does this mean really?

[lyric apex]

This doesn't contain a Zero vector. Can someone explain why?

[halcyon carbon]

a zero vector means every entry of the vector is 0

[halcyon carbon]

because of the 4

[lyric apex]

Because 0a+0b isn't 4?

[halcyon carbon]

4 is a constant no matter what a,b u pick

so u cant have a zero vector in that form

[lyric apex]

Oh so since 4 is a konstant it can't ever change. So No matter what you do to it, it will stay as a constant and never be zero?

[halcyon carbon]

yes

[lyric apex]

So a and b could be zero because we can add them together to make a vector with all zeros?

Or multiply by a scalar?

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[lean otter]

can someone help with this

[fleet condor]

there's 5 sides and they are all the same length

[lean otter]

so basically t+8

i dont get it someone help

help

help

<@&286206848099549185>

[slate marsh]

Kallila's age is x, and Bonita's age is x+2, so the product of their ages will be x(x+2)=399

multiplying the numers you willl get x² + 2x = 399

and with that you could use the quadratic formula as one possible solution, in which the equation would be x² + 2x - 399 = 0

[mortal sandal]

!nosols

[safe radish]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[slate marsh]

srry

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

oh ty

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@lean otter Has your question been resolved?

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[light rapids]

Can someone help me understand this, I don't get why in the chart the time would be 0.5 - t

[light rapids]

Bevermind I get it

Nevermind*

.close

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[lean otter]

This is what I have done

Idk how to solve further

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185>

<@&286206848099549185>

[steep vessel]

You can change h+k=7 to h=7-k
And replace all h in h^2-4h+k^2-6k=3
With 7-k to get
(7-k)^2-4(7-k)+k^2-6k=3

49-14k+k^2-28+4k+k^2-6k=3
2k^2-16k+21=3 or
2k^2-16k+18=0
Then you can use the quadratic formula to solve for k then plug in h+k=7 to solve for h and k

[safe radish]

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[dapper ledge]

hi guys can someone give me trig idenities/other ways to integrate instead of integ by parts sin(4x)cos(2x)

[peak estuary]

well you can use the product to sum identity for example

or you could express it using complex exponentials and multiply it out (will end up being the same)

[dapper ledge]

whats complex

exponential

using a trig idneity

[safe radish]

@dapper ledge Has your question been resolved?

[wheat condor]

$e^{i\theta} = cos(\theta) + i*sin(\theta)$

[fiery merlin]

4x is twice 2x, so you can use the double angle identities maybe, with sin(2u) cos(u) 1/2 du.

[flat frigate]

G. Spark

[fiery merlin]

sin(u) cos^2(u) du

Then you can probably do substitution with v = cos(u).

[safe radish]

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[lean otter]

Hello.

[lean otter]

I need help to integrate into a single expression if possible the total relational information + total correlation/conditional total correlation/dual total correlation + conditional mutual information/interaction information.

If someone knows about mutual information, please DM me.

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185>

[daring hare]

what do yu want

[lean otter]

Someone to help me with this.

[wheat condor]

The language used for mutual information varies from field to field.
Googling I get exactly one hit on "total relational information".

What field of study?

[lean otter]

Would be something like this.

Kullback

This would be the total mutual information calculated for three variables with three values.

[daring hare]

huh?

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

@lean otter Has your question been resolved?

[wheat condor]

I'd just call this "mutual information".

For discrete distributions.

[safe radish]

@lean otter Has your question been resolved?

[misty bay]

it's possible to define mutual information for all random variables with just the definition with the densities

since you can define KL divergence similarly

the rest of the question doesn't make a whole lot of sense

[lean otter]

And interaction information?

[misty bay]

haven't heard about that one before

[lean otter]

Yeah, is not used very frequently.

[lean otter]

@misty bay Does Shannon's Surprisal can be used to describe details of information content?

[lean otter]

Henceforth I reached the answer!!!
Thank you man
I truly appreciate it🫶

[safe radish]

@lean otter Has your question been resolved?

[misty bay]

I've heard of Shannon information, but not Shannon surprisal

you'd have to define what terms you're using

[safe radish]

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[little marlin]

im not sure how to start

[rough storm]

What must be fixed?

Write down what must be fixed, write down what you are trying to optimize, and formulas for these :)

@little marlin

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[hollow pagoda]

do it?

!show

[safe radish]

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

[hollow pagoda]

well.. hint:
cos(x)^2 + sin(x)^2 = 1

so cos(x)^2 = 1 - sin(x)^2

according to the hint what is 1- sin(1) ^ 2 equal to

cos(1)^2

yh

i guess u got it?

sec = 1 / cos(x)

yup

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[marsh walrus]

use the cubic factoring trick SOAP

can you see how to use this?

[molten apex]

This brings back so many memories bruh

[marsh walrus]

the trick tells you how to pull a linear factor out of a cubic in this form

so yea, it leaves a quadratic factor

when its applicable

[molten apex]

No that would be a^2+2ab+b^2

[marsh walrus]

oh i see what youre asking

,w Expand[(x-1)(x+1)^2]

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[marsh walrus]

no

right

thats what youve written here.

[molten apex]

Try expanding that

And see what happens

[marsh walrus]

no, this doesnt make sense, you have 3 x's

so you should pick up at least a x^3 term

no, its not.

,w Expand[(a+b)^2]

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[marsh walrus]

i believe it comes from polynomial division

maybe itd be helpful to just try distributing it

and confirm it works

i dont know how satisfying doing a derivation is going to be for you but you could certainly try it

like i said i think you can get it using polynomial division but id probably just assume that $a^3 \pm b^3 = (a \pm b)(Ma^2 \pm Nab + Pb^2)$ or something

[flat frigate]

jan Niku

[marsh walrus]

and match coefficients up

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[subtle robin]

Prove: $\log {3/\sqrt{b}} \sqrt{x} = -log{b} x$

[flat frigate]

龖

[subtle robin]

um

idk how to type

the 3/√b is base

and the second one b is base

[kind tinsel]

$$\log_{\frac{3}{\sqrt{b}}}(\sqrt{x}) = -log_b(x)$$

[flat frigate]

smay

[subtle robin]

oh thanks

[kind tinsel]

is this what you wanted?

[subtle robin]

$$\log_{\frac{3}{\sqrt{b}}}(\sqrt{x}) = -log_b(x)$$

[flat frigate]

龖

[subtle robin]

yeah thanks

[subtle robin]

the question is prove this is equal but idk how to do it

Prove: $$\log_{\frac{3}{\sqrt{b}}}(\sqrt{x}) = -log_b(x)$$

[flat frigate]

龖

[kind tinsel]

someone might be trolling you because this is not true lol

[subtle robin]

huh

its on a textbook

[kind tinsel]

are you sure the numerator is 3 there?

[subtle robin]

its a bit blurry

might be 1??

[kind tinsel]

it should be 1

[subtle robin]

oh

oops

[kind tinsel]

then you will get something that you can prove

but in any case, do you still need help?

[subtle robin]

wait if i have -log_√b √x can i cancel the squre root out?

[kind tinsel]

well we are going to see, do you know the properties of the logarithm?

[subtle robin]

yeah

[kind tinsel]

we are going to try to find one that is helpful for us

preferably one that can change the base of the logarithm

[subtle robin]

theo ne where u put it in a fraaction?

[kind tinsel]

There are several like that! which one do you want to use?

you can give a name or the formula for it

[subtle robin]

he 4th one

[kind tinsel]

okay great

so we have a logarithm on the left

so how are we going to rewrite it (using the one you picked out)?

[subtle robin]

oh wait i think i solved it does it turn into (1/2logx)/(-1/2logb)

and then cancel the 1/2 out

nd then u get the same amnswer

[kind tinsel]

what turns into (1/2logx)/(-1/2logb)?

and what allows you to conclude that?

[subtle robin]

oh wait

its wrong right

[kind tinsel]

well let's just apply the formula, what are we going to use for the "new" base?

[subtle robin]

b??

[kind tinsel]

okay good

so what does $\log_{\frac{1}{\sqrt{b}}}(x)$ turn into

[flat frigate]

smay

[kind tinsel]

using our new base

[subtle robin]

log(x)/log(1√b)

[kind tinsel]

yes (and you should make the base b explicit, because we are about to use that)

[subtle robin]

wait

x is square root though

[kind tinsel]

oh yeah

[subtle robin]

what does explicit mean

[kind tinsel]

okay but you have the idea, it's log_b(sqrt(x) / log_b (1/b)

by explicit i mean that you are going to write out the base of the log that you're taking

because if you leave it out people might think it's the wrong base

[subtle robin]

so then i take the square root out for 1/2?

[kind tinsel]

yes in the numerator 👍

now all that's left to deal with is the denominator

[subtle robin]

now idk what to do with the demominator

[kind tinsel]

okay, we can evaluate this explicitly

the goal is to find out what $\log_{b}(\frac{1}{\sqrt{b}) is

[subtle robin]

$\log_{\frac{1}{\sqrt{b}}}(b)$

[flat frigate]

龖

[subtle robin]

um where did the (b) come frm

[kind tinsel]

sorry i messed up this is the actual expression that we are trying to evaluate

$\log_{b}(\frac{1}{\sqrt{b}})$

[flat frigate]

smay

[subtle robin]

oh u do the change f base rule again

[kind tinsel]

well we are just trying to ask ourselves “b to the what power is 1/sqrt(b)?

because that is what the logarithm means (that's what it'll give us when we take this expression)

[subtle robin]

is it like -√1

no -1/2

[kind tinsel]

okay good

so then $\log_{b}(\frac{1}{\sqrt{b}}) = \frac{-1}{2}$

[flat frigate]

smay

[kind tinsel]

so let's put it all together

[subtle robin]

wait

but like before it didnt have a base

so it would be base 10

so how do u just change it to base b

[kind tinsel]

wait we can give it whatever base we want

look closely at the fourth rule again

[subtle robin]

oh ok

so 1/2logx / -1/2

[kind tinsel]

1/2 log_b(x) / -1/2

you should write out the base

[subtle robin]

yeah

[kind tinsel]

we can give them whatever base we want as long as they are the same base on the numerator and the denominator

okay so then simplify

[subtle robin]

yeah

i got it

thanks so much

[kind tinsel]

great!

:3

[subtle robin]

.close

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[loud osprey]

How do i do this

[median vigil]

note that least fencing = least perimeter

1. come up with an expression for the perimeter of the fencing in terms of length and width (including the internal fence)
2. come up with an expression for the area of the field
3. using the fact that the area of the field is a fixed value, solve for one variable (width or length) in terms of the other
4. plugging in your solution from step 3 into the expression for the perimeter from step 1, find the absolute minimum of the perimeter function. this will give you the minimum length or width
5. using the solution from step 3, use the minimum you found for one variable to find the minimum for the other

[safe radish]

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[subtle robin]

jquestion 9 from number 2

i understand what it means

but idk how to do it fast

like trial and error 100 times

i cnt think of how to make 200 with 2 3 and 7 for example

[obsidian oracle]

there is one last number that you can use

remember that log means log base...

(as I'm assuming)

[iron flare]

controversial 😔

[obsidian oracle]

look, We use ln for a reason xd

[subtle robin]

um im still confused

[obsidian oracle]

what is the number such that log(...) = 1?

[subtle robin]

10

[obsidian oracle]

There you go

your last useful number

[subtle robin]

im still confused how to ues the base

[obsidian oracle]

well first of

try to write 200 using 2,3, 7 and 10

[subtle robin]

10^2 * 2

[obsidian oracle]

you got it

so log(200) = ...

[subtle robin]

um but the base doesnt do anything in like the product properties

idk

[obsidian oracle]

just do the same thing you've been doing for the last questions

log(ab) = ...

[subtle robin]

log a + logb

[obsidian oracle]

yes

[subtle robin]

so 2log10 + log2?

[obsidian oracle]

yes

[subtle robin]

then how would i write that in terms of xyz

cuz 10 then isnt a base?

[obsidian oracle]

?

[obsidian oracle]

.

We've already gone through the fact that log(10) = 1

So 2log(10) = ?

[subtle robin]

2

[obsidian oracle]

yes

So 2log(10) + log(2) = ?

[subtle robin]

bruh im so confused

how do u turn 2log(10) into xyz

[obsidian oracle]

Why do you feel the need to turn literally "2"

into something else?

Like 2 is already as simple as it gets

so we're done for this term

[neat kiln]

I mean, technically you can write 2=2*x^0

[subtle robin]

so how do you write 2log(10)

[obsidian oracle]

.

[subtle robin]

oh

so u dont need to put log

[obsidian oracle]

exactly

[subtle robin]

OHH

[obsidian oracle]

if there's no remaining log there's no need to swap

[neat kiln]

2+x, or 2*x^0+x if you really want to

[subtle robin]

what is the point of writing the second one

if it just the same thing is 2+x

[neat kiln]

If you really want to turn it into x, but it's basically pointless

[subtle robin]

thanks guys

.close

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[dusky sedge]

I know QR = ML and QP=MN and I dont know how to explain that through math. Also I need to make it ASA postulate. Help?

[dusky sedge]

<@&286206848099549185>

[lean otter]

!15m

[safe radish]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[prisma acorn]

So write down the two angles you know that are equal between the two triangles

wait NVM

Think about what two angles that are the same between both triangles

for example angle Q = angle M because they are both 90 degrees

[safe radish]

@dusky sedge Has your question been resolved?

[dusky sedge]

<L and <R? But I dont know a mathematical reason to prove that

[dusky sedge]

(<L and <R ) (<M and <N)

[prisma acorn]

doesn't say to right?

[dusky sedge]

<R = <L
<P = <N

But how is it proved?

[prisma acorn]

so

[prisma acorn]

the question is just asking what do you need I think

to prove it

use SAS first

Then after that

becuase they are the same you can show this

<R = <L

[dusky sedge]

How do I know the sides are equal just knowing that they both share a right angle?

[prisma acorn]

well you said that

[prisma acorn]

there

anyway

you don't need to prove anything for the question

[dusky sedge]

Yea I said I dont know how to explain it through math

[prisma acorn]

what logic

did you use to arrive at that

The question itself does not have enough info to prove congruence

so it is asking what two angles and side do you need

[dusky sedge]

The right angles are equal so the sides must be. I dont know what that's called in mathematical terms

[prisma acorn]

that's not true

[dusky sedge]

It says above it "In the diagram below, right triangle PQR is transformed by a sequence of rigid motions that maps it onto right triangle NML."

[prisma acorn]

ok so then if it is rigid motions

then the side lengths NEVER change

so you can take it as a given that all side lengths are the same

if the sides lengths stay the same you can prove the angles are the same by SSS

[dusky sedge]

But it wants me to show ASA congruency

[prisma acorn]

okay

so then you can assume the angles never change

instead

or whatever combination of angles/sides that you want

[prisma acorn]

right

so because it is rigid

angles stay the same and so do the sides

so you just need to write

2 angles and 1 side to prove it

the reasoning you can give for these is "given because it is a rigid transformation" and thats it

[dusky sedge]

So
<R = < L / Given
QP=MN / Given
<N=<P / Given
?

[prisma acorn]

no

in ASA the side has to be inbetween the angles

so if you use angle r and angle p then the side must be side RP

Change the side to be

RN = LP

QP is not inbetween RN

[prisma acorn]

see how if your using the angle r and p then the line connecting them is rp and the corresponding line to that is LN?

[dusky sedge]

I'm getting lost

[prisma acorn]

sorry I'm giving a bad explanation

[dusky sedge]

What're you saying?

[dusky sedge]

All good

[prisma acorn]

in ASA proofs, you need to find two angles and a line inbetween them that are congruent to prove that the triangles are the same

makes sense?

[dusky sedge]

Yes. So where did I go wrong

[prisma acorn]

so over here you used angle R and L

however then line that you used for that was QP

QP does not connect R and L

does this make sense?

[dusky sedge]

A line in between them you said.

[prisma acorn]

yes

[dusky sedge]

Would you show an example of what between them looks like?

[prisma acorn]

Ok

https://www.desmos.com/calculator/jme0mqt5en here is a triangle

the point p has an angle called angle p

and point q also has an angle called angle q

the line between p and q is pq

this is what I was reffering to as "the line between angle p and angle q"

but I wasn't being specific enough

https://www.desmos.com/calculator/byhdwzxwpf

here is a graph with that highlighted

sorry my bad

not pq

pr

[dusky sedge]

Yes and you said QP doesnt connect RL

[prisma acorn]

No

sorry

can I restart

[prisma acorn]

I am going to reorder this so that the left side is triangle PQR and the right side is from triangle LMN

<R = < L / Given
QP=MN / Given
<P=<N / Given

The line QP does not go between R and P

it goes between Q and P

[dusky sedge]

Yes

[prisma acorn]

so can't use

QP for this ASA proof

You have to use RP because that is the line that goes betweeen R and P

for the other side

don't use MN use LN because that is what goes between L and N

https://www.desmos.com/calculator/3amhl8osgi

Here I highlighted the line that should be used for those angles

Does this make sense?

[dusky sedge]

Yes

[prisma acorn]

ok

so do you get what it should be now?

[dusky sedge]

<R = < L / Given
QR=ML / Given
<P=<N / Given

[prisma acorn]

No

QR does not

go between RP

it should be

<R = < L / Given
RP = LN / Given
<P=<N / Given

[prisma acorn]

see how here the line is between the two angles so RP is used

QR never touches angle P

so it can't be a ASA proof then

it would be something like SAA or AAS which don't work

[dusky sedge]

Lol I see now

[prisma acorn]

yeah

AAS lol

[safe radish]

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[dire escarp]

any hints?

[dire escarp]

stuck on this integral

i know i can factor out the r+1

[junior smelt]

What’s the derivative of q^2 (wrt q)?

[native isle]

estou nessa parte também , sobre variável.

[dire escarp]

2q?

ah

[junior smelt]

was that all good?

[dire escarp]

my answer is negative...?

wait one sec

[dire escarp]

ah

[junior smelt]

Double check that

Good choice of sub but derivative isn’t right

[dire escarp]

yea i figured that out too hahaha

should be 1/2

i got it!

[junior smelt]

it happens

[dire escarp]

thank you so much :)

[junior smelt]

My pleasure

[dire escarp]

cya around! :)

.close

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[subtle saffron]

Could someone help me out with this question?

[pallid saffron]

if you focus on one of the right triangles that composes the stage

you can use pythagorean theorem to calculate half of the base of the stage

then multiply by 2 to get the entire base

and thus you have one of the sides of the rectangle

what

<@&268886789983436800>

[subtle saffron]

Ohh lmao yeah y tf was I so confused 😭

Thanks

[pallid saffron]

no problem

[subtle saffron]

Calm down little kitten

.close

[safe radish]

Channel closed

Closed by @subtle saffron

Use .reopen if this was a mistake.

[pallid saffron]

he seems to have been banned

[subtle saffron]

lol

.reopen

[safe radish]

✅

[subtle saffron]

I've got one more question

[patent kindle]

why

why is this inverted

[subtle saffron]

Idk probably because of camara angle 😅

[edgy cloud]

,purge 20 --from 968209884745195530

[frigid spruce]

is it because that guy left?

[subtle saffron]

He's not here

Bro deleted the messages😭

[edgy cloud]

No, but I hoped I could get the cleanup thing to work anyway...

[subtle saffron]

Oh

[edgy cloud]

I'll just whack them manually. Sorry for the interruption.

[subtle saffron]

.close

[safe radish]

Channel closed

Closed by @subtle saffron

Use .reopen if this was a mistake.

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[modern nymph]

Is that correct?

[thin bridge]

yes

[hearty egret]

yep

[modern nymph]

I thought it was 1/x * derivative of the function

so I thought it was 2/x

Is that if the squared was on the x

only

so if it was ln(x^2) it would be 2/x?

[safe radish]

@modern nymph Has your question been resolved?

Channel closed

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[modern nymph]

How could I integrate sec^2 x tan x

[modern nymph]

I know differentiating sec x goes to secxtanx

which is close to sec^2 x tan x

would I have to integrate by parts to do it?

I also know tan differentiates into sec^2 x

[thin bridge]

knowing the derivitive of sec, consider
sec^2(x) tan(x) =
sec(x) * sec(x)tan(x)

by parts not needed

I also know tan differentiates into sec^2 x
would be the other way to approach it

consider subs like u=tan(x) or u=sec(x)

[modern nymph]

hmm ok

by using the derivative of sec I get integral of sec(x) * sec

but I don't get how substituting u in would help?

using u anywhere would mean the derivative of sec and tan is not possible

[thin bridge]

what do you have after substituting?

[modern nymph]

because it would be u^2*tan(x)

[thin bridge]

knowing the derivitive of sec, consider
sec^2(x) tan(x) =
sec(x) * sec(x)tan(x)

[modern nymph]

integral of u^2 tanx

[thin bridge]

u = sec(x)
what's du

[modern nymph]

oh I see thank you

I'll try it now on paper

I got sec^2 x /2 + c

which is what the solution got thank you for the help

.close

[safe radish]

Channel closed

Closed by @modern nymph

Use .reopen if this was a mistake.

[safe radish]

Available help channel!

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[upper ginkgo]

If z = ln(x-y) + tan(x+y), show that zxx and zyy how does this work?

[potent seal]

zxx and zyy?

[raven heart]

"show that zxx and zyy", that's not a statement

do you have to compute them or to show something about them ?

@upper ginkgo

[upper ginkgo]

wait hold on

[potent seal]

It's off topic but when and how is it decided when they give higher roles?

[upper ginkgo]

kinda like this

[fleet condor]

what's the rest of the question!

[upper ginkgo]

i dont know honest but thats basically it 😅

[hard crest]

is there no more to that question at all??

[raven heart]

you can self-select the Helpers role in id:customize
as for Helpful (green color), it's a question of activity in help channels mostly, the exact formula isn't known apart from the guy who makes the bot regulating that

[upper ginkgo]

yeah...

i mean look at these questions bruh istg the teacher wants us to fail XD

[fleet condor]

probably just means find z_{xx} be z_{yy} then

[raven heart]

so do you know partial derivatives ? @upper ginkgo

[upper ginkgo]

a little bit. still watching youtube lessons about it

[raven heart]

that teacher doesn't give a crap it seems

or maybe you're just looking at the questions ahead of time ?

[upper ginkgo]

true...

[raven heart]

I mean I'll let you finish to watch what you're watching

[upper ginkgo]

nah bro my brain just fried after the teacher discuses the whole module which consists of 7 lessons...

[raven heart]

and if you have questions about the videos, we can look at it

[safe radish]

@upper ginkgo Has your question been resolved?

[safe radish]

Channel closed

Closed due to timeout

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Available help channel!

Send your question here to claim the channel.

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

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

[dusky harbor]

I am going to cry.

[dusky harbor]

Why are these not equivalent to each other?

$I=\int^{3}_{0} e^{-0.3t}\cdot \cos(3t) dt$

[flat frigate]

HqppyFeet

[dusky harbor]

btw^

[main mural]

so the only thing that changed is the fact that you moved -1/50 I to the other side right?

[dusky harbor]

On the lower equation, left side = 0.102538, while right side equals 0.203066, which is the correct answer to I

yes

[main mural]

the first one says $I \implies$ something, i assume though it is an equality right?

[flat frigate]

artemetra

[dusky harbor]

yesyes

they are equal

[main mural]

,calc 1 + 1/50

[flat frigate]

Result:

1.02

[main mural]

[dusky harbor]

The fact that moving 1/50 * I to the left, then the entire thing not being equal confuses the heck out of me

[main mural]

left side as in I(1+1/50) or just I

[dusky harbor]

I have a deadline in 3 hours, and the math gods are trolling the f* out of me

Well it was I = lalala, yes? then when adding 1/50 I on both sides, you are left with I + I*1/50 on the left side

[main mural]

okay okay i see

[dusky harbor]

so I factored out I off of I+I*1/50 and It should leave me with I(1+1/50)

BUT MATH DOESNT WORK

i love math but what the fck

[main mural]

how were you checking the answers

because maybe i'm also blind but i do not see the issue

also sin(9) is radians or degrees?

[dusky harbor]

Radians

[main mural]

,w 2/3 sin(9 rad)*e^(-0.9) - 1/15 * cos(9 rad) * e^{-0.9} + 1/15

[flat frigate]

Results provided by WolframAlpha

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

Requested by arte_m_etra

[main mural]

omg i have exactly the same one

lol

[dusky harbor]

xD

[main mural]

,w integral 0 to 3 e^(-0.3t)*cos(3t) dt

[flat frigate]

Results provided by WolframAlpha

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

Requested by arte_m_etra

[main mural]

are you sure the first line is correct

like

[dusky harbor]

Can I tag helpers and brute force the issue lol

[main mural]

yes

[dusky harbor]

wait a minute

waitwait

[main mural]

let him cook 🧑‍🍳

[dusky harbor]

math is so s***defwu9eoiewronfe

<@&286206848099549185> EVERYONE BRUTE FORCE, PLEASE HELP ME AND BEAT THE MATH GODS ON THIS

I DONT GET IT

I WANNA CRY

I HAVE DEADLINE IN 3 HOURS

THIS STUPID ISSUE IS HALTINGG

[main mural]

how are you calculating the first one?

[dusky harbor]

using radians, $I=\int^{3}_{0} e^{-0.3t}\cdot \cos(3t) dt$

[flat frigate]

HqppyFeet

[dusky harbor]

which is the answer shown on GeoGebra above; Net Area

[main mural]

isn't it this

[dusky harbor]

wait a minute

[main mural]

the geogebra one is different from this one

you have 2e^-0.3t

[dusky harbor]

I have a 2

I HAVE A 2

SHIT

[main mural]

yep

🫡

[dusky harbor]

no wait I'm confused.

I'm getting 0.205076

updated

im still wanting to cry here

[main mural]

where?

[main mural]

^

[dusky harbor]

These two are not equal to each other.

[dusky harbor]

I'm multiplying that by 2, then multiplying this by the 1+1/50

[main mural]

well why are you multiplying by 2

you are probably either undermultiplying or overmultiplying the 1/50 thingy by 2

[dusky harbor]

Because I am actually supposed to work with the 2 here, which was something I completely forgot while I opened this thread lol

and it was incorporated into the right hand side of the equation.. with the the 2/3 sin(9)*e^(-0.9) and the rest

ooh I see

I'll work before I mention it

oh im so stupid, found the issue.

.close

[safe radish]

Channel closed

Closed by @dusky harbor

Use .reopen if this was a mistake.

[dusky harbor]

thank you btw ❤️

[safe radish]

Available help channel!

Send your question here to claim the channel.

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

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

[manic heart]

how do i do d)

[upper mulch]

$(a+b)(c+d)=ac+ad+bc+bd$

[flat frigate]

Good

[upper mulch]

You could seach up for binomial formulas.

[manic heart]

is it different formulas for each question

or can i stick with one formula

[mortal sandal]

Same formula

Its distributing really

$(a-3)(2a-5) = a(2a-5) - 3(2a-5)$