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#help-23
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violet gale
The formula should represent a parabola, I don’t know how to solve it in this way tho
sullen lotus
The formula should represent a parabola, I don’t know how to solve it in this wa...
ok
lets define the equation to be $y = x^2+ax+b$
wait
lets define the equation to be $y = ax^2+bx+c$
flat frigateBOT
everything_addict
violet gale
**everything\_addict**
why is the ax squared but not the bx?
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twilit lagoon
In the given figure,
∠
A
D
C
130
∘
and chord
B
C
= chord
B
E
. Find
∠
C
B
E
(in degrees)
twilit lagoon
one min srry
In the given figure,∠ADC=130∘ and chord BC = chordBE. Find ∠CBE (in degrees)
the bg
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<@&286206848099549185>
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upper nymph
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golden forge
is O the midpoint?
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crisp halo
i need help with question 3
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i need help with question 3
crisp halo
i need like 2 minutes of oral presentation only on this question
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upper nymph
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ionic breach
Hello
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ionic breach
Goodbye
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stoic robin
the temperature on the plane is given by f(x,y) = 8x² - 24x y + y². what is the maximum temperature on the region described by the inequality 8x² + y² <= 1 and on which point does that occur?
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the temperature on the plane is given by f(x,y) = 8x² - 24x y + y². what is the ...
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subtle arch
Why is this incorrect?
where did i get wrong?
subtle arch
.close
dim sphinx
Hi, in a 90 45 45 triangle the adjoints are square roots of 2. Is the hypotenuse 2 or 2 square roots of 2? According to the pythagoras theorem it turns out to be 2, but the 45 45 90 triangle principles say its 2 square roots of 2 :<
safe radishBOT
Hi, in a 90 45 45 triangle the adjoints are square roots of 2. Is the hypotenuse...
neon salmon
Hi, in a 90 45 45 triangle the adjoints are square roots of 2. Is the hypotenuse...
it is 2. by saying 45 45 90 triangle principles you mean sin45 (or cos45 whatever) = squarerootsof2 / 2 right? then it is still true, as your adjoint is squarerootsof2, so according to triangle principles it is the same as with pythagoran theorem = > hypothenuse is 2
dim sphinx
it is 2. by saying 45 45 90 triangle principles you mean sin45 (or cos45 whateve...
thank you! i just meant this thing, because it is also true i think? at least we were taught that too, so im just a bit confused
oh shit
i get it know it is 2
neon salmon
thank you! i just meant this thing, because it is also true i think? at least we...
yes, your a = squarerootsof2, so hypothenuse = squarerootsof2 squared, which is 2
dim sphinx
sorry, thank you very much
neon salmon
nevermind
dim sphinx
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final mountain
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final mountain
quick question. why is this true???
is it just assuming you plug in any positive "n" value and it'll always be positive
woeful sparrow
are you being asked to show/prove why this is true?
if so proof by induction is definetly the best method
eternal carbon
(if you're asking out of curiosity here's a nice little geometric proof)
woeful sparrow
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woeful sparrow
how would you go about doing question 2?
ive done this but obviously i cannot work out p^-1 as it isnt a square matrix
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woeful sparrow
<@&286206848099549185>
brazen galleon
You have to make a system and solve it to find the coordinates in each base @woeful sparrow
woeful sparrow
could you explain a little further please
brazen galleon
This is an example with something else @woeful sparrow
Maybe you’ll get the point
woeful sparrow
is that not question 1?
brazen galleon
is that not question 1?
Oh my bad
woeful sparrow
yeah 1 ive managed to do its just 2 where it gets a bit harder
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lean otter
I got a math question about pararell triangles.
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I got a math question about pararell triangles.
dark cairn
What do you need to find?
dark cairn
Have you done the 1st part?
lean otter
u mean a)
dark cairn
Yes
dark cairn
By the first part you will get relation between sides
lean otter
yes ED pararell with AB
also i want to let u know my teacher wants me to use a specefic method
dark cairn
also i want to let u know my teacher wants me to use a specefic method
That method is called CPST (Corresponding parts of Similar/Parallel Triangles)
Why wouldn't it
You have proved it in the first part
dark cairn
Pythagoras theorem
lean otter
how do u use that
dark cairn
What does 12,5 and 7,5 mean?
lean otter
no but ac is already the hypotonusa
dark cairn
And you put the values in the previous ratio
lean otter
u can still do that?
dark cairn
Yes
So now put all the measures in that ratio I told you before
Then you will get DE
dark cairn
Yes
lean otter
but dont the lines have to be pararell
like AC and EC
idk if i calculated wrong but i didnt get the right answer
@dark cairn
lean otter
yes it says cd is 4
dark cairn
So you need to check the parallel triangles relation correctly then find it
Use the first relation to derive the correct ratios
I might have mixed up the ratios
One moment
AB/CD=AC/CE
lean otter
AB/CD=AC/CE
but how are we supposed to get cd without knowing ed
dark cairn
AB/CD=AC/CE
Wait I am trying to verify the relation
No I think the question has some mistake
Because if we follow the condition of the first part, this is the relation, the first one I gave
lean otter
No I think the question has some mistake
yeah might be
can u help me with another question instead so i can get the hang of it
CD
brazen dragon
how to use DI method when you have 1/x? I want to integrate xlnx but i want to use DI method is it possible?
safe radishBOT
how to use DI method when you have 1/x? I want to integrate xlnx but i want to u...
brazen dragon
When i put lnx for differentiating it's just ending up with infinite integrations of 1/x
which doesn't result in 0 so i can finish the process
obtuse jackal
which doesn't result in 0 so i can finish the process
well yeah, that only happens for a polynomial
brazen dragon
okay thanks then
obtuse jackal
how to use DI method when you have 1/x? I want to integrate xlnx but i want to u...
remember to look at a line and see if it's integrable one way or another
of if you notice anything else
brazen dragon
i guess it would work only when you have algebraic plus trigo or exponential right?
because you will end 0 while differentiating only if your differentiated part is algebraic
obtuse jackal
well yeah, that only happens for a polynomial
no
obtuse jackal
never seen algebraic before
brazen dragon
x^2 is algebraic right?
and other is trigo so you can put it in diff part and it will result in 0 which will finish the operator and it will work
isn't it
obtuse jackal
"trigo so you can put it in diff part and it will result in 0"
Are you sure about that ?
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lethal path
The density of air is 1.29 g/L. What volume of air in liters, has a mass of 10.0 lbs
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The density of air is 1.29 g/L. What volume of air in liters, has a mass of 10.0...
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@lethal path Has your question been resolved?
lethal path
I got 3520 grams
I need to convert to liters
2726 liters
Can someone double check
gray gazelle
thats correct ?
safe radishBOT
thats correct ?
gray gazelle
im trying to resolve this equation
gray gazelle
yeah
placid oak
but you've missed an x in the last line
placid oak
yes, but
ln can't have negative inputs
so make sure that your x1 and x2 solutions don't give any negative values in the original expression
gray gazelle
ok thanks
glossy fjord
can someone help me with this anti derivitve
safe radishBOT
can someone help me with this anti derivitve
severe pond
let u=x^5+7
glossy fjord
substitution method
severe pond
notice that the degree on top is one less than the degree on the bottom
so u sub works great here
what’s du
severe pond
let u=x^5+7
^
glossy fjord
yes
severe pond
,w integrate 1/5u
flat frigateBOT
flat frigateBOT
severe pond
the 1/5 is a constant multiple
the x^4 canceled
when we did dx=(1/(5x^4)) du
because there was x^4 in the numerator
glossy fjord
whats next? integrate?
severe pond
yes
so we get 1/5 * ln(u)
and u=x^5 +7
so just plug back in
and ur done
then add C
because it’s an indefinite integral
severe pond
ur welcome
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patent vault
why is the limit of the riemann sum 25pi/4?
safe radishBOT
why is the limit of the riemann sum 25pi/4?
patent vault
did they use the area of a circle somehow?
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plucky elk
Do the Riemann sum and find out
wheat drum
anyone??
All I can say is that I have no idea how to do integrals, but I do have exam from it TMR
But I already got passing grade of 4
wheat drum
why is the limit of the riemann sum 25pi/4?
Might sound stupid but I have question regarding this
safe radishBOT
Might sound stupid but I have question regarding this
wheat drum
Shown sum
Has sqrt( 25 - (5n/n)^2)
But,
5n/n = 5
5^2 = 25
So
It's always sqrt (25-5) = 0
So the sum is simply 0
obsidian oracle
0 times anything + 0 times anything =0
Only the last term is sqrt( 25 - (5n/n)^2)
The other terms are sqrt( 25 - (5k/n)^2) where k varies between 1 and n
wheat drum
Only the last term is sqrt( 25 - (5n/n)^2)
But doesn't it follow the rule?
51/n (first term, so n=1)
52/n (second term, so n=2)
obsidian oracle
Which rule?
Um, n does not vary here
It's k
5*1/n, so k = 1
5*2/n, k=2
We're summing every "k" term
Where k varies between 1 and n
plucky elk
0 times anything + 0 times anything =0
Nothing is equal to zero in all terms of the sum, only the last term
wheat drum
We're summing every "k" term
You're reffering to it as
n was used in place of k
Or is it different variable but not in equation
wheat drum
Nothing is equal to zero in all terms of the sum, only the last term
That's why I am confused
With this sun
obsidian oracle
You're reffering to it as
n was used in place of k
Or is it different variable...
No, n is not used in place of k, at least not everywhere
We start the sum with the k = 1 term
So 5*1/n
Then k=2
So 5*2/n...
Until we stop at k = n
So 5*n/n
And THIS and only this gives us a null term
wheat drum
So this equation is
25- 5*k/n (simplified only to value of sqrt)
Going on until k=n
Right?
obsidian oracle
Yes, disregarding sqrt and the *5/n in front
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near shale
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near shale
Ik that you have to set up limits somehow but I'm not sure how specifically
median vigil
in order for f to be continuous everywhere, the limit should exist and be equal to the function everywhere
specifically, that should include the "boundary points" where f changes definitions
also, in order for the limit to exist, both sided limits should exist
near shale
so do i set the limits of each equation equal to each other
alright
i'll try that rn
what would the limit for the middle equation be
as x approaches 2 would work right
for the first one i did as x approaches 2^-
<@&286206848099549185>
i set it up as
lim x->2^- (x+2) = lim x->2 (ax^2 -bx +3) = lim x->3^+ (2x-a+b)
plugged in everything and got
4 = 4a-2b+3 = 6-a+b
got a as 1/5 and b as 1/3 but they are incorrect
pine spoke
Well by looking at the interval at x<2
We should establish that the left limit of x is two
So, in order for the function to be continuous, right limit of x must also be two
pine spoke
That’s the points we care about, our job is to make them continuous
For them to be continuous, the left limit and right limit must match.
pine spoke
so which equations should i find the limits of
Well we know the second equation has to equal to two when x=2 ,because we want it to be continuous
Therefore, when x=2, ax^2-bx+3=2
And subbing in the x value, you should be able to do that
pine spoke
sorry why does it need to be equal to 2 again
Because we know from the first equation, when x approaches 2, the limit equals 2 as well
I think that’s what you are muddled up with, some 2s confusing you
near shale
i thought the first equation's limit as x approaches 2 is 4
because when you factor ((x-4)^2)/(x-2) into ((x-2)(x+2))/(x-2)
you're left with x + 2 and 2 + 2 is 4
man i'm just lost
near shale
it's ok
near shale
no i'm just lost
pine spoke
So the left limit is 4
near shale
idk how to set this up
pine spoke
idk how to set this up
We want this to be continuous, remember?
pine spoke
So limits at 2 and 3 must match
Left limit of 2 is 4
Therefore right limit of 2 must also be 4
So we have Ax^2-Bx+3=4
near shale
so do i ignore the middle equation cus the other two already cover the interval
pine spoke
You don’t!
Here.
Let’s start over again.
Let me draw you a graph
Ok
@near shale
This function is fully continuous for all points
Except for two
near shale
yeah
near shale
yeah
pine spoke
Left and right limits
Equal
But:
There’s two points
So we know left limit of 2
Is 4
And for our function to be continuous
Right limit HAS to equal to 4
As well
You still with me?
near shale
yeah
pine spoke
So Ax^2-Bx+3=4
What does X equal here?
We are finding the limit at X=2
What does X equal?
Tell me bud
@near shale
What is X at this limit
One word
One word is all I need from u
Comon
You know it
pine spoke
YES
there we go!
Now we have some numbers
4A-2B=7
By simplifying the formula given
Now we have an equation
Now we move on to the limits of X=3
AT X =3
near shale
so 9a-3b+3 and 6-a+b
pine spoke
But we can do better than that
near shale
yeah ii'm plugging it in to the thing to find b
pine spoke
Remember that for the limit at 2 to equal, 4A-2B=7
near shale
hold on
pine spoke
Yes
near shale
so i solved for a in terms of b
if i plug that for a in to solve for b
then plug that in for b to solve for a
will i be good
pine spoke
We want some constant values for A and B
As the question expects
So we have two equations, 10a-4b=3
And 4a-2b=7
near shale
a=-2
pine spoke
Sub the x value in for limits, and check if they match
near shale
i put -2 for a as an answer it's incorrect
near shale
those are wrong too
pine spoke
Ok I will check that
near shale
a is right but b isn't
pine spoke
!
near shale
how did you get a
pine spoke
I’m really bad at math
near shale
same i hate this
pine spoke
…
Right.
So you know we have ax^2-bx+3=4
And x=2 so we have 4a-2b=1
This was my first mistake, I miss wrote that as 4a-2b=7 before
And from the last equation
We know that 2x-a+b=9a-3b+3
By rearranging the terms
We have 10a-4b=3
And from before 4a-2b=7
With these two equations, it’s easier to find a solution for a and b
pine spoke
Yes I made a few unnecessary mistakes
near shale
thank you for working with me for like an hour
pine spoke
Dw
near shale
Yes I made a few unnecessary mistakes
i made more
pine spoke
I’m bad at helping lol
near shale
it's ok
pine spoke
But hopefully you get the idea of limits
near shale
yeah i understand limits it was just this one question
pine spoke
They are only continuous when both limits are open
I’m sure you are tired of hearing this
Lol
Alright glad to work with ya
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cloud spade
Hi, I'm looking for help solving the PDE $u_t+uu_x+au=0$ for t, a>0 for all x and u(x,0) = f(x) using the method of characteristics
flat frigateBOT
chester0203
cloud spade
I think I've found $\frac{dt}{1}=\frac{du}{-au}$ gives $c_1=ue^{at}$ and $\frac{dx}{u}=\frac{du}{-au}$ gives $c_2=u+ax$ but I'm unsure of where to go from there
flat frigateBOT
chester0203
cloud spade
<@&286206848099549185>
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devout peak
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devout peak
how come the graphs are different
it also evaluates to 9/7 but it doesnt meet the requirements for the limit to exist
<@&286206848099549185>
true zephyr
how come the graphs are different
wfa allowed imaginary numbers
because the absolute value would get rid of it
devout peak
whats wfa?
true zephyr
wolfram alpha
true zephyr
for your purposes the desmos
devout peak
because when i evaluate the limit at 1/2 it comes to 9/7
so would it exist in this case?
because as x approaches 1/2 from the left its undefined
true zephyr
according to this, the limit doesnt exist because x->a- doesnt exist
true zephyr
yeah
true zephyr
well, if it doesnt exist it cant be evaluated
but the limit from the right can be evaluated, and exists here
devout peak
so then it wouldnt exist since - and + arent equal right
true zephyr
more precisely - doesnt exist so the limit also doesnt exist
devout peak
okay thanks
true zephyr
np
devout peak
.close
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alpine pewter
how does one solve this question, the answer to this are : 0.21, 1.89. my brain is starting to rot
flat frigateBOT
Ruby
flat frigateBOT
Ruby
prisma shuttle
take the inverse cosine or arccos of both sides
$x-\frac{\pi}{3}=arccos(\frac{2}{3})$
flat frigateBOT
Ruby
flat frigateBOT
Ruby
prisma shuttle
arccos(2/3) will give you two answers, since there are two points on a circle where x=2/3
plugging arccos(2/3) into a calculator gives one of the angles, finding the other is as simple as adding a negative sign before it
,calc arccos(2/3)
flat frigateBOT
The following error occured while calculating:
Error: Undefined function arccos
The following error occured while calculating:
Error: Unexpected type of argument in function pow (expected: number or Complex or BigNumber or Fraction or Unit or Array or Matrix or string or boolean, actual: function, index: 0)
alpine pewter
Thanks
safe radishBOT
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lean otter
I have no clue why but my middle row of correlation matrix is 0
I'm doing some feature selection in google colab for a machine learning algorithm
safe radishBOT
safe radishBOT
I have no clue why but my middle row of correlation matrix is 0
I'm doing some f...
lean otter
import numpy as np
numeric_cols = df_train.select_dtypes(include="int").columns
df_train[numeric_cols].corr()
#zero out the diagonal values
corr_matrix = df_train[numeric_cols].corr().abs()
np.fill_diagonal(corr_matrix.values, 0)
#find the columns with the highest correlation
corr_matrix.max().sort_values(ascending=False)
this is the code I'm using to calculate it
wait i'm a fucking idiot
I'm zeroing them myself
🤦♂️
.close
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gleaming sinew
So why is it no real value in the 3rd situation?
safe radishBOT
So why is it no real value in the 3rd situation?
gleaming sinew
You can see the formula above
It should give me the same value from either way
But why is it not so?
terse lichen
But why is it not so?
are these answer options or?
gleaming sinew
No
I was just thinking
According to the formula I should get the same value
Am I Missing something?
gleaming sinew
What?
terse lichen
what is the answer for sqrt(-4)
safe radishBOT
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rigid inlet
You should apply chain rule, yes
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cobalt tapir
flat frigateBOT
median vigil
what do you mean by that?
flat frigateBOT
cobalt tapir
@median vigil okay so i worked out this intergral but the answer should not be 128pi
it should be 1152pi
do you know where i went wrong?
median vigil
could you post the original question?
median vigil
note that
[ \iint_D 9x^2 - 3y^2 \dd{A} = \int_0^{2\pi} \int_0^4 9(r\cos\theta)^2 - 3(r\sin\theta))^2 r \dd{r} \dd{\theta}]
flat frigateBOT
cloud
cobalt tapir
cant i do that?
median vigil
you can separate into two integrals in this case, yes
cobalt tapir
i did that but idk why i got the wrong answer
median vigil
you forgot the factor of r when converting to polar and i don't know how you computed the integral of $\cos(2\theta)$ but it doesn't look right
flat frigateBOT
cloud
median vigil
yes
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woeful sparrow
safe radishBOT
woeful sparrow
not really sure how to even start approaching this
devout shale
This matrix
For example
Maps (1,0,0) to (0,2,15)
In the standard basis
You want to think about
What is (1,0,0) in this new basis
And what is (0,2,15) in this new basis
And likewise for the rest
woeful sparrow
so e1' = (1,-2,0) e2'=(1,0,1) and e3'=(2,1,2)
so then i say
P=
(1,-2,0
1,0,1
2,12)
is that right?
then calculate P^-1 and then do P^-1AP
@devout shale is this right?
safe radishBOT
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tough root
safe radishBOT
tough root
Find all X-matrices that satisfy the equality
i know how to solve it just confused about T
i understand it switches
i know how to continue from here i just want to know if i got it right.
lyric yarrow
you got the transpose correctly but not the matrix multiplication
lyric yarrow
oh i just saw that you only wrote the problem in terms of abcd
tough root
yeah
lyric yarrow
can you do the matrix multiplication? simplify the left hand side
tough root
the X is [a b] [c d]
the question is did i do the start good or i need to fix something i started studying this the problem the leture didnt give good examples for me to understand how to do it
i know how to continue multiplication the only thing i dont understand is the switch and when do i switch
lyric yarrow
your beginning is fine. just continue
tough root
the question here do i need to switch the [0 1] [-1 0]
where the transpose was?
or just the X
flat frigateBOT
emphatic_wax
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white magnet
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white magnet
not sure how to do these or where or how to start solving them
uncut jungle
Well I guess you know what a Riemann sum is?
So write the definite integral out using a Riemann sum
Then see if you can simplify the summation
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white magnet
Well I guess you know what a Riemann sum is?
So write the definite integral out ...
I know what a riemann sum is just not sure how to transform the definite integrals in the first questions
am I supposed to rationalize the expression
and then x^3/5 becomes delta x?
uncut jungle
Something like this
I believe that first equation and definitions is all you need for the first part
So yeah rationalise the expression after expressing it as a Riemann sum
Question 2 will probs require summation formulas
white magnet
yeah the part im struggling with is expressing it as a riemann sum
i got x^3(1+fifthroot(x^8)^-1
but i dont think thats right at all
uncut jungle
This is that same equation but substituting the delta x and xi
You've been given f(x), a, and b already
So just sub them in
uncut jungle
f(x)?
white magnet
yeah
uncut jungle
f(x) is just the function being integrated
So it's everything between the integral sign and dx
white magnet
but isnt the integrand supposed to be written as (fxi)(deltax)
in riemann sums
im asking how to represent the function
being integrated
as (fxi)(deltax)
white magnet
This is that same equation but substituting the delta x and xi
as its written there
like just looking at the integrand
how do I know what f(xi)*(deltax) is
uncut jungle
Well I think it comes from the proof of riemann sums in the limit being equivalent to a definite integral
So it's not something you will be required to show in the question
Maybe if they asked for a proof of that in the question
uncut jungle
This is that same equation but substituting the delta x and xi
But otherwise just use the first part of this
Because the Riemann sum is just adding all the slices up under the integral
Which is a discrete method, but becomes like the continuous method at the limit
unreal nest
A seasonal viral infection due to a virus named RandomV is prevalent in city. About 1 in 1000 people in city
are expected to be infected by RandomV. The virus spreads from an infected person to another person only when
a sufficient amount of viral load is transmitted from the infected person to the other. A test has been designed to
detect the RandomV infection. Among the infected, the test gives a positive result in 90% of them. Among healthy
people (that is those who are free of infection), the test is known to come up with a positive result in 10% of them.
Given the above background about RandomV, solve the following questions.
Question 1. Suppose you go to a gathering of 10 people who have come together from different parts of the city. Derive the following probabilities.
(a) You meet a randomly chosen person in the gathering. What is the probability that the person is infected with
RandomV?
(b) You meet a randomly chosen pair in the gathering. What is the probability that you end up meeting a pair of
infected people?
(c) You meet a randomly chosen pair in the gathering. What is the probability that you end up meeting a pair in
which one or more are infected?
(d) What is the probability that two or more in the gathering of 10 are infected?
safe radishBOT
A seasonal viral infection due to a virus named RandomV is prevalent in city. Ab...
unreal nest
My Soln
First up, most rudimentary of all, I have no clue how to proceed with the sample space
I think maybe the sample space is
i) a set of all possible strings of infected/non-infected (like flipping ten coins and noting heads/tails sequence), or
ii) collection of ten random people (but what does this mean precisely?)
A) Either the same as given in problem, i.e, 0.001 or, for some reason, I am thinking about 10 * 0.001.
Both answers are guesses. I would like if someone could give me a formal way to think about this using axiomatic probability with sample and event spaces
B) Random pair in which both people are infected - 0.001 * 0.001 (once again, just a guess)
C) Random pair in which at least one is infection -> first person infected or second person infected or both = 0.001 + 0.001 + 0.001 * 0.001 (a guess; does the order of first/second even matter?)
D) 0.001 * 0.001 + 0.001 * 0.001 * 0.001 + ... + (0.001)^10. (similar to B but extended to 2, 3, ... But still a guess)
This is a geometric progression and we can use the standard formula to find the sum.
safe radishBOT
@unreal nest Has your question been resolved?
uncut jungle
Ok I'll give it a try
So the sample space is the set of all possible outcomes of our random experiment
Our experiment is figuring out who is infected in the gathering
So our sample space consists of every individual in the gathering
And the event is whether they are infected or not
We know P(infected) = 1/1000 (for the city-dwellers, but the gathering is only city-dwellers anyway)
I believe we are assuming independency between people at the gathering
So we can multiply the probabilities if they are independent to find the probability of them both occuring
And of course if two events wouldnt happen at the same time, they are disjoint, and so you can add the probabilities
unreal nest
so the sample space is a 10-element set?
safe radishBOT
unreal nest
.reopen
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unreal nest
The reason why P[ a random person in the gathering is infected ] = 1/1000 is because, in that 10-element sample space, the probability of someone being infected is 1/1000
but what i dont understand, is that isn't the probability of infection (1/1000) stated for the entire city?
that is, originally, the sample space was probably the entire city
but now we've shrunk it to just 10 element
uncut jungle
I think the sample space would have two events for each person in the gathering, one event for infection, one for no infection
Only that way the sample space contains all possible events in our experiment
unreal nest
oh thats true
so it'd be something like { person1_infected, person1_not-infected, person2... person10}
uncut jungle
The reason why P[ a random person in the gathering is infected ] = 1/1000 is because, in that 10-element sample space, the probability of someone being infected is 1/1000
Yes, but that comes from the fact that any random person from the city would be 1/1000
So for example, for A
You meet a random person from the gathering, who is a random person from the city
Still just a random person, and a random person has 1/1000 chance of being infected
For B, you meet two random people
And their probabilities of being infected are independent
For C you move on to the same thing but with disjoint events so you can add them
C you would have to add the "1 infected, 1 not-infected" twice, not once
Because it does matter since we are first taking independent probabilities, and then summing disjoint events
unreal nest
So for example, for A
You meet a random person from the gathering, who is a rand...
that makes sense
but now I wonder, the event A that any person in the party is infected is {p1_infected, p2_infected, ... }.
So, by the theorem that the probability of an event is the sum of probabilities of its outcomes, we get P[A] = sum( P[ person i is infected] ) = 1/1000 + 1/1000 + ... + 1/1000 (ten times) = 10/1000 = 1/100
why is this wrong?
unreal nest
C you would have to add the "1 infected, 1 not-infected" twice, not once
Because...
thats fair
uncut jungle
"the probability of an event is the sum of probabilities of its outcomes"
Only if the outcomes are disjoint events can they be summed
Imagine a sample space as a 2d plane, you cannot add overlapping areas of the sample space, because the overlap is counted twice, they must be disjoint
But, because the probability of a person being infected is independent of other people at the gathering (assumption, but a valid one in the question since they are all random)
Then you can multiply independent events (that can happen at the same time but do not influence each other)
unreal nest
Wait, are independent events not disjoint?
Oh yeah, I guess that would be so - A and B are independent is P[A intersect B] = P[A] * P[B] and they are disjoint if P[A intersect B] = 0
the only way an event could be both indepdent and disjoint is when P[A] or P[B] or both are equal to 0
But in our question we know that this is not the case
uncut jungle
are independent events not disjoint
Nope, two different things
uncut jungle
Yeah
Only if events are disjoint can you sum them
Only if events are independent can you multiply them
"We say that two events are disjoint if they cannot occur at the same time. We say that two events are independent if the occurrence of one event has no effect on the probability of the other event occurring."
unreal nest
right
so thats why our only option is to say that, like you said, the probability of someone being infected at the gathering is equal to the probability of them being infected in the general context of the city
or is there some axiomatic way to come to this conclusion (something like the "probability of an event is the sum of probability of outcomes (if disjoint)" theorem)
uncut jungle
I think you may be slightly misreading the question
It is not asking for the probability of someone being infected at the gathering
"You meet a randomly chosen person in the gathering."
So that is a random person chosen from "10 people who have come together from different parts of the city", which is also random
So a random person chosen from random people from the city
i.e. a random person from the city
Which they give you in the question
Do you follow?
unreal nest
oh
yeah that makes sense
okay okay, i think im slowing getting it now. the same "random person in gathering = random person in city" can be applied to (b) and (c) as "two random people in city" and to (d) as "two random people in city" + "three random people in city" + ... "ten random people in city"
for (d), the probability of event = sum of probability of outcomes is valid because, by definition, event "two random people in city" is disjoint from the event "three people in city"
uncut jungle
Yes exactly 😄
Also you can see that this probability space is binomial
I reckon there will be ways to solve it using the binomial formula
safe radishBOT
@unreal nest Has your question been resolved?
stray ice
Hey could someone help me with finding an equation of a linear function in a graph.
I have already done quadratic and other types of equations but i can't really remember
how to find it. Could someone help?
safe radishBOT
Hey could someone help me with finding an equation of a linear function in a gra...
severe pond
!original
safe radishBOT
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.
hybrid wedge
For linear function - you need slope and a one point on the line
stray ice
okay and what do i do next
severe pond
y-y1=m(x-x1)
stray ice
and thats all?
stray ice
but what if i just have the graph
hybrid wedge
but what if i just have the graph
What do you mean?
severe pond
but what if i just have the graph
find a point
and use two points for the slope
then plug in
with a point being (x1,y1)
hybrid wedge
Like can you just send something
vestal bridge
i need helping proving\disproving
safe radishBOT
i need helping proving\disproving
vestal bridge
im clueless ill translate the question
User
A is a infinite set, for all functions f:A->A, F is surjective on A if and only if f'(g) = f∘g is injective. f': A^A -> A^A(f' is function mapping functions from A->A to functions in A->A).
Now im asked:
for all f:A->A, f' is injective iff f is surjective
i tried disproving this shit for 2 hours but no clue :(((
safe radishBOT
@vestal bridge Has your question been resolved?
vestal bridge
?
safe radishBOT
@vestal bridge Has your question been resolved?
safe radishBOT
@vestal bridge Has your question been resolved?
safe radishBOT
@vestal bridge Has your question been resolved?
primal current
why are you trying to disprove it?
and there seem to be 2 questions there
Did you prove the first one and are now trying to disprove the second one?
Assuming that @vestal bridge choose $A=\mathbb{N}$ and find a simple function $f$ that is surjective but not injective, just failing the condition for two terms is ideal.
flat frigateBOT
mophra
primal current
Then see if you can find $g,h$ such that you take advantage of the non-injectivity of $f$ to get $f\circ g=f\circ h$.
flat frigateBOT
mophra
safe radishBOT
@vestal bridge Has your question been resolved?
calm otter
Just a quick question, is this a valid extension of product rule?
safe radishBOT
calm otter
.reopen
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calm otter
Sorry yall I got something else
Is there a way to simplify this? I want to get the derivative of this without going through a huge process if possible
But a simplification onslaught looks unavoidable
<@&286206848099549185>
misty bay
logarithmic differentiation
d/dx log f(x) = d /dx f(x) / f(x)
rearranging, you get
d / dx f(x) = f(x) d / dx log f(x)
misty bay
log rules will simplify it for you
misty bay
yes
calm otter
That’s going to give me an abomination
misty bay
no it's not
well not compared to the actual answer, anyway
it's much easier to do it this way than product rule or whatever
,w differentiate f(x) = -3(x+6)^(2/3) * (x^2-2x)/(x-5)
flat frigateBOT
calm otter
well not compared to the actual answer, anyway
Yeah I need the actual derivative
And log properties make me derive the function then divide that by the original function then multiply all that by the original function
misty bay
try using log rules to simplify the logarithm before taking the derivative of it
calm otter
uh okay
I’ll try that
If I move the denominator (x-5) up to make a chain of 3 things multiplied then could I say that log(mpq) = log(m) + log (p) + log(q)?
pearl pollen
safe radishBOT
pearl pollen
each angle on the blue angled triangle is 60
Yeah because they're equilateral
What I'm asking is the opposite vertex
Is it 60 or 30?
winged flare
The same
pearl pollen
60 right?
pearl pollen
I was wondering why everyone in an fb post this was posted said it's 30 💀
It doesn't even make sense
winged flare
What?
pearl pollen
winged flare
No qay
pearl pollen
This is a supplementary angle as well
winged flare
Which one
safe radishBOT
pearl pollen
💀
winged flare
You need to find the third unknown angle
Using angle sum property
Say unknown angle of triangle is g
pearl pollen
winged flare
Then 90 + 60 + g = 180
pearl pollen
This angle right
winged flare
Yes
pearl pollen
Ohh makes sense
pearl pollen
Oh yeah makes sense
winged flare
Yes
safe radishBOT
Available help channel!
calm otter
<@&286206848099549185> I got no clue what steps to take here
Given f(x) = ax^4 + bx^5, find values a & b if (-2,1) is an extrema
lament verge
The derivative at the extrema is equal to zero
calm otter
to clarify it’s a(x^4) and b(x^5) not (ax)^4 and (bx)^5
lament verge
And you can plug in the value of (-2,1)
You should get 2 sets of equations for 2 unknowns
lament verge
I think you got something wrong with the two equations I guess
lament verge
4a(-2)^3 + 5b(-2)^4 = 0
a(-2)^4 + b(-2)^5 =1
calm otter
Set it equal to zero
lament verge
You should get these equations
lament verge
Yeah
lament verge
4a(-2)^3 + 5b(-2)^4 = 0
a(-2)^4 + b(-2)^5 =1
^
calm otter
I’m so bad at systems of equations
calm otter
okay so how do I use both
lament verge
You make it so that one unknown of both equations cancel out
Or express one unknown in terms of the other and plug it into the other equation
lament verge
You make it so that one unknown of both equations cancel out
By adding and subtracting in this case
But you will have to make the coefficient of the unknown equal b4 that
So now you have
-32a + 80b = 0
16a - 32b = 1
Let’s call the equation 1 & 2
You can see that the coefficient of a in 1 & 2 looks easy to cancel out
safe radishBOT
@calm otter Has your question been resolved?
ashen parcel
is it okay if one of yall help
safe radishBOT
is it okay if one of yall help
potent seal
is it okay if one of yall help
Substitute tanθ= u, you'll get a quadratic
potent seal
Both the angles need to be positive
ashen parcel
do i add 360 to -22.6
potent seal
One sec
ashen parcel
yeye
spice grove
ashen parcel
whats the diff from adding 360 or 180
ashen parcel
so when do i add 360 or 180 to a neg angle
potent seal
tan(180+x)= tanx
Over here if x=-22.6⁰ it's correct
And adding 360⁰ is also correct
ashen parcel
ohhh so it doesnt matter if i add 180 or 360?
potent seal
no