Last time I did this shit was in 8th grade
#help-28
desert moat
But if you did it in 8th grade you could probably solve it
I have send you req accept it
sleek spoke
Is this high school level?
sleek spoke
No university level
tf
desert moat
Bro please you also help me
sleek spoke
Brother are you gonna send
tender sonnet
Bro please you also help me
My computer is updating lol
desert moat
@tender sonnet broo pleaseee
tender sonnet
I won’t be able to help in time sorry
desert moat
But you are messaging so it means you can see my ques you just have to solve it
tender sonnet
If this is the only thing you need help on you should be able to pass
tender sonnet
But you are messaging so it means you can see my ques you just have to solve it
Won’t be able to solve it in time
torn jolt
why not use kirch law its like no brainer
desert moat
why not use kirch law its like no brainer
If its easy for you please solve it
I really need help or ill fail
torn jolt
If its easy for you please solve it
i am just lazy to solve
i can tell tho who to do it
sorry
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torn jolt
Luis has a car that uses “97 octane” gasoline, he is currently in a shopping center and is analyzing the prices per gallon of different establishments in a district near the shopping center to go and refuel his car, searching on the internet get the following table:
Establishments / Selling price per gallon / Distance from the shopping center to the establishments according to Google maps
Consider that a gallon is equivalent to 3.78 liters and also that Luis's car travels 20 km per liter of fuel. Next, answer the following questions:
a. Calculate the amount of fuel (in gallons) that Luis's car would consume if he chose to go from the shopping center to store A.
torn jolt
My answer: 0,0352
in the book: a. La cantidad de combustible a usar será 0,352 de galón.
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torn jolt
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vast tinsel
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royal pawn
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royal pawn
first i did t = d/s --> 5m/2m/s --> 2.5
then i did integration from 0 to 2.5 of 20-0.5x
and got roughly 48J, don;t think it's right tho
glossy valveBOT
royal pawn
is the 1000 for density?
royal pawn
so you mean do 46875/1000 ?
wise wyvern
Something like that yes. How'd you get 20-0,5x
royal pawn
So the 20L is just 20kg then i did 1L/2m/s and did 20-0.5x
it was from a video i watched
wise wyvern
Why 1/2?
wise wyvern
no
It's already 1l/s
Which means it's already 1kg/s
And you don't want to mix that with the speed.
royal pawn
oh i see where i mixed that up
wise wyvern
The only use of that speed was to find time.
royal pawn
t = 5m/2.5m/s
royal pawn
why?
royal pawn
oh yes writing too fast lol
then use that time as bounds? 0 being lower and 2.5 being upper?
then integrate 20-0.5x? Or is there some other expression I need to integrate over
royal pawn
mass
wise wyvern
Correct.
royal pawn
should i multiply 20 with g?
royal pawn
well the 0.5x i got from doing 1kg/2m/s then I added the x for distance
wise wyvern
Well you should actually have a very clear understanding of what you're integrating and what your equations are.
So for example, you have water leaking out at 1l/s, you can also say that's the same as 1kg/s
royal pawn
true
royal pawn
ohhh
wise wyvern
But you want work
royal pawn
should it be 20-x?
wise wyvern
for mass it should be 20-x BUT
You need work
And you haven't written an expression for work yet
royal pawn
so then i can use mass to find force to multiply (20-x)9.8?
wise wyvern
But the mass would actually be 20-x where x is actually time
royal pawn
but we know time is 2.5s
wise wyvern
Honestly it depends what work they're asking for. But I think it's most probably the work that's done to maintain the bucket at the constant speed cause even though the mass is changing they've maintained speed
wise wyvern
but we know time is 2.5s
That's the final time. This is a general expression for mass.
royal pawn
hmm
wise wyvern
Honestly it depends what work they're asking for. But I think it's most probably...
By work they could alsi mean work done by gravity and shit.
I honestly don't know what work they're talking about. Is there more to the problem?
royal pawn
nope that's all
glossy valveBOT
Result:
5
That's the final mass.
Or final volume in l
Not the work.
wise wyvern
It depends on what work you want to calculate.
Are you somewhat positive it's to do with the work done by gravity?
royal pawn
yes for sure i know we use F=mg
royal pawn
give a second ill show you
wise wyvern
You can, it's fine but I more or less understand the problem.
Alright do you know what work is?
By definition.
Or like the expression for that
royal pawn
Force multiplied by displacement
royal pawn
power is not something we've talked about
wise wyvern
Ah.
Well in any case
$W = \int \vec{F} \cdot \vec{\dd x}$
What do you think the force is?
glossy valveBOT
! What the hell am I doing here?
royal pawn
I think it'd be work done by pulling it up - work done by gravity
wise wyvern
Well, what's the force though?
royal pawn
yeah that would be the net force
wise wyvern
what would?
royal pawn
pulling it up - work done by gravity
royal pawn
oh whoops i meant force required to pull it up - force done by gravity
wise wyvern
Yeah, but because it's constant velocity you can say the force is just its weight.
They're both equal.
royal pawn
true
royal pawn
20kg
royal pawn
no because water is leaking
wise wyvern
At t = t, what's the mass?
wise wyvern
when the bucket is pulled up 5m it will contain only 17.5L
Yes, that's true for t = 2,5 s
But what about a general expression?
For mass.
In terms of time.
You can use t for time.
royal pawn
mass would be 20-2.5t and t being any time
royal pawn
yeah i see why
royal pawn
not sure
wise wyvern
You did 20 - 1 * 2.5 for final.
You did 20 - 1 * 0 (essentially 20) for t = 0
What would you do for t = t?
royal pawn
20-t?
wise wyvern
in any case, that's the mass as a function of time.
royal pawn
agree
wise wyvern
So would you have any problems if I said the work done was\
$W = \int (20-t)g \dd x$
glossy valveBOT
! What the hell am I doing here?
royal pawn
no seems ok
royal pawn
20-t would be mass in terms of time then g would be gravity so F=mg then dx is displacement
royal pawn
change in height with respect to time?
wise wyvern
Which is?
royal pawn
work?
wise wyvern
Read the question.
"Change in height wrt time"
"Change in displacement wrt time"
What might that be?
royal pawn
rate?
wise wyvern
Did you read the question?
royal pawn
yes
wise wyvern
How is the height of the bucket changing?
marsh swan
F = dmv/dt
use chain rule to work out the force
then plug it into F.dx
the integral
wise wyvern
That's done.
Already.
However, op is having some hard time substituting a few of those values/expressing one variable in terms of another.
royal pawn
yes
royal pawn
velcoity is the change in displacement over time
royal pawn
right the 2m/s
marsh swan
then just use jacobian
wise wyvern
(you an replace the dx in the original integral)
marsh swan
yes
royal pawn
OHHHH I see
wise wyvern
And once you have dt you already know the bounds too.
So that's the right integral.
And not any random integral.
royal pawn
so integral from 0 to 2.5 of (20-t)2 dt?
wise wyvern
g
royal pawn
so integral from 0 to 2.5 of (20-t)g2 dt?
wise wyvern
yeah
royal pawn
Wow thank you so much!
wise wyvern
But you should always write the correct expression for what is being asked and not just integrate randomly. You integrated time wrt displacement or smth like that earlier, smh.
royal pawn
my fault
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tardy copper
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acosx+bsinx
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simple cargo
My goal is to basically find the relationship between the track the front wheel and back wheel of a bike produces. So far I have derived a tractrix function but don't know how to procede. I have found a paper with a formula but they skim past how they arrive at the formula. The following is a picture of my problem, -
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mental jasper
I'd like to know how to get f(-2)
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mental jasper
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stable lynx
Can you zoom it in please
mental jasper
stable lynx
struggling to understand the question
mental jasper
same i'm a bit confused
stable lynx
also the graph
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valid sage
Hey!
I have a random value that can have a value between 1 and n. Each value has a probability of 1/n. I wanna know how to calculate the average value.
It's been a long itme since ive done any stats. I have tried using a sommation. However some people put i in the somation instead of 1 and i have a really hard time understanding that
muted summit
i think you can calculate it using an integral
integral from 1 to infinity of 1/n i misunderstoof
valid sage
my value p can only go from 1 to n
stiff musk
Hey!
I have a random value that can have a value between 1 and n. Each value has...
this is just summing the probabilities (1/n), the result will always be 1
to get the mean, you want to sum (i times the probability)
stiff musk
$$\sum_{i=1}^n i\left(\frac{1}{n}\right)$$
glossy valveBOT
Bungo
stiff musk
1/n is the probability, multiplying that by i and summing over i gives you the mean
stiff musk
mean of what
stiff musk
oh you mean like sample average
valid sage
yeah
stiff musk
(not the same as the statistical mean)
stiff musk
you wouldn't sum the probabilities in that case anyway
you'd have something like s(k) = 1 if heads, -1 if tails, and if you flipped 50 times, the number of heads would be
$$\sum_{k=1}^{50} s(k)$$
and then your sample average would be
$$\frac{1}{50}\sum_{k=1}^{50}s(k)$$
glossy valveBOT
Bungo
valid sage
1/50?
stiff musk
normalizing by the number of trials
valid sage
ok, i get why using s(k) would work here
but not in the original exa
but not in this osmmation
My value p can have a value ranging from 1 to n
With this sommation, we are taking every possible outcome and multiplying them by their probability
and then adding them
but how does that give the mean?
wait this is litteraly the definition of the meanb
every outcome divided by the number of possibilities
since they all have the same probability
holy shit im dumb
I have another question that's similar
I have an array of n bits. There is a 1/n+1 chance that the bit is on. I wanna know the mean number of bit's that are on. I have made this
this would work right
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serene violet
Provide a trigonometric equation. Considering only the space between 𝑥 = 0 𝑎𝑛𝑑 2𝜋, the equation must only have solutions at 𝑥 = 1 and 𝑥 = 2.
viral jasper
You could try making a sine function equal to zero only at x=0 and x=1
serene violet
You could try making a sine function equal to zero only at x=0 and x=1
is f(x)=cos(x+0.5708)(x-2) a trigonometric equation
bungo i saw u wrote something pls halp
serene violet
yes
stiff musk
seems more in the spirit of the question to try to do it with only trig functions
serene violet
bro im struggling with making these type of equations
stiff musk
a single sinusoid won't work because if it's zero at 1 and 2, it's gonna be zero at 3 as well
but maybe the product of two sinusoids
basically replace (x-1)(x-2) with the product of two sines that are zero at those values of x but which have slow enough variation that they're not zero anywhere else in [0,2pi]
i'm sure there are other ways as well
but who knows what they really want, they didn't define "trigonometric equation"
my initial smartass thought was, ok, (x-1)(x-2)cos(0.000000001x)
serene violet
so how do i make a product of two sines with my desired values
so when i went to gpt, it was suggesting a trig equation is suppossedly like cos(pi x)=0
but i think my course wants f(x)=acos/sin(k(x-d)+c
stiff musk
so how do i make a product of two sines with my desired values
what if you did something like sin(a(x-1))sin(b(x-2))
choose a and b small enough that there are no more zeros inside [0,2pi]
(a and b could be the same number)
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serene violet
hol up solving
serene violet
what if you did something like sin(a(x-1))sin(b(x-2))
so my equation is f(x)=sin(0.5(x-1))sin(0.5(x-2))
stiff musk
yea that works
serene violet
how do i justify 0.5 tho
cuss they want my explanation
ig i could say i needed a very small number for k for the graph to meet within range of
0 to 2pi
is it called horizontal stretch
when k is less than 1
anyways thank u again bungo
serene violet
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tawdry grove
im not sure how to do this
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im not sure how to do this
tawdry grove
is it d?
civic bay
if you know your answer has to be of the form Ax^2 + By^2 = C, then you can compute dy/dx using implicit differentiation and get dy/dx = -(Ax) / (By). then you know from your given dy/dx that -Ax = 2x so A = -2 and B = 1, so -2x^2 + y^2 = C. then you plug in your point (3,2) to get -2(3)^2 + 2^2 = -18 + 4 = -14 = C, so C = -14. then you get -2x^2 + y^2 = -14, so 2x^2 - y^2 = 14, giving D
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steel veldt
When do you use WLOG?
fast peak
warm abyss
When do you use WLOG?
You usually use it if you have two or more possible cases which both go similar/are symmetric. E.g if you have two numbers a, b you can say wlog a >= b
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night bane
Could anyone help me with this homogenous differential equation?
night bane
I got IxI = e^y . e(x)
I thought it was possible to get that because Organic chemistry teacher also had this on a different homogenous excersise
night bane
yes
torn jolt
can u show work
night bane
ok but its bad handwriting
night bane
and obtain dy/dx = v + x dv/dx
I got dy/dx = v - 1
torn jolt
For the diff eq $y' = \frac{y}{x} - 1$ we use the substitution $y = vx$. Inputting this, we have $$v + x\dv{v}{x} = v - 1$$
glossy valveBOT
45
torn jolt
which reduces to $\dv{v}{x} = -\frac{1}{x}$
glossy valveBOT
45
torn jolt
integrating this you obtain $v = -\ln(x) + C$
glossy valveBOT
45
torn jolt
but $y = vx$, so $v = \frac{y}{x}$
glossy valveBOT
45
torn jolt
so the solution should be $y = -x\ln(x) + Cx$
glossy valveBOT
45
torn jolt
product rule
night bane
I have dy/dx = v - 1
change dy to vdx + xdv
torn jolt
$y = vx \implies y' = vx' + xv'$
glossy valveBOT
45
night bane
$y = vx \implies y' = vx' + xv'$
right yeah but what I would think that the next step would be to divide the fraction (vdx + xdv)/dx into 2
torn jolt
wdym
torn jolt
yes
night bane
and then we can move that v to the other side
torn jolt
its not really a fraction but yes
night bane
its not really a fraction but yes
so we get dv/dx = v - 1 - v wait wtf
torn jolt
yes
night bane
this deviates from what you explained but what went wrong with the reasoning
it makes sense to me
i wanna know the reasons behind these processes and not just remember them so that's why im asking so much
sorry if its annoying btw
oh i forgot to carry the x
night bane
which reduces to $\dv{v}{x} = -\frac{1}{x}$
<@&286206848099549185> I have a question about this
the excersise is solved when you multiply both sides by dx
and the rest you can solve
but the whole answer changes if you swap the x in the denominator with the dv in the numerator
night bane
but the whole answer changes if you swap the x in the denominator with the dv in...
and iirc this is mathematically not wrong
not incorrect
so my question is, why is it mathematically incorrect?
: (
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vernal ruin
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vernal ruin
Yes
Its 5sinx + 7
Numerator should be -7 -sinx, im not sure how the other cos and and sin got cancelled out tho
shell apex
this should be your answer, g(x) is -7sin(x)-5
or wait a sec
what do u need to find out to be more specific?
the top part of the fraction of f'(x)?
because f'(x) is well..what u can see there
shell apex
sin^2(x)+cos^2(x) is a trigonometry identity that always is equal to 1
no matter what x is
for example, sin^2(5000y+41521)+cos^2(5000y+41521)=1
provided the thing in the brackets is the same for both
vernal ruin
ohhhh i see, makes so much more sense
thats why i got lost forgot abt trig identities
but yeah thank you for the help!
shell apex
no worries man, good luck;p
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gusty carbon
What makes the left one (-♾️,♾️) and the right one DNE(does not exsist)
tribal urchin
What makes the left one (-♾️,♾️) and the right one DNE(does not exsist)
They are inequalities
The fist one is: where is r^2 - 3r + 9 greater than 0?
The second one: where is j^2 -5j +8 less than zero?
gusty carbon
yes
tribal urchin
try graphing them
tribal urchin
well both of them are always greater than 0
you can test this by finding the lowest point; which is the vertex
Where x = -b/2a
gusty carbon
x=3/2
tribal urchin
now substitute r=3/2
gusty carbon
j=5/2
tribal urchin
for the second one, the vertex should be at 5/2
don't forget the negative sign in -b/2a
tribal urchin
now substitute those values into the quadratic expressions
gusty carbon
for the firs one I got 27/4 >0
shell apex
Im guessing for the second one you will get something >0 being <0 which is impossible
tribal urchin
for the firs one I got 27/4 >0
so you see that the lowest value it takes is greater than than 0
so it's greater than 0 everywhere
tribal urchin
Im guessing for the second one you will get something >0 being <0 which is impos...
and as this fellow says, the second one should also be greater than 0 everywhere, meaning it's less than 0 nowhere
gusty carbon
For th second one I got 7/4<0
tribal urchin
7/4 is greater than 0...
gusty carbon
So if the inequality I get when I replace the letter with the x=-b/2a is possible then the answer is (-oo,oo) and if its not possible then it is DNE?
tribal urchin
not quite
here's the thing: both of these functions open upward
this is the graph
when a > 0, the function opens upward
when a < 0, the function opens downward
if a function opens upward, then the vertex has the smallest value
but if it opens downward, the vertex has the greatest value
do you follow that so far?
gusty carbon
Yes I just dont know how to graph quadratic equations other than entering the equation into a graphing calculator
tribal urchin
good practice would be getting some graph paper and graphing the points (x,y) = (x,f(x)) for quadratic function f(x) and a few integers x
then you connect the lines with a curve and quickly you'll start to understand how quadratics graph
gusty carbon
so is it DNE just because 7/4 < 0 is not true?
potent fossil
but every r will make 27/4 > 0
gusty carbon
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wide latch
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wide latch
this is the equation i came up with but when i plugged it into the calculator the answer i got is different from the book
and i'm not sure why
tulip beacon
this is just eyeing it
but if it doubles every half hour
shouldnt it be 2 instead of e?
wide latch
shouldnt it be 2 instead of e?
i don't think
cus it's in terms of hours
if it was in terms of every 30 mins it would be 2 i think
idk
wide latch
tulip beacon
so it has to be times by 2 each time
wide latch
wait why no e
tulip beacon
y=y0 * 2^t
when t = 1
y=2y0 which is correct
after 1 half an hour
it wold be doulbe original
afer 2 half an hours
it would be y = y0 * 2^2 = 4y0
which it would be
as it would double again
wide latch
ic
tulip beacon
im not mathematician so idk why its not e, but my guess is that normally it is e
we are just told its 2 in this case
wide latch
gotcha
the book will just throw curve balls without saying anything about it in the teaching section
😭
so insane
but thank you for the help
tulip beacon
just remember y=y0*A^t where y0 is the original amount, A is the facotr it increases after t amount of time
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proud bone
stuck i made a mistake somewhere
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stuck i made a mistake somewhere
shell hamlet
what is -12-12-16
potent fossil
30!
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drowsy onyx
I don't have work for this one I'm not sure what to do
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I don't have work for this one I'm not sure what to do
snow reef
Derivative of f(x) in terms of limits is given as lim h-> 0 (f(x+h)-f(x))/x+h-x
Where x is 3
So compare
And find the function
drowsy onyx
So compare
what am i comparing
like what do i go to find the original function when I'm given the derivative one
undone vector
what am i comparing
The definition of the derivative to the right side of the equation you are given. It looks quite like the definition of the derivative
river bough
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river bough
can some one explain this question
deft tulip
so am i understanding this correctly...it's giving you the information that cos B = 5/13 and wants you to find sin B ?
deft tulip
ok
ya it's just using the sin^2 + cos^2 = 1 identity
and you plug in the cos
and you use the pi < B < 2pi to determine the sign of the sin
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deft tulip
@river bough so you still need help with this?
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quaint minnow
in this is P(AnB) = p^3
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in this is P(AnB) = p^3
quaint minnow
Cause P(AnB) = P(A) * P(B)
wild sleet
it's not
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next basalt
Determine X so that $(AX+B)^{-1} = A$
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Determine X so that $(AX+B)^{-1} = A$
glossy valveBOT
Merineth
next basalt
A =
1 1 1
1 0 1
0 1 1
B =
1 2 3
4 5 6
7 8 9
thick hedge
I suggest you first solve the matrix equation for any arbitrary matrix
do you know how to do that?
thick hedge
I mean solve for X
quaint prawn
First find the matrix M so that (M)^-1 = A
next basalt
Where are you coming up with M from?
quaint prawn
Then solve AX+ B = M
quaint prawn
Where are you coming up with M from?
Just a name I gave to it, call it whatever you want
thick hedge
**Merineth**
first find X, but don't sub the values of A and B
quaint prawn
first find X, but don't sub the values of A and B
That doesn’t make any sense
thick hedge
That doesn’t make any sense
you don't need the matrices A and B to find X, you can express X in terms of A and B
quaint prawn
That is overcomplicating it, and I think taking the steps in the wrong order
next basalt
I know that if i multiply a inverse with it's noninverse i get the identity matrix
Can i use that somehow?
quaint prawn
Okay well I agree that’s what she should start with, but maybe it’s not clear that’s what you meant
thick hedge
I know that if i multiply a inverse with it's noninverse i get the identity matr...
try eliminating the inverse on the LHS first
quaint prawn
Can i use that somehow?
If M^-1 = A, what is M
(Not in terms of the actual entries)
quaint prawn
If M^-1 = A, what is M
Answer this
quaint prawn
That’s fine
M would be A^-1
Do you understand now what I meant?
If M^-1 = A
Then M = A^-1
Do you agree
next basalt
No, because i still don't understand why you are making up M out of nowhere
quaint prawn
It doesn’t matter this is a basic property of matrices
next basalt
$(AX+B)^{-1} = A$
quaint prawn
M is a matrix, just like A
next basalt
This is what i have
glossy valveBOT
Merineth
quaint prawn
Yeah I know what you have
thick hedge
yes
quaint prawn
That’s exactly what I’m telling you how to do
next basalt
And to get rid of the inverse i multiply with the noninverse
quaint prawn
Wow how’d you figure that
thick hedge
you have to take the inverse on both sides, is that what you meant?
next basalt
you have to take the inverse on both sides, is that what you meant?
Hmm i'm not sure
I just know that i can't just isolate the X immediately because i have the inverse on the LHS
So i guess i'd have to multiply both sides with the noninverse?
thick hedge
Hmm i'm not sure
OK, one basic property of matrices is $(M^{-1})^{-1}=M$
glossy valveBOT
Why am. I here
thick hedge
where M is an arbitrary matrix
next basalt
Is that the same concept for transposing?
thick hedge
yeah
next basalt
Aah i see
thick hedge
$(A^T)^T=A$
glossy valveBOT
Why am. I here
thick hedge
OK, one basic property of matrices is $(M^{-1})^{-1}=M$
Austin,, why the skull? did I say something wrong?
glossy valveBOT
Merineth
next basalt
Something like this?
next basalt
Iirc i can't divide matrixes ?
glossy valveBOT
Why am. I here
thick hedge
where I is the Identity matrix
next basalt
Ooh so if i multiply both sides with the inverse of A^-1 I get X isolated?
glossy valveBOT
Why am. I here
next basalt
Does the A on the LHS disappear ? Or is substituted with I?
thick hedge
Another property $MI=M$
glossy valveBOT
Why am. I here
thick hedge
again, M is an arbitrary matrix
next basalt
So any identity of M is = M?
thick hedge
The product of any matrix M and the Identity matrix of the corresponind order is M
next basalt
$X= A-A^{-1}B$
glossy valveBOT
Merineth
next basalt
Would this be correct?
glossy valveBOT
Why am. I here
next basalt
No worries
thick hedge
$AX=A^{-1}-B$
glossy valveBOT
Why am. I here
thick hedge
right?
next basalt
Yea
thick hedge
now, pre-multiply both sides with $A^{-1}$ again
glossy valveBOT
Why am. I here
thick hedge
remember, matrix multiplication isn't commutative
that should give you $X=(A^{-1})^2-A^{-1}B$
glossy valveBOT
Why am. I here
glossy valveBOT
Merineth
next basalt
And tha twill be X?
thick hedge
uh, $(A^{-1})^2-A^{-1}B$
next basalt
Can i square a matrix?
glossy valveBOT
Why am. I here
thick hedge
yeah
next basalt
Do i just take each individual within the matrix and multiply them by itself?
1 2 3
4 5 6
1 4 9
16 25 36
like so for example?
thick hedge
Also $(M^{-1})^n= (M^n)^{-1}$
glossy valveBOT
Why am. I here
thick hedge
where n is a natural number
thick hedge
1 2 3
4 5 6
1 4 9
16 25 36
mind writing that in TeX
next basalt
I sadly don't know matrix in latex :(
thick hedge
\begin{align*}
\det(A) &= \left| \begin{array}{ccc}
a_{11} & a_{12} & a_{13} \
a_{21} & a_{22} & a_{23} \
a_{31} & a_{32} & a_{33}
\end{array} \right|
\end{align*}
glossy valveBOT
Why am. I here
thick hedge
oops, just a monet
*moment
\begin{align*}
\det(A) &= \left| \begin{array}{ccc}
a_{11} & a_{12} & a_{13} \
a_{21} & a_{22} & a_{23} \
a_{31} & a_{32} & a_{33}
\end{array} \right|
\end{align*}
glossy valveBOT
Why am. I here
thick hedge
\begin{pmatrix}
a_{11} & a_{12} & a_{13} \
a_{21} & a_{22} & a_{23} \
a_{31} & a_{32} & a_{33}
\end{pmatrix}
glossy valveBOT
Why am. I here
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
thick hedge
this is sort of better
the square brackets are missing, but that's fine
\begin{bmatrix}
a_{11} & a_{12} & a_{13} \
a_{21} & a_{22} & a_{23} \
a_{31} & a_{32} & a_{33}
\end{bmatrix}
glossy valveBOT
Why am. I here
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
thick hedge
yeah, use this
thick hedge
no problem !
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opal pivot
How does the second picture come? Where is this n come from?
ivory cairn
E(xi) is the expected value of xi, which is mu.
the sum of a constant from 1 to n is just n times that constant.
opal pivot
Ok, I got what you mean
But I as you said that is from 1 to n
So that should be 1mu + 2mu +3mu....+nmu
that is big different.
opal pivot
E(xi) is the expected value of xi, which is mu.
the sum of a constant from 1 to ...
Hello
OMG, my bad
I got wrong
.close
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strong pawn
Show that Q is not finitely generated.
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Show that Q is not finitely generated.
next sail
contradiction
strong pawn
contradiction
Assume Q is finitely generated. But then we can always increase denominator. So is not. Good?
next sail
almost
strong pawn
??????\
next sail
need to be a bit more rigorous
for example if we assumed it was generated by 1/2 and 1/3 you can't use 1/6 as a counterexample
even though 6 > 2 and 6 > 3
you would want to use 1/5 or something
strong pawn
for example if we assumed it was generated by 1/2 and 1/3 you can't use 1/6 as a...
Assume Q is finitely generated. But then we can always increase denominator to the next prime since the set of primes is infinite. So is not. Good?
next sail
sure
maybe i would say a little more about why using the next prime works but that's basically it
strong pawn
maybe i would say a little more about why using the next prime works but that's ...
Cuz u cant reach the prime denominator with the previous numbers rite
strong pawn
but yeah that's the general idea
Assume Q is finitely generated. But then we can always increase denominator to the next prime since the set of primes is infinite, and we can't reach the next prime with the previous numbers in the denominator. So is not.
fathom saddle
Well, we can just add that prime in, and then we can generate all of Q, no?
strong pawn
Well, we can just add that prime in, and then we can generate all of Q, no?
since the set of primes is infinite
fathom saddle
How do you know we didn't get all the other primes too?
strong pawn
How do you know we didn't get all the other primes too?
If we got all the other primes then since the set of primes is infinite then the Q is not finite generated no?
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torn jolt
cos(x) = sin(90-x) - I understand this is the trig identity.
However...
cos(x+90) = sin(90-x-90)
How does this break down please? I thought it would be sin(90-(x+90)) no?
torn jolt
and that would be what
sin(90-(x+90))
I'm trying to understand how that isn't the case because of this:
the theta - 90 being there instead of theta + 90 is what is confusing me.
bro
sin(90 - (x+90))
the - changes parantheses sign
so it becomes
sin (90-x-90)
oh yeah I just see it now
I do this long enough since morning I start to go a bit crazy.
thanks
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torn jolt
I am so lost by ii
Explain to me the solution here it is
For S1 (1 digit numbers) it’s obvious
But for the 2 digit, why P(3,1)?
What are they permutating?
For S2, the sum 1+3+5+7 appears 3 times yes
fathom saddle
For every unit digit you choose, there's 3P1 choices for the second digit
torn jolt
For every unit digit you choose, there's 3P1 choices for the second digit
?
What do you mean by 2nd digit, isn’t the unit the digit the last one?
fathom saddle
Or, if you want to call it "the tens digit", sure
torn jolt
I’m lost lol
We are solving the total sum of unit digits
Then after we solve the sum of 10s, then hundreds then thousands
fathom saddle
So how many numbers in S2 have unit-digit 3?
torn jolt
I need to list them all?
fathom saddle
Bingo. So that adds 3×3 to the total
fathom saddle
We need to know how many there are.
torn jolt
Yes
So for the 1s
How many end with 1
3 again
And I would assume 3 end with 5
And 3 with 7
So you get 3x1 + 3x3 + 3x5 +3x7
Which is 3x(1+3+5+7)
fathom saddle
Ye, and you can see they have that as 3P1(1 + 3 + 5 + 7)
fathom saddle
Basically, because it will correctly get the amounts later on, when counting gets more difficult
There's 3P2 numbers, that have 3 digits, and end with 7.
torn jolt
And how did you find that
I mean I could list all the possible 3 digit numbers but that would be tedious
How do I do this in my head
Unless I don’t and I have to list them all
I may be lazy. When mathematicians need to solve problems do they brute force it first then try to find a pattern?
torn jolt
There's 3P2 numbers, that have 3 digits, and end with 7.
For the 3 digit numbers this was brute force:
Those are all the 3 digit numbers
fathom saddle
4×3P2
torn jolt
4×3P2
Ohhh that’s the amount of numbers
Yes there are 24
Still confused why they use permutation lol
They could simply say there are 6 x (1+3+5+7)
I think I am starting to understand @fathom saddle
Why they use permutation
Because if we choose 1 digit we have 3 left
Now if its a 2 digit one then we just need to choose 1
If it’s 3, we need 2
If it’s 4, we need 3
So that is why
I see
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peak pike
Any way to get x?
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granite torrent
Any way to get x?
if your diagram and labels are correct then no
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peak pike
.reopen
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peak pike
if your diagram and labels are correct then no
How so?
strong pawn
120 people say yes, and 80 people say no on a survey. P hat is 0.60. What's the sampling distribution of P hat?
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120 people say yes, and 80 people say no on a survey. P hat is 0.60. What's the ...
@strong pawn Has your question been resolved?
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gritty rose
!15m
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gritty rose
Also holy shit that's a lot to look at
still pasture
Also holy shit that's a lot to look at
ah sorry for that
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still pasture
is anyone here? just wondering
glacial pasture
my honest advice is that a barrage of images puts people off, i would just send them one at a time
still pasture
ah, good to know thanks!
azure burrow
if you have associativity do you have commutativity? a + (b + c) = (a + b) + c
granite torrent
if you have associativity do you have commutativity? a + (b + c) = (a + b) + c
not necessarily
azure burrow
hmm or is associativity just saying that it does not matter which operands you operate on first
hollow spire
Not always
azure burrow
I was trying understand why there was a group and a commutative group if a group must have associativity. I was thinking then wouldn't it also have commutativity. But I think I have my answer now? Is it just that commutativity says that the order in which the operands are listed does not matter, however that doesn't mean we can operate on the operands in whatever order we want? and Associtativty is saying we can operate on whatever operands we want but it does not say that the order in which they are listed does not matter. Now that I think about it, I would sometimes write associativity like this (a + b) + c = (b + c) + a, I believe this is not a correct way to represent associativity right since it is reliant on commutativity? If someone could clarify for me
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azure burrow
Also for the multiplicative identity must the element "1" be an member of R, just wanted to make sure
trail lance
if there is a multiplicative identity or unity, we usually name it 1, or denote it by $1_R$
glossy valveBOT
이재현
drifting trellis
Also for the multiplicative identity must the element "1" be an member of R, jus...
yes, the * operation only makes sense between elements of R
drifting trellis
I was trying understand why there was a group and a commutative group if a group...
and yes, associativity does not imply commutativity. the usual example is the group of invertible matrices under multiplication
trail lance
I was trying understand why there was a group and a commutative group if a group...
(a+b)+c=(b+c)+a is not a correct way
drifting trellis
associativity says (ab)c = a(bc) but there's nothing to make sure that (bc)a = a(bc). btw the + notation can be confusing when discussing commutativity in groups
because we are already used to some rules with +
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timber veldt
Tried finding the derivative of the equation and it was wrong
Started out the equation like this then used the product and chain rule
am i starting it wrong?
craggy tapir
you only differentiate with respect to L
timber veldt
you only differentiate with respect to L
Okay
craggy tapir
everything else are constants, so you can treat it like a number and throw it out of the derivative
timber veldt
Okay ill try
timber veldt
everything else are constants, so you can treat it like a number and throw it ou...
and the methods im using are okay? like the way i re wrote the function?
craggy tapir
yes
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opal pivot
I am wondering how does the second function in picture come?
opal pivot
I find the similar result here. But I am still confussing
languid junco
I am wondering how does the second function in picture come?
every element a, 2a, ..., (p-1)a is congruent to exactly one of 1, 2, ..., (p-1)
which is basically what you said
so where is the confusion coming from?
gritty rose
try writing out for a small prime like p=5 or 7 and any coprime a
opal pivot
so where is the confusion coming from?
For example, a congruent to 1 (mod p) how do we derive this?
gritty rose
For example, a congruent to 1 (mod p) how do we derive this?
no where is "a is congruent to 1 mod p" claimed
gritty rose
try writing out for a small prime like p=5 or 7 and any coprime a
do this
gritty rose
I find the similar result here. But I am still confussing
write this whole thing
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inland cloud
