help-13

[obtuse wedge]

do you know what logarithm is?

[shy garnet]

$\frac {2^{x}+2^{x+1}+2^{x+2}+...+2^{2x}}{2^{x+y+1}-2^{y}}\
\
= \frac {2^{x}(2^{0}+2^{1}+...+2^{x})}{2^{x+y+1}-2^{y}}\
\
= \frac {2^{x}(2^{0}+2^{1}+...+2^{x})}{2^{x}(2^{y+1})-2^{y}}\
\
= \frac {2^{x}(2^{0}+2^{1}+...+2^{x})}{2^{x}(2^{y+1})-2^{y}}$

is this it?

ah shi

hol up

[shy garnet]

i do know but i know I'm not supposed to use that to solve this

[manic acorn]

Are u allowed to do that in the denominator

[shy garnet]

Do what

[manic acorn]

You did -y

Is that allowed?

[shy garnet]

I presumed $2^x-2^y = 2^{x-y}$

since $a^x+a^y = a^{x+y}$

[balmy apex]

no?

[manic acorn]

I have never seen this 💀

[balmy apex]

lmao that is false

[shy garnet]

ah

a h

that's multiplication

[balmy apex]

yes

[shy garnet]

oh well

sad denom gotta change

alright this is the peak of what can be done then

[wraith dagger]

Javaan T

[obtuse wedge]

factor out 2^x in denom too bro , write it as 2^(x+y+1) = 2^x * 2^(y+1) ...... 2^y = 2^x * 2^(y-x)

[shy garnet]

Tf

so you're sayin..

$\frac {2^{x}+2^{x+1}+2^{x+2}+...+2^{2x}}{2^{x+y+1}-2^{y}}\
\
= \frac {2^{x}(2^{0}+2^{1}+...+2^{x})}{2^{x+y+1}-2^{y}}\
\
= \frac {2^{x}(2^{0}+2^{1}+...+2^{x})}{2^{x}(2^{y+1})-2^{y}}\
\
= \frac {2^{x}(2^{0}+2^{1}+...+2^{x})}{2^{x}(2^{y+1})-2^{y}}$

[wraith dagger]

Javaan T

[shy garnet]

i love deadends

[manic acorn]

I think the 2nd part of the numerator can be worked on

[shy garnet]

how's this problem taking this long
yet i only had 1 minute to solve it on paper

like bruh

[manic acorn]

Its not long, im sure someone whos good at sns can do it very fast

[shy garnet]

Ah
so nobody here's proficient at it?

[manic acorn]

Im not proficient is all i know xd

[shy garnet]

lol

[manic acorn]

Whats the formula of gp?

[shy garnet]

still great that you admit to not knowing

[manic acorn]

The 2nd part of numerator is a gp

[shy garnet]

Bro stop using acronyms and just say the whole thing

[manic acorn]

Geometric progression

[shy garnet]

gp in my mind can mean grand potato ffs

The geo prog is...

$\sum_{i = 0}^{x} 2^{i}$

[wraith dagger]

Javaan T

[cedar kiln]

@shy garnet Has your question been resolved?

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[junior timber]

@void echo sorry could u help me?

[elder pewter]

@junior timber do you need help?

[junior timber]

yes

[junior timber]

could u help?

[elder pewter]

I can try

[austere hearth]

ight so

[junior timber]

okayy

question: What is the first four terms of an arithmetic seqeunce with a common diff of 3 1/3 if the first term is 4

[elder pewter]

do you know how to write the nth term of an arithmetic sequence?

[junior timber]

nth term as in the first term?

cuz probably not

kinda new to this topic

[elder pewter]

nth term is the formula to find any term of the sequence

it is a + (n-1)d

where a is your first term

d is your common difference

and n is the position in the sequence

so if you want the first 4 terms, you sub in n = 1,2,3,4

along with your a and d values

[junior timber]

wdym by position

ohh

[elder pewter]

[1,2,3,4,5,...]

1st term, 2nd term so on

[junior timber]

so if i plugged in everything

it would be 4+(1,2,3,4-1)*3 1/3

?

[elder pewter]

no

use n =1

then n = 2

then n =3

then n = 4

to get each of your 4 terms

[junior timber]

ohh got it

ook

is 4 +(1-1)*3 1/3 = 4??

also the second term is 7.33333 do i round it?

[elder pewter]

depends if you need to round

I would to 2 dp

[junior timber]

? sorry

[elder pewter]

2 decimal places

[junior timber]

ohh

[elder pewter]

so 7.33

[junior timber]

alr

another one

starting at 777 and counting back by 5's, what is the last number that is greater then 1

[elder pewter]

what is a and d

[junior timber]

a = 777

d= 5

[elder pewter]

are you sure it is 5

[junior timber]

yup it says

[elder pewter]

counting back

is it 5 or -5

[junior timber]

-5

[elder pewter]

good

[manic acorn]

Tn>1

[elder pewter]

a + (n-1)d > 1

solve for n

[junior timber]

?

[manic acorn]

Its the same thing

[junior timber]

alr

[manic acorn]

Tn is how i write nth term💀

[junior timber]

idk how

i think

[manic acorn]

Just try

[elder pewter]

imagine the > is an =

rearrange for n

[junior timber]

k

[cedar kiln]

@junior timber Has your question been resolved?

[junior timber]

156.2??

n = 156.2?

i think i did something wrong-

nvm

its 2

[manic acorn]

So n cant only be a natural number, so u take 156

[junior timber]

yes thats what i di

*did

whats the value of 1+2-3-4+5+6... +45+46-47-48+49

the pattern is - - + +

[cedar kiln]

@junior timber Has your question been resolved?

[junior timber]

can someone helppp

[torpid fulcrum]

what's the question

[torpid fulcrum]

if i rewrite it as:

1-3+2-4+5-7+6-8+...

can you see a pattern?

@junior timber

[junior timber]

yes

[torpid fulcrum]

what pattern do you see

[torpid fulcrum]

(1-3)+(2-4)+(5-7)+(6-8)+...+(46-48)+49

we basically rearranged the numbers

[junior timber]

ohh

so 2+2+2+2+...2+2+2

[torpid fulcrum]

-2+-2+-2

[junior timber]

ohh

[torpid fulcrum]

and then add 49 at the end

[junior timber]

wdym add 49?

[torpid fulcrum]

the 49 doesnt have a pair to match with

[junior timber]

ohh ok

so its -2*24

[torpid fulcrum]

yes and add 49

[junior timber]

ok ty

[junior timber]

can u help me with another one

[torpid fulcrum]

what's the question @junior timber

[junior timber]

try to determine how many terms in each arithmetic sequence?

a. 3,6,9,12, ... 96
b. 4,7,10,13, ... 91
c. 5,12,19,26, ... 145
d. -18,-12,-6, ... 60
e. 123,119,115, ... 43

[torpid fulcrum]

for question a

what is the common difference

[junior timber]

a. 3
b. 3
c. 7
d. -6
e. 4

[torpid fulcrum]

so (for question a) how many times do we have to add 3 to 3 to reach 96?

[junior timber]

ohh

32 times

32 terms?

@torpid fulcrum

[torpid fulcrum]

yes that's it

[junior timber]

ok

@torpid fulcrum can u help

[torpid fulcrum]

which one?

[torpid fulcrum]

after henry says 34, what is the next number he says

[junior timber]

32

[torpid fulcrum]

there are 5 students at the table

[junior timber]

he said 29 then

no waiy

t

yes 29

[torpid fulcrum]

yes so if we represent the numbers henry say as an arithmetic sequence, what would the common difference be

[junior timber]

-5

[torpid fulcrum]

yes so as a sequence, henry says the numbers 34-5n

what is the last number henry will say then

[junior timber]

yes

uh

[junior timber]

5

oops sorry

4

i think

[torpid fulcrum]

yes 4

the student's seating order is: fred, jennifer, henry, emily and george

[junior timber]

so fred would say 1

[torpid fulcrum]

yes

correct

[junior timber]

ok ty

[junior timber]

.close

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[lusty oasis]

anyone her know derivitives

[chrome spear]

I need help

[lusty oasis]

what

wait i got ot go nvm

[chrome spear]

<@&286206848099549185>

[eternal comet]

.close

[eternal comet]

#❓how-to-get-help

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[heavy merlin]

https://cdn.discordapp.com/attachments/970718585238458419/984128646694453318/unknown.png

question 6

i was trying to resolve tension, T sin theta = W

however, i dont have any idea of T cos theta

if T cos theta = F_c, it isn't equilibrium

[cedar kiln]

@heavy merlin Has your question been resolved?

[cedar kiln]

@heavy merlin Has your question been resolved?

[cedar kiln]

@heavy merlin Has your question been resolved?

[dry relic]

I need help, I’ve been trying since 20 mins ago.

[dire geode]

Read #❓how-to-get-help

[cedar kiln]

@heavy merlin Has your question been resolved?

[cedar kiln]

@heavy merlin Has your question been resolved?

[crimson sedge]

The area of the rectangle itself is 192, you can try this if this works

[lament kraken]

hi do you still need help?

[heavy merlin]

yea 🥺

[cedar kiln]

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[heavy merlin]

.reopen

[cedar kiln]

✅

[reef steeple]

maybe F_c is in outwards direction

[dire geode]

.close

[cedar kiln]

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[cedar kiln]

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[fleet temple]

hi how do u figure out

where to put the values

like how do i know where D goes

where E goes

and where F goes on the triangle

[velvet mortar]

Wdym?

[fleet temple]

like for this question i have DEF

when i draw a triangle how do i know where to put

D

E

and F

like the values

like which ones correct

nvm i got it

.close

[cedar kiln]

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[velvet mortar]

It doesn't matter lol

All of them are correct

[cedar kiln]

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[near vale]

shouldnt the first expansion be (-3-n) ??

where do they get the (-3-n+1) from

[cedar kiln]

@near vale Has your question been resolved?

[full trail]

these are combinations right?

[near vale]

It's a expanded series according to the problem

Binomial series

[dire geode]

https://math.stackexchange.com/questions/1619651/negative-binomial-coefficient

[near vale]

so theoretically it should be

-(1)^n+1 * -3*(-2) .... (-3 + n - 1) / n!

but in their example, its the opposite?

instead of going up its gonig down?

[cedar kiln]

@near vale Has your question been resolved?

[dire geode]

just simplify both and compare

should be the same

[near vale]

.close

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[slow atlas]

hi

[slow atlas]

whats the domain of this i don't know can someone help me

[balmy apex]

what do you think

[slow atlas]

its all real num except something

@balmy apex ?

[balmy apex]

yes

[slow atlas]

but i dont know how to find this something :((

cot2x = cos2x/sin2x

so we should find what can make sin2x = 0 ?

@balmy apex ??

<@&286206848099549185>

hello anyone there?

[dire geode]

yes

cot(y) is undefined when sin(y) = 0

[slow atlas]

so its 0,±2π,±4π,±8π,±16π etc

right?

@dire geode

[dire geode]

there's more you're missing

[slow atlas]

32π,64π?

if thats right when i should stop

i edited it u mean like this ?

guys please help me i still waiting since 45 min

<@&286206848099549185>

[balmy apex]

!15m

[cedar kiln]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[balmy apex]

you're not entitled to help

@dire geode kids these days, amirite

[slow atlas]

??

[dire geode]

me in this server: 👨🏻‍🍼

[slow atlas]

wtf is wrong with u guys

i asked for help

wdym?

[balmy apex]

you do know

• we aren't being paid

• we are voluntary workers

• you are not entitled to help

• this is literal luxury

• if you want quick and good help get a paid tutor

[slow atlas]

i know bro and ty so much for it

but i didnt understand

i waited u to answer me but u didnt

thats all of it

[balmy apex]

lol I have homework of my own to do

I also have a life

just like you

[slow atlas]

alr then dont reply to my ticket

[balmy apex]

it's not a ticket?

also I did help you a bit

you got closer to the solution

[slow atlas]

cuz i want someone to help me understanding this

[balmy apex]

isn't that what counts

[slow atlas]

could u please tell me if this is the right answer?

i just wanted u to tell me if this is the right answer or not

[dire geode]

it's only partially correct

[slow atlas]

what i missing i dont get it

[crimson delta]

let's remember that we are looking for when sin(2x)=0

[slow atlas]

oh i got it

[dire geode]

,calc sin(2 * pi / 2)

[wraith dagger]

Result:

1.2246467991474e-16

[dire geode]

bad calculator

[slow atlas]

ty so much guys and sry for being a bit rude ❤️

.close

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[high coyote]

Find the roots a and b and then

1x²+2x-48 = 1·(x-a)(x-b)

Do you understand why?

Revisit the remainder theorem

[blissful pagoda]

I see

Roots are 6 and -8. Just plug those into the equation ?

[high coyote]

So what us the factored form?

[blissful pagoda]

(x-6)(x+8) = 0

[high coyote]

good

[blissful pagoda]

Thank you ( :

.close

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[blissful pagoda]

I'm a bit confused on how to graph this. Should the only value I should be worrying about is the Y intercept ?

[dire geode]

are you convinced that it's not the second option?

[dire geode]

Does knowing the y-intercept give you A?

[blissful pagoda]

I believe so , that would invert the graph ?

[blissful pagoda]

I don't think so

[dire geode]

try plugging in x=0 into your equation

[blissful pagoda]

That gives me a straight line

[dire geode]

it's not a straight line. it's a point on the curve

do you know what y-intercepts are?

[blissful pagoda]

Yes

[dire geode]

what are the coordinates of the y-intercept of your graph?

[blissful pagoda]

(0,2)

My equation is y = 3^x * 2

[dire geode]

how'd you get this? that's not of the form $Ae^x$

[wraith dagger]

riemann

[blissful pagoda]

I tried throwing it into DESMOS and that gives an asymptote that looks similar

Would it be y = 2e^x instead ?

[dire geode]

right

[blissful pagoda]

Great, thank you for the reminder ! ( :

.close

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[wintry wasp]

Earlier i posted a question, asking how to prove that an elementary row operation of the sort Ri --> Ri+λ.Rj does not change the solution set of a system of linear equations. I think i have a proof now but im not sure if its valid.

In short and in words i define a system S1 of linear equations Ra (a_1x_1+a_2x_2+...+a_nx_n = b_a ) and Rc (c_1x_1+c_2x_2+...+c_nx_n = b_c) in n unknowns with a solution set of {s_1,s_2,...,s_n) Then i construct a second system S2 with linear equations Ra and Ra+λRc. Then i go on to write Ra+λRc as (a_1x_1+a_2x_2+...+a_nx_n) + λ(c_1x_1+c_2x_2+...+c_nx_n) = b_a + λb_c. Then i substitute λ(c_1x_1+c_2x_2+...+c_nx_n) with λb_c and bring it over to the right side so im left with (a_1x_1+a_2x_2+...+a_nx_n) = b_a + λb_c - λb_c. Meaning that the solution set of S1 is the same for S2 since S1 = S2 after some algebraic manipulations.

I feel like this is not a valid proof since in the end im adding the row "Ra+λRc" with the row "-λRc" which gets me in a circle. Ive basically used the row operation Ri --> Ri+λ.Rj to prove that Ri --> Ri+λ.Rj does not change the solution set. Did i go wrong, if so where and how can i prove this?

[cedar kiln]

@wintry wasp Has your question been resolved?

[wintry wasp]

<@&286206848099549185>

[crimson sedge]

ohh wait i can help

nvm sorry

[wintry wasp]

Go ahead 🙂

Oh

<@&286206848099549185>

My question put simply: is my proof correct? (the proof is written above)

[mild robin]

Uavibi

[cedar kiln]

@wintry wasp Has your question been resolved?

[cedar kiln]

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[cerulean star]

Looks like if fill in S_n as 950,273 and subtract 1 from both sides,

That the number on the left needs to be the product of a power of 2 and an odd number

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[crimson sedge]

what’s the value of x

in degrees

and how did u get it

step by step

[teal vault]

Ok so what’s the angle of a straight line?

[crimson sedge]

180

[teal vault]

Yeah

So then that’s the whole angle

You then subtract part of it to get x

So then what would be the equation?

[crimson sedge]

x=180-91

[teal vault]

Yep

Good job

[crimson sedge]

thanks

[teal vault]

No problem

[crimson sedge]

qucik question

is this

109

like the answer

i’m just checking

No

what’s the answe

then

Oh

The answer to x

Sorry

Yes that one x = 109 as well

[cedar kiln]

@crimson sedge Has your question been resolved?

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[vapid schooner]

will a times 0 be equal to 0?

[elder pewter]

anything multiplied by 0 is 0 yes

[silent yew]

$\infty(0)$ ?

[wraith dagger]

Lelouch

[elder pewter]

it is 0

[silent yew]

That's indeterminate form

[vapid schooner]

so 0=mSin(0)+n will get rid of m?

[silent yew]

Yessir

[vapid schooner]

ah ok thanks

.close

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[crimson sedge]

.reopen

3 shop owners (A,B,C) are all in the same line of work and each own a seperate store. Each owners profit isuniformly distributed between 0-100k. What is the probability that A makes more money than B and B makes more money than C. What is the probability they all make exactly the same amount.

[silent yew]

Do you have the answers to this? Or have u done some work that i could see?

[crimson sedge]

Sorry I don't have the answers to this

and i'm stuck on how to start it aha

[crimson delta]

is this uniform distribution discrete or continuous?

[silent yew]

I don't know about the second question, but the probability that A makes more money than B and B makes more money than C should be 1/6, according to me but i could be wrong

[crimson delta]

depends on if more money means > or >=

and if it is discrete or continuous

[silent yew]

Yeah, do we have to use calculus here

But i feel like 1/6 is the only answer that makes sense , given the information

,rotate

[crimson sedge]

Continuous

[silent yew]

And the answer to the second part so far according to me is $\frac{1}{10^{15}}$

[wraith dagger]

Lelouch

[crimson sedge]

More money is > so A>B and B>C

[silent yew]

But i am not sure entirely how i am supposed to treat these no.s

[crimson delta]

If it's continuous then 1/6 shoud be correct and the second should be 0

[silent yew]

Ur second answer is wrong then , no?

Cuz technically it is $$\frac{1}{10^{15}}$$ , it is quite small but it's there :3

[wraith dagger]

Lelouch

[crimson delta]

No, that's the difference between continuous and discrete here

[silent yew]

OH YEAH

Cuz i didn't count this scenario in the answer of 1/6

So the answer to the first should be corrected to $\frac{1}{6}$ - $\frac{1}{10^{15}}$ and the answer to second part would be $\frac{1}{10^{15}}$. But that only if it's discrete

[wraith dagger]

Lelouch

[silent yew]

If continuos then this

[crimson delta]

For discrete you also have to count cases like A=B>C etc

[crimson sedge]

Can you explain how you got to 1/6?

[crimson delta]

There are 6 ways to arrange A,B,C

Each of them is equally likely

[silent yew]

;-; imma study now, thank you :3

Bye

[crimson sedge]

Thank you for your help!

[silent yew]

Np

[crimson delta]

And if it is continuous we don't have to worry about the difference between A>=B>=C and A>B>C etc

[crimson sedge]

So is it like 3 permute 2 = 6 and one of those permutations is where A>B>C

[crimson delta]

So these 6 options cover all possible options

[crimson sedge]

Just out of curiosity if I need to find the probability that A>B would it then be 1/2?

[crimson delta]

Yes

Symmetry arguments like this are very nice

[crimson sedge]

Ah ok

And how did you get 1/10^15?

[crimson delta]

That's in the discrete case

Although now thinking about it it isn't correct I think

Should be 1/10^10

[crimson sedge]

How did you get that?

[crimson delta]

Let A earn whatever. There are 10^5 options for what B can earn and in only one of those is it equal to A. Same for C

So 1/10^5 * 1/10^5=1/10^10

[crimson sedge]

Ahhh okok

Right I forgot about the interval 😅

So if the probability that A>B is 1/2 shouldnt the probability that B>C also be 1/2 and then shouldnt the total prob be 1/4?

[crimson delta]

Uhm...

Hmm

I'm gonna say the events A>B and B>C aren't independent

But not sure right now

Intuitively, if we for example already knew that A1...A100 > B, then B should be small so C>B is more likely than B>C

[crimson sedge]

Yeah that was something I was struggling with like if A is randomly very high then the probability of B<A would be higher

But ig if you average out over the whole interval it will converge

[crimson sedge]

So would this be only if A,B,C are independent?

[crimson delta]

They are independent

But that doesn't mean the events A>B and B>C are independent

Because they both include B

[crimson sedge]

ahh right sorry ignore that

[crimson sedge]

Yeah that makes more sense

[crimson delta]

I have to go now. Cya

[crimson sedge]

Thank you for your help!

Bye bye

.close

[cedar kiln]

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[tacit musk]

Ok, I have a build in Minecraft I'm planning out, the length is 500 cubic meters, the length will be 250 cubic meters, and the height will be 150 cubic meters, what is the total number of blocks I would need for the project so far?

[tacit musk]

1 cubic meter = 1 block

See I have a possible awnser but I'm just in denial that it's correct

[crimson delta]

Yeah

[tacit musk]

Is it correct?

[crimson delta]

Yeah

[tacit musk]

Oh no

Thanks anyways

[crimson delta]

Welcome to volume and how we humans have no intuition about it

[tacit musk]

Lol

.close

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[lunar saddle]

How to solve this? I've tried by change this to √x² form and got √((√8 - 3)²) + √((2 - √2)²) but the answer is not that

[livid hound]

are you familiar with the piecewise definition of the absolute value

[lunar saddle]

No

[livid hound]

$|x| = \begin{cases} x \ &\text{if } x > 0 \
-x \ &\text{if\ } x\leq 0 \end{cases}$

[wraith dagger]

ℝamonov

[lunar saddle]

Yes

[livid hound]

that's referred to as the piecewise definition

anyway the values inside the absolute value are known

you can tell whether the inside is positive or negative and then use the appropriate piece

[reef venture]

is $\sqrt{8} > 3$?

[wraith dagger]

Swas.py

[lunar saddle]

But how to calculate the sqrt?

[reef venture]

no need

just square both sides

x^2 is an increasing function so the inequality doesn't change

[crimson sedge]

is 8 bigger than 9

[lunar saddle]

So, the answer is 5-3√2?

[livid hound]

yes

[lunar saddle]

Ok, thanks all

.close

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[earnest kettle]

would it be ok to ask for help with physics? Or that’s out the question-

[reef venture]

you can

it depends

just ask your question

[earnest kettle]

could you explain this to me?

[reef venture]

which one?

the formula for center of mass

or 3d

[earnest kettle]

The thirds

like

task 1

what is a 3 dimension Cartesian coordinate system ?

[reef venture]

do you know what a 2d one is?

[earnest kettle]

2d one?

[reef venture]

2d cartesian coordinate system

[crimson sedge]

2 Dimension Cartesian

[earnest kettle]

Idk what that is

[reef venture]

its the xy plane

[earnest kettle]

oh

okie

[reef venture]

now if you add another axis to it (called the z axis) it becomes a 3d system

[earnest kettle]

oh

O:

[reef venture]

and you can locate points in 3d space with 3 coordinates (x,y,z)

so (X, Y, Z) stands for the position of the center of mass

and (x1, y1, z1) and (x2, y2, z2) are the positions of the two 2 masses

[earnest kettle]

you lost me at this part

[reef venture]

those are just coordinates for 2 bodies with masses m1 and m2

[earnest kettle]

ohhh

okie

[reef venture]

and this is the relationship that gives you what X, Y, Z are

got it?

[earnest kettle]

ohhhhh

[earnest kettle]

oui oui

thank you 💖

what’s a magnitude

O:

[cedar kiln]

@earnest kettle Has your question been resolved?

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[rustic ridge]

hi im new to multivariabpe calculus and im kinda confused

[rustic ridge]

i have this function that calculates the cost of a business with two variables x and y

and then theres a restriction like

5x+10y=80

can i just substitute y for x and make the function one variable😅

[tulip island]

Yes

You can do that

[cedar kiln]

@rustic ridge Has your question been resolved?

[cedar kiln]

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[quartz vale]

just wanted to clarify: dv/dx = 1 right?

[upper abyss]

Only if -ω²x/v = 1

If v is velocity and x is displacement, then no, dv/dx is not 1 for any random curve

[balmy apex]

context?

what you're asking is like "a/b = 1 right?" without giving any context

[radiant topaz]

Hello there

[quartz vale]

context

[quartz vale]

why not? v^1 ... 1v^(1 - 1)?

is v a function of x? because it doesnt say so

[balmy apex]

v is a function of x

[quartz vale]

how do yk?

[balmy apex]

velocity is the derivative of displacement

[quartz vale]

wrt to time?

[balmy apex]

yes

[quartz vale]

so v = dx/dt

whats dv/dx then

like the inverse of time..?

[balmy apex]

dv/dt would be acceleration, no idea about dv/dx tho

I'm bad at physics lmao

[quartz vale]

oh but

if v is a function of x

then what is that function?

[crimson sedge]

#old-network then post it in physics server ig

[quartz vale]

aight

.close

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[manic acorn]

This is wrong but why

I have found the correct ans through another approach

[balmy apex]

,rccw

[dire geode]

You shouldn't use n for both index and final term

That's like saying n+n+n when you mean 1+2+3

[manic acorn]

By index do you mean the thing on the sigma?

On the bottom?💀

[cedar kiln]

@manic acorn Has your question been resolved?

[cedar kiln]

@manic acorn Has your question been resolved?

[cedar kiln]

@manic acorn Has your question been resolved?

[tawny warren]

consider rewriting Tn as ((n+1)-1)n!

u should end up at a telescoping series

[manic acorn]

I have

And i did get the correct answer that way

But im asking why is this process wrong

[tawny warren]

this?

[manic acorn]

Yes

[tawny warren]

cuz n-1! is not a constant

[manic acorn]

Also could you explain what the index and the final term means💀

[tawny warren]

so u can't take it common

this is what creates confusion

[manic acorn]

But n(n!) And n!=1.2.3....(n-1).n, here the 1 and 2 can also be written in terms of n?, so those are also not constant?

[tawny warren]

avoid taking the same variable for the general and final terms

[manic acorn]

General term and final term of the series?

[tawny warren]

yes

[manic acorn]

Can you give an example of how it would have been better to write it as

[tawny warren]

gimme a moment i'll get back

[manic acorn]

Alright

[tawny warren]

$\sum_{r=1}^{n}r(r!)$

[wraith dagger]

newbienoob

[tawny warren]

@manic acorn this

[manic acorn]

Can i write that same thing but Tr to the right of sigma?

[tawny warren]

yes

[wraith dagger]

newbienoob

[manic acorn]

But Tr in our class was taught means the rth term

[tawny warren]

yeah so that's what it is

[manic acorn]

So the rth term is something im taking to be the general term?

Instead of Tn?

[tawny warren]

right

[manic acorn]

I see okay

[tawny warren]

it's the same thing

hold on

[manic acorn]

Alright

[manic acorn]

Was there anything you wanted to say?

[shy garnet]

this pains me

[shut reef]

My future isn't looking bright

[manic acorn]

😡

[shy garnet]

Hey no offense! lol
you're making good progress

[manic acorn]

The emoji means im joking

Emoji is never srs

[manic acorn]

.close

[cedar kiln]

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[crimson sedge]

how do i calculate the limit. I dont know how to even start

[gaunt hamlet]

What have you tried?

[crimson sedge]

i dont know where to start

infinite - infinite

[gaunt hamlet]

Well, when you see something plus a square root or something minus a square root, it might be worth trying to multiply and divide by the conjugate

[crimson sedge]

alrightt

thanks for the help

.close

[cedar kiln]

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[vernal pike]

I have to confirm y = 2e^-x + 3e^-2x is a solution to the differential equation y'' + 3y' + 2y = 0, how can I confirm it?

[vernal pike]

$$y=2e^{-x}+3e^{-2x}$$
$$y^{\prime \prime }+3y^{\prime }+2y=0\rightarrow r^{2}+3r+2=0\rightarrow r_{1}=-1,\ r_{2}=-2\rightarrow y=Ce^{-x}+De^{-2x}$$

[flint plinth]

plug it into the differential equation and see if it's true

[vernal pike]

You mean I have to take the first and second derivative?

[flint plinth]

yep

in your typeset version, you wrote $e^{-2x}$, but should it be $3e^{-2x}$ like in your first comment?

[wraith dagger]

OurBelovedBungo

[vernal pike]

No, why?

Hmm

Or yes

[flint plinth]

"confirm y = 2e^-x + 3e^-2x is a solution"

[wraith dagger]

AuHasard

[vernal pike]

There

[flint plinth]

yep

so take the first and second derivatives, plug them into the differential equation, and see if you get zero

[vernal pike]

$y=2e^{-x}+3e^{-2x}\rightarrow y^{\prime }=-2e^{-x}-6e^{-2x}$

[flint plinth]

that's the most direct way

[wraith dagger]

AuHasard

[vernal pike]

Is this right?

[flint plinth]

yep

[vernal pike]

$y^{\prime \prime }=2e^{-x}+12e^{-2x}$

[wraith dagger]

AuHasard

[vernal pike]

And then this?

$y^{\prime \prime }+3y^{\prime}+2y=0\rightarrow \left( 2e^{-x}+12e^{-2x}\right) +3\left( -2e^{-x}-6e^{-2x}\right) +2\left( 2e^{-x}+3e^{-2x}\right)$

$2e^{-x}-6e^{-x}+4e^{-x}=0;\ 12e^{-2x}-18e^{-2x}+6e^{-2x}=0$

[wraith dagger]

AuHasard

AuHasard

[vernal pike]

So we can confirm it's a solution right?

[flint plinth]

correct

[vernal pike]

and this is right?

which shows it's a solution

[flint plinth]

yep, after you plug in and simplify you get zero, hence it's a solution

[vernal pike]

Thanks.

.close

[cedar kiln]

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[midnight basin]

I think A B E F are true

Im not sure how to solve C AND D

[cedar kiln]

@midnight basin Has your question been resolved?

[midnight basin]

@uncut veldt

[cedar kiln]

@midnight basin Has your question been resolved?

[cedar kiln]

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[midnight basin]

.reopen

[cedar kiln]

✅

[midnight basin]

.close

[cedar kiln]

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[cedar kiln]

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[crimson sedge]

.open

[analog zenith]

Can anyone help my figure out how to do this?

[reef venture]

do you know where to start?

[analog zenith]

I dont 🥴

[reef venture]

so you need to find the equations of lines tangent to y = 2 + 1/x

do you know how to find those?

[analog zenith]

I have a sneaking suspicion that it has to do with derivatives though

[reef venture]

it does

[analog zenith]

Um, not really, I have learned it like 6 months ago but havnt seen it since

[reef venture]

you need it here

the derivative of a function gives you another function that tells you the slope of the tangent

lets take the function y = 2 + 1/x and differentiate it

can you do that?

[analog zenith]

I dont really know where to start, its 100% different than all the other derivitives ive done

[crimson sedge]

Get a derivative table up

[analog zenith]

usually im finding things like (3x+7)(4x+5)

theres a table 0_0

[crimson sedge]

Google should do the trick

[reef venture]

$2 + 1/x = 2 + x^{-1}$

[wraith dagger]

Swas.py

[reef venture]

then its just a simple power rule

[analog zenith]

ohhhhhhh I remember that!

[crimson sedge]

I almost said 1/x derivative is ln x

[analog zenith]

i never knew how to use it

[crimson sedge]

I need help

[reef venture]

ping me once you have the derivative

[analog zenith]

Im sorry im lost 😦 I only learned that formula yesterday, this is the first time im using it lol

[reef venture]

$\dfrac{d}{dx} x^n = nx^{n-1}$

[wraith dagger]

Swas.py

[analog zenith]

Sorry im alittle math stupid, takes me a minute to learn it =/

[reef venture]

sub n=-1 into that

can you tell me what the derivative of x^-1 is now

[analog zenith]

wouldnt u just move the negative to the outside since anything to the negtive first power would jsut be itself negative?

[reef venture]

no?

2^-1 is 1/2 not -1/2

[analog zenith]

Ugh, i suck at math lol

Ok, so I need to convert it to 2+n^-1

But how do I use that to find the trajectory of the missiles?

would I want to plug the X from the misslies into the equation?

so 1, 2, 3

[reef venture]

that would give you slope of the line

y = mx + c

where m = dy/dx

you'll need to find c by substituting the points

[analog zenith]

So I need to put it in slope intercept form?

so m=2x+1?

why does calc make me feel so dumb lol

[cedar kiln]

@analog zenith Has your question been resolved?

[analog zenith]

I dont get how I can get a trajectory off this

Im so confused

Would I use the cords of the rocket and do Y=1+3/X and graph that?

could u point me in a direction to research?

Im super lost and really wanna get this done tonight if i can

[cedar kiln]

@analog zenith Has your question been resolved?

[tough aurora]

You plot the tangent, and you see where it goes

Then set the tangents to 0

[analog zenith]

How though? Ive never seen a question like this 😦

[tough aurora]

And see if you can find an x solution that's one of the 4

[analog zenith]

This discussion gives me no guidance and I cant find it in my ebook 😦

[tough aurora]

Then do it without your ebook

$y = f'(a) (x-a) + f(a)$

[wraith dagger]

Bolly

[tough aurora]

Tangent equation of a function f(x), at x=a

[analog zenith]

so i need f prime to use this? so 2+x^-1?

[tough aurora]

That is not f'

[analog zenith]

oh

[tough aurora]

I'll help you for the first

0 = f'(1)(x-1)+3

Solve for x

[analog zenith]

Id appriciate that, If I can see one done I can at least kinda grasp what its asking =/

[tough aurora]

Solve for x in what I said

It will help you to understand

[analog zenith]

holy crap my answer was wrong 0_0

mathaway got a whole different answer

[tough aurora]

Oh boy here we go

[analog zenith]

i did it on paper first 😦 I was just wrong

[tough aurora]

Calculate f'(1)first

[analog zenith]

wiat wouldnt a prime of a number with no exponent be 0?

ohhhh

[tough aurora]

Bro what

Derivate 2+1/x

💀

[analog zenith]

Im alittle dense with math =/

[tough aurora]

Take it slow

Just derivate ur function

You got this

[analog zenith]

Im so lost tbh, I just barely learned the power rule

https://tenor.com/view/lost-charlie-charlie-lost-guys-where-are-we-lost-tv-show-gif-17236561

[tough aurora]

Please just derivate the function

[analog zenith]

how? I was shown that I could multiply the coefficient by the power and then negate the power, but in that case it would make this 1

[gaunt hamlet]

Remember that 1/x = x^(-1)

[analog zenith]

The only other way I know to find a derivitive is F(x+h)-f(x)/h

[tough aurora]

Sure do that if you want

[tough aurora]

Or apply this

Just find the derivative please

[analog zenith]

I genuinely dont know how

this equation isnt like anything ive done

[gaunt hamlet]

How do you differentiate x²?

[analog zenith]

multiply the 2 be the coefficient, 1x and negate the power, 2x would be its derivative

[gaunt hamlet]

What about x³?

[analog zenith]

3x^2

same way

[gaunt hamlet]

Now what about x^(-1)?

[analog zenith]

-1?

can i do that with a negative?

[tough aurora]

Yes

What is - 1-1

[analog zenith]

-2

[gaunt hamlet]

You can do it for any xⁿ

[tough aurora]

Now answer again

[analog zenith]

i didnt know that worked for a negative power

[tough aurora]

Differentiate x^-1

[analog zenith]

2 then right? cause it would end up -1+3

[gaunt hamlet]

Why +3?

[analog zenith]

0=f'(1)(x^-1)+3

f'(1)(-1)+3

[tough aurora]

One step at a time please

differentiate x^(-1)

Brig the -1 in front and "negate" the power, what so u end up with

[analog zenith]

-1

[gaunt hamlet]

Where'd the x go

[analog zenith]

Doesnt nagating a power of 1 remove the exponent?

[tough aurora]

What is -1 - 1

[gaunt hamlet]

You're subtracting 1 from the exponent

[analog zenith]

so -1x^-2

[tough aurora]

Yes

$-\frac{1}{x^2}$

[wraith dagger]

Bolly

[tough aurora]

We're getting there

So then the derivative of 2+1/x is...?

[analog zenith]

-1/x^2

[tough aurora]

Great

Now

Knowing this

What is f'(1)

[analog zenith]

-1/x^2

0=-1/x^2(x-1)+3 then?

[tough aurora]

No

Again

f'(x) =-1/x^2

What is f'(1)

[analog zenith]

-1/1^2

so -1

[tough aurora]

Yes

Can you get me then tangent equation at 1

[tough aurora]

Here

[analog zenith]

are all a's -1? or just f'

[tough aurora]

A is where you want the tangent

We want the tangent at 1

So a is 1

Plug 1 in a

[analog zenith]

so f'(1)(x-1)+1?

[tough aurora]

What is f(1)

It's not 1

[analog zenith]

-1

[tough aurora]

That is f'(1)

[analog zenith]

so d'(-1)(x-1)+1

[tough aurora]

f(x) = 2+1/x

What is f(1)

[analog zenith]

function of 1?

[tough aurora]

Calculate it

[analog zenith]

calculate the function of 1?

[tough aurora]

Yes

[tough aurora]

This

[analog zenith]

wouldnt that be 0 since thre isnt an exponenct?

[tough aurora]

f(x) = 2+1/x
f(1) = 2+1/1
f(1) = ??????

[analog zenith]

3

[tough aurora]

Ok

Getting somewhere

So to recap

f'(1) = - 1
f(1) = 3

$y = f'(1) (x-1) + f(1)$

[wraith dagger]

Bolly

[tough aurora]

Plug those known values here, and find the tangent equation at 1

[analog zenith]

(-1)(x-1)+3

[tough aurora]

Yes

Now simplify

[analog zenith]

-x+2

[tough aurora]

You made a mistake, try again

[analog zenith]

-x+4

[tough aurora]

Yes

Okay now, we know that the ennemies are on the x axis

So y = 0

So we want to know where our tangent crosses the x axis

Can you figure this one out?

[analog zenith]

y is 4 and then -1 slope

i mean x 4

[tough aurora]

Is there an ennemy at x=4?

[analog zenith]

np

wait yes

[tough aurora]

So will the missile fired from (1,3) hit an ennemy?

[analog zenith]

yes it will

[tough aurora]

Finally

Now do all that for the rest

That's it

[analog zenith]

ok! thank you! appriaicte it

[tough aurora]

Been 50 minutes so I'll get back to sleeping, good luck for the rest

Np

[analog zenith]

i have 6 hours til work so i understand haha

[tough aurora]

@analog zenith

[analog zenith]

bombs away!

[tough aurora]

Try to plot the functions so it gives you an idea of what we have been doing

[analog zenith]

im just writting down what u told me so i wont forget it, i wont have time to finish this tonight sadly

im well into my sleep as is xD ive been on this for 3 hours lol

[tough aurora]

Just remver to find the tangent and check where it crosses the x axis

[analog zenith]

will do, TY

.close

[cedar kiln]

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[cedar kiln]

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[opaque night]

i am unsure about the terms here

<@&286206848099549185>

[torpid fulcrum]

https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/A_Spiral_Workbook_for_Discrete_Mathematics_(Kwong)/07%3A_Relations/7.02%3A_Properties_of_Relations

[cedar kiln]

@opaque night Has your question been resolved?

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[round nymph]

Hi, I have a cdf F(x), and have derived the quartile function F^-1(x) =Q(x). The former gives me the P(X<=x) and the latter allows me to convert a given probability value to a value, eg Q(0.5) returns the median value.

I am to plot a histogram of the distribution, with the bars representing a given interval of time (x) . If tried generating many samples via Q(rnd()) which gives a nice approximation but surely there must be a way to get a better plot?

I realise I need to somehow quantise the cdf into intervals but the details somehow elude me

[round nymph]

so, F(x) gave the probability of something having occurred by time x; I need to histogram by-the-hour.

if I do F(n) - F(n-1) I will get the probability of the event occurring in the interval n-1 to n. Do I just use this to create the histogram directly, with width = n - (n-1) and height = F(n) - F(n-1)?

<@&286206848099549185>

[cedar kiln]

@round nymph Has your question been resolved?

[cedar kiln]

@round nymph Has your question been resolved?

[cedar kiln]

@round nymph Has your question been resolved?

[cedar kiln]

@round nymph Has your question been resolved?

[cedar kiln]

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[cedar kiln]

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[crimson sedge]

hi

[crimson sedge]

need help with this

im not able to calculate the limit

[torpid fulcrum]

Divide all the terms by the fastest growing term in the denominator

[crimson sedge]

whats the fastest?