help-23

[polar knot]

and put null in

[modest holly]

but how is that the vertex?

isnt the formula

[polar knot]

look

[modest holly]

-b/2a

[polar knot]

thats the x

let me show u

[modest holly]

huh?

[polar knot]

-2(x-3)^2 +50

x-3 tells us

x is at 3

so the vertex is at 3, 50

look

[modest holly]

but thats not what i do

[modest holly]

look

-2x^2+12x+32

[polar knot]

its just another way to find it...

i nkow

-12/4

[modest holly]

12/-4

yea

[modest holly]

-4

not 4

[polar knot]

my bad

[modest holly]

ye

[polar knot]

= 3

here x= 3 too

no difference

[modest holly]

so why is the equation like that

[polar knot]

its just another way to put it

[modest holly]

(x-3)^2

[polar knot]

because we can find the vertex

x - 3, means x = 3

if its x+3

[modest holly]

its not null

i tried it

not null

[polar knot]

it means x is at -3

how the fuck

it literally doesnt increase

how would there be an interval

[modest holly]

let me press find solution

[polar knot]

of increase

if there is no increase

no

dont

[modest holly]

yes

its okay

[polar knot]

i legit dont get

ok i think

so u submitted

with vertx form

[modest holly]

yea

[polar knot]

and standard form righ?

try the

[modest holly]

yea

[polar knot]

factored form

and if it doenst work

[modest holly]

bro its not null

[polar knot]

i cant help u

[modest holly]

it literally isnt

i tried it

[polar knot]

but the parabola legit doesnt increase

[modest holly]

let me see the solution

[polar knot]

i know maybe the form is wrong

[modest holly]

see

i told u vertex

is the max

[polar knot]

i said select vertex form

[modest holly]

ok yea

but i dont get that part

[polar knot]

ok ur problem like

[modest holly]

we had too?

why tho

[polar knot]

wording is trash

becasue

what it says

it means this:

[modest holly]

wait

what if it was positive parabola

its infinite, right?

[polar knot]

well realistically yes,

but the way ur problem is meant to be interpreted

it should be just

[modest holly]

how would i do this

[polar knot]

the vertex

thats why im amd

mad*

[modest holly]

yea, since the parabola was neg

wait

[polar knot]

this is calclus

ur not meant to do it

[modest holly]

can u help me understand the vertex?

[polar knot]

the way your problem is worded

makes me think it wants me to find the interval

its just badly worded

[polar knot]

so

a paraboal

opens

with2 lines

[modest holly]

yuh

[polar knot]

and theres. a centre

right

[modest holly]

yea

[polar knot]

the center is the vertex

so if a is positive

the vertex is the minimum

if a is negtaive

vertex is maximum

you know why?

[modest holly]

wait what?

[polar knot]

so when

for example

-2x^2

would the vertex of that parabola be the minimum value of the parabola or the maximum value?

[modest holly]

like in this case

what would i do?

[polar knot]

okay so

this parabola

open up

uh

i guess it wants the vertex

so you see

(x-2) and -32

right

so x - 2, tells us the x is at +2

so the answer is

[modest holly]

?

how

[polar knot]

-2, -32

[modest holly]

is it 2?

[polar knot]

x-2

negate the 2

thats why its called vertex form

we can find the vertex

super easily

[modest holly]

ohh so i did 2(x-2)^2-32

and got

4x^2-16x-40

and vertex is 2

pos 2

[polar knot]

why?????

[modest holly]

so x=2

[polar knot]

ok

[modest holly]

now plug in

[polar knot]

and the -32 at the end

tells us

that y is at -32

ok you need to know this

the reason why its called vertex form

[modest holly]

,calc 4(2)^2-16(2)-40

[flat frigate]

Result:

-56

[polar knot]

is because it tells us

no

[modest holly]

yes

[polar knot]

u did it wrong

[modest holly]

its wrong

how

[polar knot]

2(x-2)^2-32

is

[modest holly]

wait

i did it wrong

[polar knot]

2x^2-8x-24

thus y = -32

so its 2, -32

[modest holly]

how did u get -24?

ohh yea

damn

ur right

-24

and then u do the vertex form

[polar knot]

ITS ALREADY

IN VERTEX FORM

THIS IS VERTEX FORM

ITS CALLED VERTEX FOMR

[modest holly]

yea 2,-32

[polar knot]

BECAUSE IT SHOWS US THE VERTEX

WITH 1 LOOK

IF YOU SEE THE (x-2)

[modest holly]

ohh

[polar knot]

YOU NEGATE THE -2

WHICH BECOMES 2

[modest holly]

wait so x is the opposite?

[polar knot]

AND THE -32 AT THE END IS THE Y

YES

SO ITS 2, -32

[modest holly]

ohh

wait

i got -4

-16/4

[polar knot]

??????????

-4 for wht

[modest holly]

no

it should be 16/4

pos 4

[polar knot]

WHAT SHOULD

[modest holly]

u do vertex form

[polar knot]

wh

[modest holly]

,calc 2(4)^2-16(4)-24

[flat frigate]

Result:

-56

[modest holly]

how

[polar knot]

X is not 4

[modest holly]

but vertex form

[polar knot]

this is not vertex form

[polar knot]

i told u

this is vertex form

and it tells us the vertex

if you just

negate x

and the -32 at the end is the y

[modest holly]

but i do -b/2a

this is different

[polar knot]

also if you were to do -b/2a

it would be

-(-8)/4

which is 2

[modest holly]

wait what?

how

[polar knot]

where did you get 16 from

[modest holly]

its 2x^2-16x-24

16/4

wait

[polar knot]

HOW

did yo uget 16

[modest holly]

,calc (x-2) (x-2)

[flat frigate]

The following error occured while calculating:
Error: Undefined symbol x

[polar knot]

look

2(x-2)^2-32

right

[modest holly]

yea

[polar knot]

2(x-2)(x-2)-32

2(x^2-4x+4)-32

2x^2-8x+8-32

2x^2-8x-24

[modest holly]

wait what?

(x-2) (x-2) is x^2-2x-2x+4

[polar knot]

yes....

-2x-2x = -4x...

[modest holly]

yea

[polar knot]

-4x * 2 = -8x

[modest holly]

yup

,calc 8-32

[flat frigate]

Result:

-24

[modest holly]

2x^2-8x-24

not we do the form

8/4

which is 2

now we sub

[polar knot]

and y = -32

[modest holly]

boom

see

that way is better

[polar knot]

...

[modest holly]

and consice

[polar knot]

you can find that

in 1 second

[modest holly]

but its not the answer

[polar knot]

with vertex form

[modest holly]

i put it in

it isnt the answer

[polar knot]

2, -32

[modest holly]

yea

its not the answer

i put it in

[polar knot]

did you select vertex form

[modest holly]

yup

i got one more try

[polar knot]

what the actual fucking shit is this fucking problem

who the fuck wrote it its

[modest holly]

wait, its positive

[polar knot]

so inconsistent and

[modest holly]

so its infinite

[polar knot]

yes

[modest holly]

let me do that

its not infinite

wait im confused

[polar knot]

ok i fucking

[modest holly]

since this parabola is positive

its infinite

[polar knot]

-32, infinity

?

[modest holly]

im pressing solution

[polar knot]

stop

its

(-32, inf)

[modest holly]

x>2

wanna do one more?

this would be vertex form?

[polar knot]

WHAT IS THE

FUCKINg NASWER

HOW WOULD YOU EVEN WRITE THE ANSWER

[modest holly]

is it 4,12?

[polar knot]

YOU WRITE x>2?????

[modest holly]

yea

[polar knot]

YES

SO

[modest holly]

x>4?

lets see

its wrong

im so fucking confused

[polar knot]

<

smaller than

cuz the parabla

opens down

instead of up

[modest holly]

i did that

it didnt work

the maximum value in this case would be the vertex

and i tried (4,12)

didnt work

im pressing solution

[polar knot]

HOW TUEFFCUk

NO

BRO

its at (4, 12)

that means

[modest holly]

its just 12

[polar knot]

OH MY GOD THIS

[modest holly]

maximum means y value

so its 12

[polar knot]

yes

but WHY IS IT WORDED

AS

[modest holly]

wait maximum means y value?

[polar knot]

INTERVAL INCREAS?????

WHY DOES IT SAY INTERVAL INCREASE

WHEN IT DOESNT EVEN MEAN

INTERVAL INCREASE

you know what

i give up

you know vertex form

[modest holly]

one more

[polar knot]

im happy about it

ok

where x is negative

[modest holly]

what form

[polar knot]

vertex

[modest holly]

k

(2,-9)

[polar knot]

where x is negative

oh shit

it should bde

fractored form

[modest holly]

?

why?

5 -1

yo i dont get this

help

[polar knot]

iwjdoi1j09jfe

∑øƒ´˚πø®˚

[polar knot]

so it wants

where x is engative

negtaive

right

[modest holly]

yea

[polar knot]

my bad

[granite idol]

no, where f(x) is negative

[polar knot]

its meant to be

where

yea

so still vertex form

at 2, -9 right

@modest holly my bad its vertex form

[modest holly]

yea

i got that

but i dont get what to do

the vertex is 2,-9

[polar knot]

so where f(x) is negative

[modest holly]

bro i got a final tmmrw 2

[polar knot]

means when the parabola is in the negatives

[modest holly]

pls help

[polar knot]

I also have

i jhave like 5 finals

[modest holly]

on parabolas?

[polar knot]

for all my subjects

😭

no

on everything

trig

paraboal

cubic

etc

[modest holly]

u should be good for math

[polar knot]

its almost mdingih

[modest holly]

damn

[polar knot]

no i am like

dying

😭

[modest holly]

no ur not

u will pass

[polar knot]

so vertex form tells me

that 2, -9

[modest holly]

yea

[polar knot]

and the -9 tells us

the lowest point

of the parabola is at -9

so the interval should be

[modest holly]

-9?

[polar knot]

from 0 to -9

right

thats when the parabola is negative

[polar knot]

hello, please chec

check*

im scared of that website now

[modest holly]

so -9?

[polar knot]

yeah see

[modest holly]

so i just type -9?

[polar knot]

im not sure

[modest holly]

because i did

and its wrong

[polar knot]

im scared of that wbesite

[modest holly]

somehow

[polar knot]

like

[modest holly]

what else can it be

[polar knot]

i bet its

that section

-1, -5

[modest holly]

huh?

[polar knot]

so when the

entire parabola is negative

is between

-1, 0 nad 0,-5

thats when

both the x and y coordiantes are negative

<@&286206848099549185>

[modest holly]

should i try it?

[polar knot]

try but

i cant help anymore

let the hlpers help

its been way more than 15 mins

[polar knot]

you got it right?

[modest holly]

na

i plugged in points

like (,)

not -1<x<5

[polar knot]

ok i give up i have

too much stuff to do

and my english sucks

[modest holly]

and its also factored

not vertex

lmao

[polar knot]

so i cant understand

[modest holly]

so u were right

[polar knot]

those interval sthing

[modest holly]

i dont know why u said its vertex

it was factored

[polar knot]

because i thought

it meant

[modest holly]

like u said

[polar knot]

i thought it meant this

[modest holly]

i dont understand this

[polar knot]

it doesnt matter

https://tenor.com/view/crying-emoji-dies-gif-21956120

i need to

prepare and sleep

byebye

[modest holly]

gn

guys help

pls

[proud pewter]

why are you solving ques that are above your level of understanding

it cannot be explained better

[modest holly]

wdym

i got this one right

thats good

what would i do

[polar knot]

-6 < x < -4

or ist

-4 < x < -6

[modest holly]

how did u get that

its wrong

lol

[polar knot]

aaaaaaarghuhtī3

[modest holly]

so what do we do

[polar knot]

u tried bth

?

[modest holly]

yea

its fine bro

get some rest

u got finals

i have time

lots of it

ima close it

.close

[safe radish]

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[polar knot]

sorry

[modest holly]

y

[polar knot]

FUCK

ill tell u in dms

.cloe

.cloe

.close

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[safe radish]

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Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[junior wagon]

Not sure how to identify for this one?

[proud pewter]

ok

[proud pewter]

try to multiply eqn 2 by 2 and then square and add both the equations

you may obtain the eqn you are looking for

[junior wagon]

like b?

for eqn 2

[safe radish]

@junior wagon Has your question been resolved?

[junior wagon]

. lose

.close

[safe radish]

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Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

[tall hare]

can someone walk me through this, no videos are helping

I know it's IROC but I feel like I'm missing something

[left karma]

I think you have to use an approximation since we're only given a few points and the closest approximation we can get is the slope from point B to C

[tall hare]

so would i just use AROC

[left karma]

Yes, I don't think it's possible to get the exact instantaneous rate

[tall hare]

-0.058

[left karma]

That's what I got

[tall hare]

okay. you would need a formula for IROC, right?

you can't do it with a graph

[left karma]

Yeah you'd need the actual formula and derive it

[tall hare]

okay that's why i was so confused

thanks

.close

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Channel closed

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Use .reopen if this was a mistake.

[tall hare]

.open

.reopen

[safe radish]

✅

[tall hare]

says it was wrong

I think it does want IROC somehow

<@&286206848099549185>

[left karma]

Maybe someone else will weigh in with a better way to do it, but if you're willing to eyeball the graph it does seem like -0.092 matches better since it drops by about 0.1 from f(5) to f(6)

[tall hare]

i feel like there should be a way to get the answer without eyeballing it

<@&286206848099549185>

.close

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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[willow rain]

Hi. Can anyone help me with this please?

[willow rain]

Please start on scratch

[main ice]

find the arc length of QOP

[willow rain]

The reason why I'm here

And u just repeat the question

What is the process that will help find the arc length?

[final halo]

Find the angle POQ using the information you are given

[willow rain]

Idk

[wheat cave]

formula time

[willow rain]

?

What formula

[final halo]

Area of a sector

[willow rain]

Pi * r^2

64pi

[final halo]

That's the area of the whole circle

What fraction of the whole circle is the sector

[willow rain]

Idk

[final halo]

What's the area of the sector

[willow rain]

8pi

[final halo]

So what fraction of the whole circle is the sector

[willow rain]

1/8?

Right?

[final halo]

Yes

So if you know the circumference of the circle.you now know the arc length of the sector

[willow rain]

Don't know

C=2pi(R)

That's the circumference of a circle

So now what

The circumference of the circle is 50.27

<@&286206848099549185>

[unborn dirge]

If you know the circumference and you know that it is 1/8 the area. What should the arc length be?

@willow rain you asked for help?

[willow rain]

Yes

[unborn dirge]

^

The circumference is the arc all the way around the circle

But you only want how much of the circumference?

[unborn dirge]

Ya, I know

[willow rain]

PRQ

[unborn dirge]

Exactly but, if that sector is 1/8 of the pie

then how much of the crust did you have?

[willow rain]

7/8?

[unborn dirge]

no, 1/8. You only had an eigth of the crust

7/8 is the rest of the crust that you didn't eat

Make sense?

[willow rain]

Yea

[unborn dirge]

So, how much of the circumference do we have?

[willow rain]

1/8 of 50.27

[unborn dirge]

yup!

There you go, you solved it!

You could also write 1/8 of 16pi which would be 2pi

Nice work!

[willow rain]

So the answer is 2pi

[unborn dirge]

Yup!

[willow rain]

It's not correct

[unborn dirge]

hmmm

[willow rain]

Is it 16/8 pi

Cuz it says leave it as fraction

[unborn dirge]

that is the same as 2pi

ahhh

That would make sense

[willow rain]

Bruh

[unborn dirge]

Get it wrong again?

[willow rain]

It's 14pi

[unborn dirge]

loooolll

Yea, because it is PRQ

So it is the long way around

So it would be 7/8x 16pi which is 14pi

[unborn dirge]

Make sense?

[willow rain]

No

[unborn dirge]

The arc PRQ is the circumference excluding the arc in the sector

[willow rain]

Can you help me with this

[unborn dirge]

Um, ya. Can you give me 5 min?

[willow rain]

Sure

[unborn dirge]

Aight, so.

In this case we know that WVX is 45 degrees

The question is, how much of the circle is that?

[willow rain]

45/360

[unborn dirge]

Yup, which simplifies to 1/8 right?

[willow rain]

Yes

[unborn dirge]

So, WX is 1/8 of the circumference correct?

Do you see why that is?

[willow rain]

Yes

[unborn dirge]

ok, and we know the area of the sector is 1/2pi right?

[willow rain]

Yea

[unborn dirge]

but what did we just find, how much of the total area is the sector?

[willow rain]

1/2

1/8

[unborn dirge]

yea, 1/8

so if the area of the sector is 1/2 pi. What is the area of the full circle?

[willow rain]

2/2pi

Or just pi

?

[unborn dirge]

uh, it is 1/8 so there should be a total of 8 sectors (8 x 1/2 pi) right?

[willow rain]

Oh yea

[cosmic raft]

e

[willow rain]

8/2pi

[unborn dirge]

So what is the total area?

[willow rain]

8/2

[unborn dirge]

8/2pi=?

[willow rain]

4pi

[unborn dirge]

Yup! So given that. What should the circumference be?

[willow rain]

4pi

[unborn dirge]

Yup, so if WX is 1/8 the circumference. What is WX?

[willow rain]

1/2

[unborn dirge]

1/2... should have something else?

[willow rain]

1/2pi

[unborn dirge]

There ya go!

[willow rain]

Isn't that the area of the shaded sector

You could have told me that

[unborn dirge]

It does happen to be the area as well. But normally the circumference is very different from the area

[willow rain]

Got it thanks

I got another one

[unborn dirge]

Oh, boy! Go for it!

[willow rain]

VUW is half as much as arc VW correct

Or the same

[unborn dirge]

One sec

No, it is literally the same thing

So, 11x +49 =56

[willow rain]

11x+49=56

[unborn dirge]

The half angle is when it is inscribed

[willow rain]

So it's congruent or half?

[unborn dirge]

It is equal

So what is x if 11x+49=56

[willow rain]

11x=7

[unborn dirge]

Yup

[willow rain]

So 7/11

[unborn dirge]

Exactly

[willow rain]

If you round it like it said it's 0.6

Thank you so much for your help

Sorry to take a lot of time from you

Bye

.close

[safe radish]

Channel closed

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[unborn dirge]

Np, I enjoy math! Feel free to ask more questions!

[safe radish]

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Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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

[abstract comet]

Hi!
So there's this question that a friend asked and I solved with combinatorics, but not in the most satisfactory way. It's about probability, and I don't have background in that, since the probability course comes next semester.
The question was to find the expected price for completing a figurine album. They come in packages of a fixed amount of figurines each, and there are no repeated ones in a given package.
What I found was a formula for knowing what your odds are of completing the album if you spend a given amount of money.
This feels very close to what I want, but it's still not the expected price.

[abstract comet]

This is what the graph looks like.
X axis is the price you pay, and Y axis is the probability of completing the album with that money.

My idea was doing finite differences (taking derivative in this discrete graph) to get a valid distribution, but it peaks at x=32200, which sets your odds to 36.25% (woah that is very close to e^-1). I'm sure that was not the way. So my question is. How do I find the expected price using the graph from above?

[safe radish]

@abstract comet Has your question been resolved?

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@abstract comet Has your question been resolved?

[dull sequoia]

Isn’t this the collectors coupon problem?

Just a little bit changed

[abstract comet]

Maybe, I didn't hear about that. This was my naive approach and I got stuck so I wanted some guidance on how to finish this

[safe radish]

@abstract comet Has your question been resolved?

[abstract comet]

.close

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[junior wagon]

I dont know how to find the plane

The function describes a line since every component is linear

[hot thistle]

what do you know about the intersection of two planes?

[junior wagon]

they are the line that the function describes

[hot thistle]

they are a line

unless the planes have parallel normal vectors

but anyways

can you tell me if a plane containing this line will be unique?

[junior wagon]

ni

no

i imagine you can rotate the plane

[hot thistle]

yes exactly

[junior wagon]

infinitely number of rotations

[hot thistle]

so now just take any vector orthogonal to that line

and let that be the normal vector to the plane

[junior wagon]

right

but how do you find that normal vector

[hot thistle]

.

any vector orthogonal to the line will do

[junior wagon]

ok

<-1,1,2> is the direction vector of the line

so say, <1,1,0>

[hot thistle]

yeah that works

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@junior wagon Has your question been resolved?

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@junior wagon Has your question been resolved?

[stoic dune]

Did you have a question?

[junior wagon]

.close

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[subtle kernel]

Hello need some help with this

[subtle kernel]

I’m pretty sure Part A I got right

I got .2963

I’m not too sure with B and C

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@subtle kernel Has your question been resolved?

[subtle kernel]

<@&286206848099549185>

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[subtle kernel]

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[lean otter]

Direct proportion is when a value increases the other increases.
Inverse proportion is when a value increases the other decreases.

Is that correct?

[gleaming ravine]

yeah

[lean otter]

Ty.

.close

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[safe radish]

@harsh olive Has your question been resolved?

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@harsh olive Has your question been resolved?

[harsh olive]

<@&286206848099549185>

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@harsh olive Has your question been resolved?

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@harsh olive Has your question been resolved?

[unborn dirge]

@harsh olive Looks great to me!

[harsh olive]

Thanks!

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[solar sonnet]

how can this be solved

is there a rule

[dull sequoia]

equate the functions

[solar sonnet]

i know

but then

[dull sequoia]

Where are you up to

Show your work

[solar sonnet]

i cant am on pc

but there is no other way

?

[dull sequoia]

Take a picture

[solar sonnet]

i solved it

thanks

.close

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[keen steppe]

hello guys can someone help me with this probability problem, im stuck on trying to understand why are we multiplying negatively twice the 300/1200

[safe radish]

Please don't occupy multiple help channels.

[keen steppe]

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[lean otter]

$$ \int_1^{2} x^2 log (x) dx$$
I have to do integration by parts 3 times to solve this right?

[flat frigate]

Brandon H

[quasi sentinel]

nah

[lean otter]

if not integration by parts then what would it be?

[quasi sentinel]

theres no need to do it 3 timed

[lean otter]

numerical integration?

oh

just one time

because x^2/x

[quasi sentinel]

its not x²e^x

if it was x²ex tgen u would have to

do ibp

[lean otter]

So the anti derivative wouldn't be this?

[quasi sentinel]

multiple times

no

[lean otter]

[quasi sentinel]

F(x)g(x) - int(F(x)g'(x))

[lean otter]

oh

i messed up

[lean otter]

if not ibp then what?

[quasi sentinel]

i never said using ibp was wrong

[lean otter]

oh

just that i didn't have to do it multiple times

[quasi sentinel]

yes

[lean otter]

$$\frac{1}{9}x^3(3ln(x)-1) + C$$ so i got this

[flat frigate]

Brandon H

[lean otter]

I'm looking at this and idk how i would get the value by hand

ln(2) is that a number i'm supposed to remember?

[quasi sentinel]

theres no ln2

wdym

[lean otter]

$$ \int_1^{2} x^2 log (x) dx$$

[flat frigate]

Brandon H

[quasi sentinel]

oh

no you dont have to

[quasi sentinel]

r

[lean otter]

Thank you

.close

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[calm sigil]

Hi! I don't have any idea to solve this question. Could anyone tell me what should I learn to solve it?

[lean otter]

find the normal to the plane alpha

[calm sigil]

I searched on yt and it showed this. are these correct videos? which one you prefer first?

[lean otter]

idk, I havent watched any of them

but I've heard good things about the organic chem tutor

khan academy would also be a good place to learn linear algebra

[calm sigil]

so I need to learn linear algebra and vector?

[lean otter]

yes, that would be helpful

https://www.khanacademy.org/math/linear-algebra/vectors-and-spaces/dot-cross-products/v/normal-vector-from-plane-equation

[calm sigil]

I see

[calm sigil]

Thank you for the link!

[lean otter]

yw

[calm sigil]

.close

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[lean otter]

Hlo

[lean otter]

I've a pretty simple question

Let's say there are two numbers

2^55, 3^33

Which one is bigger??

How do I identify it ??

I take HCF Of the powers and divide it, then compare???

If so why??

[peak estuary]

2^55=(2^5)^11=32^11 and 3^33 = (3^3)^11 = 27^11

then you notice that a^11 is increasing so 32^11 is bigger than 27^11

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@lean otter Has your question been resolved?

[lean otter]

Umm OK

.Close

.close

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[vivid current]

what went wrong? The answers im supposed to get are something close to 1.2 or 1.9

[vapid anvil]

Can't tell what the equation is

Is it $4cos(2t) - sin(t) = -4$

[flat frigate]

ColdTee

[vivid current]

yep

[quasi bison]

@vivid current cos(2t) is not equal to (sin(2t))^2 and also (sin(2t))^2 is not equal to 2 (sin(t))^2

[vivid current]

ohhh

what does it equate to then?

would*

[quasi bison]

do you know double-angle identities?

specifically the ones for cosine

[vivid current]

hmm is it the 2pi - cos stuff?

[flat frigate]

What the hell am I doing here?

[spice grove]

These, basically.

[vivid current]

Ohh i see

Which one should i use in this situation

i assume the second one?

[spice grove]

Yes, that one.

[vivid current]

could i get an example as to how to apply the formula to an equation?

i am very new to this topic

[gleaming ravine]

Just aplly the second formula to cos(2t)

the cos(2x) = 1 - 2 sin^2(x)

apply this one

and you will get a quadratic equation

assume sin(t) as m and solve the quadratic

[safe radish]

@vivid current Has your question been resolved?

[vivid current]

i got this, is it correct?

[gleaming ravine]

yeah

[safe radish]

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[charred spoke]

Could some explain what I have to do for this questions please? :)

[lean otter]

do long division for a

[charred spoke]

ty very much! 😊

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[tall pumice]

Calculus/Real Analysis
Hey fellas
I'm trying to solve the following question, I have the solution on the tip of my tongue but I can't quite communicate it:

The problem:
Given a series (a_n) which does a_n+2 - a_n ---> 0 as n approaches infinity
Prove that (a_n) / n ---> 0 too

Explanation
Intuitively, I understand why that's true - essentially the derivative of a_2n and a_2n-1 approaches 0, whilst n's remains at 1 forever (Of course, there are no derivatives here)
I can't quite figure out how to prove this though. Any help would be much appreciated

[tall pumice]

(Sidenote: I don't want the solution spoon - fed, just a hint if possible!)

I have tried:
Separating the series (a_n) into two sub-series as mentioned earlier
Using the cauchy definition for a converging series
Using the "regular" definition for a converging series and fiddling with equation
Using big O notation to try and prove why it's impossible for the limit to be anything but 0 (Got a little brave with this one)

[safe radish]

@tall pumice Has your question been resolved?

[safe radish]

@tall pumice Has your question been resolved?

[safe radish]

@tall pumice Has your question been resolved?

[safe radish]

@tall pumice Has your question been resolved?

[peak estuary]

maybe double https://en.wikipedia.org/wiki/Summation_by_parts ?

[safe radish]

@tall pumice Has your question been resolved?

[thick sparrow]

Seems proving the contrapositive statement will be easier.

Problem Statement: If $\lim_{n\to \infty} \frac{a_n}{n} \ne 0$, then $\lim_{n\to \infty} (a_{n + 2} - a_n) \ne 0$.

[flat frigate]

jimmy1234

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[short birch]

help how do you solve thiss?

[hot thistle]

do you know how to find the slope of a line using 2 points

@short birch

[short birch]

is it using y2 - y1 / x2 - x1?

[hot thistle]

yes

(y2 - y1)/(x2 - x1)

[short birch]

then its m-3 / 1-m

what do i do after that

[hot thistle]

what did they say the slope was equal to

[short birch]

nothing

[hot thistle]

reread your question

[short birch]

greaterthan zero

[hot thistle]

reread your question

what did they say the slope of the line was

i'm looking for a letter

[short birch]

letter m

[hot thistle]

yes

so (m-3)/(1-m) is equal to what

[short birch]

equal to m

[hot thistle]

yes

write that out

[short birch]

m = m-3/1-m

[hot thistle]

with parentheses

but yes sure, i get what you mean

you should be able to solve that for m

[short birch]

oaky

i did

m/ 1 = m-3 / 1-m

i cross multiplied

so i got m (1-m) = m-3

distribute m in the LHS

m - m^2 = m-3

i transpose m from the RHS to the LHS so the 2 ms will cancel so i'm left with -m^2 = -3

and i think im wrong

[hot thistle]

that was all correct

you're almost there

[short birch]

sqrt of -m = sqrt of - 3

[hot thistle]

multiply by -1 first

[short birch]

if i multiply by 1 i get sqrt of m = sqrt of 3

and im left with

sqrt of 3

[hot thistle]

yes

[short birch]

but the answer is supposed to be 5

[hot thistle]

i can assure you it's not

[short birch]

this was the choices given to me

and it told me the correct answer is 5

but i dont know how it came to be

[hot thistle]

those are different points

than what you wrote

[short birch]

Oh what the heck

[hot thistle]

the methodology is the same

[short birch]

Okay sorry about that i was sleep dperived

okay ill sovle once agian

[hot thistle]

if you want to confirm the answer is 5, you can repeat the steps

[short birch]

Oaky i'll try

i tried and i came to a point where

m^2-2m = 15

I dont know how to proceed

[hot thistle]

do you know how to solve a quadratic equation?

you can:
factor
use the quadratic formula
complete the square
and more

im sure you know some of these methods

[short birch]

Ill try factoring

m(m-2) = 15

[hot thistle]

i meant

factor m^2 - 2m - 15 = 0 into (m-a)(m-b) = 0

[short birch]

ohhh

okay

(m - 5) (m+3)

and through elimination idk the term

[hot thistle]

so what are the two roots

[short birch]

m = 5

and m = -3

but m > 0

so the second is incorrect

therefore its 5

ahhh i see it now

thank you!

.close

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[quasi bison]

that's not how these channels work

you don't open a channel to ask if anyone needs help