oh
#help-36
muted ore
Basically its the same as saying det = lambda_1 * lambda_2
should be equal to height x length
which is true ?
desert mantle
yes
desert mantle
well now the corners are at other places
muted ore
determinant formula doesnt change
so its correct that its 1
1 * 1-lambda * 0 = 1
as for L_a(M) im not 100% sure
desert mantle
if only you had done the previous step properly instead of skipping it halfway through
muted ore
what was the proper way ?
desert mantle
well I tried to tell you several times
desert mantle
for example I described it here
muted ore
right, so we times A with a vector (v1,v2) where v1 and 2 are between 0 and 1
desert mantle
yes
muted ore
and then ?
Why between 0 and 1 anyways when the question wants lambda set to 2 and 3 for example
desert mantle
because (v1,v2) is in M
muted ore
So what happens after we times it with values between 1 and 0
We get a matrix like
0.5 0
0 0.5 for example
muted ore
How do you want to multiply a 2x1 with a 2x1
desert mantle
they are from the start
muted ore
Yeah and they can be from 0 to 1
Times the matrix we can get a matrix with:
0.5,0
0,0.5
desert mantle
why should we get a matrix
we are doing $\begin{pmatrix} 1 & 0 \ 0 & 1 \end{pmatrix} \cdot \begin{pmatrix} v_1 \ v_2 \end{pmatrix}$
soft zealotBOT
Denascite
desert mantle
that will give you a vector
muted ore
**Denascite**
I thought we are doing
v1 * (a,b)
muted ore
that will give you a vector
Yes, okay
muted ore
because its stated here
v1 * ... + v2 * ...
anyways
if v1 and v2 = 0.5 and lambda 1 and lambda 2 = 1, then we get a vector (0.5, 0.5)
The point is that v1 and v2 between 0 and 1 form a square when multiplied with the original A
and you can shift the values of lambda to get different squares
the corners still remaining the same
muted ore
yes
corners move
but you still have the position being equal to (0,0), (lambda1, 0), (0, lambda2), etc
that is always the same
desert mantle
yes
muted ore
right
idk how to show that L_a(M) = 1 here
determinant is 1 because: 1 * 1-lambda * 0 = 0
desert mantle
what is A*v where v are the corners (0,0), (0,1), (1,0) and (1,1)
muted ore
(0,0), (lambda, 1), (1,0), (lambda+1, 1)
desert mantle
draw that
muted ore
mhm
ah, I see
height = 1
its just that position is lambda, 1 and lambda+1, 1
which also shows that the width is only 1
nice
desert mantle
well width is the wrong word here
final saddleBOT
@muted ore Has your question been resolved?
muted ore
.close
tranquil pine
\textbf{Question:} A class in advanced physics is composed 10 juniors, 30 seniors, and 10 graduate students. final grades show that 5 of the juniors, 10 of the seniors, and 5 of the graduate students received an A for the course. If a student is chosen at random from this class and is found to have earned an A, what is the probability that he or she is a senior?
\vs{5 mm}
\textbf{My attempt:}
\vs{3 mm}
Let $A$ be the event that someone receives an A \[2 mm]
Let $B$ be the event that someone is a senior. Then: [
\m\P{A\cap B} = \f{10}{50} = \f15 \
\m\P{A} =\f{20}{50} = \f25
]
which implies [
\m\P{B\given A} = \f{\ff15}{\ff25} = \f12
]
final saddleBOT
\textbf{Question:} A class in advanced physics is composed 10 juniors, 30 senio...
soft zealotBOT
robust mulch
Yeah
final saddleBOT
final saddleBOT
Available help channel!
full pagoda
could someone please help me with this?
final saddleBOT
could someone please help me with this?
full pagoda
I have one more try left
stone wagon
is this a test
final saddleBOT
@full pagoda Has your question been resolved?
final saddleBOT
@full pagoda Has your question been resolved?
final saddleBOT
@full pagoda Has your question been resolved?
final saddleBOT
@full pagoda Has your question been resolved?
green ibex
!status
final saddleBOT
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
thick ledge
line 3 to line 4
pale oracle
You removed the parentheses after 6
thick ledge
$$6(2x^2-x-8x+4)=0$$ is correct, and your grouping is right, but you need to make sure theyre all in parenthesis like so
$$6(x(2x-1)-4(2x-1))$$
soft zealotBOT
light
pale oracle
You should focus on the inside
tranquil flume
Wdym by "x term"?
4(2x-1) itself is a term
Just get rid of the 6 from second line
Divide both side by 6
Life easier
fossil shuttle
did I match them correctly?
fossil shuttle
.close
gusty pond
Which proof is better for if n^2 is even integer, then n is even integer
gusty pond
n^2/2 = even number
((N x N))/2 = even number
N Must be an even number
<@&286206848099549185>
final saddleBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
@gusty pond Has your question been resolved?
urban maple
What do you mean which proof is better?
You proved the contrapositive (n odd implies n^2 odd) and that's valid
your direct proof needs to be worded with the same rigour that you had above i.e. n^2 = 2k, for some integer k, show that this implies that k also needs to have a factor of 2, so you really have n^2 = 4 j (or whatever number) so n = 2 k
gusty pond
What do you mean which proof is better?
Which is more accurate?
final saddleBOT
Which is more accurate?
gusty pond
They both work, I am pretty sure
urban maple
if they both work then they're both accurate, one isn't more accurate than the other
gusty pond
if they both work then they're both accurate, one isn't more accurate than the o...
Which one do you prefer as a mathematician?
urban maple
because of the difference in rigour of how you wrote them, I like the contrapositive one better. Your direct proof needs some work. But all else being equal, there's no preference on contrapositivse vs direct proof. The thought is usually if there's a direct proof, why not go for it?
also your direct proof isn't right maybe? why does n^2/2 have to be even? If n^2 is even, all we know is that n^2/2 is an integer
tranquil crest
What would be a good way to describe complex numbers?
final saddleBOT
What would be a good way to describe complex numbers?
soft zealotBOT
SWR
urban maple
In what sense?
final saddleBOT
@tranquil crest Has your question been resolved?
polar tulip
How to solve a 2 step linear equation
final saddleBOT
How to solve a 2 step linear equation
rotund citrus
add or subtract to isolate terms with the variable on one side, then divide both sides by the coefficient of the variable.
i.e.
4x + 7 = 9 given
4x + 7 - 7 = 9 - 7 subtract
4x = 2 simplify
(4x)/4 = 2/4 divide
(4/4)x = 1/2 simplify
x = 1/2 answer
@polar tulip Has your question been resolved?
shut willow
I need help with these questions. For 57 so far I have that x = salary of warehouse manager
final saddleBOT
I need help with these questions. For 57 so far I have that x = salary of wareho...
@shut willow Has your question been resolved?
final saddleBOT
@shut willow Has your question been resolved?
trail fern
convert from polar to rectangular coordinate
r^2 = 3cos(theta)-5rsin(theta)
ancient thistle
Why is the modulus only in sin(theta)?
trail fern
modulus?
trail fern
oh thats just the way the problem is gaven to me
ancient thistle
Didn't you learn polar coords as "x + yj = rcos(x) + rsin(x)"?
ancient thistle
What is the question exactly?
trail fern
trail fern
just need to convert into rectangular coordinate but im not sure if i should have done conversions first or multiply both sides by r
.close
faint panther
I need help translating a word problem into a standard form
final saddleBOT
I need help translating a word problem into a standard form
sly rapids
and the problem is?
faint panther
and the problem is?
I'm on number 2 right now
marsh temple
,rccw
soft zealotBOT
sly rapids
@faint panther what did you do so far
sly rapids
@faint panther how about you take the number of 4 pound balls as x
Now if you read it again, you'll know that the number of 3 pound (B) balls are 2x-1
There you have a linear equation
final saddleBOT
Available help channel!
fiery rose
Can someone explains why it's<1 and <2 pls
final saddleBOT
Can someone explains why it's<1 and <2 pls
strange rune
wdym why?
why its different?
just study the given functions and you'll see those are probably the best constants
strange rune
study the function
differentiate it, find the maximum, stuff like that
or just bound it
with inequalities
fiery rose
differentiate it, find the maximum, stuff like that
Maximum is just >0 ?
fiery rose
Can I just sub y->infinity ?
strange rune
why would you?
its helpful to say that the function is bounded
because its continuous
but it doesnt give you the bound
fiery rose
Isn't continuous mean the left hand side must be equal to the right hand side too?
strange rune
left hand side and right hand side of what?
fiery rose
left hand side and right hand side of what?
The limit is equal
shut adder
how do i get 2-0/4-0? wasn't it 4-0/(7-0)?
final saddleBOT
how do i get 2-0/4-0? wasn't it 4-0/(7-0)?
@shut adder Has your question been resolved?
zenith sierra
final saddleBOT
@shut adder Has your question been resolved?
edgy ibex
Trying to figure out how I solve #5 I’ve gotten 51 and 23 as the possible measures but I don’t know if I did it the right way
final saddleBOT
Trying to figure out how I solve #5 I’ve gotten 51 and 23 as the possible measur...
torpid meteor
Not clear
edgy ibex
#5
I need to find measure Z
I’m not sure if I did it right but I think the measures are either 33 23 or 51
.close
final saddleBOT
final saddleBOT
Available help channel!
tranquil charm
how should i determine which sets of matrices are linearnly independent and which are not?
final saddleBOT
how should i determine which sets of matrices are linearnly independent and whic...
tranquil charm
sets: ${(M1),(M2),(M3)}, {(M1),(M2),(M4)}, {(M1),(M3),(M4)}, (M2),(M3),(M4)}$
soft zealotBOT
Slowaq
tranquil charm
matrices
${(M1),(M2),(M3),(M4)} =
{ \begin{pmatrix}
1 & -1 \
-1 & 1
\end{pmatrix}
\text{,} \begin{pmatrix}
1 & 1 \
1 & 1 \
\end{pmatrix}
\text{,} \begin{pmatrix}
1 & 0 \
0 & 1 \
\end{pmatrix}
\text{,} \begin{pmatrix}
-1 & 1 \
1 & -1 \
\end{pmatrix}}$
soft zealotBOT
Slowaq
final saddleBOT
@tranquil charm Has your question been resolved?
tranquil charm
<@&286206848099549185>
scarlet sequoia
how should i determine which sets of matrices are linearnly independent and whic...
Matrices n*n are just vectors of R^(n^2) written differently, so use the same technique you were using for (dis)proving independence in R^n
final saddleBOT
@tranquil charm Has your question been resolved?
tranquil pine
the tangent plan to a graph for a function is (f(x,y) = xy + y^2*x + x^2 in the point (1,0,1)
final saddleBOT
the tangent plan to a graph for a function is (f(x,y) = xy + y^2*x + x^2 in the ...
tranquil pine
first i find the gradient for f_x and f_y
then i take my point (x=1, y=0, z=1) and insert it
tranquil pine
then i get
dry light
plug in the point first for fx and fy
tranquil pine
2(x-1)+1*(y-0)+z0
2x-2+y+1
= 2x-1+y
but why do i need to add the z0 at the end?
@dry light
I've solved it, but i dont understand why the z_0 is there
final saddleBOT
@tranquil pine Has your question been resolved?
zinc slate
can a critical reagion of binomial distribution be an 'equal' sign?
final saddleBOT
can a critical reagion of binomial distribution be an 'equal' sign?
final saddleBOT
@zinc slate Has your question been resolved?
zinc slate
<@&286206848099549185>
final saddleBOT
@zinc slate Has your question been resolved?
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@zinc slate Has your question been resolved?
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@zinc slate Has your question been resolved?
inner wind
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shadow aspen
Why are you evaluating f at those specific values (2.2,2.4,2.6…)
Also you can’t say f(a+b)=2^a+2^b (I think thats what you are doing but I cant really tell)
inner wind
cause the function is 2^x and delta x is 0.4 so the middle of that is 0.2
inner wind
Also you can’t say f(a+b)=2^a+2^b (I think thats what you are doing but I cant r...
i originally did 2^1.2 but my sum was wrong so i thought maybe the mistake was not spliting it
but its still wrong 
shadow aspen
cause the function is 2^x and delta x is 0.4 so the middle of that is 0.2
Ok I agree with this, but I do not see how you are jumping from this to that. the function f passes through the mid point of each rectangle. You want to get the height of each triangle. To do this you need to evaluate the function at the x values that are midpoints of the rectangles
shadow aspen
Yeah I like that much more
inner wind
im not geting exactly the midpoint of each rectangle
im getting the midpoint of the first
adding 0.2 which is the left point of the next
and so on
inner wind
Yeah I like that much more
great! let me see if that fixes my bug
thanks that worked!
shadow aspen
Nice
smoky bane
How do I not get this wrong? I can sort of do it but I only get it second try bc my first one is always wrong!!!!!
For this I found x by making y a 0 so it’s gone and same for finding y. I got
X = 3
Y = -1.5
Ok so 2 of the options have a y intercept of -1.5 how do I determine which of the two is correct?
final saddleBOT
How do I not get this wrong? I can sort of do it but I only get it second try bc...
fossil geyser
Just for clarity, you narrowed it down to which two options? @smoky bane
smoky bane
The second and the last
fossil geyser
Above is > and below is < right
that will work if you solve the inequality for y first
smoky bane
How?
fossil geyser
like y = mx+b form
smoky bane
Ohhh
fossil geyser
except it won't be =
smoky bane
It’s in standard form right now ?
fossil geyser
yes
smoky bane
How can I change to ymxb form
fossil geyser
would you know how to do it if it was an = sign instead of > or <
fossil geyser
yeah
you've got 2x-4y all on that side
so what can you do to get rid of the 2x?
and just leave -4y
smoky bane
-2x
fossil geyser
yeah
smoky bane
Ok ok
fossil geyser
so now you've got what
smoky bane
-4y > 6 -2x ? I think I accidentally changed the sign here
smoky bane
Divide -4
fossil geyser
yep
and when you divide by a negative number, the inequality sign changes direction
smoky bane
Y < -1.5 + 0.5x ?
fossil geyser
since you divided by a negative number, -4, the inequality sign flips
so it should be y <
actually, for figuring out which side of the line is shaded, that's the only thing that matters
is whether or not you need to flip the >/< sign
smoky bane
And to figure it out I need to change to y intercept form?
smoky bane
Are they easier
fossil geyser
sorta, but you need to be able to move equations around like you just did anyway
smoky bane
Yes I should practice
fossil geyser
like in general for your class
but yes, you can also figure out which side of the line needs to be shaded by just choosing a point on one side and seeing if it works for the inequality
which is probably easier
smoky bane
Would I choose the one inside or outside of the shaded area?
Bc they told us to pick a point and try it but I didn’t know which one
fossil geyser
yes
if you pick a point above the line and plug it in, and the inequality is true
then shade above the line
otherwise, shade below the line
it should always be true for one side or the other
smoky bane
Hi can you please help me again?
There is a question “describe the graph of y > mx, where m > 0” but I don’t understand this.. m is greater than 0 ok but what’s next
@fossil geyser
fossil geyser
do you have choices or is it open ended?
fossil geyser
ok well
what can you tell me about the graph of y > mx
if m > 0, in other words m is positive
fossil geyser
yes exactly, it has positive slope
or you could say it's increasing
what else can you say?
fossil geyser
y can be anything, positive or negative
fossil geyser
just like x can be anything, (x,y) can be any point on the graph
whether or not that point is shaded in is whether or not the inequality is true (in this case, if y > mx is true)
remember before once you put it in y > mx + b form
you could see whether it was shaded above or below
smoky bane
Yes
fossil geyser
that's something else you can describe about the graph
smoky bane
And it would be dotted line right
fossil geyser
yes, awesome
dotted line with a positive slope
I think there's a couple other things you can say
smoky bane
Ok it says correct and I see other possible answers where it passes through the origin
How to tell?
Is it bc there’s no + b because it’s 0 ?
fossil geyser
np 👍 good work
final hornet
final saddleBOT
final hornet
Hi, I'm a bit lost doing this question, I am trying to write the constraint and draw the pictures, but I don't know how to do it.
final saddleBOT
@final hornet Has your question been resolved?
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@final hornet Has your question been resolved?
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@final hornet Has your question been resolved?
final saddleBOT
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Available help channel!
coral bluff
final saddleBOT
soft zealotBOT
! What the hell am I doing here?
final saddleBOT
@coral bluff Has your question been resolved?
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@coral bluff Has your question been resolved?
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Available help channel!
plush ember
is this correct
final saddleBOT
is this correct
plush ember
Also correction
It should be (2x * 2x * 2x)/(6x * 6x * 6x) but the xs' would just cancel out
random forge
,rccw
soft zealotBOT
soft zealotBOT
plush ember
what's the limit going to? 0?
yes
plush ember
if so your answer is indeed right
alright thank you
random forge
plush ember
is there a better method of solving it tho because i feel my method is not very traditional
random forge
I'm sure there is but I don't have time to look at it too much, hopefully someone else can help
opal plinth
$\frac{sin^3(2x)}{sin^3(6x)} = (\frac{2}{6}\frac{sin(2x)}{2x}\frac{6x}{sin(6x)})^3$
soft zealotBOT
Nel
opal plinth
$$\lim_{x \to 0} \frac{sin(ax)}{ax} = 1$$
soft zealotBOT
Nel
soft zealotBOT
Nel
opal plinth
@plush ember
plush ember
**Nel**
nvm i see, yea this is the same thing i did, i just didnt need to expand the equation
thanks
opal plinth
plush ember
<:catthumbsup:614540188747563008>
now for the stuff i dont get, application of derivatives, im not quite sure where to start on this
so i know for (a) you find (t)' and (b) (t)'' but from (c)-(e) im not sure waht to do
opal plinth
You should open a new channel
plush ember
oh ok
opal plinth
.close this one first
plush ember
.close
urban dust
can anyone calculate an integral for me in mathematica
i did an integral but wolfram alpha can't calculate it symbollically
final saddleBOT
can anyone calculate an integral for me in mathematica
i did an integral but wol...
amber holly
If wolfram alpha gave you that then the integral is most likely non-elementary
urban dust
well wolfram alpha gives me a decimal
amber holly
Being able to approximate a number doesn't mean there is a closed form for it though
Wait
,w integrate e^(sin(x)cos(x)) from 0 to pi/2
soft zealotBOT
urban dust
how do i calculate struve function and bessel function in wolfram alpha
amber holly
,w bessel function at 1/2
soft zealotBOT
urban dust
besel I
modified
,w pi/2 * ((modified bessel function of order 0 at 1/2)+(modified struvefunction of order 0 at 1/2))
uh huh
soft zealotBOT
Requested by eigenmirai
amber holly
Make it evaluate each function at 1/2 and just enter their approximations instead
,w struve function at 1/2
soft zealotBOT
urban dust
,ask (pi/2)*(StruveL[0, 0.5]+BesselI[0, 0.5])
soft zealotBOT
urban dust
yayyy i got the right result
amber holly
Great
urban dust
this integral was so cool
amber holly
By the looks of it, it should be
vale reef
For this
vale reef
I don’t understand the last step/why they’re doing it
cosmic warren
To make the LHS of the extended matrix equal to I
shrewd timber
You roll 4 dice and sum their values, what is the probabilty their sum is odd
random forge
what condition do the numbers need such that the sum is odd?
shrewd timber
for this I think you need 2 odd and 2 even numebers which is 4C2 * 1/2^4 ?
shrewd timber
Is it 1 odd number and 3 even
random forge
yep there you go
sturdy cypress
this method is too hard
shrewd timber
Can I do 2 * 4C3 * 1/2^4
sturdy cypress
you can do 1/2
random forge
Can I do 2 * 4C3 * 1/2^4
yes
its intuitively 1/2 as well as frog is probably explaining, but its good to know the math*
* the combinarical way
sturdy cypress
if the first 3 numbers sum to odd, you have 1/2 chance that it stays odd with the 4th roll
if the first 3 numbers sum to even, you have 1/2 chance that it becomes odd with the 4th roll
shrewd timber
Ah okok
sturdy cypress
it's important to understand that rolling 4 dice at the same time has the same outcomes as rolling one at a time
shrewd timber
Then does the actual amount of dies mattter, is it the sum for n die always has a 1/2 chance of being odd
sturdy cypress
doesn't matter
shrewd timber
Interesting I guess a number can only be even or odd lol
Thank you both for your help!
.close
quick ether
i just want guidance, i learnt calc2 basics and now i want to tackle these problems. where should i begin with, any forum or playlist which can help me with geometrical part of calculus
final saddleBOT
i just want guidance, i learnt calc2 basics and now i want to tackle these probl...
@quick ether Has your question been resolved?
quick ether
<@&286206848099549185>
final saddleBOT
@quick ether Has your question been resolved?
primal geode
I am finding x=3 while the awnser is x=4 what am i doing wrong
final saddleBOT
I am finding x=3 while the awnser is x=4 what am i doing wrong
primal geode
.close
final saddleBOT
charred chasm
you got it?
charred chasm
that should be -5x+5
primal geode
Thanks
final saddleBOT
✅
worldly spruce
What have you got in the second line
6x + 3?
We get $15 \cdot \frac{2 \cdot (x+1)}{5} = 3 \cdot 2 \cdot (x+1) = 6 \cdot (x+1) = 6x + 6$
soft zealotBOT
USS-Enterprise
worldly spruce
**USS\-Enterprise**
Look at this
primal geode
Oh right multiplied it by 3 :/
worldly spruce
Yes
primal geode
Thanks figured it out now 😃
worldly spruce
😄
primal geode
.close
stray stump
How do you show that $\lim_{x \to \infty} x^n = \infty$?
final saddleBOT
How do you show that $\lim_{x \to \infty} x^n = \infty$?
soft zealotBOT
WhoTao
stray stump
This is the original question
stray stump
**WhoTao**
I have factored out $x^n$. And Now I just need to show this thing is true.
soft zealotBOT
WhoTao
stray stump
And also x to negative infinity of x^n is - infty
final saddleBOT
Available help channel!
languid yoke
I'm having some trouble reordering this integral into dy dz dx
final saddleBOT
I'm having some trouble reordering this integral into dy dz dx
languid yoke
I think the inner integral would be from 0 to 2 still and the outer from 0 to $\frac{1}{2}\sqrt{36-4x^2-z}$, but I'm not sure about the middle.
soft zealotBOT
Ari
woeful yew
wondering if i am considering this question correctly
final saddleBOT
wondering if i am considering this question correctly
woeful yew
if statement p(n) is false in statement a, then p(n+1) is also false as otherwise p(n+1) is true and p(n+2) could be false, which is bad. then for b, i think same logic applies
clearly a is case b=1 for statement b, but i think logically they're equivelant. if p(n) is true, then p(n+1), p(n+2)... must be true for statement to be true i.e. statement b is true. converse works as well
only hesitant about logic when P(n) false and P(n+1) false, making statement true, (F -> F) which i think is equivelant to b
final saddleBOT
@woeful yew Has your question been resolved?
woeful yew
<@&286206848099549185>
final saddleBOT
@woeful yew Has your question been resolved?
final saddleBOT
@woeful yew Has your question been resolved?
woeful yew
ok different question, am i approaching this correctly? 0 is a natural here and we are considering inductive k-1 so should be positive integers to compensate for 0?
woeful yew
<@&286206848099549185>
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proud void
Find the hexadecimal expansion of (111101)2 .
final saddleBOT
Find the hexadecimal expansion of (111101)2 .
proud void
This is what i got and i just wanted to make sure if it was right or not
cobalt lodge
usually $(\text{stuff})_2$ means the stuff is in base 2
soft zealotBOT
IV
proud void
so i missed a step? im having a hard time understanding
cobalt lodge
it means the question is asking you to convert the binary number 111101 to hex
not a hexadecimal number 111101 to binary
proud void
so how would i go about starting that?
so instead for instance 1 * 16^5 i would do 1 * 2^5 ?
pale mortar
What you're doing here is converting binary to decimal, which is a good first step
Now put it into a calculator and see what you get
proud void
i get 61!
pale mortar
So in binary it's 11101, and in decimal its 61
Now you can convert 61 to hexadecimal
Have you learned how to do that?
proud void
its kinda foggy would it be okay to go over it?
OH actually I remember let me try it real quick!
i got 3D!
pale mortar
exactly
modest perch
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modest perch
hey yall
trying to get this series to converge to about 1/7
1/6**
this particular series is obviously undefined as you can see
but why is this?
and why does the substition sin(x) = 2sinh(x/2) cosh(x/2) make this converge?
my best guess was that ok youve got sinh in the denominator, so when it is zero that's undefined
and afaik cosh has no zeroes in the reals
but even when sinh is in the numerator this is undefined
why might that be?
final saddleBOT
@modest perch Has your question been resolved?
rustic wedge
trying to get this series to converge to about 1/7
why?
rustic wedge
and why does the substition sin(x) = 2sinh(x/2) cosh(x/2) make this converge?
well have u tried substituting yourself?
modest perch
Yes
rustic wedge
this particular series is obviously undefined as you can see
why is it undefined again?
modest perch
Thats what im trying to figure out
But an equivalent function with the mentioned substitution causes it to go to 1.67, which is what i wanted
.close
ancient thistle
Hello
ancient thistle
What does K trans mean here?
cold gorge
Kinetic energy due to translatory motion.
ancient thistle
Kinetic energy due to translatory motion.
What does that exactly mean?
What's the difference between K rotational
cold gorge
Well, K rotational is kinetic energy due to the object's rotation.
These are two different motion types, in translatory motion the orientation of the body remains same throughout the motion.
However in rotation the orientation changes as well as the object rotates about an axis.
An example for all this could be a ball rolling.
When it's rolling, it moves forward and also rotates if you see that.
The motion that's causing the ball to move forward is translatory motion and the other is rotation.
For instance, if the ball had no translatory velocity it'd be rotating at its place without moving forward.
However because of the translatory velocity it moves forward.
So they are two different things.
Similarly it is also possible for the ball to move forward without rotating.
ancient thistle
Similarly it is also possible for the ball to move forward without rotating.
Oh so you mean, K trans can exist with K rot?
cold gorge
With or without, yes.
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rugged yoke
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torn crescent
So i have an AP Sn = k, Sk = n, find Sn+k, n != k.
final saddleBOT
So i have an AP Sn = k, Sk = n, find Sn+k, n != k.
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
hallow lantern
!show
final saddleBOT
Show your work, and if possible, explain where you are stuck.
@torn crescent Has your question been resolved?
torn crescent
2
my idea is to write out Sn and Sk and then add them and plug into Sn + k. But this is too long and probably not the way to solve it.
this is way too long
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jaunty pewter
i’m having trouble determining end behavior, this is the answer to the problem but i’m confused with the process of finding this answer? i would like a quick reply as I wont be available past 10-15 ish mins
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i’m having trouble determining end behavior, this is the answer to the problem b...
jaunty pewter
the two things I am mainly concerned abt finding is domain and end behavior
I think the end behavior reflects on whatever the horizontal asymptote is, can anyone clarify? ty
<@&286206848099549185>
.close
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broken steppe
The second value I entered is wrong... how can I solve this?
final saddleBOT
The second value I entered is wrong... how can I solve this?
broken steppe
If it rains today, it will also rain tomorrow with 0.662 certainty
If it rains today, it will not rain tomorrow with 0.338 certainty
If it doesn't rain today, it will rain tomorrow with 0.250 certainty
If it doesn't rain today, it won't rain tomorrow with 0.750 certainty
It will not rain on monday, and I want to know the chance for it to rain on wednesday so i do calculate the matrix products
The certainty for it to rain on wednesday is 0.353
It will rain on thursday, whats the chance for it to not rain on sunday?
<@&286206848099549185>
dire trail
hi
broken steppe
Hi!
Dont know if the ping already counts, but I try again with <@&286206848099549185>
broken steppe
Hi
cobalt barn
Lemme solve this
cobalt barn
<@&286206848099549185>
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broken steppe
<@&286206848099549185>
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@broken steppe Has your question been resolved?
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@broken steppe Has your question been resolved?
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whole pecan
What
heavy plaza
🔥
quiet zinc
you need to find a?
warm ether
(a^8)^(a^8)=8^8
a^8=8 is a quick one
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cold gorge
<@&268886789983436800>
random scaffold
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random scaffold
I understand how to verify the linearity of the transformation and
how to find the kernel
But I want to know how to determine the image
For Q25
The kernel is by inputting the general degree 2 polynomial f(t) = a + bt + ct^2
f'(t) = b + 2ct
f''(t) = 2c
T(a + bt + ct^2) = 2c + 4(b + 2ct) = 2c + 4b + 8ct
2c + 4b + 8ct = 0 -> b = c = 0
Kernel consists of functions in P2 of the form f(t) = a
trim crown
T(a + bt + ct^2) = 2c + 4(b + 2ct) = 2c+4b+8ct
random scaffold
T(a + bt + ct^2) = 2c + 4(b + 2ct) = 2c+4b+8ct
Thats the image? all polynomials of the form 2c+4b+8ct?
trim crown
c is free here
8ct is free
for 2c+4b, b is also free
so 2c+4b is free
free means it can be any value without constraint
we can use a single variable for the free terms
so we can write 2c+4b+8ct as x+yt
random scaffold
hm
never seen something like this before. c and b are free because they aren't t I'm guessing right
the independent variable of the function f(t)
I've just never seen free variables done outside of matrix stuff I guess
trim crown
idk what other calls it
sage tusk
how would you solve a question like this?
final saddleBOT
how would you solve a question like this?
subtle dragon
I'm tryna look at it
sage tusk
thanks
subtle dragon
I'm very inclined to say that it's 0.5, because D is the midpoint
But I wouldn't say so for sure
What class even gave you this problem?
subtle dragon
In uni? Or hs?
sage tusk
hs
sage tusk
haha
subtle dragon
But here in Ontario we have nothing like this
sage tusk
weird
I think I'm supposed to find 2 possible paths that lead to E
and then use algebra to substitute it in
subtle dragon
Well for sure we have that the ratio u which we're looking for would be the ratio of the area of triangle OEB to the area of triangle OAB, but i don't know at all how we can grab those areas
If EB was a perpendicular bisector to CA that would be much helpful
But we don't have that
It's just a random bisector
subtle dragon
its just the vectors
Yeah you're right , I'm not exactly thinking of it in terms of vectors tho I'm supposed to. I'm thinking if it as like lines and triangles, and ik that if two triangles have the same height then the ratio of their bases is equal to the ratio of their areas
subtle dragon
Are you in some kind of enriched program or smth ?
Only if ur comfortable Sharing ofc
sage tusk
(british education system)
A level maths is very common subject chosen by students in britan
subtle dragon
I see
sage tusk
maybe diff country so you were taught something diff
subtle dragon
<@&286206848099549185> lol I'm not supposed to be a helper pinging helpers
sage tusk
we're a bit stuck
final saddleBOT
@sage tusk Has your question been resolved?
sage tusk
Can you show me some other hw problems you've done?
stuff like this
subtle dragon
I see
@sage tusk you may as well close the help channel to free it for someone else. I have some rlly smart friends I can ask about this. And I can dm you
sage tusk
<@1146980611622457365> you may as well close the help channel to free it for som...
yes, please do that
.close
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small relic
i don't know how to solve this part underlined and i'ts not in the solutions
small relic
equilibrium is
y_0=3/4
y=u+3/4
u'=-u^2-u/2
not sure where to go from there.
i can write y(10) - 3/4 = b but then what?
which would be
ce^(-10/2) = b
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true flume
Hello! How do you find "c" in order to get only one result of the equation? Thanks!
final saddleBOT
Hello! How do you find "c" in order to get only one result of the equation? Than...
autumn geode
Hello! How do you find "c" in order to get only one result of the equation? Than...
what should the discriminate equal to
once you figured that out
you have solved the problem basically
stone wagon
there's only one solution if it's in the form of a(x-b)^2=0
stone wagon
do you know what a discriminant is?
some schools study it, some don't, so just clarifying
stone wagon
b^2 - 4ac
it's the thingy under square root in the quadratic formula
if it's equal to 0, then there's only one solution
true flume
autumn geode
b^2 - 4ac = 0
stone wagon
yes
true flume
But if i don't have the value of "c", how can i do it?
stone wagon
you solve for it
b^2 - 4ac = 0
b = 13
a = -4
c = c (lol)
subtitute those values and solve for c
true flume
Oh yes i did that but i'm stuck here:
i don't know what to do with 16c inside of square root
true flume
Oh
stone wagon
solve 169+16c=0
lyric garden
All 26 letters of the alphabet A, B, C, D, E, ... X, Y, Z perfectly (uniformly) randomly shuffle. What is the expected number of letters that will remain in place in the alphabet?
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All 26 letters of the alphabet A, B, C, D, E, ... X, Y, Z perfectly (uniformly) ...
@lyric garden Has your question been resolved?
Available help channel!
obtuse pagoda
broken shale
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crystal mirage
how do i figure out the probability of drawing out two blocks of the same color from a box if there’s 12 red blocks, 5 blue blocks, 9 yellow blocks and 8 white blocks? i already did some tasks that r linked to this one but i can’t even figure out how to start this one like do i just start with the probability of drawing out one block which is 1?
final saddleBOT
how do i figure out the probability of drawing out two blocks of the same color ...
crystal mirage
this is assuming that the first block you took out isn’t put back into the box after drawing the first one out
final saddleBOT
@crystal mirage Has your question been resolved?
eternal lichen
This is the multivariate hypergeometric distribution
crystal mirage
i have never heard of that word ever
eternal lichen
You can look up that to find the probability of drawing one block of a given color
crystal mirage
yes
so first i’m supposed to find out the different probabilities of drawing out a block of a specific color?
so then it’d just be 12/34 for red 8/34 for white 5/34 for blue and 9/34 for yellow
for the first draw
?
eternal lichen
Mhmm, there might be a simpler way to figure this out
crystal mirage
i don’t even understand what’s going on 😭
eternal lichen
All we care about is the probability of drawing a second block that is the same color as the first
crystal mirage
yes
eternal lichen
For the first draw, there are four possibilities, right?
crystal mirage
yes
eternal lichen
Have you heard of the law of total probability?
crystal mirage
it might have a different term in my language
i speak norwegian
explain it and i’ll know if i have heard of it?
crystal mirage
wow really?
eternal lichen
Does any of this ring a bell?
crystal mirage
nope
crystal mirage
like p(a)* p(b)
eternal lichen
No, that's different. That's for independant events
eternal lichen
Alright, then my approach will be hard to understand
crystal mirage
hmm
crystal mirage
okay
eternal lichen
What is the probability that your second draw is also a red block?
crystal mirage
11/33
eternal lichen
Read as "probability of drawing two red blocks given that the first block you drew was red"
| <- this means "given"
crystal mirage
i think i understand
eternal lichen
Now, we can write the same sort of probability for the other colors
P(BB | B), P(YY | Y), P(WW | W)
crystal mirage
okay
eternal lichen
Now I think you can use the law of total probability to write P(XX) using these four conditional probabilities
P(XX) is the probability of drawing two of the same color
Mhmm, you know what, I thought of a simpler way to explain this
crystal mirage
okay
crystal mirage
i’m not too sure honestly this was supposed to be a short chapter so i think we’ve only covered the p(a) * p(b) thing
eternal lichen
Okay, what about something like this: P(A or B)=P(A)+P(B) for mutually exclusive events
also known as disjoint events
crystal mirage
wait let me check what those terms are in norwegian
no haven’t covered it yet but i understood what those terms meant after checking
eternal lichen
Ok, good. This will be much simpler
So, the events of interest are RR, BB, YY, WW
And these events are mutually exclusive
crystal mirage
just to make sure mutually exclusive events are events that cannot happen at the same time right?
eternal lichen
Yes
crystal mirage
oki
eternal lichen
So if you take a block out, it can only be one color
crystal mirage
yes
eternal lichen
Okay, what about something like this: P(A or B)=P(A)+P(B) for mutually exclusive...
Now we use this to write P(XX) = P(RR)+P(BB)+P(YY)+P(WW)
They are all disjoint, so you can sum up the probability, right?
Here, XX= RR or BB or YY or WW
crystal mirage
so i’m supposed to plus together the probability of drawing two red, two blue, two white and two yellow?
crystal mirage
okay
eternal lichen
Now, we know that if you draw 1 R, the probability of drawing the second was 11/33, right?
crystal mirage
yes
eternal lichen
Now we just need some basic conditional probability to write P(RR)
crystal mirage
which would mean?
crystal mirage
okay