help-10

[fervent comet]

You agree with that right?

f(a)=5-a

f(3)=5-3

=2

f(b)=5-b

f(4)=5-4

=1

Do you notice how the ‘a’ value, which had the lowest domain has the greatest range

And how the ‘b’ value, which has the highest domain, has the lowest range

Idk if u understand what I’m saying so I’m gonna stop it here

[obtuse pebble]

@stoic anchor Has your question been resolved?

[obtuse pebble]

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[drifting jay]

Find the minimum value of $$f(x,y)=e^{x^2+2(x-y)+y^2}$$

[drifting jay]

$$f(x,y)=e^{x^2+2(x-y)+y^2}$$

@warm shale

[verbal pendant]

$f(x,y)=e^{x^2+2(x-y)+y^2}$

[warm shale]

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

[verbal pendant]

huh

[drifting jay]

no idea why that doesn't work

Works perfectly fine in a math block in Notion

Anyways, to find the minimum value of this function, I have taken the partial derivative to x and y respectively

Getting this

[verbal pendant]

where's the issue?

[drifting jay]

So am I able to solve to get x=-1 using f_x and y=1 using f_y

but I am not sure how to solve e^{x^2+2(x-y)+y^2}

[rigid pine]

Maybe you could say that f(x, y) will be at it's minimum value when x^2 + 2(x-y) + y^2 is at it's minimum value.

[verbal pendant]

just plug your values for x and y into this expression and leave it in terms of e

[drifting jay]

So I need to find the minimum for that separately?

[verbal pendant]

that approach will give the same answer you just got

[drifting jay]

So I can just ignore that part?

[verbal pendant]

well e to the power of anything is always greater than zero

[drifting jay]

Oh wait I can reject the e^that

[verbal pendant]

yeah.

[drifting jay]

I see, so it can just be rejected as it is not possible

Thank you so much, that was the part I was stuck on

Actually, since any function f(x)=e^x would be minimized when x is minimized, instead of making the differentiation complicated for the first part

can I just state that and then find the minimum value of x^2+2(x-y_)+y^2 directly

[verbal pendant]

yeah you could do it that way too but like i said you'll get the same answer you already have

[drifting jay]

Yes, I was just thinking of it incase I encounter a similar question for a test or sth

Thanks

.close

[obtuse pebble]

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[glossy sparrow]

any help guys?

[glossy sparrow]

i let x = sqr x^2

but i got stuck after that

[zenith spade]

Conjugates

[glossy sparrow]

can you elaborate please

@zenith spade

[zenith spade]

If you substitute infinity directly, you would get infinity - infinity, which is an indeterminate form

To resolve this, you can multiply the expression inside the limit by it’s conjugate divided by itself

[warm shale]

CST

[glossy sparrow]

og

ohh

[obtuse pebble]

@glossy sparrow Has your question been resolved?

[zenith spade]

How’s your progress?

[obtuse pebble]

@glossy sparrow Has your question been resolved?

[glossy sparrow]

im stuck here

[zenith spade]

Why did you divide by x^2?

Keep in mind that all the x^2 terms were in square roots

I feel like the best way to deal with the floor function in the numerator is to use the squeeze theorem

[obtuse pebble]

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[ripe quartz]

https://media.discordapp.net/attachments/778224140771000360/958334011556651068/unknown.png

[ripe quartz]

Why isnt z the centre of this pyramid

Since triangle ATD is congruent to triangle TCB

wouldnt that mean TX=TY

[obtuse pebble]

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[obtuse pebble]

@ripe quartz Has your question been resolved?

[obtuse pebble]

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[valid raft]

Hey

[valid raft]

The exercise says that y = 3 cuts f(x) 3 times

I need to find the cutting points, will appreciate if someone will assist

[lethal sand]

what happens when two graphs intersect?

[valid raft]

they have different gradients

[lethal sand]

not really

[valid raft]

slope i mean

[lethal sand]

what can you say about their y-values?

[valid raft]

that their y is 3?

[lethal sand]

well in this case, f(x) would have an output of 3, yes, but generally, when two graphs intersect, their y-values are equal

[warm shale]

WhipStreak23

WhipStreak23

[valid raft]

so

i take x as a common factor ( 0 = x(x^2-4x+3)

so i get x = 0 x = 1 x = 3?

👀

so my points should be overall

(0,3) (1,3) (3,3)?

and if i have to find the equation of a line to each one of them

it means that they all share the same slope?

^

@timid silo do you mind to tell me how do I find the equation of a line to each one of them?
I struggle to solve that too

i get 0

everywhere

oh

i managed to solve it

[obtuse pebble]

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[atomic bronze]

guys how can i find groups of vectors of these 5, which are linearly dependent / independent? ive already used the gaussian elimination but i dont how to proceed further

[high tiger]

it depends on how u did ur gaussian elimination

I suggest putting the vectors as rows

then see which rows become 0s

those are the ones that are linearly dependent

[atomic bronze]

one row becomes 0s

[high tiger]

but did u keep track of that row?

[atomic bronze]

wdym?

my result right now is
1 0 0 0 -6 | 0
0 1 0 0 0 | 0
0 0 1 0 0 | 0
0 0 0 1 5 | 0
0 0 0 0 0 | 0

[high tiger]

yeah but as u were doing the gaussian elimination did u keep track of which vector become the zero row?

[atomic bronze]

yes, its the v5

so if theres a row of 0s it means all of them are linearly dependent right

but i dont know how i can spot a group which are linearly dependent / independent out of those 5

[obtuse pebble]

@atomic bronze Has your question been resolved?

[atomic bronze]

okay i think ive got a solution: there is only one combination of linear dependent vectors: v1, v4, v5. can anyone agree?

[obtuse pebble]

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[high lily]

no

consider stuff like pascals triangle or factorial definition

consider stuff like pascals triangle

do you know the relation between combinations and pascals triangle

if not, its worth looking up and it will be directly applicable here
otherwise use

factorial definition
and do some algebra bashing

[obtuse pebble]

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[amber frost]

@keen cave actually one more question…how do i check that a vector space is linear

[keen cave]

wdym? You can check if a function is linear.

Or are you trying to check if vector addition and scalar multiplication is closed.

If so, the you can usually tell if you understand what vector space your working it.

[keen cave]

Then you just have to check if I(f + g) = I(f) + I(g) and I(af) = aI(f) where f, g are polynomials and a is a scalar.

[amber frost]

and integration works like that so thats easy

[keen cave]

If you have study calculus specially integrating polynomials then it should be easy.

Yep.

[amber frost]

how would i go about the null space and range

[obtuse pebble]

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[obtuse pebble]

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[umbral oasis]

can someone help me do fxy

[umbral oasis]

im so confused

[obtuse pebble]

@umbral oasis Has your question been resolved?

[obtuse pebble]

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[umbral oasis]

um

[umbral oasis]

i still need help on this

<@&286206848099549185> sorry for the ping but

[restive ridge]

if you're sorry for the ping then don't ping

[umbral oasis]

well i kind of need to 😐

its been well over 15 minutes

[restive ridge]

yea but then don't feel sorry for it lol

[umbral oasis]

ig u have a point

[obtuse pebble]

@umbral oasis Has your question been resolved?

[umbral oasis]

should i just close this

[royal solar]

do you still need help?

if yes ping me

[umbral oasis]

yes please @royal solar

[royal solar]

which part ?

[umbral oasis]

fxy and fyx

im not sure what its asking exactly

does it want me to differentiate the x function with y

or differentiate the y function with x

or something else entirely

[royal solar]

they’re the same thing.

[umbral oasis]

okay that part makes sense

[royal solar]

cool

[umbral oasis]

but then what do i differentiate

[royal solar]

and pick one to differentiate first

pick one

[umbral oasis]

it doesnt matter which?

[royal solar]

do that

nope

the order doesn’t

[umbral oasis]

okay ill try it

[royal solar]

matter

sweet

i’ll stay online if you need me

[umbral oasis]

tysm

wow it really was that simple

thanks again

[obtuse pebble]

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[obtuse pebble]

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[gilded tree]

Bert keeps honey bees on his farm. When he first started, he used a 6-frame beehive that held 40 pounds of honey. Now, he uses a 30-frame beehive. It has the same ratio of frames to honey as the smaller beehive.
How much honey does Bert's new beehive hold?

[robust sleet]

same thing

[gilded tree]

ok so

6 divided by 30

[robust sleet]

?

6*x=30

what's x

[gilded tree]

what x

[robust sleet]

an unknown variable

[gilded tree]

o its 5

[robust sleet]

yes

[gilded tree]

ok so the answer is 5

it was 200

.close

[obtuse pebble]

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[lime moon]

Would i need to parametrise this first ?

[obtuse pebble]

@lime moon Has your question been resolved?

[obtuse pebble]

@lime moon Has your question been resolved?

[eternal bloom]

Write F(x,y,z)=x^2+y^2-z^2-1. Then grad F = (2x,2y,-2z). Note that grad F is normal to the surface (which is the zero level set of F). So grad F evaluated at (1,-1,1) dot product with (x-1,y+1,x-1) = 0. This lets you write the equation

[lime moon]

Ok thanks alot

.close

[obtuse pebble]

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[wintry stream]

why isnt the last one correct?

[wintry stream]

i got 10664.35963 as my answer

wait how did u get 16650

do u mean 10650?

ur gud

yeah it works now

ty

[obtuse pebble]

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[storm dagger]

simple question but im sleep deprived and so confused

[storm dagger]

my friend disagrees with me

-(7x/11) is the same as -(7/11)x right

[quaint sequoia]

yes

[storm dagger]

ok tysm

.close

[obtuse pebble]

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[fading birch]

So erm, my mathematical notation is lacking, can someone explain me what this line would translate into?

[fading birch]

it's supposed to describe this, but I want to understand what this would mean is English

[robust sleet]

radius lol

[fading birch]

what

.close

[obtuse pebble]

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[obtuse pebble]

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[atomic bronze]

guys can if V is a vector space and i have a,b,c ∈ V, do these 3 conditions automatically tell me that they are linearly independent?

[obtuse pebble]

@atomic bronze Has your question been resolved?

[atomic bronze]

lin is the linear span

[obtuse pebble]

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[muted meteor]

am I tripping or something

[muted meteor]

For parts A and B

i've entered the function into my calculator

and my answer is still different

im not sure how the hell they got 825.551

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[opaque gazelle]

I need help in solving this question

[brave bramble]

If n is as small as possible, what would the statement be?

Select that option, haha

[opaque gazelle]

b?

Is the second option correct?

[brave bramble]

Ye

[obtuse pebble]

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[hushed raft]

does anyone know how to do these?

[brave bramble]

https://www.cuemath.com/summation-formulas/

[timid silo]

Use summation laws

[obtuse pebble]

@hushed raft Has your question been resolved?

[hushed raft]

alr wait bruh i gotta be half asleep rn or smth

thanks

[obtuse pebble]

@hushed raft Has your question been resolved?

[fleet blaze]

can somebody help

[robust sleet]

no

[obtuse pebble]

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[slow sonnet]

$\int \frac{\sqrt{16-x^2}}{x}dx$

[warm shale]

Mohad

[slow sonnet]

any ideas?

tried x=4sinu

but with that I need more substitutions and stuff

[fair crater]

yeah u get cos^2 term then split as 1-sin^2 ig

[obtuse pebble]

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[slow forge]

Is there a more in-depth explanation for how this works? My teacher showed this and it was like magic and I want to understand (if an explanation behind it even exists) or am I reading too much into this?

[fierce lagoon]

Send screenshot

[slow forge]

Ok

Mind blown

Maybe a more specific question would be "How would you know how to find this solution?"

[fierce lagoon]

That looks like something I haven't done yet

[slow forge]

It is under binomial theorem

[slow forge]

I think I could be reading too much into this like asking why 1+1=2

[obtuse pebble]

@slow forge Has your question been resolved?

[fair crater]

binom theorem problems often work with differentiation / integration n substituting x=0 or 1 ig

[obtuse pebble]

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[noble hemlock]

can someone help me on this

?

.close

[obtuse pebble]

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[buoyant totem]

how do i convert m squared to cm squared

[robust sleet]

multiply by 10k

m^2 to dm^2 is 100

dm^2 to cm^2 also 100

so 100x100

10000

[buoyant totem]

oh ok ok thankk you

i forgot but i couldnt find out the formula

[manic breach]

1m^2 is 100x100 cm so yes 10k, i always have to think about it because i never remember what the actual values are

@buoyant totem dont forget to close the channel if youre done

[buoyant totem]

oh how do i do that

im new to the server

[manic breach]

type .close

[buoyant totem]

.close

[obtuse pebble]

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[fierce vale]

$\lim_{x\to0^{+}}$ $x^{m}.(lnx)^{n} = 0$ where n and m are positive integers

[fierce vale]

How to prove this?

[warm shale]

adam03

[obtuse pebble]

@fierce vale Has your question been resolved?

[obtuse pebble]

@fierce vale Has your question been resolved?

[brave bramble]

Same as
lim ln(x)^n ÷ (1/x)^m
Except now this is inf/inf

@fierce vale

[obtuse pebble]

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[cinder acorn]

guys I have a question which is not schoolwork but I actually need the answer

[cinder acorn]

If you have to collect x number of collectible cards

how many cards do you need to have to be sure you completed the collection? let's say 99% sure

since of course there will be doubles

[obtuse pebble]

@cinder acorn Has your question been resolved?

[obtuse pebble]

@cinder acorn Has your question been resolved?

[tardy epoch]

https://en.m.wikipedia.org/wiki/Coupon_collector's_problem

Different name, same idea

,calc 50 * log(50) + 0.5772 * 50

[warm shale]

Result:

224.46115027141

[drifting wraith]

it's uh expected value

it's not really how much you buy to get 99%

[tardy epoch]

Then use the formula for Probability

It's the next line after expected value

[drifting wraith]

yeah i got that

no what

it's not on that page

this is it

[tardy epoch]

What are N, n, and m there

[drifting wraith]

this is the probability to not have full collection after buying n coupons, m is total coupons

https://math.stackexchange.com/a/1454749

source

so that solves the reverse

i don't know how to invert it, but this kinda calculates it

https://tio.run/##VYzfCoIwGMXv9xTHwKaB/yoIhEJ6gF4gEmzMNhEnuch14auvFQR5Lg5853e@01jbYx8jQ4TAK87wUYZYYdDyPpGPO7hFDgrHTehPURJ4S@MqYzmZ6BIWBxkbSsjpGGMmptqWMy1Vh0G@@C9@clzV4yY0CGdCIW2yNRY5@mTM5wOZA39XutkR8v2hTFQd49AKdSVbau0b

[tardy epoch]

The question was asking for 99% probability of having the full collection

[drifting wraith]

yep

so you can manually change n until p becomes 0.01

[obtuse pebble]

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[tardy epoch]

.reopen

[obtuse pebble]

✅

[tardy epoch]

Bad bot

[obtuse pebble]

@cinder acorn Has your question been resolved?

[drifting wraith]

@cinder acorn so what's x?

or at least how large is it, like thousands or like 50?

[obtuse pebble]

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[chrome gull]

I’m struggling on where to start with this question I’ve tried integrating the bottom one to see if it helps but I couldn’t get anywhere help would be appreciated

[short wind]

@gloomy valve do u mind helping my friend with his homework man.

Or <@&286206848099549185>. I done this one but I'm bad at teaching. I made confused him even more.

[obtuse pebble]

@chrome gull Has your question been resolved?

[chrome gull]

No

<@&286206848099549185>

[short wind]

Whoa

I know the Homeworks due on Friday.

But I only ever use 1 @.

1 every half hour so

[obtuse pebble]

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[static patio]

how to finish this induction ?

[obtuse pebble]

@static patio Has your question been resolved?

[tardy epoch]

write out the n+1 case

and show that it's true using your hypothesis

[static patio]

how ?

[tardy epoch]

on the left hand side, wherever you see an n, plug in n+1. then expand and use your hypothesis to show that it's equal to the right hand side with n+1 replacing n

[static patio]

i think i already did it

induction step is in the picture

[tardy epoch]

alright then you're done?

[static patio]

i dont know how to move further from last line of induction step

[tardy epoch]

why do you need to move further when you've already proven the n+1 case?

[static patio]

im not sure if its proven correctly

[tardy epoch]

what are you proving?

show the original question

[static patio]

the identity you posted above

my original question was only the left hand side, i calculated right hand side

i need to show that its true

[tardy epoch]

the original problem

not your handwriting

[tardy epoch]

there are no instructions

show the whole problem

[static patio]

its not in english

[tardy epoch]

how'd you come up with this then?

[tardy epoch]

i think that's enough of a proof? why do you need induction?

[static patio]

im required...idk, its weird

[tardy epoch]

Write out $\sum_{i=k}^{n+1} i \binom{i}{k}$ and use your inductive hypothesis. Then show that it's equal to $(k+1)\binom{(n+1)+2}{k+2} - \binom{(n+1)+1}{k+1}$

[warm shale]

riemann

[static patio]

do i just need to factor the RHS ?

[tardy epoch]

maybe.

you should just try different things

[static patio]

and the last line of inductive step is ok ?

[obtuse pebble]

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[obtuse pebble]

@mental oyster Has your question been resolved?

[obtuse pebble]

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[high lily]

recall basics for combining fractions through addition

not quite

double check your denominator of your first term

apply exponent laws to simplify the numerator

[obtuse pebble]

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[hushed raft]

how do you solve this using binomial probability? A shipment of thirteen smartphones contains six with cracked screens. If sold in a random order, what is the probability that exactly two of the first five sold have cracked screens?

[obtuse pebble]

@hushed raft Has your question been resolved?

[hushed raft]

i think that you have to do (5c2)(6/13)^2(7/13)^3

which evaluates to 28.51%

but the answer key says 40.793%

that makes no sense

<@&286206848099549185> 🙏 u dont gotta explain anything to me, just lmk if the answer key is wrong or if im wrong

[obsidian isle]

I think you also need a 13 c 5

,w (13 choose 5)(5 choose 2)(6/13)^2(7/13)^3

,w (13 choose 5)(5 choose 2)(6/13)^2(7/13)^3

[hushed raft]

but that ggives

linke

like*

[obsidian isle]

No nvm

[hushed raft]

42801%

[obsidian isle]

That gives you a crazy big number lmao

[hushed raft]

ye lol

is the answer key wrong then?

[obsidian isle]

Yeah I mean what you have looks correct

[hushed raft]

alr thanks then

.close

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[trim spoke]

Hey was wondering if I could get some help. I just need help creating an algebra equation

The mean is 18. I just need to prove with Σfx/Σf

Actually I think the equation is
(80 + 160 + 𝑥) / ( 8 + 8 + y) = 18

𝑥 = 30 x y

<@&286206848099549185>

I just need help solving that

#help-10

<@&286206848099549185>

[civic zealot]

what is x?

[trim spoke]

Sorry, x = y x 30

Y is the box

Need to solve for y and then we can get x.

[civic zealot]

So you really have (240+30y)/(16+y) = 18

[trim spoke]

Yes, I’ve written that. I just need help solving it

[civic zealot]

multiply by 16+y

[trim spoke]

18 multiplied by 16+y?

[civic zealot]

everything.

that's how you get rid of fractions

[trim spoke]

(240 + x) would be 3840 + xy??

[obtuse pebble]

@trim spoke Has your question been resolved?

[obtuse pebble]

@trim spoke Has your question been resolved?

[trim spoke]

.close

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[raw harness]

how do I do this

im in geometry

[visual onyx]

Maybe use ab sin c

[hybrid gull]

Start with a diagram

[raw harness]

im stupid why didnt I think of sin cos and tan

[visual onyx]

can you solve it now

[raw harness]

I think so

[visual onyx]

then please close this channel

[raw harness]

how

.close

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[raw harness]

ok I actually am still stuck on this question

[obtuse pebble]

@raw harness Has your question been resolved?

[timid silo]

what is the question asking for??

[obtuse pebble]

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[raw harness]

nevermind I put something anyway

[raw harness]

it was asking for the "x?"

[obtuse pebble]

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[storm wagon]

having trouble with question D

[storm wagon]

so since I am not given a Z-axis in both vectors, wouldn't the cross product be 0 all across?

i = 0 and j = 0

k wouldn't equal 0 though

[obtuse pebble]

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[tacit mango]

Is this correct?

[tacit mango]

Am I doing it correctly?

This is the question

[scarlet locust]

Yeah I think it's correct

[tacit mango]

Okay, Thanks ^ ^

[swift marsh]

Yes although for parts 3 and 4 you did not have to do any further calculations. Your first part was a counter-example, and your second part was an example. So you can then conclude both parts from that

[tacit mango]

Oh, so I can remove the examples for 3 and 4 coz it's optional

[swift marsh]

Yep

[tacit mango]

okay thanks

[swift marsh]

You can ‘from part (1) and from part (2)’

Just reference them and it’s fine

[obtuse pebble]

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[prime cape]

how do i do this

[royal basin]

do you know how to find average velocity over an interval?

[obtuse pebble]

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[sick pelican]

no idea how to calculate

[obtuse pebble]

@sick pelican Has your question been resolved?

[pliant marsh]

Firstly, you can use F=ma to find the net force. Since this is the NET force, you can find the force exerted by the crane itself (If you are not sure how to do this, draw Free body diagram).

Once you obtain force by the crane, you can use P=F*V to find the velocity

[sick pelican]

how bout mg?

ooo wait

ok

.close

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[lime mural]

Where did the 0.3264 come from?

[lime mural]

oh wait nvm lmao i got it

.close

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[undone ruin]

Hola

.close

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[static patio]

In how many ways can the players be divided into three teams: 9, 9 and 10 players in this order. Formally, how many partitions of set exist of sizes 9, 9 and 10?

[royal solar]

hi matey

a total of 28 players

so 28c9 * 19c9 and finally you’ll have only 10 people left

so that’s it

[static patio]

i have though exactly about this

[royal solar]

I’ll look into the induction thing now

[static patio]

ok thanks

[static patio]

but aren't we double counting some of the possibilities ?

[royal solar]

yeah sorry,9 and 9 are identical

so divide that by 2

[static patio]

2! ?

[royal solar]

same thing

2! is 2

[static patio]

yes.., if the 3 sets would have been the same i would divide it by 3! ?

[royal solar]

no, cuz team of 10 is different from teams of 9

you can’t double count team of 10

if it’s 3 teams of 9, you’d be righr

[static patio]

yes, but i was asking about how it works in general...

[royal solar]

but no see

[royal solar]

oh yeah, for n identical sets, you divide by n!

[static patio]

ok thanks a lot for help

[royal solar]

if you have two teams of 9 and two teams of 10

then /2!x 2!

a teams of 9 and b teams of 10

/a! x b!

[static patio]

yes, i got it

[royal solar]

yee

[static patio]

.close

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[brittle forum]

How do I find the jacobian of g(f(a))

also how do i find the jacobian of an implicitly defined function

[obtuse pebble]

@brittle forum Has your question been resolved?

[obtuse pebble]

@brittle forum Has your question been resolved?

[obtuse pebble]

@brittle forum Has your question been resolved?

[obtuse pebble]

@brittle forum Has your question been resolved?

[tardy epoch]

.close

[obtuse pebble]

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[quartz vigil]

alright so i need help with this equation ;
$f(x)=\frac{x-2a}{x^2} (a>0)$
i am asked to find the intercepts, maximum/minimums, etc
how do i go about this if i am not given any info about a? am i supposed to express everything using a? and if so, how do i go about it?

[obtuse pebble]

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[quartz vigil]

.reopen

wtf

/close

.close

[astral ivy]

?

[obtuse pebble]

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[final lion]

I'm lost on how to solve this system of equation

[obtuse pebble]

@final lion Has your question been resolved?

[final lion]

i tried setting the equation up for y but i end up with a xy term i dont know what to do with

<@&286206848099549185>

[shut trellis]

okay so you are on the right path

lets look at the 2y(x-1) = 0

what does that tell us?

[final lion]

x=1 and y=0

[shut trellis]

yep

now we look at the first equation

and use those

[final lion]

-3=0?

[shut trellis]

you don't use both

[final lion]

ohh ok

[shut trellis]

for 2y(x-1)

either y = 0

x = 1

or both

[final lion]

-3+y^2=0

[shut trellis]

yeah

[final lion]

y= +- sqrt(3/2)

nvm

wait

sqrt(3)

[shut trellis]

+-

but yeah

so we have 2 viable points

(1, +- sqrt(3))

but theres still some more

we used x = 1

now we try?

[final lion]

3x^2-6x=0

[shut trellis]

yep

[final lion]

3(x^2-2x)=0

then quadratic equation?

with c=0?

[shut trellis]

you could also factor it but either way works

[final lion]

3x(x-2)=0

x=0,2

[shut trellis]

yeah

[final lion]

thank you so much

[shut trellis]

np

[final lion]

.close

[obtuse pebble]

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[feral dew]

L =/= 0

[feral dew]

what does the left hand side say ?

an is a series

[dull rune]

It means that the series approaches L

Basically as n gets reallllyyyy big itll get equal L

[feral dew]

it's from n to infinity?

[dull rune]

Basically a_infinity equals L

But we dont like to say that

So we write the limit

[feral dew]

Gotcha, thanks

I'll read up on lmits

.close

[obtuse pebble]

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[jade ember]

In integration if I use U substitution, can I still make what u equates to in the equation the same?

[strong vale]

eh?

is your question about dummy variables?

[jade ember]

say I did u = square root of x. There happens to be a square root of x in the original integral. To cancel them out, can I keep that square root of x in the integral?

[strong vale]

Can you provide an example question

[strong vale]

Ok. So $u=\sqrt{x} \implies du = \frac{1}{2\sqrt{x}} dx$

[warm shale]

azeem321

[jade ember]

yeah. I can make it du * 2 sqrtx = dx

and then cancel sqrt x

[strong vale]

or you could it like $x=u^2 \implies dx = 2u ~du$

[warm shale]

azeem321

[jade ember]

is that similar to this

[strong vale]

yh

[jade ember]

but say I did what I did, its not exactly wrong right? Or is there a scenario where it would backfire

[strong vale]

No. it's fine. So it will become $\int_1^4 \frac{e^{\sqrt{x}}}{\sqrt{x}}dx = \int_1^2\frac{e^u}{u}2u ~du$

[warm shale]

azeem321

[jade ember]

ah yeah, true. Thanks

.close

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[radiant pasture]

Is this process correct

I'm new to calculus so I just need confirmation that I'm doing stuff right

<@&286206848099549185>

Wait it's been 9 minutes

Oof

I'm closing this channel cuz I'm going to sleep so bye I'll be back tomorrow

.close

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[stiff latch]

ok so I was studying and I came across a statement saying, "number that are their own inverses", but I didnt really understand the statement

[stiff latch]

can someone please help me out?

[stiff latch]

https://math.stackexchange.com/questions/3891389/numbers-which-are-their-own-inverse-are-exactly-1-and-p-−-1#:~:text=The numbers on the list,exactly 1 and p−1 heres the link for reference

[haughty coyote]

here it's more specifically to be their own multiplicative inverse in Z\pZ, i.e. x such that x² = 1 [p]

the inverse of x in Z\pZ (i.e. integers modulo p) is y such that xy=1 [p], so x is its own inverse iff y=x, i.e. x²=1 [p]

[stiff latch]

ok uhh, I dont understand the notations you are using

[haughty coyote]

just forget about the Z\pZ thing

[stiff latch]

ok

and here [p] means (mod p) right

[haughty coyote]

let's just say we're working with numbers mod p, that will be simpler

[stiff latch]

ok

[haughty coyote]

the definition is still the same though

[stiff latch]

hm ok uh

so multiplicative inverse under a module?

what does that mean

[haughty coyote]

the definition of a multiplicative inverse, for any multiplication, for any set of things (such as the integers mod p), if there's a "1" (which does nothing regarding multiplication), is defined as : the inverse of x is y such that xy = yx = 1

since here equality is done mod p, this is xy = 1 [p] under usual notations

[stiff latch]

:o

ohhh

ok ok

I understand

so if a number is its own inverse

x^2 = 1 [p]

ohh yes

[haughty coyote]

just like 1/3 is the inverse of 3. Or 1/1 = 1 is the inverse of 1

[stiff latch]

hm so under a set of mod p

if a number is its own inverse

the only such numbers are

1 and p-1

ok yes

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[steel mauve]

What is it called when theres a transformation where lines stay linear but everything else changes

[fierce lagoon]

Dilation?

Your question is so vague

There's rotation

Stretching it

Exploding it

Donating it to charity

[wanton isle]

pp

[obtuse pebble]

@steel mauve Has your question been resolved?

[steel mauve]

no, its a name like affine

but not affine

its a category of transformations

[obtuse pebble]

@steel mauve Has your question been resolved?

[obtuse pebble]

@steel mauve Has your question been resolved?

[obtuse pebble]

@steel mauve Has your question been resolved?

[tardy epoch]

.close

[obtuse pebble]

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[obtuse pebble]

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[stone marlin]

Hi

Does anyone know where does the lambda 0 come from?

Or what does it mean?

The book is introduction to mathematical statistics by Hogg and Craig

Is the section of likelihood ratio test

[obtuse pebble]

@stone marlin Has your question been resolved?

[thick fog]

lambda_0 is an arbitrary constant depending on capital lambda based on the context, but it's hard to tell without reading more than just a portion of a page

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[limber quartz]

what have you tried?

[limber quartz]

no

[rough bough]

why is (b) wrong

[limber quartz]

understand that 44C6 is the number of ways to pick 6 items from 44 where order doesn't matter

[rough bough]

isn't it for each game you play you would pick something else

[limber quartz]

but the denominator is your probability space

it is supposed to represent all possible outcomes

so you want 44P6 down there

which is 44x43x...39

[rough bough]

I think I get it now

[limber quartz]

your numerator is wrong too

[rough bough]

it is just that you want to multiply 4 to represent 4 of the differnet possiblity

[brave bramble]

That would imply that choosing the numbers in a different order is a different set of numbers, but I don't get that vibe

[limber quartz]

ok guys

so let's look at part a

[rough bough]

my part (a) is correct

[limber quartz]

oh, well duh

scuse me

[limber quartz]

@brave bramble is right, but my reasoning I think will hold...it just simplifies to what you have anyway so...nvrmnd (I think??? ugh, tapping out) dogshit

[rough bough]

i get it, can you please try this one

.close

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[violet token]

I need help

[violet token]

properties of rotation 9-3 reteach answers

I tried to figure it out

And got nowhere

[tardy epoch]

read this

[astral ivy]

I don’t think anyone here knows what this means lol

Can you post a problem?

[obtuse pebble]

@violet token Has your question been resolved?

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[timid silo]

Subtract 2 until

you have less than 5

[warm pine]

indeed

If I had $x$ items, if I give 5 items, I would have $(x-5)$ items.
If I get 3 back I'd have $(x-5+3)=(x-2)$ items.

[warm shale]

sunflame

[obtuse pebble]

@nocturne condor Has your question been resolved?

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✅

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@nocturne condor Has your question been resolved?

[fair crater]

u do this once or loop it?

not 26?

like ur original q said 26

ok let's take 26 for now

so u give 5, get 3 ryt?

so after each loop, u lose 2 in total?

y not?

s

so 26 decreases by 2 each time after the loop?

so answer is 0 since 26 is even?

maybe not lol

0 is wrong

just think

what happens when u reach 6

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[fair crater]

bruh it's nothing

u get to 4

then u can't give 5 out of 4 n it stops there

nvm then

[obtuse pebble]

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[latent tusk]

I'm not sure how to do this I need some help

[tight star]

So you have something with unit cm, and you want cm/t where t is time

what do you do?

[latent tusk]

dr/dt

[tight star]

yes, you take the derivative

and so y'(t) tells you how the radius change given t, so what do you let t be when you evaluate this formula?

[latent tusk]

Will t be 0?

[tight star]

t needs to be such that y(t) = 5 right? '

[latent tusk]

Yes

[tight star]

here $y(t)=\sqrt{1+t}$

[warm shale]

bim

[tight star]

so you solve for t, take the derivative, and plug in your t

do you see why?

[latent tusk]

So y'(t) will be 1/2 sqrt (1+t)?

[tight star]

where is the sqrt(1+t)?

[lethal sand]

(be careful, sqrt(1+t) is not the radius after t seconds))

[tight star]

ah thats true

[latent tusk]

I'm getting confused now

[tight star]

okey let us start from the beginning

[latent tusk]

Okay

[tight star]

What do you want to find?

[latent tusk]

Rate at which radius is increasing

dr/dt

[tight star]

yes

can you find the radius in the exercise ?

[latent tusk]

5cm

[tight star]

that is when you want the rate of change

so you wrote dr/dt

which means that r is a function that you take the derivative with respect to t right?

[latent tusk]

Yes

[tight star]

so what is this function r ?

tell me in words, no need to give it

[latent tusk]

I'm not sure

[tight star]

so dr/dt = change of radius with respect to time, right ?

[latent tusk]

Yes

[tight star]

so r should be the function for the radius

[latent tusk]

Yes

[tight star]

do the exercise give such a function ?

[latent tusk]

No

[tight star]

but it does give a function for the volume, can you connect the volume with the radius of the balloon?

[latent tusk]

Volume of balloon is 4/3 pi r 3

So I make r the subject of the formula?

[tight star]

well yes, so you have a formula that gives the volume for a given t, and you have another formula that gives r for a certain volume

do you see what i mean ?

[latent tusk]

Yes

[tight star]

so you should be able to express the radius of the balloon as a function of t

[latent tusk]

Okay thank you Ill try it out now

[tight star]

good luck and let me know if you need more help!

[latent tusk]

Yep thanks!

[tight star]

a general tip, if you dont understand an execise, break it down into smaller questions like i tried to do for you above

you see what i mean by that?

[latent tusk]

Im not rlly sure now

[lethal sand]

try to establish the functions slowly

like bim said, you can express v(t) in terms of r(t)

can you try to write that out?

[lethal sand]

i asked for v(t) in terms of r(t), you are trying to express v'(t) as a result of chain rule

[latent tusk]

This?

[lethal sand]

almost

but yes, v(t)=4/3pi *r^3(t)

however v(t) is not sqrt(1+t)/t

[warm shale]

waler

[lethal sand]

now instead of actually solving for r, a quicker way is to just find r'(t) in terms of r(t) and t

have you learnt implicit differentiation?

[latent tusk]

Not sure

I don't think so

[lethal sand]

right, that means we would have to solve for r(t) then

well, it's not too bad either

are you sure you havent learnt implicit differentiation? It's basically differentiation but with functions relative to t instead of differentiating functions in terms of t

i think you should know this from the fact that you wrote out the chain rule for v'(t)

[latent tusk]

I'm pretty sure I have yet to learn that

[lethal sand]

ok then

so basically just solve for r(t), differentiate r(t) wrt t, then substitute t into the derivative

[latent tusk]

How do I solve for r(t)?

[lethal sand]

just like how you would solve for x in an equation

try to look at t as a constant, then solve for r in terms of t

[latent tusk]

So do I sub t as a number?

Like t=3

Then I solve for r

[lethal sand]

no, just treat it as if it was a constant

for example y^3=x would be equivalent to y=cbrt(x), what i did was solve for y in terms of x as I took the cube root on both sides

[latent tusk]

Yes

So I just move all the things except for r to the right side with t?

[lethal sand]

sure

[latent tusk]

I do not think this is it right?

[lethal sand]

seems good, try to write the cube root bigger so you dont misunderstand it as the cube root of only the numerator

now the only thing left is to differentiate r

[latent tusk]

Oh okay

[lethal sand]

and dont forget to solve for t when r(t)=5

[latent tusk]

So it will be dr/dt ?

[lethal sand]

yes

[latent tusk]

Which am I suppose to do first

[lethal sand]

doesnt matter

[latent tusk]

The derivative or r(t)=5

Oh okay

[iron ether]

hi

i'm stumping so bad lmfao

nvm occupied sorry

[latent tusk]

Sorry but I'm stuck on finding the derivative

It is too complicated as it has cube root and square root together

However I got t

[lethal sand]

right, lets just say if we had f(x)=cbrt(x), what would f'(x) be equal to?

[latent tusk]

1/3cbrt(x)

[lethal sand]

we are finding the rate at which the radius is changing when the radius is equal to 5 not 4

[lethal sand]

eh no, check again

[latent tusk]

It is 5

[lethal sand]

this looked like a 4....

[latent tusk]

HAHAHA it's a 4

[lethal sand]

but anyway, if you wrote a 5, the rest should be good if you didn't miscalculate anything

anyway, the derivative of cbrt(x) is 1/(3cbrt(x^2))

[latent tusk]

1/3cbrt x2

Oh

Okay

[lethal sand]

ok good, but we also have another function inside that cube root

hence the chain rule needs to be applied

what's the derivative of 3/(4pi)*sqrt(1+t)

[latent tusk]

3/8pi*sqrt(1+t)

[lethal sand]

if you meant 3/(8pi*sqrt(1+t)) then yes

[latent tusk]

Yes that's what I meant

[lethal sand]

anyway, the derivative according to what we have found should be r'(t)=$\frac{1}{3\cdot \left( \frac{3\sqrt{1+t}}{4\pi}\right)^{\frac{2}{3}}}\cdot \frac{3}{8\pi \sqrt{1+t}}$

jeez

right, finally

i hate big codes

[warm shale]

waler

[lethal sand]

so you have the derivative, you have the time at which you need to find the rate of change

now you just need to plug it into the derivative

you can simplify this if you want to, im too lazy for that

[latent tusk]

Okay thanks for ur help I think I know how to solve it from now

Sorry if I was not getting u at times

[lethal sand]

nah

glad could help

this problem could have been solved much quicker if you had known implicit differentiation, but too bad you havent learnt it

felt like this would have been a better exercise after you have learnt that

[tight star]

YEY YOU !

[latent tusk]

.close

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[sour lantern]

1. is the blue underlined part (dxdy) an infinitely small rectangle on the xy plane?
2. is the reason why integrating dx the range is from 0 to a because a length is parallel to the x axis?