help-39

[gusty prism]

hello

this question i make a solution

good or bad

[maiden hatch]

Looks good!

[gusty prism]

Nice thnx so much

[pearl pond]

@gusty prism Has your question been resolved?

[pearl pond]

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[gusty prism]

Some pls help

Like i know how to get the vertex

but how did the equation go from -2(x-1)^2+3

to -2x^2

and thnx

[midnight haven]

what's $(x-1)^2$

[jolly parrot]

pulse

[gusty prism]

aaahh

x^2+1

o

mb

x^2-2x+1 ok

help pls some1

[cursive wraith]

can you link to this video? I would like a bit of context

[gusty prism]

Sure

https://www.youtube.com/watch?v=UKkOAbz0UPE&t=860s

he does this around

12:15

NVM

The guy in the video gives no context or formula himself i n my opinion idk tho

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[mystic pawn]

how can i verify that

[mystic pawn]

oop the negative

[old marsh]

what have u tried

[mystic pawn]

i tried putting cos x - sin x as the numerator and eliminating the bottom sin x

[old marsh]

show ur work

this is essentially a 1 step manipulation, and then some identity usage

id recommend getting the entire left side into 1 fraction

[bold wagon]

did u try to multiply the first part by sin(x)-cos(x) ad the second by sin(x)+ cos(x)

[mystic pawn]

i have not actually

[bold wagon]

u'll get cos(x)sin(x)-cos^2(x)_sin^2(x)-cos(x)sin(x) i believe

[old marsh]

let them do the work elena

but yes bleeder, you want to get a common denominator on the left

[mystic pawn]

hmmm alrightyo

[pearl pond]

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[pearl pond]

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[agile parcel]

how does this work

[agile parcel]

the seperate the powers and write as a systems of linear equations

[plucky nebula]

Is this for partial fraction decomposition

Also, what they are doing is equating the coefficients due to poly equality

[pearl pond]

@agile parcel Has your question been resolved?

[agile parcel]

yea

i figured out their reasoning tho

[pearl pond]

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[agile parcel]

.reopen

wait no

[pearl pond]

✅

[agile parcel]

why are they seperating it into systems of equations

[plucky nebula]

To solve for the constants

[pearl pond]

@agile parcel Has your question been resolved?

[agile parcel]

but like why does it solve for the constants how do you know it works out

[plucky nebula]

You solve for the constants by solving the system of equations and in all cases you will be given all the relevant info in order to solve them

[agile parcel]

i know what it does

[plucky nebula]

Why do you want to solve for the constants?

Is that your question

[pearl pond]

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[midnight haven]

Hello

[long herald]

post your question @midnight haven

[midnight haven]

I don’t understand it at all

[long herald]

then you need to learn interest continuous compound function

[midnight haven]

I already did it thanks

I just lost brain cells

Over the break

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[regal ore]

i need help

[regal ore]

can someone explain how is cardinality of Natural numbers the same as Real numbers?

why is #(N)=#(Q)?

isn't cardinality number of elements in the set?

[vestal tapir]

Q is rational

cardinality is considered the same if you can do a bijection

so like even though there's "more rationals", multiple rationals per natural, they are considered equally large infinities

[pearl pond]

@regal ore Has your question been resolved?

[regal ore]

so you mean u cant do a bijection between N and R?

[vestal tapir]

yeah

only rationals are the same cardinality, reals are larger

i don't understand it beyond that

[regal ore]

weird, doesn't make sense, but it is what it is I guess

[cinder flower]

where’d ya hear that?

[regal ore]

Well I was studying set theory

then I encountered Continuum hypothesis

it said that there is no set A such that #(N)<#(A)<#(R)

so while further research in internet,

I encountered this.

#(N)=#(Q)

[cinder flower]

so wait i don’t understand, was there a typo here or smth?

[regal ore]

I was just asking if cardinality of both Naturals and reals is same there

[cinder flower]

oh

ic

[regal ore]

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[icy patrol]

$\alpha$ of an angle is 3 radians. which one is correct ?
a. $\sin(\alpha) < \tan(\alpha)$
b. $\sin(\alpha) < \cos(\alpha)$
c. $\sin(\alpha) > \tan(\alpha)$ or $\cos(\alpha)$

[jolly parrot]

Bunnings

[glacial sequoia]

Do you know how much 1 radian is approximately in degrees?

[icy patrol]

i think c correct

yes, 3 rad is 171 deg

[glacial sequoia]

,w 3 rad to degrees

[jolly parrot]

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Requested by NEONPerseus#2128

[glacial sequoia]

alright

[icy patrol]

sine is positive in second quadrant and tan and cos negative right ? so c correct ?

[glacial sequoia]

yup seems right

[icy patrol]

thanks.

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[tulip cradle]

guidance on how to start this?

[pearl pond]

@tulip cradle Has your question been resolved?

[serene wave]

the trick is dealing with the k^2 after factoring out a k
try to do some kind of +constant -constant trickery

you'll end up with a situation where at least one factor must be a multiple of 3

[tulip cradle]

ok thx

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[civic cliff]

Would like help on finding the maximum and minimum values

[keen marlin]

What is the max and min of the sin function?

[stuck crow]

^

[civic cliff]

Like for the y and x?

Cause the y for the max would be 4

[stuck crow]

no

just

[civic cliff]

And the min for y would be -4

[stuck crow]

a normal sin

[keen marlin]

What is the maximum and minimum value for the sin function in general

In other words, what is the maximum y and minimum y value u can achieve for a given x

[civic cliff]

Would it be negative and positive 2?

[keen marlin]

Well, for this question yes.

[fleet sky]

bingo

[keen marlin]

But I was asking u in general...

[civic cliff]

Well in general it would be the a value

[keen marlin]

No..

[civic cliff]

Ow dang

I’m stupid :/

[keen marlin]

The max of the sin function is 1

and the min is -1

It doesn't not matter what is inside of the sin function. And since the entire thing is being multiplied by 2, u know that the max and min of this given function is 2 and -2

[civic cliff]

Doesn’t that apply if there’s no vertical translations happening

Like for the 1 and -1

Doesn’t that only apply if the sin function has no vertical translations

Like a stretch or shrink

?

[pearl pond]

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[little wave]

How would I go about taking the limit of this to find if it conv or div

[little wave]

n - (n^2 - 2n)^1/2

I assume you take out an n^2 to get this

n - n(1 - 2/n)^1/2

But that still leave an indeterminate form of inf - inf

[ember cloak]

Multiply and devide by n+sqrt(n^2-2n)

[little wave]

What do you mean

If you mult and div by the same thing doesn’t it just cancel out

[ember cloak]

Yes, you multiply by 1, so it doesn't change the limit. But it helps to transpose this term into a fraction that you can handle (using 3rd binomial formula)

[little wave]

Ok .close

.close

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[iron epoch]

i completely am stuck on this

rule is m<p= (wz-xy)/2

[stuck crow]

well what did you try

[iron epoch]

i literally dk where to even start

[stuck crow]

can you find ZWX

[iron epoch]

i know wzy=200

wxy=160

but idk zwx

<@&286206848099549185>

[pearl pond]

@iron epoch Has your question been resolved?

[pearl pond]

@iron epoch Has your question been resolved?

[pearl pond]

@iron epoch Has your question been resolved?

[pearl pond]

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[midnight haven]

how do i go from the first part to the 2nd part?

[regal elm]

multiply both numerator and denominator by $\sqrt{x^2+1}$

[jolly parrot]

Micni9

[midnight haven]

tysm

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[midnight haven]

how to they get to the 2nd step?

[tulip ember]

take common x2 from the root

aand take it out of the root

and cancel it from numerator

[midnight haven]

oh i see

and how is it |x| from sqrt(x^2) and that is somehow positive for inf and negative for -inf?

[pearl pond]

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[trim knot]

Little confused on what to do atm

I'm thinking making the sin/cos and cos/sin into tan and cot

But that feels like it's wrong

[feral sedge]

i think combine the fractions

[trim knot]

so sin times cos/ cos times sin?

[blissful abyss]

thats not how math works

do this and see what happens

[trim knot]

Got that by doing that, trying to figure out what to do next

Stuck atm once again smh

[blissful abyss]

alright

do you know some trig identities?

what is sin^2 + cos^2

[trim knot]

1

[blissful abyss]

yup nowwww continue

[trim knot]

1/cos times sin?

[blissful abyss]

yup now manipulate that into one of the answers

[trim knot]

i looked at the answer key because I thought I had it and was wrong, it's supposed to be sec csc

just confused on how to get that

i somewhat see why but not fully

[blissful abyss]

because 1/sin = csc, 1/cos = sec, therefore 1/sincos = sec csc

you basically just rewrite it with identities

[trim knot]

that's what I was thinking

I just thought it was wrong at first

[blissful abyss]

well you got it! be more confident haha

[trim knot]

yup! thank you!!!

I'm finally grasping these lol

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[rustic arrow]

Could I get help solving some word problems. Such as : Lina Chen invested $24000, part at 8% and the rest at 7.2%. How much did she invest at each rate if her income from the 8% investment is two thirds that of the 7.2% investment.

[brisk pike]

What have you tried??

[rustic arrow]

Nothing yet

Im pretty lost

[brisk pike]

Okay..well let the part she invests at 8% be $x. Can u tell me what part she invests at 7.2%?

[rustic arrow]

Would it be ($-$x)

[toxic lichen]

($-$x)??

[brisk pike]

Huh??

[rustic arrow]

Aw man

[toxic lichen]

did you yourself understand what you meant or did you throw together symbols randomly and hope for the best

let x be the amount in usd invested at 8%
then what's the amount invested at 7.2%?

[rustic arrow]

I mean I saw $ and thought total money and then saw x and thought that’s the percentage of interest

[toxic lichen]

incorrect

you didn't read what itzkraken2 said

try not to react to only individual symbols like that...

[rustic arrow]

Ok let me try again

Would it be 24000-x

[toxic lichen]

indeed.

ok, now

the investment of x dollars at 8% interest

what is the interest that it gains?

[rustic arrow]

0.08x?

[toxic lichen]

indeed.

and for the other investment?

[rustic arrow]

0.072(24000-x)

[toxic lichen]

great

do you understand how to proceed

[rustic arrow]

No

[toxic lichen]

what are you told about the relationship between the interests from each investment

[rustic arrow]

That one is 2/3 of the other

Specifically 0.08x * 2/3 = (24000-x)0.072

[toxic lichen]

other way around

0.08x = 2/3 * 0.072(24000-x)

do you understand how to proceed from here?

[rustic arrow]

No?

[toxic lichen]

this is a linear equation

do you know how to solve linear equations?

[rustic arrow]

Wait do I use .08x = 2/3 * 0.072(24000-x) to solve for x?

And then plug it in

To the other expressions

[toxic lichen]

0.08 not .08
but yes... you solve for x, which is one of the two values you are asked for.

[rustic arrow]

Ok so the 7.2% investment is 1080 and the 8% investment is 720

Wait no no no

The amount invested at 8 would be 9000

And the amount invested at 7.2 is 15000?

It’s late I gtg just gonna hope that’s right

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[tight flint]

hi, this is a calculus problem. My answer was 48950 (no decimals), would it be D?

[pearl pond]

Please don't occupy multiple help channels.

[tight flint]

am i suppose to divide by 100

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[quartz path]

hey im learning about simpsons rule and im curious on how somebody recognized, (1/3)h(2ah^2+6c), was also equal to (1/3)h(x_0+4x_1+x_2)

it seems like a completely random jump that, while 100% equal, would be very difficult to find if there wasnt some step that helped the rule creator see this pattern, so is there an intermediate step that im missing that somebody else recognized or is it really just a random jump?

[limber oasis]

see at something like 6 or 7 minutes
https://www.youtube.com/watch?v=ckSMWYOq6Pw&ab_channel=EddieWoo

it just comes from looking at how the polynomial is found

with enough experience it's quite easy to spot

[quartz path]

alr

ohhh yeah that actually does make a lot of sense

yeah i do see if you were to try to solve for the A and C that it comes natrually you plug in the h -h and 0 to a quadratic

then solve it like a system of lin equations

but then there is a very obvious similarity in the 3 systems to the area under the curbe

that makes sense, thanks for the help!

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[lone belfry]

why did it become x^2k+1 and not just x^2k

[wind wigeon]

because it changed from k = 0 to k = 1

as the start of the summation

[wet osprey]

There’s a 2 at the front of the k

[lone belfry]

OH

[wet osprey]

The k+1 sub gets multiplied by 2

[lone belfry]

and then it dstributed

ohhhhh thanks

[wet osprey]

Yeh

[lone belfry]

yea ik

alright thanks

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[midnight haven]

how do i prime factor this in a parenthesis

[midnight haven]

Can you send the whole question just in case?

That is the entire task, just to factor it

Sure but if you know that that means they told you

Meaning it must be written down somewhere

And while I'm 90% sure I know what "to factor it" means this is not what it is typically called

So if you could send a screenshot of the whole question so that I can avoid saying something stupid that would be great

my bad, i mean solve it by factoring

[autumn fossil]

that sounds even worse tbh

[midnight haven]

Again that's not what it's typically called, you can't solve a fraction

I insist, please send a screenshot of the whole question

Ah, much better

Basically "simplify these fractions"

yeah

Start with the x^2/x^3 part

Simplify this down

x*x/x*x*x

or 2x/2x*x

Hmmm no

x*x is not 2x

i meant x^2

x+x is 2x, x*x is x^2

x^2/x^2*x

so x^2/x^2*x

16/20x

Indeed, now you can do the same for the 16/20 part

4*4 / 4*5*x

4/5x

i was really over complicating this one

Once one points out that (16x^2)/(20x^3)=(16/20)(x^2/x^3) it becomes trivial

it really did, thank you

You can now close this channel by typing .close, unless you have more questions

thats it thanks

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[tepid ingot]

How would I do this

https://gyazo.com/deb255d1402f1f71fe155f4dfe44ea0e

[tepid ingot]

I understand the first one but the second is not 45n?

[viscid sierra]

45n is wrong

[tepid ingot]

But why

[midnight haven]

Because the expression is not properly simplified

[viscid sierra]

we multiply (n+9) by 5

[tepid ingot]

n+9 = 9n

[viscid sierra]

no

is 5+9=5*9

[tepid ingot]

Im confused sorry

Can you simplify that please?

[viscid sierra]

5(n+9)=5n+45

[tepid ingot]

Ohh ok

I understand

the 5 goes to N

9x 5 = 45

so

5n+45

Thanks

.clsoe

.close

[pearl pond]

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[tepid ingot]

How do I do angles?

https://gyazo.com/bd7ea4344ca41a66b8674e808cb39a03

[tepid ingot]

I struggle on these a lot

Thanks

[spice fable]

what must the angles in a triangle add up to?

[light helm]

recall basic properties of a triangle

[tepid ingot]

180

[tepid ingot]

Ok

2x+3 = 6x

I believe

[light helm]

why are you setting 2x+3 equal to 6x

[spice fable]

you have the measures of all three angles no?

[tepid ingot]

Im not sure

[light helm]

where's 6x coming from

don't do random things

[tepid ingot]

2x 6

Ok

[tepid ingot]

I got all angles written but in a format

[light helm]

there should be clear justification for what you're doing

[tepid ingot]

https://gyazo.com/627985dd28469e167fbecc04725a002e

[spice fable]

yes

[tepid ingot]

And it

tell me

https://gyazo.com/abaa765324820104e84418e108fd9154

[light helm]

recall basic properties of a triangle

[tepid ingot]

That I must show that the triangle is not right angled

[light helm]

specially what do you know about the angles of a triangle

[tepid ingot]

So a triangle is 180*

[spice fable]

Can you find x?

[light helm]

the interior angle sum is 180°

set up an equation that represents that

[tepid ingot]

180* divided by 3 would make

[light helm]

no

bad

[tepid ingot]

60

[light helm]

useless here

[tepid ingot]

Wait why

[light helm]

well you aren't told that the triangle is equilateral

[tepid ingot]

Thats right

[light helm]

you're not even given any indication that one of the angles is 60°

all you are given are expressions for the angles

the interior angle sum is 180°
set up an equation that represents that

[tepid ingot]

Im tapped in the head

I dont understand

Sorry

[light helm]

do you know what sum means

[tepid ingot]

resutl

result

Like end value

[light helm]

no

[tepid ingot]

oh

[light helm]

not specific enough

[tepid ingot]

The value after adding two diffrent values together

[light helm]

getting close but inaccurate

values don't need to be different
and you can have the sum of more than two things

[tepid ingot]

Yes tahts true

The sum is the value of adding two values which equates to the end value

[light helm]

and you can have the sum of more than two things

you have expressions for the three angles,
what's their sum

[tepid ingot]

https://gyazo.com/627985dd28469e167fbecc04725a002e

(5x=8)

[light helm]

no

[tepid ingot]

oh

[light helm]

5x isn't equal to 8

[tepid ingot]

No im writing them down

[tepid ingot]

Oh

Welllll

.close

[pearl pond]

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[opal forge]

How to calculate it, i didn't understand the sum step

[vagrant narwhal]

here's how

that's the sum

if you look at each column, you can sum it

[opal forge]

How to sum it up?

You meant geometric progression

[pearl pond]

@opal forge Has your question been resolved?

[sharp quest]

,w sum from n=0 to infinity 1/2^n

[jolly parrot]

Results provided by WolframAlpha

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

Requested by Zybikron#5611

[viscid sierra]

Its an AGP

Use GP formula from here to find the answer

[pearl pond]

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[weak surge]

is this always a good place to start? find the domain of both functions first

if I am looking for f(g(x)) does my domain need to satisfy ONLY the new function (f(g(x)) and the inner function g(x)?

technically this is all correct? or am i making a mess out of things?

[torn shell]

ye it seems a bit odd just do (x+1)/(x+2)+(x+2)/(x+1)

also they are not asking for trhe domain of f(g(x))

[pearl pond]

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[trail burrow]

How can I find the limit as (x,y) --> (0,0)?

[forest dew]

two path test

[trail burrow]

wait, wdym

[forest dew]

google it

[trail burrow]

I see, thx

.close

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[opal forge]

Is there any other method? I didn't understand it properly

[grave inlet]

Hi I overall just want to clarify whether my explanation to B is correct,
although i have written that tan(64pi/4) = 1, I believe that is incorrect because when you look at that value on the unit circle it just stays in the same position. Therefore, it is equal to 0 as you don't move from the original position.

[opal forge]

What you did with 16?

[grave inlet]

that is something else dw

[opal forge]

What?

You have removed 16 without any reason

If you convert it simply into degree it's value of 2 pie and it will be zero

[pearl pond]

@opal forge Has your question been resolved?

[pearl pond]

@opal forge Has your question been resolved?

[pearl pond]

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[midnight haven]

can someone explain how i works and, cause i was told it's sqrt(-1) and that, iirc, isn't even a real number. idk how one would use it or even put on a numberline

[jolly olive]

i is just an imaginary number i believe

it cant be used on a number line from what i know

[autumn fossil]

It isnt on real number line

it's on something called complex plane

[midnight haven]

wtf-

why is it 2d now 😭

[autumn fossil]

because you introduced another unit

[midnight haven]

how would i ever use that

[jolly olive]

what in the world

lmfao

[plush bramble]

science

[midnight haven]

what next a 3d number whatever 😭

number cube or smth

[autumn fossil]

quaternions iirc

but they're 4d

[midnight haven]

i-

oh

4d 😭

alright thx

.close

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[weak surge]

domain is all real numbers, but for asymptotes, i thought that would involve rationals, even roots, or logarithm arguments?

alright we're good

.close

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[keen wedge]

hi, i need help with statistics. how do i use a z-table to find the critical region?

[keen wedge]

i've done everything except the critical region because i really don't understand how to use a z table haha

[burnt knot]

u and me are in the same boat brother

I need to learn this shit too

[keen wedge]

haha

i could help you with stuff, just not the critical region stuff

we're learning t tables as well

[burnt knot]

do u get a graphing calculator on the test

[keen wedge]

i assume so? i also hope we get tables and stuff

ohh i dunno about graphing calculators

[burnt knot]

then u can use smth called inverse z

it gives it for u

[keen wedge]

inverse z? ooo

[burnt knot]

without using the tables

[keen wedge]

how do you do it

[burnt knot]

let me grab my calculator

On a ti-84

[keen wedge]

i have a scientific calculator

[burnt knot]

oh shit

I dont think it works then

[keen wedge]

ohh erm

i can just use a website for now

[burnt knot]

do u have a "distributions" button

[keen wedge]

i don't see one

but do you know how to use the tables?

[burnt knot]

yah

send me a pic of yours

[keen wedge]

okay for this we should use an example from my workbook so we know the answer

[burnt knot]

k

[keen wedge]

just so we know for sure we're doing it right

[burnt knot]

yah we might have diff tables

my stat teacher is a little out of it

but if they're similar I can probs help

[keen wedge]

damn "out of it"? is ur teacher ok

[burnt knot]

he's just uhh special

lol

A little bit of an idiot

[keen wedge]

dang..

sorry just a moment

so this is the example

so i just need to use the table to find "-1.645"

i just don't know how to do that

we're using this table

https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf

@burnt knot sorry it took so long to load !!

[burnt knot]

Oh ur good I just got banned from my college's discord for the stupidest thing 😭

[keen wedge]

WHAT

anyway do you know how to use a z table.. i have no idea where they got -1.645

[burnt knot]

oh yah

-1.645 is the standard for hypothesis tests

it just means the region where ur p value is .05 or less

-1.645 z value = .05 p value

[keen wedge]

so a left tailed test?

[burnt knot]

yah

so since ur z is less than -1.645

for a right tailed test it would be positive 1.645

and u would have to be greater than that

but lwk it would be easier to just convert your z on that table and compare p values, thats what I do

[keen wedge]

convert your z on that table and compare p values,
elaborate?

[burnt knot]

so u see how they got -2.08 right

[keen wedge]

yep

[burnt knot]

go to ur table on the left where it says Z

and go until u see -2.0

then u go to the right until ur in the column that says .08 at the top

that's 2.08

[keen wedge]

OH

[burnt knot]

so what I would do is find that p-value and then compare it to your critical p-value

in this case .05

if its less than that u can reject

[keen wedge]

the value i get from this is .00219 which is nowhere close to "-1.645"

what's up with that

[burnt knot]

nah that's -2.85

lol

u need -2.08

[keen wedge]

.00199?

soz my bad

[burnt knot]

that's the right one

.01876

[burnt knot]

because -1.645 = .05

on the chart

[keen wedge]

you're sorta losing me here

[burnt knot]

Ok let me restart

[keen wedge]

thanks, sorry haha

[burnt knot]

So you know how you get the z right

Do you know what ur trying to do with a hypothesis test

[keen wedge]

yeah we're trying to see whether to accept or reject the null hypothesis

[burnt knot]

right

and in this case the alpha value is .05 right

[keen wedge]

yep

[burnt knot]

that means that our experimental p-value has to be less than .05

to reject

do u get that

[keen wedge]

yeah because then it'd be in the rejection "zone"?

[burnt knot]

right and what that means in practicality is that the book wants us to make sure our experiement has a less than 5% chance that our conclusion is a false positive

5% = .05

ok so now what u need to do with ur z value is turn it into a p value

so u can compare it to the alpha value (.05) which is a p value

[keen wedge]

so we turn -2.08 into a p value?

[burnt knot]

yes

[keen wedge]

alright, how do we do that?

[burnt knot]

on the left side u find the first and second decimal places

and on the top u find the third

so the left u find -2.0

and then on the top u find the .08 part

where those two intersect is the pvalue for -2.08

Does that help? @keen wedge

[pearl pond]

@keen wedge Has your question been resolved?

[keen wedge]

Sorry i lost internet

[keen wedge]

Yes it definitely helps

Thank you!!

One last thing, how do we get from .01876 to - 16.45?

[burnt knot]

-1.645 is a z value

They just coverted .05 to a z value so u didnt have to convert 2.08

but since u converted -2.08 to a p value u can just compare the p values

[pearl pond]

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[burnt knot]

.reopen

U just need to get both things into the same type of value

[pearl pond]

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[tulip bramble]

In the context of probability and sampling distributions:
What is an experiment?
What is a trial?
What is a sample space?
What is an event?
What is the difference between all these?

[toxic lichen]

"experiment" and "trial" do not really have formal definitions

a sample space is, from a formal standpoint, one of the basic components of a probability space. the other two components are the sigma-algebra (a family of subsets of the sample space that satisfies certain properties. these subsets are called events) and the probability measure (which is the assignment of a number between 0 and 1 to every event, and said number is called that event's probability)

although wikipedia does say this for "experiment" and "trial", which according to it are synonyms:

In probability theory, an experiment or trial (see below) is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space.

[tulip bramble]

thank you

.close

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[sharp folio]

what is the difference between a converging sequence and series?

[sharp folio]

like consulting the convergence tests

how do i comfirm the convergence of a sequence?

[midnight haven]

a series is by definition a sequence.

[midnight haven]

usually you prove it's bounded + increasing/decreasing

[plush bramble]

have you learned limits

[sharp folio]

yup

ive nailed down the convergence tests

like integral

p series

direct comparison

limit comparison

alternating

absolute convergence

root test

and the ratio test

but im not sure where the line is drawn when showing a sequnce converges vs when a series converges

this was a question from my last midterm:

[sharp folio]

i got all the series convergence ones correct

but got the sequence ones wrong

yes

not sure where i should have gone for the sequences

[midnight haven]

the first reflex for sequnces should be checking monotonicity

that's what I would do

unless it trivially converges to someth

[sharp folio]

like check if it converges on the upper bound?

least upper*

[midnight haven]

no just checking if $a_{n+1} - a_n \geq 0$ or $\leq 0$

[jolly parrot]

shell.exe

[sharp folio]

ah

what did riemann mean when he asked me about the limit?

[midnight haven]

also if you find some continuous function $f$ such as $a_{n+1} = f(a_n)$ then the limit $l$ has the property $f(l)=l$

[jolly parrot]

shell.exe

[sharp folio]

yeah

uniqueness and pinching theorems

did he mean by a delta epsilon proof?

[midnight haven]

because finding the limit of a sequence means it's convergent

[sharp folio]

ahhh

cus it converges on a point

[midnight haven]

could be useful but not always necessary

[midnight haven]

yep

[sharp folio]

i think i got it

[sharp folio]

u think u can give me feedback on this post and where i should have corrected myself?

1. check for monotonicity

[midnight haven]

for the first one the sequence is clearly divergent

[sharp folio]

yup

[midnight haven]

because the sequence $x^n$ converges if and only if $|x| < 1$

[jolly parrot]

shell.exe

[midnight haven]

therefore $(10/9)^n$ diverges

[jolly parrot]

shell.exe

[midnight haven]

therefore the sequence in 1. diverges

[sharp folio]

for that one i did a direct comparison

cus of the 10/9 > 1

is that still incorrect?

or should i have worded my solution better

[midnight haven]

what do you mean by direct comparison

can you show the theorem you're referring to

[sharp folio]

like comparing the 10/9 ^n with 1

i know for series there are conditions for the root and ratio tests

here's the prof's solution

not sure why he utilized the limit of a_N

[midnight haven]

because it's enough

we only use other tools if we can't find the limit directly

[midnight haven]

that's not generaly called direct comparison

[sharp folio]

so just checking the limit with n -> inf is enough to check if a sequnce is convergence/div?

[midnight haven]

if you can find the limit then yes

[sharp folio]

i can still use lhopital rule, conjugate multiplication, etc?

whhaaaaa

[midnight haven]

of course

[sharp folio]

and when in doubt where the lim fails

then i should consult the theorems

so far i organized the following:

[midnight haven]

yes if there is no way to find the lim

[sharp folio]

are there more theroem's/tools i should note down?

[midnight haven]

this is a good summary

[midnight haven]

there is more like the $f(l)=l$ thing I mentioned

[jolly parrot]

shell.exe

[sharp folio]

ahh ok

[midnight haven]

and there is also a ratio test for sequences

[sharp folio]

ah yeah thats whats itrs called

i guess my last question b4 i close the channel is if this last bit is correct

[midnight haven]

which bit

[sharp folio]

the a_k -> as k -> the sum does not necessarily converge

i copied that section from our textbook but im trying to find a good example to understand it

[midnight haven]

yes that's true

[midnight haven]

the best example is the harmonic series $\sum{1/n}$

[jolly parrot]

shell.exe

[midnight haven]

it's divergent

and yet $\frac1{n}$ obviously converges to 0

[jolly parrot]

shell.exe

[sharp folio]

ah ok

beautiful

tysm xD

[midnight haven]

Yw

[sharp folio]

.close

[pearl pond]

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[pseudo wasp]

Why is my t-chart not getting (-2,6) I forgot what order to do things. Ex for the X table is it subtracting then multiplying. Ex Y table is it multiplying then adding?

[pseudo wasp]

.close

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[shy rampart]

how do we find the algebraic model from this graph?

[compact mesa]

Do you mean like an equation or something

[shy rampart]

yes

[late moon]

Okay

What do you notice about this shape?

Does it look familiar to you?

[shy rampart]

its pointing down

[remote roost]

in what rhetoric???

[pearl pond]

@shy rampart Has your question been resolved?

[shy rampart]

.close

[pearl pond]

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[dense ibex]

Hey there, would a data set of test results (considering there is a maximum total of points) be binomial or normal distribution? Or something else? Thank you

[pearl pond]

@dense ibex Has your question been resolved?

[dense ibex]

.close

[pearl pond]

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[solar gyro]

@viscid sierra could we continue here?

[solar gyro]

I don’t understand how u got that answer

[viscid sierra]

Yeah

[solar gyro]

Here’s the q

[viscid sierra]

Since central angle is 60

[solar gyro]

So what I did was

[viscid sierra]

The triangle is equilateral

Area of an equilateral truangle is given by (3)½/4*s²

S=10

Area=25(3)½

Now the line OB (O is centre) is height of triangle

But area is 1/bh

[solar gyro]

Can’t u assume that it’s a 30-60-90 triangle?

Bc ik that the answer isn’t that complicated

[viscid sierra]

It would be better to not

[solar gyro]

How so?

[viscid sierra]

Well, it isn't even complicated

Well, are you aware of trigonometric ratios?

[solar gyro]

No ik but that wasn’t taught

Is what I mean

[viscid sierra]

?

[viscid sierra]

Oh okay

[solar gyro]

Yeah so

Is there any other way?

[viscid sierra]

Trigonometry

[solar gyro]

Isn’t it a bisector tho

[viscid sierra]

Yoh aware?

[solar gyro]

Yeah but like

Doesn’t that line bisect the angle

[viscid sierra]

Yeah its a 30 60 90 triangle

[solar gyro]

Yeah

[viscid sierra]

And that's why I'm using trig

[solar gyro]

U could just use a special right triangle rule

So the entire radius is 10

[viscid sierra]

Well, that's even better

[solar gyro]

So the answer’s 5

Bc the radius is 10

10/2 is 5

[viscid sierra]

No

[solar gyro]

10-5=5

[viscid sierra]

No

[solar gyro]

Why not?

[viscid sierra]

The side adjacent to 30 is x*(3)½ where x is 2 times hypotenuse (here 10)

[solar gyro]

Yeah

So to go from the hypotenuse to one of the legs

U have to divide by 2

[viscid sierra]

What

[solar gyro]

That’s a rule

[viscid sierra]

Just see this

[viscid sierra]

I don't follow what you say

[solar gyro]

Ok so

[viscid sierra]

Not one of the
Necessarily the 60 degree side

[solar gyro]

To go from the hyp to the leg in a 30-60-90 triangle

U have to divide by 2

[viscid sierra]

If we go to side adjacent to 60 degree angle then yes

Side adjacent to 30 degree angle is x(3)½ as shown in the pic

[solar gyro]

Oh nvm

The answer’s 5 sqrt(3)

[viscid sierra]

Still no

The height of 30 60 90 triangle is 5*sqrt(3)

We need to find BD

Which is radius-height

[solar gyro]

Like this, right

?

@viscid sierra

[viscid sierra]

Yes

[solar gyro]

Can u think of a situation in which the answer would be 5 tho?

[viscid sierra]

When central angle is 120

[solar gyro]

I can’t remember if it was that or 60 lol

Well thx sm

[pearl pond]

@solar gyro Has your question been resolved?

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[heavy lotus]

Gonna try this again.

[heavy lotus]

I need to do this trig proof. I am stuck

[rough stream]

Looks like your /2's have entered your cos()

[heavy lotus]

Sorry, I'm not sure I follow.

[rough stream]

If the first line under the big bar is line 1, then the transition between lines 2 and 3

Or, MB, that's supposed to be that way because of the identity. I misread.

[heavy lotus]

Yeah, I think it is.

if a and b were x and y, then it would be (x+y)/2 and then (x-y)/2

[rough stream]

Okay so your line
= 2cos(x)cos(π/4)

[heavy lotus]

since a is x+pi/4, then /2 would go under the whole thing I think

[rough stream]

That's a really good line, and the work after it is taking you away from your goal

What's cos(π/4)?

[heavy lotus]

so 2cosx * cos pi/4 is then substituted with the prduct to sum formula but maybe it doesn't need to be

bc cosA*cosB = 1/2 [cos(A-B) + cos(A+B)]

[rough stream]

So if you have anything without an x, evaluate it!

cos(π/4) = √2/2

After that goes in, you've solved it

[heavy lotus]

OH yeah.

That's terrific - thank you so much!

.close

[pearl pond]

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[pearl pond]

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[pearl pond]

@midnight haven Has your question been resolved?

[jolly parrot]

Labyrinth

[pearl pond]

Channel closed

Closed by @stray bramble

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✅

[midnight haven]

I was just copying down the question so helpers wouldn't have to kill their eyes to read it

I already reopened it (hence the ✅), closing and reopening a channel puts it back at the top of the channel list which I hoped would give it more attention

,calc 8^2+3^2

[jolly parrot]

Result:

73

[midnight haven]

,calc sqrt(7^2+51)

[jolly parrot]

Result:

10

[midnight haven]

,calc 73*51

[jolly parrot]

Result:

3723

[midnight haven]

Ah I must've copied that down wrong

@midnight haven I went through it and everything seems correct, apart from the line where you expected the sines and cosines using a trig identity

$sin(\theta)cos(\phi)+cos(\theta)sin(\phi)$

[jolly parrot]

Labyrinth

[midnight haven]

This is what you should've written down

Don't forget to .close this channel

[pearl pond]

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[heavy lotus]

Hi I’m having trouble figuring out how to complete this proof

[civic crane]

In this step the numerator you can club because denominator is same so

1-2sin²x - 2sin²x / 2sinx

So 1- 4 sin²x/2sinx

Hence in last you seperate it
1/2 cscx -2sinx

You practically solved it yourself

[heavy lotus]

I can club?

[civic crane]

Yeah since denominator is same

Like normal adding

[heavy lotus]

Ah ok, just hadn't heard that term before 🙂

lemme work this out real quick

[civic crane]

Oh lol

[heavy lotus]

OK, that checks out. A little tricky putting them together and pulling them back apart. Thanks for your direction! Appreciate it!!

[civic crane]

Mhm

[heavy lotus]

.close

[pearl pond]

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[bleak owl]

I got (3W*root2)/4

[pearl pond]

@bleak owl Has your question been resolved?

[bleak owl]

<@&286206848099549185>

[pearl pond]

@bleak owl Has your question been resolved?

[pearl pond]

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[near brook]

hey is this okay?

[near brook]

if i added a +C

xd

[inland ivy]

,w integral of 1/sqrt(x^2+16)

[jolly parrot]

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[inland ivy]

well

you can simplify the last 2 terms

,w sec(arctan(x/4))

[near brook]

and would i end up with this hyperbolic function?

[jolly parrot]

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[inland ivy]

you should

if you did it correctly

this is also wrong

[near brook]

it should b 4*sec^2, right?

[inland ivy]

yep

[inland ivy]

yeah, this is technically correct except for the 1/4

[near brook]

well that removes the 1/4

[inland ivy]

but you can simplify the trigonometric terms

[near brook]

we're advised not to for tests and thats what im preparing for

how would you simplify this, tho?

[inland ivy]

remember that $\sinh^-1(x) = \log(\sqrt{x^2+1}+x)$

[jolly parrot]

kheerii

[near brook]

yea we havent learned hyperbolic functions yet

[inland ivy]

they told you NOT to simplify your answer?

that seems unlikely

[near brook]

yea for all assignments too

[inland ivy]

reference triangles

but if you're told not to simplify it then dont bother ig

[near brook]

it's calc 2 and they only want to see that we know the calculus

otherwise i would

if i could

which i cant

[inland ivy]

then this is fine except the 1/4

[near brook]

thank u friend

much appreesh

IM SO PROUD OF MYSELF