help-10

[gentle current]

well

log 5 of x =-2

[vapid pecan]

Oh

I was looking at a wrong thing

Im having a mental breakdown

[gentle current]

it s ok dw

[vapid pecan]

Ight thanks

I got 1 more including logarithma

,rotate

[vapid pecan]

Is it okay to this point

[gentle current]

what does log simple meen?

[vapid pecan]

Huh

I dont know

[gentle current]

um

[vapid pecan]

What are you talking about

[gentle current]

it s weird

it s log 2 of (log +x)

[vapid pecan]

Nah

I just cant write

Its log2(log4(x))

[gentle current]

ooooooh

ok

it s good

sorry but it s hard to read

[vapid pecan]

Y my bad

I don't think its good

,rotate

[gentle current]

ye it s good

[vapid pecan]

Naah

[gentle current]

log 2 of x is greater than 1/8

[vapid pecan]

So x should be greater than like 1/256

[gentle current]

that means x is greater than 2^1/8

[vapid pecan]

But photomath says 1<x<16

[gentle current]

um

wait ye

sorry

[vapid pecan]

What's the mistake

[gentle current]

wait i think i see it

in the first photo were you changed the base from 4 to 2

it s not x^-2

it s x^1/2

[vapid pecan]

Thats the same tho

[gentle current]

no i ts not

[vapid pecan]

2-¹ = 1/2

[gentle current]

yes

2^-1

you wrote -2

[vapid pecan]

Yeah

Cuz 1/2 = 2-¹

And up there things multiply

[gentle current]

in this case not

[vapid pecan]

Idk how to explain in english but im like 99% sure it's the same

[gentle current]

because it s not (x^2)^-1

[gentle current]

in this case that rule aplies

but here it s x^(2^-1)

[gentle current]

nope

[vapid pecan]

Yes 😭

[gentle current]

x^1/2

is square root of x

right?

[vapid pecan]

Yeah

[gentle current]

x^-2

is 1/(x^2)

it s not the same thing

search on youtube power rules

[vapid pecan]

But what about this

Naah im sure i did this like my entire life and it was good

Unless i mixed it up with something

[gentle current]

what you are saying it s true

but only is

when you have

(x^y)^z

only then they multiply, y and z

but in the case x^y^z

they don t multiply

because z is power of y

not x

[vapid pecan]

So replace -2 with 1/2 everywhere

I mean its the same thing up until the switching with t

So it should be 1/2t * 1/2t

Nah

1/2t * ✓t

Yeah that makes sense

[gentle current]

it s clear now?

[vapid pecan]

Idk i get t³<48

Well yeah because im incapable of multyplying 2 numbers

[gentle current]

xd

[vapid pecan]

Kay i get x<16

But like photomath also gets x>1

[gentle current]

yes

because

there is a log in a log

and the argument must be positive

[vapid pecan]

Well 0.5 is also positice

[gentle current]

yes

[vapid pecan]

Ooh

It cant be 1

Bcs then log of 0

[gentle current]

but it gives u a negative number if the number is between 0 and 1

and yes

it must be greater then 1 so it s not 0 ore negative

[vapid pecan]

Ight thanks

.close

[obtuse pebble]

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[gentle current]

no prob

[obtuse pebble]

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[cloud igloo]

Are these two correct?

[obtuse pebble]

@cloud igloo Has your question been resolved?

[cloud igloo]

.close

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[burnt cipher]

hey guys, is this correct?

[sage geode]

,w limit of 1/(x + sqrt(x^2 - 1)) as x approaches -infinity

[warm shale]

Results provided by WolframAlpha

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

Requested by alonelybean#0

[sage geode]

Yes

[burnt cipher]

dang why im sure it is a 0

[sage geode]

You can use software to check answers sometimes

[sage geode]

Why are you sure it's 0?

[burnt cipher]

i did but im unsure why it doesnt turn to 0

because if you lift off the root the x^2 becomes x

wait

fuck me

thanks man

.close

[obtuse pebble]

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[elfin burrow]

I came across this form of Gauss's triangular number theorem in terms of generating functions:

[elfin burrow]

Does this imply the familiar Gauss's triangular number theorem involving integers (that every positive integer can be written as a sum of three triangular numbers)?

[obtuse pebble]

@elfin burrow Has your question been resolved?

[obtuse pebble]

@elfin burrow Has your question been resolved?

[tardy epoch]

try proving it

but i don't immediately see how

[elfin burrow]

I think cubing both sides gives a generating function for the number of ways n can be expressed as a sum of three triangular numbers

but no further luck

maybe the author (Tom M. Apostol) just considers that identity to be Gauss' triangular number theorem

[obtuse pebble]

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[timid silo]

in video he says to choose any number and multiple it to get positive or negative but for the left i chose -2 i got negative instead

so how am i supposr to choose the right number to get the correct answer

[stone spoke]

-2 is in (-3,4) which is negative as he shows in the vid

[golden oriole]

-2 is to the right of -3

[timid silo]

oh

lmao

.close

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[timid silo]

why is infinite not a bracket

its part of the graph

[golden oriole]

Wdym ?

[timid silo]

its part of the graph

[native crag]

they are abusing notation

[timid silo]

like infinite, 4 , -3 and -inf r part of the graph

[native crag]

the graph' doesnt include' infinity

[tardy epoch]

it's not

[timid silo]

ok so any numbers r brackets then

?

[golden oriole]

By infinity they mean any arbitrarily large number that you could want to use
Just shows there is no upper limit

And -infinity shows there is no lower limit to that interval

[timid silo]

ok so i use brackets whenever theres real numbers

is that right

[azure anchor]

open interval vs closed interval

[timid silo]

open is paranthesis?

how do u get open in these questions tho

[azure anchor]

an interval including "infinity" cannot "include" infinity itself, because infinity is not a value in of itself.

so interval with infinity is always open

[timid silo]

Ok this is my question

So do I move the x^3 or the 49x to the other side?

[golden oriole]

Doesn't matter

[timid silo]

0<=x^3-49x

idk how to factor that

[obtuse pebble]

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[modern palm]

What form is this series in?

[modern palm]

geometric?

[lusty hearth]

nop

it's an intgral of a géometric séries almost intégrale if u factorise by x/10

and it will converge for |R|<1 where R is the raduis of convergence

with the d'alembert rule u find R=10

[obtuse pebble]

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[shadow lava]

am I on the right track here?

.close

[obtuse pebble]

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[hardy drum]

The answers say my answer is wrong, wat did I do wrong?

[timid silo]

What does the answer say?

[plain stag]

you calculated the probability of 3 defective phones; the criterion is more than 2

there are more numbers that are more than 2, than just the number 3

[hardy drum]

Answer is 0.07548 I got 0.0595

[hardy drum]

Yes but I'm not sure how to account for this

[timid silo]

You can do 1 - P(0) - P(1) - P(2)

[hardy drum]

Thank u

Is b)I) not just 1/5 × 0.07548?

[candid yarrow]

No, it isn’t, you have to calculate the probability of exactly 2

[obtuse pebble]

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[odd heath]

im stuck on this problem

[wooden cipher]

!show

[obtuse pebble]

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

@odd heath Has your question been resolved?

[obtuse pebble]

@odd heath Has your question been resolved?

[hybrid gull]

Read this:

[timid silo]

did you make a mistake in the differentiation?

you differentiate and equate it to zero, you get two values of x

based on that you redifferentiate put the value of x and find if f''(X) is +ve or -ve

there by you go upon

[obtuse pebble]

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[obtuse pebble]

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[clear sonnet]

How do I integrate this?

Having a bit trouble

My Initial attempt

[timid silo]

whats the main func

[clear sonnet]

but then I got stuck

[timid silo]

could you send that

[clear sonnet]

wdym

[stone spoke]

It looks like you'll have to do a u-sub instead

[timid silo]

i believe you can take out (1+y)^2 from the sqrt

[clear sonnet]

Can I cancel the sqaure root from the top?

[timid silo]

then the denominator is 1/sqrt(1-y^2) which u need to trig sub

[clear sonnet]

I can't use trig sub

oh wait

nvm I can

Is this valid?

[timid silo]

yeah

yes

but what do you sub in as t?

cosx?

[clear sonnet]

I forgot the dy

[clear sonnet]

hmm we haven't learned trig sub yet

[timid silo]

y = sin t?

then 1-(sin t)^2 = (cos t)^2

yeah doesnt matter

even if you use cosx

it anyways gets cancelled

with the dy term

y = sint

dy = cost dt

cost above below gone

it becomes 1 + sint dt

then just split and integrate

[clear sonnet]

I haven't learned trig sub yet

how would I evaluate without trig sub

[timid silo]

dude trig sub isnt hard

you know basic trig youll get it...

but i dont know the algebraic way sorry

[clear sonnet]

you're good

[grizzled shore]

Do you know how to solve $\int \frac{1}{\sqrt{a^2-x^2}}, dx$

[warm shale]

frosst

[clear sonnet]

would that be sin inverse?

[timid silo]

sin^-1 x/a id assume

its a thing to remember

[clear sonnet]

yeah

sin inverse of (x/a)

[grizzled shore]

Yes

[clear sonnet]

ik how to do that

[grizzled shore]

Ok

[clear sonnet]

what about the 1+y

idk what to do about that

[grizzled shore]

So we need to be a little clever here

[clear sonnet]

if I set u = 1-y^2

I can't split the fraction up either

[timid silo]

integral of (1+sin t) = integral of 1 + integral of sin t

integral of 1 dt = t,

integral of ( sin t )dt = -cos t if i rmb

[grizzled shore]

$\int \frac{1}{\sqrt{1-y^2}} - \frac{\sqrt{1-y^2-1}}{\sqrt{1-y^2}}, dy$

[warm shale]

frosst

[grizzled shore]

Hmm that might not work

[clear sonnet]

DId you multiply by the conjugate?

[clear sonnet]

oh

nvm then

[polar fossil]

$\int \frac{1+y}{\sqrt{1-y^2},dy = \int \frac{1}{\sqrt{1-y^2}},dy + \int \frac{y}{\sqrt{1-y^2}},dy$

[warm shale]

kitten.in.a.teacup
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[clear sonnet]

oh wait

This works right?

[polar fossil]

yeah

that's what i was trying to write but apparently forgot how to latex

[clear sonnet]

oh alright

Thanks 🙏

[grizzled shore]

Maybe you can do by parts

[polar fossil]

you don't need by parts; this is a very straightforward integral

once you have the trig thing

[grizzled shore]

But he doesn’t want to use trig

[clear sonnet]

I meant trig sub as in the method the person was talking about above where you do sin and cos or smth

but this is totally fine

[obtuse pebble]

@clear sonnet Has your question been resolved?

[obtuse pebble]

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[dry lantern]

Can someone solve this for me? I don’t understand how to do this question

[thick oracle]

we can't solve it for you

only guide you

[dry lantern]

oh alright

So this is what I get rn

do i have to add lines to make it a cyclic quad.?

[timid silo]

how do you know that angle ECA = EPA = x

[dry lantern]

Because PQ is tangent to the circle

So ECA = x

and EA = EC

so the base angles r equal?

[timid silo]

but theres no line parallel to PQ

[timid silo]

i would draw EB and use the inscribed angle theorem

[dry lantern]

Ohhhh alright

I think ik what to do now

Thankss

.close

[obtuse pebble]

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[vivid jolt]

lemme see

I maybe can do this

[vivid jolt]

800 should be 77.63% off

[fickle owl]

how did you figure that out?

maby i should increase the price a bit too

[vivid jolt]

Yes

[versed imp]

38 = (1+0.5)*19

Thus 240 = (1+x) * 38

Etc

[vivid jolt]

this is what I sis

did*

[fickle owl]

this feels like better price

[fickle owl]

ok

[vivid jolt]

what percent off do you want every of them to have

[fickle owl]

40, 55, 70, 85

[vivid jolt]

the 20 k 85?

[fickle owl]

feels like a good deal

[fickle owl]

i guess

[vivid jolt]

the 5k has a 85 percent off

[fickle owl]

oh

maby we can reverse it so the price is blank accept the "19" one and then figure out the price from the %off

[vivid jolt]

wdym

Tell me the exact %off you want for every product

also, is that for a game?

[fickle owl]

sure is

[fickle owl]

40, 55, 70, 85

[vivid jolt]

alright

[vivid jolt]

about what?

also, for what I can see seems like a roblox one if I am not incorrect

[candid yarrow]

have you made sure that the pricing of the orbs won’t make one deal completely useless

[fickle owl]

its a wierd concept but you basicly buy small people that follow you and fight, when you kill someone you gain orbs wich can be used to buy small guys wiuth powerups such as invisibility and strength and freeze and such. then you go around the world and do quest and explore. you can also buy helicopters and cars for traveling and some tools to

[vivid jolt]

for 85% off in 20k it should cost 1140

[fickle owl]

yea, ive coded on roblox for 3 years

[fickle owl]

wow

[vivid jolt]

ah, hit me up when you upload the game, I could play it

[fickle owl]

haha sure

[vivid jolt]

the 5 k with a 70 percent off would cost 1330

i dont think that makes much sense

[fickle owl]

that makes 0 sense

[vivid jolt]

you should make the price for 20 k higher

[fickle owl]

higher than 1140?

[vivid jolt]

Idk, just think about the prices you want to have, because 20 k is cheaper than 5 k

The 800 with a 55% off would cost 167

[fickle owl]

1140 / 4 = 285

how

[vivid jolt]

?

wdym

[fickle owl]

5k is cheaper than 20k cus it costs 280

[vivid jolt]

the 20k without a discount would be 7600

[fickle owl]

oh right

[vivid jolt]

with a 85 percent is 1140

so, maybe lower the discounts

[fickle owl]

5k should be 1900 without discount

[vivid jolt]

correct

[fickle owl]

hm

would this seem reasonable

[vivid jolt]

yeah, for me at least

i think

Maybe instead of 20 k you can but 10 k

[sage dagger]

roblox

[fickle owl]

ppl can just buy 5k 2 times

[vivid jolt]

ig

[fickle owl]

its hard to balance how much a player makes when playing and how long it takes with how much stuff cost

[fickle owl]

thanks for the help btw!

[vivid jolt]

np

[vivid jolt]

remember to do .close

[fickle owl]

cya

.close

[obtuse pebble]

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[obtuse pebble]

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[safe kite]

so i learnt partial fractions today, but idk how to solve the ones with quadratic denominators

A(x^2 + 1) + (Bx + C)(x + 3) = 4x + 2
i wrote the expression as one line then i tried both methods i learnt today

first method is to eliminate one variable, but if i wanted to elimate A in i would have to do x^2 + 1 = 0 which doesnt have a real solution, and idk if u can eliminate B and C since they're in the same bracket

method two i didnt use for partial fractions with linear denominators as first method is easier for me, but i tihnk its smth to do with simultaneous equations and solving it. After expanding the brackets idk what to do after, cus idk how to solve simultaneous equations with 3 unknowns.

i prob gotta use method 2 to solve this, so can someone pls give me some help for solving this?

[knotty crow]

yeah, you can eliminate B and C

at the same time

in order to find A

then you have only 2 unknowns so I guess you can proceed

[safe kite]

oh what

how

[knotty crow]

plug x = -3

[safe kite]

oh wait shoot

i didnt realise they were connected together

mb

so after you find A how do you proceed

[knotty crow]

you can plug other values of x

to get 2x2 system

[safe kite]

2x2 system?

[knotty crow]

2 equations and 2 unknows

[safe kite]

oh

alr

ok i got it thanks

lemme try one more q then ill close the channel if im fine

ok im fine tysm

.close

[obtuse pebble]

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[wanton hull]

$\int \frac{5x-2}{3x^2+2x+1} dx$

[warm shale]

bettim

[wanton hull]

it is literally up there

i dont know how to start

status is 0 or 1 (whichever is least)

[versed imp]

Looks like a partial fractions decomposition problem

[wanton hull]

i dont know it

is it that A times der. of denom + B?

no like my teacher gave me that hint

i have to solve by that way

[versed imp]

what is der ? derivative ?

[wanton hull]

$5x -2 = A \frac{d(3x^2 +2x+1)}{dx} +B$

[warm shale]

bettim

[wanton hull]

my teacher did this in class

[versed imp]

If he gave u this hint u should use identification

[wanton hull]

okay im trying

[versed imp]

But either this way I don't understand the hint, I don't see where this leads

[wanton hull]

i got $\int \frac{\frac{5}{6}(6x+2) -\frac{11}{3}}{3x^2+2x+1} dx$

[warm shale]

bettim

[wanton hull]

wait now i can split it

and u'/u = log u

lol

wait fuck i forgot how to do int(1/quadratic)

$\int \frac{1}{3x^2+2x+1} dx$

[warm shale]

bettim

[wanton hull]

complete the square?

[versed imp]

Looks like

[wanton hull]

ues tahnk i got it

<33

[versed imp]

U found it ?

[wanton hull]

yep

got it

somehow his hints works

[candid yarrow]

what did you get?

[wanton hull]

any idea what it means?

[wanton hull]

$\frac{5}{6} \log | 3x^2 +2x+1| - \frac{11}{3\sqrt{2}} \arctan \frac{3x+1}{\sqrt{2}} +C$

[warm shale]

bettim

[versed imp]

that ur teacher like to hurt you

[wanton hull]

,w integrate (5x-2)/(3x^2+2x+1)

[warm shale]

Results provided by WolframAlpha

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[versed imp]

(thats the good answer)

if i can help with a nice website : https://www.integral-calculator.com/

idk if i can post it

[wanton hull]

thanks tho

only reason i hate calculus is even if you did all the steps and get a final answer sometimes it turns out to be wrong

thanks guys

.close

[obtuse pebble]

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[wanton hull]

$\int \frac{x+2}{\sqrt{4x-x^2}}dx$

[warm shale]

bettim

[wanton hull]

how do i do this

[candid yarrow]

have you tried completing the square

[wanton hull]

yes wait ill show where im struck

$\int \frac{x+1}{\sqrt{2^2 - (x-2)^2}}dx$

and

[warm shale]

bettim

[wanton hull]

$du = 2(x-2)dx$

[warm shale]

bettim

[wanton hull]

no idea how to proceed

[high lily]

express the numerator in the form
k*g'(x) + c

[wanton hull]

what is g(x)

what is k

idk

[high lily]

g(x) is the stuff under the root

k is a constant

[wanton hull]

oh oh

ohhhhhhhhh

wait

[high lily]

that allows you to apply chain rule for one fraction
and then trig sub / integral identity for the other

[wanton hull]

i got k =-1/2

c =4

got it tahnk you bros

.close

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[cyan juniper]

I need help with b), I'm unsure what to do after I sub in what I found in A

[cyan juniper]

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[timid silo]

kind of silly question but we use the {{a}, {a,b}} definiton for ordered pair (a,b) because if we used {{a}, {b}} it would equal {{b}, {a}} so (a,b) = (b,a) and this is not true, right?

[royal basin]

that's one way to justify it yes

you need to be able to tell which element is the first and which is the second

[warm canopy]

yeah the latter has no way to distinguish an "order"

[royal basin]

that's the whole point of an ordered pair

[timid silo]

yeah thanks i was asking because previously i asked chatgpt and it said {{a}, {b}} doesn't equal {{b}, {a}} but simultaneously it said that the fact that they are equal is because we use the {{a}, {a,b}} and i got really confused 😭

[native crag]

i would be really careful asking gpt anything non computational

its good if you have no idea and it can vaguely point you somewhere

but you can literally make it say whatever you want if you phrase things right

[timid silo]

yeah ik but still deeply i have a hope that it would answer corerectly and explain things

[native crag]

apparently gpt4 is much better

but yeah its a little while off

[timid silo]

idk i think they nerfed it or something because in november 2022 it was a lot better

[timid silo]

so what's the other doe?

[royal basin]

i asked chatgpt

[timid silo]

ik 😭

.close

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[tawny kite]

Need help with understanding, in the closed under addition example, how did it go from x_1+x_2=y_1+y_2 and y_1+ y_2= 2(z_1+z_2) to the equation shown below? Is the scalar 2 being ignored and why?

[swift flume]

I’m not sure I see the equation you’re referring to where 2 is being ignored

Could you highlight it ?

[swift flume]

If you look at part 1 it shows that 0=2(0)

And that y=0

So if y = 0 and y = 2z then z must also be 0

[tawny kite]

That makes sense

so condition 1 is satisfied

we're learning subspaces btw

[swift flume]

Yep! Lmk if you have any other questions

[tawny kite]

what about condition 2? The part highlighted in yellow?

[swift flume]

So you’re just adding the two vectors

When you add, you just add straight across

[tawny kite]

is there an example where the two vectors cant be added together?

[swift flume]

I think the only instance would be when you’re talking about different variables? If you think about a vector 3-dimensionally, you can’t add y length to an x length. You can only add y to y

I’ll write out an example

You can kind of think about it as adding but vertically

[tawny kite]

no like i get that, i mean an example thats asking if a set is in a subspace or not

and the vector addition doesnt work

[swift flume]

Ohhh

[candid yarrow]

the third one is incorrect

[swift flume]

Oops

[tawny kite]

i was gonna say that too

cause you cant add 2x1 with 1x1

[swift flume]

I should’ve put a 0

[candid yarrow]

the second element of the third equation is not a member of the vector space that the first one is

[candid yarrow]

do you mean like all vectors (x,y,z) where x + y + z = 1?

try proving/disproving this is a subspace

[tawny kite]

can you show what you mean by that?

I understand condition 1, where theres no 0 vector

which already proves that its not a subspace

but can you show how condition 2 works, where S is closed under addition.

[candid yarrow]

can you show your understanding of it?

[tawny kite]

you have to use two vectors and add them together... smth like that

[candid yarrow]

the first two are given, the third statement is what you want to prove or disprove

that’s because the first two come from the definition of the set and the third comes from the condition required to be a subspace

[tawny kite]

ok, so how can I prove or disprove?

[candid yarrow]

can you see what the sum of the components of the two vectors’ sum is?

[tawny kite]

You mean just add them?

[candid yarrow]

why did you get 0 = 1? can you add sentences in between the equations that describe what you’re doing?

[tawny kite]

oh um no I just got 0 on the left side and 0=/=1, i was too lazy to erase it lol

[candid yarrow]

Can you add sentences in between the equations that explain what you’re doing, as if you were writing a proof?

[tawny kite]

ok

[obtuse pebble]

@tawny kite Has your question been resolved?

[tawny kite]

please let me know if im doing it completely wrong

[timid silo]

can anyone help me with math

[obtuse pebble]

@tawny kite Has your question been resolved?

[obtuse pebble]

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[rain loom]

question b

[frosty spoke]

hmmm so if you're told the mode is 29

since there are no other modes, you know that at least one of p, q, r has to be 29

jeez this is annoying to do

my best guess would then be working on the median

probably can exclude p = 29 because it would push the median away from 28

and since this has an even number of things

you know that the median is going to be an arithmetic average of things

and to make 28 from 29, you need a 27

oh

that solves it doesn't it

[polar fossil]

[sour ether]

Should it be solved by forming equations?

[obtuse pebble]

@rain loom Has your question been resolved?

[frosty spoke]

actually is the solution even unique

oh I think it does have to be

because the only other cheap trick you can do is make p, q noninteger, but that's no good because then that means r has to be 29

and then you're toast because you can't make the mean line up

[obtuse pebble]

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[rancid cliff]

idk how to continue

could someone kindly help me

thanks 🙂

[frosty spoke]

oh you're asking how to integrate 1/sqrt(t) dt?

just write it as t^(-1/2) and use the power rule

didn't check the rest of the work though

[rancid cliff]

$-\int \frac{1}{2}t^{-\frac{1}{2}}dt$

?

[warm shale]

Chuti | Spanish

[polar fossil]

yeah

[rancid cliff]

actually

$-\frac{1}{2}\int t^{-\frac{1}{2}}dt$

[warm shale]

Chuti | Spanish

[rancid cliff]

but still I dont get the same result

[polar fossil]

those are equivalent but yeah

what do you get?

[rancid cliff]

tbh

I'm stucked

there

[polar fossil]

how would you do like $\int 7x^4 dx$?

[rancid cliff]

shouldnt it be (t^1/2 )1/2

nvm

idk what to do

I'm blocked

[polar fossil]

t^1/2 is the right exponent

[frosty spoke]

u have learnt how to become a tech employee perpetually on vacation

[rancid cliff]

is this right?

[polar fossil]

yeah that's correct so far

[rancid cliff]

ok then thats t^-1/2

[polar fossil]

so when we integrate we add 1 to the power and then divide by the new power

[rancid cliff]

yes

[polar fossil]

divide by the new power (which is 1/2)

[rancid cliff]

aaaaaah

there you go

would be like this

then I replace t with what I wrote t was

and add C

ok cool

yeah I'm still learning just started yesterday

[polar fossil]

[rancid cliff]

Thanks for your help

[polar fossil]

and you can replace that with $\sqrt{t}$ if it looks nicer

[warm shale]

Hayley

[polar fossil]

well, negative sqrt t

[rancid cliff]

correct

💯

awesome

Thanks a lot

[polar fossil]

por nada

[rancid cliff]

I'll keep on studying

[rancid cliff]

de nada in Argentina 😛

[polar fossil]

es? oh se spanglish mexicano

[rancid cliff]

🤣

😄 good

Muchas gracias

[rancid cliff]

,rotate

[rancid cliff]

and what about this?

is that correct?

I'm trying with another t to practice

[polar fossil]

that's funny that that works but yeah it should, now what's your new integral?

(please don't forget the dx in the original integral)

and in your equations on the right

[rancid cliff]

u right

ok lemme see

sending the progress haha I think I'm dealing with chinese or something

hopefully I get what I'm doing this weekend of 5 days

[polar fossil]

that wasn't substituted properly

look you have $dt = \frac{x-6}{\sqrt{x^2-12x+1}},dx$ right?

[warm shale]

Hayley

[rancid cliff]

yes

[polar fossil]

solve that for dt and then make that substitution first

rather

solve that for dx

[rancid cliff]

isnt this correct?

So that I replace -x+6 with the result of the left

[polar fossil]

you need a clean cutover from x to t

[rancid cliff]

so I also pass the -x+6 ?

[polar fossil]

oh you know what you can do

you have $t = \sqrt{x^2-12x+1}$

[warm shale]

Hayley

[polar fossil]

so in that eqn you can make the left side -dt/t

[rancid cliff]

why? 🤔

[polar fossil]

so that when you make the substitution you're not mixing t's and x's in the integral

you'll have only t's

and dt

[rancid cliff]

sorry I still dont understand why this is wrong? our goal is to put everything in terms of t

[polar fossil]

and this doesn't have everything in terms of t

[rancid cliff]

ouch

🤣

wait

-dt/t

🤣

hahah

okay

[polar fossil]

yeah

[rancid cliff]

sorry mb

[polar fossil]

nw

wait where'd that other t even come from 💀

[rancid cliff]

it would be t^2

cause of this

I'll send a pic

[polar fossil]

yeah i found it

[rancid cliff]

$-\int \frac{1}{t^2}dt$

[warm shale]

Chuti | Spanish

[polar fossil]

i think that sqrt thing is supposed to be in the numerator

because what you should end up with is $\int -dt$

[warm shale]

Hayley

[rancid cliff]

the result is -t + c I think

I obviously replace t

[polar fossil]

yep

[rancid cliff]

$-\int t^{-2}dt$

🤔

[warm shale]

Chuti | Spanish

[rancid cliff]

this doesnt look right

I think

[polar fossil]

yeah that's not right

go back to your dt/dx calculations

[rancid cliff]

I did something... wrong.

I'll start all over again

and do it in order

shouldnt take much time

[polar fossil]

sure, start with $t = \sqrt{x^2-12x+1}$

[warm shale]

Hayley

[polar fossil]

differentiate both sides and keep the dx's around you can treat them just like any other variable

[rancid cliff]

ok this would be the first step, I assume its correct

[polar fossil]

t does not equal anything dx, it just equals a function of x

the dx comes from taking the derivative

(sorry i know this feels silly to worry about but it makes the math make more sense)

otherwise yeah that's right

[rancid cliff]

not sily at all, my proffesor says all of this is important

[rancid cliff]

I feel I'm near

[polar fossil]

i mean you've got it

[rancid cliff]

yeah so int of dt is t

[polar fossil]

yeah

[rancid cliff]

so I replace and end of story

ok

cool

😄

[polar fossil]

what you've done there

[rancid cliff]

👏

[polar fossil]

was basically guess the integral with your choice of t lol

[rancid cliff]

did I ?

I feel like I followed a mathematical process

[polar fossil]

i mean you did and it was sound!

[rancid cliff]

I did this mechanically

haha

[polar fossil]

but yeah scratch out that dx at the end of the t = .... line

[rancid cliff]

💯

okay

gotchu

I can now say I finished this excercise 🤣

Thanks again

[polar fossil]

[obtuse pebble]

@rancid cliff Has your question been resolved?

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[tulip kestrel]

!status

[obtuse pebble]

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

[split breach]

1

[split breach]

1

[somber marten]

If you can use a calculator to find the sin it's possible to answer by this way

[split breach]

thank you

.close

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[tight wave]

hello could someone explain how you get P(Y<=6) and P(Y>12)

i understand getting Y ~ Po(9) but not how you change them to that

since they usually just give it to you in the questions

[mild harness]

wdym

[tight wave]

like in the next one they do

[obtuse pebble]

@tight wave Has your question been resolved?

[tight wave]

the topic is poisson approximation

a level further stats 1

[tight wave]

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[safe kite]

whats the first step to simplfying this

[timid silo]

try pulling out something from the top

so that the top and bottom become the same

[safe kite]

can you factor 2^n+1 from the top to get 2^n+1(1 - (2^1))?

or -2^n+1

[timid silo]

you factored the wrong thing

[safe kite]

o

[timid silo]

try pulling out -(2^3)

because 2^(n+2) differs from 2^(n-1) by 2^3

[safe kite]

oh

uhhh would it be something like -2^3 * { 2^[(n+1)/3] + 2^[(n+2)/3 }?

[timid silo]

you need to send the latex script as its own message

i think

[safe kite]

idk how to use latex yet

[timid silo]

when you pull out 2^3, the exponent decreases by 3

not divides by 3

[safe kite]

oh

[timid silo]

you only divide the exponent when there are fractional exponents or radicals

[safe kite]

ok so its -2^3 * [ -2^(n-2) + 2^(n-1)]?

ohh then you cancel that from both sides right

[timid silo]

yes

[safe kite]

so -2*3 = -8

ok thanks

[timid silo]

.close

[obtuse pebble]

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[frosty spoke]

you finally found a use for generating functions

[mild harness]

how

[frosty spoke]

oh wait N is not independent of the Xs uhhh

[mild harness]

i dont even know how to approach

first of all how do we know its not independent

i thought it was iid

[frosty spoke]

well N depends on the X_is

I think Wald's equation might work?

[mild harness]

whats that

should i skip this problem

like is it brurtally bad

[frosty spoke]

something something from stochastic processes that lets you transfer the E inside the sum

[mild harness]

brutally

[frosty spoke]

Not sure how you would compute the distribution of N though

well maybe it is computable actually

you might be able to compute some cumulative distribution of N

[obtuse pebble]

@mild harness Has your question been resolved?

[obtuse pebble]

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[quasi harness]

Hello

need help please

can you please check my work

[obtuse pebble]

@quasi harness Has your question been resolved?

[obtuse pebble]

@quasi harness Has your question been resolved?

[candid yarrow]

your functions look right

[candid yarrow]

the first part of your justification is wrong, f(x) is not that

[obtuse pebble]

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[long hedge]

how do you do this without a calculator ?

[long hedge]

i subtracted 360 7 times from 15 times 180

are you supposed to do that without a calculator

[nocturne minnow]

As a suggestion, if it gives you a value in terms of pi, it's best to keep it in pi

[long hedge]

and solve it how

[grizzled shore]

What’s sin 0

[long hedge]

0

[grizzled shore]

What’s sin pi

[long hedge]

0

15 x 0 = 0

https://tenor.com/view/door-disassembly-door-breakdown-breaking-door-door-gif-20313531

[grizzled shore]

That’s not how it works

sin(ax) ≠ a*sin(x)

[long hedge]

ok then how

[grizzled shore]

So sin 0 is 0

sin pi is 0

What’s sin n*pi for any integer n

[long hedge]

idk

[grizzled shore]

Ok if I tell you sin(3) = k

What is sin(3 + pi)

[long hedge]

k + pi

[grizzled shore]

No!

sin(a + b) ≠ sin(a) + b

What do you know about the sine function

[long hedge]

y

[long hedge]

hello

[grizzled shore]

What’s y

[long hedge]

sin

[grizzled shore]

What about sin

[long hedge]

sinx

[grizzled shore]

What are some properties of the sine function

[long hedge]

sin(theta+2pi)=sintheta

[grizzled shore]

What about sin(theta+4pi)=sintheta

[long hedge]

yes

[grizzled shore]

What about sin(theta+15pi)=?

[long hedge]

no

[grizzled shore]

What no

[grizzled shore]

What does it equal

[long hedge]

it has to be even right

[grizzled shore]

What does adding 1 pi do

Instead of 2

[long hedge]

180

[grizzled shore]

What is sin(θ + pi)

[long hedge]

180

0

[grizzled shore]

What is sine, where did this function come from

[long hedge]

so 12pi + 3pi = 180

[long hedge]

i already said sin is y

[grizzled shore]

Sine is not y

[long hedge]

do ppl realize playing the guessing game doesn't help us learn

[grizzled shore]

Consider the unit circle

If we go some angle θ

That red dot

[long hedge]

sine is the y value of the point

[grizzled shore]

It has the coordinates (cos(θ), sin(θ))

Ok that’s what you meant

[long hedge]

can we get to the point of finding the exact value idk what this detour is

[grizzled shore]

You didn’t say about the y value of a point

So if we go around pi radians

Whats the y value of this green dot

[long hedge]

so pi 1= 180 if you go around pi 14 times you are at 0 degrees (7 times 360)= 14 x 180)
if we have 15 pi you just need to add 180 once to get to 180 degrees sin180 = 0

[grizzled shore]

Yes

[long hedge]

wow thats actually genius

[grizzled shore]

That’s correct

But also, sin(pi) = -0

[long hedge]

???

[grizzled shore]

Or sin(θ + pi) = -sin(θ)

[long hedge]

this is 15 times pi

[grizzled shore]

Yes

But 14 of them get you to the same place

sin(θ + 15 pi) = sin(θ + pi) = -sin(θ)

[long hedge]

the answer is 180 not -180

it gets to the same point anyway ig

[grizzled shore]

The answer is 0

Which is the same as -0

Which is the point

[long hedge]

how did you get rid of the 15

[grizzled shore]

sin(θ + 2pi) = sin(θ) right?

[long hedge]

sin(θ + 16 pi) = sin(θ) = -sin(θ)

^ this is right ?

[grizzled shore]

First 2 are right

Idk where you got sin(θ) = -sin(θ) from

[long hedge]

wow so i literally explained it to myself here while you expected me to magically know what you know

[long hedge]

.

[grizzled shore]

That doesn’t have 16 in it

[long hedge]

oh sin180 = sin-180

[grizzled shore]

No!!!

Wait yes

[long hedge]

i am a better teacher than you💀

[grizzled shore]

You’re swapping to degrees and not having brackets

[long hedge]

ok i have it now

[grizzled shore]

But either way, you go 7 times around

Then 1 time to the other side of the circle

But since you’re at 0, the opposite side is -0 which is still 0

[long hedge]

.close

[obtuse pebble]

Channel closed

Closed by @long hedge

Use .reopen if this was a mistake.

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[halcyon linden]

show that there are no $x$ such that $103|(x^3 - 2)$

[warm shale]

brunood

[halcyon linden]

i tried writing $x$ as $x^3 = 103k + 2$

[warm shale]

brunood

[halcyon linden]

but that lead me nowhere

i dont need the answer right away if there are any tips or important theorems i should know thats already good help

[royal basin]

so your goal is to show that x^3 can never be congruent to 2 mod 103 huh

[halcyon linden]

yea

[royal basin]

hm

[halcyon linden]

i had similar questions before but the modulus wasnt prime so it was easier bc you could factor

[royal basin]

i don't see a way other than brute force at the moment

[somber marten]

x has to be integer?

[halcyon linden]

yep

[royal basin]

of course it does

[polar fossil]

Legendre symbols might save you some computation maybe? idk that's for squares not cubes

[somber marten]

You have to show that $103k ≠ x^3 - 2$?

[warm shale]

arthur1102

[halcyon linden]

ig so but it would be more showing that there are no integer k that satisfies it

so maybe induction could work?

[wooden cipher]

Mod 9 and some other mod probably

[halcyon linden]

the one i did before was to show that there are no integer $x$ such that $x^2 \equiv 35 \mod 100$ and you did that with a contradiction, tldr $100|x^2 - 35 \implies 5|x \implies 25|x^2 \implies 25|35$ (contradition) but i cant see a way i can do that here since 103 and 2 are prime and obviously share no factors

[warm shale]

brunood

[obtuse pebble]

@halcyon linden Has your question been resolved?

[royal basin]

hmm

i have an idea but it is kind of heavy-duty and group-theoretic

the group of units of Z/103Z has order phi(103) = 102 = 2 * 3 * 17