@sinful mango Has your question been resolved?
#help-27
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sinful mango
nah not yet
hidden hinge
First find the volume of the cylinder, since you know the mass, $Density = \frac{Mass}{Volume}$ You can rearrange and solve for volume from mass and density.
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hamr
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visual brook
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visual brook
how did they get the interval for tan(t+ pie/4)
supple knot
how did they get the interval for tan(t+ pie/4)
That's the branch of tangent from the given initial condition y(0)=1
visual brook
That's the branch of tangent from the given initial condition y(0)=1
im a bit confused on what this means
supple knot
im a bit confused on what this means
Tangent function has different domains because it's undefined at specific points
visual brook
Tangent function has different domains because it's undefined at specific points
so how would i get the range of values
supple knot
Depends on the initial condition
visual brook
Depends on the initial condition
it shows on the bottom left
their initial conditions
supple knot
That's the branch of tangent from the given initial condition y(0)=1
Yes I said that already
visual brook
Yes I said that already
so what exactly shud i do
supple knot
Read this
visual brook
No
yea i dont understand the disconinuity for tangent
like isnt it -pie/2 to pie/2 is the range
supple knot
like isnt it -pie/2 to pie/2 is the range
The statement is about the domain of tangent, not range
Discontinuities refer to domain of functions, not range
supple knot
yea i dont understand the disconinuity for tangent
visual brook
The statement is about the domain of tangent, not range
oh yea i meant domain, so at n=0 its just -pie/2 to pie/2 but there is more depending on the multiple of n right
supple knot
I don't know what "more depending" is referring to
visual brook
I don't know what "more depending" is referring to
there are other domains depending on the initial condition?
supple knot
Correct
supple knot
https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:trig/x2ec2f6f830c9fb...
Watch this
supple knot
Watch this
.
supple knot
ok so heres what i found
?
visual brook
discontinuity is at pie/2 + npie
for y(0) = 0 , that means n is 0
so domain is from (-pie/2 to pie/2)
visual brook
discontinuity is at pie/2 + npie
actually isnt discontinuty plus or minus pie/2 + npie
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visual brook
?
nvm forget everytihng i said, but i got (-pie/4 to positive 3pie/4
because everyting shifts because of t+ pie/4
visual brook
?
ok so how does y = tan(t+ pie/4) shift to the left of the normal function tan(t)
i thought since its being added it would shift to the right
supple knot
No
visual brook
but yea my answers were flipped because of that
visual brook
https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:transformations/x2ec...
i get it now
visual brook
https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:transformations/x2ec...
so for non-linear equations were asked to find partial derivatives in terms of y and were asked to see if both the function and derivative is always continuous
how does that help us if partial derivative or the function itself isnt continuous
supple knot
What does this have to do with tangent function
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brazen halo
Need help with b, to sketch a graph but dont know where to start.
jade oak
Need help with b, to sketch a graph but dont know where to start.
You can sketch it on the interval -pi to pi right?
brazen halo
You can sketch it on the interval -pi to pi right?
Like this?
jade oak
Yeah
jade oak
Yeah
This interval is 2pi wide. There is a condition saying f(x)=f(x+2pi)
You can think about how to sketch the other parts by placing two fingers on the points at -pi and pi. By the earlier condition as you move your fingers, they will be at the same vertical height, so as one finger follows along the graph of the interval you drew, the other finger will be sketching in the intervals you havent drawn
Keep them the same horizontal distance apart so the condition x vs x+2pi is met
It may be obvious though without having to do this if you just think about it for a bit
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brazen halo
Hold on, still thinking this.
jade oak
Another way of thinking of this is that f(x)=f(x+a) is the definition of being periodic (it is also given in text the function is periodic) with period a. In this case a=2pi, and you already have an interval of 2pi, so you just need to copy that interval
brazen halo
So something like this?
jade oak
Yeah
jade oak
Take any point, move 2pi to the right, the output value is the same. The f(x)=x^2/pi is also obviously satisfied
brazen halo
So from here, The f(x)=x^2/pi, that function is the form of the quadratic function between -pi and pi?
jade oak
Yeah
brazen halo
Another question is, what is the maximum height?
jade oak
visually u can see it happens at -pi, which you can plug into the equation
Also happens at other places but -pi is part of the “base case” interval.
So you can directly plug it into x^2/pi
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brazen halo
Still processing and trying to understand this. Pls bear with me.
Discussing it with a friend. I think I will leave this convo open for the night.
wheat pawn
About the question of your maximum height.
If you want to do it analytically, you need to obtain the derivative of your function in the interval.
Then you need to check if there's any value of x that makes that derivative equal to zero.
The maximum value is either one of those, or one of the endpoints of the interval.
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stray cave
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stray cave
Hi need help on this question. I got 3 as my answer
am i supposeed to do (2^(4)-41)/(22^(2)-32+2) or (2^(4)-44)/(22^(2)-32+2)
so its either 0 or 3
plush vault
🤔
thick iris
It's been a long time since I did limits, but I believe you have to plug in (-2) in t's place and then reduce
long sundial
Yea
The limit is really easy in this example because nothing becomes 0 when putting -2 in
Sometimes this will happen and we'll need to use some special tricks first and then put in the limit
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wooden veldt
You must also check the points where the function is not differentiable
Yeah so look for points where the function itself is defined, but the derivative is not defined
wooden veldt
The min can either occur at places where the derivative is zero, or places where the derivative is undefined
winter patrol
considering a combination of range,domain,the above
wooden veldt
The min can either occur at places where the derivative is zero, or places where...
So unless you check both of these, you can't conclude there is no min
winter patrol
yes. the common way to find local min/max would be to first find the location of stationary points from f'(x) = 0
but as mentioned those aren't the only places local mins/max may occur
wooden veldt
Yes, but that is exactly "checking the points where the derivative is undefined"
winter patrol
or here, its also a boundary location
wooden veldt
Yes but that might be hard to do depending on the function
That's what derivatives are a tool for
winter patrol
or places where the derivative is undefined
when will
$$f'(x) = \frac{x}{\sqrt{x^2-4}}$$
be undefined
woven radishBOT
ℝαμΩℕωⅤ
winter patrol
and are there values there where $f(x)$ is defined
woven radishBOT
ℝαμΩℕωⅤ
winter patrol
not quite
you're including stuff outside of
between 2 and -2
to be more specific are there values between
-2 and 2 inclusive where
f(x) is defined
what about 2 and -2
is f(x) defined at -2 and 2?
that's how you'd use the derivative here to determine locations of other extrema
on from the range of the sqrt function, you've identified that there will be mins at these locations
calm maple
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calm maple
check if correctly mathematically written
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calm maple
<@&286206848099549185>
calm maple
😕
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grizzled harness
Two trains leave Toronto heading towards Ottawa.
Train A travels at a constant speed of 80 km/h.
Train B travels at a constant speed of 60 km/h.
However, Train B has already covered 30 km by the time Train A departs.
Determine when Train A will overtake Train B using equation(s).
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Two trains leave Toronto heading towards Ottawa.
Train A travels at a constant s...
grizzled harness
How can I do this?
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mighty copper
can someone please check if my prove is right
devout snowBOT
can someone please check if my prove is right
mighty copper
we had to prove its converging using monotonic convergent theorem
its dicreasing because denominator is bigger than the numerator. will that reasoning work?
to prove its bounded this is what i did:
1/(2n+1)! > 0
multipliying both sides by 2n-1 !
(2n-1)!/(2n+1)! > 0
since its bounded and dicreasing its convergant
to find its limit di di like
(2n-1)* (2n-2)...1/(2n+1) * (2n)*(2n-1)...1
1/(2n+1)(2n)
taking limits we get 1/infinity which is 0
so is my proof and working right?
alpine inlet
seems good to me
mighty copper
seems good to me
thanks. if you are free then can you check for another question??
ln(1+1/n) = an
taking its derivative we get -1/(n^2+n) which is always negative which means the function is dicreasing.
1+1/n > 1
ln(1+1/n) > ln(1)
ln(1+1/n)>0
which means its lower bound is 0 and its uppber bound is at a_1. so its bounded and monotone hence converging
alpine inlet
ye seems good
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bright juniper
a trapezoids bases are 4 and 12 i got a line that is parallel to the bases and it crosses the touching parts of the diagnals find the lenght of that line
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a trapezoids bases are 4 and 12 i got a line that is parallel to the bases and i...
hollow sparrow
bright juniper
Hi
lunar oar
the diagonal lines would cross in the center
so the horizontal line will be the line that is the average of both bases (in length)
bright juniper
Wrong
We don’t know the trapezoids legs and no one says that the diagnal lines would cross in the center
lunar oar
true
bright juniper
<@&286206848099549185>
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neon fable
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uncut crow
what a weird choice of variable name
restive river
I thought that e was supposed to be the nepper number
uncut crow
this whole problem is weird af honestly
restive river
doesn't that just end with e = e?
sand dove
it does
alpine inlet
First of all, the limit in there is e. Dunno if you'd have to prove that but it's a commonly known fact.
so, it's also e^1 and log_b(e^1)=1 can only hold if b=e
neon fable
First of all, the limit in there is e. Dunno if you'd have to prove that but it'...
yeah that much I'm aware of, I just... really don't know how to rewrite this equation in that manner
uncut crow
i think the question is poorly framed… whatever it’s supposed to be
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visual brook
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quasi acorn
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long sundial
What have you tried?
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restive lark
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restive lark
this is where i got substituting the polar form of z, but now im not sure what to do witht he d^2/dt^2
later the problem says:
"Note that z depends on time, meaning that both r and θ do, too. Use the product
rule to compute the second derivative with respect to time", but will i need to compute it if the equation is already second derivative = something?
does this mean that i evaluate the second derivative of the polar form of z first at the step i am currently on?
this is the whole problem
am i overthinking it and have already completed step 1, and am ready for step 2?
<@&286206848099549185> i am very lost on this problem
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wicked edge
I think it wants you to write the first as youve written, or to apply linearity to “simplify a bit”,
for the product rule, it wants you to apply this to the rcostheta and irsintheta because theta and r are functions of t,
The next two should follow readily
supple anchor
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supple anchor
Hi I genuinely don’t know how to do 3
How do I start
Do I split the x squared -1 into linear?
winter patrol
quotient remainder form
distant harbor
Use the definition of division
winter patrol
leave P(x) and Q(x) as P(x) and Q(x)
distant harbor
p(x) = q(x)*(x²-1)+(3x-4)
lost stream
hello
stuck field
What's your question again?
lost stream
this onee. This is a physics question under electric fields and its asking me to prove that the equation is equal to 4.9
stuck field
I saw the image the first time.
If your talking about 2. Then do note there's a diagram for 2. Which you've tried to hide.
And a lot of other details as well, please state the problem.
!original
devout snowBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
stuck field
Thank you!
Now asinine
This question talks about some previous question.
I wonder what that's about?
stuck field
Alright seems useless anyway.
stuck field
You have to find components of electric field?
lost stream
im really confused as to how to approach this because I have only simply tried putting in the components into the equation but always comes down to not being able to cancel the radicals
i found
a clearer image sorry
and that the charges are 12n/c
stuck field
Both q_1 and q_2?
lost stream
oh my bad
stuck field
Oh.
Well, if you know how components work
E_1 would be E_c cos(alpha)
Do you see that?
stuck field
Same for y.
That's it, I believe?
Or you want to see how exactly this E_c cos(alpha) comes from?
It's to do with vector addition
lost stream
Its just that my prof doesnt want us to use the component method but rather like what you said, vector addition
i dont know how to separate the terms
because technically i only have to add 2 vectors right
stuck field
Or you can find E_1 based on the fact E_1 is the electric field due to q_1
lost stream
because technically i only have to add 2 vectors right
how do you do this tho?
stuck field
What have you tried?
lost stream
i thought i got it but the radicals
lost stream
how?
stuck field
Do you know what it means to round off something?
lost stream
yes
stuck field
Then that's what you'd do.
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midnight bear
can someone please help me with part c?
devout snowBOT
can someone please help me with part c?
midnight bear
its my first course on real analysis, and I'm having trouble finding which direction to proceed with doing part c
I figure we need to show that each side is less than or equal to the other
so I showed that $\sup(A+B) \leq s+t$
woven radishBOT
goobybalooby
midnight bear
but I have no clue how to proceed from there. In a round a bout way, I used part (a) to prove the above inequality, so I'm assuming that proving the inequality facing the opposite direction likely involves what was proved in part (b), but I just dont see what they are getting at
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midnight bear
Wait where did that commenter go?
empty flame
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sacred thorn
sacred thorn
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sacred tiger
7 part c i need a bit of help understanding what im supposed to do
sacred tiger
I might need help with some key concepts because I wasn't able to attend the lecture for this and it wasnt recorded
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iron sun
What have you tried so far? And how did you do solve a) and b)? @sacred tiger
frail furnace
in a group of five men and four women, there are three pairs of male & female business partners and three teachers, where no teacher is in a business partnership. One man and one woman are selected at random. Find the probability that they are : EACH IN A BUSINESS PARTNERSHIP BUT NOT WITH EACHOTHER.
I'm just wondering why for the men it's 3/5 (im assuming this means 3 businessmen out of 5 men) but for women its 2/4
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in a group of five men and four women, there are three pairs of male & female bu...
stuck field
in a group of five men and four women, there are three pairs of male & female bu...
It's 2/4 wdym?
stuck field
What do you think it should be?
frail furnace
but how do u get 2/4
is it not supposed to be 3/4??
my thought process on this is 3/5 x (3-1)/4
idk how they got 2
stuck field
because 2 is infact 3-1?
frail furnace
why did they choose to minus it from the women though
and not the men
thats what im stuck on
rustic jetty
idk how they got 2
There is one woman teacher and another one is in a relationship with the man, so 4 - 1 - 1 = 2
stuck field
It's the same either way.
frail furnace
It's the same either way.
oh damn
stuck field
and not the men
It's either 1/20 * (3 * (3-1)) or 1/20 * ((3-1) * 3))
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mystic jetty
Can i solve thus with pythagreom (idfk how to spell it) theory
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Can i solve thus with pythagreom (idfk how to spell it) theory
@mystic jetty Has your question been resolved?
winter patrol
not in the way you want,
no
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winter patrol
pythag doesn't apply as you don't have a right triangle
mystic jetty
pythag doesn't apply as you don't have a right triangle
thank you
i forgot abt that
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muted blaze
hi i just want a pair of second eyes
devout snowBOT
hi i just want a pair of second eyes
muted blaze
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muted blaze
Im thinking the correct solve is an application of a balanced force
im thinking if its balanced, it will just maintain equilibrium/the velocity it already has
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formal bronze
Indeed.
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restive river
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restive river
I'm asked to prove this identity
tried working on the left side, but to no avail
the right side however
I know there's a way to seperate that fraction into two things
but I'm kinda slow rn
multiply cos(x)
on both sides
you know, I did try that
give me a sec
should work
okay I see where you're going with this
plush vault
you know, I did try that
Change LHS to sin and cos
restive river
but i'm still a tad bit confused
restive river
Change LHS to sin and cos
1/cosx+ sinx/cosx
plush vault
Then multiply with 1-sinx up and down
restive river
$\frac{cos^2x}{cosx-sinxcosx}$
woven radishBOT
mj
plush vault
Then multiply with 1-sinx up and down
Try this
restive river
Then multiply with 1-sinx up and down
for both terms?
plush vault
No in LHS
restive river
lhs being secx+tanx right?
midnight hinge
thoughts on this method
restive river
$\frac{1-sinx}{cosx-cosxsinx}+\frac{sinx-sin^2x}{cosx-sinxcosx}$
woven radishBOT
mj
restive river
$\frac{1-sinx+sinx-sin^2x}{cosx-cosxsinx}$
woven radishBOT
mj
restive river
$\frac{1-sin^2x}{cosx-cosxsinx}$
woven radishBOT
mj
plush vault
This is so simple how you making so complicated
restive river
$\frac{cos^2x}{cosx-cosxsinx}$
woven radishBOT
mj
restive river
$\frac{cosxcosx}{cosx-cosxsinx}$
woven radishBOT
mj
plush vault
You really fast
plush vault
Yeah 😅
plush vault
Just take common in demonitor and cut one cosx in numeroter
restive river
$\frac{cosxcosx}{cosx-cosxsinx}=\frac{cosxcosx}{cosx-cosxsinx}$
woven radishBOT
mj
restive river
$\frac{cosx(cosx)}{cosx(1-sinx)}$
woven radishBOT
mj
plush vault
Thank you
midnight hinge
nice ig
restive river
$\frac{cosx}{1-sinx}$
plush vault
It's so satisfying when you got a answer
woven radishBOT
mj
restive river
yep
especially with trig identities
you know you got it right when you get it right
this method is pretty clever though
but it seems almost predicted
that guy must've done the whole thing in his head
😭
midnight hinge
that guy must've done the whole thing in his head
he's good ig
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uncut mulch
hey i need help with this one
devout snowBOT
hey i need help with this one
sand dove
hint: you can start from last row and subtract the previous row.
and then find a pattern...
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uncut mulch
@sand dove hey if you know how to solve that cant you go on call with me and help me, this type of question im gonna have on exam, i know if i practice it well it could be easy
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clear cloak
A rectangular piece of cardboard measuring 25 inches by 47 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each such square. For what value of x will the volume be a maximum? If necessary, round to 2 decimal places.
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A rectangular piece of cardboard measuring 25 inches by 47 inches is to be made ...
clear cloak
I know that I need to find the volume
which is V= (47-2x)(25-2x)x
which is 1175x-144x^2+4x^3
but i got 0 idea what else to do after this step since i dont have a cal
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supple knot
but i got 0 idea what else to do after this step since i dont have a cal
Use derivatives to find the max of V
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vivid ermine
can someone help me with this?
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edgy ridge
for this question we've got: a triangle formed by A and B and C; I is the middle point of [BC]. we need to prove that vec(AB)^2 - vec(AC)^2 = -4 vec(AI)*vec(IB)
in this case vec(AB) means a vector from a going to b
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for this question we've got: a triangle formed by A and B and C; I is the middle...
alpine inlet
I assume you mean the length of the vector before squaring it
edgy ridge
I assume you mean the length of the vector before squaring it
what do you assume means that?
alpine inlet
I mean vec(AB)^2
edgy ridge
here is how my attempt went
edgy ridge
I mean vec(AB)^2
yeah
alpine inlet
idk, squaring a vector doesnt make sense
edgy ridge
idk, squaring a vector doesnt make sense
squaring a vector is the vector by the dot product of itself
so vec(u)^2 is vec(u) dot product vec(u)
alpine inlet
okay
edgy ridge
but my solution is a bit different from the solution
alpine inlet
in your first step, why should AB be the same as AI + IB?
alpine inlet
"a triangle formed by A and B and C; I is the middle point of [BC]"
I don't see this to be the same problem setup
edgy ridge
"a triangle formed by A and B and C; I is the middle point of [BC]"
I don't see ...
hmm true I haven't thought of that
one sec
alpine inlet
okay now I get it lol, was still thinking of vector lengths
edgy ridge
Yeah it still works that way
edgy ridge
here is how my attempt went
so in the last equation here vec(AI)^2 cancels out with - vec(AI)^2
my main problem is with these two
since I is the center of BC we can do vec(IC)=-vec(IB)
edgy ridge
which gets us close but the sign inverted
we get the following:
2 * vec(AI) * vec(IB) + 2 * (vec(AI)*vec(IB)
note that I filled the + in between the two sides because I changed IC to IB
the result is 4 * vec(AI) * vec(IB)
but the solution the exercise wants me to find is *vec(AB)^2 - vec(AC)^2 = -4 vec(AI)vec(IB) notice the minus sign
so it's either:
the solution is wrong
or I made a mistake somewhere
alpine inlet
from what I can tell you're correct
edgy ridge
and we haven't yet dealt with
alpine inlet
Does that not cancel out?
edgy ridge
hmmm
alpine inlet
IB = -IC
edgy ridge
doesn't the square affect anything?
oh
I guess if we think of them as lengths
then they cancel out
yeah so the answer is correct except for that minus sign
I'll ask my professor about it tomorrow
alpine inlet
maybe he intentionally gave you this so you don't use chatgpt to cheat, cuz chatgpt would imagine a wrong proof
edgy ridge
maybe he intentionally gave you this so you don't use chatgpt to cheat, cuz chat...
yeah maybe. glad I got a second opinion from you
well I'll mark this as solved for now
thanks for the help!
alpine inlet
welcome 😄
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brazen halo
Im trying to brush up my math skills. Need some explanation on this question.
When I move everything from the right side to the left side, becoming
-2x^2+5x+1=0
The roots are
x=0.1861 x=2.6861
When I move from left to right side, becoming
0 = 2x^2 - 5x - 1
or by switching sides
x^2+4x-1 = 9x - x^2
then becoming
2x^2 - 5x - 1 = 0
The roots are
x=2.6861 x=-0.1861
I put the equation on Symbolab and the latter is correct. Why do we have to switch sides?
devout snowBOT
Im trying to brush up my math skills. Need some explanation on this question.
Wh...
patent marsh
the roots are the same, they're just reflections of one another
-2x^2 + 5x + 1 (moved over to left side)
2x^2 - 5x - 1 (moved over to right side)
I think you had an arithmetic error
brazen halo
Ay yes sorry, the first part i forgot to put negative.
x=-0.1861 x=2.6861
The part where they are reflection of each other I understand. '
Does that mean all 4 x answers are correct?
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brazen halo
Just need this question answered.
devout snowBOT
@brazen halo Has your question been resolved?
brazen halo
ill just close it.
bold cypress
How will I find the highest frequency when there are 2 in this grouped data?
devout snowBOT
How will I find the highest frequency when there are 2 in this grouped data?
@bold cypress Has your question been resolved?
ivory quail
in e^x =5, why does x(1) = log5?
devout snowBOT
in e^x =5, why does x(1) = log5?
vestal dirge
do you know what e^x and log(x) are?
ivory quail
I'm aware of logarithims idk what the meaning of e^x is
vestal dirge
do you know what a function is?
eager nova
Do you know what is e?
wicked turtle
what do you mean by x(1), do you just mean x?
vestal dirge
what do you mean by x(1), do you just mean x?
Im asuming $x \cdot 1$
woven radishBOT
tobi
devout snowBOT
@ivory quail Has your question been resolved?
ivory quail
do you know what a function is?
Nah I just didn't pay attention to all of 4u advanced functions throughout the sem
grand lynx
i need help with the answers here
my gf is doing these and i honestly have no clue what the answer is
devout snowBOT
i need help with the answers here
my gf is doing these and i honestly have no cl...
grand lynx
supple knot
i need help with the answers here
my gf is doing these and i honestly have no cl...
How old are you
tender cobalt
that was quick
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whole grove
for this question:
we have 5 beers, 4 ciders, and 3 sodas
you want to get 8 drinks to go. What this means is that the order of the drinks no
longer matters - we only care about how many of each drink you have.
question: How many ways can you order 8 drinks if you order at least 2 of B1 and at least 1 of
C1?
how would i approach a q like this
inland seal
So you already have 2 beers and 1 cider, you just need to pick 5 more drinks
There are 3 beers, 3 ciders and 3 sodas left to pick from
In how many ways can you pick 5 drinks from those?
inland seal
I don't know what's B_1 or B_2
whole grove
like 5 beers
inland seal
im assuming all drinks of the same type are the same?
inland seal
so the beers are different?
whole grove
• 5 different types of craft beer, B1, B2, B3, B4, B5,
• 4 different types of cider, C1, C2, C3, C4, and
• 3 different types of soda, S1, S2, S3
yes
whole grove
• 5 different types of craft beer, B1, B2, B3, B4, B5,
• 4 different types of ci...
here?
inland seal
Yeah
What if all of our beers are of type B4?
We don't know how many
Also sorry I gtg, my food is ready
Maybe someone else can take over
whole grove
.close
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bright pawn
Hey guys. How do you graph a rectangle?
devout snowBOT
Hey guys. How do you graph a rectangle?
restive river
Hey guys. How do you graph a rectangle?
wdym by that exactly
bright pawn
I want to graph a rectangle on Desmos.
Not a circle.
Not an elipse.
But a rectangle.
Also, I want the lines to be connected, so I can actually see it. So not just four points.
inland seal
One way is to make a table
restive river
I want to graph a rectangle on Desmos.
just like write $y\le 3\set{0\le x \le 1}\set{y\ge 0}$ if you want
inland seal
Type "table"
woven radishBOT
restive river
and modify your values if you want to from there
inland seal
Type "table"
And then fill the points in clockwise or counter-clockwise order.
Press and hold left click on the colored icon, and mark the options "lines"
sand jetty
.close
halcyon yew
Your car is stuck in the snow. Desperate to leave the school’s parking lot, you ask your friend to help you push your car. Your friend does not want to help so they say, “Any force I apply to your car will be met with an equal force, creating a net force of zero; there will be no movement due of Newton’s Third Law.” What is your argument to prove your friend wrong?
devout snowBOT
Your car is stuck in the snow. Desperate to leave the school’s parking lot, you ...
halcyon yew
I dont get this
wicked turtle
that equal force acts on you, not on the car
devout snowBOT
@halcyon yew Has your question been resolved?
halcyon yew
that equal force acts on you, not on the car
?
quick radish
devout snowBOT
quick radish
Can anyone explain the underlined integration step?
supple knot
Can anyone explain the underlined integration step?
partial fraction decomposition
you can work backwards by just adding the 3 underlined terms using a common denominator
quick radish
partial fraction decomposition
can you elaborate?
supple knot
can you elaborate?
stark shuttle
Hello
stark shuttle
$\left[1:::::2\right]\left[3:::::4\right]=\left[1:::::2\right]\left[3:::::4\right]^T$
woven radishBOT
LE SSERAFIM
stark shuttle
Why does both equal 11
topaz beacon
the first one equal [3, 8]
elfin atlas
You can't multiply the first two matrices, 1×2 and 1×2
elfin atlas
😂😂😂 lmao
Since when are two 1×2 matrices multiplicable
stark shuttle
I'm so confused
stark shuttle
thats because those are vectors
So how do I compute dot products of (a, b) and (c, d)?
topaz beacon
(v1, v2) dot (w1, w2) = v1w1 +v2w2
stark shuttle
(v1, v2) dot (w1, w2) = v1w1 +v2w2
What about (a, b) and (c, d) transpose?
topaz beacon
thats just a matrix product then
topaz beacon
notice that your calculator assumed that when you meant to multiply, it assume dot prod
stark shuttle
notice that your calculator assumed that when you meant to multiply, it assume d...
I guess matrix multiplication and dot product are different?
topaz beacon
yes they are
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gloomy valve
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gloomy valve
Can someone help pls
devout snowBOT
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gloomy valve
<@&286206848099549185>
wicked turtle
show what this "constant sum" property is?
devout snowBOT
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tender grail
help
wicked turtle
is it some software doing the grading?
maybe it wants a decimal approximation
or maybe something stupid like ln(a/b) instead of ln(a) - ln(b)
your answer is right
tender grail
is it some software doing the grading?
Yes
wicked turtle
hmm
only a couple of things i can think of
maybe try ln((2 - sin(2)) / (1 - sin(1)))
or maybe log instead of ln
wicked turtle
ah bummer
software just seems wrong then
,w integrate (1 - cos(t)) / (t - sin(t)) from t = 1 to t = 2
tender grail
right then thanks
woven radishBOT
tender grail
yeah just doesn't work tho
wicked turtle
yea sorry, no idea, do you have an instructor you can ask
wicked turtle
sure, gl, hope it works out
tender grail
.close
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brisk star
Matrix square roots are expensive to compute, so is there a faster way to get from F to the eigen values of U?
devout snowBOT
Matrix square roots are expensive to compute, so is there a faster way to get fr...
brisk star
Matrix square roots are expensive to compute, so is there a faster way to get fr...
Can I just get F^TF, get its eigen values, and take their square root?
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thick wadi
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thick wadi
Need help with B
Hello
<@&286206848099549185>
<@&286206848099549185>
Helloooo
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@thick wadi Has your question been resolved?
white lava
what do they mean by restrictions right here?
devout snowBOT
what do they mean by restrictions right here?
lost laurel
values that x can't take I think
white lava
values that x can't take I think
how do i find restrictions?
lost laurel
is the function defined at 1 and -1?
raven stream
what do they mean by restrictions right here?
This question is not worth a dollar bet
devout snowBOT
This question is not worth a dollar bet
white lava
what
hollow hollow
how do i find restrictions?
Bro u need to tell that x is not equlatl to this
Equal
white lava
Bro u need to tell that x is not equlatl to this
how do i do that
raven stream
what do they mean by restrictions right here?
First step
white lava
First step
thats wrong
you can just get rid of the denominators
they equal
you can do x^2 + 2x-1 = 2
i think
elfin atlas
but make sure that you write x!={-1,1}
elfin atlas
why?
because {-1,+1} are not in the domain of the function
x/(x-1) at x=1 is 1/0
1/(x+1) at x=-1 is 1/0
both are not defined so
devout snowBOT
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frigid jetty
well
maybe 1/2(7x+10)?
so did you get answer
both ig
do you have an answer sheet
or whatever
yeah
we did inverse
damn
we have to multiply left side
not right
by1/2
yeah
what you got
devout snowBOT
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weary hedge
I don't understand how the numerator was factored. I don't get the factoring common terms
- 10 - 5, shouldn't it be still 5√ 3?
devout snowBOT
I don't understand how the numerator was factored. I don't get the factoring com...
lunar harbor
I don't understand how the numerator was factored. I don't get the factoring com...
$5 \cdot 2-5 \cdot \sqrt 3$
woven radishBOT
Civil Service Pigeon
devout snowBOT
@weary hedge Has your question been resolved?
weary hedge
I don't get it just because when the common term is 5,
10 = 2
5 = 1
isn't it? I am pondering on how it was really factored.
or is it valid that i just cancel out the two fives in the numerator with the 5 in the denominator?
lunar harbor
Yeah 5 is a common factor, so you cancel it
weary hedge
.close
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fluid flax
In the mathematical models used to describe the evolution of a disease, the average number of new infections that each infected person causes in the population is called RO. When this number is less than 1, each infected individual transmits the disease to, on average, less than one person and the disease tends to disappear. Conversely, if RO is greater than 1, the disease spreads and an epidemic occurs. When an effective vaccine against the disease is discovered, the epidemic can be controlled by vaccinating only a proportion p of the population. This is known as herd immunity. Indeed, once a proportion p E(0,1) of the population has been vaccinated, the new RO, which is called effective and denoted by Re, is the product of the original RO by the proportion of individuals who are not vaccinated , 1-p. And control of the epidemic is achieved if Re is less than 1.
c) Express, in general, the minimum population threshold that needs to be vaccinated as a function of the RO value of a disease Sketch this function for RO values between 1 and 20.
devout snowBOT
In the mathematical models used to describe the evolution of a disease, the aver...
fluid flax
I don't understand why the statement says that if R0 exceeds 1 there is an epidemic and if it is lower the disease disappears. And in question c) it says that R0 has to vary between the values 1 and 20.
<@&286206848099549185>
.close
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spring pollen
,tex d/dx sin \sqrt {cos x ^3}
devout snowBOT
,tex d/dx sin \sqrt {cos x ^3}
woven radishBOT
LeAbhi
d/dx sin \sqrt {cos x ^3}
```Compilation error:```! Missing $ inserted.
<inserted text>
$
l.49 d/dx sin \sqrt {
cos x ^3}
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.
LaTeX Font Info: Trying to load font information for OT1+lmr on input line 4
9.
(/usr/local/texlive/2023/texmf-dist/tex/latex/lm/ot1lmr.fd```
obsidian elbow
Do you know and understand the chain rule?
devout snowBOT
@spring pollen Has your question been resolved?
spring pollen
Do you know and understand the chain rule?
yes
just dont know how does root derivative work
spring pollen
ohh
bold drum
**LeAbhi**
```latex
d/dx sin \sqrt {cos x ^3}
```Compilation error:```! Missing...
or in your case it would be ^3/2
coral wraith
how would i do this problem?
devout snowBOT
how would i do this problem?
coral wraith
there must be an easier way than what im thinking
dense lynx
sounds like a job for “Newton’s Sums”
would recommend reading about it if you don’t know what it is
devout snowBOT
@coral wraith Has your question been resolved?
coral wraith
sounds like a job for “Newton’s Sums”
would recommend reading about it if you d...
But we didn’t learn about them in class
I’ll use them though
red viper
if you don't know Newton's sums, you can use this: $$x^{n+1}+y^{n+1}=(x+y)(x^n+y^n)-xy(x^{n-1}+y^{n-1})$$
woven radishBOT
Alisia
devout snowBOT
@coral wraith Has your question been resolved?
coral wraith
Thanks
devout snowBOT
@coral wraith Has your question been resolved?
devout snowBOT
@coral wraith Has your question been resolved?
coral wraith
if you don't know Newton's sums, you can use this: $$x^{n+1}+y^{n+1}=(x+y)(x^n+y...
how would i use this?
anyone?
<@&286206848099549185>
.close
devout snowBOT
coral wraith
.reopen
devout snowBOT
✅
coral wraith
how would i do this problem?
Anyone? How would I do this
weak salmon
Hmm. At least you can formulate that (x-r)(x-s) = 0 ; that might get you somewhere.
Even more useful: the r and s have the form of a-z and a+z. Now your problem looks like (a-z)^10 + (a+z)^10, where probably quite many coefficients disappear if you carefully start expanding that.
Hmm, what you get is 5 terms, all having an even number of z's there (odd ones cancel each other out), so your square roots disappear. I think it's manageable expansion -wise.
coral wraith
Hmm, what you get is 5 terms, all having an even number of z's there (odd ones c...
possibly
dense lynx
**Alisia**
this pretty much details the exact method / recursion you're supposed to use
if you know how to find the sum of the roots and the product of the roots using vieta's, then consider the case where n = 1, and you can work up until n = 9
devout snowBOT
@coral wraith Has your question been resolved?
pulsar relic
so i did this work, but i dont know what the question is trying to ask of me for c? like are they trying to ask me when y = 0 x = 5?
also is my other work right?
devout snowBOT
so i did this work, but i dont know what the question is trying to ask of me for...
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
weak cove
so i did this work, but i dont know what the question is trying to ask of me for...
What're the marks for?
weak cove
I mean is this a test/exam?
pulsar relic
no not a test / exam at 5:31am 😬
weak cove
The world doesn't share a universal timezone :p
pulsar relic
kms if i had an exam at 5:31am 😭
opal cloak
so i did this work, but i dont know what the question is trying to ask of me for...
didnt check ur other work, but look at the both the graphs, what no you notice about the points when f'(x)=0
pulsar relic
didnt check ur other work, but look at the both the graphs, what no you notice a...
when f'(x) = 0 the x value is 5?
or is it trying to allude that f(x) has its roots there....
opal cloak
dont worry about x and y values
opal cloak
or is it trying to allude that f(x) has its roots there....
got the right mindset sort of
maybe make a line at x=5
pulsar relic
oh! then...when f'(x)=0, f(x) = 0
opal cloak
oh! then...when f'(x)=0, f(x) = 0
thats not true
opal cloak
yeah that is true, but more specifically its when f(x) has a turning point
pulsar relic
ohhh.........hmmm
is turning point at f'(x) a key concept?
and by turning point we mean when f(x) goes from negative slope to positive slope?
opal cloak
yeah, at that exact point f(x) will have no slope
well not no slope but rather its just a flat line
pulsar relic
does this concept pop up more the further into calculus courses?
opal cloak
yeah it will
pulsar relic
what is the usefulness of it? if you can say it in words to help me know the importants better
is it like..when setting the derivative of a function to 0 we will find turning points for functions of higher degree which have many
opal cloak
is it like..when setting the derivative of a function to 0 we will find turning ...
yeah
opal cloak
x^3 would have 2 turning points and we can find two points
not always true
opal cloak
yeah
pulsar relic
discriminate? omg theres so much math
pulsar relic
😄 ill take it
pulsar relic
discriminant, but lcose
discriminant is b^2 -4ac
what does -b/2a find? its been so long since i touch those concepts
opal cloak
point of symmetry
devout snowBOT
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zealous gull
.reopen
Soo... my question was closed for inactivity, sorry about that... How did they get from the first line to the second using the formulas down? X,A are matrices, x,u,v_k,a are vectors
devout snowBOT
Soo... my question was closed for inactivity, sorry about that... How did they g...
@zealous gull Has your question been resolved?
zealous gull
umm
we can do something else with the trace
x^T A x = Tr(Axx^T)
so
we can replace the trace with
(v_k-u)^T A^-1 (v_k-u)
and then we can derive using (d/dx) {x^Ta}=a
devout snowBOT
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@zealous gull Has your question been resolved?
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thorn bramble
In year $N$, the $300^\text{th}$ day of the year is a Tuesday. In year $N+1$, the $200^\text{th}$ day is also a Tuesday. On what day of the week did the $100^\text{th}$ of year $N-1$ occur?
woven radishBOT
Musab
devout snowBOT
In year $N$, the $300^\text{th}$ day of the year is a Tuesday. In year $N+1$, th...
@thorn bramble Has your question been resolved?
terse leaf
Why do we have trigonometry, but don't have tetragonometry? 🧐
devout snowBOT
Why do we have trigonometry, but don't have tetragonometry? 🧐
lost laurel
what would tetragonmetry even be? The study of the relationship between the sides of a quadrilateral and its angles?
terse leaf
The exact same thing as for triangle, but for quadrilateral, right
winter torrent
dense lynx
🤔 every quadrilateral is a composition of two triangles if that helps
terse leaf
So last two messages want to say triangles are more fundamental for geometry that even gained own trigonometry topic
restive river
The exact same thing as for triangle, but for quadrilateral, right
firstly
trigonometry wasnt really made for triangles it was made for circles
terse leaf
restive river
study some history you would get it how it got from circles to triangles
terse leaf
Triangles were used to calculate chords? I suppose
Anyway, I got answers clarifying my vision for geometry so thanks for responses
.close
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supple knot
Do you know the y-intercept of your equation
Yes. Now which option has that y-intercept
Depends on the lines
Just learn to plot 2x+3
Depends on the imaginary 2 lines you're making up
2 is the slope of 2x+3
Do you know how to plot a line of slope 2
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short iron
Does this make sense for 10a? which(x,y : capital(x,y) and small(y))
devout snowBOT
Does this make sense for 10a? `which(x,y : capital(x,y) and small(y))`
@short iron Has your question been resolved?
flat raft
I need help to prove, if $f'(x)$ is even and $f(0)=0$, then $f(x)$ is odd
woven radishBOT
shrödinger
flat raft
<@&286206848099549185>
vital pasture
What proof techniques have they taught you so far?