help-10

[teal turret]

Stay off that stuff

It’ll screw u up mentally

I mean idk cold turkey or anything

But still try

Idk

Anyways, gl w ur exams

[next magnet]

been using nic since like freshman year of hs

recently started vyvanse

caffeine i think everyone is addicted to lmao

[teal turret]

[next magnet]

thank you brother same to you as well

appreciate the help

[teal turret]

No problem

Have a good one

[obtuse pebble]

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[sour blade]

I got p=5, howd they get 10?

[sour blade]

Shi nvm

.close

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[worldly trail]

Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines.
y = 5x^2
y = 0
x = 2

[worldly trail]

ive managed to find the volume of the region when revolved around the y axis and x axis but i cant figure out how to get the volume of the region when revolving it around y =20 or x = 2.

<@&286206848099549185>

[obtuse pebble]

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<@&286206848099549185>

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.close

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[reef delta]

can anybody help me with part e of the question, you're meant to turn a 3x3 matrix into a 4x4 but im not sure why or how

[obtuse pebble]

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[snow herald]

when finding the natural paramatrisation of a curve on an interval [a,b], what should I put on the lower bound of the integral? a, 0, t0 ?

[tired shell]

t0 which should usually be 0

[snow herald]

thanks

[obtuse pebble]

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[obtuse pebble]

Please don't occupy multiple help channels.

[wild veldt]

.close

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[old bloom]

so im unsure on this one

i tried making the forces equal and got x = mg/4mlpi^2

but if g is acceleration what then

[bronze nova]

im not that well equipped with the physics here, do u know of any relation between modulus of elasticity and force or acceleration

[obtuse pebble]

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[split pike]

need help with maths for a test, someone able to join a call

.open

[hybrid schooner]

1 lakh is 10 raise to power 6

[obtuse pebble]

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[pale urchin]

Is this correct, cuz im not sure what happened but what I have in my notes is completely wrong.

[hybrid schooner]

,reopen

.reopen

[pale urchin]

.close

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[pale urchin]

.reopen

[obtuse pebble]

✅

[pale urchin]

2cosxsinx = sin2x right?

[gilded estuary]

yes

[pale urchin]

pretty sure you convert that to (1-cos2x)/2 but cant remember after that

[gilded estuary]

cos x + sin 2x = 0

how'd you get 1-cos 2x / 2

[pale urchin]

power reducing sin2x

thought they needed to be same identities i guess

[unreal musk]

(also what's the aim, to solve that equation, or?)

[gilded estuary]

what's the question

[gilded estuary]

like do you have to find value of x?

[unreal musk]

(well, I will say that you probably won't want to use those identities and that the question is much simpler to solve)

[pale urchin]

?

[gilded estuary]

You're trying to solve for x, yes?

[pale urchin]

Yeah

Im not finding anything in my notes thats making this clearer

[gilded estuary]

why not just substitute the answers and see which ones match

[pale urchin]

Cuz Id like to know how to actually do it

[unreal musk]

(also the suggestion is that there's another way you can write this, a quite obvious way to...)

[gilded estuary]

cos x (1 + 2 sin x) = 0

then solve

im sorry, i didnt realise you were implying that

[pale urchin]

Ok so I keep having this issue in my notes

is 2cosx the same as cos^2(x)

[gilded estuary]

no

[pale urchin]

Still not really sure how I go about solving this though.

[gilded estuary]

equate cos x = 0 and 1 + 2 sin x = 0

then solve for x

[pale urchin]

or wait no how is 2cosxsinx become 1+sin x. My notes show 2sinx + 2cosx = 1

[gilded estuary]

you mean sin^2(x) + cos^2(x) = 1

[pale urchin]

Ok then im still lost from the start then

[gilded estuary]

Let's start over

cos x + 2 cos x sin x = 0

yes?

[pale urchin]

yeah

[gilded estuary]

now we factor out cos x to get cos x (1 + 2 sin x) = 0

[pale urchin]

Im not understanding the factoring i guess

[gilded estuary]

if I had x^2 + x

how would u factor

[pale urchin]

(x*x)+x

[gilded estuary]

x(x+1)

yes?

[pale urchin]

oh yeah

theres no squaring here though?

[gilded estuary]

as in?

[gilded estuary]

ok let's say

[pale urchin]

theres no squares

[gilded estuary]

x + 2xy

x(1+2y)

yes?

[pale urchin]

oh

ok

[gilded estuary]

x = cos x, y = sin x

[pale urchin]

Yeah i gotcha

[gilded estuary]

now if we were to equate x(1+2y) = 0

then either x = 0, or 1 + 2y = 0

[pale urchin]

so pi/2 and 3pi/2

for x

Ok I think I got it now.

[gilded estuary]

1 + 2 sin x = 0
2 sin x = -1
sin x = -1/2
x = -pi/6

[gilded estuary]

whats the domain

[pale urchin]

All real numbers are domains fo sin and cos

-inf < x < inf

but I dont need that do I?

[gilded estuary]

then you have infinite values for x

[pale urchin]

Its within the interval of 0,2pi

[gilded estuary]

so thats the domain

[pale urchin]

0 < x < 2pi

[gilded estuary]

0 <= x < 2pi

square brackets is <=

normal brackets is just <

[pale urchin]

Wasn't paying attention. I do know that lol

[gilded estuary]

oh ok

problem solved?

[pale urchin]

Yeah, answers d since those equal 0

Much appreciated running it through with me.

[gilded estuary]

np

[pale urchin]

.close

[obtuse pebble]

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[hot jacinth]

Hello

[hot jacinth]

Help me solving this please

https://tenor.com/view/amy-gif-6958642489115739715

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[left jetty]

What did i do wrong here?

[molten torrent]

Are they meant to be square roots?

I can't really read your writing sorry

@left jetty

[glass dagger]

I think I understand what kylesea is trying to do

[molten torrent]

Are they square roots though?

[glass dagger]

and I think it deserves some kind of medal for the quirkiest math I've ever seen

[glass dagger]

yes I think so

[molten torrent]

Ah okay

[glass dagger]

It's like.a u=sqrt(a)-sqrt(x) substitution, except you don't change the bounds of integration or turn the dx into du, and instead of evaluating u^3 / 3 they evaluated sqrt(a)-sqrt(u)

so yeah, a few quirks here and there

[molten torrent]

"Quirks" 💀

[glass dagger]

oh and also they're missing a minus sign at the end

[molten torrent]

Yeah there's a lot

[glass dagger]

not that it matters a lot because almost none of it makes any sense anyways

[molten torrent]

It's just flat out wrong ngl

[glass dagger]

I mean I don't wanna be discouraging

and I hope kylesea doesn't take this the wrong way

but I don't think I've ever seen a solution in my life that's both this wrong but also like obvious what they were trying to do

But there is an honest attempt and that's always commendable

[molten torrent]

^^

[glass dagger]

anyway, to get you on the right track, I would recommend expanding out the square of the binomial and then integrating it term by term

A substitution is probably gonna be difficult

[molten torrent]

Also can I get help in channel 49 once you're done here pls @glass dagger 💀

[glass dagger]

ah I was about to go to bed lol

[molten torrent]

Ah okay. It's a fairly straightforward question but all good

[obtuse pebble]

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[river portal]

Hi can someone help with 11B

[marsh geyser]

What did you try?

[river portal]

I got it wrong

It should be 4.5

[balmy mortar]

3rd to 4th line looks dodgy

even if its correct, youre doing like 2 steps at once or something

[river portal]

Do you multiply them together when it’s adding logs?

[balmy mortar]

log a + log b = log ab

[river portal]

That’s what I did

[balmy mortar]

im failing to see how.

[river portal]

I used power rule to move the 1/2 to the end then I multiplied log base 2 of 8 with log base 2 of 8 to get 1/2logbase2 of 64

[balmy mortar]

so youre trying to do 2 things at once

separate it into 2 steps

the error is here.

[marsh geyser]

The left one is incorrect

[river portal]

Is this wrong?

[balmy mortar]

lines 2 to 3 is wrong yes, which rule is that.

[river portal]

Isn’t it power rule where you bring the exponent to the front?

[marsh geyser]

Yes it should be log_2(8sqrt8)

[balmy mortar]

2 to 3

this is wrong.

[marsh geyser]

You have 1/2 there, you have to be careful

[river portal]

Wait I’m so confused

[river portal]

Can I not multiply them when 1/2 is in front?

[marsh geyser]

You can if you know how to do it

[river portal]

So I can’t do xlog a + log b = log ab

[marsh geyser]

You put 1/2 inside log again

Then u multiply

So u get log_(8sqrt8)

That would be correct

[river portal]

Oh ok

[river portal]

What should I do instead of moving 1/2 to the front then?

[balmy mortar]

you should notice that 0.5x + x = 1.5x

[river portal]

Oh ok

[obtuse pebble]

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[warm raven]

Integrate/Evaluate:
ʃ x/10x dx

[latent walrus]

$\int \frac{x}{10^x} dx$

[warm raven]

im sorry its 7. ʃ x / 10^x dx

yes

[warm shale]

AℤØ

[wooden cipher]

rewrite as x10^-x and then intergrate by parts

[warm raven]

ok ill try that now

ok so im at

∫(x10^(-x))dx = x(-ln(10)*10^(-x)) - ∫(-ln(10)*10^(-x))dx

idk how to use texit in here

[wooden cipher]

pull the -ln10 out

what do you get

also you may want to check your integration, it looks a little sus

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[modern lagoon]

whats the difference between dy/dx and d/dx, i've never really understood it

[worn yoke]

$\odv{}x$ is the derivative operator, it applies the derivative to the whatever is on its right. $\odv yx = \odv* yx$ is the derivative operator applied to the function $y(x)$

[warm shale]

cloud

[modern lagoon]

Ohhhh

so it doesn

have to be dy/dx

it could be df/dx

Thank you!!!!

.close

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[charred flume]

Whats the difference between

[warm shale]

elonmosqito96

[gritty vessel]

the first is a function of Y, the second is a number evaluated by plugging in the known value y

[charred flume]

but X is a random variable

so the second one is a distrubtion

but im not sure what the first one is/represents

[gritty vessel]

they represent basically the same things, the second is just the actual evaluation determined by plugging in the known value

[charred flume]

so then whats the reason for the distinction?

ig its kinda similar to f and f(x)

[gritty vessel]

it's like the difference between f(y) and f(2). f(y) gives an expression, and f(2) evaluated that expression for the given value 2

[charred flume]

but pX|Y=y is not an evaluation cuz the value of y is still unknown

[gritty vessel]

Y is a random variable and y is a particular value the random variable takes on

[charred flume]

ooooooooooooooooooooooh im stupid. so like the second one is like the pmf of X once Y has been determined or what ever and the first one is more of like an overview of how to find the pmf of X given the random variable Y

[obtuse pebble]

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[slim marsh]

help

[slim marsh]

someone help me

[daring rock]

"Frequency" in this context just means how times something occurs

Part (a) is just asking how many temperatures in the box are on the interval 95-100

and then 101-106, etc

@slim marsh

[obtuse pebble]

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[modern onyx]

Why is the sqrt(x + 9) In the front?

[obtuse pebble]

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[rotund vector]

How would I integrate this function?

[rotund vector]

(5x+2)/(x^2 + 2)

[modern onyx]

u-sub

where u is the deno

so then u = x^2 + 2, du = 2xdx
du/2x = dx

actually nvm ignore what i said this u sub doesnt work

[rotund vector]

Do I need to use fraction decomposition?

[modern onyx]

maybe u can just split the fraction

5x /( x^2 + 2 )+ 2 /( x^2 + 2 )

[rotund vector]

But will that work?

I still can’t integrate

[modern onyx]

prob

∫5x / (x^2 + 2) dx + ∫2/(x^2 + 2)

for the first integral u can use u sub and then the second one trig sub i suppose

[modern onyx]

Yeah trig sub works

did u get it ?

[rotund vector]

Wait so like this?

@modern onyx

[modern onyx]

wait is this a diff problem?

[rotund vector]

Yeah

Just typed the question incorrectly

[modern onyx]

u sub doesnt work

[rotund vector]

Why not?

[modern onyx]

The x's dont cancel out because they are being seperated by the + sign

[rotund vector]

Oh I see

[modern onyx]

i think u should split the integrals

[rotund vector]

So there is a quadratic factor

Could I split it up like this: Ax + b/x^2+2

?

[modern onyx]

like that

Because (a+ b) / (c + d) ==> a/(c+d) + b/(c+d)

[rotund vector]

So how would we integrate from here?

[modern onyx]

so for the integral with the 8x, you can use u sub for that

and then for the second integral you can use trig sub

tangent sub specifically

[rotund vector]

Oh ok

I’m not really sure how to do trig sub though

[modern onyx]

do you want me to walk u through it?

[rotund vector]

Yeah, that would be great

I’m sure there is another way though

[modern onyx]

ok so whenever u have x^2 + a^2 in the deno you use tangent sub

[rotund vector]

Because we haven’t actually learnt trig sub

[modern onyx]

Prob i cant think of it rn tho

are you in ab?

[rotund vector]

Oh ok

What is a^2?

[modern onyx]

a = sqrt2

a^2 = 2

[rotund vector]

Oh ok

[modern onyx]

and then x would be atan(theta)

so sqrt2*tan(theta) = x

and the derivative of that is

sqrt2(sec^2(theta))

That’s what we have so far

and then now ima replace all the values

[rotund vector]

Wait

Can’t I just use this formula?

[modern onyx]

u sub?

Oh yeah that’s basically trig sub

[rotund vector]

I get the wrong answer though

When I substitute the limits

[modern onyx]

It should be 3/sqrt2

Causw this 3 we need to pull it out front

[modern onyx]

Did u do usub on the first integral plug in ur limits and add it to the second integral

[rotund vector]

Oh okay, I get it now thanks

.close

[obtuse pebble]

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[rotund vector]

Does anyone know where I went wrong?

[finite wharf]

How are u assuming the values of A and B without solving the partial fraction equation.

I got A=-1/9
B=1/9
C=2/3

By solving the equation,
(x+1)=A(x-1)^2+B(x-1)(x+2)+C(x+2)

[obtuse pebble]

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[forest violet]

hey, what does this want me to do?

[forest violet]

i'm being tripped up by the notation

what does it want me to do with y=-pi/2?

isn't this just z=sin(x)?

[flat anvil]

Yeah seems like it

[forest violet]

but it's not DNE

nor is it 0

i got the subsequent ones right but i have no idea what it wants me to do with the info of y

[obtuse pebble]

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[forest violet]

.close

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[gloomy vector]

if ABC is an icoseles triangle and BAE=ACD, find CAE

[gloomy vector]

im not sure how to do this

wait sorry, it wants me to find this angle

[blazing junco]

the sum of blue angles

[gloomy vector]

ah ty

[obtuse pebble]

@gloomy vector Has your question been resolved?

[obtuse pebble]

@gloomy vector Has your question been resolved?

[gloomy vector]

.cloee

.cloee

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[urban kiln]

if a function f(x) is differentiable and invertible for all x in its domain,
and let its inverse be denoted by g(x)
then can I say f(g(x)) = g(f(x)) = x

[pastel wren]

yes

[urban kiln]

alrighty, thankyou!

jus wanted to confirm :)

.close

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[copper cape]

hello?

[copper cape]

merp

uhhh

does integral calculate the area or what?

imma trying to understand from wiki

[willow crater]

it does

[copper cape]

So why does it called the inverse of derivative?

uhhh

okay

maybe just that for now

just to make sure...

.close

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[sage dagger]

sometime

[copper cape]

the skeletonman will come back with an amazing facts!!!"

[obtuse pebble]

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[cunning badger]

Help

[cunning badger]

Send the written solution please

<@&286206848099549185>

[tawny copper]

💀

[cunning badger]

?

Wdym

[torpid pasture]

!15m

[obtuse pebble]

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.

[torpid pasture]

it looks easy but let me think about it for a few seconds

[tawny copper]

A very bold move asking for the solution 💀

[torpid pasture]

one way is that you can consider (x+2) sqrt(x+2) - 2 sqrt(x+2)

[marsh geyser]

we do not provide solutions

[radiant marsh]

bro thinks helpers are his personal calculators

[obtuse pebble]

@cunning badger Has your question been resolved?

[cunning badger]

Yea. I do think that

I haven't got the soln yet

So pinging noww

@helper

<@&286206848099549185>

[torpid pasture]

.

[marsh geyser]

#rules

No answer for you sir.

[radiant marsh]

if u just want a solution and don't care about learning or understanding then use photomath or something

[obtuse pebble]

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[runic laurel]

Can someone help me with this question? I have no idea what to do. It translates as: Given is the following analog non-periodic signal, where 𝑡𝑢2=3𝑡𝑢1, where tu2=3tu1
a) Define the expression for the spectrum of the signal.
b) Define the expressions for the amplitude and phase spectrum of the signal.

[fallow plank]

Which part is bugging you

have you done some previous exercises on fourier transforms and series

[obtuse pebble]

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[timid silo]

hey

[timid silo]

How can I find thelateral area and surface area of this square pyramid.'

Please dont provide answer

[versed stratus]

well the red line bisects the base

I think

[timid silo]

one second

279.3 is the lateral area?

[quaint inlet]

yep

[timid silo]

surface is 379.3

[quaint inlet]

how

i couldn't get it

[timid silo]

I can type out my calculator results however it may not look good

[quaint inlet]

np

[quaint inlet]

where does that 25 cames from

isn't it the 10 height?

[timid silo]

The number 25 comes from the calculation of the square of the half-length of the base of the pyramid

[quaint inlet]

got it

thanks

[obtuse pebble]

@timid silo Has your question been resolved?

[slow prairie]

i got a different answer for it

[timid silo]

Can you share your process?

[slow prairie]

isnt lateral area just 4(0.5)(13)(10)=260

[timid silo]

Your right

[quaint inlet]

i got that one too lol

i thought that mine is wrong

[timid silo]

360 should be surface area?

[slow prairie]

here 10 is the height of the triangle

[slow prairie]

the total surface area should be 429 i think

[quaint inlet]

yep

[slow prairie]

13^2 + 260

[timid silo]

Well im trying to make my right but it seems im wrong with it all lol

Does this seem right

[quaint inlet]

yes

[timid silo]

dang that looks horrible, im using 720p on a 4k monitor

thank you

[slow prairie]

np

[timid silo]

.close

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[vestal zenith]

So this is a numerical reasoning question that I'm looking to get advice on how to work it out, in simple terms please. No chatgpt answers. So I'll type what I've done already.

[vestal zenith]

The first column is Month 1 and second column is Month two.

M1 = type A is 60, Type B is 190
M2 = type A is 45, Type B is 205

But how will I now get the numbers into percentages for type A and B for month 1 and month 2?

Is 60 for type A (for month 1) is that 60%, but then how would I get type B for 190?

[dim temple]

Percentage of Type A will be (Amount of type A reports)/(Total amount of reports)

oh and multiply that by 100

[dim temple]

since this alone will give a decimal number between 0 and 1

[vestal zenith]

so 60 * 250 and multiply that by 100?

[dim temple]

60/250 rather

and multiply 100

[vestal zenith]

ah ok

wow, thank you very much for your help

[dim temple]

ywelcome

[vestal zenith]

I'm assuming that Is that formula for working out a percentage for a total number? I haven't touched maths in years, so just trying to practice back into it for job tests

[dim temple]

yea

to get the percentage of specific objects, just divide the amount of those objects and the total amount of objects, and multiply by 100

Im pretty sure someone can word that better

[vestal zenith]

thank you again :D - I get so confused sometimes, but will save that formula

I understood it, dw

[dim temple]

alright cheers

[obtuse pebble]

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[quiet rapids]

ould anybody help me here pls

[dim temple]

This channel is taken

[pliant lily]

Yea a see

Sry

[quiet rapids]

I tried pputting it into RREF

got this

would tgat be helpfuil \

[obtuse pebble]

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[obtuse pebble]

@quiet rapids Has your question been resolved?

[obtuse pebble]

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[frosty coyote]

How can I rearrange this

[gilded estuary]

What have u tried?

[slender oar]

Bruh

You just have to arrange it

According to the q asked

[frosty coyote]

Bro I read the question that's why I'm asking the cord

[gilded estuary]

What do you understand?

What have u tried?

[frosty coyote]

Divide it under by v

[gilded estuary]

what does that give you

[frosty coyote]

Nothing that has anything to do with that

[gilded estuary]

Basically, you want to isolate h on one side of the equation, yes?

[frosty coyote]

B is close but the h isn't there

Yeah

What would I do then?

[gilded estuary]

So you need to get pi and r^2 on the other side

What can you do?

[frosty coyote]

-pi r^2

On both sides

?

[gilded estuary]

They're multiplied

with h

not added

[frosty coyote]

What would I divide it

Both sides?

[gilded estuary]

yep

[frosty coyote]

Like that

?

[gilded estuary]

you would divide pi and r^2

[frosty coyote]

Alright

It would give me v/h =piR^2

[gilded estuary]

You're dividing V = pi * r^2 * h with pi * r^2 on both sides

[frosty coyote]

Oh

Like this?

[gilded estuary]

Not by h, only pi and r^2

[frosty coyote]

I see

So my answer would be v/pi and r^2 =h

?

[gilded estuary]

yes

[frosty coyote]

Thank u bro I understand it now

[obtuse pebble]

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[mild sandal]

I don't get 4th question's reasoning for not being a function

[gilded estuary]

You're trying to prove that y^2 = 4ax is not a function?

[mild sandal]

Basically

Is it a function?

[gilded estuary]

no

y = sqrt(4ax)

[mild sandal]

How

Ok

And then?

Oh wait

[gilded estuary]

Whats the definition of a function

[mild sandal]

I got it

Yeee thought it was square root function but forgot positives and negatives

Thanks

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[buoyant dome]

Guys, when taking the moments of a uniform rod, how do i know whether the weight in the middle will make the rod go clockwise or anti clockwise?? It's really confusing and messing up my answers and the mark schemes for the past papers don't really help in this regard. This is in relation to mechanics 1 of the edexcel exam board

[buoyant dome]

I have a question in relation to this topic but i can't get the snipping tool working for some reason. i can provide a link to the question if anyone needs me to be more specific

^not sure if its allowed to post links

[amber dirge]

Well it depends where you choose to take your moments about

The weight of the rod creates a clockwise moment at A, but it creates a counterclockwise moment at B

Forget about everything else in the diagram other than the weight and the point you are taking your moments about, and consider what would happen irl if you pushed on it at that point whilst holding it at the pivot point

[buoyant dome]

here is the question btw it’s weird to me and sorry for the dogass quality

[amber dirge]

Yeah so the direction of your moment will depend on where you choose to take your moments about (it would at first glance make sense to take them about C or D, but you can take them anywhere along the bar really)

[buoyant dome]

what isn't it an anticlockwise movement if we take it at A

[amber dirge]

Why would it be counterclockwise? Imagine you are holding the rod still at point A and pushing down in the middle, it's going to rotate clockwise

[buoyant dome]

Huh
when we take the moment at A, does it not mean that the magnitude of the reaction at A is = 0

[amber dirge]

What reaction at A

Reactions come from supports

You have reactions at C and D

and the weight of the bar acting through the centre as it is uniform

[buoyant dome]

im using your example

sorry, that wasnt clear

[amber dirge]

Oh, in which case what I wrote before was true

The moment from the reaction at A is zero

But there is still a reaction at A

The distance is just 0

Take the mass of my example rod as 10kg and 1m long

You can say that Ra + Rb = 10g

[buoyant dome]

Yeah i understand that

[amber dirge]

Then taking moments about A you can say that 10g * 0.5 - Rb * 1 = 0

Because the weight would cause it to rotate clockwise

And the reactiona t B would cause it to rotate counterclockwise

There is no moment created from A because A is the point you are taking moments about so the distance between Ra and A is 0

You could even take moments about the centre of the rod if you wanted, where the weight is acting through

Then you'd have Ra creating a clockwise rotation and Rb creating a counterclockwise rotation

0.5Ra - 0.5Rb = 0

Not that it would be sensible to do, but you could also take moments 0.1m along the bar if you wanted XD

It doesn't matter where you take the moments about, what matters is where the force is relative to your reference point, and which way it's going to cause rotation about that point

[buoyant dome]

sorry im just trying to comprehend what you're saying cuz i learned moments by doing questions only, since i wasn't in when our class learned it

im not ignoring or anything lol

[amber dirge]

It's all good

if you have a long ruler, use it to physically demonstrate to yourself what is happening

When you are taking moments, hold the ruler at the point you have chosen to take moments about

Hold it in front of you and push up/down on it in the places where your forces are, you'll see which direction each force causes it to rotate

[buoyant dome]

im trying to visualise that in my head lol

i asked this mainly cuz of part B in the question i posted

cuz when i was taking the moment at C, i got three anti clockwise movements which is wrong obv

THANK YOU!

.close

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[trail tundra]

hey all! reviewing for my final now and the whole derivative of an integral problems are messing me up

[trail tundra]

ill explain

like if we have this problem and have to use FTC

[bronze nova]

do u wanna differentiate it?

[trail tundra]

differentiate now?

its 5t^4 - 1

[bronze nova]

no like is the question

[trail tundra]

yes bascially ita

its:

[bronze nova]

okkay

[trail tundra]

wait i think we got it

find the antiderivative and then just plug in i guess

[bronze nova]

do u know chain rule

[trail tundra]

yes i know chain rule

[bronze nova]

so u evaluate for each bounds simply

[trail tundra]

is it that easy

[bronze nova]

like (2x*(x^2)^5 - x^2) - (x^5-x)

but u may be like

wow why is there a 2x term

in the start

right?

[trail tundra]

mhm

[bronze nova]

its because u chain rule so u have to take the derivative of the inner function (x^2) which is 2x and multiply it with the function that was evaluated on the bound

[teal turret]

(2x)((x^2)^5 - x^2) for the first expression**

[bronze nova]

oh right

mbmb

[trail tundra]

wegot it

just evaluate and take integral

thank you

be back shorlty with nother question lol

.close

[obtuse pebble]

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[trail tundra]

ok im back actually already

with early calculus questions

so lets say we are given that the integral of g(x) from a to b is equal to 4

so

.reopen

[obtuse pebble]

✅

[trail tundra]

how do we go about solving for lets say

not to be confused with

lost in this area

[obtuse pebble]

@trail tundra Has your question been resolved?

[river tree]

you can't figure this out with the given information

here are two examples of functions that would both have an integral equal to 4 over some a and b, but once you square them you get completely different results

in general you would just need to figure out the integral for the squared function from scratch

i'm pretty sure there's no integral trick for figuring it out

[obtuse pebble]

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[spice chasm]

part f

would it be correct to say that the experiment could have been done on a different planet where g<<9.8

cuz i made the derivation $a=\frac{m_B-\mu m_A}{m_A+m_B}g$

[warm shale]

Jash

[spice chasm]

so if g is lower then a is lower

[obtuse pebble]

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[past walrus]

Not a math Question but;
Should I take Calc 3 before Linear Algebra or should I take Linear Algebra before Calc 3. I am trying to take one of those classes for the summer and because my schools summer program is about 8 weeks long, I was wondering if someone could guide me on this

[green epoch]

I don't think 8 weeks is enough for either of those classes but linear algebra is more doable

Calc3 is better to do if you've recently done calc2 because that'll keep you in-flow and things will be easier to understand

Compared to if you do it later

[past walrus]

Im doing calc 2 rn and its going good but yeah I dont know if 8 weeks is good for a math class like calc 3 or LA

Im considering CALC 3 like u said just cuz it'll keep me in the flow but becuz its a 8 weeks long course for the summer Im also thinking abt LA since everyone I've met said its easier

[coral nest]

i think linear algebra is much easier than calc3

and it prepares you for calc3 in many ways

[half plinth]

If its intro to LA then it will be easier than calc3. But, in my opinion, a rigorous LA module is harder than calc3

[coral nest]

i agree

proof based linear algebra is hard

[obtuse pebble]

@past walrus Has your question been resolved?

[obtuse pebble]

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[fierce vale]

hello

[warm shale]

Adam Chebil

[fierce vale]

how do i prove the 3rd condition ?

[fierce vale]

in this example

[glass dagger]

The unions of the two element sets are included

The unions of the four element sets form Omega, which is included

Taking the union with Omega or the empty set is included

[fierce vale]

i need to prove that for every family of events though

like the union of {1,2} and {3,4}

{1,2} and {5,6}

{3,4} and {5,6}

[solid birch]

Just go through each iteration. It's going to take a while lol

[fierce vale]

what if the set is infinite 🙃

[solid birch]

Usually, for infinite sets (if the collection of subsets is indeed a sigma-algebra) there are already some nice conditions that allows you to take a countable union and with some effort you can show that it is indeed in the set.

In your problem, you can consider the set that contains another set in A. For example, {1,2,5,6} contains {1,2} and what can you say about that when taking unions that also contains {1,2}?

If you consider that, your problem simplifies a lot.

[obtuse pebble]

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[latent torrent]

I know mutually exclusive means two events can’t occur together but I’m having trouble understanding how the red highlighted formula demonstrates mutually exclusive events like does it mean that if a and a/b and b is equal to a separately then b separately added together if both are those are equal does that mean it’s mutually exclusive

[old lily]

P(A u B) = P(A) + P(B) - P(A n B)

[obtuse pebble]

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[latent torrent]

Ok

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[haughty pewter]

.help

[obtuse pebble]

Commands:

• clopen: .close, .reopen
• consensus: .poll
• factoids: .tag
• help: .help
• version: .version

Type .help <command name> for more info on a command.

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[mint oak]

why does y'' being negative mean its a maximum?

[brave bramble]

Means the curve is concave down

So any flat point must be a maximum

[mint oak]

ohhhh ok

sorry to bother you but why does y'' mean the curve is concave down?

i am not getting a clear picture

of wtf y'' is

@brave bramble

[brave bramble]

y" is the first derivative of y'

In other words, it's the rate of change to the rate of change

People usually link y" to the concavity of the function, though I agree setting this up in your head isn't very easy to do

[mint oak]

I see y' as the slope of a point on the function. so does that mean y'' is the

???

im confused

i cant say rate of change bc i dont understand how that works

[obtuse pebble]

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[gaunt raven]

Can anybody tell me how to find scale factor? Please? I was absent during the day we went over this.

[obtuse pebble]

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[quick haven]

does anyone know the P here? Is it 2 or 1?

[shut lagoon]

It's not in that exact form, so I guess you could claim that for large k the terms just behave as 1/k^2, but you might as well do comparison test with 1/k^2

[quick haven]

ok so what happens with teh radical though? why is not 1/k instead?

the*

is it because (1/rad(k^2))^2?

[civic zealot]

rad(k^2) = k
So for large k, the +1 inside the radical doesn't really matter.
Giveing you 1/(k * rad(k^2)) = 1/(k * k)

[quick haven]

ohhh so if i was to show work with comparison test, it would be what you said instead of < 1/rad(k^2)

because I knew that 1 didn't mean anything so I removed it before comparing

[civic zealot]

that comparison isn't helpful, the series of 1/k diverges.

[quick haven]

im aware just to make sure is 1/k(rad(k^2 +1)) < 1/k(rad(k^2)) a valid comparison?

[civic zealot]

yep, you made the denominator smaller, so the fraction is larger

[quick haven]

ok so i guess i was just premature by removing the + 1 and not considering it a comparison

thanks

.close

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[manic light]

hello

[timid silo]

Hello

[ember frost]

...? do you have a question?

[manic light]

Could you give me a tip on how to learn the multiplication table quickly and memorize it easily?

[ember frost]

man you are the textbook definition of https://nohello.net/en/, please just ask your question right away.

and also, how old are you?

[manic light]

14

[ember frost]

ok

[ember frost]

do more exercises about them

dont rote-learn, memorize them through exercises

you are better off learning how they work than purely memorizing

[manic light]

ok

thanks

[ember frost]

!done

[obtuse pebble]

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[chilly verge]

Can anyone help me with the answer? I've already answered the homework but in the comment section of the yt, the answer seems to be different my remainder is 000 while others is 100

[obtuse pebble]

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[iron bay]

,help

[warm shale]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[river falcon]

wot

[obtuse pebble]

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[dapper sandal]

Did I find dy/dx correctly?

[slim lake]

Yeah you find dy/dx

[slim lake]

Yeah that's correct

[dapper sandal]

Oh ok

Then i plug in

[slim lake]

Yeah plug in x and y

[dapper sandal]

Bet

[obtuse pebble]

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[scenic fjord]

Hello, can I know how to solve this?

I did this

Is this necessary?

Also I wonder the multiplication table should I start from 0 or just start from 1

[kind hawk]

they explicitly specified the set including 0

and 1*0 is not 1 btw

[scenic fjord]

Oh

[scenic fjord]

Actually I’m kinda blur with mod, for 01, 02 and so one actually is it all 0

[kind hawk]

yes

[scenic fjord]

So that means

So, it’s something like this

I want to ask, from this table, we can determine it’s closed right? Can we also directly say that it’s associative?

[kind hawk]

no from tables like this you can basically never tell whether its associative

but multiplication mod 7 being associative is well-known (I hope)

[scenic fjord]

But from the table we can say it’s commutative?

[kind hawk]

yes

[scenic fjord]

Yea

And my question is I’m actually blur with the identity and inverse

For identity, I think if a x e = e x a = e, then e should be 1

But is it also true for 0 if a = 0, basically from my thinking I think it’s true

[kind hawk]

small correction, a*e=e*a=a. but yes, e=1 works here

and the question for inverse then asks whether for every a there exists b with a*b=b*a=1

[scenic fjord]

Ohm so under multiplication, I still need to write * not x

[kind hawk]

worded differently, in terms of the table, in every row and column the 1 has to appear

generally never write x for multiplication

[scenic fjord]

This is for identity or inverse? Because in table for 0, I think there’s all 0

[kind hawk]

thats for inverses

and exactly, in the row and column for 0, only 0 appears

so does 0 have an inverse?

does there exist b with 0*b=b*0=1 ?

[scenic fjord]

Nope

[kind hawk]

so then 0 does not have an inverse

[scenic fjord]

so I just explain by providing this example, since for 0 does not have inverse, then it’s not a group

[kind hawk]

yes

[scenic fjord]

Can I ask you what is the meaning for this

[kind hawk]

thats bullshit

is that chatgpt?

[scenic fjord]

Like I don’t understand the (2 x b) mod 7

[scenic fjord]

Erm no, ChatGPT gives me it’s true

This is the answer in chegg

[kind hawk]

is that also AI?

[scenic fjord]

Explaining why it’s not a group but I don’t really understand that

[scenic fjord]

Nope, it’s answer by expert. But not guarantee answer, that’s why I’m asking here

[kind hawk]

its bullshit

2*4 =1 mod 7

the problem is with 0

[scenic fjord]

For me the counter example for 0 for inverse makes more sense

[kind hawk]

if you exclude 0, then it actually is a group under multiplication

[scenic fjord]

Can I also ask for (b), it’s my first time seeing this type of question with mod 2, I know I need to try with reflexive, symmetric and transitive to check whether they are equivalence relation or not

[kind hawk]

sry I have to go

[scenic fjord]

Okay, nvm, I’ll wait others to help. Thanks for you help

[obtuse pebble]

@scenic fjord Has your question been resolved?

[obtuse pebble]

@scenic fjord Has your question been resolved?

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[limber glacier]

hi can somebody help me with this question, i’m not completely sure if part a is right and i’m not too sure how to draw the argand diagram

[limber glacier]

.close

[obtuse pebble]

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[warm shale]

Chlats

[obtuse pebble]

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[edgy needle]

is vector projection the same as vector resolute?

[graceful rapids]

yes

[fossil crag]

vector projection is a generalisation of vector resolute

vector projection can be done onto any subspace, and it doesn't always have to be orthogonal

vector resolute I believe only applies to orthogonal projection of one vector onto the other

[edgy needle]

what is orthogonal

[graceful rapids]

perpendicular

[edgy needle]

.close

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[lone ferry]

.open

[timid silo]

hi can anyone help me create a product or grid table to the question “if a coin is flipped four times how many different sequences of heads and tails are possible?”

[timid silo]

same story as last time, and also you should really like add what u think to do first here

[obtuse pebble]

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[ivory flare]

Why did we mention its continuity ?

[ivory flare]

How did we even get -1

[low matrix]

is f(x) given

[graceful rapids]

here "continuous" means "has a value at x=1"

as opposed to having a discontinuity at that point

so we can just find f(1) directly, which gives you -1 i guess

[ivory flare]

Nope just this question

Which is why im confused

[graceful rapids]

oh what? f(x) is never mentioned beforehand?

[ivory flare]

Nope!!

Wait let me check

[pastel wren]

whats the whole quesition?

[ivory flare]

Oh no my bad it was included!!

Now it makes sense

But I dont get the continuity part

I’ll show you the graph

[graceful rapids]

to find a limit the first thing we try is directly reading the graph, correct?

[ivory flare]

Yeah

But why do we mention the continuity

[pastel wren]

if it wasnt continous f(1) wouldnt have a value

[graceful rapids]

*it wouldn't have a limit

x = 2 has a value but not a limit

because it's discontinuous - it jumps from -3 to 1

[ivory flare]

So saying its continuous is me telling the person that the limit of f(1) is -1?

[graceful rapids]

it's telling the person it has a limit

so yes

[obtuse pebble]

@ivory flare Has your question been resolved?

[ivory flare]

Ohokay

That applies to any other format of this question right

[graceful rapids]

yeah

[ivory flare]

Like this