help-13

[wicked remnant]

Wait

Wait

Wait

So

[grizzled birch]

85 would be 5*17

yes?

[wicked remnant]

2 x 17 = 34 right?

[grizzled birch]

yes

[wicked remnant]

So 5 x 17 is 85 too??????

[grizzled birch]

uh

ok so u take the largest common thing u see in these thingies

which is 17

that's the gcd

[wicked remnant]

What

[grizzled birch]

and

so

for

LCM

u basically

eliminate the similar parts between the two (only keep one)

so 17, right?

[wicked remnant]

Yes

[grizzled birch]

you only keep one of the 17s

[wicked remnant]

Ok

[grizzled birch]

so you get 17 x 2 x 5

[wicked remnant]

o

[grizzled birch]

which is 170

[wicked remnant]

n

g

[grizzled birch]

which is the lcm

[wicked remnant]

Wassut

Waait

[grizzled birch]

uh hope that helped lmao

[wicked remnant]

Waait

Waut

Wait

Wait

Wait

[grizzled birch]

mhm

[wicked remnant]

Don't go

Ols

Ait

[grizzled birch]

yes?

[wicked remnant]

How did you get 17

Like

How did you know it was 17

[grizzled birch]

bc
85:5 x 17
34: 2 x 17

[wicked remnant]

What

[grizzled birch]

the common thingie is 17

[wicked remnant]

So like

Everything I have to multiply it with 17?

[grizzled birch]

emmm

so you basically

get rid of one of the 17s

because it's repeating

and you multiply the rest together

u take out the repeating part

[wicked remnant]

ok

What is

Hcf

[grizzled birch]

uhhhhhhhhhhhhhhhhhhh there's a much easier way to do this but

uh

[cedar kiln]

Channel closed

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[grizzled birch]

gcf i think u mean

[wicked remnant]

.reopen

[grizzled birch]

.reopen

[cedar kiln]

✅

[grizzled birch]

greatest common factor

[wicked remnant]

Yes

Gcf

Yes

[grizzled birch]

that's 17

u get gcf

[wicked remnant]

Ohohoohohooh

Ohh

Hh

Ih

Bo

Ohh

I see

[grizzled birch]

by multiplying the similar numbers togther in a number set

like

for example

hmmmm

[wicked remnant]

What

[grizzled birch]

uh 72 and 56

72 is 2 x 2 x 2 x 3 x 3

56 is 2 x 2 x 2 x 7

the gcf is 2 x 2 x 2 = 8

[wicked remnant]

What

Can u please add me cuz I need someone to help me when I don't know what to do in math

Im bad at math

[grizzled birch]

okok

same bro

lmao

[wicked remnant]

I will sned

My brain don't function properly

Jk

Vbbyeeeeeeeeeeeeeeeee

.close

[cedar kiln]

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[wicked remnant]

.xlos

.xlo

ok

[cedar kiln]

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[ionic slate]

A flying squirrel jumped from a tree 11 feet in the air at an initial velocity of 9 feet per second. The equation h = -2t^2 + 9t + 11 models his jump where h is height in feet and t is time in seconds

[ionic slate]

when the did squirrel reach the ground?

can someone work this out theres like 10 of these and i need like a starting point

[cedar kiln]

@ionic slate Has your question been resolved?

[sweet vapor]

What have you tried so far?

[ionic slate]

ive just substituted 0 for h and tried to factor in order to get two solutions

and pick out the positive

i doubt i am doing it correct tho

d

[exotic furnace]

That is the correct solution

What answer did you get

btw if you can’t factor (although you definitely can factor this one), use the quadratic formula

[ionic slate]

i got (t+1) and (-2t+11)

wouldnt both of those be negative?

[exotic furnace]

Equate each of them to 0

solve for t

[ionic slate]

-1 and -5.5?

wait

omfg

i am so stupid

im so sorry

how did i look past that

[exotic furnace]

live and learn folks

[ionic slate]

.close

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[ionic slate]

Fireworks are fired from the roof of a 100 foot building and travel 84 feet per second. The equation h = -16t^2 + 84t + 100 models the height h of the fireworks at any given time s seconds

[ionic slate]

How high did the fireworks get?

How high were the fireworks 2 seconds after they left the roof?

I got the same answer, 204 for these. are they wrong?

[swift wind]

204 is correct for the second question but incorrect for the first one.

[ionic slate]

i mustve messed up badly

on the first one i got -16(169/16) + 84(13/4) + 100

and it came out as 204 idk y

[swift wind]

Why did you put the timee as 13/4?

[ionic slate]

i dont even know i thought i was solving for max

so i used the axis of symmetry

[swift wind]

That should give you the correct answerr, what was the formula you used for the axis of symmetryy?

[ionic slate]

-b/2a

waittt

hold on

[ionic slate]

somehow i simplified to get 13/4 rather than 21/8

i am way too tired for this LOL

[swift wind]

yeaa lmao

[swift wind]

just take a breakk lol

[ionic slate]

tyyyy

[swift wind]

npp

[ionic slate]

its 4 am LOL im tryna cram my hardest

but i endup making the worst mkistakes

.close

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[upbeat whale]

whats the transformation of 2^x+5

[upper garnet]

what's even the parent function

the function that has been transformed on

[cedar kiln]

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[vestal hare]

Continue the sequence and how

[vestal hare]

1,3,4,2,6,3,4,9,2,8,12,1

<@&286206848099549185>

[cedar kiln]

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[left hound]

does this look good?

[fathom steppe]

where is the 42 from?

[queen horizon]

where does $9 \sqrt{90}$ come?

[wraith dagger]

2022 squared

[queen horizon]

dont get it why $21 \sqrt{90}=9\sqrt{90}$

[wraith dagger]

2022 squared

[fathom steppe]

There’s a -12sqrt(90)

[queen horizon]

owh

[cedar kiln]

@left hound Has your question been resolved?

[left hound]

sorry

I'm back

-14 times 3

[fathom steppe]

you wrote it as -14sqrt(3)

[queen horizon]

i got it

just square the root

$-14(\sqrt{3})^{2}$

[wraith dagger]

2022 squared

[cedar kiln]

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[pallid temple]

Hi ! Can anybody explain these sums to me ,( any one from both sections , I'll try others) it's from the chapter relations and functions.

[south dawn]

Third row is incorrect: You want to write -

18(30) +21(V3)(V30) - 12(V3)(V30) - 14(3)

+21(V3)(V30) - 12(V3)(V30) are like terms. 9(V3)(V30)

Sorry, it was closed.

[cedar kiln]

@pallid temple Has your question been resolved?

[pallid temple]

<@&286206848099549185>

[cedar kiln]

@pallid temple Has your question been resolved?

[cedar kiln]

@pallid temple Has your question been resolved?

[lyric jungle]

,rotate

[cedar kiln]

@pallid temple Has your question been resolved?

[cedar kiln]

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[barren hinge]

Would y = -10 x = 0 work?

and is that the only solution?

[torn hare]

why would it equal zero?

[barren hinge]

for the first equation if x = 0 and y = -10 it would be

0 + -10^2

which is 100

the second would be 3(0) + (-10)

which would be -10

In short,

I plugged in random numbers

[torn hare]

have u tried solving algebraically?

[barren hinge]

I have no idea how to

Here I'll start

and tell me if I get it wrong

y = -3x - 10

x^2 + (-3x-10)^2 = 100

[torn hare]

all good so far

[barren hinge]

and I'm stuck here

[lusty willow]

dont u do x^2+9x^2+100

[barren hinge]

x^2 + (-3x-10) = 10?

x^2 - 3x = 20?

x = 20/-3 square root?

[cedar kiln]

@barren hinge Has your question been resolved?

[barren hinge]

<@&286206848099549185>

[lusty willow]

<@&286206848099549185>

[glad kestrel]

this is not your channel

[glad kestrel]

that (-3x-10) quantity should be squared, since you're substituting it in for y^2, not just y

and that 10 should be 100

[glad kestrel]

wait what you had it here

[barren hinge]

the 100 became 10 because I sqiared rooted both sides

[glad kestrel]

that's not how square roots work

[barren hinge]

oh

[glad kestrel]

if you take the square root of $a^2+b^2=c^2$, you do not get $a+b=c$

[wraith dagger]

a disappointing son

[glad kestrel]

or $a^2+b=c$, as you wrote

[wraith dagger]

a disappointing son

[barren hinge]

do I do this instead?

[glad kestrel]

i have no idea what that is or where it came from

it's just solving an algebraic equation, now

[barren hinge]

he multipled the (3x-10)^2 out

[glad kestrel]

he did not

expanding that will not get you x^2+9x^2+100

[lusty willow]

i did

[barren hinge]

nvm he did do it wrong

forgot the formula

how do I solve it algebrcially from there?

[glad kestrel]

you'll end up with a quadratic

[barren hinge]

Or How do I get rid of the square roots then

[glad kestrel]

solve it as you'd solve any other quadratic

[barren hinge]

I can't

thats why I'm asking for help

[glad kestrel]

you can't solve a quadratic?

[barren hinge]

I don't even know what that means

[viscid orbit]

Can someone help

[barren hinge]

You want me to multiply (-3x-10)^2 through FOIL method?

[viscid orbit]

How is m9/m6=8

[glad kestrel]

not your channel, you've been told multiple times to stick to your own channel

[glad kestrel]

yes

that would be step 1

[barren hinge]

Ok that I can do

give me a moment

9x^2 + 60x + 100?

[glad kestrel]

looks good

[barren hinge]

so x^2 + 9x^2 + 60x + 100 = 100

[glad kestrel]

exactly

[barren hinge]

x^2 + 9x^2 + 60x = 0

x = 0

?

[barren hinge]

So I was right? or?

[glad kestrel]

no

[barren hinge]

oh

[glad kestrel]

this is right

but it's a quadratic, it has two solutions

[barren hinge]

y = +-10?

[glad kestrel]

how are you getting 10

[barren hinge]

3x + y = -10

3(0) + y = -10

0 + y = -10

y = -10

x^2 + y^2 = 100

[glad kestrel]

you need to solve the quadratic first

[barren hinge]

0 = y^2 = 100

y = 10?

[glad kestrel]

solve 10x^2+60x=0 first

[barren hinge]

x = 0

[glad kestrel]

and?

[barren hinge]

i have no idea

[glad kestrel]

well you have options

you can factor and use the zero product property or you can use the quadratic formula

[barren hinge]

didn't I just solve it?

[glad kestrel]

a quadratic has two solutions

you only stated 1

[barren hinge]

10x^2 = -60x

x^2 - -6x

this doesnt seem right

[glad kestrel]

you shouldn't be moving 60x over to the other side

if you don't know how to factor and use zero product property, then use quadratic formula

[barren hinge]

why

[glad kestrel]

because that's not how you solve a quadratic

[barren hinge]

i can do both

i hope

10x(x+6) = 0

x = -6

x = 0 or x = -6

[glad kestrel]

there you go

now you can plug those values into your other equation to solve for y

[barren hinge]

3(-6) + y = -10

-18 + y = -10

y = 8

x = 0 or x = -6 y = -10 or y = 8?

[glad kestrel]

and, not or

those are all valid solutions

[barren hinge]

Your my best friend

thank you

.close

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[calm bronze]

Hello

[calm bronze]

I have a question on this problem

I'm wondering what the form a+bi means

I'm pretty sure I'm supposed to combine coeficients

and simplify like that, but I'm not exactly sure

[violet rapids]

@calm bronze i is a variable

simplify it as if it was any other variable

[calm bronze]

Ok

So if I did it right, it should be 140 + 40i?

-140*

[violet rapids]

,w simplify (10+10i)(-5+9i)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by sills#9713

[violet rapids]

@calm bronze nice

[calm bronze]

K

Thx

Why is there aspace?

between 40 and i

[violet rapids]

there isn't

[calm bronze]

k

Thx for the help

.close

[cedar kiln]

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[violet rapids]

np just remember i = sqrt(-1)

[calm bronze]

ik

Thx

.close

[glad kestrel]

this is misleading

[calm bronze]

.reopen

.close

[cedar kiln]

✅

Channel closed

Closed by @calm bronze

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[calm bronze]

Exactly why I came here.

[glad kestrel]

i meant the statement of "i is a variable"

cause it's not

[calm bronze]

Ik

Btw

This is 2nd option correct

I need some opinions

Some say 2nd and 3rd

I think 2nd but idk

anything times pi is irrational

but idk if t can change that statement

[crimson sedge]

how so?

[calm bronze]

pi is irrational

[crimson sedge]

what about pi*(1/pi)?

not true!

[calm bronze]

I meant with integers

7pi is def irrational

[crimson sedge]

ok then, sure

[calm bronze]

But what abt t

A fraction can't change it I don't think

[crimson sedge]

why is what Skid said false?

[sweet stag]

only rational if they cancel each other

[calm bronze]

Bc of school....?

Most cases yes, because none can terminate the other

[sand ridge]

t can be -7pi

[calm bronze]

So it's 3rd optinon?

[crimson sedge]

is pi + e irrational then?

[calm bronze]

Hm

[flint plinth]

pi and (1 - pi) don't cancel each other, but their sum is rational

[calm bronze]

No it isn't

Both are trasncental

[sand ridge]

isnt the answer basically unknowable

[calm bronze]

But I'm pretty sure it's rational for that reason

Here's the screenshot again

[sweet stag]

i mean cancel each others irrationals

[crimson sedge]

haha yea it's an open problem, I was teasing what Skid said 😛

[flint plinth]

it is not known whether e + pi is rational, but that doesn't mean it's unknowable

just that no one has found a proof one way or the other

[calm bronze]

ye

[sand ridge]

well tru

[calm bronze]

I think it's rational

But there are millions who disagree

[sweet stag]

it can be either

[flint plinth]

that would be surprising to say the least

[calm bronze]

Exactly

[sweet stag]

rational if the irrationals cancel

[flint plinth]

i would say even astonishing

[sweet stag]

if t = 7pi -1 it is 1

[sand ridge]

if you believe hard enough!

[crimson sedge]

same

[calm bronze]

Skid it can only be one value

[sweet stag]

7pi -1 is one value

...

[calm bronze]

.

7 O

I thought u meant for t

so -1 = t?

[sweet stag]

no

[calm bronze]

...

[sweet stag]

t = 7pi -1

is one value

[calm bronze]

It can only be one operation/value

like a fraction like 1/2

or 35

or 23232.323232

[crimson sedge]

7pi + t is irrational when t = pi and rational when t = -7pi

[sweet stag]

its irrational

[calm bronze]

not 92832-397539743 [phone] _29372392732

SO its the 3rd answer

Since it can be neither rather both

[crimson sedge]

yes

[sand ridge]

yes

[calm bronze]

K

[cedar kiln]

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[calm bronze]

thx

[cedar kiln]

@calm bronze Has your question been resolved?

[cedar kiln]

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[crimson sedge]

Let say, I have to unlock a 3 coded lock in my potion cabinet to get the potion. I remembered the numbers that were used, which is 2,3, and 9, and I know they do not repeat; but unfortunately, I forgot the order of the numbers used to unlock the lock. How many different codes can be used to unlock the cabinet

[crimson sedge]

I know i have to use permutation, so I plug in the permutation formula and got 6

can anybody vouch and double-check for me that it is indeed 6 ways to unlock the code?

[upper abyss]

Only three possible entries and they're all 2,3,9?

Just in any order?

Yeah, 6 ways.

[crimson sedge]

in any order

thank you, so there are 6 ways to unlock the lock

[upper abyss]

Well, I assume there's only one way. There's 6 ways to enter the code, 5 of them won't work haha

But yeah we agree here

[crimson sedge]

ahh thank oyu

so much

we use permutation right

not combination

[upper abyss]

Ye

[crimson sedge]

thank you, so much

[cedar kiln]

@crimson sedge Has your question been resolved?

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[sacred socket]

How can I solve this?

The English alphabet has 26 letters, including 5 vowels (A, E, I, O, and U).

How many strings of capital letters are there which contain exactly 3 vowels and 7 consonants, with no repeated letters?

I thought that this was the answer but it is not correct.
10! × (C(5, 3) + C(21, 7))

Here was my thinking: 3 vowels + 7 consonants is 10. You're looking for 3 vowels out of 5 and 7 consenantes out of 21 of them.

My next idea is that this is the correct answer is E out of the options below:

A 10! × (C(5, 3) + C(21, 7)) Incorrect
B 10! − (C(5, 3) × C(21, 7) ) possibly correct
C 21^7× 5^3
D 26^10−21^7−5^3
E C(5, 3) × C(21, 7) ×10! possibly correct
F None are correct

[crimson sedge]

wdym by strings

oh nvm I cant help you sorry

[cedar kiln]

@sacred socket Has your question been resolved?

[cedar kiln]

@sacred socket Has your question been resolved?

[cedar kiln]

@sacred socket Has your question been resolved?

[sacred socket]

No

[cedar kiln]

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[covert raptor]

what does the first two lines of part b)'s answer do?

[covert raptor]

and how can you get it?(just the first two lines of part b 's answer)

[cedar kiln]

@covert raptor Has your question been resolved?

[covert raptor]

<@&286206848099549185>

[dire geode]

What don't you get. They just plugged in U into the pde

[covert raptor]

like where is u_s'' come from

never mind, I get it

.close

[cedar kiln]

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[blissful ibex]

Can someone help me with 1B? I dont understand how the limit is supposed to cancel out

[blissful ibex]

https://cdn.discordapp.com/attachments/409596215697866773/960983501191139458/F9940D99-8E57-495A-96F8-3BF8D6D064B9.jpg

https://cdn.discordapp.com/attachments/935361718907985964/961035382806425640/5AA0052C-278F-409D-814A-CD8D2CDFEB3C.jpg

[rapid sigil]

if n -> to infinty

then 1/n -> 0

work with that

@blissful ibex

[blissful ibex]

i dont see how that applies here

[crimson sedge]

I think this problem is easily solved by noting cos(npi) = 1 if n is even and cos(npi) = -1 if n is odd

[rapid sigil]

Because once you run to 0

[blissful ibex]

0 * infinity is indeterminate form

and i cant have that

[rapid sigil]

you can solve with

No you replace all n with 1/n

in the expression

[blissful ibex]

why would i do that

that doesnt make sense how im allowed to just replace them with 1/n

[rapid sigil]

You know that n goes to infinity

as such you also know that 1/n goes to 0

as its the inverse

[blissful ibex]

Would Squeeze Theorum work on this problem?

[rapid sigil]

No idea what that is

[blissful ibex]

i remember my prof doing something that involved sin using squeeze theorum

[crimson sedge]

this is the key 😶

[rapid sigil]

but you can shorten then n

and then when cos runs to 0

you should get pi

[crimson sedge]

the sequence is -1, 2, -3, 4, -5, 6, ...

[blissful ibex]

im still lost

[blissful ibex]

i see how u got this

[blissful ibex]

i dont get what ot do with this

[crimson sedge]

that's why the sequence is -1, 2, -3, 4, -5, 6, ...

[blissful ibex]

the sequence that from starting at n=1 going to inf

and plugging in every increment

[crimson sedge]

I'm not sure what you are confused on 😐

[blissful ibex]

would i do something like the bottom?

for this problem?

[crimson sedge]

uhhh, no?

[blissful ibex]

Thats Squeeze theorum & comparison test thats why i was asking

[crimson sedge]

in b you want to show a sequence diverges, in the one you just sent you show a series converges

[blissful ibex]

in B

it diverges

i just need to show how i got the answer

[crimson sedge]

oops! I flipped around the words

[blissful ibex]

if comparison test fails doesnt that mean that it doesnt converge

[crimson sedge]

what does comparison test failing mean?

[blissful ibex]

that the Sequence i got diverged

that i was comparing to the orignal

[crimson sedge]

that's too vague for me to understand 😐

[blissful ibex]

Do u know what comparison test is

[crimson sedge]

yes

[blissful ibex]

So when Bn Diverges doesnt that mean An also diverges

Bn being the Sequence i made, An being the Sequence im testing

[elfin hemlock]

There are two ways to use comparison

[crimson sedge]

more detail on the comparison?

[elfin hemlock]

Find a lower bound that diverges

Then original diverges

[blissful ibex]

1/n Diverges

[elfin hemlock]

Find an upper bound that converges

[blissful ibex]

but idk how to get it to tht

[elfin hemlock]

Then original converges

[elfin hemlock]

.

[crimson sedge]

you don't need comparison test for part b

you aren't even trying to show a series diverges

it's a sequence

[blissful ibex]

Im showing if a Sequence Diverges

[crimson sedge]

and I've outlined a solution for you

[blissful ibex]

which it does but i dont get what ur saying

[crimson sedge]

what do you want explained more?

[blissful ibex]

i didnt understand what u were tlaking about

thats quite litterally the problem

[crimson sedge]

you see how I got this?

[blissful ibex]

yes u plugged in from 1 incrementing up to infinity

[crimson sedge]

hmm I didn't really do that

well I kinda did

[blissful ibex]

1 * cos 1 * pi = -1*1 = -1
2 * cos 2 * pi = 1 * 2 = 2

thats how i assumed u got it

[crimson sedge]

the sequence is ${n(-1)^n}$

[wraith dagger]

yume ♡

[crimson sedge]

using this

[blissful ibex]

So what id Say nCos(npi) = n(-1)^n

[crimson sedge]

yea you can say that

[blissful ibex]

and by alternating series test it diverges?

[crimson sedge]

why do you want to use series tests for everything+?

[blissful ibex]

Because thats All hes taught us

and its what hes asking for in the exam i beleive

[crimson sedge]

series tests are theorems about series convergence/divergence

[elfin hemlock]

Seeing how it says “sequence”

[blissful ibex]

quite litterally the last few weeks all weve covered is Tests for Series and Sequences

[elfin hemlock]

And a sequence is not a series

I highly doubt that

[crimson sedge]

any unbounded sequence diverges

and this sequence is unbounded

[blissful ibex]

unbounded meaning it goes to Infinity?

[crimson sedge]

kinda

the sequence gets arbitrarily large or arbitrarily small

small meaning negative

[blissful ibex]

so is this all the explaination needed?

[crimson sedge]

that's probably ok

[blissful ibex]

im not understanding this stuff and i got an exam around the courner

hopefully there wont be a problem as complicated as this

this is on the review tho

i can do A C and D for #1 by myself

but not b

[crimson sedge]

welp, good luck 🙂

just don't spam series tests on every question and you'll be ok 😆

[cedar kiln]

@blissful ibex Has your question been resolved?

[blissful ibex]

ye but i didnt know nay other way to solve it

[cedar kiln]

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[cedar kiln]

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[sweet ingot]

Hey

[sweet ingot]

quick question

the answers say the domain is x < 0

why isnt it x > 0?

(the answer on the book)

[south juniper]

Area?

[sweet ingot]

i mean domain

[south juniper]

Oh

Try to put x=0.5

x^2 becomes smaller than 0.5

and 2x is larger than x, so larger than x^2

and so you have a negative inside the square root, which cant happen.

Basically you need x^2 - 2x >= 0 for the function to be defined

Solving this inequality gives you x>=2, x < 0

[leaden snow]

Well it doesn't work on the interval [0, 2) because then either the term under the root is negative or the denominator becomes zero

[sweet ingot]

what would be the difference here between 0.5 and -0.5

[south juniper]

Try to put both numbers in the function, see what happens

[sweet ingot]

so 0.5 gives me -3 and -0.5 gives me 2√5

[south juniper]

Yeah you can't have a negative inside the square root

[sweet ingot]

i see

.close

[cedar kiln]

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[soft cloak]

I'm reviewing convexity with some exercises, and this one has me stumped :
Let $I$ be an open interval and $f \in \mathcal{C}^0(I,\bR)$ such that $\forall x\in I, \lim_{h\to 0} \frac{f(x+h)+f(x-h)-2f(x)}{h^2} \ge 0$. Show $f$ is convex. Indication : start with the case where the inequality is strict.

[wraith dagger]

Syst3ms

[soft cloak]

Now, this is quite easy if f is doubly differentiable

Using the Taylor-Young theorem, one can write $f(x+h) \underset{h \to 0}{=} f(x)+hf'(x)+\frac{h^2}2f''(x)+o(h^2)$, and the expression inside the limit (limitand would be a fun name) cancels out to $f''(x)+o(1)$

[wraith dagger]

Syst3ms

Syst3ms

[soft cloak]

Great. But the function in question is only known to be continuous

Following the given indication of using the strict inequality case, I noticed that having a strict inequality means the quantity is strictly positive for small enough h

So for some $\eta > 0$, I have $\forall h\in[-\eta,\eta], \frac{f(x+h)+f(x-h)-2f(x)}{h^2} > 0$

[wraith dagger]

Syst3ms

[soft cloak]

But I don't really know how to exploit this

Unless some miracle occurs, I'm pretty sure the "barycenter" definition of convexity is a lost cause

Yeah I'm stumped, any help is appreciated

[crimson sedge]

This one is hardcore. I have the full proof in french and it uses an additional lemma

[soft cloak]

Namely?

It's isn't unlikely that I'd know the result as some edge-of-syllabus thing

Also i'm French

[crimson sedge]

the lemma is : f: I -> R is convex iff for any interval [a;b] in I and for any u in R : the function g(x) = f(x) + u*x is bounded in [a;b]

[crimson sedge]

Wait I am going to screen the whole proof

[soft cloak]

"et atteint sa borne supérieure en a ou en b" is quite an important hypothesis

otherwise that's true of any continuous function

[crimson sedge]

Yeah but f here is not continuous I think

If it's continuous then the proof is simplified

but the lemma is still not trivial

[soft cloak]

I mean for the lemma

You forgot that "and attains its upper bound in a or in b" part

[crimson sedge]

Yeah you're right, my mistake

But you have the full proof now

[soft cloak]

yeah damn

Wouldn't have figured that out in the amount of time I intended to spend on it

[crimson sedge]

haha this is a hard one. But maybe there is an easier way to do it.

[soft cloak]

Although if I'm not mistaken I've seen that criterion for convexity elsewhere

gimme a sec

[crimson sedge]

Ah

Okay

[soft cloak]

I knew it, it was on one of the exercise sheets of this year

Hah, and that first question was also an exercise on there

[crimson sedge]

lol. sounds like we're supposed to know it

[soft cloak]

Not quite, our exercise sheets are compilations of oral exam problems

They're hard

[crimson sedge]

Yep definitely

[soft cloak]

That lemma was also part of an exercise on our sheet

Except the coefficient µ = -(f(b)-f(a))/(b-a) was given as an indication

[crimson sedge]

Well that hint sounds helpful

[soft cloak]

Yeah...

Anyway it's kind of jarring because the previous problem I did was significantly easier

It was to show that for all $x, y \in [0,\frac\pi{2}], x < y \implies \frac{x}{y} \le \frac{\sin(x)}{\sin(y)} \le \frac{\pi x}{2y}$

[wraith dagger]

Syst3ms

[soft cloak]

The second inequality isn't too bad as long as you know a useful sine inequality, the other one is a bit trickier

But nothing like my original question

But I digress

[crimson sedge]

Yeah this one looks more doable

let me guess : sin(x)<= pi/x or something

[wraith dagger]

Syst3ms

[soft cloak]

It's nice to have in mind

[crimson sedge]

haha nice inequality

[soft cloak]

this is a concavity inequality, but for the trickier of the two demanded inequalities you have to actually use concavity and not just this consequence

But it's high time i closed this

.close

[cedar kiln]

Channel closed

Closed by @soft cloak

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[crimson sedge]

More tricks? I'm out for now lol.

[soft cloak]

I'll let you find out

[cedar kiln]

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[crimson sedge]

haha thanks. good luck with that

[crimson sedge]

.close

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[sinful sandal]

I have to get x

[sinful sandal]

So what would i do

I got 24.86

But idk

I used the formula 1/2absin(c)

[leaden snow]

Yeah and you know the area

so just solve for x

[sinful sandal]

I got 24.86

So i wanted to check if i made an error

Cuz it seems unlikely

I don’t this it would be a decimal

So wanted to check

[leaden snow]

,w sqrt(300) = (1/2) * (x+3) * x * sin(60 deg)

[wraith dagger]

Results provided by WolframAlpha

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

Requested by Navix#0001

[sinful sandal]

Ok thx soo much

So i will only use the positive value right

Cuz you can’t have negative length

[leaden snow]

you should solve it yourself tho

[sinful sandal]

Yeah k

But thx soo much

.close

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[short token]

is there any way

[short token]

i can find the coefficient

if i have (x+a1)(x+a2)...(x+an)

can i find the coefficient

of x^(n-1)

[modern compass]

if the leading coefficient is 1 (like it is here), the second coefficient (the one on x^{n-1}) is the sum of the roots

[short token]

😮

[upper abyss]

Yes. That's Viete's formulas

[short token]

so a1+a2+...+an?

[upper abyss]

All of the coefficients are some symmetric equation of the roots

[short token]

ok ty

.close

[cedar kiln]

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[upper abyss]

Or, it's the negative, no?

Nvm Zyb is right

[modern compass]

hmmm yeah it's technically negative... depends on how you define it

[upper abyss]

Negative of the roots, but not the negative of whatever was typed above

[short token]

😄

.close

.close

.reopen

[cedar kiln]

✅

[short token]

.close

[cedar kiln]

Channel closed

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[short token]

hmm

still occupied

.close

[modern compass]

it'll go away in a minute

[cedar kiln]

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[ripe bison]

Need help with a convergence test question

[ripe bison]

I believe this is a p-series question?

Am I on the right track?

[soft cloak]

yes

when n tends towards infinity, can you find an equivalent of the fraction?

(hint : higher powers become far larger than anything of lower degree)

[ripe bison]

No, I'm struggling with this concept.

[soft cloak]

Right

[ripe bison]

I don't sub the value of n = 3 into the "n" variables?

[soft cloak]

This is a summation

3 is just the starting value

If I write $\sum_{n=3}^{10} x_n$ it's short for $x_3+x_4+\ldots+x_9+x_{10}$

[ripe bison]

I got that.

[soft cloak]

When the upper bound is infinity, it's not as simple as saying "sum infinitely many terms" (because nobody actually knows how to do that), but it's a convenient shortcut

[wraith dagger]

Syst3ms

[soft cloak]

Infinite sums are limits before anything else

Specifically, the limits of the partial sums

So here your task is to use one of the tests you already know to state whether this particular series is convergent or divergent

[ripe bison]

So converges if p > 1 and diverges if p <equalto 1

[soft cloak]

yes

well, that's for the specific form 1/n^p

By the way, "<=" is how you would write that second symbol

[ripe bison]

Thanks.

[soft cloak]

Say, which tests do you have at your disposal besides p-series (also called Riemann's criterion)?

[ripe bison]

So, Im at a loss of where to begin the problem.

Ive briefly gone over divergence, integration, geometric

root

ratio

alternating series.

Think that's all of them

@soft cloak

[soft cloak]

Not even comparison or something of the sort?

[ripe bison]

Yes, that as well.\

[soft cloak]

Right, well unfortunately you don't have equivalence, but comparison will do just fine

Although I will use equivalence as a way to find the answer. To prove it, we'll use the tools you have at your disposal

Two sequences are equivalent if their ratio approaches 1. Not too involved.

The "equivalence test" for series is saying that if the positive general terms of two series are equivalent, then the first series if and only if the other one does

So here, we'll use equivalence to reduce this problem to a simple p-series test

Now, we just need the equivalence of rational fractions. Fortunately, it's a theorem that's easy to prove and o remember.

In your case, we have (5n²+3)/(7n^3+20). The idea will be to factor out the highest-degree terms in the numerator and the denominator

[ripe bison]

5n^2 and 7n^3

[soft cloak]

Yes, factoring the constants is optional

We get n²(5+3/n²)/(n^3(7+20/n^3)) = 1/n * (5+3/n²)/(7+20/n^3)

But notice that the right-hand factor tends do 5/7 as n tends to infinity

So the general term of your series is equivalent to 5/7n

Now can you say something about the convergence of the series using the p-series test?

[ripe bison]

trying to visualize that equation

[soft cloak]

No, $5n^2+3 \ne n^2(5+3)$

[wraith dagger]

Syst3ms

[soft cloak]

You have to factor it all the way

That's as if i said 4*2+1 = 2*(4+1)

Let me format it nicely

$\frac{5n^2+3}{7n^3+20} = \frac{n^2(5+\frac{3}{n^2})}{n^3(7+\frac{20}{n^3})} = \frac{n^2}{n^3}\frac{5+\frac{3}{n^2}}{7+\frac{20}{n^3}} = \frac1{n}\frac{5+\frac{3}{n^2}}{7+\frac{20}{n^3}}$

[wraith dagger]

Syst3ms

[soft cloak]

Do you follow this ?

[ripe bison]

Yes

[soft cloak]

So what we showed is that up to something that tends towards a constant, (5n^2+3)/(7n^3+20) is more or less the same as 1/n

And what can you say about 1/n as far as series are concerned?

[ripe bison]

for a p-series I'd say it diverges because p is non existent so it is less than zero?

Er.

🥴

[soft cloak]

n=n^1

[ripe bison]

so, diverges

[soft cloak]

yes

the series of 1/n is called the harmonic series, and the fact that it diverges is quite important

[ripe bison]

why is that?

[soft cloak]

Its divergence or why it's important?

[ripe bison]

its importance

[soft cloak]

It shows that the sum of a sequence that tends towards 0 isn't necessarily finite

But i digress

[ripe bison]

Ah.

[soft cloak]

So what the "equivalence test" that you can't actually use tells us is that (5n^2+3)/(7n^3+20) behaves more or less in the same way than 1/n, which diverges

So our series diverges

And here's a general rule

When you have a rational fraction (= a fraction of polynomials), the higher degree terms "win" over the rest

So if you see something complicated like (5n^4+9n^3-πn+1)/(8n^5+42n^3-5), you can know it will behave just like (5n^4)/(8n^5), only keeping the highest degree terms

Intuitively, it's because the higher degree terms grow so much faster than the rest. For example, for very large N, N²+N ≈ N² because N² is way larger

[ripe bison]

That I'm familiar with from Big O notation

[soft cloak]

That helps I suppose

Bottom line is, you can just look at the highest degree terms

[ripe bison]

Alternating series?

[soft cloak]

since everything is positive, you'll have a hard time using alternating series

Although we weren't completely done with the previous example

[ripe bison]

Rude of me

[soft cloak]

dw

Because that was with the "equivalence test" which you can't actually use, unfortunately

So instead you'll have to resort to the comparison test

And here the idea is just to use comparisons to only make the highest degree terms appear

You already know it diverges, so if you want to show it with the comparison test, you need to bound it from below with something that diverges

And it will be easiest to bound it from below by something that looks like 1/n

To do that, we'll get rid of these pesky non-highest-degree terms

So now, two questions :

1. How can you bound 5n²+n from below to only have a term in n² ?
2. How can you bound 7n³+20 from above (it's in the denominator) to only have a term in n³ ?

[ripe bison]

Sorry, was reviewing my text book

@soft cloak

[soft cloak]

Well not quite

[ripe bison]

True

[soft cloak]

I got that wrong

You can say 5n²+n ≥ 5n² because, well, n ≥ 0

However, you can't say 1/(7n^3+20) ≥ 1/7n^3 because that would mean 7n^3+20 ≤ 7n^3

So you have to bound 20 by something like n^3 (wink wink : n ≥ 3, what is 3^3?)

[ripe bison]

I'm not following what you mean by bound

@soft cloak Looked at my textbook and some youtube examples. Its not

and 3^3 is 27

<@&286206848099549185> Anyone available?

.close

[cedar kiln]

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[quartz mauve]

I know that sec is the reciprocal of cos but how do you find the others? And how do I use tan < 0?

[cedar kiln]

Please don't occupy multiple help channels.

[dusty hazel]

Using the fundamental identities.

Any identities you know?

[quartz mauve]

I know the reciprocal identities, the quotient identities, and the pythagorean identities

[dusty hazel]

Why not use Pythagorean identities?

[quartz mauve]

so like, sin^2 + cos^2 = 1?

[dusty hazel]

Sure.

You know cos.

[quartz mauve]

so the answer would be sqrt of 32/81?

and how do I find tan?

[dusty hazel]

So many ways.

There is another Pythagorean identity that helps in doing that.
Then again you already have sin and cos. Doesn't that mean you have tan too already?

[quartz mauve]

I think I figured it out, thanks

.close

[cedar kiln]

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[livid crystal]

I need help with 4 and 5

[cedar kiln]

Please don't occupy multiple help channels.

[sonic verge]

ok my math problem is radical equations and can someone please give me a step by step proccess on doing it . √2x – 5 = x

What's the problem ?

[livid crystal]

I need help with questions 4 and 5

[vagrant breach]

.close to close channel

[livid crystal]

.close

[cedar kiln]

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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>.
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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.

[azure dock]

Please help me, how do I find the function of this graph

[upper garnet]

,rotate

[upper garnet]

piecewise

3 functions

[azure dock]

i need to write it with absolute values

if this helps, i noticed that the second part equals -2(first part)

first part is x+3, x<-3 second is -2x-6,-3<=x<-2

<@&286206848099549185>

please

[cedar kiln]

@azure dock Has your question been resolved?

[azure dock]

<@&286206848099549185>

<@&286206848099549185> please im in a hurry

[ember python]

Why with absolute value signs?

There’s no reason that graph should be like that

[azure dock]

this is from a sheet with absolute values, all the other questions had to be like that, so this one has to be like that too probably

i've been trying for 2 hours

[azure dock]

I got this

,rotate

[ember python]

Just work out the equations of the lines, it’s a piecewise function with 3 lines

Then the graph of its modulus is shown to the right hand side

This is just 2 points -> eqn of a line

[azure dock]

yes i've been trying but i cant do it

@ember python please tell me what do to

[ember python]

Your definition looks fine?

What’s the problem

[azure dock]

how to write it as a single equation

not a peicewise

[ember python]

Why?

[azure dock]

we had to do it for all the other questions on this sheet so i suppose i need to do it for this one too

[ember python]

Piecewise functions are fine

Are the other questions combinations of multiple lines…?

[azure dock]

only 2 but its absolute value

idk if its possible to write as one

[ember python]

Yeah that form is fine

You probably could

[azure dock]

well :D

[ember python]

But it’s completely unnecessary and it would almost certainly turn out more complicated than the original definition you had

[azure dock]

ok then

tnx

[ember python]

Yeah np

[cedar kiln]

@azure dock Has your question been resolved?

[cedar kiln]

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

[rose oak]

Hi

[rose oak]

oh im stupid

.close

[cedar kiln]

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[ripe bison]

Hello need help with a convergence test question

[ripe bison]

I believe ratio test is the best method?

Or root test?

[south juniper]

Root test

[ripe bison]

Struggling with this, not sure how to begin

.close

[cedar kiln]

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[south juniper]

@ripe bison Take the kth root, you get $\frac{2k-3}{4k}$

[wraith dagger]

Sup?

[south juniper]

Now take lim as k approaches infinity

[ripe bison]

@south juniper Im in room 15 now

[south juniper]

.close

[cedar kiln]

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

[crimson sedge]

hi

[crimson sedge]

going to type out my work real quick, it is a calc honors class and I am trying to find the infliction points

its a simple question really i just need to figure out how to put it into the calculator to find y value

https://cdn.discordapp.com/attachments/692430799626174494/961398539609595954/unknown.png

thats the answer to the problem

so the original equation was -x^4 + 24x^2

second derivative was -12x^2 +48 = 0

got x=2

plus or minus 2

and I put it into the table to get the concavity

now I just need to figure out how to get the infliction point

[cedar kiln]

@crimson sedge Has your question been resolved?

[crimson sedge]

<@&286206848099549185>

[scenic delta]

what's the question??

[scenic delta]

oh

inflection points are when the second derivative is equal to 0 or undefined (and concavity changes)

[crimson sedge]

how do i get the 80

what do i do on the calculator to make 80 appear

i plug something in somewhere on my calculator to get 80

[scenic delta]

80?

w8 a sec

[scenic delta]

You plugged in the x value of the inflection point into the original equation to get the y value

[crimson sedge]

understood

[scenic delta]

let's gooooooooo

[crimson sedge]

perfect

okay

thanks

how do i close the thing

[scenic delta]

do .close

[crimson sedge]

.close

[cedar kiln]

Channel closed

Closed by @simple lichen

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[wanton oak]

If I'm using Undetermined Coefficients to solve this what is the form of the particular solution?

[wanton oak]

My previous answer was Yp = (At)e^x + B

apparently this is wrong?

my complimentary solution was Yc = c1(e^t) + c2(e^-t)cos(t) + c3(e^-t)sin(t)

[gaunt hamlet]

Firstly, your solution should be in terms of x, not t. You're introducing an unnecessary t

Secondly, the guess for the particular solution of x is not Ax, it's Ax + B.

So it shouldn't be (Ax)e^x