i dont
#help-27
stuck field
Then you should know a geometric progression has something called common ratio.
Aware?
trail apex
ah yes i see
stuck field
Alright.
So in this question, you would form two equations.
And you have two variables also.
One is this very common ratio.
And the other one is the first term.
So let us assume the first term is a and the common ratio is r.
Alright?
trail apex
is there any chance u could show me on paper
stuck field
I could write it down for you.
trail apex
that would be great thanks
trail apex
yes
stuck field
Alright. Before I write anything.
Can you write "nth" term in a geometric progression?
You said you can.
Earlier.
stuck field
Yes.
trail apex
which is just 2^n
stuck field
Yes.
Now, can you do it for general values.
For example, the first term being a and the common ratio being r
trail apex
nope dont thnk so
woven radishBOT
What the hell am I doing here?
stuck field
Isn't this essentially what you did too? When you wrote it earlier.
stuck field
It's fine.
Now you know.
Now in your question.
You have been given the value of this expression
At n = 4 and n = 6
Right
trail apex
yes
woven radishBOT
What the hell am I doing here?
stuck field
Yes?
trail apex
whered u get r3 from?
stuck field
n being 4
trail apex
oh yes
stuck field
n-1 would be 3
stuck field
Now you do the same for 6.
Can you write what the equation is going to be?
It's exactly like this.
trail apex
a . r ^5 = 5 root 2 / 8
trail apex
quite confused
stuck field
We're dividing the equation you wrote by the one I wrote.\
$\frac{ar^5}{ar^3} = \frac{5 \sqrt{2}}{8} \div \frac{5 \sqrt{2}}{4}$
trail apex
right
woven radishBOT
What the hell am I doing here?
stuck field
Right now, look carefully.
trail apex
40 root 2 over 20 root 2
stuck field
That one was wrong...
trail apex
oh 20 root 2 over 40 root 2
stuck field
Yep.
trail apex
so its root 2 / 2 root 2
stuck field
Which is just 1/2
stuck field
r^2 = 1/2
That's all.
You now have r.
Use the value of r in one of the above-mentioned equations to get a.
And be sure to mention all this in your work, because apparently they want that. And you need a. So figure that out.
trail apex
wait im confused
how do i use the value sorry
@stuck field
where do i sub it into
trail apex
1/2
stuck field
No?
stuck field
No?
trail apex
oops
stuck field
r is neither 2 nor 1/2
r^2 = 1/2
This is what you had.
How do you get from here to r = 2?
trail apex
sorry
stuck field
No, don't be sorry. I'm not scolding you or anything. Just asking.
trail apex
i thought r meant like common ratio or something like that
trail apex
right ok
stuck field
well
We're only considering the postive solution.
$r^2 = \f{1}{2}$\
$\sqrt{r^2} = \sqrt{\frac{1}{2}}$
Oops
woven radishBOT
What the hell am I doing here?
trail apex
oh i see
stuck field
So what's r?
trail apex
root 1 over 2
stuck field
root 1 is just 1.
So 1/root2
trail apex
so do i now do 5 root 2 over 4 divided by 1/root 2 cubed?
trail apex
yes thank you
stuck field
You're welcome.
timid sonnet
question
timid sonnet
a train has a length of 220m
at 09 30 the train crossed a bridge of length 1400m
Calculate the time in seconds that the train took completely cross the bridge
ancient furnace
at 09 30 the train crossed a bridge of length 1400m
Does it give velocity?
devout snowBOT
pseudo basin
devout snowBOT
Available help channel!
jagged orbit
I'm struggling pretty horribly trying to understand trigonometric identities and how to factor them.
(√2sinx + 1) (√2sinx -1) + (sinx) (sinx) (sinx) (sinx) is as far as i'm getting and I'm just unsure of the steps for factoring a problem like this.
devout snowBOT
I'm struggling pretty horribly trying to understand trigonometric identities and...
raven leaf
I'm struggling pretty horribly trying to understand trigonometric identities and...
set $z = \sin^2(x)$
woven radishBOT
Xetrov
south shard
^ if you make that substitution it looks like an easily factorable quadratic
devout snowBOT
jaunty mantle
Do you know how to plot straight lines on a graph
nova idol
youre not finding the slope
youre just setting the two equations equal to find their intersection point
jaunty mantle
Plot the 2 lines first
When you draw a function on a graph
every point on that line contains pairs of numbers that fit (x, f(x))
By drawing 2 system of equations
The point at which they intersect has the values where (x, f(x)) satisfies both equations
jaunty mantle
Do you know how to plot straight lines on a graph
So no
Try substitute in y= 0
Solve for x
So for the first equation y=-x-2
If y=0, x=-2
So the point (-2, 0) is in the function
Do the same for x=0
We choose 0 because it more often than not makes it easier to solve
We just need 2 points then we can draw a straight line through them
devout snowBOT
@restive river Has your question been resolved?
devout snowBOT
@restive river Has your question been resolved?
tight estuary
is it possible to plot functions in terms of y into a t-84?
devout snowBOT
is it possible to plot functions in terms of y into a t-84?
@tight estuary Has your question been resolved?
tranquil hare
OKAY so the question is regarding finding profit and marginal profit for a company based on a model
devout snowBOT
OKAY so the question is regarding finding profit and marginal profit for a compa...
tranquil hare
light fractal
what is "monthly demand" defined as?
tranquil hare
demand is a piece used to find revenue right?
light fractal
is demand how many people purchase the product?
tranquil hare
its the economic term for how much people want to purchase the product
err
how many units of the product will be sold based on consumers willing the purchase
but anyways
So I start by creating a model for profit
which would be R = x((60000-x)/20000) to get revenue and then
P = x((60000-x)/20000) * (50000+.56x) right?
light fractal
profit = revenue - expenses so why are you multiplying?
tranquil hare
....Oh damn I didn't even notice LOL
so changing the sign to -,
I'd do P(20001) - P(20000) right?
or could/should I simplify it first?
...
@dry robin
Uhhhh??
devout snowBOT
@tranquil hare Has your question been resolved?
devout snowBOT
@tranquil hare Has your question been resolved?
tranquil hare
.close
pine phoenix
how would i even figure this out
devout snowBOT
how would i even figure this out
pine phoenix
.close
cloud thicket
devout snowBOT
cloud thicket
Im confused with proofs
I tried HL it didn't work and even though sss works where all sides are equivalent it said it wasn't congruent
pulsar hinge
k so idr this stuff tbh
but
i reccomend
zooming the pic in
kinda unclear
for those that can help
prolly be easier to for clear pic
pulsar hinge
yea that stuff is clear
sorry i cant help
but for those that can
this is better
cloud thicket
oh
cloud thicket
ok
pulsar hinge
last time i did somethign like that and no one told me and i got the assignment late
so i thought itd be better to let you know
devout snowBOT
weary canopy
#27 and 28
devout snowBOT
@weary canopy Has your question been resolved?
jolly merlin
,rotate
woven radishBOT
burnt breach
Having trouble with this. I know it’s not B or C so it’s gotta be A or D, but I can’t figure them out
jolly merlin
Having trouble with this. I know it’s not B or C so it’s gotta be A or D, but I ...
Please create a separate help channel #❓how-to-get-help
jolly merlin
28 is also wrong, try writing cos(theta) first
devout snowBOT
@weary canopy Has your question been resolved?
jovial mauve
devout snowBOT
pseudo basin
what are the symptoms of your wrongness?
oh, may you perhaps have incorrectly normalized the second column?
the norm of [2; 1; -2] is not sqrt(5).
pseudo basin
columnwise normalization feels like something you could have done programmatically, by the way.
if you're using python anyway...
jovial mauve
It is given that BB^{T} is an identity matrix
(in the answer)
Are there any other mistakes I've made?
pseudo basin
do you ask because you are second-guessing yourself or because you are getting a wrong-answer popup in your face
jovial mauve
This was the output and it's not the answer I'm supposed to get.
pseudo basin
that's because the answer is a set of four binary choices, i would think.
jovial mauve
pseudo basin
you are presented with four checkboxes
presumably, the choice of ticking or not ticking each of those boxes would constitute the answer to the problem.
and that is a different beast than the matrix numpy outputs for you.
jovial mauve
Yes, it's a Multiple Select question (MSQ)
pseudo basin
cool, that gave us zero new info.
i'm saying that there is nothing strange about your output not being the answer.
jovial mauve
It is given in the answer key that BB^{T} is the identity matrix
jovial mauve
However this was what I got.
pseudo basin
yes
can you tell me what the value of the (2, 1) entry of your matrix is
or at least its order of magnitude
jovial mauve
-1.00636560 * 10^{-16}
pseudo basin
x for multiplication grumble grumble
but yes, it is something on the order of 10^-16.
that should strike you as familiar if you know anything about how numbers are usually stored in computers.
if it does not, then say so.
vast rain
you could also use sympy or similar symbolic thing and not deal with stuff like this
pseudo basin
i think there is value in at least knowing about stuff like this.
but i shan't say a word until hazysleet tells me he knows it or doesn't but wants to.
vast rain
I mean yeah definitely, like this is basic mathematical understanding / debugging skills
jovial mauve
but i shan't say a word until hazysleet tells me he knows it or doesn't but want...
I don't know.
jovial mauve
No, I wanna know
vast rain
do you know what the e-16 means
vast rain
so how big is the number in that slot?
vast rain
so what can you say about the output that you gave?
jovial mauve
The numbers with e-16 and e-17 are very close to zero
But, why is it like this?
Is this how python works with numbers
vast rain
do you think a computer can store an infinite number of decimal digits?
jovial mauve
No.
vast rain
so what would you expect
vast rain
okay so suppose it does that
why do you expect the output to be exactly the identity then?
pseudo basin
spoilers at the end: ||a double-precision floating point number can store about 16 or 17 decimal digits' worth of significant figures||
vast rain
you can also use sympy which doesn't store the numbers themselves if it's inexact
devout snowBOT
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Available help channel!
torpid ocean
devout snowBOT
https://media.discordapp.net/attachments/441487635630784512/1085495158394589184/...
stone stump
gcd(b,c) is a common divisor of a and b
torpid ocean
yes it is
stone stump
so it has to be <= the greatest common divisor
torpid ocean
how
stone stump
by definition of what greatest means
stone stump
same thing just rearranged
torpid ocean
why is it now gcd(a,b) <= gcd(b,c);
stone stump
gcd(a,b) is a common divisor of b and c
so it has to be <= their greatest common divisor
devout snowBOT
devout snowBOT
Available help channel!
fleet gorge
Find k every value for which p(-1;2x;x²) and q(5;k;k) vectors make acute angle for any x value
devout snowBOT
Find k every value for which p(-1;2x;x²) and q(5;k;k) vectors make acute angle f...
@fleet gorge Has your question been resolved?
fleet gorge
<@&286206848099549185>
devout snowBOT
@fleet gorge Has your question been resolved?
lost gazelle
can anyone tell me why is this wrong? my teacher said finding the solution is tricky, and it could be more than one answer
devout snowBOT
can anyone tell me why is this wrong? my teacher said finding the solution is tr...
topaz beacon
What is the above tree diagram?
left robin
i think they talk about problem 3
devout snowBOT
@lost gazelle Has your question been resolved?
stone stump
B can play so that A cannot win. maybe they mean that? otherwise not sure what your teacher means
devout snowBOT
@lost gazelle Has your question been resolved?
tall knoll
h = 32000/x^2 no? That's the first thing I see that may cause issues
Second, using product rule seems unnecessarily complicated for the 2nd term
I'd say so
tulip crown
Can someone help me please?
tulip crown
<@&286206848099549185>
supple knot
,rotate
woven radishBOT
supple knot
what inequalities do you know
tulip crown
I dont know how to solve it
I found that the function x*arctan(x) -ln(x^2-1) is increasing
But i don t know how to continue
@supple knot if you know some inequality that might help please tell me
supple knot
I found that the function x*arctan(x) -ln(x^2-1) is increasing
x^2-1 or x^2 + 1?
tulip crown
+1
supple knot
I found that the function x*arctan(x) -ln(x^2-1) is increasing
if you did this on the right interval, then you're done?
tulip crown
Sorry
supple knot
f(x) <= g(x) implies int f(x) <= int g(x)
maybe 0<=f(x) is also needed but you have that in this case
supple knot
I found that the function x*arctan(x) -ln(x^2-1) is increasing
what domain did you prove this for
supple knot
then yea you're done?
tulip crown
Why?
supple knot
f(x) <= g(x) implies int f(x) <= int g(x)
unless you need to prove this
supple knot
what's p
supple knot
f(x) <= g(x) implies int f(x) <= int g(x)
what's f and g here?
for your problem i mean
tulip crown
x*arctanx and ln(x^2+1)
supple knot
reversed, but yea
tulip crown
I need to show that the function h , where h(x)= x*arctanx-ln(x^2+1) is bigger than 0
supple knot
no you don't
supple knot
maybe 0<=f(x) is also needed but you have that in this case
you need to show log(x^2 + 1) >= 0
tulip crown
Well that doesen t solve my problem
supple knot
yes it does
supple knot
x*arctanx and ln(x^2+1)
type explicitly what f(x)=? and g(x)=? equals
supple knot
x*arctanx and ln(x^2+1)
these are your two options
supple knot
f(x) <= g(x) implies int f(x) <= int g(x)
to plug into this
tulip crown
If h is bigger than 0 that means x*arctanx>ln(x^2+1) thus int of f(x) > int g(x)
f(x)=x*arctan(x)
supple knot
f(x)=x*arctan(x)
nope
supple knot
reversed, but yea
.
supple knot
f(x) <= g(x) implies int f(x) <= int g(x)
following this
supple knot
f(x) <= g(x) implies int f(x) <= int g(x)
this eliminates the need for your h(x) altogether
supple knot
f(x) <= g(x) implies int f(x) <= int g(x)
are you SURE you understand this?
tulip crown
Yes
supple knot
I found that the function x*arctan(x) -ln(x^2-1) is increasing
rearrange this and express this function in terms of f(x) and g(x)
supple knot
let f(x) be x* arctanx and g(x) be ln(x^2+1)
no
tulip crown
What no
tulip crown
Why nope
supple knot
are you SURE you understand this?
.
tulip crown
You asked me to write what g and f are
tulip crown
And how do you plan to solve it
supple knot
you're just confusing yourself by inventing a new function
supple knot
f(x) <= g(x) implies int f(x) <= int g(x)
this is all you need
supple knot
maybe 0<=f(x) is also needed but you have that in this case
and the one after
tulip crown
How do you show that f(x)<g(x)
supple knot
you said you already did that
supple knot
you're just proving the integral inequality aren't you?
tulip crown
I did not
tulip crown
you said you already did that
I did not
supple knot
tulip crown
I proved that g-f is increasing
supple knot
I proved that g-f is increasing
this
supple knot
How do you show that f(x)<g(x)
implies this
tulip crown
Well it is clear to me that you dont know what increasing means
It doesent mean that g-f is bigger than 0
supple knot
The domain neede for the integral ,[sqrt(2),sqrt(3)]
yes you also need a domain. which you already said you found
supple knot
what domain did you prove this for
which is why i asked it early on
tulip crown
Yes, and mai question was how do i prove that -f(sqrt(2))+g(sqrt(2)) is bigger than 0
supple knot
Yes, and mai question was how do i prove that -f(sqrt(2))+g(sqrt(2)) is bigger t...
where did you ask this
supple knot
...
supple knot
Well i dont know how to show that f(sqrt(2) )>0
where did you define f here?
tulip crown
Because you firstly reffered to x*arctanx-ln(x^2+1) as f(x)
supple knot
Because you firstly reffered to x*arctanx-ln(x^2+1) as f(x)
where
tulip crown
maybe 0<=f(x) is also needed but you have that in this case
.
supple knot
Well it is clear to me that you dont know what increasing means
idk do i even know what increasing is?
restive river
]
keen nacelle
which part
restive river
entire thing
restive river
]
how do ik if it's bias or not
i was gonna say
it's bias because
relative frq isn't the same for all
keen nacelle
so you can work out the relative frequencies right?
keen nacelle
relative frq isn't the same for all
yes
restive river
so you can work out the relative frequencies right?
somewhat
keen nacelle
it says an unbiased dice would have 50 for each
restive river
it says an unbiased dice would have 50 for each
o
restive river
relative freq is just freq/300 here
i gte that\
keen nacelle
went a lot harder very quickly lmaoo
restive river
went a lot harder very quickly lmaoo
yuh
lilac frost
restive river
a/(a^2 +b^2)
no
devout snowBOT
@restive river Has your question been resolved?
devout snowBOT
@restive river Has your question been resolved?
smoky gyro
can you tell if a quadratic function function is even or odd by looking at its power, for example x^2 - 9x + 7 is even?
supple knot
are there any odd quadratic functions?
are you sure the question isn't about even or not even?
smoky gyro
are you sure the question isn't about even or *not even*?
Well I just came up with it at the top of my head
I just want to know how to determine if a quadratic function is odd or even
I know x^3 is odd and x^4 even and x^1 is odd
I want to know if that sort of rule applies to when there’s other variables in the function
weak cove
those are polynomial functions
quadratics are either even, or if they are adjusted off of the origin (like it would be if you say subtract 9x) then they are neither even nor odd
but they are never odd
for polynomials without any sort of adjustment it depends on the power of x, so is x is raised to an even power it is even, and if to an odd power it is odd
and quadratics specifically are polynomials of degree 2, meaning they are raised to an even power of 2
supple knot
Well I just came up with it at the top of my head
weak cove
so if they aren't adjusted off the origin they will be even
devout snowBOT
@smoky gyro Has your question been resolved?
smoky gyro
so if they aren't adjusted off the origin they will be even
Oh okay
jolly swan
How i know if a interval is continous
devout snowBOT
How i know if a interval is continous
scarlet sequoia
you mean function is continuous on the interval?
uneven bloom
could someone walk me through this problem?
For the following exercises, eliminate the parameter t to rewrite the parametric equation as a Cartesian equation.
devout snowBOT
could someone walk me through this problem?
`For the following exercises, elimin...
hybrid snow
!status
devout snowBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
hybrid snow
Recall that $e^{-2t} = (e^{-t})^2$. This means that $x = (e^{-t})^2$. Isolate $e^{-t}$ in terms of $x$.
woven radishBOT
Umbraleviathan
hybrid snow
@supple knot starting to think it's a bit hard to read or nah?
uneven bloom
im still confused, could i do this in terms of ln?
woven radishBOT
Astassa
hybrid snow
Yeah but I would just keep it as $\sqrt{x} = e^{-t}$
woven radishBOT
Umbraleviathan
hybrid snow
Because $y = 2e^{-t}$
woven radishBOT
Umbraleviathan
hybrid snow
So you just replace e^-t
supple knot
<@261933205387477002> starting to think it's a bit hard to read or nah?
i think it's fine!
hybrid snow
Yeah
woven radishBOT
Astassa
hollow pollen
how would one go about c
devout snowBOT
how would one go about c
hollow pollen
it is clear that 3SAT is in NP
is there an easy way to write any SAT into a 3SAT?
i think i know how to deal with an even number of literals per clause
but then
how do you deal with odd numbers of literals
suppose you have 4 literals
x1 or x2 or x3 or x4
is it valid to write y1 = x3 or x4
and then write
x1 or x2 or y1 = x1 or x2 or x3 or x4
yes
.close
pseudo jacinth
I have a lot of potatoes, oil, and rice at home, but I would like to eat sushi. What to do? My Japanese neighbour will surely give me wasabi if I bring her both beef and fries. With potatoes and oil, I can make fries as well as potato salad (as much as required, of both). For sushi, I need fish and rice and wasabi. My other neighbor (who just turned veggie) will certainly give me fish and beef if I get him some rice and potato salad.So in the end, will I be able to have my sushi? Please answer this question using resolution.
devout snowBOT
I have a lot of potatoes, oil, and rice at home, but I would like to eat sushi. ...
pseudo jacinth
discrete math problem
devout snowBOT
@pseudo jacinth Has your question been resolved?
devout snowBOT
@pseudo jacinth Has your question been resolved?
devout snowBOT
@pseudo jacinth Has your question been resolved?
nova idol
discrete math problem
vast rain
what have you tried
this seems like an application of some everyday logic
maybe you have to formalize it but you should at least be able to answer the question with a yes/no
devout snowBOT
@pseudo jacinth Has your question been resolved?
jaunty dagger
devout snowBOT
jaunty dagger
how would i split this up to use partial fractions?
graceful cosmos
A/x + (Bx+C)/(x² + 2x + 5)
hexed ocean
how do you do 21a?
devout snowBOT
how do you do 21a?
cursive totem
have you tried drawing it out
hexed ocean
I can't really draw it out if i don't know any points
fathom thicket
how do you do 21a?
i wouldve done $A = \frac{1}{2}| (A_2 - A_1) \cross (A_3 - A_1)|$
woven radishBOT
doctor99268
hexed ocean
**doctor99268**
what is A1 A2 A3
fathom thicket
the question litearlly tells you
fathom thicket
@hexed ocean they are coordinates
vector coordinates
@hexed ocean how much of vectors have you learnt
hexed ocean
let me see
oh i havent learnt crap about them
we went over them for a few weeks
but thats it
fathom thicket
then you wont know how to use my method
hexed ocean
:(
hexed ocean
whats that
fathom thicket
to put it simply, the cross product between 2 vectors, gives another vector that is perpendicular to both of them
hexed ocean
ah ok
fathom thicket
and the magnitude of that vector is the area of the parralelogram made by the 2 vectors
and since the triangle area is half that area
its why i did 1/2
you can achieve the same area though
if you just draw everything out
but for me i find that very long
hexed ocean
I can probably do it with distance formulas and what not
but idfk what they mean by making trapeziums
and dropping perpendiculars
.close
devout snowBOT
fathom thicket
.reopen
devout snowBOT
✅
fathom thicket
@hexed ocean
this is what they mean
find the area of the triangle
by findin the area of the total rectangle
and minusing it from the areas that arent the triangle
youll get the right answer by doing this
fathom thicket
honestly though, you should learn what cross product is, itll be advanced for you, but it makes vectors alot easier
like, if two vectors are collinear
the cross product between them is 0
doing the cross product itself is just something you memorise
restive river
Hello i wanna check this result but wolfarmalpha is not responding ,w integration of x ^ n * e ^ (- k * x ^ m) dx 0 to infi = n!/k^(n+1)/m
devout snowBOT
Hello i wanna check this result but wolfarmalpha is not responding ,w integratio...
restive river
whats the integral meant to be
,w integration of x ^ n * e ^ (- k * x ^ m) dx 0 to infi
woven radishBOT
restive river
whats the integral meant to be
This ^^
too many constants bro
wtf is the original problem lol
vale dew
Isn’t that similar to gamma function?
restive river
wtf is the original problem lol
Its not a problem its just a general result that is mentioned in our book
woven radishBOT
Ann
pseudo basin
@restive river is it this result
restive river
<@456226577798135808> is it this result
In the power those n+1/m are together
pseudo basin
ok then you misplaced your parentheses
and it's meant to be $$\int_0^{+\infty} x^n e^{-kx^m} \dd{x} \overset?= \frac{n!}{k^{(n+1)/m}}$$
woven radishBOT
Ann
pseudo basin
i am highly sus of it tho
restive river
,w integration of x ^ n * e ^ (- k * x ^ m) dx 0 to infi
But why it is not responding to this input?
restive river
pseudo basin
for n=0, k=1, m=2 it gives 1 as the value of the integral
and yet
,w int[0,infty] exp(-x^2) dx
woven radishBOT
pseudo basin
what, exp(-x^2)?
vale dew
No
restive river
For that integral
Oh can you please share?
vale dew
For this
pseudo basin
ok then out with it
restive river
I do know how to calculate using u sub but it will take ages
vale dew
pseudo basin
,rccw
woven radishBOT
pseudo basin
When 2=n, x=alpha and m=4
x=alpha?
restive river
,w integrate x²e^(-alphax⁴) dx from 0 to infi
restive river
it's k that is alpha
Uh its a question that i solved which involves this result
So just to verify
Itbwas this precisely
woven radishBOT
restive river
Uh
restive river
Are you sure it's correct?
restive river
Uh
So the numerator should be (-1/4)!
If it was ((1-n)/m)! Then it would have made sense
But i am really not sure
,w integration of x ^ n * e ^ (- k * x ^ m) dx 0 to infi where n=1,k=1,m=827
woven radishBOT
restive river
,w ((1-n)/m)!/(m(k^((n+1)/m))), where n=1,k=1,m=827
woven radishBOT
restive river
,w integration of x ^ n * e ^ (- k * x ^ m) dx 0 to infi where n=1,k=1,m=8
,w ((1-n)/m)!/(m(k^((n+1)/m))), where n=1,k=1,m=8
,w calc gamma(2/827)/827
restive river
,w (1/((k ^ ((n + 1)/m) * (m))) * ((n - m + 1)/m)!), m=2, n=2, k=1
,w integration of x ^ n * e ^ (- k * x ^ m) dx 0 to infi where m=2, n=2, k=1
restive river
,w Gamma symbol capital
woven radishBOT
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sonic ravine
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sonic ravine
i have a problem
i want to put in {7 <= y <= 10} but it doesnt let me
whenever i put it in, the line on the graph disappears immediately
i want the line to show just from y = 7 to y = 10
sonic ravine
can you graph 7<=y<=10 as its own thing
i put it in a blank one
it still disappears
pseudo basin
does it show you a ⚠️ symbol
sonic ravine
yes
pseudo basin
what does it say if you click on that
sonic ravine
oh
it only works for x and y
because i put z in there
is there any way to fix?
or do i just change back to x as variable
pseudo basin
... you didn't tell me what it says when you click on the warning symbol
sonic ravine
ah yeah
i was just trynna make it smth diff, not x
but ig i have to make it x
ty
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wraith dirge
can someone explain steps pls
devout snowBOT
can someone explain steps pls
wild aspen
For the first fraction, multiply $(x^{2}+5x+4)$ to the numerator and denominator
woven radishBOT
RomeNunt
wraith dirge
first one as in (2x-5)/(x^2+5x+4)?
wraith dirge
Then subtract or add the terms in the numerator
Sorry do u mind explaining a little more in depth
it's not making sense to me
wild aspen
Could you vc, it's hard to explain with text
wild aspen
nah, vc private
kind cedar
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kind cedar
what do they mean by a function f from [1,5] to [1,7]
restive river
domain = [1,5] and [1,7] is the codomain
restive river
yeah
restive river
yw :)
restive river
yeah
peak bear
How I find the volume of the body limited by this equation in cylindrical coordinates?
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How I find the volume of the body limited by this equation in cylindrical coordi...
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@peak bear Has your question been resolved?
restive river
For elimination you need the same x or y, in this case none are the same
So you can find the lcm and then multiply to get the same number
For x it would be the least common multiple of 250 and 1, which is 250 so you multiply the bottom equation by 250
For y it would be the least common multiple of 150 and 1, which is 150 so you multiply the bottom equation by 150
Yeah true, the top equation can be simplified to 5x - 3y = 43 but it’s not needed
mild ore
Hi can someone help me? I have to prove that the only null Lagrangians are the total derivatives?
devout snowBOT
Hi can someone help me? I have to prove that the only null Lagrangians are the t...
mild ore
The converse is easy to enough to prove
To be precise I am only interested in the case for a Lagrangian with up to second order derivatives
I tried this but
Got stuck with this pde
flat mulch
is this a right triangle
mild ore
This was after proving that a null lagrnagian must be a of the form g(x,y,')y"+h(x,y,y')
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weary holly
is this a right triangle
No
solemn ginkgo
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visual lark
can someone help me solve this equation? https://gyazo.com/ce5e4d058964d2d8e614db66c5fd81f3
devout snowBOT
can someone help me solve this equation? https://gyazo.com/ce5e4d058964d2d8e614d...
austere hollow
I think you might be going the wrong way using the tan fucntion
and having a cosx as the denominator
visual lark
I checked It should work since cosx is not = 0
although I do not see any other way atm
austere hollow
I'd suggest you try to use the fact that cos(a-b)=cosacosb+sinasinb
you know that indentity ?
visual lark
yes
austere hollow
aight lemme give you a hint
visual lark
yes
austere hollow
using the identity I told you aboce
above
and now you can solve knowing that x is in 0 2pi
visual lark
although how did you get this?
austere hollow
you know 1/2 = cos(pi/3)
visual lark
yes
visual lark
although I do not know how I would think of this on my own (;
austere hollow
for the trig functions
austere hollow
yea no problem it'll come with time
I mean I haven't fully thought about, it might work
juste seems pretty sketchy
austere hollow
yea yea it's allowed cause 0 pi and 2pi arent solutions
but we don't really knoiw how to solve these kinds of equations
visual lark
.close
vagrant zodiac
Need help with understanding spectral decomposition. I understand that it is supposed to be a way to express a matrix as a sum of spectral matricies and eigenvalues like $$A=\lambda_1 v_1 v^T + \lambda_2 v_2 v^T ...$$ but when I attempted to find the SD of $$A =\begin{pmatrix} 4 & 1 \ 1 & 4\end{pmatrix}$$, I ended up getting the original matrix times 2.
$$\lambda_1=5, v_1 = \begin{pmatrix} 1 \ 1\end{pmatrix} \lambda_2=3, v_2 = \begin{pmatrix} -1 \ 1 \end{pmatrix}$$
$$5 \begin{pmatrix} 1 & 1 \ 1 & 1 \end{pmatrix}+3 \begin{pmatrix} 1 & -1 \ -1 & 1 \end{pmatrix} = \begin{pmatrix} 8 & 2 \ 2 & 8 \end{pmatrix}$$
plz halp :3
devout snowBOT
Need help with understanding spectral decomposition. I understand that it is sup...
woven radishBOT
Giga5
vagrant zodiac
do I have to normalize the eigenvectors first?
torn vessel
yes
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signal ginkgo
hello, I am stuck in solving this task, we are not allowed to use L'hopital's rule I need to expand the fraction with something, I tried both the upper and lower part but I can't finish it. (Btw solution is -1)
devout snowBOT
hello, I am stuck in solving this task, we are not allowed to use L'hopital's ru...
woven radishBOT
wooden veldt
you probably want to rationalise the denominator
signal ginkgo
I tried to do the difference of squares above, but the lower part of the fraction is constantly tending to zero
wooden veldt
difference of squares how?
signal ginkgo
grand siren
,rotate
woven radishBOT
supple knot
I tried to do the difference of squares above, but the lower part of the fractio...
well you have to multiply it out and simplify
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supple knot
,rotate
woven radishBOT
supple knot
okey, now i got -x up, but how to make lower part just x?
oh i missed it the first time. you rationalized the numerator instead of the denominator
should be sqrt(1+x) +1 instead
signal ginkgo
Okey, now this ugly part is up, it needs another rationalization, but how? This is a new topic to me i am really sorry if i am a bit boring😅
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gilded wharf
Hey guys can you please check if I did this question correctly?
devout snowBOT
Hey guys can you please check if I did this question correctly?
gilded wharf
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gilded wharf
<@&286206848099549185>
<@&286206848099549185>
Come on guys I spent 9 hours thinking about this question 😩
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gilded wharf
<@&286206848099549185>
small nest
What is the problem?
gilded wharf
<@&286206848099549185>
gilded wharf
<@&286206848099549185>
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jade falcon
is the following statement correct?
If the enlargement factor is F, then the pressure on the bottom face of the cuboid is = pressure * F.
pseudo basin
you are using the letter F to refer to two different things are you not
jade falcon
so it means that is the enlargemnt factor is 25 then force in the eqaution of pressure is also 25
at least thats what i thinl
thats the qeustion that i was asked
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woven radishBOT
benevo
jade falcon
but how
sly viper
V is volume
n is moles (quantity of gas)
R is a constant
T is the temp. of the room```because the gas is in a sealed vessel n cannot change, and T is ignored as it assumed that the gas will reach the same room temp after some time as in the initial conditions.
and because r is a constant it can be ignored
so we have the simplified formula for gas pressure change with volume change
$PV=C$
woven radishBOT
benevo
sly viper
where C simply remains constant
P is the pressure of the gas, to find force you multiply the pressure by the area it is exerted upon to get a force measurement.
$Pressure * Area = Force$
woven radishBOT
benevo
sly viper
does this all make since so far?
jade falcon
ya
sly viper
can you finish the problem with the information I have provided?
jade falcon
ya i think so
sly viper
respond to my last message if that changes, good luck. :)
jade falcon
ok, thanks a bunch
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vapid flare
i need help
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boreal blaze
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