So you have 0=lim(ε-l) /x <f(x) <lim(ε+L) /x =0
#help-0
ionic trail
crystal tiger
red kindle
is there any more efficient way to compute something like $3781 \mod{54}$ by hand without doing long division?
ocean sealBOT
bot
red kindle
Fermat's little theorem says that if $p$ prime and $a$ an integer where $a$ doesn't divide $p$, then $a^{p-1} \equiv 1 \mod{p}$. So, is $3620^3 \mod{73}$ solve-able with fermat's little theorem?
ocean sealBOT
bot
lone heartBOT
@red kindle Has your question been resolved?
wicked elk
0.37 as a simplified fraction.
red kindle
huh
lone heartBOT
@red kindle Has your question been resolved?
pallid trout
**bot**
a = 3620^3, p = 73
apply (3620^3)^(73-1) = 1 mod 73
That gives you a big ass number = 1 mod 73, and then you just apply the actual theorem "p divides aᵖ⁻¹ - 1"
OR
to get a nice clear answer
((3620^3)^(73-1)-1) mod 73 = 0
If you do get that, then you confirm it's a prime
The teacher was really just being tricky by using a number with an exponent already on it so people would try to do something like 3620^3-1 = 1 mod 73, I think
tardy torrent
Anyone know what I'm doing wrong here?
lone heartBOT
Anyone know what I'm doing wrong here?
tardy torrent
My suspected issue was that I was getting an incorrect t
When I solved by hand, I got t = 2000 + 25q - q^2
Which when I multiply by q, I get the total revenue (T) to be 2000q + 25q^2-q^3
Derivative would be 2000+50q-3q^2 of that.
When I set that equal to 0, I got something weird.
And don't know if I should even bother trying to move forward with that direction.
lone heartBOT
@tardy torrent Has your question been resolved?
tardy torrent
<@&286206848099549185> Still haven't figured out. Pls help.
lone heartBOT
@tardy torrent Has your question been resolved?
tardy torrent
😤
ancient saddle
My suspected issue was that I was getting an incorrect t
Hello, how are you getting that value for t? I think you should explain the process involved to find T in terms of t because it looks like there are economy concepts that not everyone knows
lone heartBOT
@tardy torrent Has your question been resolved?
faint bronze
Find y if sin (y + 6) = cos 2y, if y is acute.
I don't understand how to solve these type of questions, if someone could help it would be great
tight locust
Find y if sin (y + 6) = cos 2y, if y is acute.
I don't understand how to solve ...
degrees or radians
i'm assuming degrees
sin sum formula
sin(y)cos(6) + sin(6)cos(y) = cos(2y)
now then, double angle cosine
cos(2y) = 2sin(y)cos(y)
cos(6)sin(y) + sin(6)cos(y) = 2sin(y)cos(y)
faint bronze
i havent been taught these formulas, ive been taught only simpler formulas. so there must be another way which is a bit more "basic"
tight locust
transcendental equations usually do not have closed form solutions
faint bronze
okay
faint bronze
okay ill try that one sec
faint bronze
can you please frame that with the values, so i understand better?
tight locust
wdym
i gave you the formula
use a little bit of brainpower. the cosine of a number always equals the sine of the sum of 90 and that number
faint bronze
im sorry im not really good and trigonometry, ill try this one
tight locust
so what is the cosine of 2y?
if cos(x) = sin(90+x) then cos(2y) = sin(90 + 2y)
it's just a straight substitution
that's how you use formulas
lone heartBOT
lone heartBOT
Available help channel!
exotic marsh
lone heartBOT
exotic marsh
Can I please get help on this.
I have no work on this one right now because I’ve been trying multiple problems but I keep getting the answers wrong
charred flint
slope is (change in y)/(change in x)
exotic marsh
I know but when I get an answer it says it’s wrong
charred flint
-4/3?
woeful pulsar
show your working?
exotic marsh
I have no work on this one right now because I’ve been trying multiple problems ...
^^
woeful pulsar
show your working to compare
alpine sable
24 971 cm 2 to the nearest 100cm2
woeful pulsar
you seem not to be calculating change in y correctly
exotic marsh
Oh
woeful pulsar
Take (-2, 2) (5, -2)
as well as change in x
sometimes the coordinates were added instead of subtracted
which may seem confusing because you are working with negative numbers
woeful pulsar
along the same line?
like for example (8, 16) (10, 10)
this one was all positive
but the coordinates were added?
exotic marsh
along the same line?
Nono like another question I’m stuck on
woeful pulsar
ig should be fine
woeful pulsar
as you know, slope = rise/run right?
exotic marsh
Yes
woeful pulsar
can you calculate the rise and the run?
exotic marsh
My brain just died when you said that.
woeful pulsar
hmm, is it because you are familiar with finding the rise and run between 2 points?
but not when there are no points to find a slope?
exotic marsh
I think?
woeful pulsar
okay, which two points are easy to reference the slope from?
maybe a start point and end point for the slope?
lone heartBOT
woeful pulsar
lol i guess that's resolved
lone heartBOT
Available help channel!
worthy verge
lone heartBOT
worthy verge
mortal mica
worthy verge
I dont understand how to transform it into a simpson formula
its usualy h/3 ( y0 + yN + 4(y1+ y2+y3+...) +2(y2+y4+...)) right
Wait nvm
I understand it
.close
lone heartBOT
lone heartBOT
@silver tangle Has your question been resolved?
alpine sable
chrome salmon
Bye
formal sentinel
What does the ^ notation refer to
restive spruce
could somebodyhelpwith calculus
i dont understand this question it is about optimization
wary stream
https://gyazo.com/09df300e91d91f05ae2ce383ceaf58dc
Don't ask in an occupied channel
Read #❓how-to-get-help
restive spruce
ill give you six thousand dollars if you help me
wary stream
No
formal sentinel
No
lone heartBOT
@silver tangle Has your question been resolved?
lone heartBOT
@silver tangle Has your question been resolved?
crisp grove
@silver tangle ?
what the hell is a a+bx+series...?
also what's the question?
$\hat{\cos(x)}$ means the fourier series of $\cos(x)$ not cos x itself
ocean sealBOT
Ryuzaki
crisp grove
you have a initial data?
you can't assume it'll have a form like that
it may not
you might have got the idea from heat equation
but no, these equations are inherently different
depends on the initial data like say you are given
\begin{align*}
u_{tt} &= c^2u_{tt} \
u(x, 0) &= f(x) \
u_t(x, 0) &= g(x)
\end{align*}
then your solution will be of the form $u(x, t) = \frac{1}{2}(f(x-ct)+f(x+ct))+\frac{1}{2c}\int_{x-ct}^{x+ct} g(x) \dd s$
ocean sealBOT
Ryuzaki
crisp grove
but if you are given boundary data instead of initial data, then It'll be something + a fourier series
that something may not always be a "a+bx"
why are you assuming you'll have something like a+bx+ct+dxt ???
as I said it can even be e^x or a discontinuous function
alpine sable
can someone teach me how to do math? I have no idea of what these letters mean.
misty dagger
can someone teach me how to do math? I have no idea of what these letters mean.
Honestly, watching YouTube is your best option.
crisp grove
ie assuming the solution is of the form $X(x)T(t)$ and not of the form $a+bx$
ocean sealBOT
Ryuzaki
alpine sable
Honestly, watching YouTube is your best option.
alright, I'll be back.
crisp grove
read the chapter/notes carefully
misty dagger
Ye
misty dagger
alright, I'll be back.
Practice makes perfection xd
crisp grove
OK so he's not ASSUMING solution is of the form
He's simply solving a BV problem and showing if \lambda=0 is a eigen value then only possible value for X(t) = a+bx, together with the BV conditions mean taht a=b=0, so, only trivial solution
he's now showing that it's a solution but showing that it's not
No
if your boundary conditions allow a solution like a+bx then you do
but SLBVP problem don't allow that in general, they'll only have +ve eigen values
0
ok maybe that depends on what you call lambda
but the standard equation is $X''+\lambda X=0$
ocean sealBOT
Ryuzaki
crisp grove
you'll get non trivial solutions (i.e. eigen functions) iff lambda > 0
if you are using -lambda, then <0
$\widehat{\cos(x)}$ is the fourier series of cos(x)
ocean sealBOT
Ryuzaki
crisp grove
it's already written in form $0+1\cdot \cos(1\cdot x) + 0\cdot\cos(2\cdot x)+\cdots$ so as you see $a_n=0$ unless $n=1$
ocean sealBOT
Ryuzaki
crisp grove
or -1
that's what it's saying
what is the fourier series of cos(x)?
really?
a_n=1?
for all n?
pseudo lagoon
Hi can someone explain how the 3+root3 came
pseudo lagoon
<@&268886789983436800>
tame falcon
Please don't ping moderators or other users randomly for math help. Also, read #❓how-to-get-help and use a new available channel.
winged ruin
what is the close form of this recursive function
even a link/article appreciated
fading zephyr
what is the close form of this recursive function
even a link/article appreciate...
read #❓how-to-get-help , don't hijack other people's channels
winged ruin
read <#488120190538743810> , don't hijack other people's channels
what do you mean
ok
let me see
pseudo lagoon
Please don't ping moderators or other users randomly for math help. Also, read <...
Sry meant to tag helpers
<@&286206848099549185>
tame falcon
Please use an available help channel. Don't step over a channel already in use by someone else.
Consider reading #❓how-to-get-help once.
pseudo lagoon
?? It’s been like 2hrs since last question???
winged ruin
ok
lone heartBOT
@silver tangle Has your question been resolved?
high wraith
chrome kite
well, no, the range of your 3 functions is -1 <= y <= 1
the range of your piecewise* function is that
your range has to be strictly greater than 3, and less than or equal to 1
alpine sable
oh shit wrong channel, sorry
wanton jasper
summer mesa
i need help
crisp grove
it's pandemonium over here
inner shore
Hi
<@&286206848099549185>
I need help with a problem
Now let's make this easy and say that the premium paid product is just a $100 lifetime fee.
Now let's say that all free users on the site that still haven't paid after month 1 (month 2 free users), will then be 50% less likely to convert compared to the first month free users. And then subsequently for month 3, those existing month 3 free users will then be 50% less likely to convert compared to the month 2 free users, and so on, etc...
What is the average lifetime value in dollars (or equation) generated for free users if we extrapolate out to one year?
alpine sable
is coshx a parabola
Noooooo.
It looks like one but noooooo.
,w plot cosh(x), x^2, |x^3| from -10 to +10
ocean sealBOT
alpine sable
Hold on.
alpine sable
alpine sable
couldn't it be a parabola if we add up constants
No. cosh is an exponential function. It will always exceed a polynomial.
Just realized this channel is someone else's.
Next time, open a new channel to ask.d
past hornet
ohh
alpine sable
Or #discussion
alpine sable
https://youtu.be/AYIQYZuQNMw
@past hornet Watch this tho'.
Great explanation of cosh and catenary.
sonic wyvern
am stuck on this
i figured the limit of that value at the bototm
would be 1^inf
which is 1
magic geyser
your final simplification form is correct
now the limit
both num and denum are inf
?
oof sorry
magic geyser
ok it dumbs down to the fact that lim as n -> inf of (1 + 1/n)^n = e
it's 1/e
alpine sable
?
earnest ice
can anyone help me with my 8th grade home work
severe sluice
can anyone help me with my 8th grade home work
just ask 🙂
fervent tartan
i need help
strong hornet
i need help
zealous bloom
i need help
I mean, we can't see the table for how much he gets paid....so....
fervent tartan
the table
zealous bloom
the table
You're in 2 different channels. I'll default to whomever is helping you in the other channel.
fervent tartan
You're in 2 different channels. I'll default to whomever is helping you in the o...
👍
cerulean kite
So In my calc class we're learning how to integrate by using u-substitution. And i'm having trouble finding what value "u" should be. trying some practice problems. was wondering if somebody could point me in the right direction as to where to start and what u should be in this problem.
raw shard
what is that exponent on -1/x^2
cerulean kite
3/8
misty dagger
raw shard
i can’t but it’s definitely possible
wait a second
you might be able to do u sub actually
rewrite it as multiplication instead of division
cerulean kite
it says to make u=-1/x^2 in the hints
raw shard
yes that’s right
raw shard
d/dx -1/x^2 = d/dx -x^-2 = 2x^-3 = 2/x^3
cerulean kite
ahh you smart smart
i see what you did there.
so lemme try it.
like this right.
cerulean kite
yes your right
so then don't i have to do the whole. du=-2/x^3 *dx
and then solve for dx
so that I can substitute du into the integral.
raw shard
messed up
u = -1/x^2, du = 2/x^3 dx
which are both in the integral
the original integral
no multiplying by a constant or moving terms around necessary
at least i don’t think
ok multiplying by -1 is necessary
but that’s it
cerulean kite
so your saying I don't need to solve for dx, I just put what we have for du wherever dx is?
raw shard
no
find whatever du is equal to in the original integral
if you have all that stuff replace it all with du
cerulean kite
I'm some trouble understanding this.
raw shard
-(u)^(3/8) du
should be the only thing in the integral now
the way you did it had two variables in the integral
which you don’t want
cerulean kite
could you write that one part out? i'm not too sure what you mean.
raw shard
which part exactly?
cerulean kite
like after you find out what u and du are. how exactly does that go into the integral?
raw shard
ok so you already know that whatever u is defined as is in the original integral so we don’t need to talk about that
cerulean kite
yes
raw shard
we have du = 2/x^3 dx
can you find something like that in the original integral?
if not you can multiply both sides by a constant
cerulean kite
well yeah in the original integral you could just split it into 2/x^3 * -1/x^2^3/8 right
raw shard
no
wait i misunderstood
yes
your lack of parenthesis confused me but i figured out what you meant
cerulean kite
sorry i just saw that.
raw shard
although that’s not necessary here
because u sub will work
wait never mind you didn’t mean what i was thinking of
yes you can do that
you found something that resembled du
cerulean kite
would you be able to go into voice so I can share my ipad screen with you?
raw shard
the problem is that that is positive and du is negative, although we can multiply du by -1
sorry no
cerulean kite
okay well ima try and work this one out. thanks for your help.
raw shard
this explains it better than me, https://tutorial.math.lamar.edu/Classes/CalcI/SubstitutionRuleIndefinite.aspx
sage raptor
can someone help me find perimeter
eager pebble
you use pythagorean theorem for the longest triangle side
then you find circumference and divide by two
then add that+long triangle leg+bottom triangle leg
sage raptor
so 9 ^2 + 14^2 =c^2?
eager pebble
yea
sage raptor
ok thank u
alpine sable
can someone help me find perimeter
this is a very funky ice cream cone.
lone heartBOT
@silver tangle Has your question been resolved?
alpine sable
Oh cool this server has texit
alpine sable
How could I simplify:
lone heartBOT
How could I simplify:
alpine sable
$80+84+88+92+96+100...+n_{36}$
ocean sealBOT
Lambdalo
alpine sable
as in, just write this as a nice formula
fleet hearth
**Lambdalo**
The Sum symbol
alpine sable
yeah I knew that, just how specifically
fleet hearth
The top part is the highest integer it goes to and the bottom part is the integer it starts at.
And the formula in the middle
alpine sable
?
wait
$\sum_{k=80}^{36}k+4$
wait but probably switch 36
with the actual result
ocean sealBOT
Lambdalo
fleet hearth
You put the formula there which is in this case. 76 + 4n
silver viper
**Lambdalo**
if you switch 36 and 80, this would mean
(36 + 4) + (37 + 4) + ... (79 + 4) + (80 + 4)
alpine sable
which is incorrect, that's true
fleet hearth
The bit at the bottom is the starting value for N. So n = 1
$\sum_{N =1}^{36}76+4n$
ocean sealBOT
Phaseloli666
alpine sable
is that true though?
the problem is, that 76 rises as well, which it doesn't in my original series
silver viper
**Phaseloli666**
this would mean
(76 + 4*1) + (76 + 4*2) + (76 + 4*3) + ... + (76 + 4*36)
= 80 + 84 + 88 + ...
alpine sable
**Phaseloli666**
oh wait you're right
fleet hearth
You can find the formula from $T_n = a + d(n-1)$
ocean sealBOT
Phaseloli666
alpine sable
so only the variable that you define as the starting point actually rises, interesting
fleet hearth
You can find the formula from $T_n = a + d(n-1)$
All i did was 80 + 4(n-1)
As 80 is the start Point and d is the difference between the terms
alpine sable
many thanks
raven girder
Is it correct to say Z/2Z = {0, 1} or would that be wrong?
raven girder
Nvm, different question
what exactly is the operation in Z/2Z?
is it basically a group (Z, z mod 2)? Hope that makes sense
bleak ridge
Is z a complex number
bleak ridge
Or I mean Z or z or wotever
raven girder
Z are the integers
glass lichen
what exactly is the operation in `Z/2Z`?
Z_2 has 2 operations..
- and *
cause it's a field
raven girder
we didn't learn about fields yet, only groups
hope group is the right term
group homomorphisms and stuff
I wonder how I can show that this is a group homomorphism
the second set there has * as operator
but idk what the operator is in Z/2Z
f([x] * [y]) = f([x]) * f([y]) is what I wrote down
but then I thought wait, how do I know that * is defined in Z/2Z
isn't the operator in Z/2Z mod?
glass lichen
No
raven girder
or am I misunderstanding
glass lichen
Z_2 is just {0,1} with modular + and *
raven girder
ohh I see
glass lichen
ie 1+1=0 since 2 is 0 mod 2
raven girder
hm but then I'm not sure if I have to pick modular + or * for the equation I wrote above
to show that it's a group homomorphism
usually we only deal with groups that have 1 operation
glass lichen
I'd guess it's R * on the right group
raven girder
R?
raven girder
but what about the left group Z/2Z
it has + and *
I have to pick * I suppose
I figured out that it's not a group homomorphism hope that's right
or do I actually need to use both + and * to show that it's a group homomorphism?
I also wonder, if I have a map Z/2Z -> Z, [x] -> x, let's take as an example [16]. [16] = [0] in Z/2Z. But if I put [16] in the map, do I get [16] -> 16 or [16] -> 0 <=> [16] -> 16 mod 2? 🤔
the latter I hope
lone heartBOT
@raven girder Has your question been resolved?
raven girder
.close
alpine sable
Why do I need lhopital to prove this is zero?
lone heartBOT
Why do I need lhopital to prove this is zero?
alpine sable
i could just plug the minus infinity to e^x and it'd be 0, no?
what am I missing here?
raven rover
@alpine sable x^3 -> -∞
raven rover
You're not multiplying ∞ by 0 explicitly
alpine sable
When do we know if we should use lhopital or not?
raven rover
You're multiplying a number that gets bigger and bigger and bigger without stopping by a number that gets smaller and smaller and smaller (closer to 0) without stopping
raven rover
When do we know if we should use lhopital or not?
When you get a situation like ∞ • 0, -∞ • 0, ∞/∞, 0/0
The first two you can rewrite so you get one in the form of the last two
glass lichen
They did LH
e^(-x) differentiates to -e^(-x)
However you could say it's 0 from the get go via growth logic
alpine sable
You rewrote the limit incorrectly
ok but are the general steps correct?
alpine sable
However you could say it's 0 from the get go via growth logic
what’sthis?
How do I close help channel?
@glass lichen @raven rover thanks for your help guys
proven veldt
Just type .close
alpine sable
Why is this 1 and not 0?
lone heartBOT
Why is this 1 and not 0?
alpine sable
it seems the solution wants me to take exponent but i don't understand why i need to
alpine sable
oml it was that simple LOL
@zealous bloomwait so does that mean you can only use l'hopital when there's ∞ • 0, -∞ • 0, ∞/∞, 0/0 (like what shen said?)
zealous bloom
I don't recall all forms necessary to use L'Hosptal's rule...I remember 0/0 was one, but that's all I can recall for now.
crisp grove
0⁰ DNE
sour dove
Anything raised to the 0 = 1, even 0
Wait I thought that was undefined/indeterminate
alpine sable
0⁰ DNE
so... im not supposed to just plug in the zeros?
the solution raised everything with an exponent
i still don't understand why it did that
crisp grove
never said the limit doesn't exist
only said that Lhopital is not applicable in the ∞/0 case
alpine sable
oh
crisp grove
also 0⁰ is undefined
ruby ether
hello
noble sinew
ruby ether
ah i see, yeah i was thinking that too, but i just doubt if my answer is correct or not since i cant find it on google and need to pay for the answer ;-;
okay 1 more question
how do i determine truth or falsity?
especially the (c) one
got me confused
are my answers correct if all of the statements are false except (a)
alright thank you ❤️
.close
ruby ether
no open again
lone heartBOT
no open again
ruby ether
it's just huwaa
for the (a)
isit correct if i made a statement
Everyone does not like strawberry
indicating that without the negation it will become
Someone likes strawberry
did it do correctlyyy
i am so confused on predicate logic
placid zinc
We're talking about (a)?
Yeah that's correct
More strictly:
"It is not the case that someone likes strawberries"
ruby ether
ahh... i see i see, so it's equivalent to ∀x~P(x) right
and literally just ~∃xP(x) without the bracket
ebon pier
can someone tell me the solution of this instead of x is 1/2 ,the second one?
ruby ether
maam
placid zinc
ruby ether
this is my channel
ebon pier
sorry
ruby ether
😭 its ok
ruby ether
and literally just ~∃xP(x) without the bracket
sometimes the bracket got me
dammit
but i will try my best to understand this topic
"study logic" is a statement right?
nvm its not
n.n im done .close
.close
void magnet
If I have the function f(x) = 64x^3 - 16x^2 + 12x -1 how do I find f^-1(x) =
zealous bloom
If I have the function f(x) = 64x^3 - 16x^2 + 12x -1 how do I find f^-1(x) =
There's a few methods to finding inverses of functions. One is to "change" f(x) to y, so it will be y = 64x^3 - 16x^2 + 12x -1.
Then, switch the x and y's so it will be x = 64y^3 - 16y^2 + 12y -1.
Then, solve for y.
At then end you'll have y = answer, and just stick your inverse notation back in: f(x)^-1 = answer
But this is just A method.
void magnet
So how do I rearrange it for y, I've always been bad at rearranging.
I just don't know where to start
zealous bloom
What do you mean rearrange for y?
void magnet
rearranging to make y the subject of the formula
zealous bloom
I already rearranged it for you, so you actually just have to solve for y.
void magnet
I guess I should factorise it to take y out of the brackets
zealous bloom
? Are you asking how to solve for y?
zealous bloom
I guess I should factorise it to take y out of the brackets
Or how to rearrange it? I'm confused
alpine sable
lone heartBOT
alpine sable
<@&286206848099549185>
buoyant kayak
do you know the equation for point slope form?
buoyant kayak
yep
buoyant kayak
not in the slightest, no
buoyant kayak
because you're correct
alpine sable
but you said your not sure if im right
buoyant kayak
exactly
alpine sable
bcs i said is the answer that and you said yep
buoyant kayak
yeah it is
buoyant kayak
yep
alpine sable
are you sure?
buoyant kayak
not in the slightest, no
alpine sable
k
red galleon
Find the graph of this
hollow zephyr
lone heartBOT
lone heartBOT
@hollow zephyr Has your question been resolved?
lone heartBOT
@hollow zephyr Has your question been resolved?
lone heartBOT
@hollow zephyr Has your question been resolved?
alpine sable
can someone help?
@alpine sable
hollow zephyr
bro how dare you
ionic trail
Derivate of ln(u) is u'/u
Not 1/u
That's your mistake
I wasn't blaming you @hollow zephyr
Bro 
lone heartBOT
lone heartBOT
Available help channel!
potent pebble
lone heartBOT
novel cape
lone heartBOT
pale terrace
hello
pale terrace
can someone show me how she found the derivative of A(x) to be that?
what rules did she use
open the original image because this is hard to see
raw geyser
Find the graph of this
use desmos
lone heartBOT
@pale terrace Has your question been resolved?
mortal turtle
".close"
candid atlas
Hey guys
so
I'm not sure if this is right
Bc it doesn't make sense
Idk
is it correct?
I got 2.9558 grams for part b
and 117.2316 seconds for c
until 20 grams remain
mortal turtle
see #❓how-to-get-help , you should claim your own channel
lone heartBOT
Available help channel!
fleet axle
how would I factor this out im supposed to be able to factor out (h-2)
toxic meadow
can someone help me
lone heartBOT
can someone help me
severe sluice
can someone help me
you can calculate the full area of the pizza first
and then get the radius
(and then get the arc length)
hidden knoll
5/6 radians = (180/π)*(5/6)
900/6π degrees
150/π degrees is about 47.74 degrees
47.74/360=13.26% of the circle
20/13.26%=150.82
the full pie is 150.82 square inches
πr^2=150.82
r^2=150.82/π
r=√(150.82/π)
r=6.928
d=2r
d=13.85
27. the diameter of the pizza is 13.85 inches
ill let u do 28
toxic meadow
hmm
hidden knoll
u can do that or
20=(1/2)(r^2)(5/6)
48=r^2
√48=r
r=6.928
d=2r
d=13.85
toxic meadow
somehow my teacher got 4sqrt6 inches
but she didn’t send the work which is what i’m trying to find out how to do
toxic meadow
you can calculate the full area of the pizza first
how
hidden knoll
√48 simplifies to 4√3
since diameter is 2*radius, it should be 8√3
ur teacher probably multiplied 2 to the √3 on accident
severe sluice
how
uh
the angle is 5/6 radians
the angle in the full pizza is 2*pi radians
(area proportional to angle)
hidden knoll
no
glass lichen
full circle isnt 2rad
hidden knoll
full pizza is 2π radian
toxic meadow
it’s 2pi
toxic meadow
damn alright thanks
hidden knoll
anyways #28 should be easy to do
since ur calculating arc length and we have the angle in radians u can just use arc length = radius * radian
toxic meadow
anyways #28 should be easy to do
since ur calculating arc length and we have the...
is it 10sqrt3/3 ??
hidden knoll
the radius is 4√3, multiply that by 5/6
hidden knoll
u are correct
hardy cypress
if you're trying to find a 4 digit code, and the first digit is 7 and for the other 3 digits are the first digit multiplied 2 times, what is the answer
hidden knoll
the first digit is 7
the other 3 digits can be calculated by 7^3 (7*7*7) as ur multiplying 7 by itself twice
7^3 is 343
your answer is 7343
devout summit
if you're trying to find a 4 digit code, and the first digit is 7 and for the ot...
What do you mean by other three digits are first digit multiplied by 2? 7*2=14??
lone heartBOT
@hardy cypress Has your question been resolved?
median yoke
Hey, I know this is math help but anyone good a organic chem here?
misty dagger
Nope
lone heartBOT
@median yoke Has your question been resolved?
white drum
How do we find the angle working backwards from area
lone heartBOT
How do we find the angle working backwards from area
severe sluice
How do we find the angle working backwards from area
how did you do it forwards?
just calculating the areas of the sectors and subtracting, right?
to do it backwards
(wait a sec - creating diagram)
white drum
To do it forwards I did A= (theta/360)*3.14159r^2
severe sluice
wait a sec
what's R?
anyways
we have this
just calculate the highlighted area between the circles (uh i can't highlight that in geogebra)
the wiper would sweep that area if it were to turn for 2pi radians
area wiped is proportional to angle
white drum
r is radius
severe sluice
but which?
white drum
The length of the wiper
I found the are aby first calculating with the 22" wiper
Then calculating the 6" that were not cleaned
And subtracting
severe sluice
yeah that's right
white drum
We arent calculating area though
I am tryingto calculate the angle if area sweeped is 10"^2
I have to leave but thanks for the help
If you can respond to my question in one message please do I will read it over once I get home
severe sluice
We arent calculating area though
i mean
area is proportional to angle
so you know the area
thus you can calculate the angle from there
white drum
How
The area is 508.24
Not sure how to ratio that down to ten
Nvm
Divide both sides by 50.824
No that wasnt it
severe sluice
i mean
white drum
My dumbass got 50.824 mixed with 50.284
white drum
Tysm got it
severe sluice
(assuming that the area is actually 508.24 - i haven't checked @white drum)
jaunty bramble
You got it right?
lone heartBOT
@white drum Has your question been resolved?
ancient tapir
help
violet iron
How do I know if I should use sine or cosine or tangent to find the total height of something?
wary stream
Based on where the angle is located
violet iron
So if it is touching the base and the hypothenuse?
wary stream
Are you given values for the base and hypotenuse?
wary stream
So which trig function relates the hypotenuse and the height?
violet iron
I don’t remember 😭
violet iron
I remember like the formulas but not how you use it
wary stream
Yes
violet iron
Why though?
wary stream
Because you need the height. Given the position of the angle and the value of the hypotenuse, you will either use sine or cosine. If you used cosine, you'll be finding the base and that's not what you want. So by process of elimination, the logical one is sine
severe sluice
.close
wary stream
.close
The one who opened the channel has power to close the channel. And helpers, and mods
lone heartBOT
@violet iron Has your question been resolved?
honest umbra
Hi
honest umbra
I have to graph the black function on paper but after i factor im getting a different looking function...
tacit lodge
I have to graph the black function on paper but after i factor im getting a diff...
u are factoring it wrong.see the numerator
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
I was actually doing a physics question which asked to calculate work done by Force F after block reaches height h from ground but I can't understand that if x axis is l and y axis is h then why the professor has taken dx and dy and hypotenuse as dl
lone heartBOT
I was actually doing a physics question which asked to calculate work done by Fo...
@alpine sable Has your question been resolved?
pearl jasper
@alpine sable I think those are two separate diagrams and the labels are not related to each other
alpine sable
no, prof took a small part which he called dl out of the path, it is of 1 question only
pearl jasper
path of what?
the wedge or the block on the wedge?
can you share the the full question, it's hard to guess what your professor was doing based on half a screenshot
pearl jasper
ah okay
alpine sable
and this is the part I have doubt
pearl jasper
and l is the horizontal distance?
alpine sable
and this is the part I have doubt
well if u take dl as dx and dh as dy here and hypotenuse as something else, it will still cancel out after being multiplied with cos theta and give same input
pearl jasper
okay wait, what is dw?
alpine sable
work done
pearl jasper
ah alright
alpine sable
umgcos theta is the force and dl is the distance covered
this is what he did next step
pearl jasper
okay that makes sense
I think he shouldn't have used l and dl to mean different things
wherever he has used dl just rename it to another variable like ds to avoid confusion
alpine sable
yeah, dx is basically dl right? and dy is dh
pearl jasper
yes, and hypoteneuse is ds
alpine sable
yeah, that's what I also thought, hypotenuse be just another variable
thanks a lot for the help @pearl jasper
pearl jasper
cool 🙂
alpine sable
.close
grim vessel
Find the mass of a particle which has a speed of 5.0 m/s and a kinetic energy of 5.0 J ?
crisp grove
KE=½mv²
grim vessel
.close
alpine sable
hello! could someone go through this with me?
lone heartBOT
hello! could someone go through this with me?
harsh girder
You can calculate the derivative to determine the monotonicity of the function
alpine sable
You can calculate the derivative to determine the monotonicity of the function
ok so the derivative of the function, do you know what i need to do afterwards?
harsh girder
ok so the derivative of the function, do you know what i need to do afterwards?
if f'>0 then f is increasing，if f'<0 then f is decreasing.
alpine sable
ok
ripe wasp
If derivative equals zero, the time is the answer.
alpine sable
when it says 'during the first four hours' is there a certain calculation that i do as well ot determine that?
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
.close
limber lava
what is the underline thing mean? I am confused
lone heartBOT
what is the underline thing mean? I am confused
limber lava
Maybe I am domb
teal turtle
It's the result from dot multiplication of n and (p-p1)
n⋅(p-p1) = (ai + bj + ck) ⋅ ((x-xp)i + (y-yp)j + (z-zp)z) = the result you underlined
limber lava
K..?
Ok wait a sec bro let me read it
Ok the result you gave me is different than the underlined result though
How do I translate it to the underlined result
teal turtle
Okay I'll explain how you do dot multiplication then
teal turtle
Alright, so now you have to do the same with
(ai + bj + ck) ⋅ ((x-xp)i + (y-yp)j + (z-zp)z)
Treat x-xp like a single constant
Same with y-yp and z-zp
limber lava
Ok
teal turtle
Doing so you should find that the expression is equal to
a(x-xp) + b(y-yp) + c(z-zp)
teal turtle
what is the underline thing mean? I am confused
Multiply a, b, and c in and you get the underlined thing
alpine sable
how do i get the limit of this term?
lone heartBOT
how do i get the limit of this term?
alpine sable
ah, the limit here looks a bit weird, were meant to get the limit of the whole term, not just the numerator
pearl jasper
this does not look like one of the 7 indeterminate forms
do you know what those are?
alpine sable
im looking them up rn
okay, the idea is to take the limit of the numerator and the limit of the denominator and take the quotient?
pearl jasper
yes
solid bloom
gello
solid bloom
hello
The 12th Term of an arithmetic progression whose 15th term is 53 and whose 67th term is 261 is?
lone heartBOT
@solid bloom Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
coral pasture
1.) 16.041=-15sin(31.5-C)+D
2.) 0.332= -15cos(31.5-C)
can someone solve for c and d plz?
jaunty bramble
The numbers are not so nice.
lone heartBOT
@coral pasture Has your question been resolved?
digital steeple
lone heartBOT
digital steeple
I am trying to understand how to dynamically rotate a vector3 point in respect to both a pivot point, and based on an axis (im using it for programming atm) (as well as an angle ofc)
how can i dynamically or mathematically to be exact find the vector direction in which i should rotate?
i will provide some pictures to show what i mean from the unity engine, but i implore you to think of this as a mathematical problem since i already made it work, but i wanna make it more clean
per example here
if i select X i expect it to distribute around my target, as well with respect to the X direction
jaunty bramble
Sad
digital steeple
similarly with y etc
feel free to ping me once you have any suggestions to solve this vector3 problem
lone heartBOT
@digital steeple Has your question been resolved?
digital steeple
<@&286206848099549185> is there someone who could potentially assist me with the vector3 logic?
finite flax
oh god you're asking about quaternions.
digital steeple
yes pardon, it also includes quaternions
finite flax
3blue1brown demystified it in a couple (three?) videos but they are long and I never watched them all in one sitting. I have no idea rn
digital steeple
yea thats understandable i am myself kinda confused about quaternions
But what i know about them is in a nutshell they are vector3 with angles
finite flax
^ not the first one
for Unity's purposes....
but it has more to do with complex analysis
(broadly)
I didn't finish complex analysis.
digital steeple
no i simply need to understand my question for now, and afterward i can spend time studying quaternions and complex analysis properly in my spare time
but i pinned your video in my list
finite flax
right. But that's the closest I ever came to understanding it.
digital steeple
ah i see
finite flax
In Unity, most tutorials implore you to use the conversion functions angleToQuaternion or whatever
digital steeple
thats why i emphasized essentially to think of this as a mathematical problem
i know the methods to a point, i know how to use them, i dont know how to put them together
and thats not due to my lack of programming knowledge, but more on my lack of quaternion and vector3 when they play together knowledge
finite flax
@digital steeple watch that one video because I just did and now I at least feel confident about the math involved
digital steeple
ill have a look shortly
finite flax
don't look there though
walk through this
you can actually fiddle with the numbers while he's talking, it's amazing
digital steeple
don't look there though
Walking through it i wanna rephrase my issue
As i watched i realized my question was probably not targeted properly to what i am trying to figure out
I am trying to figure out the euler angles ill have to rotate (since unity like you mentioned allows you to simplify initializing a quaternion by giving it a euler set of angles) that respect a target pivot and target axis
Per example:
Vector3 actualAxis = Vector3.zero;
if (axis.x > 0)
{
actualAxis.z = 1;
}
if (axis.y > 0)
{
actualAxis.x = 1;
}
if (axis.z > 0)
{
actualAxis.y = 1;
}```
here you are gonna notice i am mockingly using a second vector, which i adjust manually to figure out the 2 different pointsquaternions will always find the shortest angle traversal between two points on a sphere.
bleak ridge
In this case euler angles are kinda an unsimplification
digital steeple
its simpler to understand for me due to x - y - z
finite flax
it will trace an arc of a Great Circle
digital steeple
while quaternions look like rotation matrices
finite flax
you're not gonna make sense of it in euler
digital steeple
i am not following
bleak ridge
Does unity have a quaternion library
digital steeple
yes it does
bleak ridge
It should be fairly easy to solve then
Quaternions just take an axis to rotate about and an angle
The imaginary part are the three components of the vector to rotate about and the real part is double the angle
digital steeple
yea my issue is just distincting what axis do i offset my target point dynamically, based on the axis i wanna rotate towards
rancid frost
hello lads i have no contribution to this conversation and i am shit at math but whats the 4th dimension ive always wondered
in really simple terms
bleak ridge
Do you mean for the pivot point
rancid frost
nah i mean just in general
finite flax
nah i mean just in general
math equivalent of photobombing or leaving shit on the porch
digital steeple
target point => Offset point from my pivot
target point offset axis => what axis do i use to offset my item using math?
axis => my intended axis i wanna distribute my vector3 around
i know target point, i know axis
rancid frost
math equivalent of photobombing or leaving shit on the porch
is this talking about me or 4th dimension haha
digital steeple
i dont know the offset axis (or to rephrase, the offset direction)