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[lucid wadi]

Hi

[lucid wadi]

so we're doing L hopitals rule

how do I plug in infinity?

to evaluate this?

[bitter vault]

Use L'Hopital's rule. Just plugging in infinity gives you infinity/infinity, which is an indeterminate form. So apply L'Hopital's

[lucid wadi]

we're gonna keep getting e^x cause it's derivative is always that, wouldn't the answer always remain infinity/infinity

[bitter vault]

No. Actually put pen to paper and try it.

[lucid wadi]

I did

i got 2+e^x over 2+e^x

and if we plug in infinity to that

still infinity over infinity

[bitter vault]

That's 1 then. So the limit is 1

[bitter vault]

Maybe simplify a little before plugging in

[lucid wadi]

sorry, so did you simplify that to 1 and then lim as x approaches infinity of 1 is just 1

[bitter vault]

yes

[lucid wadi]

alright thank you

have a good day

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[next pulsar]

can a homeomorphism exist between a connected and disconnected space?

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[last ether]

This is from an online review homework. I don't know where to start.

[lament glen]

write the differential equation, solve for constant using t = 0 part, then solve for k using t = 2 part

[lone heart]

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[last ether]

Diffeeential equation for what

I'm assuming it's gonna be something like

P(20-P)

Oh wait

Hold on

Do I just use the equation $\frac{k}{M}P(M-P)$

[ocean seal]

Umbraleviathan

[lament glen]

the rate at which a chemical element decays is proportional to the amount of the element remaining

you can write this part as a differential equation

[last ether]

Yeah that confuses me

[lament glen]

let's say there is a function M(t) that gives us how much of the element is remaining

then dM/dt is the rate it decays at

and this rate is proportional to M itself

[last ether]

Oh that proportion

Yeah I'm starting to feel like I should know this lol

[last ether]

So this

Which is dP/dt where P(t) is how much is remaining

[lament glen]

what is M there?

[last ether]

Carrying capacity

[lament glen]

anyways you're overcomplicating things

I think the question just wants you to dP/dt = kP

[last ether]

Which would mean $\ln{|P|} = kt + C$, and I can use (2, 5) to find C, right?

[ocean seal]

Umbraleviathan

[lament glen]

you can also find P as $Ce^{kt}$

[ocean seal]

Doggo

[last ether]

Yeah I just realized that

I just remembered that lol I was writing that down

So

$20e^{2k} = 5$

[ocean seal]

Umbraleviathan

[lament glen]

yeah

[last ether]

Which would make sense now that I should've remembered the logistic growth model

Aight thanks

[lament glen]

np

[last ether]

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[sonic bay]

I dont understand how the degree is 7

[peak summit]

There is a typo, it's actually b^4

[sonic bay]

oh

but how would the degree be 7?

[peak summit]

3+4=7

[sonic bay]

why would it disregard 5a^2 and 2b^2?

[buoyant kayak]

it's just finding the degree of each term

5a^2b and 2b^2 are different terms

[peak summit]

Degree is the highest power in any term

[sonic bay]

it doesnt define to find the degree of the a term

so i dont understand

ohhh

[sonic bay]

now i do

[peak summit]

Great

I'm not good at defining stuff

[sonic bay]

oh i dont

[peak summit]

Next time i shall copy paste

[peak summit]

Lol

[sonic bay]

a and b terms are different

[peak summit]

Yes they're

[sonic bay]

so why would they add

[peak summit]

But to calculate the power in a term, you gotta add all the individual powers of variables

[rotund plank]

Because the degree of a term is the total ‘power’ of all variables combined

[peak summit]

If asked why, it's a rule

[sonic bay]

but why arent 5a^2 be included

[peak summit]

Because it's a separate term

[sonic bay]

just like a and b are different terms

so i dont understand

[peak summit]

You don't know what term is

Uhh I'm so bad at putting words

May I redirect you to a yt vid?

[sonic bay]

yes you may

[peak summit]

That should solve your problem https://youtu.be/ffLLmV4mZwU

[sonic bay]

thanks

[peak summit]

Np

[sonic bay]

wait

i think i understand

so

3 + 4 + 2 + 1 - 1 - 2 = 7?

all the exponents combined is the degree?

[sonic bay]

^

thanks for the help

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[median mason]

Anyone who had experience on taking continuum mechanics? Anyone who can give some hints such as helping solving the problem would be perfect

[median mason]

Appreciate it

[tacit arch]

there's a physics server in #old-network

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[clear badge]

Hey, I have a quick stats question

[clear badge]

Can I normally distribute any data set, or does it have to be a data set which is already normally distributed

Like if I just take the mean and st dev of any data set, can't I put it on a bell curve?

[tacit arch]

define "can't"

[placid zinc]

So the normal distribution is special because of the central limit theorem. Take the sum of a ton of random variables, the mean will be normally distributed

But in general, you can't expect any random data set to follow a normal distribution. Fitting it to one may be a poor fit.

[clear badge]

So I can fit a relatively normally distributed data set on a bell curve using the central limit theorem?

[tacit arch]

maybe you should read the conditions of CLT

https://www.youtube.com/watch?v=4YLtvNeRIrg

[clear badge]

Will do

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[violet lichen]

Find the equation of the curve $\vec{r}=\vec{r(s)}$ with torsion $\tau =0$ and curvature $K=\frac{1}{as+b}$ where $a>0, b\in \mathbb{R}$, and $s>0$ is the arclength parameter.

[ocean seal]

dudi

[proper tangle]

can you remind us the formula for torsion and curvature?

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[violet lichen]

$K=\frac{|r'×r''|}{|r'|^3}$
$\tau=\frac{[r',r'',r''']}{r''^2}$
In arclength parameter, it is
$K=|r''|$
$\tau=\frac{[r',r'',r''']}{r''^2}$

[ocean seal]

dudi

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[median mason]

this is not physics field, its in mechanical and mathematical field

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[civic abyss]

Could someone assist me with this problem?

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[buoyant kayak]

"select one"?

[civic abyss]

My bad

[woeful pulsar]

some sort of chain rule might help

or implicit differentiation (differentiate by t)

[buoyant kayak]

remember that $\dv{y}{x}=\frac{\dv{y}{t}}{\dv{x}{t}}$

[ocean seal]

a disappointing son

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[woeful wasp]

Super quick question

[woeful wasp]

What is another way to write x^2 when it comes to calc 1

is it (x-1)

[tacit arch]

Are you asking if x^2 = x-1 ?

[woeful wasp]

yes but moreso, is x^2 = (x-1)

[tacit arch]

no

[woeful wasp]

Doing Fundamental Theorem of Calc / MVT with Integrals

[tacit arch]

it's not true for almost all real numbers

[tacit arch]

do you have a concrete textbook problem or question about your notes or homework problem

[woeful wasp]

it is homework problem I'll write it out

[tacit arch]

a picture/screenshot is best

[woeful wasp]

"Find the c that satisfies the MVT for Integrals f(x) = x^2 over [0,4]"

What I did is set it up so far like 1/b-a so that is 1/4
and then I wrote it as

1/4 int top(4) bottom(0) x^2

[tacit arch]

did you read the MVT for integrals?

[woeful wasp]

I am not sure what you mean by that so I am gonna say no

[tacit arch]

typically when you're told something in a question, you should understand the thing in the question

in this case MVT for integrals

https://www.youtube.com/watch?v=bLeglo-c5Tw

[woeful wasp]

Oh wow I did not expect my question to be the first example question on that video

Thanks riemann

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[alpine sable]

Hi can anyone help me on some algebra questions?

[silver adder]

[real solar]

depends how difficult the algebra is

[alpine sable]

this is the question,

[real solar]

Well for the first part when it asks if the function is increasing, if you are struggling to find a way to justify this you can ask yourself if the slope is ever positive anywhere on this graph

then the same for decreasing but look for if the slope is negative, and also same for constant but slope would be 0.

be careful with your interval notation with the open circles, its a small mistake that I see people overlook all the time

[alpine sable]

oh i see thank you

[real solar]

im not too sure how much of a help that was, but if you need further explanation I will help

[alpine sable]

yea, I'm just majorily confused with the entire graph itself but thank you

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[warped sluice]

just for clarification

[warped sluice]

is #1 13 and number #2 27

[alpine sable]

Yes

[warped sluice]

ty

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[long scarab]

quick question how do i show directionality in a graph

[long scarab]

specifically a rose

[tacit arch]

an arrow

[long scarab]

ok

.close

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[fiery sand]

How To do dis

i thought about comparing the height of the 2 cones to the surface area of the cones but there are 2 unknowns

[ripe rain]

Yea so? 2 equations 2 unknowns

[fiery sand]

i can only make 1 equation

[ripe rain]

We also have some information in first line

[remote kettle]

its not that hard

[remote kettle]

true

[fiery sand]

it looks easy and ive literally done the question before but cant do it now

[remote kettle]

ohhh

it also happened to me lol

[fiery sand]

can u show some steps i still dont get it

[remote kettle]

hmm

lemme do it in the white board

[ripe rain]

Theres one thing i think ur missing is “Similar”

@fiery sand

Relation between heights is given so can we find relation between radius?

[fiery sand]

ahh

i tried to do it with height and surface area

how woukld u do that exactly

[ripe rain]

Ratios of radius and height will be equal

[fiery sand]

yeah so if the radius and height of the smaller cone is r and h

the radius and height of the larger cone is 2r and 2h?

[ripe rain]

Yes if u take radius and height for small cone to be r and h

[fiery sand]

uh i got the answer but in a different way

[ripe rain]

And note: in (a) u need to find only the Curved surface area and not the values of R and H

[fiery sand]

i did (2h/h)^2 = (A1/A2)

[ripe rain]

You can

Wait but

[fiery sand]

so the ratio of A1:A2 is 4:1 so i divided the 780 in 5 parts and smaller cone should be only 1 part of it

[ripe rain]

Wait no

I guess it’s wrong

What and did u get?

[fiery sand]

156pi

[ripe rain]

I got : ||156||

[fiery sand]

o nvm i got it now

the answer key says 156 pi

wait lemme do it on a paper

[ripe rain]

Hmm

Opps ya correct

I made error

[fiery sand]

yeah

thanks tho

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[alpine sable]

Why can't I solve this?

[drifting hull]

show ac<ad and ad<bd

[alpine sable]

yes

how

[drifting hull]

what do you know about the "<" relation?

[alpine sable]

that one is less than the other

[drifting hull]

but which properties does it have?

[alpine sable]

I'm not sure what you're asking

[drifting hull]

I'm asking about which properties of "<" you can use without proving them. Like "if a>0, b>o, then a+b>0" or "if a>0, b>0 then ab>0" or similar things

[alpine sable]

Yeah this is clear

[drifting hull]

try to write ac<ad in the form of the later property, ie as xy>0

[alpine sable]

0 < a < b, 0 < c < d

ac < bc, bc < bd

because bd > bc
ac < bd

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[visual spade]

Need some help with an inifinite series problem

[visual spade]

How do I simplify this

där is swedish for where

it is in order to check for what x the series is absolutely convergent

what x:es

[alpine sable]

I think it’s convergent for x=0

Lemme check tho

Yeah

@visual spade

This summation is convergent for x=0, since all the terms in the summation then become 0

[visual spade]

that's just one of the answers tho

[alpine sable]

How many have they asked for?

All x such that the series is convergent?

[bitter vault]

Simplify this and take the limit to infinity. It converges when the |ratio| is less than 1

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[visual spade]

the issue is that I'm unsure of how to simplify it

[bitter vault]

What have you tried so far?

[visual spade]

I've tried dividing a_2 with a_1 and a_3 with a_2 and so on

which gives different answers

I just don't really know how to do it with a_n

I know x^n+1/x^n is x

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@visual spade Has your question been resolved?

[bitter vault]

You are already given $a_n.$ Try writing down $a_{n+1}$ and then write the ratio. There will be a lot of cancellation

[ocean seal]

1345631

[visual spade]

working on it now

[visual spade]

limit when n goes to infinity?

[noble sinew]

Yes? I’m sure there is a lim in front of what you posted here

[visual spade]

alright, I'm a bit out of the math brain mode

I've been on vacation and putting this assignment off for a while

.close

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[vocal fulcrum]

Vectors

[vocal fulcrum]

Can I solve it this way

The part I cut out

To find the angle between vAB and vCD
I took out the cross product
Since it came to be 0
Sin theta should be 0
But theta can be 0,pi etc.

How to solve ahead?

<@&286206848099549185>

[barren wren]

Dépends on the exercice, there is no bijection

U should use "proof by exhaustion"
It's like listing each case in ordre to défine général rule

In this case that mean that they are parallel ==> they do not cross (I guess)

That's it, for k real u have vAB = k*vAC

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[vocal fulcrum]

Would be parallel if 180
But the q had asked to prove it collinear
But since Parallel Vectors are collinear I wrote them together

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@vocal fulcrum Has your question been resolved?

[barren wren]

Yeah sure, in order to proof that they are collinear u can just write them with multiplier

Cause they are the base of a 1-d vector Space

So you can wrote them as linear combination

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[hasty gale]

I am doing exam prep, and need some help for this question

[hasty gale]

I thought the gradient would be -1/2, but here they use the negative reciprocal 2

uhh

?

[hasty gale]

Hey I was using this channel, would you mind using another empty channel for your question

[compact vault]

sorry

[hasty gale]

its fine

help 2, 14, 16, 20 are all open so

[hasty gale]

my question is

[hasty gale]

with this

.close

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[gray isle]

what have you tried?

[torpid wraith]

I tried substituting all the x with 2 and then equate the equation to -3

I got stuck

[gray isle]

use the other piece of info

[torpid wraith]

I used it too

I dont what to do next

[gray isle]

what do you currently have

[torpid wraith]

When I used the f(2) i ended with 4A + 2B= -14, the for f(-2) i ended with 4A - 2B= -16

Am i doing it right?

[gray isle]

you have a system of equations
you can solve it to determine the values of A and B

[lone heart]

@torpid wraith Has your question been resolved?

[torpid wraith]

Is this part right?

[gray isle]

yes.

[torpid wraith]

In 4A + 2B= -16 and 4A-2B=-16, if I want to get the value of A i should Isolate the B first right?

[gray isle]

use whatever method you are comfortable with to eliminate B

also your -14 changed to -16 for some reason

[torpid wraith]

Oh mb

I typed it wrong

For the 4A + 2B= -14, the value that I got for B = -14-4A/ 2. Is this right?

[gray isle]

it's a bit tedious,
also missing parentheses

if you use the elimination approach instead of sub
adding the equations eliminates B immediately

[torpid wraith]

(-14-4A)/2

What is the elimination approach

[gray isle]

add the equations you had

[torpid wraith]

So 4A+2B+4A-2B=-16+(-14)

Is this right?

[gray isle]

yes

[torpid wraith]

So A=-15/4

[torpid wraith]

.close

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[golden sequoia]

How can I prove this by contradiction?

[rotund plank]

Suppose we have a smallest positive real number n

How can we prove it’s not actually the smallest one

I.e how can we make the number smaller whilst still being positive

[golden sequoia]

we can divide by a really large number?

[rotund plank]

We could

Doesn’t have to be really large though

But you’re pretty much there

[golden sequoia]

Okay thank you so much

[rotund plank]

Yeah np man

[golden sequoia]

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[harsh belfry]

Would this graph be decreasing?

[pine kettle]

,rotate

[harsh belfry]

Its the derivative of another function

however I believe its increasing

I was told that if its below the y axis

that this is not the case for derivatives

[pine kettle]

recall when the derivative is negative, the slope of the original function is negative

[supple tundra]

so the function is decreasing

[harsh belfry]

ahh ok

[pine kettle]

because the derivative graph is (x, f'(x))

and f'(x) is the slope at point x

[harsh belfry]

ah ok

and if I wanted to determine whether its continous

would I perhaps just scan to the right and left?

it does containa square root

which leads me to believe its not continous

[pine kettle]

just remember what determines if a function is continuous

if you can draw it without your pencil

For a function to be continuous at a point, it must be defined at that point, its limit must exist at the point, and the value of the function at that point must equal the value of the limit at that point.

is there any point can you see where a value does not fit one of these descriptions

[harsh belfry]

I dont think so no

ah okay

so its definitely contious

ty

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[pseudo kraken]

Construct a trapezoid ABCD: α = 75°, │AC│= 4 cm, │BD│= 5 cm, ԑ = 120° (ԑ is the angle between diagonals)

[lone heart]

@pseudo kraken Has your question been resolved?

[pseudo kraken]

Not in a rush but I NEED TO KNOW

[tight locust]

Which angle is supposed to be α

Does it matter?

[pseudo kraken]

At the point A

[pseudo kraken]

<@&286206848099549185>

[tawny condor]

What's... the question?

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[astral grove]

I don't know how I specifically ask this question but is there any way to prove the ambiguous case in trigonometry before you try it yourself?

[supple tundra]

ambiguous case?

[astral grove]

in a side side angle triangle case of trigonometry, there is an ambiguous case where sometimes u don't get a solution and sometimes u do

<@&286206848099549185>

[sleek ferry]

Fish

[astral grove]

wdym

[supple tundra]

Do you mean the sine rule ambiguous case

[astral grove]

yes

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[astral grove]

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[empty forge]

Can anyone help with this? I'm trying to find the series expansion. I do not know how to deal with the square.

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[thorny lantern]

I am having trouble understanding how to create the 2 tables described in this thesis. I find the description difficult to understand. I have included the first table. I believe it is correct. Can you assist me on how to construct TABLE 2?

[thorny lantern]

Columns = ??? Rows = ???

[lone heart]

@thorny lantern Has your question been resolved?

[thorny lantern]

This page came from page 45 of the thesis. The thesis is located here: https://era.library.ualberta.ca/items/455ae570-e851-42e8-bd53-4b2c5e4411a9/view/f8cf03fb-58f0-4f9b-940e-070431b7f0b8/MQ34401.pdf

I am learning about opponent learning.

I think Table 1 might be wrong as well. I am so confused.

[lone heart]

@thorny lantern Has your question been resolved?

[thorny lantern]

<@&286206848099549185>

[fathom mantle]

maybe read the section again

[thorny lantern]

Hi

I have read it 15 times. LOL.

I haven't done Calculus 2 in 30 years. I am an older.

Is Table 1 correct?

[fathom mantle]

there is only one table.

[thorny lantern]

There is? I thought there was 2 tables.

Formula 7.1 and 7.2 = 2 tables ?

[fathom mantle]

no

[thorny lantern]

The table is described as rows = "Game rounds"(0,1,2,3) and columns = "index" (0,1,2+)

Is that correct?

Wait a minute. I'm wrong again.

Is the table actually: rows = Game rounds(0,1,2,3) and columns = Action taken(fold, check/call, bet/raise).

I don't understand the explanation well enough.

There seems to be 3 pieces of information. The Game Rounds, The Actions Taken and the Bets to Call. That's 3 pieces of information.

Help?

<@&286206848099549185>

[thorny lantern]

Anyone home?

[thorny lantern]

<@&286206848099549185>

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@thorny lantern Has your question been resolved?

[thorny lantern]

<@&286206848099549185>

.close

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[lusty kelp]

.close

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[cunning jackal]

how does u go away in the dominator?

i know the correct answer is C but i dont get how the u goes away

[finite flax]

when an image posts sideways, please remove it, reupload it, and do ,rotate

whoops, you're good

[cunning jackal]

never mind i got it thanks tho

[finite flax]

glad I could help 👍

[thorny lantern]

Hi

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[zenith olive]

hii

[thick talon]

each length of the smaller rectangle is being multiplied by 2 right

to get the larger one

so if you have V = l * w * h, then 1432 = 2l * 2w * 2h

[zenith olive]

ye

[thick talon]

so simplifying the 2nd equation, you get 1432 = 8 * l * w * h

[zenith olive]

ye

[thick talon]

and we know l * w * h = V

so 1432 = 8V

[zenith olive]

o

is v 179

[thick talon]

yeah i think so

[zenith olive]

uhhh

i acc had another working out can u help me get around with it lol

[thick talon]

sure lol

[thick talon]

that's not right

[zenith olive]

oh?

[thick talon]

for the top it would have to be 1/8 * x^3

bc you're getting half of each side

(1/2)^3 * x^3

the thing you wrote would only be true if V was half the volume of 1432

[zenith olive]

well i did other questions using that method

and they were correct

[rose hollow]

I need help

[thick talon]

oml

[zenith olive]

💀

[rose hollow]

Its killing my brain cells

[thick talon]

#❓how-to-get-help

[zenith olive]

oop

[rose hollow]

Im bored to read

Should i call the police

To get help

[thick talon]

no that doesn't sound like too great of an idea

[rose hollow]

Hmm

[thick talon]

can u show those problems

[zenith olive]

sure

like this

v = 2160

[thick talon]

how did you set up the proportion

[zenith olive]

ill write it down

[thick talon]

kk

[thick talon]

yeah that works but ur not doing it the exact same way for the other problem

[zenith olive]

so v is 179?

is that the answer

[thick talon]

i think so

[zenith olive]

oh okay

that was right

alr ty

[thick talon]

np

[zenith olive]

.close

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[finite parrot]

x³ - 27/x³ - 9x -9/x = 125

[finite parrot]

whats the next step to find the value of x³ - 27/x³

how do i shift 9x - 9/x

[noble sinew]

Wont have nice closed form solutions

[tight locust]

this is a 6th degree polynomial

[finite parrot]

umm

[tight locust]

not very nice

[noble sinew]

Did you mean litterally find value of x^3-27/x^3, as solving y-9/x-9/x=125 for y?

If not then you likely did something wrong earlier in the question, since the question is for sure not solving it for x

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[dull oak]

how do you do C

[vale wigeon]

it is a little unclear from this problem whether triangles that share at least one vertex are always considered to overlap

[dull oak]

wdym

[vale wigeon]

if two triangles share at least one vertex, does that make them overlapping for the purposes of this problem?

the problem does not say.

[harsh swallow]

like this

do these overlap because they share the same vertex

[dull oak]

no

[vale wigeon]

okay so then what about two triangles that share a side?

do those overlap?

[dull oak]

yeah

[oak perch]

Number of non-overlap=3 times number of choosing 6-gon I think

[dull oak]

oh wait no

[oak perch]

Choose a 6-gon, you have three ways to construct a pair of not overlap triangles

[dull oak]

can u explain this abit more

[oak perch]

Conversely a pair of not overlap triangles form a 6-gon

[dull oak]

wow

[oak perch]

So 3C(12,6) I think

And number of overlap is the answer of b minus this

[dull oak]

damn

[oak perch]

And b is C(12,6)C(6,3)

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[night sigil]

can someone confirm whether or not this is wrong?

[night sigil]

I think the dilation should be log2(e) instead of 1/(log2(e)

or is this wrong?

.close

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[quaint mica]

Help me understand the binomial coefficient

[quaint mica]

For the binomial distribution formula we must find the probability of one sequence of independent events and then multiply it by the binomial coefficients to account for all possible sequence of events- hence using the combination formula

But if The binomial coefficient n choose r tells you how many success-failure sequences, of the set of all possible sequences, will result in exactly r successes. take For instance 10C4. But 10C4 would have all possible combinations which would include combinations without 4 successes.

<@&286206848099549185>

[noble sinew]

"will result in exactly r successes"

so will result in exactly 4 successes

how does it include anything other than that then in your mind?

[quaint mica]

Yes but combinations are lists of four things not ten things

That’s what I’m trying to get at

[noble sinew]

?

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[alpine sable]

Can someone help me

[alpine sable]

Why is a = -1 and b=3/2?

if I complete the square of x
its (x+1)^2
and for y its (y-3/2)^2

Why are the signs flipped

if x = -1

x + 1 = 0

which is what you want

likewise

if y = 3/2

y - 3/2 = 0

I don't understand @alpine sable

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[boreal prawn]

Hi I was wondering how to approach the question "demonstrate how it is possible to calculate (1.2)^5 to 1DP without using a calculator and with minimal working (but working must be evident)"

[boreal prawn]

Thank you!

[gray ingot]

do you know this expansion
$$(1+x)^n = 1 + nx + \frac{n(n-1)}{2!}x^2 ...$$

[ocean seal]

Swas.py

[boreal prawn]

No sorry

I think we are meant to use Pascal's triangle to find the coefficients

[gray ingot]

yep that would work too, this has infact been derived using the binomial theorem

could you try to expand (1+x)^n using (a+b)^n?

I'm assuming you know how to expand (a+b)^n

[boreal prawn]

would you please be able to let me know what that formula, so I can research it further?

Yup! I think I get how to do it, but I'm not sure what constitutes "minimal working" because this method requires quite a bit of working

[gray ingot]

nope it's actually the easiest way to calculate it by hand

(1 + .2)^5 = 1 + .2*5 + 5*4/2(.2)^2 = 1 + 1 + 10*4/100 = 2 + 0.4 = 2.4

[boreal prawn]

oh I see

is .2*5 = 0.2 raised to the power of 5?

[gray ingot]

yes, ** is the same as ^ in python

[boreal prawn]

Ohh ok thank you

Would you be able to explain how you got the term 5^4/2(0.2)^2

oh no nevermind! So sorry. I completely understand now. Thank you for all your help!

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[sudden flame]

$how do i go about evaluating:\
\int_{}3(x²+3x)^{-2}(x+1) dx$

[ocean seal]

aetherclouds

[sudden flame]

oh my

i don't know how to turn the 2nd part into (2x + 3) or if that's the path to take

$(2x+3)^{-1}$ actually

[ocean seal]

aetherclouds

[vale wigeon]

$\int \frac{3(x+1)}{(x^2+3x)^2} \dd{x}$?

[ocean seal]

Ann

[sudden flame]

yeah!

is there some crazy rule you can apply to that

[sudden flame]

@hybrid hearth helped me out with this but i don't see the whole picture

[last ether]

Yeah use u-sub

@sudden flame you know what that is right

[sudden flame]

no sjdkfjwixgk

[last ether]

https://youtu.be/sdYdnpYn-1o

[vale wigeon]

i would try pulling some partial fraction shit first

denom factors nicely

[last ether]

It's gonneb easier if you just use u-sub

$3\int \frac{(x+1)}{(x^2+3x)^2} \dd{x}$?

And then it should be more visible

Well actually

I guess you're gonna have to find x in terms of u

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[sudden flame]

sorry guys I think this is beyond what i know so I'll research on it later

i appreciate all the comments tho!! thank you

.close

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[lone heart]

@alpine sable Has your question been resolved?

[tall holly]

Can u show the work you used to solve it

The equation seems correct enough

[lone heart]

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[autumn night]

Could someone help me with this question, I'm familiar with the newtons method but not sure how to approx. the global maximum using it

[noble sinew]

Use it on f’

Since Newtons is for finding roots

And root of derivative is critical point

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[autumn night]

oh okay thanks, so i would first take the derivitive of the function, then apply newtons method?

[noble sinew]

Si

[autumn night]

thankss

[autumn night]

ope forgot to ask

how do i use the interval in this case

[noble sinew]

Wdym? Its just using the method which you said you understood

[autumn night]

i mean the interval of (0, pi/2)

im not sure wherethat would come in

i see the reasoning of the solution

lemme keep trying though

wait im dumb

dont worry about that xD

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[alpine sable]

is this incorrect

or am i smoking some

OH

nevermind it says natural

smh

.close

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[cyan saffron]

isn't there supposed to be 0 as well?

[alpine sable]

.reopen

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[alpine sable]

@cyan saffronI think this book defines N without 0

But yeah my solution was {0 < x^3 : x in Z}

I'm so confused

different problem

A = {... -7, -4, -1, 2, 5, 8, ... }

This holds for both K = {3x - 1 : x in Z} and J = {3x + 2 : x in Z} ? How am I supposed to know

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@alpine sable Has your question been resolved?

[alpine sable]

no

<@&286206848099549185>

[ocean seal]

Edwin25

Edwin25

Edwin25

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[alpine sable]

if the perimeter of a square is 8cm, what length of its diagonal

[alpine sable]

Help ASAP !!!

Perimeter = 4 * Area

Diagonal = root2*area

You can write those both algebraically and solve them

And would that be ???

Can't just give you the answer

8=4a

Oh!

2

Yes :)

Now you know the area

Diagonal = root2 * Area

?

So

4?

Square root of 2

Multiplied by the area

[alpine sable]

16?

Is that even the same question?

No that’s the next one

I just wanted to have the image uploaded

Since the internet here is bad

Put into your calculator root 2 * 2

So

I’m sorry but this isn’t what I learned

I think its just an easier way of doing it

$$\sqrt{2}*2$$

[ocean seal]

Glitch

[alpine sable]

Wouldn’t that be 2?

OH

2.8

Yeah, root2 squared would be 2

2.8

So it’s 2.8?

2.82843cm

Alright!

Can we do the next one?

[alpine sable]

Here

@alpine sable

!leave

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[unborn lantern]

Does anyone know how to determine? I understand there are various ways like mean etc.

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[fallen musk]

Hi, I have this question from one of my homework assignments, but we just started the lesson and I don’t understand very well.

Find the values of a so that the ordered pairs (a;-2) , (-1;a) , (a;a) will be solution to the equation : 3x-2y+1=0

I didn’t send a picture since my series is in French, if you could elaborate on how you did it well it would be nice, thank u

[tight locust]

Plug those points into x and y

See what happens

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.reopen

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[fallen musk]

F i went afk sorry, yeah I did that and it was correct, thanks man

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[alpine sable]

yo

[alpine sable]

https://cdn.discordapp.com/attachments/963825410741768272/966387856358666280/unknown.png

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[real solar]

i would try to combine the left using log properties and exponentiate

so ln(x(x+1)) = ln(2)

then x(x+1) = 2

[alpine sable]

wdym exponentiate

[tall hearth]

also x(x + 1) > 0, if you're only dealing with real log values

[real solar]

just put in an e to both sides to get rid of ln

[karmic rapids]

there are no complex solutions

[alpine sable]

gotcha ill use this to start

[gray ingot]

Then you just need to solve a quadratic

[alpine sable]

sir yes sir

thanks

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[violet musk]

Helppppp

[violet musk]

Fam this might be a special question yeah

But e^y differentiates to e^y dy/dx

Am I right?

[karmic rapids]

no

[violet musk]

Huhhhhh

What is it then

[karmic rapids]

e^y dy

[violet musk]

Nah fam you sure

So d/dx (e^y)

Is what ?

[karmic rapids]

0

[violet musk]

Stop the cap

[karmic rapids]

what

e^y is a constant there

,w d/dx e^y

[ocean seal]

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Requested by illuminator3#0001

[violet musk]

Bruh

The mark scheme says it becomes e^y dy/dx

It’s implicit differentiation or smt

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@violet musk Has your question been resolved?

[violet musk]

Nah fam

[torn forge]

I guess you’re right

since y is a function of x

so just e^y dy/dx

[violet musk]

Ahhh calm fam thanks

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[wet spindle]

4 is what percent of 16

[wet spindle]

so 16 is the whole, 4 is the part

4/16 = 1/4 = 25%

[last tangle]

yeah

[wet spindle]

that's pretty straightforward

the same as 13/20 = 0.65 = 65%

what about where 150 is the whole and 700 is the part

[last tangle]

thats how percentages are defined

[wet spindle]

so 700/150

[last tangle]

thats about 4.66666.....

so 466.6666....%

[wet spindle]

ohhh

I counted it wrong rip

alright yeah, it's the same

pretty straightforward

okay thanks

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[wet spindle]

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[wet spindle]

also for 13/20 and 4/16 you can make the denominator 100 pretty easily

for 13/20 just multiply it by 5 and for 4/16 or 1/4 just multiply it by 25

[last tangle]

what's your question

[wet spindle]

nvm I got it by writing it out

70/15 times 6,66666666 will get you 466/100

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[wet spindle]

for something like 111/300 where you can't simplify it

you can't make the denominator 100 where you can easily tell what the percentage is

[last tangle]

yes

its not easy to determine the percentage any other way either

[wet spindle]

hmmm

[last tangle]

its 111/3 %

[vale wigeon]

111/300 = 37/100

bad example there

[wet spindle]

hmm I did have a gcf

[vale wigeon]

better off with 121/300 which indeed cannot be reduced

[wet spindle]

alright

where's this formula from?

I don't get the intuition

[vale wigeon]

this is the definition of percentage...

are you confused why the number is 100 and not 42069?

[wet spindle]

no

why is the equation like that

[vale wigeon]

percentages are parts out of a hundred...

there is not much else to it

[placid zinc]

It sounds a bit like you're having trouble using the equation. Have an example you're struggling with?

[wet spindle]

I don't have a problem with it at all

[alpine sable]

Huh lmao

[placid zinc]

You might be trying to solve this problem:
"they took the word 'percentage' and found this equation with it, how did they do that?"

But that's not really how it is. It's more like:
"We have this useful equation that helps us rationalize things. I guess we need a word for it. How about 'percentage'?"

[wet spindle]

no it's not that

I think I need more time thinking what part/whole means lol

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[hybrid harness]

if I have this

[hybrid harness]

how do i find the area of this

so im first going to integrate the curve from 0 to 1

then subtract this area from it

[hybrid harness]

but how do I find this area

[karmic rapids]

just do

red from (intersection of red and blue) to (intersection of red and purple) - blue from (intersection of red and blue) to (intersection of red and purple)

[hybrid harness]

oh yeah i could do that too

thanks

[hybrid harness]

but if I had to find the area for this portion, how would i do that?

[karmic rapids]

piecewise

[undone hinge]

is this area 5/24?

[karmic rapids]

don't spoonfeed ffs

[hybrid harness]

idk I dont have the answer key

but ill do it and check

[undone hinge]

wdym

[karmic rapids]

spoonfeeding IS NOT helping!!!

[undone hinge]

i tried to solve it myself i dont know if its correct bruh

[hybrid harness]

yeah im supposed to show the working too so i cant really do anything with the answer

[undone hinge]

yea illuminator overreacted

[karmic rapids]

go open your own help channel then

[undone hinge]

are you going to help me there?

🥺

[hybrid harness]

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[nimble field]

I have that An = Sn + 80001

Q = 10

An = 10^(n-1) x 9

Sn = 10^(n) - 1

[nimble field]

Need to find n

[plucky lynx]

We have to the equation 10^(n-1) * 9 = 10^n + 8000. So
10^(n-1) = 10^n / 9 + 8000/9 thus
10^(n-1) - 10^n / 9 = 8000/9.
(10^n / 10) - (10^n / 9) = 8000/9.

You can now factor 10^n.

@nimble field

[nimble field]

I’m here xd

Trying to understand

[plucky lynx]

10^n / 10 = 10^(n-1).

[nimble field]

Yup

Ok thx I’ll try it on notebook

[plucky lynx]

np, remember to close channel.

[nimble field]

Ye I’ll do when I finish xd

Wait how u do it after that

10^n /10 - 10^n /9 = 80000/9

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@nimble field Has your question been resolved?

[nimble field]

@plucky lynx can u explain last thingy pls xd ?

[plucky lynx]

Sure.

Still there?

@nimble field

[nimble field]

Yup

[plucky lynx]

What do you want me to explain?

[nimble field]

How u factor this ?

[plucky lynx]

By factoring 10^n. 10^n / 9 - 10^n/9 = 10^n * (1/10 - 1/9).

[plucky lynx]

Do you know about logs?

[nimble field]

Ye

[plucky lynx]

We have 10^n * (1/10 - 1/9) = 8000/9, what do you think we should do?

[nimble field]

Oh k I got it now

1/10 -1/9 = -1/90 x 10^n = 80000/9 ?

Then I multiply by 9 so it’s -1 x 10^n /10 which is 10^n-1

= 80000

Then I do log ?

With calculator I do log 80000 / log 10 ?

By that I get 4.903 = n-1

5.903 = n