Available help channel!
#help-10
obtuse pebbleBOT
Available help channel!
dry oak
Is there a faster way to solve this? I think that I'm doing something wrong because it is taking me too long, and I feel it should be a lot easier
obtuse pebbleBOT
Is there a faster way to solve this? I think that I'm doing something wrong beca...
shut thorn
I would simplify the equation (in this case just by dividing by 2 on both sides) and then just plug in each pair of values to see what satisfies the inequality
shut thorn
so it would be 2y ≤ 4?
$x - 2y \leq 4$ yes
then just plug in the values, so the first one would be
$(-4) - 2(0) = -4 - 0 = -8 \leq 8$
warm shaleBOT
elgene
shut thorn
And so it is a solution
shut thorn
No problem, good luck!
jaunty stirrup
hi
jaunty stirrup
i need help
when i distribute 6 with x^-2, i know how to distribute 6 with x but what do i do with the ^-2?
bc 6*x= 6x, but then what do i do with the leftover ^-2
void pelican
$6\cdot x^{-2}=6x^{-2}$
warm shaleBOT
gmod
jaunty stirrup
oh
void pelican
you just bring the -2 along
jaunty stirrup
oh
void pelican
it is part of the x
jaunty stirrup
ok thanks
void pelican
np
jaunty stirrup
.close
twin kayak
obtuse pebbleBOT
wooden cipher
correct
twin kayak
yes
twin kayak
but why is x ^x/lnx also e^x
just this part
wooden cipher
at the start of row 2, you use exponent laws which say you muliply the exponents together
twin kayak
yes
wooden cipher
the lnx/lnx simplifies to 1
twin kayak
yes
wooden cipher
so (x*lnx)/lnx simplifies to just x
wooden cipher
ok i still need help with markov chains
obtuse pebbleBOT
ok i still need help with markov chains
wooden cipher
lemme go grab a problem rq
I have this matrix
@brave bramble are you available right now?
brave bramble
Heyo. Was watching, haha
wooden cipher
:D
brave bramble
Weird
brave bramble
So let's put that 1 back in the bottom corner
wooden cipher
oh right
brave bramble
And recall that taking the nth power of this matrix gives us the probability of getting two heads in a row in any of n flips
,w matrix {{0,1/2,1/2},{1/2,1/2,0},{0,0,1}}^10
wooden cipher
warm shaleBOT
brave bramble
So doing it within 10 flips happens with a probability 880/1024
brave bramble
Phw? EV?
wooden cipher
expected value
brave bramble
Anyway, taking powers of matricies is hard. We can instead diagonalize the matrix to do this quickly
wooden cipher
Phw is the entry in the matrix of row R col W
brave bramble
,w diagonalize matrix {{0,1/2,1/2},{1/2,1/2,0},{0,0,1}}
warm shaleBOT
brave bramble
So I thought it was interesting that you mentioned phi, because there it is
wooden cipher
i didnt mention phi lol
brave bramble
And if I do the matrix multiplication I need to pull this specific number out...
wooden cipher
when i raise a diagonalized matrix to a power, i only raise the inside (J) right?
brave bramble
Exactly. That makes this much easier to take powers of
The hope is to get a closed form for the probability
And with that, we have a pdf, and an expected value
brave bramble
Maybe there's an easier way to do this? Would you have expected the question gets so complicated? Lol
wooden cipher
no
i was just expecting "use the markov chain to set up this equation and boom"
im starting with a simple problem but i have weather ones for later
should we do one about weather?
maybe it lends itself to a solution better
wooden cipher
we can learn this together lol
we can start with a simpler problem, i can make one rq
A particle can either spin CW or CCW.
Every minute, the particle may change spin.
When spinning CW, it has a 2/5 chance of changing spin.
When spinning CCW, it has a 3/8 chance of changing its spin.
A scientists just observed the particle to spin CW. After 10 minutes, what is the probability it still spins CW?
@brave bramble imma do some research again, closing this for now
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
barren crag
So, i'm given 2 lists a and b, such that x = b-a for each element (that is, if a=[1,2] and b=[3,4], then x=[2,2]=[(3-1),(4-2)].
I aim to use x to determine how similar the two lists are.
In application, a and b both represent the fast fourier transforms of two wav files, so essentially x is the difference between their ffts and will be used to check programmitcally how similar the two songs are.
Unfortunately, x is primarily comprised of complex numbers. So, I was wondering if taking a modified mean standard error would work for this. I was thinking of basically finding the squared magnitude for each element in x, then just averaging those. My question is, bascially, would this work? Or maybe there's a better way of doing this? Thank!
obtuse pebbleBOT
So, i'm given 2 lists a and b, such that x = b-a for each element (that is, if a...
@barren crag Has your question been resolved?
barren crag
<@&286206848099549185>
obtuse pebbleBOT
@barren crag Has your question been resolved?
obsidian isle
charred plume
Not sure exactly what's required in your case (i.e. what properties are required for your notion of 'similarity') but taking the average of the squared magnitudes of the components of x is one good option. You might also play with taking the square root of that average -- that tends to get used more often as a notion of length / distance for lists/vectors of complex numbers. Again, depends on how this 'similarity' is expected to behave. Also, a minor point, but if the number of components in x never changes, there's not much point in dividing by that number (i.e. taking the average).
obtuse pebbleBOT
@barren crag Has your question been resolved?
obtuse pebbleBOT
minor cypress
.close
wanton dagger
I know what mean is, it’s just that I’m having difficulties interpreting it from this graph which is avoiding me from finding it
obtuse pebbleBOT
I know what mean is, it’s just that I’m having difficulties interpreting it from...
royal basin
what do you mean by "interpreting"?
also i think you meant preventing and not avoiding...
wanton dagger
Yeah
royal basin
you're not supposed to simply guess the mean by looking at the graph here
also, what do you want the mean of? quiz 1 scores? quiz 2 scores? everything?
wanton dagger
For quiz 1
royal basin
right
then you should not have cropped out the words "quiz 1" when posting the question
so in that case
you know the frequency of each quiz 1 score
so take the weighted average of the scores with those frequencies as weights...
wanton dagger
What do I divide by?
royal basin
do you know how to find a weighted average?
if you do then you should know what to divide by.
sweet socket
obtuse pebbleBOT
sweet socket
Can anyone tell me if this exercise is correct?
I've been trying to do it for hours
cursive jolt
Also I don't know if it's like a standard notation but I find strange the way the + and - are written
lean sigil
Like here
lean sigil
Also I don't know if it's like a standard notation but I find strange the way th...
yea its really weird
cursive jolt
Like they should be before the number, not right after the preceding number
And there are no + and - on the first row
Like
+1 -1 +4
+0 +3 -2
+0 +1 -1
(Sorry if it's a matrix from a wrong calculation, it was just for the example)
sweet socket
ye i mean
1-1+4=-13
0+3-2=19
0-1-1=7
lean sigil
No, it should be:
1-1+4=-13
0+3-2=19
0**+**1-1=7
instead of what you wrote
because you are multiplying the first row's middle term (which is already negative) by minus one
sweet socket
alr im gonna change that right now
but the answers seems right?
lean sigil
No, it should be:
1-1+4=-13
0+3-2=19
0**+**1-1=7
The way that you solved the equations are good, but I guess the final answer are wrong because of this
You can do the exact same thing with the plus instead of the minus and it should be good
sweet socket
alr ! tysm
muted bear
so i said that c is the hypotenuse because its the largest
obtuse pebbleBOT
so i said that c is the hypotenuse because its the largest
muted bear
but i dont know how i could go about proving that
i tried saying that c^2 is a^2+b^2 and playing with it but it didnt amount to much
maybe i should do something with the right side?
royal basin
a^6 + b^6 = (a^2+b^2)(a^4 - a^2b^2 + b^4)
muted bear
a^6 + b^6 = (a^2+b^2)(a^4 - a^2b^2 + b^4)
ok lemme replace that
how do i get rid of that 3\
ive thought of getting somehow (a+b)^3 so i can have a 3 in there
to eliminate the one down there
but i dont think thatd work
i would like going left to right but idk how that would work
timid silo
3a²b²c²=c⁶-a⁶-b⁶
A=a² B=b² C=c²
3ABC=C³-A³-B³
A+B=C
3AB(A+B)=(A³+3A²B+3AB²+B³)-A³-B³
3A²B+3AB²=3A²B+3AB²
muted bear
how did you get this? 3a²b²c²=c⁶-a⁶-b⁶
timid silo
multiply 3
muted bear
well doesnt that kind of start with the conclusion?
timid silo
well doesnt that kind of start with the conclusion?
u can start with the conclusion
u just have to prove if the equation is always true
timid silo
3a²b²c²=c⁶-a⁶-b⁶
A=a² B=b² C=c²
3ABC=C³-A³-B³
A+B=C
3AB(A+B)=(A³+3A²B+3AB²+B³)-A...
look at the last line
its basically 0=0
obtuse pebbleBOT
royal basin
try to count the complement of that
ie the election results in which they have the same major
obtuse pebbleBOT
@slow timber Has your question been resolved?
royal basin
are you familiar with the concept of subtractive counting
or complementary counting
to give a vivid example:
if you have a room with a bunch of ppl in it and you want to count how many of them are wearing red shirts, it is sometimes easier to count the total number of ppl in the room and then subtract the number of ppl NOT in red shirts.
right
well
you are asked to count the election results in which the prez and vp have different majors
what does it mean for that not to be the case?
before you calculate that, state WHAT you would be calculating.
you would be calculating the number of election results in which _______
FORGET ABOUT MULTIPLICATION
i'm trying to walk you through the LOGIC
you are asked to count the election results in which the prez and vp have different majors
even if you understood it you were unable to articulate it clearly so forgive me for being somewhat doubtful.
so, we now set out to calculate the number of results in which prez and vp have the same major.
can you LIST the majors held by our pool of candidates?
do nothing else until i tell you to.
just write out a LIST of the majors that we have here to work with.
they have names...
math, CS and education
M, C and E then if you insist
but i think there is value in talking shit through.
so
if prez and vp have the same major,
then they are either both math majors, or both CS majors, or both education majors. these possibilities do not overlap and there are no others.
do you understand this? Y/N
okay
now
how many math majors do we have?
NO
did i not tell you to not do anything other than what i instruct you to?
don't jump ahead.
answer the questions i ask
not the questions in your brain
i am trying to walk you through this shit step by step in a way that ensures you understand what the fuck is going on.
okay great you gave the numbers for all majors
now
how many ways are there to elect a prez and a vp who are both math majors?
yes
how many ways are there to elect a prez and vp who are both CS majors?
yes
that is what we have been doing all along
i am glad you came to this conclusion
find the number of ways to pick one of each major and the number of ways to assign majors to offices (3!)
this would be multiplication if anything lmao
obtuse pebbleBOT
Available help channel!
limber eagle
The distance between the centers of two circles of radii 10 and 17 is 9. A triangle with sides 10,17,and 9, passes through which three points?
- The center of the large circle, the center of the small circle, and the point collinear with these two on the large circle.
- The points on the external tangent to these two circles, and the big circle's center
- The center of the large circle, the center of the small circle, and a point common to both circles
- The two intersection points of the two circles, and the center of the big circle
obtuse pebbleBOT
The distance between the centers of two circles of radii 10 and 17 is 9. A trian...
high lily
have you drawn a diagram
high lily
where are the circles
charred remnant
The distance between the centers of two circles of radii 10 and 17 is 9. A trian...
That all?
does it said the circle intersect each other?
limber eagle
yeah
charred remnant
Nice
limber eagle
it probably has to, or else the distance won't be long enough
cause the radii for the bigger circle is 17, and the radii for the smaller circle is 10, which is both bigger than 9, so they need to intersect in order for their disdtance between their center to be 9
is that right?
obtuse pebbleBOT
@limber eagle Has your question been resolved?
limber eagle
.close
feral sedge
@timid silo Let's do it step by step.
First of all, what can you deduce for h'(4)=16?
wide orchid
hello guys
obtuse pebbleBOT
hello guys
wide orchid
can someone please help me in probability
a bag contains 5 white balls and 6 black balls, if 3 balls are drawn at random without replacement , find the probability that 2 of them are black
wide orchid
a bag contains 5 white balls and 6 black balls, if 3 balls are drawn at random w...
also tell me how would we do it with replacement
steep harness
this is a fun one. it's really hard to find the probability directly, but we can find it indirectly. what would the probability be that none of them are black?
wide orchid
5/11 x 4/10 x 3/9 ??
wide orchid
this is a fun one. it's really hard to find the probability directly, but we ca...
yeah it came in one of my exams and i couldn't do it :(
steep harness
5/11 x 4/10 x 3/9 ??
that's correct, so what is the probability?
steep harness
alright, so what would be the probability of drawing 3 balls out of the bag?
steep harness
we're pulling three balls out of a bag, right? what's the probability that we'll pull three balls out?
wide orchid
1
wide orchid
we're pulling three balls out of a bag, right? what's the probability that we'll...
it will be 1 since its given that we are actually doing that
steep harness
it will be 1 since its given that we are actually doing that
good. so that's the probability of all possible combinations of balls. we know the probability of no black balls, so what would the probability of at least one black ball be?
wide orchid
5/11 x 4/10 x 3/9 ??
idk , will it be 5/11 x 4/10 x 6/9?
wide orchid
good. so that's the probability of *all possible combinations* of balls. we kn...
now that's where i am confused
wide orchid
idk , will it be 5/11 x 4/10 x 6/9?
4/33
steep harness
now that's where i am confused
alright, if we took all possible combinations, and got rid of every combination that had no black balls, what would be left? only combinations with at least one black ball, right?
wide orchid
alright, if we took all possible combinations, and got rid of every combination ...
i think what would be left is combinations of all black balls
¯_(ツ)_/¯
steep harness
i think what would be left is combinations of **all** black balls
does black,white,white have no black balls?
wide orchid
does black,white,white have *no* black balls?
this combo has 1 black ball
steep harness
this combo has 1 black ball
so would we take away this combo when we take away all combos with none?
let's check it another way, as well: what would be the probability of pulling all black balls? (without replacement)
wide orchid
i am confused
lets put all the info we got till now again
P(no black balls / only white balls all three) = 2/33
P(we will draw 3 balls) = 1
wide orchid
let's check it another way, as well: what would be the probability of pulling *a...
yeah i can do that, wait
steep harness
gotta double check the numbers themselves real quick
wide orchid
let's check it another way, as well: what would be the probability of pulling *a...
6/11 x 5/10 x 4/9
= 4/33
steep harness
alright, now then, do we want 3 black in our answer?
steep harness
ok, so let's take (all black) away from (draw 3 balls)
wide orchid
1-(4/33)
steep harness
is that the same as (all white)?
wide orchid
yeah
steep harness
what is the probability of (all white)?
wide orchid
29/33
wide orchid
calculate it directly
yeah i did
wide orchid
why doesn't this agree?
wdym?
steep harness
the probability of 3 white balls is (first white)x(second white)x(third white) right? that's 5/11x4/10x3/9
wide orchid
that's correct, so what is the probability?
naah here what i did was replaced 3/9 with 6/9 since i considered the last ball to be black
wide orchid
the probability of 3 white balls is (first white)x(second white)x(third white) r...
yes, correct
steep harness
so why doesn't (all possible combos)-(all black)=(all white)?
wide orchid
so why doesn't (all possible combos)-(all black)=(all white)?
yes that should be correct
oh no
steep harness
no, it shouldn't
wide orchid
yeah, it shouldn't
wide orchid
yeah, makes sense
it shouldn't
but if it shouldn't , it makes things even more complex for me
steep harness
Well, what are all possible combinations? (All black)+(2 black)+(1 black)+(all white)
wide orchid
yeah
steep harness
So we can take away (all black) and (all white), right? What would that leave us with?
wide orchid
(2 black) and (1 black)
steep harness
Seems to make this simpler, doesn't it? Now we need to find 1 black to take away, which is a little trouble, but not as bad
So, how many orders can we get 1 black ball and 2 white balls?
wide orchid
2 combos
steep harness
A few more than that
wide orchid
😵💫
wide orchid
Bww
Wbw
Wwb
but should we even consider the order? the question doesn't say order is important
steep harness
but should we even consider the order? the question doesn't say order is importa...
Does the order change the probability for the last ball?
wide orchid
yeah it does apparently
steep harness
Can you calculate each of those individually?
steep harness
That's ok, that's why we're double checking. Being smart is just being dumb but faster
So what's the specific probability of getting wwb?
Here's our end goal:
(2 black)=(all combos)-(none black)-(all black)-(1 black)
And we need (1 black)=(bww)+(wbw)+(wwb)
wide orchid
5/11(white) x 4/10(white) x 6/9(black) = 4/33
steep harness
Alright, can you work out the other two combos?
wide orchid
yeah,
wide orchid
5/11(white) x 4/10(white) x 6/9(black) = 4/33
this is one black
steep harness
It's not all of them though
wide orchid
all black would be 6/11 x 5/10 x 4/9 = 4/33 again
steep harness
Oh, wait, I might be extremely dumb
Multiplication of fractions is freely commutative across numerators. You're right
We do still have to care about the fact that there's 3 unique orders though
So it's just 3(wwb)
wide orchid
we have to find (wbb) cause 2 black
steep harness
Sure, but we can do that as (all)-(all black)-(3(wwb))-(all white)
Alternatively, it should be 3(bbw)
I'm giving two methods just to make sure they agree so we're not wrong
obtuse pebbleBOT
@wide orchid Has your question been resolved?
tidal valley
obtuse pebbleBOT
tranquil arch
then you can calculate
$$(a \sqrt{a}+b \sqrt{b})^2$$
warm shaleBOT
秋水
tidal valley
okay i will
obtuse pebbleBOT
@tidal valley Has your question been resolved?
tranquil arch
$$(a \sqrt{a}+b \sqrt{b})^2 = a^3+b^3+2ab \sqrt{ab}$$
warm shaleBOT
秋水
tranquil arch
$$a^3+b^3 = (a+b)^3-3ab(a+b)$$
warm shaleBOT
秋水
exotic creek
obtuse pebbleBOT
exotic creek
anyone?
got no idea how to do linear interpolation
<@&286206848099549185>
too late
.close
amber torrent
obtuse pebbleBOT
amber torrent
anyone knows how to solve this limit with taylor polynomials?
wooden cipher
wouldnt you use lhopitals?
tardy epoch
anyone knows how to solve this limit with taylor polynomials?
Substitute the second order Taylor expansion for each log and sin function
amber torrent
wouldnt you use lhopitals?
I tried using hospitals (taking the derivative of both the denominator and the numerator, right?) But you keep getting a zero in the numerator
amber torrent
Substitute the second order Taylor expansion for each log and sin function
Why is a second order sufficient?
Isn't the highest power an x^4?
wooden cipher
you can use lhoptials multiple times if you get another 0/0
wooden cipher
ah
amber torrent
So why is a second order Taylor polynomial sufficient?
obtuse pebbleBOT
@amber torrent Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
neon falcon
obtuse pebbleBOT
neon falcon
Is D a polynomial?
timid silo
Yes
warm canopy
Why do you think its 1/7?
warm canopy
Sure but what's the definition of degree?
Also what's the full question, not a very well defined question as is
warm canopy
Eh they should really say which letter they are considering to be a variable
Luckily in this particular one it's all the same
Let's say x is the variable
What's the definition of degree
neon falcon
What's the definition of degree
I actually do not know. They didn't mention the definition, they just told us how to do it.
obtuse pebbleBOT
@neon falcon Has your question been resolved?
gaunt girder
the degree of a polynomial basically means the maximum power of a base in the given polynomial
neon falcon
Yea it's 2
gaunt girder
yea
chilly cliff
Hi.
q(x) = 2(x-i)(x+i)(x-4i)(x+2)
I want to write the zeroes of q(x) in exponential form. i and -i I've got, but how do I get the other two?
obtuse pebbleBOT
Hi.
q(x) = 2(x-i)(x+i)(x-4i)(x+2)
I want to write the zeroes of q(x) in exponent...
royal basin
they are 4i and -2
chilly cliff
I would just say x=4i equals to e^(4pi/2) being a full circle
chilly cliff
how can I derive that?
royal basin
same as you would do for writing any number in exponential form
modulus * e^(i*argument)
maiden radish
combien de maniere on peut mettre k ballons dans n sachet tel que le sachets ne peut prend pas plus de s ballons
obtuse pebbleBOT
combien de maniere on peut mettre k ballons dans n sachet tel que le sachets ne ...
maiden radish
Help plz
hearty basin
ya i got u
what is the question
yo hablo un poco de espanol
tu hables?
tu es frances?
maiden radish
Oui
Fancais
How many ways we can put k baloons in n bags such that the bag can not take more then s baloon
hearty basin
4
vagrant pebble
hearty basin
vivi?
hearty basin
The question is how many ways to put k balls in n bags
could be n!\2!4! to the power of 2
maiden radish
No
timid silo
combien de maniere on peut mettre k ballons dans n sachet tel que le sachets ne ...
alright
so to translate
what he is asking is
maiden radish
We havn't any number of balls or of bags
timid silo
How many ways can we put x balls in n packets such that the number of packets is never bigger than s balls
maiden radish
No
timid silo
tu peux juste montrer le question original
maiden radish
The number of balls is x and the packet can't take more then s balls and we don't know if x is biggef or smaller then s
There no original quetion it is just a problem from my teacher
Do find a answer
obtuse pebbleBOT
@maiden radish Has your question been resolved?
obtuse pebbleBOT
@maiden radish Has your question been resolved?
maiden radish
.close
stuck zinc
Anyone can help me? What do I'm doing wrong?
obtuse pebbleBOT
Anyone can help me? What do I'm doing wrong?
fresh bramble
where did you get that first formula from
stuck zinc
I found in a site. It's in portuguese.
seems to be correct.
But apparently there's something wrong with my calculations.
hasty crag
right hand side, you squared each term in the sum
but it's the entire sum that is squared not each individual term
so you first do $\sum_{i=1}^{n} X_{i}$ and then square the result
warm shaleBOT
texaspb
stuck zinc
hasty crag
are you sure that this formula is correct
I mean have you tried to derive it yourself
obtuse pebbleBOT
@stuck zinc Has your question been resolved?
molten escarp
3x-5y>6 graph the inequality
obtuse pebbleBOT
3x-5y>6 graph the inequality
molten escarp
I understand I have to find y so I added 5y 3x>6+5y that’s where I’m stuck
Do I divide by 3 or 5 or am I completely wrong
Wait no so would it be 3/5x>6/5?
slim cove
So you're trying to solve for y right
if you have 3x > 6 + 5y, how do you get the y by itself?
obtuse pebbleBOT
@molten escarp Has your question been resolved?
molten escarp
@slim cove I would subtract the 5y
slim cove
well that doesn't work because then you get 3x-5y > 6 which is what you started with
you need the y by itself
molten escarp
Then divide 3x I think
slim cove
think about the 6 + 5y side
what do you do to undo the "6 +" part
Ah wait okay I gotta go but I'm sure others will be able to help just as well
karmic vale
one definition of congruent shapes is that: Two figures are congruent if and only if there exists a series of rigid transformations which will map one figure onto the other. are there other definitions of congruency that are used?
obtuse pebbleBOT
one definition of congruent shapes is that: Two figures are congruent if and onl...
slim cove
one definition of congruent shapes is that: Two figures are congruent if and onl...
An equivalent definition would be that every corresponding side and angle is the same, I don't know of any really different definitions though
That seems like a good definition for congruent shapes
obtuse pebbleBOT
@karmic vale Has your question been resolved?
heady prawn
are densities always measurable maps?
obtuse pebbleBOT
are densities always measurable maps?
heady prawn
.close
wanton dagger
How could I find the amplitude of this graph?
obtuse pebbleBOT
How could I find the amplitude of this graph?
wanton dagger
Would the amplitude be approx 26 as it’s the height of the graph?
cedar lichen
No
Amplitude is the distance from the center to a peak/troph, aka, half the distance from peak to troph
timid silo
dumb question but when using descartes rule if i had 1 possible positive zero, do I need to also put 0 possible positive zero or does the -2 only apply for when the number of possible pos/neg is greater than or equal to 2
obtuse pebbleBOT
dumb question but when using descartes rule if i had 1 possible positive zero, d...
@timid silo Has your question been resolved?
timid silo
<@&286206848099549185>
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
frozen kindle
obtuse pebbleBOT
frozen kindle
I'm really confused how to do this question please help <@&286206848099549185>
proven zephyr
!15m
obtuse pebbleBOT
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.
proven zephyr
because this is not math?
frozen kindle
then why am I doing it in maths
snow solstice
true
frozen kindle
rail fence is the zig zag one right
yep
frozen kindle
here read this there is a really good example
alrdy did
timid silo
then where are you facing problems
obtuse pebbleBOT
@frozen kindle Has your question been resolved?
drifting wraith
wikipedia says pad the text to 2(n-1) where n = 3
so pad to 20, then L = 20, K = 5
"icehi tedoderoed tfsn_"
dang
drifting wraith
i don't get it
there's not much to trial and error even
19 letters will break up into 5,9,5
so it's unambiguously "ITDE CDTOED FEHR SOIEN"
which is gibberish
oh, maybe i'm supposed to go bottom-up
not that
atomic bronze
obtuse pebbleBOT
@frozen kindle Has your question been resolved?
frozen kindle
5 rail, "I hoesd dictet n freedo"
Thx for trying
obtuse pebbleBOT
Thx for trying
frozen kindle
Ur like the only one
Anyway the answer was like “I decoded the first one” or something
drifting wraith
"decoded"
frozen kindle
Autocorrect
frozen kindle
it's unpossible <:angerysad:602329540131553290>
“Impossible”
drifting wraith
that word is not funny
slender kindle
.reopen
if sin theta times cos theta= sin 2theta
then sin 120 can be represented as sin2(60)
which should be equal to sin60xcos 60
but sin60xcos60= root three/4
and sin 120 is jus root three/2
obtuse pebbleBOT
Available help channel!
stiff cosmos
obtuse pebbleBOT
stiff cosmos
anyone know how to do this
limber quartz
anyone know how to do this
Isn't this a practice problem?
limber quartz
Will it tell you if you got it right?
stiff cosmos
yeah
limber quartz
Ok
stiff cosmos
but i wanna know the explanation
limber quartz
Why did you check the first two and not the last one?
limber quartz
What does : mean
stiff cosmos
not sure
stiff cosmos
the vector space
limber quartz
Alright and what is P_3
stiff cosmos
polynomial w degree 3
limber quartz
Ok. Just to make sure its clear, it's the set of all polynomials of degree 3
stiff cosmos
thanks
limber quartz
And R^3 is the set of all 3d real number vectors
So each of these questions is just asking if the definitions provided guarantee that these vector (or polynomial) subsets are subsets of R^3 and P_3, respectively
And tbh, assuming there isn't a contradiction in the definitions they are providing, the very first thing each line says is that the set we are considering is a subset of R^3 or P_3
stiff cosmos
yeah lets begin with A]
limber quartz
Ok, well the zero vector is clearly in both subsets A and B
If we have a vector satisfying A or B, and scaled it up by an arbitrary scalar s, we could factor s out of each equation, and dividing it through by s would yield the original solution. Thus, if <a,b,c> in A or B, then s*<a,b,c> is also in A or B
stiff cosmos
Makes sense.
Now what about addition
<a,b,c> + s*<a,b,c>
is still within the subset
limber quartz
I think you would just add both equations with the separate vector solutions plugged in and factor out the coefficients
Let u=<a,b,c> and v=<d,e,f> be solution vectors. Then
4a+9b+7c=0,
4d+9e+7f=0, so then
4(a+d) + 9(b+e)+7(c+f)=0
That is
stiff cosmos
yeah got it
limber quartz
[4,9,7]*(u + v) = 0
stiff cosmos
still within the set
Would a violation example of the 3rd Set be something like, (-x^3+ax^2+bx+c)+(x^3+ax^2+bx+c) = 2ax^+2bc+c
Thus violating the addition rule, because now it's not within the set
limber quartz
Problem there is that the leading coefficient isn't variable
I mena that sounds funny
But look at it
Its often useful for analysis to divide out the leading coef anyway
But I think they did it on purpose here
stiff cosmos
oh right
limber quartz
Maybe it's the analog to the zero vector for this
Like we can't make it spit out a function whose constant value is 0?
I'm not sure suddenly if that's what it is
We can't do axiom 2
Either
stiff cosmos
Why is that
limber quartz
Because we can't factor out the scalar multiple completely
stiff cosmos
makes sense
limber quartz
See if its just C that fails
limber quartz
Its practically the same problem, you tell me how to do it
stiff cosmos
First one I'd use your method
It satisfied 0 vector
And then -2(a)+7b-4c=0
-2z+7x-4y=0
-2(a+z)+7(b+x)-4(y+c) = 0
this fulfills the 2nd axiom
stiff cosmos
3rd axiom is always fulfilled because if you times the equation by a scalar, A, It will always be in the set
A(-2z+7x-4y)=0
Because it is in R3
Set of all vectors in 3rd Dimension
limber quartz
Good
stiff cosmos
Now for the second one
0th vector exists for (x,y,z) and 3x-6y+2z=8
Actually no, im not sure it exists for 3x-6y+2z=8
I dont think it does because inputting (0,0,0) it does not yield a zero, RHS is 8
So this violates the 1st axiom I think so.
Is this correct?
limber quartz
Actually no, im not sure it exists for 3x-6y+2z=8
stiff cosmos
lol
limber quartz
I dont think it does because inputting (0,0,0) it does not yield a zero, RHS is ...
Good
stiff cosmos
Now for the 3rd one
stiff cosmos
p(-1)=p(6)=4
I'm not sure how to test the first axiom, the zeroth vector.
How would I go about it
limber quartz
Really? I dont think thats what it says at all
stiff cosmos
function can't be cubic perhaps
limber quartz
Ok! So we have a cubic with 2 points fixed on a horizontal line
stiff cosmos
yep
limber quartz
I'm trying to think if that's actually a thing for a cubic with more than one set of coefficients
I doubt it
stiff cosmos
cubic could look like this
limber quartz
Make geogebra can help
limber quartz
cubic could look like this
Oh, if you flipped it upside down
The points would stay fixed
stiff cosmos
yea
limber quartz
That would fix 1 or 3 points though, not 2
I think it fails because I dont think it exists the way it is defined
I think the subset is empty
limber quartz
I dont think so, because there should be a 3rd point that is also equal to 4 and the definition doesn't list it
1 or 3 points will have the same value, not 2, in a cubic
stiff cosmos
makes sense
limber quartz
But...maybe they just didn't list it on purpose
limber quartz
What
stiff cosmos
so it does fullfill all the axioms, i just don't know how
let me check again
ok sorry my bad
it's only 1
lol
limber quartz
Only A, you mean
limber quartz
Good
stiff cosmos
so you're saying
for it to be a cubic
it must be something like
p(-1)=p(6)=p(y)=4
limber quartz
Np
stiff cosmos
wait i got another one
if u dont mind
alright 1st and 2nd one violate the zeroth vector axiom. So it leaves us with C being the only possibility
last one seems to fulfill all the axioms
crystal cloud
Help
proven zephyr
crystal cloud
Ik bruh just taking picture of problem
crystal cloud
,rotate 270
warm shaleBOT
crystal cloud
<@&286206848099549185>
crystal cloud
i tried putting
well no
i tried putting n to 500
and t to 0
and then see
how much t changes by
per hour
i got 2.4 but im 100% sure its wrong
proven zephyr
i tried putting n to 500
you mean n_0?
crystal cloud
nono
i tried seeing how much t changes by per hour
honestly not sure what to do tbh
crystal cloud
i dont
proven zephyr
ig so
proven zephyr
yes
crystal cloud
so does that make n = 500 as well
proven zephyr
because current time is 0
now
at hour 1
number of bacteria = 1200
try inserting it to the equation
proven zephyr
np
warm shaleBOT
crystal cloud
How do I plug that in
proven zephyr
just put 1 in time
crystal cloud
But how did u know t is time
proven zephyr
because that's the formula?
proven zephyr
but it's the formula
proven zephyr
crystal cloud
Like sped
timid silo
a
proven zephyr
ok he stopped spamming
crystal cloud
Anyway I solved for K
proven zephyr
ok
hot hazel
@timid silo don't spam
proven zephyr
K is growth
proven zephyr
rate of growth
crystal cloud
Is it how much it grows from initial value
proven zephyr
not rlly, but yes
proven zephyr
because it is wrong (nvm)
proven zephyr
,calc ln(2.4)
warm shaleBOT
The following error occured while calculating:
Error: Undefined function ln
proven zephyr
,w ln(2.4)
warm shaleBOT
crystal cloud
So is it right
proven zephyr
<@483962566977126401> sir are u alive
no
crystal cloud
Ok u know how to do it or no
proven zephyr
0.87546 should be correct
crystal cloud
But look at 55a
crystal cloud
a
crystal cloud
So how tf do I solve that if ifk what K is
proven zephyr
wdym you dont know what K is
proven zephyr
k is rate of growth..
crystal cloud
Ok so how many bacteria are there after 4 hours
proven zephyr
crystal cloud
Everytime t increase k increase with ig
It*
So always same
Omg
@proven zephyr thx
.close
obtuse pebbleBOT
proven zephyr
np
obtuse pebbleBOT
Available help channel!
torpid scroll
(x^3 - 2) ^3 / x^2 dx how would i go by this question?
obtuse pebbleBOT
(x^3 - 2) ^3 / x^2 dx how would i go by this question?
timid silo
to integrate? either expand it, or see that d/dx(x^3)=3x^2
torpid scroll
to integrate
warm shaleBOT
GoldenPhoenix
torpid scroll
yeah
steep harness
I think the best approach here, as toby said, would be a u substitution
try using the substitution $u=x^3-2$
warm shaleBOT
GoldenPhoenix
torpid scroll
thats the u du way right?
steep harness
yep
torpid scroll
oh i see
steep harness
often with problems like this, the hardest part is finding what the substitution should be
torpid scroll
often with problems like this, the hardest part is finding what the substitution...
I saw a video about it
and was confused how to pick which one to substitute with u
steep harness
that's fair. It's often not easy to intuitively see
basically you want to find a good u that will let you cancel some things out when you eventually substitute dx=f(u) du
torpid scroll
hmm
steep harness
where f(u) is the extra bits of the substitution that you need to make them match
if we use the sub I suggested above, can you find out what dx will turn into?
torpid scroll
if we use the sub I suggested above, can you find out what dx will turn into?
Igot a little confused here id have to get du then dx right?
steep harness
yes. we have the equation of the substitution, what we need to do is take the derivative of both sides, and remember that the derivative of u is du, and the derivative of the equation with x will have a dx at the end
torpid scroll
Wait im sorry my pc just suddenly shut down
steep harness
take your time, math can get tedious, there's no rush
torpid scroll
Im confused i think i got the answer but just shookt about the pc is it du / 2x² =dx
steep harness
yes
torpid scroll
Ngl my phone started hanging and wouldn't work its like i was hit by an emp or soemthing
steep harness
now we just need to make sure we only have u in our new equation, which isn't too bad, we just need to solve for u
torpid scroll
so we substitute dx with du/ 2x^2 in the equation?