I hope someone sees it
#help-28
balmy karma
inland moth
do you have all those sums?
cold island
yes i sent the pics
inland moth
then just plug it into the formula
cold island
i know its not the pearson one right? it looks similar but not yk
balmy karma
they have two formulas for pearson, that one and yours.
so I assume they are the same
inland moth
its equivalent
you can get one from the other from the sums of squares
anyways it doesnt matter
so lets start for the numerator
cold island
n is 5
inland moth
are you sure?
cold island
sum of xy is 6730
inland moth
dont you have 6 data points?
cold island
i think i sent the wrong data
one second
i apologize for that
here sorry again :(
inland moth
ok then start plugging it in
balmy karma
didnt you hear her? she said she needed help with step-by-step
cold island
ya bro didnt you hear her
cold island
thank you so much yall
inland moth
in the numerator
the first term is n(Σxy)
do you have the sum of x and y multiplied together?
it appears that you dont
can you first get that?
cold island
yes it would be 5(6730) right?
inland moth
yep
cold island
here
inland moth
then the next is (Σx)(Σy)
cold island
sum of x (420) sum of y (84)
inland moth
if you multiply them and subtract them you get?
cold island
that would be -1630
inland moth
ok thats the numerator
now the bottom
you'll need to open a square root first
inside it is n(Σx²)-(Σx)²
what are the values for those?
cold island
ok this is how i wrote it out rn [5(37,450)- (420)²] [5(1496)-(84)²]
inland moth
ok thats good
cold island
if i start with the ones you said the answer for that part would be [10850] ?
and [424] for the other!?
cold island
ok r=-.76 or .7599??
balmy karma
its not either, plugged it into desmos
cold island
did you try solving it yourself
balmy karma
no
i use desmos for correlation because I can just never remember the formula, and its insanely long and hard. Its impossible to detect mistakes too.
cold island
no i understand, the professor wants us to do it by hand to get an idea of the formula, we use spss so it does it automatically but it is long and hard ur right
balmy karma
no i understand, the professor wants us to do it by hand to get an idea of the f...
and again, if you make a mistake, you can almost never find it
cold island
yeah exactly, but i see where my mistake is now so i guess its good
inland moth
ok r=-.76 or .7599??
both is fine
cold island
@inland moth thank you for the guidance I MADE A MISTAKE WITH THE SQUARE ROOT D:
inland moth
?
inland moth
is it not -.76?
inland moth
i use desmos for correlation because I can just never remember the formula, and ...
what command is that
balmy karma
use the table in desmos. then plug in your values. In the top left corner of the table is a line with points. Click it (make sure it is on linear correlation) look at the info, and you should find r
cold island
awesome, chez maybe you plugged in the values wrong, can i see what you did?
cold island
oh ok
thanks for the website i will for sure use it in the future, does it provide step by step solutions?
inland moth
thanks for the website i will for sure use it in the future, does it provide ste...
no
balmy karma
i reccomend SnapXam for that
it uses word problems too
but it only allows so much problems
full forumBOT
full forumBOT
Available help channel!
vast snow
What am i supposed to do here bro 😭
full forumBOT
What am i supposed to do here bro 😭
long sky
What am i supposed to do here bro 😭
Did you get any data
vast snow
Did you get any data
This is only other thing we got
ah nvm i got it, i just have to make my own graph based on these 🙂 alr thanks ig
.close
valid hornet
Hey
valid hornet
Im needing some help with this question
∫
1
0
ln
(
x
)
ln
(
1
−
x
)
d
x
.
woops
im new to this server so idk
banned
mods ban him
Thanks
Can i get some help please?
valid hornet
Really?
solar wolf
If you do integration by parts you get to the integral of lnx/(1-x) which is known to not be elementary expressable
valid hornet
Oh I see
Well then im not sure
I have another question im unsure about too
3x^4 - 7x^2 + 2 = 0
And I still dont get how to do x3+y3+z3=k
Im new to diophantine equations
analog shale
yeah this is hard. One solution is to write ln(1-x) as an infinite sum and interchange sum and integral
analog shale
3x^4 - 7x^2 + 2 = 0
you can just solve for 3u^2-7u+2=0 and then solve x^2=u?
analog shale
And I still dont get how to do x3+y3+z3=k
this probably shouldn't be in the help channel, I don't think it is easy to find integer solutions
valid hornet
Really
?
This is mostly what i get but the proffessor said it was a challenge
So ig its fine
analog shale
This is mostly what i get but the proffessor said it was a challenge
why would they leave it as a challenge
https://en.wikipedia.org/wiki/Sums_of_three_cubes
full forumBOT
@valid hornet Has your question been resolved?
rocky mortar
Hi, im trying to determine if the function f does have a limit when (x,y) approaches the origin. There is no solutions to this question so I am not exactly sure if I have it correct. I tried testing for x and y approaching origin in the positive axis. As well on the negative side of the function, which returns (0,0). I also tried direct subsitution for x and y for two independently, which returns -1 for when x->0 and 1 for then y->0. So do I assume there is no limit since they both return different values?
stiff summit
Hi, im trying to determine if the function f does have a limit when (x,y) approa...
Yes, there is no limit, which you just proved. It can also be made rigorous by the equivalence of sequential continuity and continuity
rocky mortar
Ahh I see
when it mentions 'iterate' limits, does it mean you need to find the limit for the first variable then second like what I did on right side of my working out?
full forumBOT
@rocky mortar Has your question been resolved?
full forumBOT
full forumBOT
Available help channel!
weary vector
I am stuck somewhere imma show what i did until now
full forumBOT
I am stuck somewhere imma show what i did until now
weary vector
1/√5 [(4√10+2)/4 - (4+2√10)/2] * 1/√5 (15/4 + 11/2 -7/1 - 3/3)
idk is this is right or not.
onyx glen
so far so good but more simplification can be done there
weary vector
so far so good but more simplification can be done there
1/√5 (4√10 +2 -8-4√10)/4 * 1/√5 (15/4 + 11/2 -10) ?
onyx glen
how did -10 happen at the very end?
onyx glen
3/3 is not 3
weary vector
ops
onyx glen
3/3 is 1 not 3
anyway this is ok so far but why not collect the two 1/sqrt(5) factors you pulled out & combine them into one 1/5
weary vector
1/√5 (4√10 +2 -8-4√10)/4 * 1/√5 (15/4 + 11/2 -10) ?
1/√5 (4√10 +2 -8-4√10)/4 * 1/√5 (15/4 + 11/2 -8) ?
onyx glen
that and simplify (4sqrt(10)+2-8-4sqrt(10))
weary vector
1/√5[(-6)/4 + (15+22 -32)/4]
weary vector
should be a multiplication
i see it i think
onyx glen
also 1/5 not 1/sqrt(5)
weary vector
also 1/**5** not 1/sqrt(5)
how come
from the start we have 1/√5 i do not see where it changes to 1/5
onyx glen
collect the two 1/sqrt(5) factors you pulled out & combine them into one 1/5
your expression is:
1/sqrt(5) * (some shit) * 1/sqrt(5) * (some more shit)
weary vector
I thought we just common factor them
onyx glen
you misunderstand
if your expression was
1/sqrt(5) * (some shit) plus 1/sqrt(5) * (some more shit)
then we could take out a single 1/sqrt(5) as a common factor
but the plus sign is not a plus sign. it's a multiplication
weary vector
but the plus sign is not a plus sign. it's a multiplication
Oh bec we have multiplication we multiply them.
so we get 1/5
1/5[(-6)/4 * (15+22 -32)/4]
pale steppe
full forumBOT
pale steppe
Could someone help me understand these
So basically I found thr awnser already but I just don't understand how the method works
Basically for 23 I used this
And got an estimate of the total digits
Then just times 9 according to my friend
Then got another number then finally I got the correct anwser
But I'm just not sure why it has to be 9?
And for number 24 I was able to make it to 2023²⁰²³ = 67 mod 100
The anwser was 67
But I still don't have an idea on why the awnser is 67
onyx glen
But I'm just not sure why it has to be 9?
the sum of the digits is at most 9 times the count of digits, bc each digit is at most 9
onyx glen
And for number 24 I was able to make it to 2023²⁰²³ = 67 mod 100
wait, so... you managed to calculate that 2023^2023 = 67 mod 100, but you don't understand your own work for that?
pale steppe
wait, so... you managed to calculate that 2023^2023 = 67 mod 100, but you don't ...
Yea xd
My friend js told me to find 2023^2023 = x mod 100
And x is the anwser
I js went along with it but didn't understand how it worked
onyx glen
last two digits == remainder modulo 100
pale steppe
the sum of the digits is at most 9 times the count of digits, bc each digit is a...
Yea ik but im js wondering wouldn't the awnser be a little off if we only do times 9 each time?
onyx glen
btw the letter W in the word "answer" keeps drifting to the left when you type the word
pale steppe
last two digits == remainder modulo 100
Oh, literally just that. ._.
onyx glen
Yea ik but im js wondering wouldn't the awnser be a little off if we only do ti...
i think you might misunderstand here somewhat
pale steppe
~~btw the letter W in the word "answer" keeps drifting to the left when you type...
Huh
onyx glen
answer
it's spelled n-s-w in that order. the pronunciation does nothing to help you figure that out tho.
onyx glen
Yea ik but im js wondering wouldn't the awnser be a little off if we only do ti...
anyway here's the thing, for a formal solution you would need to phrase it in terms of bounds, like
S(2023!) <= 9 * (number of digits in 2023!)
and then S(S(2023!)) <= 9 * (number of digits in S(2023!))
and so on
pale steppe
answer
it's spelled n-s-w in that order. the pronunciation does nothing to help...
Xd yea ik I'm just so used to typing awnser it's been a habit since uh 6 yrs or smthing
onyx glen
habits can be changed, including those of spelling
pale steppe
anyway here's the thing, for a formal solution you would need to phrase it in te...
Oh alright
So js cus we js take the max js in case
pale steppe
habits can be changed, including those of spelling
Nah imma keep this habit :> I spell like 5 words also wrong
Idk what they are cus I forgot but yea
Anyways tym
Ty
.close
full forumBOT
full forumBOT
Available help channel!
real cypress
Without aproximating the sqrt, show that the whole part of N=26
N= sqrt5+sqrt6+sqrt7+...+sqrt13
real cypress
I did wrote that sqrt5+sqrt13 is the same as sqrt6+sqrt12 is the same and wrote it as pairs with "+3" because of sqrt 9
Now i don't really know what to do.
real cypress
sorry... i have no idea what to do tbh
i dont have an idea where to start
that was the only thing that I could think of , I don't know how to solve this without aproximating
onyx glen
you need to show somehow that this sum lies between 26 and 27 then
real cypress
the only thing that I could say is that 18 is than "N" but and 36 is bigger than S
onyx glen
what is S?
real cypress
I don't have the slightest idea how to norrow the "result"
full forumBOT
@real cypress Has your question been resolved?
pliant kernel
full forumBOT
pliant kernel
how do i solve part a
wanton pawn
pliant kernel
nothing
wanton pawn
Well you could try finding t1 and t2, write them in form of the general term of a GP and you should be able to see how to get the common ratio
full forumBOT
@pliant kernel Has your question been resolved?
steel solar
Add the two given equations together.
delicate bay
Hey guys I'm rather bad at math because I missed out on huge blocks of core math growing up moving around schools and such I'm going back for my ged and am looking to learn in general i do love math I just never had teachers that would take the time to get me caught up so I've got some things that are missing that a lot of people would find very basic and I was wondering if I could get some laughs in explaining this shit to me 😂🤣 okay so my first question is what are the rules on rearranging or solving a simple equation like 5 = x/12 why is it that you multiply 5 by 12 but if it was 5 = 12/x you would divide the division symbol doesn't change so why wouldn't it be multiplication either way... ik it's probably really simple but I'm confuzzled
subtle hatch
Whatever you do on the left, you do on right (law of equality)
delicate bay
So am i understanding the law of equality is what matters the most and to cancel something out you do the inverse operation
Maybe this will help I do have a pretty decent understanding of this I just have holes in my logic that are being a bugger I'm learning basic SohCahToa and these two questions are what are confusing me
So I understand law of equality needs to happen but why do I choose to multiply if the variable is the numerator and divide if it's the denominator my brains saying it's a division to get it away from x I would need to multiply and do the inverse... does that make sense?
full forumBOT
@delicate bay Has your question been resolved?
frigid phoenix
we have F defined everyhere and not at origin. and Curl of F is zero.
She says, we can have a curve that not contains the origin and we can use green theorem there, and a curve which DOES contains the origin, and we use the extended green's theorem making a hole in there, adding a boundary.
i get this.
but then the does this: draw the larger circle around origin, which for this specific F we know to have line integral = 0. So this means also the inner curve must have line integral= 0.
but i'm not totally convinced about the reasoning.
frigid phoenix
the reasoning, as i understand it:
if the outside curve integral is zero, and the area inside has curl zero, then also the line inside must have integral = 0.
but i'm not sure for this argument i need to create the "dnout" area..
wouldn't it be enough to say: this other curve that contains the origin has line integral zero, the area inside has curl zero, then any curve that contains the origin has line integral = zero.
without the need of connecting the 2 curves and only considering the area betweeen them
frigid phoenix
yes the exercise is about that
it seems i want to prove that any curve has integral= 0 here.
even if it contains an undefined region
so the theorem baiscally says ignore the undefined poitns
slender onyx
you CAN apply it to domains with excluded points but the theorem mainly applies to curves with multiple components as shown above
the point is
applying extended green to ur problem, integral curlF over R = integral F over C2 + integral F over C3
we know LHS=0 and integral over C3=0
thus integral over C2=0
frigid phoenix
ok another question then.
if curl F = 0 , the integral of a curve containtin the origin can be non zero?
slender onyx
yes
frigid phoenix
ah ok
slender onyx
or any undefined point
frigid phoenix
ye
slender onyx
but integrating curlF on a region excluding the undefined points gives 0, using normal greens
frigid phoenix
so is this a special case where i have a curve around the undefined point with integral= 0
slender onyx
yeah so the takeaway is
if ur region contains an undefined point, u want to go away from it
frigid phoenix
yea i get that
slender onyx
the usual strat is remove an epsilon radius circle around the point
then that circle becomes another part of the boundary via extended greens
frigid phoenix
ok, so i can calculate that integral which might be easier
slender onyx
then ur allowed to apply greens which says
slender onyx
integral curlF on punctured region = integral F on outside curve + integral F on epsilon circle
frigid phoenix
ok so to find the integral of inside, i just solve for it with this equation basically
slender onyx
now thing is we’re not really done
frigid phoenix
cause i'm considering another regio instead of the region inside the curve
slender onyx
this is an integration technique u usually only see in complex analysis
we put an epsilon circle around singularities/undefined points
do all computations and get a result in terms of epsilon
the argument works for all positive epsilon
so we may take the limit epsilon->0 in our result
frigid phoenix
so like the circle can be infinitesimally small close to origin in this case
since itìs only 1 point
slender onyx
yes by infinitesimally small we rigorously mean epsilon circle in the limit epsilon->0
anyway this integration technique is far beyond the scope of this problem. all we need to do is use extended green to prove conservative
but u can use the technique for classic problems like this
the one where going round the origin gives 2pi
the classic strat is directly compute line integral
but now with epsilons u can integral curlF then let eps->0
u should still get 2pi
frigid phoenix
ok i get the idea i think
slender onyx
hmm am i speaking outta my ass
integral curlF on punctured disk = integral F on unit circle + integral F on epsilon circle
u still need to compute the unit circle…
this is more what i had in mind
frigid phoenix
i'll review again the problem, i think i am missing the objective of my problem.
yeah i get the idea
i'm trying to make sense of the steps that connects one idea to the next
slender onyx
sry for distracting with this, its just very similar to an imtrgration technique in complex analysis
frigid phoenix
and why are those all necessary, and i cannot skip one
frigid phoenix
what if integral of c3 was something else
it means it's not conservative?
right?
slender onyx
yes
frigid phoenix
ok so. wait
slender onyx
and u dont need to use extended green
u just say “heres a closed curve with nonzero integral hence nonconservative”
frigid phoenix
why cant i say, if this curve integral is zero, then all other curves integral will be zero
slender onyx
i general its like saying
frigid phoenix
isnt having curl = 0 and having a curve integral =0 enough to say the field is conservative?
slender onyx
“i checked this dog and it has fleas so all dogs have fleas”
in general u must check ALL closed curves
frigid phoenix
i need to rethink about what the problem was asking
i get the idea anyway, thankyou very much
it's late and i have low energy now
slender onyx
i need to rethink about what the problem was asking
is F conservative?
frigid phoenix
for all n
slender onyx
and u check integral=0 on every closed curve where F is defined and continuous
frigid phoenix
but f is not continuous, so that would already tell me NO, not everywhere.
frigid phoenix
ah ok that is a detail i missed
slender onyx
thats the fundamental condition for line integrals...
u only need continuous on the curve
frigid phoenix
i'm tired i can't think straight
need to stop here
🙂
thanks a lot
i'll refresh this tomorrow
frigid phoenix
.close
full forumBOT
full forumBOT
Available help channel!
round turret
How is it that this integral yields sec^4(x)/4 + C but I get (tan^4(x)/4) + (tan^2(x)/2) + C
wraith ether
How is it that this integral yields sec^4(x)/4 + C but I get (tan^4(x)/4) + (tan...
reverse chain rule
so you know that the derivative of sec(x) = sec(x)tan(x)
so you have the integral of sec^3(x) d(sec(x))
desert bane
you can have multiple solutions for the same integral they just look different but are the same really
gentle salmon
How is it that this integral yields sec^4(x)/4 + C but I get (tan^4(x)/4) + (tan...
+C makes them equal
rocky vale
How is it that this integral yields sec^4(x)/4 + C but I get (tan^4(x)/4) + (tan...
Pythagorean identity, sec^2(x) = tan^2(x) + 1
The two solutions only differ by a constant, they are both valid antiderivatives
full forumBOT
full forumBOT
Available help channel!
unborn moth
full forumBOT
unborn moth
I got -1 but then I realized
It wasn’t one of the options
Bro. I keep getting -1 😭
full forumBOT
@unborn moth Has your question been resolved?
uncut badge
what is your question
wet hinge
I have this question in my books that im a bit confused about. It only calculates the population + the incoming population. Why doesnt it account for the people who leave to the other city / suburbs?
median gust
In a volleyball match, a player tries to make a perfect serve that hits vertex A of the rectangular court shown in the figure below. To do this, the player positions themselves at the edge of the court, at a distance x from vertex C, makes an extraordinary jump, and serves the ball, which barely clears the net, with a height of 2.5 meters.
Knowing that the ball traveled so aggressively fast that its trajectory followed a line segment AB measuring 20 meters, what distance x did the player position themselves at?
median gust
uncut badge
what have you tried?
alpine ibex
In a volleyball match, a player tries to make a perfect serve that hits vertex A...
,tex \sqrt {51}
glossy valveBOT
Sigma Boi
\sqrt {51}
```Compilation error:```! Missing $ inserted.
<inserted text>
$
l.49 \sqrt {
51}
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.
LaTeX Font Info: Trying to load font information for OT1+lmr on input line 4
9.
(/usr/local/texlive/2023/texmf-dist/tex/latex/lm/ot1lmr.fd```
uncut badge
its just pythagorean
median gust
its just pythagorean
How could I use pythagorean there? simply 18² + x² = 20 or something like that?
I know that BD is 5
uncut badge
How could I use pythagorean there? simply 18² + x² = 20 or something like that?
is it asking the height as well ?
median gust
In a volleyball match, a player tries to make a perfect serve that hits vertex A...
No, the only thing that the question asks is here
But I thought that BD = 5 would help at something
uncut badge
oh wait hang on
uncut badge
But I thought that BD = 5 would help at something
alr nah i think i got it
oh bruh it says AB is 20 🐱
i was tripping
but yeah you use 20
because the hypotenuse is the same
median gust
Could you gimme a hint or something like that, so I can try to get to the answer by myself
uncut badge
like if its copied on floor
median gust
That would help a lot if possible
uncut badge
Could you gimme a hint or something like that, so I can try to get to the answer...
you already got it
i said pythagorean
and you did the correct formula
well almost
18^2 + x^2 = 20^2
do you understand why you can use 20 as the hypotenuse though
median gust
Not really, I am struggling with the fact that it is appearently third dimensional, so I thought I couldn't use pythagorean because the player isn't going to serves the ball in the ground you know
median gust
The problem is that I am struggling with the fact that in my mind it does not seems to be a diagonal because it is kind of third dimensional you know, I get that if you see from the top it seems to be a diagonal, but it is weird in my mind
Anyways, I am going to try that one, it simply seems to be weird in my roockie mind
uncut badge
makes sense, thats why it a tricky question
a good tip is to always draw it if you arent sure
especially if the question is in seemingly in multiple dimensions
median gust
Yeah, I think it cannot be seem from top because the statement said about the height of the net, if we see from the top, this height is useless you know
uncut badge
wait
💀
oh wait wait
hang on
nvm you cant just use 20
okay i see my error now, so you do use pythagorean
i mistook that AB=AD
median gust
np
uncut badge
you can easily solve for AD using pythagorean though
20 is the hyp and you know the BD is 5
this will give you AD which you can then use with 18^2
sorry
median gust
Oh, that makes sense, lemme try that one
median gust
you can easily solve for AD using pythagorean though
Oh great, that one was relatively easy actually
The answer is sqrt(51)
Thank you very much, have a great day
.close
full forumBOT
full forumBOT
Available help channel!
dapper yoke
Can someone help me derivate this. I’m stuck and I don’t know how to process
woeful hatch
,rotate
glossy valveBOT
flint hull
what are you deriving with respect to
lunar veldt
comment tu dérives x^n
dapper yoke
Even the a ?
flint hull
since you arent taking the derivative with respect to a i believe it should be implied as a constant
dapper yoke
Ohhhh ok
flint hull
and after that you should be able to use chain rule
dapper yoke
Thanks 😭
flint hull
yeah np
lunar veldt
$x^n =n x’ x^{n-1}$ , here x=(b-at)
glossy valveBOT
tm
full forumBOT
@dapper yoke Has your question been resolved?
full forumBOT
full forumBOT
Available help channel!
winter escarp
using chain rule
full forumBOT
using chain rule
winter escarp
seem to be okay with other ones
but for some reason getting drastic different answers then what ive been given
I let y = (u)^(5/2)
u = 3x^4 - 2x
then dy/du = 5/2(u)^(3/2)
du/dx = 12x^3 - 2
and then dy/dx = (5/2)(12x^3-2)(3x^4-2x)^3/2
.close
toxic yacht
full forumBOT
stiff summit
time to use lagrange interpolation to “show” that the glacier will retreat 10000 kilometers by 2020
toxic yacht
.close
full forumBOT
full forumBOT
Available help channel!
winter panther
Find a prime number p such that p + 2 and p + 4 are prime numbers too.
winter panther
help me
gritty flax
Only one ?
desert bane
3
gritty flax
In that case yes
desert bane
did you even try lmao
winter panther
idk why its 3 (my answer is 1)
winter panther
oh nah i forgor 1 has only 1 factor
craggy tapir
wait
craggy tapir
the number has also be prime
gilded flower
pancakes
full forumBOT
If you are done with this channel, please mark your problem as solved by typing .close
winter panther
.close
full forumBOT
shadow tide
this is a partially ordered set btw
haughty nebula
you're correct
full forumBOT
full forumBOT
Available help channel!
minor crater
full forumBOT
minor crater
before i had questions with modeling like linear data or exponential data
but i have no clue how to linearize this
onyx glen
howd you do those
from my pov this is a matter of finding the least-sq solution to the linear system $$\textbf{y} = \bmqty{1&-1&1 \ 0&0&1 \ 1&1&1 \ 4&2&1} \bmqty{a\b\c}$$
glossy valveBOT
Ann
minor crater
huh
oh
i mean
hm
so the first column is just the square of the second one right?
ohh
okay
okayyy
this makes total sense
the t^2 confused me but here it's just a constant
minor crater
from my pov this is a matter of finding the least-sq solution to the linear syst...
thank you!!!
.close
full forumBOT
full forumBOT
Available help channel!
spring bay
When solving for sin(2x) = 2sin(x), the answer is x = πk, k ∈ z.
But when you solve for
2 - 3sin(x) = cos(2x), the answers would be x = π/6 + 2πk, k ∈ z and x = 5π/6 + 2πk, k ∈ z.
Why is the first question +πk, whereas for question two, it’s +2πk? Can someone please explain
grizzled otter
When solving for sin(2x) = 2sin(x), the answer is x = πk, k ∈ z.
But when you s...
did u solve both the equations..
spring bay
did u solve both the equations..
yea
grizzled otter
in first the solutions are sinx = 0 or cos x = 1 .. => x = k pie
in second solution is cos x = 1/2 or cos x = 1 therer +2pie as cos repeats after 2 pie interval..
spring bay
wait what I’m confused 😭
grizzled otter
wait what I’m confused 😭
um
can you show your working
maybe i can lead you from there
spring bay
wait what does the 2πk mean in general
spring bay
can you show your working
alright
grizzled otter
wait what does the 2πk mean in general
if k belongs to z then its -2pie.. 0 .. 2 pie.. 4 pie etc
spring bay
spring bay
why are you stuck?
this is the work i did in class with my teacher. but I still dont understand where the +2pik and +pik came from😭
grizzled otter
this is the work i did in class with my teacher. but I still dont understand whe...
as you can see the answers for first one are all lie.. pie , 2 pie , 3 pie so to denote that we use k pie
if we put k = any integer we will get all the value
for eg: k = 1 , we get 1 pie
k = 2 , we get 2 pie
and so on
is the first part clear now
grizzled otter
how would u know which one to use when solving for problems like these
what do u mean .. like its a denotion u can check if it satisfies
it gives all the answers if we keep putting the integers
the solutions match .. like we get 1 pie by k = 1 .. we get 3 pie by k = 3
spring bay
cuz I thought for the first question, it would be x = 0 + 2πk
grizzled otter
cuz I thought for the first question, it would be x = 0 + 2πk
if you would do that how would you achieve the answer 1 pie
1 pie appeared in the solution right?
so for what k in 2 pie k will you get 1 pie? you will have to put k = 1/2
which is not an integer.. and we assumed k to be Z which is an integer
spring bay
which is not an integer.. and we assumed k to be Z which is an integer
ohh that makes sense
spring bay
so for the second question, for sin(x)=1/2, would the solutions be like pi/6, 5pi/6, 13pi/6, 17pi/6 and so on?
and k would represent the number of cycles which r multiples of 2pi u add to the base solutions pi/6 and 5pi/6?
grizzled otter
and k would represent the number of cycles which r multiples of 2pi u add to the...
yeah as sin graph and cos graph repeat after 2 pie right
so if it gives us a solution for x .. it will also give a solution for x + 2 pie k
repeating logic.. you can draw a graph a check
spring bay
so if it gives us a solution for x .. it will also give a solution for x + 2 pi...
oh wait omg that makes sm sense now
grizzled otter
yay
full forumBOT
full forumBOT
Available help channel!
summer cypress
Howdy, I have a question I'm getting a bit stuck on in my calc 1 course. I'm doing implicit differentiation of trig functions, and have been given $x+y=\sin y$ and told to find the second derivative of it, but I've been repeatedly getting what I believe to be incorrect answers.
glossy valveBOT
Thoth
umbral dome
can you show your work?
summer cypress
sure! one moment
$\frac{d}{dx} (x+y=\sin y)$ \
First derivative: $1+y'=y'\cos y$ \
Second derivative: $0+y''=y''\cos y + y'(-y'\sin y)$ \
\
First derivative solved for $y'$: $y'=\frac{1}{\cos y - 1}$ \
Second derivative solved for $y''$ and substituted for $\sin y$ and $y'$: $y''=\dfrac{-\left(\dfrac{1}{\cos y-1}\right)^2(x+y)}{1-\cos y}$
umbral dome
it's not 0 because y is still a function of x, so the chain rule applies
summer cypress
I figured, but I'm then at a loss of what to do. $\frac{1}{\cos y-1}$ also doesn't seem to represent the slope of the original graph
glossy valveBOT
Thoth
summer cypress
I'm confused as to where you got this formula 😅
I'm only familiar with $y-y_1=m(x-x_1)$
glossy valveBOT
Thoth
umbral dome
yes and then i rearranged it for x
and also used x = sin(y) - y from the original eqn
summer cypress
I suppose firstly I'll ask, what made you arrange it for x?
umbral dome
it wasn't strictly necessary, i just thought it made the equation more readable
summer cypress
okay so, where did I go wrong?
umbral dome
the demonstration shows that the slope formula is correct, as it produces a correct-looking tangent line
summer cypress
the demonstration shows that the slope formula is correct, as it produces a corr...
so I'm still rather confused. Let me type something out to express my thoughts.
Firstly, given $y'=\frac{1}{\cos y-1}$, how do you go about graphing, or even checking values, as there's no direct $x$ paramater? Secondly, given my second derivative of $\frac{-\left(\frac{1}{\cos y-1}\right)^{2}\left(x+y\right)}{1-\cos y}$, how do I verify it gives an appropriate value?
glossy valveBOT
Thoth
summer cypress
Thirdly, how did you come up with your clever little slider that follows the graph in desmos? Fourthly could you explain how you came about the $x=\frac{y-a}{g(a)}+(\sin(a)-a)$ equation? 😅
glossy valveBOT
Thoth
umbral dome
well you can graph y' vs y on a graph, although it will not have the relationship with the original graph you're used to
summer cypress
well you can graph y' vs y on a graph, although it will not have the relationshi...
I'm not entirely sure what you mean
umbral dome
this tangent line graph is one of the examples preloaded in desmos:
https://www.desmos.com/calculator/fs3lx8gptb
umbral dome
I'm not entirely sure what you mean
as in, you can graph y' on the vertical axis and y on the horizontal axis, which at least gives you a way of visualizing it
summer cypress
this tangent line graph is one of the examples preloaded in desmos:
https://www....
ah, I see, so you just reversed it to be in terms of y
That leaves only part of my first, second, and fourth questions
umbral dome
to answer the fourth question, since g(y) is the derivative and setting y1 = a, we have
y - a = g(a) ( x - x1)
and x1 = sin(y1) - y1 = sin(a) - a, so we have:
y = a + g(a) ( x - (sin(a) - a))
and i rearranged for x simply because it involved a lot of parentheses and was pretty long when written out that way
and to answer the second question, you can do a similar thing to the tangent line using the second order taylor polynomial, although i think that ones a bit harder to judge
it might help to simplify it a bit more than you've done so far
summer cypress
it might help to simplify it a bit more than you've done so far
got it, heh
full forumBOT
@summer cypress Has your question been resolved?
summer cypress
So perhaps you can walk me throug hsome of this so I can understand it. I take the first implicit derivative, $1+y'=y'\cos y$ correct?
glossy valveBOT
Thoth
summer cypress
And even so, you say you don't need to put it in terms of x, but I can't seem to figure out a different way. Perhaps I'm just tired, but I'm lost
umbral dome
your procedure is correct, it just feels wrong to you
summer cypress
your procedure is correct, it just feels wrong to you
How again did you come by (sin(a)-a, a)?
summer cypress
Ah
summer cypress
https://www.desmos.com/calculator/dopkhr6jm0
And then from there, was it a similar process for solving for the line equation you used here?
umbral dome
yes. if you want to you can leave it in y = form instead, desmos doesn't care
summer cypress
what would x_1 and y_1 be in that case?
this is where I'm at, how do I get from my last cell to the tangent line equation? Perhaps that'll help me understand
umbral dome
the tangent line equation has nothing to do with the second derivative
summer cypress
OH of course
sorry
I suppose how do I get from the first derivative to the tangent line equation 😅
umbral dome
all it was was to demonstrate that the first derivative was correct, it's not necessary for the problem
summer cypress
I know, but I think it might assist me in understanding the process
umbral dome
if you fix a point $(x_1,y_1)$ the tangent line is given by
[ y - y_1 = \odv yx_{\substack{x = x_1 \ y = y_1}} (x - x_1) ]
glossy valveBOT
cloud
umbral dome
fix one and solve for the other using the equation of the curve
summer cypress
ah, that makes sense
my issue I think is that the first derivative doesnt seem to have an $x$ variable
glossy valveBOT
Thoth
summer cypress
so $\odv yx{\substack{x=x_1 \ y=y_1}$ doesnt click in my brain
glossy valveBOT
Thoth
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
umbral dome
so you plug in y = y1 and don't worry about x
summer cypress
hm
umbral dome
if you have f(x) = 5 then f(300) = 5, it's still "plugged in" even when there was nothing to plug into
umbral dome
mostly correct, but x1 is not given by f(2)
umbral dome
solving for x in the curve equation
umbral dome
yes
summer cypress
I see now
awesome, I think I get it, sort of
just need to practice
I really appreciate your help
does this server do any sort of reputation?
full forumBOT
full forumBOT
Available help channel!
boreal folio
Hi; I do not want the answer, just clarifying on how to approach this problem:
boreal folio
So far, i discribed Col(s) to be the group of $\phi, \psi \in S_6 $ with the mappings $\phi: {1,2,3} \rightarrow {1,2,3}$ and similarly $\psi$ maps {4,5,6} to itsself
glossy valveBOT
oklmaosad
boreal folio
Then i set X = {1,2,3} and Y = {4,5,6}
My proof depends on showing that they are internal direct products
as they are disjoint, its easy to show they commute and only have identity in their intersection
is there a way to go about showing the first requirement or am i completely on the wrong foot in this proof?
full forumBOT
@boreal folio Has your question been resolved?
celest fulcrum
<@&286206848099549185>
full forumBOT
full forumBOT
Available help channel!
tacit prairie
im doing homework and im so confused about how to do these equations some help would be very appreciated
gritty flax
Look the number in front of x
You have a starting of x² + 2bx
For the first one b = 3
So you need to complete it as a square
You want to write (x+...)² + ...
Since you have found that b = 3
It will be (x+3)² + ...
But to write this
You must compensate and substract by b²
So here b² = 9
So it will be (x+3)² - 9
gritty flax
So it will be (x+3)² - 9
And this is equal to x² + 6x
And so just minus 7 to have your expression
tacit prairie
thank you
full forumBOT
Available help channel!
woven prism
what is x tetration to a fraction? What is x tetration to a negative fraction? What is the formula?
full forumBOT
what is x tetration to a fraction? What is x tetration to a negative fraction? W...
@woven prism Has your question been resolved?
full forumBOT
amber robin
I don't think a formula for that exists
full forumBOT
Available help channel!
hidden bane
We do the washer method right? I don't know how to get the outer and inner radius
grave elm
so you are rotating this green region around the red line
the outter radius would be the blue length (so it depends on x). The inner radius is the constant yellow length
is that understandable? Can you imagine it?
hidden bane
is that understandable? Can you imagine it?
Yesss i can imagine it. I'm going to write the formula out. Could you let me know if it's right?
grave elm
Sure
hidden bane
oh wait the black line isn't the y-axis in ur drawing yea?
hidden bane
Would the formula for Outer radius - Inner radius be
pi * [ (5+(y-1)^2)^2 - (2)^2] * dy ??
hidden bane
the outer radius looks wrong
oh wait not 5 but 2? so 2+(y-1)^2)^2
if it's still completely off can you let me know how to do it
grave elm
its not a square, its a square root
Note that the orange and blue make 5 together
and orange is given by the formula
so blue = 5 - orange = ?
hidden bane
Note that the orange and blue make 5 together
Ohh so you'd just subtract instead of add?
(5-(y-1)^2)^2
grave elm
(5-(y-1)^2)^2
still not
the formula is y = 1 + sqrt(x)
you should probably be using x instead of y
hidden bane
OH yeaa i've been doing dy instead of dx
so it'd just be
pi * [(5-(1 + sqrt(x))^2 - (2)^2] * dx ??
grave elm
seems right
winter locust
full forumBOT
uncut badge
<@&286206848099549185>
what method did you use
cylindrical shell ?
redundant question i already know
full forumBOT
@winter locust Has your question been resolved?
full forumBOT
full forumBOT
Available help channel!
paper bane
full forumBOT
umbral dome
the resistors inside the batteries represent internal resistance
paper bane
the resistors inside the batteries represent internal resistance
meaning the ohm is multiplied by the current correct?
V=IR
umbral dome
yes
paper bane
so when going from the outside loop counterclockwise starting at a is what the blue is
its at the 6 where I think im lost
umbral dome
why is the emf divided by 2?
paper bane
Ive tried this question multiple times
Ive been working on it since yesterday...
So Ive tried so many ways
apparently 9 was as close as I got since it says this
umbral dome
ok so we are looking to use kirchoff's loop rule. you can choose to either sum up the voltage drops or the voltage gains.
- the emf voltage gain or drop is just equal to the emf. the sign depends on which direction the battery faces
- if you are traveling in the direction of current, the resistor voltage drop is V = I*R (it will instead be a voltage gain if you travel in the opposite direction)
paper bane
well so I did the green
I also inputed it without the division sign
or sorry 18*
and 22
umbral dome
can you show your work in that case?
paper bane
so for red its the inner loop, so -4+4+18=18
umbral dome
which inner loop?
paper bane
Im finding emf 2 so the one connected to emf_1, the red arrows in the white figure
blue would be: 22
im tried both those for emf_2
I got emf_1 its 18
umbral dome
you don't appear to be factoring in the 1 ohm internal resistances?
paper bane
thats the orange in the top right
paper bane
you don't appear to be factoring in the 1 ohm internal resistances?
so add the * 1 for the voltage values?
paper bane
ok wait, I think I gotcha
not cutting you off tbc*
just think it hit me. Ill write it and double check
my + - signs are right though correct?
do I need to worry about that?
umbral dome
not entirely
glossy valveBOT
Ousel
umbral dome
why is E2 on the left?
glossy valveBOT
Ousel
umbral dome
maybe let's walk though it one step at a time
starting at a, and going clockwise, what is the first circuit element you meet?
umbral dome
no, you reach something before that
umbral dome
no, you were on track the first time
umbral dome
<#1349581689696944252>
paper bane
thats counterclockwise
umbral dome
true, my bad
paper bane
so 2A * 1ohm = emf_2
umbral dome
wdym = e_2
umbral dome
there is a resistor and the emf
paper bane
i dont mean THE e lol
umbral dome
the resistor and the emf don't have anything to do with each other other than being inside the same battery
paper bane
so is it 2A * I = V?
umbral dome
2 A * 1 ohm = 2 V drop, yes
paper bane
i understood it as just -emf_2 in the formula
oh I put it in the #1021175428326633542 #1349581689696944252 but this is literally everything I know on this
basically just the example on page 2
umbral dome
<#1349581689696944252>
there are two different things in this battery, a resistor which you just treat as a normal resistor, and a voltage source which has the emf
that's how we model it for the purposes of circuit analysis
paper bane
so is it A = emf_2 / 1ohm?
umbral dome
the emf and the resistor have nothing to do with each other
paper bane
ok
so 2A goes through the voltage source
got it
i literally on this on a formula basis
so thats how I explain things, sorry, ill try to stop
umbral dome
ok so first we go through the resistor, which gives us a 2V drop. then we go through the voltage source.
does the voltage source have a voltage gain or drop?
umbral dome
yes
since we are adding drops, we will add it then
so so far we have
2(1) + e2 + ... = 0
what is the next circuit element?
paper bane
a - to + resistor
umbral dome
wdym - to +
paper bane
umbral dome
remember that resistors have a voltage drop in the direction of current. and we are still moving in the direction of the 2A current
paper bane
umbral dome
see how in the direction of the loop current (in that case clockwise) they both have a voltage drop
paper bane
I think so
Its divided by a positive voltage, then a negative multiplication of the resistor (which would cause a negative value in voltage?)
umbral dome
V = IR
the current is the same because there aren't any branches
there's nothing more to it
paper bane
well thats why I mentioned the voltage change. Thats more what I was focusing on
cuz its all about a change in voltage right?
umbral dome
yes?
so the resistor always has the "+" terminal where the current enters and the "-" terminal where the current exits
so what is the voltage drop across the 2 ohm resistor?
umbral dome
ok great so from a to b we have gotten
2(1) + e2 + 2(2) + ... = 0
going along the outer loop, what is the next circuit element we encounter?
paper bane
6 ohm so 1(6)
umbral dome
yes
paper bane
so just + 1(6) - 20?
umbral dome
-20 V would be the voltage drop due to the emf, yes
what do we hit after the voltage source?
umbral dome
you've missed something
umbral dome
why -?
paper bane
oh
cuz I guess I just thought, thats what I mean the voltage drops werent really explained
my teacher blew through this
umbral dome
as we move along the circuit, the voltage drop is how much the voltage decreases on the far side compared to the near side
paper bane
so the "resistor" also stays postive inside the voltage drop
umbral dome
so the voltage is 4V lower on the right side of the 2 ohm resistor than on the left
paper bane
so -20+1(1)? (nvm)
umbral dome
the voltage drop of a resistor is always positive if you travel in the same direction as the current
if you were to travel in the opposite direction as the current then it would be the opposite
paper bane
so so far we have
2(1) + e2 + ... = 0
wait so yeah would it be +1(1)?
umbral dome
yes
paper bane
umbral dome
yes
paper bane
OK so it was the 1ohm that was messing me up.
So the voltage drop...drops it, then the resistor brings it back up (depending on direction of the + on the emf)?
umbral dome
resistors cause voltage drops
umbral dome
we are counting voltage gains as negative here because we are adding up the drops
umbral dome
the emfs are gains or drops depending on where they're facing
paper bane
so if it was flipped it would also be drop.
umbral dome
if you go from + to -, it's a drop and if you go from - to + it's a gain
young lark
Is that real?
full forumBOT
Is that real?
unique wagon
tender nacelle
yeah the two integrals are independnt of one another
fast peak
if you want to do it a bit slower, note that $\cos^2x$ is independent of $y$, so you can pull it out of the integral with respect to $y$, so you get $\int_{x=0}^{2\pi} \cos^2 x\int_{y=0}^a y dy dx$
glossy valveBOT
Denascite
fast peak
but now, $\int_{y=0}^a y dy$ is just a number, so you can pull it out of the integral with respect to $x$
glossy valveBOT
Denascite
fast peak
leaving you with $\int_{y=0}^a y dy \cdot \int_{x=0}^{2\pi} \cos^2 x dx$
glossy valveBOT
Denascite
full forumBOT
paper bane
.close
full forumBOT
Available help channel!
normal zinc
how do i start, do i just try and estimate using the diagram?
normal zinc
and then eliminate the options which just dont seem right?
<@&268886789983436800>
.close
full forumBOT
full forumBOT
Available help channel!
sleek quest
How do i solve this? Idk where to start
Let 𝑛 𝜖 ℕ, with 𝑛 > 2. Prove that the number 𝑛 − 1 is a Fermat witness for 𝑛 if and only if 𝑛
is even.
what is the def of fermat witness?
sleek quest
what is the def of fermat witness?
A Fermat witness is a number 'a' (where 1 < a < n) that, when used in Fermat's little theorem, reveals that a number 'n' is composite (not prime) because 'a^(n-1)' is not congruent to 1 modulo n
sleek quest
so then you need to compute a^(n-1) mod n here for a=n-1
wdym by compute it
fast peak
how much do you know about modulo
sleek quest
a good amount
fast peak
then you should be able to find out what (n-1)^(n-1) mod n is
sleek quest
its just -1 or 1, depending on whether n is odd or even
full forumBOT
full forumBOT
Available help channel!
inland sand
good evening guys im having trouble putting my answer into webworks
leaden ermine
good evening guys im having trouble putting my answer into webworks
today no rainbow keyboard
inland sand
no hihi this is from my tutoring session