I keep getting one yet it’s wrong. What am I supposed to do?
#help-23
dapper mango
safe radishBOT
I keep getting one yet it’s wrong. What am I supposed to do?
hot thistle
can you show your work?
dapper mango
I don’t really know how to start the problem
pseudo scroll
$$\int_a^b f(x) \dd x = -\int_b^a f(x) \dd x$$
$$\int_a^c f(x) \dd x + \int_c^b f(x) \dd x = \int_a^b f(x) \dd x$$
flat frigateBOT
NEONPerseus
pseudo scroll
Do you know these properties
dapper mango
Yeah
pseudo scroll
Have you tried using them
dapper mango
I just don’t understand how you would get 15
flat frigateBOT
NEONPerseus
flat frigateBOT
NEONPerseus
pseudo scroll
Using the two given integrals can you find F(8) and F(1)?
dapper mango
I’m blanking
pseudo scroll
Hmm
If I say the integral of f(x) is F(x), what would the first integral evaluate to
hot thistle
i think there's an easier way to visualize this than with F(x)s
pseudo scroll
hot thistle
(it's the same thing but keeping it as an integral)
pseudo scroll
**NEONPerseus**
You can do it with these properties I guess
Try to get the bounds of the two integrals in the way that second property is laid out
hot thistle
yeah i think that's enough
dapper mango
Wouldn’t integral 8 to 1 of f(x) just equal 1 tho
hot thistle
how did you get that
dapper mango
After combining the two integrals
hot thistle
ye
pseudo scroll
Also do you mean 1 to 8
hot thistle
so we have $\int_1^8 f(x), dx = 1$
flat frigateBOT
maximo
dapper mango
Yeah
pseudo scroll
Just the 2 bit
dapper mango
But wouldn’t your final answer be 3 because you just add them or am I in the complete wrong direction
hot thistle
well
pseudo scroll
You need to make sure the bounds match up
What you did was correct by flipping the bounds on the first I assume
You're integrating from 1 to 5 and adding on the area from 5 to 8
hot thistle
But wouldn’t your final answer be 3 because you just add them or am I in the com...
are you saying $\int_1^8(f(x) +2), dx = 3$?
flat frigateBOT
maximo
pseudo scroll
Oh
dapper mango
Yea
pseudo scroll
sorry for barging in neon
Nah I think it's good you came in 
hot thistle
have you heard of this $$\int(f(x) + g(x)), dx = \int f(x), dx + \int g(x), dx$$?
flat frigateBOT
maximo
hot thistle
it's part of the linearity of the integral
dapper mango
Yeah
hot thistle
we should apply this here
dapper mango
I still just don’t know where 15 comes from at all
flat frigateBOT
maximo
hot thistle
**maximo**
let's split it like i split this integral
hot thistle
by limit you mean integral yeah?
dapper mango
Yeah
hot thistle
if so yes, it's not just the number (usually)
dapper mango
I’m reviewing all the units right now
They’re mixing together
Thank you for the help
hot thistle
no problem
dapper mango
.close
safe radishBOT
safe radishBOT
Available help channel!
void agate
I need help with number 9
safe radishBOT
I need help with number 9
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
icy lance
start by finding the inverse of h
icy lance
how did you get h^-1(x) = 1/2?
void agate
Am I wrong?
void agate
say x=2y-1 and make y the subject
it would be..
x + 1 = 2y
(x + 1)/2 = y
Sorry my mistake for doing it carelessly
@icy lance
Sorry for pinging you alot..
icy lance
its alright
yeah h^-1(x)=(x+1)/2
now just use the function as per the question and then solve for m
void agate
Oh so would it be like this..
h^-1(5m - 1) - h^-1 (9 + 1)/2 =15?
safe radishBOT
@void agate Has your question been resolved?
sour hornet
Hello
sour hornet
I have a query regarding Pythagoras' theorem
hazy elbow
Just ask
hazy elbow
I have a query regarding Pythagoras' theorem
L spelling tho
sour hornet
PQRS is a rectangle in which PQ= 9 cm and PS=6cm. T is a point on PQ such that PT= 7cm and RV is the perpendicular from R to ST. Calculate ST and RV.
hazy elbow
Notice PTS is a right triangle
same for SVR
SVR is a bit tricky. It'll require construction
weary blaze
or you can get angle VSR and use trig to find the side RV
hazy elbow
or you can get angle VSR and use trig to find the side RV
That'll require calculator
tanx=7/6
safe radishBOT
@sour hornet Has your question been resolved?
hazy elbow
@sour hornet You there?
sour hornet
Yes I am
hazy elbow
Yeah so you need to connect R and T
sour hornet
Ok... and then?
hazy elbow
Use pythagoreas theorem to find RT
from triangle TQR
and yeah find ST also using pythagoreas
sour hornet
Listen... If you look closely, the triangle TQR is a triangle but I will need at least 2 sides to apply the Pythagoras' theorem
This is the diagram that is supposed to form according to the question and told by my teacher
hazy elbow
Listen... If you look closely, the triangle TQR is a triangle but I will need at...
yeah so you have qr and tq
qr is 6 and tq is 2
hazy elbow
Well the answer isn't over
we need to find vr and we have only found tr
Now vr is perpendicular to st
so area of triangle str can be given by 1/2xSTxVR
hazy elbow
But area of triangle str is just area of rectangle- area of pts- area of tqr
so equate them
assuming vr=x
sour hornet
What are you labelling as x here?
sour hornet
ok got it
hazy elbow
Yeah good
sour hornet
thanks
safe radishBOT
@sour hornet Has your question been resolved?
faint raptor
No idea where to start with this question, can someone walk me through the process?
safe radishBOT
No idea where to start with this question, can someone walk me through the proce...
faint raptor
nvm i figured it out
i was simplifying my partial sums wrong
i found the pattern
.close
frosty granite
dumb but would sin6theta= 2 sin3theta cos3theta
safe radishBOT
dumb but would sin6theta= 2 sin3theta cos3theta
safe radishBOT
obtuse plover
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Available help channel!
unreal spoke
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unreal spoke
I need a little clarification to help my understanding of the last sentence.
secx = 1/cosx. So if secx = 1 does that mean then that I'm just looking for where cosx = 1?
tiny wraith
safe radishBOT
unreal spoke
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unreal spoke
I thought tan(0) was undefined at the values where sec=0 which is pi/2 and 3pi/2
unreal spoke
zesty&festyII — Today at 2:34 PM
I thought tan(0) was undefined at the values where sec=0 which is pi/2 and 3pi/2
unreal spoke
Yep.
So, this is the check against a larger problem given
Where we get x=o
so secx = 1 at (1,0)
And the screen shot above is checking to remove erroneous solutions.
It's saying to plug in 0 into the Pyth ID that was used earlier in the problem.
sec(0) is showing in the check as =1
thin bridge
I thought tan(0) was undefined at the values where sec=0 which is pi/2 and 3pi/2
that still made no sense and isn't really relevant to the question
,W sec(0)
flat frigateBOT
thin bridge
tan(0) is defined, it's value is 0
unreal spoke
sec0 is 1/cos right, so wouldn't I be looking at where sec is 0?
thin bridge
sec(x) = 1/cos(x)
thin bridge
so what?
unreal spoke
I'm explaining my thought process, which is obviously wrong somewhere.
tan0 is undefined at those values.
(0,1) and (0,-1)
thin bridge
tan(0) is defined, it's value is 0
you don't really care about where cos(x) is 0 here
unreal spoke
tangent of (0,1) is sin/cos = 1/0 = undefined
thin bridge
you don't have those values in your potential solutions
unreal spoke
you don't really care about where cos(x) is 0 here
Ok, I think my confusion is coming from knowing I need to look at sec0, which I have to transform to 1/cos0.
thin bridge
you can express that in standard trig functions when evaluating/solving you find that more convenient
unreal spoke
you don't have those values in your potential solutions
Yes, agreed. But they're in the check I"m asking about.
thin bridge
overcomplicating/overthinking
unreal spoke
tan0 but I guess, maybe it seems like I need to be looking at where tan is = 0, which is (1,0) and (-1,0)?
I know, this is a tough subject for me.
I don't get a lot of explanations in this class so I have no idea what the bounds or rationale should be.
thin bridge
why do you keep typing tan0
unreal spoke
thin bridge
tan(0) is defined, it's value is 0
faint raptor
im getting confused just reading this lol
unreal spoke
I know.
I just don't understand how this check is supposed to be helpful for me. It has very little context.
It's in the book, and it's about all I have to rely on.
thin bridge
checking is what you do if you aren't confident with your work and/or if there are certain steps that potentially generate extraneous solution
unreal spoke
Yes, I get that, but this particular check. tan0 is defined at -1 and 1. I don't see how that's helpful for me to understand generally why this calculates correctly.
thin bridge
no
for the 5th? time?
tan(0) is defined, it's value is 0
tan(0) is defined, it's value is 0
tan(0) is defined, it's value is 0
tan(0) is defined, it's value is 0
unreal spoke
right, what I'm saying is, tan 0/1 = 0. I know that the value is 0.
plucky elk
,calc tan(0)
flat frigateBOT
Result:
0
then why do you keep saying stuff like
tan(0) is defined at -1 and 1
that makes no sense whatsoever
unreal spoke
Because it's only defined at -1 and 1.
thin bridge
tan(0) is defined, it's value is 0
plucky elk
Because it's only defined at -1 and 1.
What do you think this means?
unreal spoke
its undefined at (0,1) and (0,-1)
plucky elk
its undefined at (0,1) and (0,-1)
What does tan(0)=0 have to do with these two points?
mortal fern
i think i get what he says
unreal spoke
What do you think this means?
Means it can produce a legitimate value at that location on a graph. sin/cos = 0/1 = 0. But you can't divide by zero, so at the other locations -1/0 is not a valid value.
unreal spoke
What does tan(0)=0 have to do with these two points?
No clue. That is why this makes no sense to me.
mortal fern
it's undefined at π/2 by your reasoning, which is right.
unreal spoke
Yes, thank you.
plucky elk
Means it can produce a legitimate value at that location on a graph. sin/cos = ...
That's not a useful way to think about functions
faint raptor
i think you're misunderstanding something here? at no point do you find sec=0 for pi/2 and 3pi/3. you're just plugging x in for sec(x) - 1 = tan(x)
unreal spoke
Ok, please help me.
mortal fern
And -π/2
plucky elk
,w plot tan(x)
flat frigateBOT
unreal spoke
That's not a useful way to think about functions
It isn't useful, perhaps, but I'm not sure how else to because this teacher doesn't actually teach. I'm trying to teach myself. Tutoring has not been helpful either. I promise I'm not trying to just annoy everyone.
faint raptor
ok wait
thin bridge
you don't seem to be using correct terminology which is making it very difficult to understand what you're trying to say
faint raptor
perhaps it would be helpful to start over from the beginning cause everyone's getting confused here
unreal spoke
you don't seem to be using correct terminology which is making it very difficult...
I honestly don't doubt it.
plucky elk
It isn't useful, perhaps, but I'm not sure how else to because this teacher does...
It's better to ask for explanations than to insist on you knowing something you don't
thin bridge
post the original and highlight the first thing line you have an issue with
unreal spoke
It's better to ask for explanations than to insist on you knowing something you ...
That's what I've been trying to do, but I keep being told that an answer is an answer. I don't know how else to ask the question.
plucky elk
Ramonov and others here can't both help you and decipher the stuff you're saying at the same time
plucky elk
That's what I've been trying to do, but I keep being told that an answer is an a...
Told by who
unreal spoke
post the original and highlight the first thing line you have an issue with
It's this. Generally.
in my mind - what I think I am supposed to do to check is to figure out where sec = 0.
thin bridge
checking is what you do if you aren't confident with your work and/or if there are certain steps that potentially generate extraneous solution
faint raptor
you just plug it in to sec(x) - 1 = tan(x)
if it matches up
it works
if it doesnt
its invalid
thin bridge
the original question that you didn't explicitly post seemed to be solve
sec(x)-1 = tan(x)
squaring both sides of an equation may lead to extraneous solutions so it's a good idea to check here
unreal spoke
that's not what you're doing
Ok hear me out. I guess, it's I"m thinking not just of this problem. But other problems in the future I will need to perform the check for. If somehow the value is 5 instead of 0. I'd need to know what sec(5) is, just as an example. Right?
unreal spoke
the original question that you didn't explicitly post seemed to be solve
sec(x)-...
Agree, it is not.
faint raptor
Ok hear me out. I guess, it's I"m thinking not just of this problem. But other...
im confused on how exactly you will be applying this check
what is this check for
unreal spoke
im confused on how exactly you will be applying this check
This particular problem says when I'm applying squares to a trigonometric function, like Ramonov mentioned above.
faint raptor
??
thin bridge
not limited to trig
faint raptor
Where we get x=o
i think that check is literally just for this, so you check the answer you got from these steps, forget the check after this
unreal spoke
(secx-1)^2 = (tanx)^2 for ex.
faint raptor
huh
unreal spoke
When you square a function, it says you should check it.
faint raptor
i think the checks just saying
for f(x)^2 = g(x)^2 f(x) = g(x)
at the x value where
ok disregard me
im confused now
thin bridge
but none of this addresses why you kept saying stuff about
tan(0) is defined at -1 and 1
unreal spoke
but none of this addresses why you kept saying stuff about
> tan(0) is defined a...
Sure.
Because when I think of where I need to look at values of zero for tan, I'm looking at where on the unit circle that might be.
Unless I am just fundamentally missing something.
thin bridge
tan(0) = sin(0)/cos(0)
faint raptor
i think maybe you're trying to talk about arctan(0)
thin bridge
if you really want to use the unit circle
tan(0) is the ratio of the y and x coord of (1,0)
unreal spoke
Yes, but you can't divide by zero. So for places on the circle that cosine is 0, there can't be a tan value, is that not right?
unreal spoke
if you really want to use the unit circle
tan(0) is the ratio of the y and x coo...
Yes, same page.
mortal fern
no, you need to look at the angle
mortal fern
not the value on the circle
faint raptor
i think you may have a fundamental misunderstanding of how the unit circle works
thin bridge
and that's all you really consider here when checking whether x=0 is a solution here
you don't need to concern yourself with anything else
mortal fern
cos0 is not where cos is 0
thin bridge
you don't need to concern yourself with stuff like pi/2 when that doesn't come even up in the solving process
unreal spoke
cos0 is not where cos is 0
Ok, question... so, cosx and x=0 is that not where cos = 0?
thin bridge
no
mortal fern
no, i would consider watching a slow and easy YouTube video on unit circle in trig.. it will make it easier
unreal spoke
you don't need to concern yourself with stuff like pi/2 when that doesn't come e...
Sure, I was just looking at where sec = 0. I think that's why I thought tan 0 would be in relation to where sec is 0. but it's not, here, obviously.
thin bridge
your seem to have a major confusion with the inputs and outputs of a function
unreal spoke
k, thank you.
mortal fern
if you have any other problems just ask again but i suggest you watch a video : )
faint raptor
i think your issue is just a misunderstanding of how trig functions work
cos(x) does not mean you find the angle of where cos = x
thin bridge
functions in general
unreal spoke
i think your issue is just a misunderstanding of how trig functions work
definitely.
unreal spoke
cos(x) does not mean you find the angle of where cos = x
No no, I do know that.
faint raptor
no, i would consider watching a slow and easy YouTube video on unit circle in tr...
this is sound advice tho
unreal spoke
in this check problem though, x was 0, and zero was put back into the problem as sec(0) - where otherwise it would be secx.
unreal spoke
this is sound advice tho
I plan to.
thin bridge
cos(t) when t = 0
is cos(0)
which gives the x cood of the point on the unit circle with an angle (anticlockwise from the positive x-axis) of 0
unreal spoke
cos(t) when t = 0
is cos(0)
which gives the x cood of the point on the unit circ...
Actually I am glad you said this. I had written down a question about this very thing.
thin bridge
should change a variable there to make it clearer
faint raptor
the unit circle is derived from special triangles (30/60/90) and (45/45/90) so i would suggest looking at that too
thin bridge
and avoid using a variable to represent different things
unreal spoke
Alright, yes, agree. Thanks everyone, I really appreciate you. I'll move along!
.close
unreal spoke
should change a variable there to make it clearer
I think I just understood what you said. I didn't look at these as functions because they've been calling them equations. not functions. Yes, it makes complete sense within the context of a function. Input a value returns an output value.
viral beacon
The exercise is: There is a new food which includes three ingredients (A, B, C). The ingredients can have the vitamins B1, B6 and B12 (From the picture you can read which ingredients have how much of the vitamins; The Values are in %, so 0,1 is 0,1%). The new food has a total 0,05% B1 and 0,075% B6
Now we have to find out,
- how big the portion of ingredient B in the new food is
(Output in %) - and what the portion of B12 in the new food is
(Output in %)
My problem is:
There are three equations and four unknown variables. The output for B12 can't be a clear percentage. There will always be a dependency.
Am I wrong ? Can anyone help me find a solution?
safe radishBOT
The exercise is: There is a new food which includes three ingredients (A, B, C)....
obtuse jackal
Indeed. You could take 1 of C then 1.5 of B, or 0.5 of A then 0.5 of B
They don't give the same amount of B12
viral beacon
Indeed. You could take 1 of C then 1.5 of B, or 0.5 of A then 0.5 of B
They don...
Also muss ich hier in Abhängigkeit von einem bestimmten Variablen weiterrechnen.
Könnte ich jetzt sagen: (die erste Reihe - zweite Reihe) 0,1a + 0b + 0,05c - ( 0,1a + 0,05b + 0c) = 0,05-0.075
=> b = (0,025+0,05c)/0,05
Wäre dann "(0,025+0,05c)/0,05" der Anteil B in der neuen Futtersorte?
obtuse jackal
Just because I answered doesn't mean I speak german fluently though
viral beacon
Just because I answered doesn't mean I speak german fluently though
Oh, I am so sorry 😶 (saw your name and thought you were from Germany)
So I have to continue calculating here depending on a certain variable.
Could I now say: (the first row - second row) 0.1a + 0b + 0.05c - ( 0.1a + 0.05b + 0c) = 0.05-0.075
=> b = (0.025+0.05c)/0.05
Would "(0.025+0.05c)/0.05" then be the proportion B in the new feed?
obtuse jackal
It's a joke with eigenrocket and eigenzeta
obtuse jackal
Oh, I am so sorry 😶 (saw your name and thought you were from Germany)
So I ha...
Why do you subtract the rows ? You can't add B1's and B6's like they're the same unit
obtuse jackal
It's a joke with eigenrocket and eigenzeta
Just realized my about me can't be clicked
viral beacon
I created a "System of linear equations" and tried to get the variables a, b and c
obtuse jackal
A, B and C are more like vitamin vectors though
Operations on columns make sense
Rows, not so much
viral beacon
This is what I thought.
Now you could use Gaussian elimination and try to get the value of the variables
Why isn't it allowed to say I - II or II - I and then solve for b
obtuse jackal
Yeah actually
viral beacon
"yeah actually it is"
obtuse jackal
Yeah you can
viral beacon
hmm, ok!
Thx for your help
obtuse jackal
Why do you subtract the rows ? You can't add B1's and B6's like they're the same...
My physics brain taking over
When it shouldn't
viral beacon
.close
modern nymph
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modern nymph
I don't understand what you would do here
arg(z-8) - arg(z-2) = pi/2
The points 8,0 and 2,0 are on x axis so how can there be an angle between them
also the angle pi/2 would just be a verticle line upwards so how would that work
safe radishBOT
@modern nymph Has your question been resolved?
vagrant pasture
(A) ∀x∃y (x ≥ y) (B) ∃y∀x (x ≥ y), x and y are natural numbers
safe radishBOT
(A) ∀x∃y (x ≥ y) (B) ∃y∀x (x ≥ y), x and y are natural numbers
safe radishBOT
@vagrant pasture Has your question been resolved?
safe radishBOT
@vagrant pasture Has your question been resolved?
faint raptor
A. For all x there is some y such that x >= y B. For some y all x are >= y
is that what it's saying
shouldn't b entail a too
vagrant pasture
.close
safe radishBOT
safe radishBOT
Available help channel!
paper dagger
I have kinda no idea how to start this problem. I recognized it as a M/G/1 queue with arrival rate 8 and service rate 2k but I'm not sure what to do with that information
safe radishBOT
I have kinda no idea how to start this problem. I recognized it as a M/G/1 queue...
paper dagger
I'm thinking for part (a) by PASTA principle we can find $\pi(0)$ to find the time that the professor is idle and the stationary distribution of the number of letters to be written is just $1 - \pi(0)$
flat frigateBOT
heheitsop
safe radishBOT
@paper dagger Has your question been resolved?
paper dagger
<@&286206848099549185>
safe radishBOT
@paper dagger Has your question been resolved?
paper dagger
<@&286206848099549185>
safe radishBOT
@paper dagger Has your question been resolved?
paper dagger
<@&286206848099549185>
safe radishBOT
@paper dagger Has your question been resolved?
lusty spear
I have a questoin on the following probability exercise
safe radishBOT
I have a questoin on the following probability exercise
lusty spear
you have to pick one of these boxes with closed eyes and then pick a ball out of that box you've chosen previously. Whats the probability to pick a white ball
now the point I am struggling with is, I need the probability of each box, and my brain tells me its 1/3 each but my math tells me that bs because then I always end up with false probabilites
quasi bison
what "false probabilities" are you ending up with, and how?
lusty spear
so lets say we name the boxes B1 B2 and B3
then I calculate
P(W | B1) so the probability to pick a white ball given I picked box 1 and that probability is greater than 1
which, afaik, is bs
quasi bison
P(W | B1) so the probability to pick a white ball given I picked box 1 and that probability is greater than 1
how is that happening?
quasi bison
yeah P(W&B1) is not 5/6
P(W|B1) is 5/6
P(W|B1) is the probability to pick a white ball given that you already know your box is #1
quasi bison
it's the probability that you get the first box AND draw a white from it
lusty spear
hm I always thought of it like, what are the elements that are both in W and B1
quasi bison
P(W n B1) would actually be 5/18 here
quasi bison
there are in fact 18 balls to choose from that are all equiprobable
(because all the boxes have an equal number)
lusty spear
I think I am having something mixed up in my head
one second
this is another exercise I did previously
we have 640 females and 360 males
and 15% of F smoke and 20 % of M
now that would make 96 female smokers in total
quasi bison
R = smokers?
lusty spear
here I imagined it like we have a pool of 640 females and I intersect it with those who smoke
yes in german it is raucher
and now here it was totally clear to me what the intersection would be
but with the boxes and balls I am a bit confused
or no, I think I can work with that. I'll just accept this for now. 5/18 is not too incomprehensible for me.
thank you for your help !!
.close
open wren
\
granite idol
i've seen this exact question posted before I think
but the topic is combinatorics/counting
open wren
but the topic is combinatorics/counting
Do you know any youtube channels that explain good pls?
brave wolf
Probability - https://www.khanacademy.org/math/statistics-probability/probability-library
Counting and combinations - https://www.khanacademy.org/math/statistics-probability/counting-permutations-and-combinations
granite idol
I don't know of any personally, sorry. I don't know if Khan Academy has any videos for it. You could try seeing if Harvard's course STAT110 has any videos/lectures online
well, there you have it lol
safe radishBOT
Available help channel!
floral valley
Hi can someone help me with question 1
safe radishBOT
Hi can someone help me with question 1
floral valley
faint seal
do you know about the unit circle?
blissful harness
if u say u know about the unit circle, what value of angle (x) has their cosine value = cos ( pi/3 )?
find those x that lies within the interval u want
floral valley
60 degrees
blissful harness
what else?
floral valley
1/2
blissful harness
there are more than one such x if we consider from 0 to 2pi
do u know how sine and cosine function value oscillate between -1 and 1?
floral valley
Oscillate?
blissful harness
floral valley
No
floral valley
Yes I know these values I got confused with this
blissful harness
sine is essentially the y value and cosine is the x value in the graph, (tangent = y value / x value)
floral valley
Ye ye I know that
blissful harness
so in what degree/ radian that share the same cosine value as pi/3
other than pi/3
just between 0 to 2pi
floral valley
5pi/3
blissful harness
yes
and if we consider larger interval or in real number every 2pi the pattern repeats
ur question ask for 3pi/2 to 2pi so udh to consider others but in generally there is more roots
floral valley
Oh okay so I’m essentially using the value given and I’m just adding/subtracting 2pi until it fits into the domain
/restriction
blissful harness
not rly adding or subtracting 2pi, it depends on the function
sine, cosine, tangent each has different pattern
for example for tangent, u just keep adding/subtracting pi
floral valley
Wouldn’t it be easier just to subtract the maximal value from pi/3
blissful harness
$cos (x) = cos (k)$,
$x = 2n\pi \pm k$
flat frigateBOT
wannabe
floral valley
And even in the next question for sine pi/4, I would just do pi-pi/4
blissful harness
not like this
floral valley
Wdym
blissful harness
if next question change to cos x = cos (pi/4), find x in (pi/2, pi)
there would be no solution
i mean u can argue that ur hw wouldnt have "no solution" as ans
floral valley
if next question change to cos x = cos (pi/4), find x in (pi/2, pi)
Where have you gotten that from
blissful harness
and what if ur question doesnt give "nice" interval, like sin x = sin(pi/4), find x in (2pi, 4pi)
blissful harness
Where have you gotten that from
just some random question
floral valley
Oh okay
floral valley
i mean u can argue that ur hw wouldnt have "no solution" as ans
Ye fair enough
Because even if you try to fit that into the given domain
You cannot
Based on adding/subtracting pi
blissful harness
its better to understand the concept or pattern behind instead of, trial and error for each npi +- k
like if the range get rly large, u dont rly want to find them one by one
floral valley
**wannabe**
So in terms of understanding this formula how does it work
blissful harness
the easiest way it is to visualize it like how sine, cosine, tangent value changes if u dw to memorize the formula
floral valley
So what’s n?
blissful harness
any integer
floral valley
For example?
blissful harness
cos x = cos (3pi/2) = 0
x = 2npi +- 3pi/2 for all integer n
..., -3pi/2, -pi/2, pi/2, 3pi/2, ... are all possible ans for x
then just pick those that lie in the interval u want
if $sin (x) = sin(k), k\in[-\pi,\pi]$, then
$x = n\pi + (-1)^{n}(k)$
flat frigateBOT
wannabe
floral valley
then just pick those that lie in the interval u want
Yep yep
So I’d just let n = -3 to 4 (for example)
Depending on my domain
then I would find the values of x that locate within my domain
blissful harness
if $cos (x) = cos(k), k\in[0, 2\pi]$, then
$x = 2n\pi \pm k$
flat frigateBOT
wannabe
blissful harness
So I’d just let n = -3 to 4 (for example)
not sure how u get n=-3 and n=4
blissful harness
yea sure
little sorrel
safe radishBOT
little sorrel
can someone confirm this didnt get integrated properly
as the two 1/2's didnt get integrated properly and ones missing
glacial bronze
I guess its correct
warm oriole
safe radishBOT
warm oriole
,rotate
flat frigateBOT
safe radishBOT
@warm oriole Has your question been resolved?
orchid dust
Which one is the problem you need help with?
full horizon
Which one is the problem you need help with?
He said 8
twilit trail
I’m confused on whether to use shell or washer method here ?
safe radishBOT
I’m confused on whether to use shell or washer method here ?
@twilit trail Has your question been resolved?
zealous mason
Did I do this well?
Q: Adam lives in Bocianowo, and his friend Bartek - in Zabno. Adam made an appointment with Bartek in Zabno at 18:00. He left Bocianowo on a scooter at 17:20. Adam's average speed was 25 km
On a square grid, Adam shows a diagram of the route he is following.
What time did Adam arrive to meet Bartek? Save calculations.
hazy elbow
Distance from stawisko to bajorko can be calculated using pythagoreas theorem
like this
safe radishBOT
@zealous mason Has your question been resolved?
hazy elbow
4 kms
no
it is 4 km up and 3 km right
so a 3 4 5 right triangle
distance between stawisko and bajorko is 5
frosty granite
if ur integrating ln x all squared
safe radishBOT
if ur integrating ln x all squared
split ether
Seems like a valid approach
split ether
That works as well, cause you will then have to integrate 2lnx
In fact that is the better way
safe radishBOT
safe radishBOT
Available help channel!
viscid quest
Two numbers, x and y are positive integrals. Which numbers are x and y if, x/3 + y/11 = 31/33
safe radishBOT
Two numbers, x and y are positive integrals. Which numbers are x and y if, x/3 +...
viscid quest
I've first gotten a common denominator: 11x/33+3y/11 = 31/33
(11x+3y)/33 = 31/33
So 11x+3y = 31
subtle steppe
yea
viscid quest
How do I solve
still charm
Theres only a few cases
subtle steppe
How do I solve
just try it one by one
viscid quest
is that the only solution
subtle steppe
no
viscid quest
can't I do it another way
subtle steppe
but that's the easiest
viscid quest
yea ofc
still charm
You know that 0<=x<=2, because if x is 3 then it's bigger than 33
still charm
You could use a greedy algorithm here
Find out how many 11s go into 31
Then find out how many 3s go into whats left
still charm
Yes
viscid quest
just a question, when do I know when I should use a greedy algorithm
still charm
In general its a good starting point for question like these
You might have to modify it a bit
viscid quest
got it thanks mate
still charm
Like for instance if you instead had 11x + 3y = 23
Then two 11s would give you 22, and 23-22=1, and 3 doesnt go into 1.
So then try one 11, then 23-11 = 12, and 3 goes into 12
So that works
It's an iterative process
viscid quest
but it works for all equations with two variables?
still charm
Yeah you'll eventually get the right answer, it's an algorithm
safe radishBOT
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lean otter
how come
lean otter
-29 mod 3 = -1 and not -2
I understand there is some formula or whatnot but I can't understand it logically
if 29 mod 3 = 2
because you can fit 3, 9 times inside
then have remainder of 2
opal zodiac
light shoal
-29 mod 3 = -1 and not -2
are you sure you're not inadvertently calculating -(29 mod 3) as opposed to (-29) mod 3?
lean otter
are you sure you're not inadvertently calculating -(29 mod 3) as opposed to (-29...
I can't really understand -29 mod 3
conceptually
light shoal
also, beware that different programming languages (and maybe different calculators) will have different conventions for this
lean otter
I can understand with the formula and the explanation
light shoal
a mathematician would expect the result to be 0, 1 or 2
but computer people have their own weird desires
lean otter
ah gotcha
I'm learning modular arithmetic for math competitions
not interested in programming or any of the sort
light shoal
what source is telling you that the answer is -1?
lean otter
Khan Academy
light shoal
interesting
lean otter
wait nevermind
it says
1
but I still don't understand it conceptually
how it's 1
light shoal
ah that's correct then
the idea is this:
add or subtract multiples of 3 to -29 until you get a number between 0 and 2
in this case:
-29 + 3x10 = 1
light shoal
yep exactly
lean otter
gotcha
and an alternative way to do it
would be
-29 + (9*3) = -2
-2 mod 3
subtract a 3
-2 = -3 + R
R = 1
light shoal
yep that works too
safe radishBOT
light shoal
sure, cheers
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Available help channel!
wintry radish
safe radishBOT
flat frigateBOT
Stephen
flat frigateBOT
riemann
wintry radish
huh
I am as lost as possible right now with the problem
<@&286206848099549185> (sorry for the second ping but i really really need help)
safe radishBOT
@wintry radish Has your question been resolved?
wintry radish
😭
safe radishBOT
Show your work, and if possible, explain where you are stuck.
wintry radish
I have no idea where to start
spiral bane
its asking for the rate of change at some time
how do you find the rate of change at a time
wintry radish
you derive?
spiral bane
the word derive isnt a calculus thing
derive just means like figure out
i think you mean differentiate
wintry radish
oh yeah
spiral bane
and how do we find the rate of change at a specific time t
spiral bane
it would just be dD/dt and you plug in some number for t
dD/dt is some function of t
wintry radish
uh huh
spiral bane
so do you know how to take these derivatives
wintry radish
sure
spiral bane
what is dD/dp and dp/dt
spiral bane
,w derivative of 7225/(3p+13)
flat frigateBOT
wintry radish
thats what i got
spiral bane
okay cool just checking
wintry radish
cool
wintry radish
so t is 36 and p is 24?
so then that means that the rate of change is like -9/4?
that makes no sense how can there be negative blenders
spiral bane
wait slow down
wintry radish
ok
wintry radish
I plugged the values
spiral bane
which is just the instantaneous slope of demand
wintry radish
also we are looking at the rate of demand
wha
spiral bane
so that can be negative
spiral bane
any decreasing function that has a positive value has negative slope
wintry radish
i suppose it makes sense now then
spiral bane
okay cool
wintry radish
I have another question i was wondering if you could help with this one too
or do i need another help channel
helloooo
spiral bane
I have another question i was wondering if you could help with this one too
you can just ask it here
!volunteers
safe radishBOT
Helpers are just people volunteering their time to help you. Be polite.
spiral bane
watch some videos on related rates
these are honestly annoying to explain every time
strange plaza
safe radishBOT
strange plaza
I have 2 more questions at the end of this practice test that I could not solve.
The first one, I was able to understand how to get the final answer
just now how to elaborate
let me get the table
I understand that X can represent the "questions correct"
but I wanted to know a better way to word this
lean thorn
One way to consider it is you have a binary choices. A coin flip has either H and T. True or false has either T or F. Yes no has yes and no. 2 options only
When you flip the coin n times and you want x of an outcome, you have a probability of nCx/2^n. The 2^n is there because we have 2 options with n trials.
lean thorn
open a new channel #❓how-to-get-help
heady bobcat
Sorry I'm new
lean thorn
np! Head to that channel and it'll explain how to get help 🙂
lean thorn
You have the same number of choices for each style.
For example, if you were to ask 10 people which ice cream they'd prefer: vanilla or chocolate, you are only providing 2 choices.
strange plaza
For example, if you were to ask 10 people which ice cream they'd prefer: vanilla...
I do understand all that, still trying to figure out how to write it out in a way which gets the full 3 marks
Or 2 marks, I assume the final answer is the last mark
lean thorn
I would use the term "binary choice". You get one or the other. Something like: "When flipping a coin, we have a binary option between heads and tails. Since answer can only be true and false, this is also only two options, so you would use the same combination of 10Cn/2^n for each P(X=x)". To find out the probability of getting five or more questions, we get: (10C5 + 10C6 + 10C7 + 10C8 + 10C9 + 10C10)/2^10 = (252 + 210 + 120 + 45 + 10 + 1)/1024 = 638/1024 ≈ 62.34%"
or something to that degree
strange plaza
I would use the term "binary choice". You get one or the other. Something like: ...
Thank you, this really helps a lot.
lean thorn
yep np!
strange plaza
.close
whole gale
wwwwwwww
whole gale
What are the answers
spiral bane
What are the answers
!nosols
safe radishBOT
What are the answers
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
whole gale
then how would I find the answers
spiral bane
brute force
whole gale
brute force
What
spiral bane
find all the zeroes
daring edge
. help
sturdy briar
How can the common denominator be xy when the numerator only has an x???
thin bridge
not sure what you mean
thin bridge
they employed the idea of multiplication by 1 to simplify the fraction
in this case they multiplied the numerator and denominator of the big fraction by the lcd which in this case is xy
sturdy briar
flat frigateBOT
Azka Aska
sturdy briar
maiden fossil
no
sturdy briar
**Azka Aska**
Ok I got it now
That was easy
Could you by any chance help me with one more thing that's been stumping me for 3 hours now?
I have no clue what to do next
maiden fossil
maiden fossil
okay
okay i did it out
good
from here
simplify numerator on your left hand side
2(x-2)-x =??
maiden fossil
yes
and now you can cancel out x-2 on both sides
leaving you with x-4/x=-4/(x+2)
sturdy briar
Alright, got that
maiden fossil
now cross multiply
sturdy briar
Can I do that even though they're on opposite sides of the = sign?
maiden fossil
yes that's precisely the case to cross multiply
sturdy briar
Would I be left with a denominator, or is (x-4)(x+2)-4x all that I'm left with now?
sturdy briar
Would my final answer be (x-2)(X+4) = 0
Which gives me teh solutions x=2,-4?
It is
You actually made my life a million times easier
thanks so much
.close
safe radishBOT
safe radishBOT
Available help channel!
wise venture
safe radishBOT
wise venture
How did we end up with (a.c)(a.c) here?
Shouldn't it be [(a.c)a].c
plucky elk
How did we end up with (a.c)(a.c) here?
Shouldn't it be [(a.c)a].c
they're the same
wise venture
😮
plucky elk
an easy way to see that is to let some other variable t=a.c
then [(a.c)a].c = [ta].c = t[a].c = t(a.c)
wise venture
Assuming that t is some scalar right.
plucky elk
if a.c is dot product of a with c, then a.c is a scalar yes
safe radishBOT
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Available help channel!
lean otter
what is the highlighted part in set symbols ??
safe radishBOT
what is the highlighted part in set symbols ??
brave wolf
p=|(X u Y u Z)'| I guess
brave wolf
is it (X union Y union Z)'
yeah
the cardinality (number of elements) would then be denoted with | |
so p = |(X union Y union Z)'|
lean otter
the cardinality (number of elements) would then be denoted with | |
oh ok
thx
.close
safe radishBOT
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Available help channel!
lean otter
A coin is tossed 3 times then the total possible number of events is ( 2^3 = 8 ).... right??? (just confirming)
safe radishBOT
A coin is tossed 3 times then the total possible number of events is ( 2^3 = 8 )...
safe radishBOT
@lean otter Has your question been resolved?
inland ibex
there is a x,y function contained in this area (im working with joint functions, statistics) and im trying to get the y function from that function, how do I do this?
safe radishBOT
there is a x,y function contained in this area (im working with joint functions,...
inland ibex
lets call that function idk f(x,y)=1/2, just to make it simple?
I know that I need to take integrate x away from that joint function but idk how
I tried integral(1/2) dx from x=y+1 to y-1 but that doesnt seem right at all
split ether
I would let x go from -1 to 1 and y go from x-1 to x+1
But what you said seems to be right as well, except it should be from y-1 to y+1
inland ibex
But what you said seems to be right as well, except it should be from y-1 to y+1
how come? I thought area under y-1 to the x axis is positive minus the area above y+1 to the x is negative, so you get the total area?
Im more confused with the actual solution:
inland ibex
im struggling to understand what he means by taking the integral from x=y-1 to 1, what does this exactly mean?
also the function was a bit more complicated than 1/2, I dont really care about solving the integral, im stuck understanding the boundaries and what the integrals are trying to do
split ether
First they integrated the area above x-axis and then the one below x-axis it seems
But that is a really weird step
What's the final answer btw?
split ether
But what you said seems to be right as well, except it should be from y-1 to y+1
Okay nvm it's not
Here is what letting y go from -1 to 1 and x go from y-1 to y+1 yields
inland ibex
inland ibex
als= if , elders = elsewhere
split ether
So we are just doing the inner integral? (the one with respect to x)
inland ibex
So we are just doing the inner integral? (the one with respect to x)
I dont really understand what you mean by inner integral tbh but we integrate that joint function with respect to x, over the domain of x where y lies
split ether
Assuming the region given is that
inland ibex
Ah, so integrate that from y-1 to y+1?
yeah it doesnt seem right, especially compared to the solution
split ether
Oh I think I see what they did now
Like I was thinking, they simply cut the shape in half
And integrated each separately
inland ibex
wait I dont get how for example for y=0to2, that integrating from x=y-1 to 1 gets you that purple area
wont you get that 1 square minus the area under y-1, that you form the triangle above that purple triangle/area?
I was looking online for similar problems and it seems I dont understand this one thing
solution was
and I again thought that it was 0 to y
so why are we doing the 'opposite'?
split ether
wont you get that 1 square minus the area under y-1, that you form the triangle ...
Why would you consider completing the square there though, it doesn't help when integrating a multivariable function
split ether
and I again thought that it was 0 to y
It's from y to 1 because the triangle is located between x = y and x = 1
Not between x = y and x = 0
Then it would be the other triangle yeah
inland ibex
<:thonk:406575732563902485> Why would you consider completing the square there t...
wait Ill just show what I mean
inland ibex
<:thonk:406575732563902485> Why would you consider completing the square there t...
, nvm I see my mistake lmao, Ill just quickly redo the 'opposite'/correct way and see how that works and ill close the thread, thx btw
altho I think I still have a question, why split the 2 areas up from y -2 to 0 and y=0 to 2?
inland ibex
<:oof:918359668005425173> , nvm I see my mistake lmao, Ill just quickly redo the...
wait I take it back
inland ibex
It's from y to 1 because the triangle is located between x = y and x = 1
but isnt this located between x=0 and x=y?? so if you do y to 1, dont you get this one where you do green minus purple?
split ether
Why are you subtracting purple from the green?
inland ibex
isnt that what we basically do when integrating from y=x to, oh, I might see my mistake, wait a sec
ok yeah now Im confused how that blue/purple area gets defined from x=y to x=1?
please explain like im 5 lmao
split ether
Can you name the lines between which that triangle is located?
inland ibex
y=0, x=y and x=1
split ether
Right, so it's between x = y and x = 1 (and y = 0)
inland ibex
yeah
split ether
Meaning x goes from y to 1
inland ibex
yes
inland ibex
so what do you get if you do 1 to y
inland ibex
and so we split this in 2 because there are to many lines for an integral with 2 boundaries?
split ether
Yeah
You can do it as one integral but
That would involve min and max functions
Which require dividing the shape anyway
safe radishBOT
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eager prawn
i am given a function $k(x_1, x_2, x_3, T)$, each argument except for T has an absolute error value. T is given as 5 possible values and i can calculate k 5 times. I can also calculate the gaussian error (based on error propagation of uncertainty using $ \delta k = \sqrt{\sum_i (\frac{\partial k}{x_i} x_i)^2}$).
I need to present k as its average over thsoe 5 possible T values, how can i get the guassian error of the average then?
safe radishBOT
i am given a function $k(x_1, x_2, x_3, T)$, each argument except for T has an a...
flat frigateBOT
derdotte
eager prawn
I remember that i can not simply average all 5 errors as that isnt how this works. Do i take the largest error of the prior k and add/subtract it to δk?
safe radishBOT
@eager prawn Has your question been resolved?
eager prawn
<@&286206848099549185> anyone mind helping?
lusty shell
Yes
eager prawn
.close
safe radishBOT
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Available help channel!
native storm
$$\forall n\in Z \text{ : } n\ge Z\implies n^2\ge 4$$
safe radishBOT
$$\forall n\in Z \text{ : } n\ge Z\implies n^2\ge 4$$
flat frigateBOT
BachToReality
native storm
I was watching a lecture online, where the professor gave this as an example for implication.
How does this hold true, for say n=0 or n=1?
1 >= 1 implying that 1*1 >= 4? Am I doing this right?
compact ferry
This is wrong in a lot of ways
split ether
Did you mean n >= 2?
peak estuary
are you sure you didnt misread what they wrote?
compact ferry
Are you sure you wrote it right
peak estuary
n>=Z makes no sense at all
n>=2 would make much more sense and additionally would make the implication true
native storm
You might be right.
I would've mistook it for 2. It's a lecture from MIT OCW, guess my wet dream of disproving MIT profs will never become reality.
Thanks for your help!
.close
whole merlin
safe radishBOT
whole merlin
Confused on what this is asking for
worthy hemlock
Confused on what this is asking for
Do you know what an augmented matrix is?
whole merlin
No
worthy hemlock
Then that is where I suggest you start looking into
It wants that system of equations in augmented matrix form
This is useful
https://www.khanacademy.org/math/algebra-home/alg-matrices/alg-representing-systems-with-matrices/a/representing-systems-with-matrices
