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#help-33
marsh citrusBOT
wary kite
you as well
marsh citrusBOT
Available help channel!
toxic dome
marsh citrusBOT
toxic dome
Hello!
I’m having trouble finding the rest of my dots in this quadratic graph
I was wondering if anyone can lead me in the right direction
Almost got the hang of this but so confusing
I’m on question D I tried to lay out my steps as best as possible
Sorry if it’s messy
hidden dawn
I’m having trouble finding the rest of my dots in this quadratic graph
in other words, graph ur quadratic?
fallen swallow
i just want to check if the final answer is okay, going from polar coordinates to cartesian
marsh citrusBOT
i just want to check if the final answer is okay, going from polar coordinates t...
@fallen swallow Has your question been resolved?
fallen swallow
<@&286206848099549185>
main idol
i just want to check if the final answer is okay, going from polar coordinates t...
Looks fine so far
Oh no
r = sqrt(x^2 + y^2)
So r^3 = ?
fallen swallow
oh [sqrt(x^2 + y^2)]^3
i get stuck when operating with this, i recognize the form of each term in polar coordinates but my teacher said to also graph the equation. basically i get lost trying to simplify
main idol
oh [sqrt(x^2 + y^2)]^3
Square both sides at this step
fallen swallow
you mean this?
i know that step but after doing so i struggle to simplify and obtain a familiar polar equation
i was thinking of a Lemniscate but i cant get that form
main idol
you mean this?
No idea what this is supposed to be
main idol
i just want to check if the final answer is okay, going from polar coordinates t...
I meant square your last line once you fix the mistake
fallen swallow
No idea what this is supposed to be
cartesian to polar and then finding the graph
fallen swallow
I meant square your last line once you fix the mistake
why though? that would just make the right side a mess with a cubic root. or is it necessary?
main idol
why though? that would just make the right side a mess with a cubic root. or is ...
No
,tex .exp rules
elfin berryBOT
riemann
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ruby matrix
hi i have found that the rank of the rref is 2. does this mean it spans a plane?
static quarry
yep that's what it would mean if the rank is 2
viral edge
I don't understand this at all could someone help?
marsh citrusBOT
@ruby matrix Has your question been resolved?
elfin berryBOT
ego
ember jolt
junior copper
Haha
elfin berryBOT
ego
marsh citrusBOT
@bright meteor Has your question been resolved?
marsh citrusBOT
@bright meteor Has your question been resolved?
marsh citrusBOT
tight furnace
what will the terms be?
sure
you need a description of how the terms are ordered based on the b_i
that is true but you need more than that
find a simpler way to describe when one term is bigger than another without actually using the /7 stuff
b1 = 3, b2 = 6, b3 = 6, b4 = 6
b1 = 4, b2 = 0, b3 = 0, b4 = 0
which one is higher
ah whatever
this is just decimal expansion in base 7
the digits are b1, b2, b3, b4 in order
$0.b_1b_2b_3b_4$
elfin berryBOT
Dreyuk
tight furnace
so you do this the same way you compare decimals
yes
No it's not gonna be both of them
Oh wait
what are you getting for all 4 values?
oh maybe i'm off by 1
2020th from the top is 402nd from the bottom
,w 402 in base 7
elfin berryBOT
elfin berryBOT
tight furnace
ok yea looks good
marsh citrusBOT
tight furnace
no worries lol
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vague tendon
i calculated the individual probabilities using the binomial pd list function on calculator and tried to use the complement rule to find 1-P(1st group has less successes) but that clearly takes too much time
marsh citrusBOT
i calculated the individual probabilities using the binomial pd list function on...
vague tendon
so what's the correct way
wary kite
if the number of successes in the first is at least the number of successes in the second then x_1 >= x_2 hence x_1 - x_2 >= 0
marsh citrusBOT
@vague tendon Has your question been resolved?
vague tendon
if the number of successes in the first is at least the number of successes in t...
im srry but im not rlly fully getting it
vague tendon
<@&286206848099549185>
marsh citrusBOT
@vague tendon Has your question been resolved?
marsh citrusBOT
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lyric kelp
b right?
lyric kelp
.close
marsh citrusBOT
void elm
lyric kelp
ok tyty
faint narwhal
idk
jade edge
what is the equation of f(x)
faint narwhal
We don’t know
jade edge
We don’t know
Answering something that the data wasn't given
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misty plume
Extremely sorry I'm making another channel
A question came in my test today, it said: Let $L$ be a line $x + y + 1 = 0$, find the inclination of it from the y-axis.
I answered $\frac{\pi}{4}$
But I want to know, what's the complete definition of inclination of a line from another line.
marsh citrusBOT
Extremely sorry I'm making another channel
A question came in my test today, it ...
elfin berryBOT
@misty plume
misty plume
If I say let my line be $L_1$ whose inclination from $L_2$ is asked, is it necessary that the angle swept must be taken from $L_2$ to $L_1$ counter-clockwise ?
elfin berryBOT
@misty plume
deep plinth
How do I
deep plinth
No
sharp sonnet
how am i supposed to calculate the tolerance?
marsh citrusBOT
how am i supposed to calculate the tolerance?
sharp sonnet
i'm solving a for now
do i use R_s and then make a jacobian matrix?
a 1 row 3 collumn jacobian matrix
first partial wrt R_1 second wrt R_2 and third wrt R_3 ?
then what can i multiply it by?
marsh citrusBOT
@sharp sonnet Has your question been resolved?
sharp sonnet
<@&286206848099549185>
sharp sonnet
damn no one
no
its in my math book
its first order approximations
no partial derivatives
but it ain't physics 💀
sharp sonnet
.close
marsh citrusBOT
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burnt abyss
lim x->- inf of (x^3+x+1)/e^x
marsh citrusBOT
lim x->- inf of (x^3+x+1)/e^x
tight kite
you can use l'hopital when you have an indeterminate inf/inf or 0/0
both x³ + x + 1 and e^x go to infinity as x grows
burnt abyss
oh mb i meant x-> - inf
main idol
why can i use l'hopital's rule here
what do you get if you use l'hopital
main idol
but it's wrong
so you can't use l'hopital then
main idol
you can use l'hopital when you have an indeterminate inf/inf or 0/0
because it's not of this form
burnt abyss
is it because -inf/inf isnt indeterminate
so this
elfin berryBOT
riemann
burnt abyss
because it's not of this form
if i get something like inf/0 it just means that my approach is wrong?
main idol
the signs generally have to be the same, but you can just factor out a - sign from the fraction outside the limit
this implies they have to be the same sign
marsh citrusBOT
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red parrot
how do I find the diagonal asymptote for this function? (x^2)/(x-1)
marsh citrusBOT
how do I find the diagonal asymptote for this function? (x^2)/(x-1)
red parrot
I'll have to search that up but thanks!
quiet anvil
one second, and I'll show you a different example.
red parrot
Oki
quiet anvil
ok sorry
going to start now
I'm going to divide x^3 + 3x^2 + 3 by x+2
First, we write down our division in long division form. Except instead of powers of 10, we're concerned with powers of x. Other than that it's remarkably similar, and actually somewhat simpler (as our "ones" cannot affect our "tens" so to speak)
_____________________
x+2 | x^3 + 3x^2 + 0x + 3
Now we consider x^3 + 3x^2, how many times does x + 2 go into this value?
It goes into it x^2 times!
x^2
_____________________
x+2 | x^3 + 3x^2 + 0x + 3
Now we multiply x^2 by x+3 to get x^3 + 2x^2 and subtract.
x^2
_____________________
x+2 | x^3 + 3x^2 + 0x + 3
-x^3 - 2x^2
-----------
x^2 + 0x
Next, we consider how many times x+2 goes into x^2, this is x times.
x^2 + x
_____________________
x+2 | x^3 + 3x^2 + 0x + 3
-x^3 - 2x^2
-----------
x^2 + 0x
-x^2 - 2x
---------
- 2x + 3
How many times does x+2 go into -2x + 3? That's -2 times.
x^2 + x - 2
_____________________
x+2 | x^3 + 3x^2 + 0x + 3
-x^3 - 2x^2
-----------
x^2 + 0x
-x^2 - 2x
---------
- 2x + 3
-(-2x - 4)
----------
7
Finally, we can't put x+2 into 7, so we have 7 as our remainder.
So this mean:
[
\frac{x^2 + 3x^2 + 3}{x+2} = x^2 + x - 2 + \frac{7}{x+2}
]
elfin berryBOT
OmnipotentEntity
quiet anvil
And so our asymtote is going to be the parabola x^2 + x - 2
and the remainder goes to zero as x becomes large.
burnt abyss
this is eally amazing
red parrot
ahh okay
junior copper
I WAS WATCHING THIS THE WHOLE TIME
quiet anvil
It's literally the same thing.
lone heart
i suggest using synthetic division rather than long division
It's the same thing, one is just a shortcut
burnt abyss
nope synthetic is simpler and faster
quiet anvil
Yes, but I'm doing this to teach why it works
burnt abyss
at the end you get the same result
red parrot
I switched schools and I have no clue what those things are😭 I'm writing a test tomorrow
elfin berryBOT
CaptainNova22
quiet anvil
oh good, at least I didn't screw up 😄
lone heart
nope synthetic is simpler and faster
Synthetic is shortcut to long division
burnt abyss
yeah
red parrot
oki
junior copper
wow you can do poly divisionhere ??
red parrot
I'll go over it and see if I get the write answer then
quiet anvil
anyway, use synthetic division or polynomial long division, whichever you feel more comfortable with.
to find the limiting behavior of the function
red parrot
will do
burnt abyss
!!!!!!!!!!
remember
synthetic division only works when the polynomial you're dividing by has degree 1
otherwise you have to use long division
red parrot
okay
red parrot
Thank you!
quiet anvil
slick latex function btw
elfin berryBOT
CaptainNova22
lone heart
There's teh synthetic division
red parrot
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marsh citrusBOT
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sharp sonnet
anyone can help with this? i need to use first order approximation to find the overall tolerance.
marsh citrusBOT
anyone can help with this? i need to use first order approximation to find the o...
glossy flint
how do I find the diagonal asymptote for this function? (x^2)/(x-1)
You could also subtract and add 1 in the numerator (and then split the fraction)
sharp sonnet
no worries take you time
if you can help that'd be great
three ?
😂
790 and not 20%
less
yeah
what did you do to get it
damn
yeah
and the resistance
,
not .
elfin berryBOT
elfin berryBOT
sharp sonnet
should come out to about 59.96
sharp sonnet
for B its 5.64
elfin berryBOT
Requested by revita787
sharp sonnet
thats what the answer key says
yeah
probably
its an approximation so
yes please
uhh okay
you used this to find the final value
yeah
nono i did understand
thank you
.close
marsh citrusBOT
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quasi cedar
How did he get the -1
marsh citrusBOT
How did he get the -1
marsh citrusBOT
@quasi cedar Has your question been resolved?
quasi cedar
5-x is like -1*(x-5)
I dont understand
main idol
5-x is like -1*(x-5)
this is correct yes
quasi cedar
this is correct yes
Im confused
jaunty idol
I solved a) pretty easily, slope =-1 and intercept @ L.
For b, I've managed to find that $\beta = \varphi - \theta$ since using the interior sums of the triangle $\beta=\pi - (\theta + z)$ where $z$ is $\pi - \varphi$
This feels like it should be simple trig rules but i've been inventing so many new useless angles and I could use some help 🫠
marsh citrusBOT
I solved a) pretty easily, slope =-1 and intercept @ L.
For b, I've managed to f...
elfin berryBOT
NyanSequitur
marsh citrusBOT
@jaunty idol Has your question been resolved?
jaunty idol
this angle is $\pi-\pi/2-\sigma$ i think
elfin berryBOT
NyanSequitur
jaunty idol
<@&286206848099549185>
marsh citrusBOT
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steel moth
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brave marsh
What is it asking?
steel moth
Graph the following piecewise functions, using graphing techniques. Also, determine their domain and range.
brave marsh
Can you graph $3-(x+2)^2$?
elfin berryBOT
Azyrashacorki
steel moth
I need graph 3 - (x+2)^2; if -4 < 4 < x < -1
2 + √x+1; if x > -1
brave marsh
I know. The point is that if you can graph $3 - (x+2)^2$, then you can draw it between $-4$ and $-1$.
elfin berryBOT
Azyrashacorki
steel moth
Yes
marsh citrusBOT
@steel moth Has your question been resolved?
steel moth
<@&286206848099549185>
elfin berryBOT
ziming
north wadi
solve for the 2 x intercepts
y intercept
vertex
and you should have enough to graph
north wadi
this is a piecewise function?
ah nvm i see
plug in the x boundary values of this inequality
you have your vertex
so plot your vertex first
plot it up to -1
then plot your second function
steel moth
i need one helper let him speak spanish
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quiet lake
marsh citrusBOT
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wise oxide
How they know R=1
marsh citrusBOT
How they know R=1
brave marsh
The geometric series converges to 1/(1-t^3) if |t^3| < 1, so that is equivalent to |t| < 1.
Multiplying by t and integrating doesn't change the radius
wise oxide
The geometric series converges to 1/(1-t^3) if |t^3| < 1, so that is equivalent ...
So I always put the r in 1/1-r into <1 and that’s it?
So it will always be 1
brave marsh
I mean in this case yes, but if you had like $\frac{1}{1 - \frac{t}{2}}$, then your radius would be 2
elfin berryBOT
Azyrashacorki
wise oxide
The geometric series converges to 1/(1-t^3) if |t^3| < 1, so that is equivalent ...
So u cube root the 1 also right? Cus u always wanna get x alone in order to get radius?
Is that how it works
brave marsh
Yes
wise oxide
Ok also for all these types of questions that says evaluate the integral that already has an integral in front I don’t need to find what c is?
brave marsh
No, because C can be anything, so you couldn't find C even if you wanted.
wise oxide
No, because C can be anything, so you couldn't find C even if you wanted.
Yeah I meant for any single question that asks for power series representation that has an integral sign already
marsh citrusBOT
@wise oxide Has your question been resolved?
hot island
hi just had a quick question
marsh citrusBOT
hi just had a quick question
hot island
this question here i got an awnser like (−∞,−4)∪[1,2)∪(2,∞).
but when i saw an lecturer example of a simular question like
they gave an awnser like
do i need to reformat my solution to what my lecturer did im not sure anymore
<@&286206848099549185>
hot island
<@&286206848099549185>
marsh citrusBOT
@hot island Has your question been resolved?
hot island
yeah i would but this coursework due in too soon
so i dont rlly have time
however if the awnser above is also correct
its still an interval isnt it
uhhh well its a university lecturer
so your not rlly personal with them
but if i was to guess im not sure tbh
yeah alright ill give it a go and see what he say
marsh citrusBOT
If you are done with this channel, please mark your problem as solved by typing .close
alpine basalt
marsh citrusBOT
alpine basalt
couldn't part (ii) be done without bringing in the supremum norm?
WHy even mention it
seems so random
neither the definition of the unfirom convergence nor uniform cauchy requires it
do you have brain damage
??
tired oxide
gone
static quarry
couldn't part (ii) be done without bringing in the supremum norm?
WHy even menti...
you don't have to explicitly use the supremum norm, but the condition:
f_n(x) - f(x) < epsilon for all x in D
is equivalent to
||f_n - f||_infinity < epsilon
so you can say it either way
alpine basalt
you don't have to explicitly use the supremum norm, but the condition:
f_n(x) - ...
so basically, I get to save a few words
and not say "for all x in D"
static quarry
yes
but then you have to do extra work for the triangle inequality part
using the fact that uniform convergence is equivalent to convergence in the sup norm just makes life easier in general
marsh citrusBOT
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near elbow
marsh citrusBOT
near elbow
Guys, in which situation do we use Way A, and in which situation do we use Way B?
Way A is adding the column of “others (other letters beside P and E)”
Way B is adding all multiplying all columns (Letter O, Letter R, and other letters beside O and R) in each row and then adding each row
marsh citrusBOT
@near elbow Has your question been resolved?
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@near elbow Has your question been resolved?
near elbow
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marsh citrusBOT
native frigate
🦕
vast magnet
🦕
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languid zodiac
how do I do part B ?
marsh citrusBOT
how do I do part B ?
languid zodiac
Im new to matrix my answers for 1a) is k = 2 , and eigenvalue = 12
amber birch
Im new to matrix my answers for 1a) is k = 2 , and eigenvalue = 12
great so you need to find the eigenvectors of A now
amber birch
you need to solve the system $6x - 3y = 12x$ and $2x + 7y = 12y$ then
elfin berryBOT
south, just south
amber birch
it already gave me that no?
well the point is to find m, n
amber birch
you need to solve the system $6x - 3y = 12x$ and $2x + 7y = 12y$ then
this comes from $Ax = \lambda x$
elfin berryBOT
south, just south
static quarry
Im new to matrix my answers for 1a) is k = 2 , and eigenvalue = 12
um ```
A = [6 -3; 2 7]
A =
6 -3
2 7
eig(A)
ans =
6.5 + 2.39791576165636i
6.5 - 2.39791576165636i
it also can be arranged into $(A - \lambda I)x = 0$
elfin berryBOT
south, just south
amber birch
um ```
>> A = [6 -3; 2 7]
A =
6 -3
2 7
>> eig(A)
ans =
...
oh good point
languid zodiac
um ```
>> A = [6 -3; 2 7]
A =
6 -3
2 7
>> eig(A)
ans =
...
did I do something wrong in part a?
static quarry
well first of all, the trace is the sum of the eigenvalues
so they can't be 4 and 12
languid zodiac
oh
static quarry
so use that to find the second eigenvalue
then use that the determinant is the product of the eigenvalues in order to find k
amber birch
very very smart
languid zodiac
so use det(A-eigenvalue2) = 0?
static quarry
yea you can do it that way
languid zodiac
how to i stop occuping this chat ?
vast magnet
dot close
amber birch
how to i stop occuping this chat ?
.close
marsh citrusBOT
languid zodiac
ty
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marsh citrusBOT
I need help
sly fractal
solving this
amber birch
solving this
which part?
marsh citrusBOT
@sly fractal Has your question been resolved?
brave spire
yo mathcord
marsh citrusBOT
yo mathcord
brave spire
its been a while
STEMS by CMI, problem 5, 2024, Category-A
Where do I even start?
runic temple
linEx
brave spire
linEx?
runic temple
linearity of expectation
brave spire
uhh i think u mean i gotta do sum prob*outcome?
runic temple
whats the expected minimum of any random 2tuple
then you have 5 tuples
et voila
done
brave spire
whats the expected minimum of any random 2tuple
i dont know 😐
that is precisely the problem
i know the expectation is a+b/2 i think
runic temple
given a pair, what is the probability 1 is the minimum of said pair
better question
how many items are in your sample space
and how many of them have one as a minimum
brave spire
9?
brave spire
given a pair, what is the probability 1 is the minimum of said pair
well..thats almost always true no?
until and unless its a doublet
which cant happen in this case
brave spire
oh right cus 10C2
brave spire
so its 5*9/45?
runic temple
no
you have to figure out the probability that 2,3,4... are minimum
and add that to your expected value
marsh citrusBOT
sly fractal
which part?
end part
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Available help channel!
spare idol
marsh citrusBOT
spare idol
i did the whole Lagrangian and then minimised it
$\mathcal{L}(w, \lambda, \gamma) = \frac{1}{2}w^\prime \Sigma w + \lambda(1 - w^\prime 1) + \gamma(\mu - w^\prime z)$
elfin berryBOT
DW1
spare idol
$\frac{\partial \mathcal{L}}{\partial w} = \Sigma w - \lambda 1 - \gamma z$
elfin berryBOT
DW1
spare idol
$\frac{\partial \mathcal{L}}{\partial \lambda} = 1 - w^\prime 1$
elfin berryBOT
DW1
spare idol
$\frac{\partial \mathcal{L}}{\partial \gamma} = \mu - w^\prime z$
elfin berryBOT
DW1
marsh citrusBOT
@spare idol Has your question been resolved?
spare idol
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marsh citrusBOT
@spare idol Has your question been resolved?
humble oasis
<@&286206848099549185> quick douibt, what is integral from 1 to 2 ,x^2 d(lnx)
here since its wrt lnx, so lnx belongs to [1,2] right? and not x
humble oasis
d(lnx) is 1/x
yea but obviously limits will change
humble oasis
so ur just integrating x from 1 to 2
no
humble oasis
limits will change to ln(2) and 0
wont it be from e to e^2
spare idol
wait sorry my brain is completely fried
honestly im pretty sure the limits dont need to be changed
idk tho
its bedtime
marsh citrusBOT
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marsh citrusBOT
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vague tendon
im not sure how id solve this tbh
marsh citrusBOT
im not sure how id solve this tbh
amber birch
im not sure how id solve this tbh
Venn diagram it
yeah I think this question is conditional probability
but the Venn diagram part helps with finding P(woman AND goes out of business)
marsh citrusBOT
@vague tendon Has your question been resolved?
summer geyser
help solving this?
last hound
Hi I have this it says study the continue and the derivability of F and G and then calculate G'
What steps should I do here?
Also consider if the bound goes to inf what will change?
marsh citrusBOT
Hi I have this it says study the continue and the derivability of F and G and th...
@last hound Has your question been resolved?
last hound
<@&286206848099549185>
obsidian aurora
E
limber trellis
Hi I have this it says study the continue and the derivability of F and G and th...
are both supposed to be F
last hound
are both supposed to be F
Oh sorry, second one is G
limber trellis
Oh sorry, second one is G
g looks straight forward you can bring e^x(x+1) out of integration sign
as we are integrating wrt to t
last hound
as we are integrating wrt to t
Yeah, but I wanna study the continuous and the derivability of these 2 integrals and I guess using theory , not directly calculate the integers
limber trellis
Yeah, but I wanna study the continuous and the derivability of these 2 integrals...
i mean g is just a normal exponential function so it would be continous and dif on R
last hound
i mean g is just a normal exponential function so it would be continous and dif ...
Alr, so what about F
limber trellis
Alr, so what about F
im not sure honestly are sure its -x^2.t^3 in the power
marsh citrusBOT
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marsh citrusBOT
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turbid tinsel
How would the finished product of constructing a parallelogram ABCD look like if AB = 7cm and AD = 5cm but A=30°
marsh citrusBOT
How would the finished product of constructing a parallelogram ABCD look like if...
@turbid tinsel Has your question been resolved?
turbid tinsel
<@&286206848099549185>
proud ice
How would the finished product of constructing a parallelogram ABCD look like if...
!original
marsh citrusBOT
How would the finished product of constructing a parallelogram ABCD look like if...
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.
proud ice
How would the finished product of constructing a parallelogram ABCD look like if...
!status
marsh citrusBOT
How would the finished product of constructing a parallelogram ABCD look like if...
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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
2
marsh citrusBOT
Show your work, and if possible, explain where you are stuck.
@turbid tinsel Has your question been resolved?
hot pewter
Sketch Re(ln(z)) = 2 on an argand diagram
marsh citrusBOT
Sketch Re(ln(z)) = 2 on an argand diagram
hot pewter
.close
marsh citrusBOT
fathom ridge
@hot pewter did you get it?
marsh citrusBOT
Available help channel!
hot pewter
<@713315095270391899> did you get it?
yh i did
hot pewter
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marsh citrusBOT
marsh citrusBOT
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proven stump
Help
proven stump
Help especially with 3.1 is the anyone with macro economics knowledge
🙏
<@&286206848099549185>
marsh citrusBOT
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.
marsh citrusBOT
marsh citrusBOT
Available help channel!
green plume
Me and my classmate took a 20 item multiple choice exam and we got the same score and even had the same answers in each item, what is the probability of that happening
marsh citrusBOT
Me and my classmate took a 20 item multiple choice exam and we got the same scor...
spare idol
theres a 1 in 4 chance that both of you match on one question
so there'll be a (1/4)^20 chance that you match on all 20 questions
$\left( \frac{1}{4} \right)^{20}$
elfin berryBOT
DW1
marsh citrusBOT
@green plume Has your question been resolved?
slate gazelle
This is a question from a national high school exam in a central european country.
Complex numbers are not a part of the high school syllabus there so students are not expected to know they exist when writing the exam.
The task is to solve the equation:
marsh citrusBOT
This is a question from a national high school exam in a central european countr...
slate gazelle
the equation has 3 real solutions, and 2 complex solutions.
According to the markscheme the correct answer is the 3 real solutions.
And now the actual question:
- is the markscheme wrong? The three real solutions are not all the existing solutions
- if a student answers with real and complex solutions, can their answer be then treated as incorrect?
tight kite
,w solve (x³ + 125)(x² - 64) = 0
elfin berryBOT
slate gazelle
“Solve the equation:”
tight kite
do you have a screenshot?
slate gazelle
proud ice
the equation has 3 real solutions, and 2 complex solutions.
According to the m...
- is the markscheme wrong? The three real solutions are not all the existing solutions
No. If the equation exists in the domain of real numbers, then there are only three solutions
- if a student answers with real and complex solutions, can their answer be then treated as incorrect?
Probably.
If the student cannot explain that they choose 3 real and 2 complex solutions, then the grader has no way to know. Ultimately, the wording of the problem is poor. It should ask "find the number of distinct real solutions", or the beginning of the exam should clarify that all solutions are expected to be real-valued numbers.
slate gazelle
The wording is as it is, and there is no clarification at the beginning. The domain isn’t mentioned. It’s just assumed that no one who takes the exam knows what complex numbers are. The markscheme says to reward the two points only if the answer is -8, 8 and -5. Any other answer, less/more solutions, etc and the student receives 0 points as the grader must follow the markscheme
Considering all the facts, is the question/markscheme wrong or am I missing something?🤷♂️
proud ice
Considering all the facts, is the question/markscheme wrong or am I missing some...
It has left the realm of right or wrong. It is simply poorly worded.
marsh citrusBOT
@slate gazelle Has your question been resolved?
lilac siren
Discrete Fourier Transform Q
marsh citrusBOT
Discrete Fourier Transform Q
lilac siren
I have some signal [0,1,0,-1] and the DFT of it is [0,-i/2,0,i/2] and I have no interpretation as to why
I get that the first DFT value must be 0 since the constant component of the signal is 0
but why for frequency 1 the value -i/2 and for frequency 3 the value i/2 idk
I thought I'd use this signal as simple example as it mimics a sine curve, so I thought I'd get only one component in the DFT with magnitude 1, but instead I have 2 now
ebon solar
did you get this DFT from python?
or did you calculate it
for python you have to be careful because it returns the FFT in a specific way
marsh citrusBOT
@lilac siren Has your question been resolved?
lilac siren
or did you calculate it
calculate
yes numpy doesn't normalize, it'd yield [0,-2i,0,2i] instead
I mainly don't get how the DFT explains the initial signal
ebon solar
oh i see
i understand ur q now
your signal [0,1,0,-1] is a sinusoid
a REAL sinusoid
aand
$\sin(x) = \frac{e^{ix}-e^{-ix}}{2i}$
elfin berryBOT
rain
ebon solar
so you decomposed a sine into its two complex exponentials
and also
if the signal is real
then the transform is conjugate symmetric
marsh citrusBOT
@lilac siren Has your question been resolved?
marsh citrusBOT
lilac siren
I watched 3B1B's DFT series in parallel :]
marsh citrusBOT
Available help channel!
lime pumice
missed a day in class what is this vector chart????
marsh citrusBOT
missed a day in class what is this vector chart????
grizzled sonnet
x vs t being displacement vs time and v vs t being velocity vs time
lime pumice
how do i relate that visual to the graphs?
grizzled sonnet
well you already drew v vs t it looks like
sort of
are you having trouble with x vs t?
grizzled sonnet
okay, well let's think about what the visualization means in real life
suppose you move at a constant velocity for 1 second.
you have some x0 before you started moving, and some x1 after
what can we say about the relationship between x0 and x1? assuming your velocity is positive, is x1 greater than x0, equal or less? if it's greater or less, how does it change with respect to time (is it linear [smooth] or quadratic [curved])
lime pumice
looks pretty smooth to me
grizzled sonnet
suppose these two lines describe a points position with respect to time
can you visualize what their motion might look like
are either of them moving at a constant speed (initially)? what does the flat line mean?
lime pumice
the speed and velocity of the line and the curve are the same though the speed of the linear lines is constant and the red speeds up with respect to y
the blue ones speed and velocity are faster because the path is more direct
grizzled sonnet
you are right that the blue line is linear, and that that implies constant speed, but an important thing to realize here is that this says nothing about path
these particles are both traveling in a straight line
lime pumice
but the total distance of the red one is higher because the path is less direct
grizzled sonnet
the path is not less direct, they are both traveling along the same path
let me try to illustrate this
lime pumice
the velocity which is the x of the graph
grizzled sonnet
time is x, displacement is y
grizzled sonnet
suppose these two lines describe a points position with respect to time
"position with respect to time"
lime pumice
1/3(y/x) is the velocity but the distance is different, if you integrated and then found the +x and the +y of a couple points the distance would be different??? this is what my teacher taught me
im just confused about the motion map
grizzled sonnet
im just confused about the motion map
im trying to build your intuition for the motion map
grizzled sonnet
suppose these two lines describe a points position with respect to time
imagine each of these slivers as being different momentsi n time in the motion of these particles
you can see that they both take a straight line to get to their destination
the path is, literally, the same
the blue line in the graph i drew represents the motion of the blue dot, you can tell it has a constant speed because it moves the same distance between every instant (assuming these instants are equally spaced, which they are)
the red line represents the red dot. you can tell its speed isnt constant because it starts out slower, and then ends up getting to the end first. essentially, it accelerated.
the flat line at the end depicts when they stop
even though there speed is zero, they are still displaced from their original starting position
they arent moving, so it doesnt go up, but they are still displaced. if they returned to their starting positions, the graph would show a fall back down to 0.
grizzled sonnet
missed a day in class what is this vector chart????
let's look at this example now
this is sort of what you should "see" when you look at a visualization like that
it moves at a constant speed, then stops. then repeat.
the reason that this visualization is so helpful is because it actually draws the line for you
does any of this not make sense?
lime pumice
yeah i never got told any about the motion map i dont get why its going up
grizzled sonnet
the y axis is displacement
the further away from your starting position you go, the more it should go up.
lime pumice
where from the map does the displacement come from
grizzled sonnet
velocity
its velocity vs. time
if you move at a constant speed, then in a given amount of time you move a set distance (the same distance no matter what)
look at these side-by-side
in the first "section" of the velocity graph, you are moving
so from t=0 to t=1, you move some distance
in the second section, you arent moving
so from t=1 to t=2, you havent moved
in the third section you move again, so from t=2 to t=3, you've moved the same distance you moved the first time (i.e. "constant" velocity)
lime pumice
awesome i see so velocity 4/7 bc 4up 7right?
grizzled sonnet
i mean, sure, but units, units, units. each of those gaps could be 10m, and so your velocity would be 40 meters in 7 seconds.
the numerical values aren't really the point, its more the trend you have to see
but yes, 4/7 is a constant, so if you wanted you could say (4/7 m) / second, you'd get the same trend
still confused?
lime pumice
on getting the motion map to the t,x graph not really i think but could you explain the v vs t
lime pumice
0
grizzled sonnet
right, so if its velocity vs. time, where will the line be during those times?
lime pumice
+1v
lime pumice
on the ground and the other one is +1v
lime pumice
how do you write a math expression for that
grizzled sonnet
well, you wouldnt normally need to. but if you are curious, let's say you have constant velocity for c time, and then 0 velocity for c time, back and forth
t is current time & v is the constant velocity you travel at, and v(t) describes the function of velocity vs time,
v(t) = v*mod(floor(t/c), 2) i believe?
lime pumice
im not sure thats what im asking lol
grizzled sonnet
well, you wouldnt normally need to. but if you are curious, let's say you have c...
nvm this is wrong, its something like v(ceil(mod/t/c, 2) - 1)
grizzled sonnet
im not sure thats what im asking lol
oh weird
lime pumice
i was trying to find that earlier i couldnt get it lol
grizzled sonnet
oh wait
no i think i was right, lol
yeah i just put it in wrong
well actually its v*mod(floor( (t-c) / c, 2)
for intervals of length 2 and velocity 10, for example
lime pumice
strange ill just ask him tomorrow
grizzled sonnet
i do find that question odd i wonder if thats actually what hes asking
im not sure you can do that without modular division and it seems unlikely to see that in a physics course
well, an introductory one
grizzled sonnet
im not sure thats what im asking lol
i dont think your answer to part d is right
lime pumice
4/7= 0.57?
grizzled sonnet
thats for a straight line, though. if you evaluated that at t = 1 you would not get what you expect
lime pumice
yeah it woulld be 0.60x/t
grizzled sonnet
grizzled sonnet
yeah it woulld be 0.60x/t
no, in general you cant use slope here
grizzled sonnet
notice how at the yellow line the blue != red
red is your actual line, blue is what slope (rise/run) will give you
lime pumice
well the red line linearized is the blue line which is what he wants i believe i missed a day lol
grizzled sonnet
actually this is more accurate but same idea
grizzled sonnet
well the red line linearized is the blue line which is what he wants i believe i...
blue line is basically just an average
if that's what he wants thats what he wants
but that's an odd way to phrase it
grizzled sonnet
no the velocity of the red line is constant
grizzled sonnet
im not sure thats what im asking lol
the graph on the right is what the velocity of the red line is
it doesnt increase w time
lime pumice
ik the velocity of the red and blue is the same right
grizzled sonnet
the blue line doesnt really have much significance here; its basically a heuristic to guess where the particle is given t. without knowing what intervals it stops at
grizzled sonnet
ik the velocity of the red and blue is the same right
on average.
same distance/time overall but in general red is either faster or slower depending on if its moving or not
its like if you raced usain bolt, except he took breaks
lime pumice
well yeah i forgot it is called Vsubscribt(avg)
grizzled sonnet
oh
well, yeah if that's what you are looking for. still dont think that the way the question was asked implies that at all
lime pumice
so would it would like 1xbreak1,1xbreak1,so on
if u get my thinking
like how would you write one
grizzled sonnet
that one is a bit harder, tbh
lime pumice
i added bc i saw the mutual server
grizzled sonnet
i added bc i saw the mutual server
im not really active there anymore
lime pumice
also i have another question about the graphs
grizzled sonnet
ye
lime pumice
you can see i sorta added the area and got 6.5xt @ t=5 and the other was 3x^2/t @=5 obvioulsy it happens because they are different kinds of graphs but the units i got are different and could or couldnt be equal???
is this a weird question?
grizzled sonnet
why are you adding the area ? basically just integrating
lime pumice
im sorta a nerd and just thought to for some reason
yeah basically
yeah this was the idea but the integration is crossed out bc my teacher said integration bad
do you think the answers i got for each graph could be the same?
grizzled sonnet
you shouldnt integrate displacement, you get something called absement which is a topic you'll probably never see
the integral of velocity is displacement, though.
so if you sum up all those areas you under v vs t you should get the final displacement
lime pumice
why doesnt x*t work though?
grizzled sonnet
displacement * time?
thats absement
its just a unit you wont use
it works but it doesnt mean anything useful
lime pumice
but is it equal to the disp or you cant know bc its with time?
grizzled sonnet
you are confusing me .-.
dt as in Δtis change in time
dt as in dt in an integral, is the integration of any function with respect to the variable t, usually velocity or acceleration with respect to time t
the velocity / acceleration comment was an analogy. im saying the units you create by completely arbitrarily choosing to take the integral of position, create "absement" and that "absement" is as different from displacement as velocity is from acceleration. neither pair really makes sense to compare to each other.
grizzled sonnet
distance / time is speed
distance / time * time = distance, which is displacement
so, distance * time would be absement. the integral of a constant displacement d with respect to time, is d*t, yes. this would be in units of "meter seconds"
lime pumice
metre-second is wild
grizzled sonnet
not meters per second or feet per second, just.. "per second"
grizzled sonnet
meter second
weird
lime pumice
its was just a bunch of random units on x and y
welp goodnight im not active on osu server but i play
marsh citrusBOT
@lime pumice Has your question been resolved?
weary trench
Does anyone know of a variant of the Bradley-Terry model that deals with ties and player-/match-specific control variables? Is it a sensible approach for a logistic regression implementation to just add explanatory variables on top of the player dummies? https://en.wikipedia.org/wiki/Bradley–Terry_model
marsh citrusBOT
Does anyone know of a variant of the Bradley-Terry model that deals with ties an...
@weary trench Has your question been resolved?
marsh citrusBOT
@weary trench Has your question been resolved?
still temple
how to know when is x^2 - x is decreasing in magnitude after 0
marsh citrusBOT
how to know when is x^2 - x is decreasing in magnitude after 0
grizzled sonnet
how to know when is x^2 - x is decreasing in magnitude after 0
you mean on what interval?
still temple
yes
grizzled sonnet
find the derivative, set it equal to 0 and solve for x, this is the "critical point"
when its not changing at all, that means its flat, and on either side of that point it must either increase or decrease
find the side its decreasing on and then you should have the interval
for example if it decreases after the critical point (from x = k to infinity), then your interval is $[k, \infty)$
if it decreases before the critical point, your left bound is 0 (per the problem), so the interval is $[0, k)$ (or if 0 is not included, $(0, k)$
actually its been years since i did cal 1, i dont remember if you include the critical point here
i dont think so though
elfin berryBOT
Karma
still temple
wait
What's the answer then?
I am asking decrease in magnitude, not decrease in value
grizzled sonnet
huh? is this something i havent heard of lol? is the magnitude not the y value?
still temple
The magnitude is abs(f(x))
grizzled sonnet
oh, duh
wouldnt it just be inverted
at the critical point in the normal function, it is decreasing on the left and increasing on the right
in the abs function, it is decreasing on the right, increasing on the left
still temple
So the answer is from 0.5 to 1?
grizzled sonnet
well, yes, but the abs adds extra steps to get there
in general:
solve for the 0s of the original function
take the derivative
find the critical point
plug that into the original function
if its positive, dont invert when checking increasing/decreasing
if its negative, invert
the answer is then the critical point to the (post inversion if applicable) zero of the original function in that direction, if there is none, the infinity in that direction, unless you have another bound
i believe
grizzled sonnet
in this case, critical point is x = 0.5, and it decreases on the left. but in the original function, f(0.5) is negative, so we go right. the zero to the right of x = 0.5 is x = 1, so the bound is 0.5 to 1, in this case
wary kite
if you want to do this analytically just note that the derivative of |x| is x/|x|
wary kite
if you want to do this analytically just note that the derivative of |x| is x/|x...
would you like to know why?
$|x| = \sqrt{x^2}$
elfin berryBOT
knief
wary kite
hence
$\frac{d}{dx} |x| = \frac{d}{dx} \sqrt{x^2} = \frac{x}{\sqrt{x^2}} = \frac{x}{|x|}$
elfin berryBOT
knief
elfin berryBOT
knief
wary kite
2x-1 from chain rule
then for it to be decreasing we require this to be < 0
$\frac{(x^2-x)(2x-1)}{|x^2-x|} < 0$
elfin berryBOT
knief
wary kite
denominator is always nonnegative, so for this to be less than zero we need 2x-1 < 0 and x^2-x > 0 or x^2-x < 0 and 2x-1>0
for the first the intersection of the two intervals is x<1/2 and (x<0 or x>1) hence we have x < 0 but we said we were ignoring that in your question
we get x<0 btw because x<1/2 and (x<0 or x>1) is equivalent to (x<1/2 and x<0) or (x<1/2 and x>1) the second part is the empty set since x cannot both be less than one half and greater than 1, so we just consider the first part and the intersection of x<1/2 and x<0 is just x<0
now for the second intersection we have 0<x<1 and x > 1/2 hence we just have x > 1/2
@still temple
@red nimbus did you really just 🔥 because i said positive instead of nonnegative lol
red nimbus
<@587715738484211754> did you really just 🔥 because i said positive instead of ...
in fact
wary kite
lol
red nimbus
the denominator must be always positive
marsh citrusBOT
@still temple Has your question been resolved?
still temple
.close
marsh citrusBOT
winter anchor
the disrespect is crazyy
wary kite
what
wary kite
the disrespect is crazyy
wdym
winter anchor
wdym
I'll look at your messages later
damn, you helped them and they hit u with that
red nimbus
it’s all good
still temple
?
wary kite
lol
still temple
$\frac{d}{dx} |x^2-x| = \frac{(x^2-x)(2x-1)}{|x^2-x|}$
elfin berryBOT
anjali
still temple
How you got 2x-1
still temple
this step
wary kite
why
still temple
idk chain rule lol
still temple
nope
wary kite
oh lol then yea this won’t help you
wary kite
the channel had already been closed
marsh citrusBOT
Available help channel!
deep grail
How do I find the domain and range of this function
marsh citrusBOT
How do I find the domain and range of this function
deep grail
What I usually do for the domain x > 0 and solve
And the range I get from the graph
But I can’t draw this function
grizzled sonnet
domain is "what values of x is it defined on"
we know we cant sqrt negative numbers
and we know we cant do 1/0
everything else is fair game
so if we cant do 1/0,
When is $\ln(1-2x^2) = 0$
elfin berryBOT
Karma
elfin berryBOT
Karma
grizzled sonnet
your domain is "everything else"
@deep grail
as for range, its the max and min value you can get out of this function. can you think of how we might approach that?
grizzled sonnet
ln(x) = y means e^y = x
so e^0 = 1 - 2x^2
so 1 = 1 - 2x^2
so 0 = -2x^2
more simply, any log(x) = 0 when x = 1, so just set the inside = 1 whenever you see that
grizzled sonnet
let's see if you can figure out the logic. start somewhere, and we'll go from there.
think about what makes the function really small, and what makes it very large.
deep grail
as for range, its the max and min value you can get out of this function. can yo...
Find the limit when x approaches infinity and negative infinity?
grizzled sonnet
not quite
when x is negative infinity, the sqrt term is undefined.
these things are case-by-case, honestly
limits are a good spot to start though, the thinking is similar
deep grail
when x is negative infinity, the sqrt term is undefined.
Ok right
We said that the domain was R/{sqrt(1/2)}
So we get the limit there and infinity
We should have alp the values there
grizzled sonnet
We said that the domain was R/{sqrt(1/2)}
?
deep grail
Oh I miss calculated mb
grizzled sonnet
The smallest value $f(x) + g(x)$ can produce is $\min(f(x)) + \min(g(x))$.
Therefore the smallest value $\frac{1}{\ln(1-2x^2)} + \sqrt{x}$ can produce is $\min(\frac{1}{\ln(1-2x^2)}) + \min(\sqrt{x})$
elfin berryBOT
Karma
grizzled sonnet
Oh I miss calculated mb
i dont even know what you meant by that, where'd you get sqrt(1/2)?
deep grail
Nvm😂
grizzled sonnet
lol
its undefined for negatives, and for when the ln term is 0
so whats the domain?
deep grail
(0,infinity)?
grizzled sonnet
yup
grizzled sonnet
The smallest value $f(x) + g(x)$ can produce is $\min(f(x)) + \min(g(x))$.
There...
now this for the range
deep grail
I don’t get it
grizzled sonnet
whats the smallest value for 1/u
deep grail
If its 0 it approaches infinity but its not 0
grizzled sonnet
If its 0 it approaches infinity but its not 0
1/0.1 is 10
1/0.01 is 100
1/0.001 is 1000
we want the minimum value
that's getting larger
grizzled sonnet
well whats the minimum value?
deep grail
Close to 0
grizzled sonnet
yes, why?
deep grail
And that gives us infinity