help-27

[teal zodiac]

You also know that A1 having happened affects the chance of A happening.

Otherwise, it would say P(A | A1) = P(A).

Also, if by "constant" event you mean A1 always happens, then no. It says P(A1) > 0 (which means there is a nonzero chance of A1 occurring), but it doesn't say P(A1) = 1 (which would mean A1 has 100% chance of occurring).

[devout snow]

@floral lodge Has your question been resolved?

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[sturdy mango]

h tending to pi/2 -

[sturdy mango]

howww

i tried expanding and got 4 sin h- sin h/2/ 4h^2

not sure how to proceed

[fierce rune]

you mean x tending to pi/2?

then its an indeterminate form of 0/0

[sturdy mango]

yea

i tried putting h->0 where i replaced x with pi/2 -h

[visual sundial]

are you allowed to use L'Hopital's rule

[fierce rune]

ah you dont have to

[sturdy mango]

yep but i just wanna

learn

so i avoid using lhopital

[fierce rune]

what did you get to using this?

[small jackal]

You still get 0 at the bottom

[sturdy mango]

?

[fierce rune]

what form did you get it in

did it help?

[visual sundial]

repeated L'hopitals rule huh

[small jackal]

Except you apply it more than once

[sturdy mango]

i got it too

4 sin h- sin (h/2)/ (4h^2) where h tends to 0

i mean i might be thinking of expansion but

[visual sundial]

literally what is the point of your message, L'hopitals rule allows for using it multiple times in the definition

[sturdy mango]

not sure that much effort is gonna work out

[sturdy mango]

doesnt work when u have sometimes have cyclodifferentiable functions

[fierce rune]

hm

substituting h=pi/2 - x gives you a product of two well known limits in trig

[sturdy mango]

i have squared in the bottom

not h

sin h/h would be easy but i have sin h/ h^2

1/h cant be put 0 here since it will get to infinity

[upper schooner]

there's a more useful form you could've had the expression in...

[fierce rune]

1-sin(pi/2 - h) = 1-cos(h)

[sturdy mango]

well yea

damn

🤦🏻‍♂️

[visual sundial]

yeah but it's not the case here

[sturdy mango]

yea

itll be big tho

ugly

[visual sundial]

fair enough

personally I'd rather just take the derivative and deal with it

[sturdy mango]

yeah but im trying to learn limits mostly without it

because obv i can differentiate if nothing works

[visual sundial]

yeah then x= pi/2 +h is the way

[devout snow]

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[nocturne plume]

(trigonometric identities) my solution to this gave me 2 angles (within the interval 0 - 2pi), but in case you factor this its possible to end up with 4 angles as solutions, should i disregard the extra two angles you get from factoring or was my solution wrong?

[nocturne plume]

my solution:

alternative solution using zero product property

[nocturne plume]

this lands you four angles (solving for sin = 0 and 1/cos - 2 = 0)

i only got the couple from 1/cos -2 with my solution

is it wrong or missing something in any way

[small jackal]

This is correct

[nocturne plume]

i see, so the pair of solutions wed get from factoring are disposable

thank you

.close

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[sand dove]

Uh

[sand dove]

Doing this you lose solutions from sin(theta) = 0

Because when sin(theta) = 0 you're dividing by 0

[nocturne plume]

ohhhh did i divide by 0 there

[sand dove]

This solution is better

[sand dove]

You divided by something that could have potentially been 0

[nocturne plume]

i see, thanks a lot for your input

[devout snow]

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[sleek laurel]

I am unsure how to proceed

[jagged harbor]

sub

[sleek laurel]

What do you mean?

[jagged harbor]

sub

[faint gorge]

sub

[small jackal]

Substitution

[woven radish]

bacc

[jagged harbor]

spot the ugly bit and see if the derivative of the ugly bit is present

that's how we saw it

[faint gorge]

let me flip this

derivative of cot(x) is just -csc²(x)

so the csc term will cancel

[sleek laurel]

wait but the radical means that it would look like this no?

[faint gorge]

how did you get this

[sleek laurel]

i dont know. I thought that is what you had said

[faint gorge]

No

Literally write instead of cot(x) replace this with u

and now since we did a substitution

we need to change dx into du

ao we take

u = cot(x) and differentiate both sides

so you'd get

du/dx = -csc²(x)

so

dx = du/-csc²(x)

and now you replace dx with that and you should get something cool

[sleek laurel]

thank you

.close

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[gritty bone]

34 and 36

[gritty bone]

<@&286206848099549185>

[sage burrow]

!15min

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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.

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[gritty bone]

<@&286206848099549185>

[noble sky]

xd

why me ping

[supple knot]

you signed up for the role.

[gritty bone]

36

Not 34

I figured 34 out

[sage burrow]

dont you have a more readable picture?

[gritty bone]

Uh

I'll type it out

In ∆ABC , AB= 8 CM , BC = 12CM, M<(A) - M<(C) = 90°
THEN TAN C =

@sage burrow

[sage burrow]

USE SINE RULE

[gritty bone]

I did?

what does a - c = 90°

Mesn

I got no angled to use sin rule

Sine

Ok can you type out the answer so I could understand

[sage burrow]

type the sin rule or (maybe called law of sines) with the given sides.

[sage burrow]

!noans

[devout snow]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[sage burrow]

@gritty bone are you gone?

[devout snow]

@gritty bone Has your question been resolved?

[devout snow]

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[ancient valve]

How do I find the support for x?

[faint gorge]

,, x^2 \leq 1 \Rightarrow \abs{x} \leq 1 \Rightarrow x \leq 1 \textbf{ and } -x \leq 1 \Leftrightarrow x \geq -1 \Rightarrow x \in [-1,1]

[woven radish]

bacc

[ancient valve]

Can u explain the method

[faint gorge]

Ok

You are given $x^2 \leq 1$ and you just wanna solve for it

[woven radish]

bacc

[faint gorge]

You can also consider it graphically

,w plot x^2

[woven radish]

Results provided by WolframAlpha

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

Requested by adoniszgks

[faint gorge]

So you want all values in the range of less than 1 (and technically greater 0)

So that is the interval x between -1 and 1

I took an algebraic approach however

[ancient valve]

So you used fact that x squared less than or equal to one from the y support

[faint gorge]

y support?

I took a look at this

this is the region

[ancient valve]

This is not y support?

[faint gorge]

idk the english terminology

support

but this is where our function is defined basically the region we integrate over

[ancient valve]

And if I integrate by dx first?

[faint gorge]

draw the region and figure the bounds

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[lavish canopy]

How do I do #9?

[misty crest]

for an odd function what does f(-x) =

@lavish canopy

good talk man

very insightful

[lavish canopy]

What?

[lavish canopy]

-1, I think

And isn’t it 1 for even functions?

[misty crest]

-1?

do you mean -f(x)

word

[lavish canopy]

I don’t remember

What did f(-x) equal, again?

[devout snow]

@lavish canopy Has your question been resolved?

[lavish canopy]

You there?

@misty crest

[misty crest]

i told you already

an odd function is a function that satisfies f(-x) = -f(x)

so you know f(-6) = -f(6)

and so on

[devout snow]

@lavish canopy Has your question been resolved?

[devout snow]

@lavish canopy Has your question been resolved?

[thorny marten]

odd function if you rotate it 180º it remains the same

-f(x) = f(-x)

[devout snow]

@lavish canopy Has your question been resolved?

[lavish canopy]

What about even?

[thorny marten]

symmetrical y axis

f(x) = f(-x)

so for that question u just rotate the graph 180 degrees

and draw

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[pulsar mural]

How to add,subtract,multiply and divide at scientific notation (don't make it too confusing please ty!)

[restive river]

!original

[devout snow]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

@pulsar mural Has your question been resolved?

[deep vortex]

For adding and subtracting, factor a 10^k out

For multiplying and dividing, use exponent laws

[steep tide]

Yeah this is right

[devout snow]

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[sturdy mango]

wait clockwise torque is negative why did they assume positive

[cold bone]

assigning the sign is just a convention to solve a problem
no matter which sign you take, you'll get correct answer if you take those other things according to your assumed direction of positive/negative

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[plain dust]

for the equation of the line i got y = -10/4(x) -2/4

what next

also would this equation be right?

[coral heron]

to get the point that the line passes the x axis (the x-intercept), set y to 0, and then solve for x.

[plain dust]

so 0=-10/4(x) -2/4

[coral heron]

correct.

[plain dust]

how do i solve that tho the fractions are confusing me

[coral heron]

move -2/4 to the side with 0, so you get $\frac{2}{4}=-\frac{10}{4}x$. then, just multiply both sides by 4, then the fractions are gone.

[woven radish]

fish

[tender wren]

Algebra

That's something you need to help yourself with.

[plain dust]

-1/5 right?

[coral heron]

correct

and we know y=0, so now you have all the information for the point.

[plain dust]

-1/5,0

[safe knoll]

i dont think this equation is correct btw :C

can u send working?

[coral heron]

oh, i forgot to check that. the slope of your line is correct, but your value for y-intercept is incorrect.

[plain dust]

oh

ik where

i didnt get the y intercept properly

would it be

y = -10/4 - 6/4

[safe knoll]

u can always use ur point to check if ur line equation is correct
Like plug in x = 1 and check if u get y = -4

[coral heron]

yeah, that's correct.

[plain dust]

now i do the same thing

and x is -5/3

but why does the answer say x = 3/-5?

oh nvm

.close

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[finite briar]

i wanna get my explanation checked

so theres clearly only 3 distinct choices of location of 1 and 2

(as other 3 can be rotated)

and for each choice of location of 1 and 2, we got 2^3 possibilites (2! (cyclic permutation of 3,4,5,6) * 2 (color of 3,4,5,6) * 2 ( color of 1,2) )

so 3 * 2^3 = 48

(answer is 48 for context)

<@&286206848099549185>
and uhh is there a purely combinatric way to approach this

am confused as hell..am i supposed to count all the possibilities?

[nimble pebble]

i cant think of a better way but here is a genius approach

let t(n) be the number of ways to tile a 2xn rectangle using 1 2x2 tile and n dominoes

the question wants us to find t(7)

[dusk token]

IOQM 2023

[nimble pebble]

and p(n) same thing but without the 2x2 tile

now to calculate t(n), focus on the piece coveriing the right top corner in the 2xn rectangle, there are 3 cases
1: its a vertical 2x1 dominoe, in which case you need to fill the 2x(n-1) remaining rectangle using a 2x2 tile and n-1 dominoes, which is basically t(n-1)

2: its a horizontal 2x1 dominoe, in which case you need to fill the 2x1 area left under that (to not leave any gaps), which means a 2x(n-2) rectangle is left to fill using a 2x2 tile and n-2 dominoes, so t(n-2)

3: its a 2x2 tile, which means you need to fill the remaining 2x(n-2) rectangle using n dominoes, of course since there are no overlaps you can only use n-2 dominoes, which means its just p(n-2)

so t(n) = t(n-1)+t(n-2)+p(n-2)

to calculate p(n) you just apply same logic to get p(n) = p(n-1)+p(n-2) (omg its fibonacci !!!!!!!!!)

and just start from p(1) p(2) t(1) t(2) and build up to t(7)

[devout snow]

@finite briar Has your question been resolved?

[finite briar]

yeah

[finite briar]

sheesh thats genius

[dusk token]

I'm nervous for tomorrow

[finite briar]

fr

[nimble pebble]

ikr

[dusk token]

good luck

for tomorrow

[finite briar]

u mind checking q7?

[nimble pebble]

whats q7

[finite briar]

.

read the msgs after it

[nimble pebble]

uh

did you understand the solution tho

[nimble pebble]

omg this question is so ugly T_T i dont think there is a good way to solve except brute force

first of all, since 2 dices are the same if they are rotated, i will without loss of generality assume 1 is at the top (and 2 is at the bottom), and also assume 3 is on the right (i can rotate however i want), now the cube cant be rotated anymore so you can ignore the rotation thing and calculate normally

4, 5, 6 in the other 3 faces have 6 possibilites, and then each 2 faces can be either red and yellow, which means 2x2x2 possibilities

so 8x6 = 48 is the answer

[finite briar]

yes so okay i think i had the right solution

i amma keep this open

if i need help in the future

so

For this sequence

is

$\left(a_{n+1}\right)^2 - a_na_{n+2} = 7^n$

[woven radish]

rak³en

[finite briar]

true?

got it from here

https://www.fq.math.ca/Scanned/33-1/melham4.pdf

<@&286206848099549185>

[deep ice]

sequences be hard

[finite briar]

fr

[fervent hornet]

am i tripping or does this not work for n=0..

[deep ice]

what's it actually asking?

[nimble pebble]

last line . . .

man this question is so bad

[deep ice]

what is a divisor

[nimble pebble]

ive been thinking about it T_T

[deep ice]

90% of questions asked on this server are written by fucking idiots

4 is an intiger divisor of 24 and 16 right...

[nimble pebble]

a is a divisor of b when b/a is an integer

[deep ice]

that shit?

ok cool

[nimble pebble]

i dont think this applies here the question is just ugly T_T

[deep ice]

we know it's a GP so we got that down

[nimble pebble]

what is GP

[deep ice]

:/ broh

what

https://tenor.com/view/daeth-funi-periflight-dies-from-gif-22212023

geometric progression

[deep ice]

maybe simplify?

find rule for nth term if you can

[nimble pebble]

bro you were just asking about divisors 💀

[deep ice]

I was ensuring

https://tenor.com/view/richard-nixon-twitter-gif-6755347737707332000

[nimble pebble]

[deep ice]

Anyway this question is wack

[nimble pebble]

yeb

i dont like it

[deep ice]

the fuck is that

also isnt a the 1st term?

[nimble pebble]

a_50 x a_50

[deep ice]

Yeah... isnt ti meant to be T50

[nimble pebble]

yea the 50th term

[deep ice]

yuh ok

its a big fucking number

7^49

[nimble pebble]

ok yea this sells the question so hard

you can very easily prove it by induction

and ig its not that crazy hard to notice if you expirement with small cases

meaning that question is very boring

[devout snow]

@finite briar Has your question been resolved?

[finite briar]

🤦‍♂️

[finite briar]

its true?

no it isnt

should be n+1

.close

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[dusty sigil]

can anyone help? i need to solve for x im stuck here

[supple knot]

Use quadratic formula in cos(x)

[dusty sigil]

wdym?

[small jackal]

Let y=cosx

Solve for y

[supple knot]

,tex .quadratic formula

[woven radish]

pizzanator

[small jackal]

Then solve for x

[dusty sigil]

wait but i checked the ans its suppose to be an easy factorize

oh got it

xareless

[devout snow]

@dusty sigil Has your question been resolved?

[restive river]

tan^2x = sec^2x -1

oh nvm

you got it

[devout snow]

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[lyric echo]

i've got y = (-a/b)x + a

[faint gorge]

nice

[lyric echo]

i'm working on something here

hang on i think i got it figured out lol

just use this equation to rewrite for both a and b

from then on i suppose it's... basic simultaneous equations to get exact values

[faint gorge]

Area of equilateral triangle is $\frac{\sqrt{3}}{4}b^2$ where $b$ is the base

[woven radish]

bacc

[lyric echo]

yes, i understand this much

am i overcomplicating things?

[faint gorge]

We need to integrate

[lyric echo]

just take the integral without searching for exact a and b value?

[faint gorge]

,, \int_0^b \frac{\sqrt{3}}{4}y^2 : \dd x

[woven radish]

bacc

[lyric echo]

that's not the problem here i can do that perfectly, the question asks for an exact volume

[faint gorge]

Since a and b are not given, I assume the volume will be in terms of a and b

[lyric echo]

i see

well thats fine then

[faint gorge]

It could also be that they cancel out the variables, we will see

[lyric echo]

okay hangon then

how do i type math?

[faint gorge]

what you wanna type

[lyric echo]

hangon

[faint gorge]

on what

[lyric echo]

your pearls dude idk

look

idfk the latex

but

you rewrite y as -a/b * x + a

take the root 3 / 4 out

but now you have a weird -a / b situation or should a and b just be treated as constants?

[faint gorge]

treat them as constants

[lyric echo]

hilarious integral this is

[faint gorge]

,, \frac{\sqrt{3}}{4} \int_0^b \left ( -\frac{a}{b}x + a \right )^2 : \dd x

[woven radish]

bacc

[lyric echo]

yh

[faint gorge]

It's some quadratic shit

[lyric echo]

yeah you can't even make it easier

[faint gorge]

,, \frac{\sqrt{3}}{4}a^2 \int_0^b \left ( 1-\frac{x}{b} \right )^2 : \dd x

[woven radish]

bacc

[faint gorge]

You can substitute 1-x/b = u

[lyric echo]

wait i did the quadratic fully out now

ill try both ways lemme

[faint gorge]

bruh

some pearls type shit

[lyric echo]

fym pearls dawg

[faint gorge]

,, \frac{\sqrt{3}}{4}a^2b \int_0^1 u^2: \dd u

[lyric echo]

no

[woven radish]

bacc

[lyric echo]

for christsakes

i got the question right but

we were supposed to do perpendicular to the y-axis

shoot me now

[faint gorge]

Isn't that what we did?

I mean technically we would have to switch variables

[devout snow]

@lyric echo Has your question been resolved?

[devout snow]

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[timber pebble]

hmm i get a different solution

@barren garden you make a mistake early

$\mu = e^{4 \log x}$

[woven radish]

jan Niku

[timber pebble]

its not generally true that $e^{C \log x} = Cx$

[woven radish]

jan Niku

[timber pebble]

actually, $e^{C\log x} = x^C$

[woven radish]

jan Niku

[timber pebble]

this mistake tracks through

maybe you can try starting from here, after using inverse product rule, you arrive at:

$\dv x \qty(y x^4) = 45x^2 \log x$

[woven radish]

jan Niku

[barren garden]

why is it clogx?

[timber pebble]

save you a little algebra

sorry, im using log and ln interchangably

[barren garden]

when integrating 4/x It's 4lnx + C

[timber pebble]

it is

[barren garden]

and then when I raise both sides to e why cant I split them up?

[timber pebble]

you dont need to add the +C now, by the way

remember were going to integrate again, later

[barren garden]

so just fully ignore the C until I integrate the whole thing at the end?

[timber pebble]

yea, or you can keep it, if you are nervous

i think it gets in the way

[timber pebble]

you are looking for the integrating factor

[barren garden]

that still doesnt change anything tho I think

[timber pebble]

so we do $e^{\int \frac 4x \dd x}$

[barren garden]

wont I still end up with 4x?

[woven radish]

jan Niku

jan Niku

jan Niku

[timber pebble]

algebra rule is that there needs to be nothing in front of the log in order for it to cancel with its base

you might think of this like ....

[woven radish]

jan Niku

[timber pebble]

see where this is going?

[barren garden]

x^4?

[timber pebble]

yea

[barren garden]

ahhhh

[timber pebble]

so $e^{4 \ln x} = x^4$

[woven radish]

jan Niku

[timber pebble]

which we might get to by just applying the property $C\log x = \log (x^C)$ first, but who is counting

[woven radish]

jan Niku

[barren garden]

great thanks, and you said for the integrating factor just completely forget about the constant

and then just add the constant in the end when you multiply the equation by the integrating faactor?

[timber pebble]

a better suggestion would be to skeptically add it in, and make sure to pay attention what happens to it

make a decision for yourself whether it was important or not to add it at this stage

maybe you want to invent an easier problem to try that on

in any case, yea

[barren garden]

alrighty i'll give it another go and let you know, thanks

[timber pebble]

[barren garden]

Did you get something like this?

[timber pebble]

lemme see

i crumbled up the paper

so you start from $\dv x \qty( yx^4 ) = 45 x^2 \log x$ right

[woven radish]

jan Niku

[barren garden]

yep

[timber pebble]

this is $yx^4 = 45 \int x^2 \log x \dd x$

[woven radish]

jan Niku

[timber pebble]

,w integrate x^2 log x

[woven radish]

Results provided by WolframAlpha

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

Requested by janniku

[timber pebble]

so $yx^4 = 5 \qty( x^3 (3 \log x - 1) ) + C$

[woven radish]

jan Niku

[timber pebble]

this looks like ...

[barren garden]

I think thats the same as what I got?

[timber pebble]

y = $\frac 5x \qty( 3 \log x - 1) + Cx^{-4}$

[woven radish]

jan Niku

[timber pebble]

you have to finish it out though

i think so, though

[barren garden]

ye will do 1s

when I have like 45 * C (the constant of integration)

do I take it as 45C

or do I just write it as C

or does it not matter

[timber pebble]

you can just absorb constants, yea

[barren garden]

got this as the final answer (I applied the condition y(1) = -1 )

[timber pebble]

its not simplified

but yea, i think youre there

one way to find out

just kidding id send it

[barren garden]

,rotate

[barren garden]

here ^

[timber pebble]

seems like we got the same answer

[barren garden]

aight i'll send it

lets see

yep its right

tysm

.close

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[nimble wraith]

hello can any one tell me what does the 6 stand for in this price string
0.0₆1051

or can you give me please the actual number in this string , does it mean there are 6 zeros after 0.0 ? like 0.00000001051 ?
i took the string from this screen

i'm basically trying to figure out what was the set profit percentage for the 10 part that was sold 18,462 .

i see the user bought 184,620 tokens worth 0.0001000 solana and and split the supply by 10 parts then sold one part for 0.001947 sol and the sold second part for 0.001942 sol
trying to figure out what was the profit percentage he set for each part to be sold ? is it 9500% ?

[smoky nimbus]

Yes I believe that's what the 6 means, that there are going to be 6 zeros

[nimble wraith]

super , thanks for the answer dear .
any idea what was the % profit set for ?

i got it ! it should be 19,370%

all solved thanks

.close

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[lime star]

Can someone help how to prove this?

[eager nova]

Have u tried anything?

[lime star]

So I was watching a video about this topic, but have literally no idea how to do this with a log4

omega = lowerbound, so maybe something with log4(4n^2 +5n+8) = log4(5n)?

[eager nova]

Wait what?

You should compare with 4n^2

Also is mot equal

Is greater or equal

Something like

Log_4(4n^2+5n+8)>=log_4(4n^2)

And log_4(4n^2)>=log_4(n^2)

[lime star]

I was watching a video and he said to drop the lower terms

[eager nova]

The lower terms are

5n+8

You keep 4n^2

[lime star]

what about this example because the lower terms is 3n+4 but it's OMEGA(n) so he used 3n

[eager nova]

I see there 2n^2 not 3n

Not sure what he does in that video tbh

But i would rather try to focus on your exercise first

[lime star]

I am so confused 😭

[eager nova]

Ok go here

[eager nova]

.

[lime star]

Log_4(4n^2+5n+8)>=log_4(4n^2)

[eager nova]

Do you agree with that?

[lime star]

yes

[eager nova]

And that is obviously bigger than log_4(n^2)

Now you simply use log properties to make the 2 from n^2 out of the log

[lime star]

2log4(4n)

[eager nova]

And u got your omega times log(n) that u were looking for

Not 4n

[lime star]

why

[eager nova]

U are looking the for the lower

Aren t u?

[lime star]

for example log3(n^2) = 2log3(n) right

[lime star]

which lower

[eager nova]

Yes but you skept one step

Log_4(4n^2)>=log_4(n^2)

[lime star]

Oh

because log4(4) = 1?

[lime star]

or what is the rule for that

didnt see that one before

[eager nova]

You are just making it smaller

[lime star]

Alright

and then 2log4(n)

[eager nova]

That looks like it already

[lime star]

what if it was log4(3n^2)?

[eager nova]

Who cares

U do the same

Log_4(3n^2) >= log_4(n^2)?

[lime star]

No but I need to understand why u remove the 3

Is there a rule or

[eager nova]

Why did you remove all terms except 4n^2?

[lime star]

to simplify

[eager nova]

At largest values

It is what is important right?

Now

If u get 4n^2

U get 1+log_4(n^2)

Right?

[lime star]

yes

[eager nova]

And what is 1 doing there?

Is it relevant or not?

[lime star]

no

[eager nova]

So we take care of

Log_4(n^2)

Same would happen with 3n^2

Cause log_4(3) is still a plain number

Irrelevant

[eager nova]

Now ur algebra gets really easy from here

[lime star]

I lost where the values are now

[eager nova]

What do you mean exactly. Ok lets do one thing

Try doing yourself and when u do something u dont get why u do

Ask about that

[lime star]

Ok

.close

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[tribal cypress]

i have no idea how to find B the video i was provided with didnt tell me anythiiing abt it…

[acoustic leaf]

it says f(0) = B in the table

[floral adder]

hey guys

help

[acoustic leaf]

!occupied

[devout snow]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[tribal cypress]

yess but i dont lnow how to find B

it might be like super obvious but i seriously cannot understand 😭😭😭

[acoustic leaf]

let's say you have a function g(x) = 3x^2 - 2x. then g(3) = 3(3)^2 - 2(3). we substitute 3 for x

[tribal cypress]

yess

[tribal cypress]

just realized A is more likely to be 1…

[devout snow]

@tribal cypress Has your question been resolved?

[tribal cypress]

ugh actuslly now more like
how is the answer for b, 2

[tame palm]

Second column, row two. It states f(0) = B.

[tribal cypress]

yes but i dont understand how b=2

[tame palm]

f(x) = x^3 -2x^2 - x + 2. Just plug in 0 for x.

f(0) = (0)^3 - 2(0)^2 - (0) + 2

[tribal cypress]

OH TYSM

[tame palm]

yw

[tribal cypress]

The video literally sint include that ik it was probs so obvious but been doing math for past 5hr graaah

.close

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[glad valley]

Is there any quick way to prove that $${x=(x,y)\in \mathbb{R}^2\mid x>0, y\geq 1/x}$$ is closed?

[woven radish]

Zander

[restive river]

yes, this is the intersection of two closed sets A = {(x,y) : x ≥ 0} and B = {(x,y) : xy ≥ 1}. Showing A is closed is easy enough, for example, the function (x,y) -> min(0,x) is continuous, A is the preimage of {0} which is closed subset of real. As for B, it is the preimage of [1,infty) over the continuous function (x,y) -> xy.

there might be some slip-ups, I'm about to sleep, but you get the idea

it is all about finding continuous functions, and closed subset, take their preimages, which are again closed by continuity; and the intersection of closed sets is closed

[glad valley]

yes!! clever idea, much better than balls and complements :)

[devout snow]

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[jaunty dagger]

How is the binary of a 11 bit number calculated as having a max number of 2^11-1. I understand that it works but is there a reasoning behind the formula?

[restive river]

a 2-digit base 10 number has max number 99 = 10^2 - 1

does it make more sense

[jaunty dagger]

no, why is that

I get its true for exponents but just curious as to the reasoning

oh

I was thinking of it as adding 2^10+2^9+2^8.....

but I think that makes sense, i didnt expect he logic to cary over

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[umbral sleet]

how do you do this

[supple knot]

Find the first few lengths and then find a pattern

[devout snow]

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[lime sinew]

Could someone help me with a logarithms problem? please I need it in minutes

[lime sinew]

please help me

save me

I promise to come back here to help when i am better with this

[ripe hollow]

<@&286206848099549185>

[lime sinew]

[ripe hollow]

I'm sorry I can't help you with this I've not studied log much

[lime sinew]

calm down someone will come

[lusty igloo]

i also wish i could help, all i konw is that ln means natural log

[lime sinew]

hahaha thanks anyway

[visual hazel]

you have a fraction inside the log

if you have a fraction inside the log which formula can you use

[lime sinew]

By applying the formulas I couldn't get further than this

[lusty igloo]

since xe^3x is in a cube root, can you turn it into e cuberoot(x^x)?

and since x^2 + 1 is in a square root, it turns into x sqrt(1)?

[lime sinew]

I think it is not included in the cube root.

[ripe hollow]

I've a method

Not sure tho

[visual hazel]

get further than?

[visual hazel]

and no thats not how it works

[lime sinew]

samples maybe you have an idea

[lusty igloo]

i was taught a lie?

[visual hazel]

sqrt(x²+1) is not x*sqrt(1)

!showwork

[devout snow]

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

[visual hazel]

@lime sinew have you done it?

[lime sinew]

I don't know much what to do, I suppose it's a matter of derivation, but I don't know.

[visual hazel]

whats ln(e)

[fluid perch]

idk

[lusty igloo]

is it 1?

[silk dagger]

its 1

[visual hazel]

yes its 1

[silk dagger]

do you have to find the derivative of y?

[visual hazel]

ln(e) = 1

[lime sinew]

yep but it doesn't help much for the derivative

[lime sinew]

yep

[visual hazel]

well you can simplify 3x * ln(e) to just 3x

[silk dagger]

then its simple

[visual hazel]

because ln(e) is 1

[lusty igloo]

what's a derivative

[silk dagger]

d/dx(lnx) = 1/x

[visual hazel]

and the last ln you shouldnt have a cube root anymore since you already have that 1/3

then finding the derivative is just differentiating every term at this point

!noans

[devout snow]

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

[lusty igloo]

when helping someone, if i give them a direct example on how to do something, is that the same as giving them the answer?

[silk dagger]

oh mb

[ripe hollow]

We can break the natural logs like:

ln(a×b×c) = ln(a) + ln(b) + ln(c)

So

[silk dagger]

the denominator in every term cannot be cube root(5x+2)

[lime sinew]

Oh and I can derive that point by the chain rule.

[lime sinew]

yeah I did that but in another order first with the denominator or is it not worth doing that way?

Oh no

I think that's fine there

[lime sinew]

It was bad at that point, I hadn't seen it.

Alright?

Thanks for your help, I don't know why I got stuck in that hahaha

.close

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[robust oracle]

I need help with calculating truss members.

[devout snow]

@robust oracle Has your question been resolved?

[robust oracle]

Why did I pick engineering?

.close

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[frail osprey]

hi can someone show me how we factor the LHS out pls?

[frail osprey]

i dont get it

[terse solar]

multiply bx by a/a

[frail osprey]

yes, but what about the first term

a^n * 1 = a^n

but isnt that being raised to n as well

so it becomes a^(n^2)

[terse solar]

nah

[frail osprey]

i tried foiling it out but im pretty sure i messed something up

[sand dove]

x^n * y^n = (xy)^n

[terse solar]

yeah that

[sand dove]

so [a+bx]^n = [a(1+b/a*x)]^n = a^n (1+b/a*x)^n

[terse solar]

yup

[frail osprey]

would it be possible to show this in latex if u dont mind? i tried writing this down to check it out but im not sure if i wrote it right

oh nevermind, i got it!

thanks

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[meager ferry]

how do i study for math, when i have 6 exams for different subjects in a couple of days and i’ve forgotten everything about math

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[lost laurel]

#1260937723452330155 message

[devout snow]

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[glacial ether]

someone help me

[soft umbra]

[glacial ether]

@faint gorge

or someone who speak german

i stuck at (c)

i found the extrem points but

how can i find Wendepunkte?

[faint gorge]

Die findest du mit der zweiten Ableitung

f''(x) = 0

[glacial ether]

yeahh but zweiten ableitung is

4/(x-2)^3

isnt it impossible that 4=0

[faint gorge]

Dann hat das Ding keine

[glacial ether]

was sollte ich schreiben

[faint gorge]

Hat keinen Wendepunkt

[glacial ether]

4=0 unmoglich deswegen hat diese Funktion keine Wendepunkt

[faint gorge]

ja

[glacial ether]

okay danke schön

[faint gorge]

Das notwendige Kriterium wird nicht erfüllt

[glacial ether]

btw what is it called in english

[faint gorge]

wenn du das schreibst wechselt dein Lehrer beruf

[faint gorge]

inflection points

[glacial ether]

was sollte ich schreiben?

[faint gorge]

.

[glacial ether]

danke

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[glacial ether]

need help

[glacial ether]

g'(4) = 3 does this mean k = 3 ?

[jolly bane]

i dont undersrand german

but is the question to find the equation of g(x)?

[glacial ether]

similar

i need to draw the tangent line using those 2 conditions

[jolly bane]

yup

[glacial ether]

and then should draw possible curve from them

[jolly bane]

you can use the formula

[glacial ether]

i threw the tangent line

but im not really sure about it

[jolly bane]

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

[glacial ether]

but seems like k from tangent line is 3 right

[jolly bane]

yup the slope is 3

[glacial ether]

is it for tangent line

[jolly bane]

y=3x−13

[jolly bane]

yes

[glacial ether]

thank you !

but what about the possible curve

can i just draw random curve on the point (4,-1)

[jolly bane]

what is the primitiv of a linear function?

do you know it?

[glacial ether]

no

[jolly bane]

it is a quadratic function

like a parabola

do u know that?

[glacial ether]

so should i draw a parabola

[jolly bane]

yes you should

[faint gorge]

Ist das Abiturniveau?

[jolly bane]

with a slope of 3 at x=4

[glacial ether]

ja ähnlich

[jolly bane]

but u dont have more info so just do smthg random

[glacial ether]

ergänzungsprüfung

[glacial ether]

ok thank zou

you

[jolly bane]

no problem

[faint gorge]

seit wann gibts sowas

[glacial ether]

für Ausländer

[faint gorge]

bin selber einer

[glacial ether]

mein Zeugnis nicht gültig hier

[faint gorge]

achso

also musst du dich erneut beweisen

[glacial ether]

ja genau

[faint gorge]

viel glück

[glacial ether]

danke schön

.close

[devout snow]

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[sage pawn]

Was wondering if these two are equal

[restive river]

I have a feeling the above one can be converted into an infinite sum. something like

$\sum\limits_{n=1}^\infty \frac{1}{1+n} \cdot (\frac{1}{n}-\frac{1}{n+1})$

[woven radish]

gautamdb

[sage pawn]

I already did the integral I just want to verify if it's true

[restive river]

The reason is that 1/x takes values between 1 and infinity, and that whenever x is between n and n+1, or in other words when 1/x is between 1/n and 1/(n+1), the value of the integrand is constant at 1/(1+n)

[restive river]

Yea and I think the way to find that out is to check if this infinite sum is equal to 2-pi^2/6.
What do you mean by "I did the integral"?

[brisk panther]

clearly not

look!

[sage pawn]

The decimal values are close or maybe because it's being rounded I don't know

[brisk panther]

hmmm

[restive river]

The sum can be split into two parts where the result is probably known:

Sum above =

$\sum\limits_{n=1}^\infty \frac{1}{n(n+1)} - \sum\limits_{n=1}^\infty
\frac{1}{(n+1)^2} .$

[woven radish]

gautamdb

[brisk panther]

Try converting 1/x to x

[sage pawn]

For that I got 1-(pi^2/6 -1)

[restive river]

Exactly. So they are equal.

So it’s resolved then, right?

[brisk panther]

b b b but

where the proof at

[restive river]

So, the second sum is almost the same as the sum of 1/n^2 from n=1 to infinity, which is know to be pi^2/6. But the second sum has n+1 instead, so it starts without the first summand, so the result is pi^2/6 - 1.

[brisk panther]

i meant

how do we prove thats equal to the integral

[restive river]

My explanation above

[restive river]

This

[sage pawn]

I was just wondering at the start if I Did it right based off me showing a screenshot of desmos, how else would I know the answer without calculating it before hand

[restive river]

I got the same result so you are probably right

[restive river]

The integrand is something which is always constant on intervals where 1/x lies between n and n+1. That is why you can turn it into a sum. You just multiply the length of these intervals (x lies between 1/n and 1/(n+1) ) with the value the integrand takes there, 1/(1+n), and sum it for n=1 to infinity

[sage pawn]

I guess if the decimal values is the same even if it differs a bit is the same

[brisk panther]

ye

[restive river]

Since the approximation of pi is more accurate, I'd say the second decimal approximation is correct.

[sage pawn]

Without solving the integral would you say the two numerical values are the same from the picture provided, want to make sure this is 100% correct

[brisk panther]

hey

you're acc right btw

cuz

i did x = 1/x sub

and

i have a sum of integral

integrals

the integral becomes

1/2(1-1/2) + 1/3(1/2-1/3) + 1/4(1/3-1/4) ...

[brisk panther]

which is just

this

[restive river]

I'm not sure what more you want. The integral is equal to 2-pi^2/6, I explained a proof, so it is correct if my proof is correct . The numerical values you show are different, because the calculator uses numerical methods to approximate the value, and it has limitations, so the values differ, but they are actually the same. And if you are looking for the exact value as a decimal number, I suggest you take the second one.

[brisk panther]

yes

it is

i confirmed rn

i mean you did way before

but

[brisk panther]

desmos is not that great at solving integrals

,w integral of 1/(1+floor(1/x)) dx from 0 to 1

[woven radish]

Results provided by WolframAlpha

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

Requested by diddletoucher

[sage pawn]

I guess for now on I’m going to have to trust if I did everything right or not

[brisk panther]

why dont oyu show your working

[brisk panther]

hmm wolfram doesnt give an answer

[sage pawn]

It's basically the same as @restive river proof

[brisk panther]

so whats the issue

[sage pawn]

At the start I asked if these numbers are essentially the same but maybe it's because desmos numerically solves it while 2-pi^2/6 is the analytical solution

[restive river]

Exactly. The proof is more reliable than a calculator.

[sage pawn]

They have the 0.355065 term in common

[restive river]

Yes, so that shows that it is the same.

The value for the integral calculated by desmos is just not accurate beyond the 5th decimal place.

[sage pawn]

I guess this resolves my question. Appreciate the confirmation from the both of you.

.close

[devout snow]

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[glossy solar]

Do these answers seem right? could anyone please check over if i messed up anywhere?

[tame palm]

You made a mistake in 1. It looks like you used g(-3) instead of g'(-3).

[glossy solar]

Ah. one sec.

any other mistakes?

wait, i feel like i messed the entire thing up

looking back at it

[tame palm]

Checking.

[glossy solar]

better?

[tame palm]

Yes.

[glossy solar]

please don't say i messed up the quotient rule

that thing takes so long to redo

[tame palm]

2 doesn't look correct either.

[glossy solar]

Where did I go wrong?

[tame palm]

Difficult to tell because you did not show all of your work.

[glossy solar]

I suspect it's with the derivative of 2g(x)

i was considering 2, but my head told me chain rule works there aswell

[glossy solar]

that's my bad. i tried to do it mostly mentally

[tame palm]

It looks like you multiplied 8 by 2 instead of squaring 8 in the denominator.

[glossy solar]

oh, denominator

Ah, I see what I did

i forgot to multiply by 2 for the 4 and i squared 4

better?

[tame palm]

Yes.

3 is incorrect.

It looks like you multiplied wrong in the last step.

[glossy solar]

this, people

is why you don't wake up and go on flvs to do a dba

[tame palm]

The 3 isn't part of the ()^-1.

[glossy solar]

without breakfast or properly waking up

[glossy solar]

-12/e

corrected

ty

how do i do math well in class but the moment i'm alone i lose all my abilities 😭

well, i guess it's because there's also my roommate's music blasting and i haven't eaten or properly gotten out of bed

[tame palm]

🙂

Gotta go to the library. 😉

[glossy solar]

Thank you for your help, lad

and yeah, true. libraries are great for this stuff

[tame palm]

4 looks good. The inverse derivatives have always caused me problems. 😛

[glossy solar]

quotient rule and implicit differentiation are NOT my friends

[tame palm]

B(i) is incorrect.

[glossy solar]

DAMNIT

Derivation? simplifying? where did I go wrong?

[tame palm]

-2xy requires the product rule.

[glossy solar]

ah

gotcha

-2y-2x(d/dx)

hrm

does the result not even change?

this is an addition of -2y

[tame palm]

It changes.

[glossy solar]

but y is 0

one sec, gotta make my bed

[tame palm]

It's not 0 yet. You still need to find dy/dx.

[glossy solar]

i meant the answer for ii

[tame palm]

But you got that wrong as well.

[glossy solar]

CHRIST

[tame palm]

3/2 * -1 = -3/2, not -2.

[glossy solar]

WHAT IS UP WITH ME TODAY

where'd i get -2

i could've sworn i wrote -3/2

oh my god i wrote -2

[tame palm]

I don't know. You had it correct in the previous line.

[glossy solar]

it was just an error in transferring it because of the distraction ig

not an actual miscalc

why am i doing calculus at a 6th grade level right now, jesus

..i should grab a bite to eat

anyways, is that better?

[tame palm]

You owe the university six push-ups.

[glossy solar]

not even uni

[tame palm]

You owe your school six push-ups.

[glossy solar]

i'm a sleep deprived highschooler taking 5 APs in-person and one on FLVS

I'm taking AP Calculus BC and AB at the same time

because i needed to take AB over the summer and complete a good chunk of it to do BC properly

hilariously, my grade in BC is better

because i operate better when i'm doing math in-person with the only distractions around me being math

instead of a roommate cursing out his tv playing gta with music playing at a level you can hear it all around the house

[tame palm]

Well, you have a basic understanding of derivatives. You just need to double-check the actual math.

[glossy solar]

i'm not usually this sucky at the actual math part

i got out of bed and opened my laptop to start calculating

i brushed my teeth in the cooldown between your messages lmao

[tame palm]

Try not to write everything out on one line. It makes everything messy.

[glossy solar]

hold on, foster sibling is cussing out my roommate for the music

[tame palm]

eg.

Nice and tidy.

[glossy solar]

my apologies for the BASIC ARITHMETIC FAILURES