help-0

[fringe sleet]

multiply first one by x^2 in both top and bottom

then both parts have x^2 in their denominator

so they can just be added on top as a fraction

[dense fiber]

huh

can u show it being done visual

[fringe sleet]

$3my^2-\frac{4m^2y^2}{x^2}=\frac{3mx^2y^2}{x^2}-\frac{4m^2y^2}{x^2}=\frac{3mx^2y^2-4m^2y^2}{x^2}$

[ocean seal]

Duh Hello

[fringe sleet]

either way both answers are right

[dense fiber]

mk

so on that one

u just cancel

on the problem we just did

and do exponets neg or pos

whichever as stated

[fringe sleet]

yeah

while remembering these 3 incredibly important properties

[dense fiber]

mk

are u busy

or do u got time

[fringe sleet]

i can help a bit more if ud like

[dense fiber]

mk thanks

so on 18 here would u apply the same rules

[fringe sleet]

i dont know what its asking for

need to see the text explaining the problem

[dense fiber]

it legit just says

add

add:

and 18 being one of the 2 probs

[fringe sleet]

ill assume it wants you do have it as a singular fractions then

so yes here you are looking for the least common multiple of the denominator

[dense fiber]

mk

[fringe sleet]

so what is the least common multiple of a, b and 3?

[dense fiber]

uh

1

[fringe sleet]

uhh, thats not what least common multiple means

[dense fiber]

mb

3

idk

[fringe sleet]

it is just the product of all 3

[dense fiber]

oh wait

3ab

mb

mb

[fringe sleet]

yep, so what do you need to do to the first one to get the denominator to be 3ab?

[dense fiber]

uhm

[fringe sleet]

you want a to be 3ab

what do you have to multiply a by to get 3ab?

[dense fiber]

b

[fringe sleet]

if you multiply a by b what do you get?

[dense fiber]

wait wdym

[fringe sleet]

you want all 3 denominators to be the least common multiple, the one we found to be 3ab

and the first denominator is a

so what do you need to do with a to make it 3ab?

[dense fiber]

uhm

3b

[fringe sleet]

yep

[dense fiber]

but why do u just randomly

times the denom

by 3b

[fringe sleet]

well since we are going to multiply the denom by 3b

then you should know that we need to do the same to the top

[dense fiber]

wait so

[fringe sleet]

otherwise it is not the same

[dense fiber]

ok so then its

3a

on the next one

[fringe sleet]

yep

[dense fiber]

and ab on the last one

[fringe sleet]

correct

[dense fiber]

so then

[fringe sleet]

so now once you do that, you will notice the denoms are the same, and now you can simply add the fractions together

[dense fiber]

9b+ 3a+ab/3ab

[fringe sleet]

yeah

[dense fiber]

damn its rlly that easy

bro how do i not know how

[fringe sleet]

happens

once you know how to do it most things get quite easy

[dense fiber]

aye lmk if u need to go

[fringe sleet]

got time for 1 more

[dense fiber]

alr bet

23

ik its the same

but when it asks for exponets

in

like demon

or numerator

what would i do

do i just flip my answer

to make all my exponets

accordingly

[fringe sleet]

yeah

this one you should be able to manage

[dense fiber]

wait so say

mk

[fringe sleet]

feel free to give it a go yourself and just ping me to check your solution

[dense fiber]

ok

dude its so coinfusing when the fraction

is the one

outside

the parenth

[fringe sleet]

$a(b+c)=ab+ac$

[ocean seal]

Duh Hello

[fringe sleet]

its just that

but with a more advanced a, b and c

now if i have them all be fractions, we would have $$\frac{a}{b}\left(\frac{c}{d}+\frac{e}{f}\right)=\frac{a}{b}\frac{c}{d}+\frac{a}{b}\frac{e}{f}$$

[ocean seal]

Duh Hello

[fringe sleet]

notice that its the same thing

just that we have that the variables just happen to be fractions

[dense fiber]

solution i got

[fringe sleet]

you are missing some negative signs in the 2nd fraction

[dense fiber]

oh wait

when u flip

u change

sings

[fringe sleet]

yep

[dense fiber]

correct?

regardless

alr

thats pretty easy

i get the concept of those now

im assuming that was ur last now

[fringe sleet]

yeah think ill call it there

[dense fiber]

alr thanks

rlly helped me there

can i screenshot

befoire u delete

[fringe sleet]

no worries, there are still plenty of others who will help you if you are planning on doing some more maths

[dense fiber]

oh ok

[fringe sleet]

not sure what you mean by me deleting something

the channel will be up, just will be renamed to something different so that others can use it if that is what you are asking about

so you can just search from:"your discord id" and look back at the conversation if needed

[dense fiber]

ok

thNks

thanks

[fringe sleet]

👍

good luck

[dense fiber]

thanks

Yo can i get a new helper on just one last problem its for my test and ill be good from then

[fringe sleet]

.close

[lone heart]

Channel closed

Closed by @fringe sleet

Use .reopen if this was a mistake.

[fringe sleet]

.reopen

[lone heart]

✅

[fringe sleet]

@dense fiber post the question

ur at the top again now so more likely someone will see it

[dense fiber]

ok thanks

20

[lone heart]

@dense fiber Has your question been resolved?

[lone heart]

@dense fiber Has your question been resolved?

[limpid turret]

what's your remaining question(s), @dense fiber?

[dense fiber]

number 20

on the sheet i pur above

put

[limpid turret]

,rotate

[limpid turret]

Looks like you got a good start, dividing it into rectangles.

[dense fiber]

ik top and bottom

is 140

total

i just do t know lateral surface

area

ive tried one by one

but i keep getting wrong

[limpid turret]

you have top and bottom right. btw there's a little trick here to make it ever so slightly easier. Instead of summing all three small rectangles, you could find the area of the 9x10 whole rectangle, then subtract out the 5x4 cut. Same answer, less math.

[limpid turret]

This is the way to do it, so if getting wrong, probably a small error, could you show your work?

[dense fiber]

yeah in a sec sorry im away from my desk

i gotta do somethkng rq

but asp

[limpid turret]

np

[dense fiber]

i will ping u

[limpid turret]

take your time

[dense fiber]

ok thanks

[jade sluice]

are these yellow dots a lattice? would/could they be mapped out with a formula? https://i.imgur.com/ocYNk7V.png

ah i see help-0 is listed as occupied so maybe i''m not meant to ask here even though the instructions showed asking to help-0

i'll try one of the unoccupied rooms!

[dense fiber]

ok im ready

[limpid turret]

Ok

[dense fiber]

so

whats the trick?

[limpid turret]

I asked you to show your work

[dense fiber]

oh mb

500 total i got

@limpid turret

[limpid turret]

What are 300 and 160?

Not sure what the small and big rectangles are

[dense fiber]

big rectangle lateral surface area

for the bigger shape i split

smaller one

is the other

know what i mean

[limpid turret]

I see

[dense fiber]

ye

[limpid turret]

Not sure you got 300 for the big one.

Maybe I'm missing something

[dense fiber]

oh

can u see with the trick what we get

[dense fiber]

<@&286206848099549185> please help

i keep getting 500 and im pretty sure its wrong

[ashen raptor]

Que no ?

[dense fiber]

huh

why u talking in spanish

if someone could just dm or leave me the intrustions on how to do if overnight that would be nice gn

[ashen raptor]

I just asking which question number from. That picture

[lone heart]

@dense fiber Has your question been resolved?

[lone heart]

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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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[spice badger]

Tried 0.6 + 0.4 - 0.24

But want to know if im correct

[lone heart]

@spice badger Has your question been resolved?

[spice badger]

<@&286206848099549185>

[sleek totem]

help

<@&286206848099549185>

[lone heart]

@spice badger Has your question been resolved?

[viral wyvern]

Can somebody help me

[lone heart]

@spice badger Has your question been resolved?

[brittle thorn]

How can I solve this

[lone heart]

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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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[vale beacon]

I'm kind of stuck with this probability question. How do I approach it? (question deleted)

[strange meadow]

bro just consider a probability tree

[vale beacon]

I don't know how that would help me find the probability mass function...?

[sullen bane]

can nayone expain to me what is natural log of constant

[strange meadow]

@sullen bane get your in help channel

own*

[sullen bane]

where

[strange meadow]

yeah

[sullen bane]

ah tq

[strange meadow]

@vale beacon

draw the tree

then add the probabilities

for each value of X

[vale beacon]

Alright. I'll try that.

[alpine sable]

i want to improve my mathematics where should i start

my basics are not cleared

[strange meadow]

@alpine sable #❓how-to-get-help

[rancid dome]

which class are you in?

[lone heart]

@vale beacon Has your question been resolved?

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• Show your work, and if possible, explain where you are stuck.
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[crystal mason]

Let $Z_3$ be a ring over addition modulo 3
what is $Z_3 \times Z_3$

[ocean seal]

Zabbx

[crystal mason]

I have $Z_3={[0],[1],[2]}$

but no idea what that 'times' is supposed to do

[ocean seal]

Zabbx

[wary inlet]

If this is direct product then

[crystal mason]

I belive its supposed to be the kartesian product, so
$Z_3 \times Z_3 = {(0,0),(1,0) etc..}$

[ocean seal]

Zabbx

[wary inlet]

Yeah

I was about to say that

[crystal mason]

i see

.close

[lone heart]

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[crystal mason]

ty

[lone heart]

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[runic kelp]

is this a hemisphere with a hole?

[lone heart]

@runic kelp Has your question been resolved?

[lone heart]

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[willow dawn]

you're supposed to find the length of "DB"
I have found the length of "AC" and "BC". The areal is 10.

[rancid dome]

apply the area of a triangle formula

area = 1/2 x base x height

[willow dawn]

yeah, which is 5x4/2

since the height is C and down, and the Base is "AB"

[rancid dome]

1/2 x BD x AC = 10

with BD as height

and AC as base

[willow dawn]

huh

but how do you know AC is 5?

oh

[rancid dome]

i don't

you told me you know what length AC is

[willow dawn]

yes

ohhh

and the area is the same, so

ahhhhhhhh

[rancid dome]

yes

[willow dawn]

ahh okok

I get it

thank you

[rancid dome]

np

[willow dawn]

.close

[lone heart]

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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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[void agate]

How do I work this out?

[alpine sable]

We know $dm = \rho dV$ right? @void agate

[ocean seal]

♡LexQa♡

[void agate]

I'm in highschool so I've no knowledge of that formula.. could you please answer in terms of density = mass / volume?

[alpine sable]

Oh okay just

$m = \rho \cdot V$

[ocean seal]

♡LexQa♡

[void agate]

Yes got it

[alpine sable]

Okay so

[void agate]

What's next?

[alpine sable]

What's the formula of a cube's volume

[void agate]

x^3

[alpine sable]

Yeah

[keen plinth]

cancelling out the d

[alpine sable]

They just do 😏

[keen plinth]

what's the volume of a box

[void agate]

So here it became 1/2 x^3

Right?

[keen plinth]

ye

[alpine sable]

Hmm

[void agate]

The answer is D btw

8 rho

[alpine sable]

Shouldn't it be

[keen plinth]

wait

i read wrong

it's not

[alpine sable]

[void agate]

ah is this wrong

[keen plinth]

thought it was only one side oops

[void agate]

let me know guys

[keen plinth]

all 3 sides become 1/2 of the original

so your x becomes x/2

[alpine sable]

(A/2)^3

[void agate]

1/2 x * 1/2 x* 1/2x

ah so

the volume is 1/8 x

So now if rho = m / v

And the mass stays constant

The density is the inverse of the volume

[alpine sable]

[void agate]

THAS MY GUESS

Can you guys help me out here?

https://cdn.discordapp.com/attachments/490557019623915520/1049632102859145216/image.png

So the new volume is 1/8 x

[alpine sable]

Shouldn’t it be 8 then?

[void agate]

Could someone mathematically work it out and show me

I'm a bit lost

[alpine sable]

The more compact a cube is the more dense it I’ll become

If it’s 1/8ths then it’ll become times 8

Done ez

[void agate]

AH

THAT MAKES SENSE

[alpine sable]

Check the answer tho

[void agate]

Yeah its 8

[keen plinth]

that's the original

[alpine sable]

Aight hugs

[keen plinth]

now for the new volume

[alpine sable]

Ggs*

[void agate]

Go on snow I would humbly like to see your logic as well

[alpine sable]

Bruh what’s wrong with my autocorrect

[keen plinth]

typing latex on a phone is pain

[alpine sable]

Agree

[void agate]

OH

That is a great algebraic explanation

Thanks so much guys

[keen plinth]

[void agate]

thank you

[alpine sable]

G job

[void agate]

and thank you @alpine sable @alpine sable

now peace out friends

.close

[lone heart]

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[summer crescent]

hi? can someone give me idea what is this all about?

.close

[lone heart]

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[split heath]

Can someone able to help me with question 6 - iii)? I don’t know what to do :/

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@split heath Has your question been resolved?

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[lavish pier]

hello does the yellow formula move the parabola to the right and the blue formula move it to the left or is it the other way around thank you!! (:

[minor needle]

yes it's true

exactly as you said

[lavish pier]

love you so much

please kiss me

.close

[lone heart]

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[wind cloak]

kiss em modus

dont leave them hanging

[unreal idol]

One way to think about it is like this, the x intercept is when x = h. So if h was a positive number, say, 3. Then you'd have y = (x-3)^2. In this case, you see that since h is positive, the intercept will be in the positive x axis. Whereas if you have a negative h, such as -3, you'd have (x - (-3))^2 -> (x+3)^2. Now, since h is negative, the intercept is in the negative axis

[scarlet robin]

hi

[lone heart]

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[lone heart]

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[delicate lake]

I need help

[delicate lake]

9. idk what to do

<@&286206848099549185>

[peak summit]

Kindly get a better picture

[delicate lake]

Ok

[delicate lake]

Sorry about the first one

Can u help me pls

[peak summit]

I'm not sure how to do it. You gotta wait for someone

[delicate lake]

Kdjahahahahsjs

I’m gonna die

I can’t find it online or anything

nsnanansnnkelsman

Jahejsjsksks

rip

[peak summit]

Be patient, someone will be there soon

[delicate lake]

ok I need help with this problem instead

It’s easy

but I need help with it

@peak summit

do u know it sir?

[peak summit]

Unfortunately nope. Also don't call me sir. I'm just a amateur

[delicate lake]

Sorry

[ocean seal]

Mehdi_Moulati

$\vec{u} \cdot \vec{v} = ||\vec{u}|| \cdot ||\vec{v}|| \cdot cos(\vec{u},\vec{v} )$

Mehdi_Moulati

Mehdi_Moulati

[hollow sparrow]

@delicate lake

[delicate lake]

Hi

I got that one

does it simplify to 19.6

?

[hollow sparrow]

,w 38cos(35)

[ocean seal]

Results provided by WolframAlpha

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

Requested by Mehdi_Moulati#1210

[hollow sparrow]

yes

[delicate lake]

can u help me with another one pls

@hollow sparrow

do u know how to do it?

[hollow sparrow]

i guess it's :
$\vec{V} {north}= \vec{V}{pilot} + \vec{V}_{wind}$

[delicate lake]

wait what??

[delicate lake]

how does that work

[ocean seal]

Mehdi_Moulati

[delicate lake]

ok

I understand

but idk how u actually do it

[hollow sparrow]

$V_{north} = 450 mph$

[ocean seal]

Mehdi_Moulati

Mehdi_Moulati

[hollow sparrow]

$V_{pilot}$ is what we looking for

[ocean seal]

Mehdi_Moulati

[delicate lake]

So it’s 430

[hollow sparrow]

no wait

[hollow sparrow]

those are vectors

[delicate lake]

yes

[hollow sparrow]

since the direction must be north

you need to multiply each vector by $\vec{j}$

[ocean seal]

Mehdi_Moulati

[delicate lake]

what’s j ?

[hollow sparrow]

is a vector in Cartesian coordination

[delicate lake]

ok

wait could u walk me through the problem pls

with the specific calues

Values

@hollow sparrow pls bro

I understand how u got the speed tho

wait

Do I have the directional angle and bearing right? @hollow sparrow

[hollow sparrow]

This is how I imagine the problem

[delicate lake]

ok

[hollow sparrow]

i'm not sure if it's true or not

[delicate lake]

wait I think the speed is 470?

right?

[hollow sparrow]

nope because the wind reduce the speed of the pilot

imagine yourself running against the wind

[delicate lake]

bro

the problems asking what speed the pilot should fly at

So if he wants to fly at 450 mph and there’s 20 mile wind he must fly 470

[hollow sparrow]

the pilot wants to go north but the wind is going against him ( south of west )
if I understand the problem

[delicate lake]

bro

do I have the directional angle right or wrong?

[hollow sparrow]

I need to understand the problem first

[lone heart]

@delicate lake Has your question been resolved?

[lone heart]

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[lone heart]

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

[stiff cypress]

Help pls

[lone heart]

Please don't occupy multiple help channels.

[stuck cape]

🤣

[wind cloak]

💀

Integrate $\int_0^{\pi} \sqrt[3]{\tan x}dx$

[ocean seal]

NEONPerseus

[wind cloak]

That should give you the answer

[stuck cape]

[wind cloak]

Just draw a 4 by 6 grid

:/

[boreal verge]

that would be the solution if there were enough desks

[lone heart]

@stiff cypress Has your question been resolved?

[delicate lake]

@hollow sparrow

nevermind

I’d misunderstood the question

you were right

[river copper]

Hi

[delicate lake]

my teacher showed us how to do it

hi babe @river copper

[river copper]

Sorry if I'm wrong channel idk I rlly need some help

[delicate lake]

ok

send me your questions

I will answer

@river copper

[river copper]

Can u pls explain what f'(x) is and how do I get it from f(x)

The topic is remainder and factor theorem

[delicate lake]

ah yes

send me an example problem

I will teach

[lone heart]

@stiff cypress Has your question been resolved?

[hollow sparrow]

@delicate lake open a new channel

[lone heart]

@stiff cypress Has your question been resolved?

[hollow wasp]

hello guys

can someone help me , ı need find zeta distribution applications

[storm oxide]

I need to repeat things to 8th grade term exam

(i have it tomorow)

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[alpine sable]

did u plot it

graph it even

find bounds of ur integral by finding the roots

of the equation

then just use washer method

[late star]

I found the roots do I just sub them in then integrate ?

[alpine sable]

the roots are ur integral bounds

whats the integral u have rn

[late star]

(0,8)?

[alpine sable]

ohh

i thought u were rotating around

the x axis

sorry

ignore the washer method bit

[late star]

Nah it’s all good

[alpine sable]

just do integral from a to b of f(x)

a and b are your roots

[late star]

Ok

This is what I got but it’s still wrong.

I integrated and subbed in my roots (taking them away from each other)

[alpine sable]

,w 8-3x^2=0

i dont think ur roots are 0 and 8?

@late star

[late star]

Ohh shoot ok I’ll get back to u when I’ve figured it out

Thanks anyway ❤️

[alpine sable]

sure id just use quadratic formula

i dont think its a nice factor

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[rocky summit]

I'm wondering if someone can walk me through this generating functions counting question

[rocky summit]

I think I get the basic idea, but once things move beyond the most basic examples, I think my understanding gets a little shaky

How many ways are there to distribute 20 cents to n children and 1 parent if the parent receives either a nickel or a dime and each child can receive any amount?

Firstly

Is this the right initial representation?

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[rocky summit]

Halp?

[rocky summit]

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[limpid garnet]

i need help

[limpid garnet]

could not find the patern

[alpine sable]

what did you compute?

[limpid garnet]

i compute 4(-5)+11 and so on

and for 4 then 4, etc

dont know what the pattern is

[alpine sable]

try and find f(n+1) in terms of f(n-1)

[limpid garnet]

wdym

[alpine sable]

write out f(n+1) in terms of f(n) using the recursion formula

then substitute f(n) in

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[slow wraith]

can anyone help i dont get it

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[potent sinew]

I'm trying to find an expression with x^{0} d[m,n] and alpha for this expression

[potent sinew]

How do I go about it?

x[k+1] = x[k] + a*x[k]

x[k+1] = x[k-1] + a2x[k-1] + a^2 * x[k-1]

[1]
[1, 1]
[1, 2, 1]
[1, 3, 3, 1]

I've got a function that iterates over k times, each times it iterates the x adds to the next variable x

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[dreamy ember]

I need help to determine the equation for this.
The differences don't seem to be the same when I add/minus/multiply/divide. How can I figure out the equation for this exponential table?

I'm not sure if it's P(t) = ab^t
Or a different equation

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[alpine sable]

I'm not sure which method to use

Helppp

[dense fiber]

!help

[lone heart]

Please read #❓how-to-get-help

[lavish forum]

yo whats 2+2

[lone heart]

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[alpine sable]

<@&286206848099549185>

please

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[pastel flame]

ik u have to solve the derivative = to 0 but how do i solve it im kinda dumb

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[small token]

For geometric progressions, does (S_10 / S_5) = r?

[small token]

If not, does (S_10-S_5)/(S_5) = r?

ok, evidently not

.close

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[wise jewel]

how am i supposed to do this?

isnt the answer just (.8)^12?

how am i meant to draw a graph for that

[placid zinc]

That would be the answer if X = 12, yes.

What if X = 11? X = 6?

Probability distribution of X: A graph that graphs the probability for each possible outcome of X.

[wise jewel]

ohhhhhhhhhhhhhhhhh...12 trials. so I just do binompdf for each value x can be?

is there anyway binomcdf can be used here? i heard its for if x is multiple values

or is that only if it was asking x is greater/less than or equal to a certain value

[placid zinc]

Cumulative density function: probability that X is less than or equal to a choice in value

So for example, the CDF evaluated at X = 3 is the probability of 0,1,2 or 3 blue spins.

Your function will find this, or you can manually find that by adding the individual cases together

[wise jewel]

i see, and so that doesnt apply here since we need to find the individual prop. for each attempt rather than combine them all?

[placid zinc]

Really, binompdf() with the correct values is the probability density function.

[wise jewel]

so, i understand how to plug it into a calculator

like for example for x = 0, binompdf (12, .8, 0)

but if I wanted to write it out alternatively

would $_{12}C_0\cdot .8^{12}\cdot .2^0$ work?

[ocean seal]

Kold

[wise jewel]

wait no that cant be right cuz thats .068

im trying to figure out how to put it into the formula

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[wise jewel]

why is cos165 not equal to cos135 + cos 30?

[placid zinc]

Why would it be?

[wise jewel]

sin 105 = sin 60 + sin 45

[placid zinc]

Basically, cos() doesn't distribute over +, like most things don't.

[placid zinc]

Recheck.

[wise jewel]

sin 105 = sin 60 + sin 45 = sin60cos45 + cos60sin45

according to the formula we were given

[placid zinc]

sin(105) = sin(60)cos(45) + cos(60)sin(45)
I completely agree with

[ocean seal]

The following error occured while calculating:
Error: Undefined function sind

[wise jewel]

so then why doesnt cos 165 = cos135cos30 - sin135sin30

[tacit arch]

Cosine has its own sum identity

https://www.cuemath.com/trigonometry/sum-and-difference-identities/

[wise jewel]

which our teacher told us is cos(x+y) = cosxcosy - sinxsiny

[tacit arch]

Oof dark mode

Anyway just click the link for the formulas

[wise jewel]

but i did the formula

[wise jewel]

.

[placid zinc]

It does? Why do you think it doesn't?

Make sure your calculator is in degrees

[wise jewel]

omfg

im stupid

thats why 🤦‍♂️

so sorry

[placid zinc]

lol it happens to the best of us

[placid zinc]

Did you figure this out btw?

[wise jewel]

i did i just switched where the 0 with the .8 and the 12 with the .2 lol ty tho

[stuck cape]

*dies with heart attack

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[wraith sun]

How it's calculate?🥲

Probably by separation of variables?

anyone please

.close

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[brave frigate]

hi i need help with a numerical anaylisis question i am currently reviewing a sample quiz question on conditional numbers and one of the steps require you to do b -ax which has an equation i don;t quite understand

[brave frigate]

it shows right here [5 4] - [2 1 1 2] [2.0002 1.0001]

im not sure if its adittion or multiplication

and my goal is understanding and being able to do this by my self obviously

<@&286206848099549185>

[lone heart]

@brave frigate Has your question been resolved?

[brave frigate]

i have a different question i figured out the top part is related to this equation. i solve the first part which is x(1) but when i do second one i get [3.5 and 5] instead of [1/2 and 1] liked shown

Here is my work

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[balmy crane]

How do I calculate the indefinite Integral of cos(x)/(sin(x)+1)?

[alpine sable]

U substitution is Ur bestie

[echo socket]

Substitute for sinx + 1

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[brave frigate]

.reopen

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[balmy crane]

.reopen

[lone heart]

✅

[balmy crane]

would this look fine? doing this for the first time and just saw an example on the internet, and tried to do it similarly

[worn fox]

,w int cosx/(sinx+1)

[ocean seal]

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[little drum]

nicely done. Ah, usually you'd consider the integral of 1/z dz = ln |z| + C, where there's an absolute sign on 'z' but since sin x + 1 ≥ 0, you're fine

also, you should probably add the "+ C" to ln (z) as well.

[balmy crane]

ah kk ty!

.close

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[chilly raven]

If two sets A and B have n elements in common, then show that the sets AxB and BxA will have 2^n elements in common.

[chilly raven]

Please someone send the sol

[alpine sable]

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

and are you sure its 2^n?

[lone heart]

@chilly raven Has your question been resolved?

[chilly raven]

Yeah 2^n

My soln is just a generalized way but not the actual soln

[alpine sable]

if A=B, AxB doesnt even have 2^n elements...

[chilly raven]

Do you know how to solve it

?

[alpine sable]

yes

if A=B has n elements, how many elements does AxB and BxA have in common?

[chilly raven]

Its n2 i know but this question is asked in prev years in university

[alpine sable]

yeah, you can adapt that proof to this question

the answer should be n^2

[chilly raven]

I think you have to solve this ques with sets and relation properties

[alpine sable]

ok

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[alpine sable]

I cannot visualize it. Can I have a rough sketch?

[wooden crag]

do you know how to draw ellipses?

[alpine sable]

yeah i can use ggb anyways

[wooden crag]

ok, in ggb draw the stage as a rectangle whose front left corner is at 0, 0 and put the center of the platform at 9, 7

here's the equation of an ellipse to help you out

[alpine sable]

this fine?

[wooden crag]

that major axis is not 12 units

[alpine sable]

by front edge, do they mean the y axis or x axis?

[wooden crag]

I have no idea, it's pretty ambiguous lol

[alpine sable]

well, if it it not 12, then?

oh

wait no nvm

what will it be?

The wordings always confuse me 😓

extends to within 3 ft of the edge

<@&286206848099549185>

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[paper sage]

hey

[paper sage]

i need help

[wind cloak]

Same 😔

[paper sage]

$y''+6y'+9y=4e^{-x}$

[ocean seal]

Yousssef

[wind cloak]

Differential equation weeeeeeee

[paper sage]

can someone help me with this one please

[paper sage]

do u have any clueee

[wind cloak]

Nope sorry 😓

I'll try

[paper sage]

np

$yh=(Ax+B)\cdot e^{-3x}$

[ocean seal]

Yousssef

[paper sage]

but i dont know how to find my particular solution

please help

$y''+6y'+9y=4e^{-x}$

[ocean seal]

Yousssef

[keen plinth]

undetermined coefficients?

[paper sage]

what u mean

[shut estuary]

could anybody here help me understand how they got $110?

[paper sage]

brother get out

[paper sage]

how do i approach my particular solution

so i tried with sub

$yp=z(x)\cdot e^{-x}$

[ocean seal]

Yousssef

[paper sage]

then i get $y'p=z'\cdot e^{-x}-z\cdot e^{-x}$

[ocean seal]

Yousssef

[paper sage]

i'm on right path?

[keen plinth]

i mean like using the method of undetermined coefficients

[paper sage]

Did I do right then?

[keen plinth]

well i think you'd typically guess y_p = Ce^-x

for constant C

[paper sage]

Oh so I didn’t have to do the Z

I mean the sub

[keen plinth]

?

i mean you can probably proceed like that

just

pain

[paper sage]

So I mean that I shouldn’t wrote z(x)*e^-x

I could just guess C*e^-x

[keen plinth]

yes

[paper sage]

Oh okay then I understand

[inner beacon]

Hello is this channel occupied? I really need some help huhuhu

[paper sage]

So that z is just useful maybe when we have (x+1)*e^-x

Then we can say z=x+1

Right

[keen plinth]

uh

not really sure what you mean there

[paper sage]

$y”+3y’+2y=(x+1) * e^{-3x}$

[ocean seal]

Yousssef

[paper sage]

For example this problem

My particular solution could be written as $yp=z(x) \cdot e^{-3x}$

[ocean seal]

Yousssef

[paper sage]

Then I pursue from there

[keen plinth]

uh

yeah

[paper sage]

Good

[keen plinth]

but then you might guess like

[paper sage]

How would you approach

It

[keen plinth]

(Ax + B) e^-3x or something

i dont quite remember

[paper sage]

Ah okay

I would just break it down by doing the Z thing

[keen plinth]

general z might be a bit overkill

you end up with a big mess

[paper sage]

Yea of course

But there isn’t any general method

[keen plinth]

you really just want something like (Ax + B)

[paper sage]

The problem is that we don’t know what we want

[keen plinth]

well

you have a pretty good idea

if the inhomogeneity is (x+1)e^-3x

then your particular solution isnt gonna be some arbitrary z(x) e^-3x

its only gonna be something like (Ax+B)e^-3x

or maybe (Ax^2 + Bx + C)e^-3x depending on the actual equation

using general z(x) is gonna give you a big mess to calculate

[paper sage]

This is how I did

[keen plinth]

,w x^2 + 3x + 2 = 0

[ocean seal]

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[paper sage]

Yeah I know that but I meant for the particularly solution

[keen plinth]

no i was checking

its probably fine

[lone heart]

@paper sage Has your question been resolved?

[hollow sparrow]

it's correct

[paper sage]

thank you brother

[hollow sparrow]

,w y'' + 3y' + 2y = (x+1)e^(-3x)

[ocean seal]

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[lone heart]

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[paper sage]

$y''+2y'+y=e^x+e^{-x}$

[ocean seal]

Yousssef

[paper sage]

what is my particular solution

kelb

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[misty pivot]

anybody good at dynamics here

[fathom mantle]

dynamics has a lot of subjects. Physics, meteorology ?

[misty pivot]

inertia matrix

im struggling to calculate Ixx, Iyy and Izz

[fathom mantle]

oh man. it has been a while.

I guess you can use your book for reference

[misty pivot]

ill show u answer n maybe u can work backwars

so first part is slender rod about fixed end

then parallel axis theorm

[alpine sable]

Is there someone who speaks swedish?

[lone heart]

@misty pivot Has your question been resolved?

[lone heart]

@misty pivot Has your question been resolved?

[lone heart]

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[mossy talon]

Here is my problem:

[mossy talon]

$$ y = \int_{5}^{x^2} sin(t^6) dt $$

[ocean seal]

Evo

[mossy talon]

I just cant seem to find anything abt this

Its non-elementary and idk what to do for it

Taylor series approx?

[little drum]

Are you supposed to evaluate the integral? or find y' ?

[mossy talon]

Evaluate integral

I found stuff for when t is raised to the 2nd power but nothing to the 6th..

[little drum]

,w integrate sin(t^6) from 5 to x^2

[ocean seal]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by Ansh_#3502

[little drum]

hmmm nothing (⁠ヘ⁠･⁠_⁠･⁠)⁠ヘ⁠┳⁠━⁠┳

[mossy talon]

Ive checked all of them 😔

[worn fox]

This does look so much like a FToC question

Where is this from

[mossy talon]

Someone just sent me it as calc practice

[worn fox]

And what exactly did they say

[little drum]

more like troll practice (⁠ヘ⁠･⁠_⁠･⁠)⁠ヘ⁠┳⁠━⁠┳

[mossy talon]

💀 they just said solve it

And they sent uh

wait

[worn fox]

Then they're messing with you

[little drum]

Lol

[mossy talon]

Idk what that is

But thats what they sent?

[worn fox]

They are messing with you

[mossy talon]

so theres no solution?

💀

[lament glen]

ah I remember the good ol' 1700's when I solved this in kindergarten /s

[worn fox]

Well yes there's a solution it's right there

But they just shoved it into a calculator

[mossy talon]

😔 i just want to understand how the calculator got an answer

None of mine work either

Like wolfram alpha doesnt give anything for me

[worn fox]

Well then devote your life to the study of non elementary integrals

[mossy talon]

💀 guess thats where im headed

[lone heart]

@mossy talon Has your question been resolved?

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[sterile vale]

Hello why is this wrong?

[alpine sable]

You can't just "bring down" The 2 when it is raised to the power of the entire logarithm

[sterile vale]

Oh here it’s ln(n)*ln(n)?

[alpine sable]

I'd assume so yes

[sterile vale]

So what can I do with this equation?

[alpine sable]

Not sure either..

Seems complicated

[sterile vale]

😞

[tacit arch]

$[\log(n)]^2 \neq \log(n^2)$

[ocean seal]

riemann

[tacit arch]

,calc log(10)^2

[ocean seal]

Result:

5.3018981104784

[tacit arch]

,calc log(100)

[ocean seal]

Result:

4.6051701859881

[alpine sable]

Yeah that issue is already settled I think, but that limit sure is fishy

[sterile vale]

Yes but what do I do about this?

[tacit arch]

Fix your mistake and reupload

[lone heart]

@sterile vale Has your question been resolved?

[sterile vale]

I got it actually thank you

.close

[lone heart]

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[tough dove]

Does anyone know how I can get the biggest difference between these two functions?

[worn fox]

Plot |f(x)-g(x)|

[tacit arch]

am i blind or are those two functions the same

[tacit arch]

can you regenerate your plot without changing the function

[tough dove]

no

it's f(t) = 20 x 0,9920^t
and g(t)= 20 x 0,9879^t

Both wheels are having a beginning speed of 20 km/h and I have to find the biggest difference in speed

[alpine sable]

you could subtract them and maximize the new function but riemann probs has smarter way

[tacit arch]

if you know f > g, then you can just maximize f-g

[tacit arch]

JOKES ON YOU, MY IDEA IS THE SAME AS YOURS

[alpine sable]

WOW

[worn fox]

Goteem, riemann never has a smarter way

[tacit arch]

,rotate

[tough dove]

this is what I wrote down

but I copied it from a friend

it's dutch so i guess you won't understand it

[tacit arch]

do you know how to find extrema of functions?

[tough dove]

Yeah in cas

[tacit arch]

yea do that for

[tough dove]

I got this

[tacit arch]

i don't see a derivative anywhere

[tough dove]

i got

it

[tacit arch]

,w max 20 * (124/125)^x - 20(0.9879)^x on [0, 1000]

[ocean seal]

Results provided by WolframAlpha

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Requested by riemann#2529

[tacit arch]

looks right?

[tough dove]

I don't know what you just did

[tacit arch]

100.4 is the time which the max velocity was achieved. not the max delta velocity itself

to get max delta velocity, you plug in t=100.4 to the function f-g

[tough dove]

got it

[tacit arch]

assume it's the same thing as you did in CAS

[tough dove]

yes

thanks