we reduce the system
#help-0
vale wigeon
no bc the method requires the determinant of A to not be zero...
because det(A) goes in the denominator of everything
sharp iris
what about this example
wait
Solve the following real systems using Cramer's method.
(S2):
2x+3y=3
x- 2y=5
3x+2y=7
what should i do here
A is not square
can i reduce it
vale wigeon
pick 2 equations, solve those with Cramer, check solution against the third
vale wigeon
but it is also under-determined
sharp iris
no i forgot the -
vale wigeon
the system is under-determined
it is not possible to solve this with cramer at all, not even shoehorned like last time
vale wigeon
are you under a legal requirement to use cramer and only cramer
sharp iris
yes
vale wigeon
then you are cooked.
sharp iris
what should i do
vale wigeon
talk to whoever is imposing this requirement
ask them if you are expected to comply with it and if so how
lone heartBOT
@sharp iris Has your question been resolved?
next stratus
so for this question i just assumed a=d, and b=-c and i got (c) b,d are non parallel, but I'm pretty sure that isn't the right way to solve
next stratus
can anyone tell me how to check each part
soft trench
can anyone tell me how to check each part
hi
so
cross product of a- x b- gives ab sin alpha
next stratus
oh so alpha must be 90?
soft trench
yes
the angle b/w the cross product is 90
degrees
similarly the cross product b/w c and d gives sin beta
you can think the dot product b/w them as (a x b) (c x d) cos gamma
next stratus
ah so gamma is 0
soft trench
where
γ
is the angle between the vectors
a x b and c x d
soft trench
so for this question i just assumed a=d, and b=-c and i got (c) b,d are non para...
if the dot product b/w the cross products is 1
then Given that this dot product equals 1, we have:
sin(α)sin(β)cos(γ)=1
sin alpha is 90
beta is 90
cos gamma is 0
yes
hence they are parallel
got it?
next stratus
hence they are parallel
um what how does that imply they are parallel? Also which vectors are you talking about?
lone heartBOT
@next stratus Has your question been resolved?
lone heartBOT
@next stratus Has your question been resolved?
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vestal talon
I need help with some of my code - the issue is math based though something with my algorithm is messed up Im trying to calculate the change in volume of a body of water on a per year basis
vestal talon
the main issue is that after like 10 years the volume hits a minimum or maximum and changing the variables doesnt fix the issue
remote heron
what do you mean code
vestal talon
These are the relevant variables
vestal talon
what do you mean code
Visual Basic Subroutines
I think maybe the issue is with my inflow calculation
remote heron
code 
vestal talon
Sub CalculateInflow()
Dim InflowEstimate As Double
Dim rainfallFeet As Double
Select Case True
Case IsEmpty(Range("I9").Value)
MsgBox "Rainfall is Empty Please Input Data and Run Again"
Exit Sub
Case IsEmpty(Range("I11").Value)
MsgBox "Runoff Coefficient is Empty Please Input Data and Run Again."
Exit Sub
Case IsEmpty(Range("I14").Value)
MsgBox "Watershed Area is Empty Please Input Data and Run Again."
Exit Sub
End Select
rainfallFeet = Range("I9").Value / 12
InflowEstimate = rainfallFeet * Range("I14").Value * Range("I11").Value
Worksheets("Data").Range("O9").Value = InflowEstimate
End Sub``` InflowEstimate = rainfallFeet * Range("I14").Value * Range("I11").Value
Worksheets("Data").Range("O9").Value = InflowEstimate```wtf kind of cursed language
vestal talon
Visual Basic bruh its ancient
vestal talon
```rainfallFeet = Range("I9").Value / 12
InflowEstimate = rainfallFeet * Ran...
if the issue is with inflow it should either be in here or in my volume calculation later
so the calculation seen here is
Rainfall Conversion to Feet
rainfallFeet = Rainfall(inches) / 12
InflowEstimate = rainFallFeet * Watershed Area (Acres) * runoff coefficient
remote heron
please tell me this comes from a written problem we can refer to
vestal talon
please tell me this comes from a written problem we can refer to
You wish, im rawdogging this from scratch
haha
remote heron
then why did you choose visual basic
vestal talon
Well for my excel / Visual Basic Class of course!
this is part of my final project
this is pretty much the last part of my project is fixing whatever issue im having here
I dont have the mind for math
remote heron
I'm not suer its possible to help you given what youve posted-
at the very least youre missing lables on cells
vestal talon
Call CalculateRecharge
recharge = ws.Range("O10").Value
outflowLoss = currentVolume - (ws.Range("I13").Value * currentVolume)
currentVolume = currentVolume + recharge - outflowLoss
xVals(yearCounter) = startYear + yearCounter
yVals(yearCounter) = currentVolume
If numYears <= 10 Then
myValue = MsgBox("Would you like to update the input variables for Year " & (startYear + yearCounter) & "?", vbYesNo)
If myValue = vbYes Then
startPage.Show
End If
End If
Next yearCounter
```
Or the issue is in herei mean you have inputs label in the code
assuming those are from something in the image
not being able to understand very much of whats going on
have you tried checking the dimensions of all of your variables?
vestal talon
i mean you have inputs label in the code
😣 Which are you referring to?
remote heron
"I13" presumably
vestal talon
The named inputs are calculated in the code I posted
vestal talon
"I13" presumably
Those are values pulled from the image
remote heron
but the image isnt labelled
vestal talon
I11 is Column I Row 11
remote heron
but
vestal talon
as you can see in my chart down there I max out
remote heron
my advice is still to check the units
do you know how to do that
or have you done it
vestal talon
Explain slightly further
I can see the values of everything every time theyre calculated if I so chose
remote heron
```For yearCounter = 0 To numYears - 1
Call CalculateRecharge
r...
like here you have a variable current volume
so everything in that sum should be a volume
recharge must be a volume. outflowloss must be a volume.
vestal talon
Yes they're all standardized to acrefeet
and the current volume is also acrefeet
The main confusion im having is that the value lands on a specific value and does not change
remote heron
maybe its supposed to
vestal talon
It may well do but im not versed enough to check that properly
remote heron
its common
vestal talon
hmmm
remote heron
i mean, its common for some equation or system or model to behave interestingly in some small region
and not very interestingly globally
so it just depends on the model
itd help if you had some more uhh
idk
its hard to help with the visual basic haha
vestal talon
well just a sec ill try something
remote heron
it looks like an ODE problem im just having trouble reading it
you know if you had something like uhh
V' = - A * e where V is volume and A is area and e is some evaporation rate volume / area
youd expect something like that to eventually come into equillibrium
vestal talon
So the issue may be consolidated to my variable values
Which I can only estimate so hard and I cant easily have changing with every year while remaining accurate without a level of research I simply dont have time for
ive been altering the inputs to try and get the graph to slowly run out to zero
but ive been unsuccessful so far
vestal talon
Its not a very slow slope either its a drastic change
vestal talon
yes its certainely exponential
I can tell that from setting my runoff coefficient very low
remote heron
change in volume = (some function of volume and time)
this will probably result in some kind of exponential decay
unless its non linear or something strange
vestal talon
I think you found the entire crux of my issue
I think that the reservoir im simulating must not be at any sort of drought risk
remote heron
well maybe it is for some parameter values
if we can extract the model we can do dynamic analysis of it
vestal talon
and thus if I simulate this for an extended period using the same variables for water input and output then it always reaches an equilibrium sooner than anticipated
I also have the capacity to simulate an aquifer
remote heron
im guessing its basically a tank problem
vestal talon
oh ive got it all messed up now I think
remote heron
this is just exponential decay in the other direction
vestal talon
thought the reservoir cannot handle a bulk calculation without varying variables between years
youre completely right though this is designed like a tank problem
I think a cube shaped tank
I think its in an okay shape now were gonna run with it thank you niku I have too much else to mess with right now to dwell
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strange rampart
hello
strange rampart
is someone good at dilation (transformation) in part 1 given says that h(D) = E but when finding h(DG) the solution is line (BC) but i still dont understand why
strange rampart
so if we were talking segments it would be [EF] or something ?
so even if h(D)= E that doesnt necessarily mean that H(DG) = (E..)
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devout helm
Hi I feel that there’s something wrong with this
lone heartBOT
Hi I feel that there’s something wrong with this
velvet briar
Hi I feel that there’s something wrong with this
first step is wrong
devout helm
first step is wrong
so I just add the numbers in the bracket
devout helm
whats =/=
velvet briar
not equal
devout helm
(a+1)^2 =/= a^2+1^2
I dont really understand what your tryna do here
velvet briar
I dont really understand what your tryna do here
have you done quadratics
velvet briar
I dont really understand what your tryna do here
im showing you (through setting it to a so its more akin to the standard A+B), that what you did was incorrect
vale wigeon
$$(A + B)^2 \text{ is } \textbf{NOT } A^2 + B^2$$
ocean sealBOT
Alberto Z.
vale wigeon
$(A+B)^2$ is \textbf{NOT} $A^2 + B^2$
ocean sealBOT
Ann
winter light
Yeah I know it
But I didn't want to rewrite it lol
I also hate it to write \text a lot of useless times
devout helm
(a+1)^2 =/= a^2+1^2
Based off your logic is it like this
winter light
Have you ever seen $(A+B)^2 = A^2 + 2AB + B^2$?
ocean sealBOT
Alberto Z.
devout helm
Have you ever seen $(A+B)^2 = A^2 + 2AB + B^2$?
yeah
velvet briar
Based off your logic is it like this
looks correct
devout helm
Then you can (and should) use it
ok wait let me do that way
devout helm
Then you can (and should) use it
dude I'm getting back the same answer as my original one
winter light
Mmh weird
devout helm
.close
alpine sable
lone heartBOT
zealous wolf
Do you know conditions for common roots?
alpine sable
nope
vale wigeon
you are suggesting that OP memorize that?
zealous wolf
You want proof? I can attach that asw
vale wigeon
why not simply subtract the two equations and note that their common root will be a root of the new one?
much easier this way and like 200 times more straightforward
no need for this absurdly complicated formula
no i don't want proof of that formula
zealous wolf
I am not familiar with your method i apologise
vale wigeon
it is barely even a method, it is just almost a natural consequence of the concept of a "common root"
zealous wolf
I get it im just too used to using cramers rule for these stuff
alpine sable
i got ax-bx + bc-ca = 0 after subtracting
vale wigeon
ok so that's (a-b)x + c(b-a) = 0
you know that a ≠ b otherwise the two equations would have been literally the same
so you know their common root can only be c
devout helm
are these correct?
lone heartBOT
are these correct?
void nymph
first isnt
shell agate
You need to substitute another variable right
void nymph
second isnt even factorised
shell agate
I don't see your substitution
void nymph
so no
shell agate
@devout helm substitute with another variable
Hint: Try to make it quadratic by substitution
devout helm
<@1017151697967124480> substitute with another variable
how I even do that
devout helm
How can you make a) quadratic
yeah
shell agate
How?
devout helm
so that means the first qn is x^4 + x^2 =6?
void nymph
<@1017151697967124480> substitute with another variable
he did that
shell agate
so that means the first qn is x^4 + x^2 =6?
no it will be y^2+y-6=0
It will be quadratic which you can solve
devout helm
no it will be y^2+y-6=0
how does the x become y
shell agate
You replace x^2 with y
gray isle
with the idea you had for a), the substitution isn't really needed
you made the mistake in finding your pair of values
shell agate
He didn't substitute for 1st Q so got 2nd wrong
devout helm
with the idea you had for a), the substitution isn't really needed
you made the ...
oh yeah it should me +3
shell agate
how does the x become y
You know to solve a quadratic right?
devout helm
You know to solve a quadratic right?
can give an example
shell agate
Helping you to understand how to replace
Because you did not solve 2nd question
You know how to solve a quadratic so you could solve if you convert 2nd question to quadratic form
void nymph
with the idea you had for a), the substitution isn't really needed
you made the mistake in finding your pair of values
devout helm
let me get this straight, for part a, we dont have to substitute anything right?
gray isle
technically you don't "have to" for either
but it does help with the process if you can't recognise you have a hidden/disguised quadratic
devout helm
technically you don't "have to" for either
but it does help with the process if ...
but aint gonna lie doing the substitution way is way more harder than what I did
desert raptor
are these correct?
For the second one you should let (x+3) = y and continue from there
gray isle
depending on how comfortable you are in recognising the hidden,
sub is just extra lines of unnecesary work
devout helm
depending on how comfortable you are in recognising the hidden,
sub is just extr...
exactly
gray isle
try applying the same idea for b)
for a), you had (x^2)^2, x^2
for b) you have (x+3)^2, (x+3)
the approach to the factorisation is similar,
the numbers you'd want to focus on are
a=2, b=-5, c=-12
lone heartBOT
@devout helm Has your question been resolved?
marble knot
Can someone explain how you substitute and simplify this to get the equation shown.
ocean sealBOT
@zinc bolt
marble knot
When I substitute y I get this
So how do I get from:
(x - a)² + (-x/a + 1)² = d²,
to:
(x - a)² * (1 + 1/a²) = d²
zinc bolt
,rccw
marble knot
<@946379454056386560>
wow thank you
zinc bolt
!done
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marble knot
.close
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flat vector
how do i find the perimeter of a circle
lone heartBOT
how do i find the perimeter of a circle
flat vector
how do i find the perimeter of a circle
unique dune
winter light
how do i find the perimeter of a circle
Repeating the question twice has no effects, actually the effect is that fewer people will be willing to answer
Also, your answer can be found by just searching on the Internet or looking at a basic math book
flat vector
Repeating the question twice has no effects, actually the effect is that fewer p...
i know now it has no effect i only repeated it because i wanted to see what happens or if smth like a bot answers after i clicked smth
lone heartBOT
Helpers are just people volunteering their time to help you. Be polite and patient.
vale wigeon
emphasis on helpers being PEOPLE not bots.
@flat vector if you want to get help from a bot, this is not the place.
flat vector
i js dont know what to do
royal star
Type .close if you don’t have a question
vale wigeon
@tight pier why the ⚠️ react?
vale wigeon
i js dont know what to do
google and/or youtube "how to find perimeter of circle"
flat vector
.close
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Available help channel!
fervent seal
lone heartBOT
fervent seal
I have tried factorizing a x^pi and then having there a remarcable limit, but i couldn't continue
I'm talking about lim sin(x)/x = 1 when x->0
near steeple
Try using taylor series to expand sinx
x^pi term will cancel out
x^(pi+2) will be all the matters
fervent seal
the thing is that i haven't yet learned taylor series
fervent seal
i will look into it
north rover
I mean, I guess you can try to split the fraction and consider the sinc limit.
Let me try it out.
Oh yeah, it works perfectly fine
I see no need for a Taylor Series.
fervent seal
could you please send me the way you solved it?
i got what you said but when i split it in two i get 1/x^2 - 1/x^2
fervent seal
the answer should be pi/6
north rover
I don’t think you can really split it here...
The best I could think of was L’Hopital’s but it doesn’t work too nicely
fervent seal
yeah it's a lot of work with l'hopital
north rover
Could there maybe be a way to subsitute something nicer to deal with (not pi in the exponent)?
fervent seal
yeah i took into consideration a substitution, but haven't found it
fervent seal
<@&286206848099549185>
olive garden
To get pi/6 I feel l hospital is the best way
Nah don’t do l hospital
Did you try using series expansions ?
fervent seal
i haven't learnt that either
wary fable
what are you allowed to use?
fervent seal
everything
but the thing is this is from an exam for admission at univeristy
and i'm trying to work with what i learned till now, i don't really have time to learn new things right now
wary fable
consider taylor expansion for sin(x)/x @fervent seal
lone heartBOT
@fervent seal Has your question been resolved?
lone heartBOT
@fervent seal Has your question been resolved?
fervent seal
.close
carmine topaz
i have no idea what part c is doing and i dont get the solution either
dusty grove
buoyant saddle
i have no idea what part c is doing and i dont get the solution either
you already found the amount from 0 to 30 now you just have to find the rest from 30 to K
but p(h) was only valid for 0 <= h <= 30
and they tell you it’s modeled instead by f(h) for h >= 30 at the top of the page
but we can’t find f(h) explicitly so they just ask you to give an upper bound on the amount of plankton in the vertical column
buoyant saddle
same reason from before
carmine topaz
area = 3?
carmine topaz
but like how would i know this?
carmine topaz
but like all three integrals was *3 i wouldnt know they will all have same area
carmine topaz
ok
so we js gotta show that the the one from b + 3*int 30 to K f(h) will be less than 2000 mil right
buoyant saddle
so we js gotta show that the the one from b + 3*int 30 to K f(h) will be less th...
yes
carmine topaz
and that 3 * int 30 to K f(h) is less 3 * int 30 to inf u(h)
buoyant saddle
mhm
carmine topaz
they could have said it in easier way but decided to write like shakespeare
anyways thanks for helping 😀
buoyant saddle
lol
carmine topaz
.close
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buoyant saddle
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carmine topaz
i dont get why it plugs x=1 in part d like nowhere did it talked about G(x) = 50 when x=1
carmine topaz
wait so i have to plug in to know that not that i was given that info?
grave matrix
That's what the => means, yeah
kind trellis
Yes, it says at the top of the last picture
warm drift
@everyone
proper tangle
.close
floral whale
i dont get how to do part c
lone heartBOT
i dont get how to do part c
floral whale
it says im meant to differentiate this but when i do i get the wrong asnwer
remote heron
what answer do you get?
ocean sealBOT
jan Niku
floral whale
32.8
am i meant to times the differentiated value by -0.05 then substitute 50 as t?
remote heron
yea
floral whale
yeah i dont know why id do that
remote heron
but it doesnt make sens you get a positive number
remote heron
yeah i dont know why id do that
because $T'(50)$ is the rate at which the temperature of $S$ is decreasing in the instant $t=50$
ocean sealBOT
jan Niku
remote heron
because youre diffe0rentiating
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alpine sable
couple of doubts
- elements of AxA ( cross product on a set) if A is an empty set
- if a relation is transitive and symmetric , then its reflexive too right ? ( if the sets are non empty)
- for empty sets , why is it not ? why is it transitive and symmetric but not reflexive ?
modern sedge
cross product on a set
Do you mean the cartesian product?
cartesian product of empty set with anything is empty
alpine sable
yes sorry
modern sedge
A x B includes all pairs (a, b) with a in A and b in B. So if A is empty, then there is no a in A, and so no pairs (a, b) that could be in A x B
alpine sable
cartesian product of empty set with anything is empty
no elements ? not even null element ?
alpine sable
2^0 = 1 element ?( 2^mn , m,n=0 ; no of relations of set)
i though that 1 element is null
modern sedge
2^0 = 1 element ?( 2^mn , m,n=0 ; no of relations of set)
number of elements in A x B is |A| * |B|
you might be confusing it with something else
P(A) has 2^|A| elements
alpine sable
modern sedge
okay, but that's not what cartesian product is
zinc bolt
!nogpt
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Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
alpine sable
P(A) has 2^|A| elements
yes , p(a) is the no of relations too right
modern sedge
yes , p(a) is the no of relations too right
relation by definition is subset of A x B
zinc bolt
yes , p(a) is the no of relations too right
P(A) is the powerset of A
modern sedge
the set of all subsets of A x B is P(A x B)
alpine sable
P(A) is the powerset of A
yea ik
modern sedge
the set of all subsets of A x B is P(A x B)
so the sets of all relations on A, B is P(A x B)
alpine sable
no of relations is indeed 2^mn
modern sedge
and the caardinality of that set would be:
|P(A x B)| = 2^|A x B| = 2^(|A| * |B|)
alpine sable
couple of doubts
1. elements of AxA ( cross product on a set) if A is an empty s...
2,3 ?
modern sedge
so null elemtn only exists in the powerset to represent it ?
the null element is not in A x B if you mean that
alpine sable
the null element is not in A x B if you mean that
but it is in P(AxB)
alpine sable
regarding 2, try proving it
uhh its hard to type it out , could you just answer or do i need to type it all out :/
ill ig
modern sedge
you dont need to, have you thought about it tho? Have you tried proving it at least in your head?
or disproving it
consider the empty relation e.g.
it's certainly not reflexive
alpine sable
for non empty sets
transitive and symmetric relations
(a,b) exists , then (b,a) should also exist ( symmetric)
as it is transitive (a,a) and (b,b) also exists
modern sedge
is it transitive? Is it symmetric?
alpine sable
for non empty sets
transitive and symmetric relations
(a,b) exists , then (b,a) ...
so , its reflexive too
modern sedge
for non empty sets
transitive and symmetric relations
(a,b) exists , then (b,a) ...
if (a, b) is in the relation
unless (a, b) is in the relation, (b, a) is not there
so you cant really use transitivity
alpine sable
yes
modern sedge
is it transitive?
alpine sable
yes
alpine sable
idk , yes ig ? cuz reflexive says if a exists , then (a,a) should exists right ? eh , but a doesnt exist
alpine sable
(assuming it's relation on some non-empty A)
what 😭
modern sedge
idk , yes ig ? cuz reflexive says if a exists , then (a,a) should exists right ?...
It's not about existence
alpine sable
empty relation on non empty A?
modern sedge
okay, i think you're confused on what a relation is
we can have a set A = {1, 2, 3}
no relation on A is any set of ordered pairs with elements only from A
so e.g.
{(1, 1)} is a relation
{(1, 3), (2, 1)} is also a relation
{} is also a relation (the empty one btw)
but {(1, 4)} isn't a relation on A
alpine sable
yea ik
modern sedge
{} is also a relation (the empty one btw)
yeah, so this would be the empty relation in this case
and it's not reflexive
modern sedge
if it were to be reflexive, it would have to contain (1, 1), (2, 2) and (3, 3)
modern sedge
how is reflexive defined
relation on A is reflexive iff it contains (a, a) for every a in A
so e.g. relation on {1, 2} is reflexive iff it contains (1, 1) and (2, 2)
relation on {} is always reflexive
relation on {a, b, c, d} is reflexive iff it contains (a, a), (b, b), (c, c), (d, d)
modern sedge
but {(1, 4)} isn't a relation on A
so out of these relations on A, none is reflexive
because none contains all of (1, 1), (2, 2), (3, 3)
alpine sable
so an empty set isnt reflexive cuz it doesnt contain (a,a) for the elemtn in it , which is nothing ? ehhh , what
modern sedge
so an empty set isnt reflexive cuz it doesnt contain (a,a) for the elemtn in it ...
reflexivity depends on the context
you cant decide whether a relation is reflexive unless you know what the "parent set" is
alpine sable
i just wanted to solve a small question 😭 ive diverted faaar away from my topic and running short on time lmao
modern sedge
if {} is a relation on A = {1, 2, 3}, then it's not reflexive (because it doesnt contain (1, 1), (2, 2) and (3, 3)
alpine sable
but ty tho
modern sedge
if {} is a relation on {}, then it is reflexive
alpine sable
you said it isnt
alpine sable
and it's not reflexive
.
modern sedge
you said it isnt
It depends on what the "parent set" is
alpine sable
ahhh 🤕
modern sedge
if {} is a relation on {}, then it is reflexive
this is a relation on empty set
alpine sable
so if its on an empty set its an equivalnce relation
if its non empty sets and empty relation , then its not reflexive
modern sedge
so if its on an empty set its an equivalnce relation
yeah
modern sedge
if its non empty sets and empty relation , then its not reflexive
yes
alpine sable
but its symmetric and transitive
modern sedge
yes
brisk oak
what does this mean? i dont understand
lone heartBOT
what does this mean? i dont understand
brisk oak
how is y a function of f what..
lethal belfry
how is y a function of f what..
It most likely means the partial derivative wrt f , x or y
brisk oak
give the full context or look in the book's index
thermodynamics, they call it eulers chain rule
i dont understand it tho
tacit arch
which line here do you get lost first
brisk oak
which line here do you get lost first
first like idk what a total differential is and how its different from a partial differential
brisk oak
https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/12%3A_Functi...
oh so to prove that this is a total differential i just have to integrate the first part with respect to x and the 2nd part with respect to y?
and if they differ its not a total differential
tacit arch
yea it's also called exact differential
https://en.wikipedia.org/wiki/Exact_differential
tacit arch
you're leaving out too much context to answer
lone heartBOT
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earnest lance
i have no clue where to starts on 43
lone heartBOT
i have no clue where to starts on 43
earnest lance
what are the 50°and 96°??
arcs
bleak heath
oh ok
waxen flame
Pretty sure those are the arc measures of GJ and JI.
Look up the Inscribed Quadrilateral Theorem and Inscribed Angle Theorem.
bleak heath
so GKI would be 50+96?
waxen flame
so GKI would be 50+96?
Yes.
bleak heath
and then we know that the angle subtended would be double of GHI at GKI
earnest lance
and then we know that the angle subtended would be double of GHI at GKI
what does subteneded mean
earnest lance
k
earnest lance
and as it is cyclic quadrilateral, GJI+GHI=180
so how do we get ghi
bleak heath
and then we know that the angle subtended would be double of GHI at GKI
using this
it's a theorem
The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
earnest lance
so it would be 73?
earnest lance
The angle subtended by an arc at the centre is double the angle subtended by it ...
alrigth ty i got it
.close
lone heartBOT
bleak heath
so it would be 73?
GHI would be 73 yes
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next stratus
how do i do this
lone heartBOT
how do i do this
next stratus
I let eqn of first circle be (x+3)^2+y^2=1
and other be (x-3)^2+y^2=1
and P(0,0)
let the point at which C and C1 touch be Q
using pythagorean theorem i found PQ=2sqrt(2)
north rover
Okay
patent vale
Okay
north rover
What did you let the center of C be?
next stratus
What did you let the center of C be?
(0,k) by symmetry
next stratus
sqrt(k^2-8)
north rover
Am I tweaking or can you extend the radius to the centers of C1 and C2
Then use similar triangles
Have you tried that yet?
next stratus
Have you tried that yet?
no, i extended, but i haven't done the similar triangles part lemme try
north rover
Yep, it definetely works
||1/(2sqrt(2))=2sqrt(2)/r|| so ||r=8||
Don’t look at this, this is my working
next stratus
||1/(2sqrt(2))=2sqrt(2)/r|| so ||r=8||
Don’t look at this, this is my working
uhh i took triangles PC1C and QC1P for similarity
then PC1/QC1=C1C/C1P
=>3/1=(R+1)/3
=>R=8
yeah thanks a lot!
north rover
:D
next stratus
.close
lone heartBOT
silver plume
How do I find y intercept and a second point?
lone heartBOT
How do I find y intercept and a second point?
buoyant saddle
y intercept is a point
buoyant saddle
oh nvm it wanted interval notation
not an interval, a point
lone heartBOT
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split whale
split whale
<@&286206848099549185>
modest robin
this is like a physics probkem?
lone heartBOT
@split whale Has your question been resolved?
lone heartBOT
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plush flicker
lone heartBOT
near steeple
man i dont really know how to do it with a double integral
But i can find the area without it, but that’s not the problem
i mean one way is to find the area of both regions seperately and substract the overlap region once
for that area we can setup a double integral
like area of r=sintheta is the double integral of dA i.e rdrdtheta
r=sin theta
plush flicker
yeah I know how to do that, but idk how to do it with a double integral either
ocean sealBOT
SuppaHotFreshFire
near steeple
The intersection area is very easily 1/4 cz they are orthogonal unit circles
does that work?
the final answer comes out to be pi/2 - 1/4
just verify it whenever you return @plush flicker i gtg for an examination rn
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foggy vector
lone heartBOT
foggy vector
- solve the following initial value problems specifying the domain of the function
solving 1) right now
AFAIK i need to find the particular and homogeneous solution
we know y' - 3y = 0
lone heartBOT
@foggy vector Has your question been resolved?
shadow fjord
we know y' - 3y = 0
Do you know the homogenous solution?
foggy vector
Do you know the homogenous solution?
nope. trying to figure that out right now
shadow fjord
It is a separable differential equation.
you can write it as dy/dx = 3y
or dy/y = 3dx
foggy vector
or dy/y = 3dx
shadow fjord
Good, except don't forget the constant of integration (+C).
shadow fjord
So you have ln|y| = 3x+C
shadow fjord
You should simplify/solve for y.
foggy vector
You should simplify/solve for y.
this?
shadow fjord
Yes. y = C_1e^{3x}.
shadow fjord
In any case it will be a constant, so you can drop the +-.
+-e^c is a constant I mean
foggy vector
yeah yeah
shadow fjord
Ok, do you know how to find the particular solution?
foggy vector
what i mean is it's any R number which can be positive or negative
honestly, no. i'm kind of skipping a bit of stuff here
shadow fjord
You have to guess the form of the solution. You'll have to practice and memorize forms of solutions, but in this case, since you have a e^{2x}, you will guess y_p = Ae^{2x}. Where A is a constant.
So basically you take derivatives, plug into the DE, and solve for A.
foggy vector
alright
is this similar to linear algebra
where you'd find a particular and hom solution
for the null space of a matrix?
foggy vector
interesting
foggy vector
You have to guess the form of the solution. You'll have to practice and memorize...
so you get the particular sol from just guessing??
no theorems to get there?
shadow fjord
There are a couple ways to do it, but the guessing method is a common one.
In fact, for a first order like this, you could use the integrating factor method.
That would give you the whole solution at once, actually.
foggy vector
okay i see that here in my notes uhhh
shadow fjord
Well, since you've started this method, you might as well finish it. Then you can try it again using integrating factor.
foggy vector
$\mathbb{S}_H = span{e^{-\int P(x) dx}}$
shadow fjord
That looks right.
ocean sealBOT
ransik (gmdn)
foggy vector
so wait i just "plug in" my function here and solve?
will this be my hom or particular solution
is P(x) y=Ce^3x or my initial function
heavy prairie
shadow fjord
Yes, that is the method
heavy prairie
im glad you brought this up i need to refresh on this stuff for my exam
heavy prairie
i have one in 18 days but it is too soon, i will try to take it later i think
foggy vector
it's okay i always make it out in the end
heavy prairie
they host calc 2 every 2 months or so at my uni
foggy vector
Yes, that is the method
cheers, thanks
heavy prairie
which is nice
foggy vector
they host calc 2 every 2 months or so at my uni
oh what you can do that
the way it works here is you have two midterms
i guess they're not midterms
they're called partial exams
heavy prairie
oh i see, yeah so calc 2 is such a common course here they host it 4 or 5 times for the year
foggy vector
each semester you have a class right this semester i have math 2 (basically calc 2)
you have like 6-8 weeks of class and a partial exam
then 6-8 more weeks and another partial
your partials need to average into the passing grade
shadow fjord
i'm kind of cooked 💔
You seem to be doing fine. Just keep practicing, and remember on the test you can't use a computer to help. So at some point you should make sure you can do a problem and with nothing but a blank piece of paper work through the whole thing.
foggy vector
once you pass you qualify for the final
you can take the final 3 times
fail it and you retake the class
heavy prairie
nice, we get a sheet with 8 calc 2 related problems, full marks for a question scores you 5 points. you need 18 to pass, pretty generous tbh
foggy vector
you can only fail one partial exam. fail both you retake the class.
foggy vector
You seem to be doing fine. Just keep practicing, and remember on the test you ca...
yeah i usually just rawdog it into learning the basic concepts and go from there
heavy prairie
we also had some turn-in assignments
foggy vector
i hammered out sequences in like a day
foggy vector
we also had some turn-in assignments
we don't have those at all
or at least not for math, chem, physics
actually physics does but it's only a bonus
heavy prairie
turn-ins weren't really graded, like you passed or you didn't
and for exam, you could get a passing, passing but without praise and passing with praise
foggy vector
exams are just graded /10
you pass with a 4/10 which seems bad but in reality either the exam requires 60% of the exam to be correct in order to get a 4
or the exam is structured in such a way that a 40/100 is deserving of a passing grade
heavy prairie
oh yeah i should have said
foggy vector
they're very stringent with corrections. most mistakes will nullify the entire exercise
foggy vector
ah, i see
foggy vector
45%
heavy prairie
i scored a 12, but i forgot everything since the last time i took the exam
i wasn't learning to learn just cramming info and formulas
i didnt understand a single thing
how are you handling the convergence tests?
foggy vector
oh not great yet
yeah i'm
like i said i'm having a hard time
but it's okay i was able to get in most of linear alg in a week too
i might be fine
heavy prairie
i got in most of linear algebra over the course of 2 months, i do feel confident for when i take the exam
probably in june or august
i dont like the convergence tests
foggy vector
i'm just really bad at doing my work during the classes
so i end up cramming before the exams
heavy prairie
i just dont go to class
or lectures
but there are tutors in the evening at uni
and most people dont go so
i end up alone with a 3rd or 4rth year student
who is pretty strong at math
foggy vector
but there are tutors in the evening at uni
ohhh that'd be awesome
heavy prairie
yes that is awesome
foggy vector
sadly my uni is like a 40m drive away lol
heavy prairie
they are there from 17.15 - 19:00 every monday- thursday
foggy vector
1:30h with traffic
heavy prairie
should i watch House MD?
foggy vector
yeah it's a good show
great for putting on while studying
i like watching "dumb" shows whilst studying
think the office, house md, etc
stuff that doesn't require much attention
heavy prairie
i have only seen a couple of episodes
it looked interesting
he just gets weird cases over and over
and is very rude to people
foggy vector
yeah
that's the format
repeat for 8 seasons
it personally never got stale for me
foggy vector
give it a go
it's a good show
maybe slow in the first season
anyways. i gotta go
cheers mate
lone heartBOT
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alpine sable
hi! i was hoping to get some resources to help study/re learn highscool math ie: geometry and algebra and stats for a TABE math test
summer dirge
Khan Academy is generally cited as an excellent source for that material
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
i got a thing for what i need to work on most
lone heartBOT
i got a thing for what i need to work on most
ornate ginkgo
Do you have a question
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
Do you have a question
i was wondering bout any resources i could use to help me improve on what i did poorly in on the ss
old sinew
lone heartBOT
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devout helm
I'm not sure on how to find qn 4c
lone heartBOT
I'm not sure on how to find qn 4c
devout helm
at t=4-7 s velocity is constant no?
so what do I have to find?
twilit dome
no, you dont have to differentiate, but finding the slope of a line is equivalent to calculating the derivative
devout helm
no, you dont have to differentiate, but finding the slope of a line is equivalen...
the gradient?
devout helm
wdym by finding the slope of line
twilit dome
yes
devout helm
so its 10-(-5)/4-7?
twilit dome
yes
lone heartBOT
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Available help channel!
royal harness
Uhhh... i9 and i10. What shall I do?
lone heartBOT
Uhhh... i9 and i10. What shall I do?
exotic canopy
,rccw
ocean sealBOT
exotic canopy
Uhhh... i9 and i10. What shall I do?
would be great if you provided translation
if you have two matrices in C their sum is also in C?
for i9
and their product is also in C foe i10
is that correct?
royal harness
We consider the crowd C. Prove that, whatever X,Y belong to C, we have X+Y belong to C
I translated
exotic canopy
in english, what you referred to as "crowd" is called a "set" :)
royal harness
Oh, sorry
exotic canopy
We consider the crowd C. Prove that, whatever X,Y belong to C, we have X+Y belon...
take X to be the matrix
[x 0
0 x]
for some x in R, and Y be the matrix
[y 0
0 y]
what would X+Y look like?
royal harness
Ohhhh
exotic canopy
Oh, sorry
don't apologise, i think it's really cool that it's called a crowd in romanian ahah
royal harness
don't apologise, i think it's really cool that it's called a crowd in romanian a...
How did you know it's Romanian?
exotic canopy
language nerd + i have some romanian friends
royal harness
take X to be the matrix
[x 0
0 x]
for some x in R, and Y be the matrix
[y 0
0...
(X+y 0 0 x+y)
exotic canopy
ah alright
exotic canopy
(X+y 0 0 x+y)
does this matrix belong to C?
exotic canopy
yes exactly!
wet magnet
PART C
lone heartBOT
@wet magnet Has your question been resolved?
wet magnet
<@&286206848099549185>
rustic coral
i try doing OB crossproduct with OD to obtain normal to BD
Isn’t it easier to note that plane is normal to BD -> the normal vector is parallel to BD
So you can just take the normal vector to be vector BD
Since you found the coordinates of B and D in (a)
wet magnet
Isn’t it easier to note that plane is normal to BD -> the normal vector is paral...
shouldnt it be perpendiculart
rustic coral
shouldnt it be perpendiculart
The plane is perpendicular to BD
And the normal vector is perpendicular to the plane, and hence parallel to BD
rustic coral
so its the same?
You can take the normal vector to be BD, yes.
wet magnet
oh ok i get it now
but wait
why doesnt cross product work
which components would i need for that to work?
rustic coral
why doesnt cross product work
Why would it?
wet magnet
Why would it?
thoose are not the same?
rustic coral
wait cross produc5t doesnt give normal
That’s if you have two vectors in the plane tbh
b/c then you’re taking a vector perpendicular to two vectors in the plane
Which will result in a vector that’s perpendicular to the plane itself
Aka the normal vector
wet magnet
but it doesnt work here?
rustic coral
That’s if you have two vectors in the plane tbh
wet magnet
but we got OB and OD they lie in the same plane
rustic coral
“the plane” as in the plane you want to find
Just draw the plane yourself
You should see that’s not the case
wet magnet
can you draw it, im still confused pls
ocean sealBOT
wet magnet
Idk what you’re drawing
like if we only focus on OBD and the Plane
it's a one dimension sketch but yeah might be a bit bad
You there still?
@rustic coral you still there ?
bro pls help
.close
lone heartBOT
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slow sleet
Im a bit confused as to what the confidence interval means
lone heartBOT
Im a bit confused as to what the confidence interval means
slow sleet
what does it look like graphically?
jaunty wharf
as in 95 % confidence intervals and such?
slow sleet
ye
cuz i got like stuff with normalcdf and stuff in highschool but i dont know if this is the same
or not
jaunty wharf
depends on the type of question youre facing
slow sleet
i am tryuing to understand what confidence interval means
and how i can use it
not a specific question bound to it
jaunty wharf
okay confidence intervals are basically a range of values that a particular random variable can take with a particular probability of it being the true value of the RV in that context
for instance, if you're given a 95 % interval of X as say 15.4 - 18.9, it means the true value of X in context of that particular problem will lie in that range 95% of the time
there are different methodologies regarding how to arrive at these intervals, im sure you'll come across them if you already haven't
they do require knowledge of critical points of certain distributions, mostly normal
slow sleet
but wdym real value, is this just the lower and upper bound of the distribution such that a random value in that distribution has a x chance of lying within the bounds?
jaunty wharf
no no
a confidence interval only comes into play when youre given real life data about the parameters of an RV which follows a theoretical distribution
slow sleet
whats an RV?
jaunty wharf
a random variable
jaunty wharf
graphically , you're correct but this graph can also refer to a basic theoretical distribution in which case you wouldnt call it a confidence interval, get it?
slow sleet
graphically , you're correct but this graph can also refer to a basic theoretica...
but i mean a normal distribution
oh wwait
the confidence interval is also true for non normal distributions?