tardy stone
so ye im an oldie
#help-26
tawdry storm
well ok
topaz sinewBOT
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junior nimbus
hi
junior nimbus
what method do i use
for calculating
[ \sum_{n=1}^{\infty} 2^{-n} = 1 ]
sorry
wrong series
$\sum_{n=1}^{\infty} \frac{n^2+1}{2n^3-n^2+5} $
junior nimbus
im thinking of comparison
reef fjord
are you trying to see if it converges or diverges or calculate/evaluate it
comparison only works for testing convergence/divergence
junior nimbus
no just converge diverge
reef fjord
then comparison could work yes
reef fjord
well what series does this sort of look like? note the n^2/n^3 terms
reef fjord
so you need only show that this series is greater than some scaled version of a harmonic series for every term beyond certain term N
junior nimbus
hmm
ok i will try
i dont know what to do with the constants
do i remove the 1 or 5?
or both
reef fjord
just show that this sequence is always GREATER than 1/(2n) after n=2
you could try dividing numerator and denominator by n^2
junior nimbus
ok
1/(2n)
if i just remove constants
so thats just divergent harmonic
now i dont know if its smaller or bigger
than the original one
reef fjord
$\frac{n^2+1}{2n^3-n^2+5}=\f{1+\f{1}{n^{2}}}{2n-1+\f{5}{n^5}}$
thorny flameBOT
đ«MooseyMooseMooser đ«
reef fjord
$\f{1}{2n-1+\f{5}{n^5}}<\f{1+\f{1}{n^{2}}}{2n-1+\f{5}{n^5}}$
thorny flameBOT
đ«MooseyMooseMooser đ«
junior nimbus
yes
but we dont know if theyre divergent or convergent
ohhh
if i do the limit of the left one
its basically just 1/2n and thats just 0
no thats inconclusive
so divergence test doesnt work
reef fjord
???
reef fjord
yes
topaz sinewBOT
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haughty wren
How would I proceed from there?
topaz sinewBOT
How would I proceed from there?
mint crescent
srry if you want to do it that way then idk
haughty wren
Wdym that way. I did exactly what you sent
But with alpha instead of n
And that doesnât change anything. Iâm stuck at the sum at the bottom
mint crescent
Wdym that way. I did exactly what you sent
nah the way I didn't do it didn't involve the gamma function
haughty wren
So then how would you go about the integral 1/(1+n^2sin^2) without geometric series?
Cause thatâs what you get after deriving the function
mint crescent
So then how would you go about the integral 1/(1+n^2sin^2) without geometric ser...
$\frac{\csc^2 x}{n+\csc^2 x}=\frac{\cot^2 x +1}{n+\csc^2 x}=\frac{\csc^2 x}{1+n+\cot^2 x}$ then do substitution
thorny flameBOT
Civil Service Pigeon
mint crescent
alternatively, tangent half angle sub should work too
mint crescent
Ah the Weierstrass sub?
yeah
ripe meadow
Hey, I'm learning algebraic topology, and apparently the inverse of ${[f]}$ in the fundamental group for some path $f$ is ${[\Bar{f}]}$ where $\Bar{f}(s)=f(1-s)$ and I just don't see how $f*\Bar{f}$ could be homotopic to $e_0$ (the constant path). Can someone please explain?
topaz sinewBOT
Hey, I'm learning algebraic topology, and apparently the inverse of ${[f]}$ in t...
thorny flameBOT
friendlyneigborhoodtopologydonut
ripe meadow
Because I'm imagining this on the torus and it seems like it just can't be the case.
topaz sinewBOT
@ripe meadow Has your question been resolved?
strange whale
there's an algebraic topology channel #point-set-topology
@ripe meadow
might be better posting there
sour roost
Question: Prove 1/2+1/4+...+1/(2^n) = 1-1/(2^n) by induction
P(1) = 1/(2^1) = 1-1/(2^1)
= œ = 1 - 1/2
P(1) is true
P(k) = 1-1/(2^k) Assume this is true
P(k+1) = 1-1/(2^k) + 1/(2^k+1) = 1-1/(2^k+1)
I'm not sure where to go from 1-1/(2^k) + 1/(2^k+1). In the answers it became 1-2/(2^k+1) + 1/(2^k+1) than 1-1/(2^k+1). I'm not understanding how they got there.
topaz sinewBOT
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sour roost
to get a common denominator for your fractions
Thanks
topaz sinewBOT
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mellow aurora
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mellow aurora
Why are they using 4 here instead of 5 if its a bound and the next term would be 5 no>
?
glacial adder
the P_4 stands for 4th degree, not the 4th term
so they did use the next term
which would be the 5th degree term
topaz sinewBOT
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vapid notch
topaz sinewBOT
restive inlet
careful when taking even roots
you should have |z|, not just z
vapid notch
n^2 p is wrong, the bottom isnt
simplified to n^9/4 * p^7/8 / n^1/4 * n^-1/8
putting an exponent from num/denom or vice versa flips its sign so do that to the denominator terms to make 9/4 --> 2 and 7/8 --> 1
vapid notch
careful when taking even roots
you should have |z|, not just z
that was the problem ty
<@&286206848099549185>
errant grove
wondering if i did this problem right. basically knowing the surface area before and after dilation i did 1408 x k^2 = 198 and i used that to find k or the scale factor and i got 0.375, so now knowing the scale factor, i know that means every length measure on the wrapped box has to be multipled by that scale factor, so to find the new height i just did 8 x 0.375
topaz sinewBOT
wondering if i did this problem right. basically knowing the surface area before...
icy sky
looks good to me
errant grove
the only thing i was kinda confused on is since the entire box is wrapped, is that still surface area? since doesnt the formula i used just find the surface area of one side?
but its not volume either ofc
icy sky
yeah
you can imagine laying all the faces flat on the same plane, doing the dilation, and then putting the pieces back together
errant grove
would that change my answer at all? or is it the same thing
icy sky
no, its the same
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small flint
Is it mandatory to put the factors of denominator from smallest to biggest in partial integration? Like this question I changed the integrand into a/(2x+1)+b/(x-2) instead of the solution shown above and got different solutions for a and b and different answer when integrating
topaz sinewBOT
Is it mandatory to put the factors of denominator from smallest to biggest in pa...
loud oasis
it doesn't matter which order you do them in, but you should get the same answer regardless
quick nebula
yeah i remember having a crisis about this when i first did it, as long as you dont mix up a and b you will be fine
quick nebula
because they were over different denominators than in the sample solution, if they weren't different you would actually have a problem
there is no "mixing up" a and b, they are arbitrary values
oh hold on
no these are actually different values
i would check your system of equations, but it isn't because of your choices of where to put a and b
small flint
Ohhh mb I messed up the part doing the comparing
It works now thx it was a mistake of my own
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small flint
Why does the solution requires me to change the ln fraction
And how do I change it
modern rock
ln(a)-ln(b)=ln(a/b)
quick nebula
I canât imagine why you would be required to, but instead of seeing it as ln|x-1|-ln|x+1|, you could see it as -ln|x+1|- -ln|x-1|, which can be simplified to ln|-(x+1)/-(x-1)|=ln|(x+1)/(x-1)|
Oh wait
Ignore that lol
small flint
Soo does that mean both the 2nd and last line are correct?
modern rock
oh wait sorry u were looking at those lines
modern rock
ln(x-1/x+1) = ln[(x+1/x-1)^-1]
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harsh shell
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harsh shell
what does this actuallyt look like graphically
i picked concave up just because the second derivative gives a positive number
i dont actually understand the reasoning
dusky mango
what does this actuallyt look like graphically
U can type the equation in google if u want graph
deft holly
isnât it just
when fâ(x)>0 its concave up
and the opp for fâ(x)<0
itâs just the property of fâ(x)
it shows concavity
quick nebula
it shows concavity
Thatâs correct
Furthermore when fââ(x) = 0, it indicates a possible inflection point
topaz sinewBOT
@harsh shell Has your question been resolved?
neon iron
hey could someone explain to mhow to solve this i would like to compare answers
fluid herald
topaz sinewBOT
@neon iron Has your question been resolved?
topaz sinewBOT
neon iron
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wraith night
For integration by parts, should I usually set dv = sin(x) or cos(x)?
wraith night
not specific to this question but this question is why im asking^
nvm i think i use trig identities
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neon iron
oak fjord
well to my knowledge
for A you should add S(cube)+S(square pyramid)
for B you should find the S(solid cylinder)-S(Empty empty square pyramid)
for C you should find S(solid square pyramid)-S(empty square pyramid)
topaz sinewBOT
neon iron
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topaz sinewBOT
@neon iron Has your question been resolved?
neon iron
why it must be the largest among the three here?
topaz sinewBOT
why it must be the largest among the three here?
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wooden osprey
7 people P, Q, R, S, T, U, V, sit on a long chair facing north. Each one of them has different weight (in kg), which is one of these values 79, 83, 85, 87, 89, 92 and 96. P sits third to the right of the heaviest person. The lightest person sits at the outermost and between the lightest person and R is the heaviest person. The third lightest person sits next to R and that person is not P nor sits next to P. Q sits third to to the left of the person with a weight higher next to R. R's weight is not 87kg. P's weight is not 92kg nor 79kg. T weighs 83kg. S is heavier than V but is not the heaviest person.
- Who's the third lightest person?
- How many people sit between R and U?
- Who sits second to right of the heaviest person
- How many people are lighter than S?
topaz sinewBOT
7 people P, Q, R, S, T, U, V, sit on a long chair facing north. Each one of them...
wooden osprey
not sure if i can derive a valid config of this
closest i got is
85 92 87 96 83 89 79
Q R P U T S V
but even this is not quite correct either
i managed to find a valid combination (?)
85 89 96 92 83 87 79
Q R U S T P V
but i cant answer the second question with this combination
craggy haven
i managed to find a valid combination (?)
```
85 89 96 92 83 87 79
Q R U S T...
if this is a valid combination then the answer appears to be 0
wooden osprey
this is a multiple choice question, 0 isnt an option for the second question
craggy haven
i don't understand what
Q sits third to to the left of the person with a weight higher next to R
means
wooden osprey
yeah i struggled with translating this a bit, basically means Q sits third to the left of a person with a weight that is directly the next element to R's weight of the ascending ordered set of weight
so example if R is 89kg, then the person Q sits third to the left to here is 92kg
craggy haven
then the arrangement seems right to me
wooden osprey
i managed to find a valid combination (?)
```
85 89 96 92 83 87 79
Q R U S T...
i honestly dont know if this is valid either, the original question was worded poorly, even i dont quite understand it in its original language
wooden osprey
then the arrangement seems right to me
yeah, ill look into this, but so far my config should be correct as it satisfies all of the conditions afaik
thanks for helping!
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timber zenith
can somebody explain to me or give me some advice on how to do this question?
topaz sinewBOT
can somebody explain to me or give me some advice on how to do this question?
@timber zenith Has your question been resolved?
dense crescent
topaz sinewBOT
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sour jackal
I have to prove for what values of m the Tn is positive.
topaz sinewBOT
I have to prove for what values of m the Tn is positive.
@sour jackal Has your question been resolved?
sour jackal
<@&286206848099549185>
topaz sinewBOT
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.
topaz sinewBOT
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polar drum
how can i approximate $1.02^2\cdot 2.003^3\cdot 3.004^3$ using differential?
thorny flameBOT
Slowaq
polar drum
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brave oyster
topaz sinewBOT
brave oyster
why is the left side not a
like -1<x
but -1<=x
answer is -1<=x<1
if that makes sense
topaz sinewBOT
@brave oyster Has your question been resolved?
brittle wigeon
how did you solve this question
brave oyster
oh like
converges mean go to 0
so x values where when n increases it decreases
so -1 and 1
below that
so it goes to 0
brittle wigeon
converges mean go to 0
what goes to 0
brave oyster
the limit
topaz sinewBOT
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thorny flameBOT
Casiel368
Prove that $GL_n(\mathbb{K})$ is a semidirect product between $SL_n(\mathbb{K})$ and $\mathbb{K}^{\times}$.
static jacinth
No clue about this. Both SL and the units of K are normal in GL
topaz sinewBOT
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proper swan
this is a simple question but I'm confused. If 2 | n, does that imply that 2 | n^2 ?
topaz sinewBOT
this is a simple question but I'm confused. If 2 | n, does that imply that 2 | n...
long stirrup
limber ridge
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cursive sky
Iâm currently taking diff eq, but I have a question about this part. Iâm confused why the book uses hyperbolic trig when my professor told me to do it the way I did in the notebook. Weâre currently doing partial diff eqs.
topaz sinewBOT
Iâm currently taking diff eq, but I have a question about this part. Iâm confuse...
cursive sky
Do they both work?
cinder sequoia
yes both work
if you look up how cosh and sinh are defined in terms of exponentials, you'll quickly see why both methods do the same thing
topaz sinewBOT
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devout falcon
I'm trying to find the intersection points, but how can I make them equal to each other?
topaz sinewBOT
I'm trying to find the intersection points, but how can I make them equal to eac...
cursive patrol
I'm trying to find the intersection points, but how can I make them equal to eac...
convert one of the equations from rectangular or polar, or from polar to rectangular
cinder sequoia
probably easier to go from rectangular to polar here, so the line becomes rcos(theta) + rsin(theta) = 0
this is a stupid problem if r = 0, so divide by r to get cos(theta) = - sin(theta)
uhh wait that's
devout falcon
this is a stupid problem if r = 0, so divide by r to get cos(theta) = - sin(thet...
i was told that r can't be zero
for my class at least
cinder sequoia
okay then you know y = -x, then using x = rcos(theta) and y = rsin(theta) you get that sin(theta) = -cos(theta)
so you could solve for the theta for which this is true
which is where tan(theta) = -1, which is at angles like 3pi/4 and -pi/4
did they give you a domain for theta
cause there's inf many
devout falcon
nah, that the whole question
cinder sequoia
okay i guess you can always add the angles in later
so you know theta has to be angles like 3pi/4 or -pi/4, we'll account for shifts of 2pi after
cursive patrol
cause there's inf many
there's only finitely many cartesian points...
cinder sequoia
there's only finitely many cartesian points...
oh shit we're going back to cartesian
perfect didn't read that bit
okay so yeah if theta = 3pi/4 or -pi/4, then sin(theta) = 1/sqrt2 or -1/sqrt2, so the corresponding points from r = 1- sin(theta) are (r, theta) = (1 - 1/sqrt2, 3pi/4) and (1 + 1/sqrt2, -pi/4)
do you see how i got that
devout falcon
do we not care about r=1-sin(theta)?
cinder sequoia
we do, after i found the values of theta that have to be satisfied at the intersection points, i plug those into r = 1 - sin(theta) to find the distances
cinder sequoia
okay so yeah if theta = 3pi/4 or -pi/4, then sin(theta) = 1/sqrt2 or -1/sqrt2, s...
that's what i did to get 1 - 1/sqrt2 and 1 + 1/sqrt2 in those two points here
sounds good?
devout falcon
that's what i did to get 1 - 1/sqrt2 and 1 + 1/sqrt2 in those two points here
thank you. i finally got it now
was looking at this question for like 30 min
cinder sequoia
great, then to convert from (r, theta) to cartesian, you just need (rcos(theta), rsin(theta))
so your two points of intersection are ((1 - 1/sqrt2) * cos(3pi/4), (1 - 1/sqrt2) * sin(3pi/4)) and ((1 + 1/sqrt2), cos(-pi/4), (1 + 1/sqrt2)*sin(-pi/4))
and you can simplify those
devout falcon
do we get intersection points for (0,0)?
devout falcon
cartesian coordinates (0,0)
do we just have to know what the graphs look like? or can we work it out algebraically?
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topaz sinewBOT
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spiral sandal
topaz sinewBOT
stuck on this one https://media.discordapp.net/attachments/1103863659517722674/1...
spiral sandal
We want to know the average age at which women give birth to their first child in the lac-st-jean region. To do this, we take a sample of 10 women in this region who have children. The age at which each of these women gave birth to her first child is given below: 23, 26, 32, 35, 23, 21, 33, 34, 28, 28. Knowing that the age at which women have their first child is distributed according to a normal distribution, estimate, using a confidence interval at the 99% level, the average age at which women in the Lac-St-Jean region give birth to their first child.
ik i need to do student distribution cuz its small sample
but idk abt the rest
topaz sinewBOT
@spiral sandal Has your question been resolved?
glacial adder
so you just need to create a 99% confidence interval for the population mean yeah?
spiral sandal
ye
but the normal distribution thing confused me
step 1 was on finding the average age and standard deviation of the sample
spiral sandal
Knowing that the age at which women have their first child is distributed according to a normal distribution
glacial adder
i assume that was what it meant
yeah
so that means the normal condition for the confidence interval is satisfied
since the population distribution is normal, the sampling distribution must also be too
spiral sandal
sofor step 3 i did student distribution and i arrived at 2,764
glacial adder
mm what does the 2764 represent?
spiral sandal
its probability
glacial adder
2.764? or 2764
spiral sandal
2.764
glacial adder
also probability cannot be greater than 1 so i doubt it
that looks like the t critical for a confidence level of 99%
is that what it is perhaps?
spiral sandal
i got a table for finding student distribution
glacial adder
a t distribution table?
spiral sandal
glacial adder
yeah alright
so you found the value that corresponds with 99% and a df of 9 i assume
glacial adder
yep
spiral sandal
yeah when i calculated the margin of error (t distribution x standard deviation) i felt like my result didnt make sense
cuz i arrived at 13
glacial adder
did you do $2.821\frac{s}{\sqrt{10}}$?
thorny flameBOT
y0shi
glacial adder
if so, then it should be correct
spiral sandal
lemme check
glacial adder
our level of confidence is quite high so it might be plausible
spiral sandal
it didnt make sense logically for someone to have a first child at 13 on an interval lmaoo
but idk maybe it works mathemtically
spiral sandal
i arrived at 4.9
thorny flameBOT
y0shi
spiral sandal
thts weird the way i learned to calculate margin of error was just t distribution x standard deviation of sample
corner right
wait no
im stupid
glacial adder
all good
spiral sandal
with that 13 im supposed to just do
average - 13 and average + 13 to get my interval
but i arrive to an interval of 13,47;41,12
which is weird
but thats seems fine considering both ends are extremely inprobable
thanks a lot
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unborn kiln
since .01 is 1%
Shouldn't you be finding the critical value at .005
spiral sandal
huh
unborn kiln
Wait why is it one tail
spiral sandal
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glacial adder
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spiral sandal
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spiral sandal
no its not
glacial adder
it should be the 4.37 i got up there with that t critical
but yeah our critical value was wrong regardless so
glacial adder
yep
spiral sandal
i get 3.250
glacial adder
yeah around that
now just add and subtract that from our sample mean and thatâll be it
do you need to interpret it or is that enough?
spiral sandal
interpretation is simple so i shud b fine
glacial adder
alright then
spiral sandal
ye i get 22,26;32,33
glacial adder
looks good
glacial adder
yw!
spiral sandal
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static venture
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knotty ledge
on the 4th line the power of cosh(2x) in the first term should be n
then things will cancel nicely for you
static venture
do u mean 4th line starting from the second derivative
knotty ledge
yes
topaz sinewBOT
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ionic jay
The amount of mineral water consumed by a person per day on the job is normally distributed with mean 19 ounces and standard deviation 5 ounces. A company supplies its employees with 2000 ounces ofmineral water daily. The company has 100 employees. Find the probability that the mineral water supplied by the company will not satisfy the water demanded by its employees.
A) Find the probability that the mineral water supplied by the company will not satisfy the water demanded by its employees
I got 2.28% by finding the Z score of the sample using the mean of the sample and the standard deviation of the sample in (Z = 2000-1900/50) where a z score of 2 is 97.72% on a normal distributions table
B) Find the probability that in the next 4 days the company will not satisfy the water demanded by its employees on at least 1 of these 4 days. Assume that the amount of water consumed by the employees of the company is independent from day to day.
C) Find the probability that in the next year (365 days) the company will not satisfy the water demanded by its employees on more than 15 days. Assume that the amount of water consumed by the employees of the company is independent from day to day.
B and C are where I get confused... I don't even know where I should start. Some help would be greatly appreciated. I am terrible at statistics.
topaz sinewBOT
The amount of mineral water consumed by a person per day on the job is normally ...
novel dew
for b i think you are supposed to use binomial pdf
ionic jay
so use binomial and make p (success) 0.25 and q (fail) 0.75?
thin adder
Find the probability that the company will not satisfy the water demanded on any given day using the normal distribution. Then take that probability for a binomial pdf to find the probability that the company fails at least once out of 4
ionic jay
alright so nCx * 0.25^2000 * (1-0.25)^-100
where nCx is 100!/(1900!*(100-1900)!)
i think, i'm realllly bad at using my TI-83... can't get it for the life of me
or just binompdf(n,p,c)
but binompdf(4,0.25,2.28) doesnt calculate... all i get is error domain
thin adder
im not sure your answer to A is correct
your method seems fine but the standard deviation you used to calculate the z-score doesnt look right
scaling a normal distribution:
ionic jay
your method seems fine but the standard deviation you used to calculate the z-sc...
it's the standard deviation of a sample so i'm pretty sure it's 5/sqr100
which is 50
thin adder
im confused. what sample?
ionic jay
the 100 employees, i'm pretty sure that's what it's asking for
thin adder
100 employees is the population
thin adder
nono
we are scaling the normal distribution for 1 person by 100 (c = 100)
because there are 100 employees
we can then write a new normal distribution for the water consumption for all 100 employees using this formula
then use the new mean and standard deviation (for the 100 employees) to calculate the probability that the company will not satisfy the employees' water demands
ionic jay
yeah i don't understand... i'm just gonna give up, failing the class anyways. what's another 0? thanks for your help.
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unborn kiln
im not sure your answer to A is correct
2.28% seems correct
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vivid pivot
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thin adder
2.28% seems correct
i dont think so. Especially seeing how it was calculated. Mean is 1900 and std is 500. but theyve used 50 which is wrong
z score should be (2000 - 1900)/500 which yields a probability of close to half
vernal matrix
Any idea how to go about this one?
unborn kiln
i dont think so. Especially seeing how it was calculated. Mean is 1900 and std i...
Take the sqrt of the variance
Sqrt(100 * 5ÂČ)
thin adder
Sqrt(100 * 5ÂČ)
its 100^2 5^2
c = 100
variance is (100^2 x 5^2) so sqrt for std = 500
vivid pivot
Any idea how to go about this one?
Idk, i thought it would be 3 or 5 (0, 3, -1 plus the endpoints, but that doesnt seem to be the answer
vernal matrix
Endpoints? Are there endpoints given for f?
Anyways, as theyâre asking about relative extrema, youâre basically wanting to find if you can find any local max or min points
vivid pivot
Anyways, as theyâre asking about relative extrema, youâre basically wanting to f...
Like 0, 3, -1?
vernal matrix
Like 0, 3, -1?
Those are all potential maximum and minimum points, sure, but key word âpotentialâ
thin adder
Idk, i thought it would be 3 or 5 (0, 3, -1 plus the endpoints, but that doesnt ...
how do you know 3 (or 5) isnt the answer?
vivid pivot
Those are all *potential* maximum and minimum points, sure, but key word âpotent...
Wdym?
vivid pivot
how do you know 3 (or 5) isnt the answer?
Theres like a bank of answers
And i already used 3 and 5
vivid pivot
Those are all *potential* maximum and minimum points, sure, but key word âpotent...
How do i know which answer wont be a relative extrema?
thin adder
Those are all *potential* maximum and minimum points, sure, but key word âpotent...
am i tripping? why isnt the answer be 3?
OH
do you know what a point of inflection is?
like the one in the graph of y = x^3
vivid pivot
do you know what a point of inflection is?
Yea but i dont see why that matters
thin adder
a stationary point of inflection satisfies f'(x) = 0 but is not a local/relative extremum
one of those points (x = 0, 3 -1) could be a point of inflection
you need to classify each of the stationary points; are they a relative minimum, maximum or point of inflection? then u will get the correct answer
vivid pivot
you need to classify each of the stationary points; are they a relative minimum,...
So i should find the second derivative then?
vivid pivot
a stationary point of inflection satisfies f'(x) = 0 but is not a local/relative...
Doesnât it satisfy fââ(x) = 0 not fâ(x)?
vernal matrix
So i should find the second derivative then?
(Well, you can, but donât need to, and is more work than itâs worth)
vivid pivot
(Well, you can, but donât need to, and is more work than itâs worth)
How would a point of inflection have a derivative of 0 anyways?
thin adder
Doesnât it satisfy fââ(x) = 0 not fâ(x)?
yes. But a stationary point can also satisfy f''(x) = 0, called a stationary point of inflection, meaning it is not a local extremum
thin adder
(Well, you can, but donât need to, and is more work than itâs worth)
i actually dont know the other method u are hinting at
vernal matrix
i actually dont know the other method u are hinting at
tl;dr ||"a maximum is where you 'go up then start going down', a minimum is where you 'go down then start going up' and all" - sign analysis on f'||
vernal matrix
How would a point of inflection have a derivative of 0 anyways?
And e.g. a point of inflection is where the derivative changes from increasing to decreasing (or vice versa), so for the x^3 example, the derivative of that is 3x^2, which increases for x > 0, and decreases for x < 0 - this is also the motivation for the second derivative test
vernal matrix
i actually dont know the other method u are hinting at
(I shall take the react as you volunteering to explain that for me 
)
thin adder
(I shall take the react as you volunteering to explain that for me <a:kanna_Fire...
HAHA no. Tbf you already did a good job ^^
vernal matrix
it was worth a try 
vernal matrix
tl;dr ||"a maximum is where you 'go up then start going down', a minimum is wher...
Anyways @vivid pivot, you could find the second derivative if you wanted (but that at least involves expanding the expression out and then differentiating, or product rule, both of which 
)
thin adder
im going to sleep. it's 2am here lul. @vivid pivot gl. hope this helped !
vernal matrix
But also you can notice what happens at (relative) maxima and minima: for a maxima, it's like you "go up as you approach, then go down as you leave", and for minima, you "go down as you approach, and go up as you leave" - of course, "go[ing] down" being "decreasing" and "go[ing] up" being increasing
Of course, you can relate decreasing and increasing to the first derivative, so check around those points how the derivative behaves, if it changes sign, then it's a maxima/minima, if not, then it's neither
vivid pivot
Anyways <@667197780099334156>, you could find the second derivative if you wante...
Well for this problem it seems doable
vivid pivot
im going to sleep. it's 2am here lul. <@667197780099334156> gl. hope this helped...
Thanks for the help @vernal matrix @thin adder
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topaz sinewBOT
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neon iron
Help
pastel oracle
use a ruler?
lucid crypt
^
pastel oracle
you didn't start at 0, and you have to measure in centimeters
topaz sinewBOT
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tall plover
topaz sinewBOT
tall plover
Idk where is my error
brave pike
Is that a 4x^3 or a 4x^2
dusky mango
Hey
dusky mango
brave pike
yeah
dusky mango
This should be inside integral isn't it?
tall plover
Hmmm what is my error. I don't understand well
dusky mango
Hmmm what is my error. I don't understand well
When you took u=sec X $\int sec^4(X).tan(X)dx$ where u=sec x
thorny flameBOT
Monarch of Eternal Night
tall plover
When you took u=sec X $\int sec^4(X).tan(X)dx$ where u=sec x
I did the integral per part by the way
dusky mango
I see
thorny flameBOT
Monarch of Eternal Night
tall plover
i did that i think
dusky mango
Now tan^2x=sec^2x-1
tall plover
yes
dusky mango
Suppose integral of sec^3 is I
tall plover
yes i did
dusky mango
Then 2I= $secxtanx+\int secx$
thorny flameBOT
Monarch of Eternal Night
tall plover
it is not like 9/2 ?
tall plover
yea the teacher give
dusky mango
Do you understand now?
tall plover
Do you understand now?
i did exactly what u said but did not get the right answer đ
is it my triangle ?
dusky mango
The traingle
dusky mango
Inside
dusky mango
You'll get double of what u got
tall plover
<@&286206848099549185>
nimble sluice
please share proper question
what do you need to do with x=3/2..?
how do you get the second equation?
tall plover
please share proper question
I explain everything in the discussion
tall plover
what do you need to do with x=3/2..?
Which line ?
nimble sluice
The main equation
is this is the question? which you need to solve?
tall plover
is this is the question? which you need to solve?
yea
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formal egret
I dont know if I can ask this here but this is related to permutations and combinations.
Can someone explain why, for probability questions, you are multiplying by 2C1 for each case to select 1 letter from 2 if they repeat
But if you were to just find the number of selections, you wouldn't do the 2C1
topaz sinewBOT
I dont know if I can ask this here but this is related to permutations and combi...
vernal vale
I dont understand your question
it appears to be in cases where its not clear which A or T they are taking
formal egret
Well I don't know if you know about combinations and selections (no intent of being rude) but if you have to find the number of selections, you wouldn't do 2C1 if you are selecting one letter from duplicate letters in a word because they are the same and can't be differentiated but with probaility you would do
well actually I guess i understand now. sorry for this
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atomic wadi
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hidden mauve
pls help with algarbriacly solviong part b i am able to get the lower value but not the upper
topaz sinewBOT
pls help with algarbriacly solviong part b i am able to get the lower value but ...
neon iron
pls help with algarbriacly solviong part b i am able to get the lower value but ...
I can't understand this
pastel oracle
is gg(5) supposed to be g(g(5))?
neon iron
What is algarbriacly
hidden mauve
im tryna find the range of g(x)
neon iron
is gg(5) supposed to be g(g(5))?
I was going to ask that
hidden mauve
not algeabricaly but more formaly beacuse currently i had to do pout in the largest x value i could to get it
hidden mauve
is gg(5) supposed to be g(g(5))?
im doing a level maths thats prob why
neon iron
Is it saying that x>=5
hidden mauve
yes
neon iron
Ok
hidden mauve
subbing that in gave me the biggest value
and subbing in 10000000000000000000000000000000 gave me 2, smallest value
but want to do it more methodocially uk
hidden mauve
so it there no algaberiac way
neon iron
Well
hidden mauve
just oput in the biggest number haha
neon iron
I don't know
hidden mauve
ah ok
tbf mark scheme just says range is stated but quite anoying haha
surely theres a proper method tho
topaz sinewBOT
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fringe apex
I have no idea how to solve these kinds of questions, I tried using mean to figure it out but im not sure
topaz sinewBOT
I have no idea how to solve these kinds of questions, I tried using mean to figu...
tall viper
I have no idea how to solve these kinds of questions, I tried using mean to figu...
you can start by finding average of all the slopes between each 2 points
if no data is given, yo uneed to eyeball it
here, for the company A, you can kind of observe a repetetive pattern of each point appearing at every 1000 mark for the last 3 points, similarily you can predict the next point to be 1000 units above the last (5000) point. thus being 6000 (closest answer being 5900)
@fringe apex was that helpful?
fringe apex
dunno, average is the mean so I checked for the mean of all the points
which gave me an answer closest to 7200
tall viper
average of the slope, not the values themselves
fringe apex
the slope is the values themselves no?
tall viper
oh nono, slope is the change in x and y cordinates between 2 points
fringe apex
so was I supposed to add the slope increases together?
like jan minus feb
check all of those then do the mean process maybe?
tall viper
not in this question specifically, as you didnt have the appropriate data given to do so
here you needed to eyeball it, just guess where next point will be depending upon the recent most change between points
as i said, the last 3 points all had a difference of 1000 units between each of them, so going by intuition, you can predict the next point to have a difference of 1000 too
fringe apex
what if the change isnt constant in the last 3 or 2 for example
tall viper
what if the change isnt constant in the last 3 or 2 for example
usually they should give a constant change for last few points
as you are assked to eyeball the next point
but even then, if the last 3 points dont have exactly a constant slope then: (one sec ill send an image)
fringe apex
đ
tall viper
ok so assume the red line is the x and y axis, yellow line is the change in values that we are working on
the green lines are 2 parallel lines which are used for reference
fringe apex
alr
tall viper
if you observe, the change slope of yellow is changing quite a bit overall
and its hard to expect where it will go next
we drew some green lines which give us an idea of the generic direction of yellow line
fringe apex
mhmm
tall viper
and we can "predict" where the line will continue, as being between the 2 green lines
ofcourse, this may or may not be true, as its simply a prediction. but for the sake of solving such questions
this can be utilised
fringe apex
because it goes up and down in the same distance you mean
tall viper
because it goes up and down in the same distance you mean
not exactly the same distance
its just the "generic" direction the yellow line is going
fringe apex
đ€
alr I'll note down to look out for repetitive patterns, but what if its not a slope?
I had a question that just showed the values themselves and I was asked to find t he next value
tall viper
something similar to this is also used as stock market patterns, drawing 2 reference lines and predicting the next movement
tall viper
I had a question that just showed the values themselves and I was asked to find ...
well you just find the average difference between values each time
note if it is a net positive change or net negative change
and predict next point depending upon the same average difference in units
fringe apex
well you just find the average difference between values each time
so what I said earlier basically
tall viper
difference is the key word here
fringe apex
wait let me find the question
tall viper
if a,b,c,d are 4 values given, ill find (b-a) as first difference, c-b as second, d-c as third difference,
then add all these 3 difference values and divide by 3 to get average difference
if you understand what im trying to say
tall viper
you see, the average length is given to be 2.35 inches. here, there is no prediction needed
tall viper
average is given for all 14 frogs, you have values for 13 frogs, assume the 14th frog to be x, and find mean of all of them
tall viper
that wasnt the correct answer I think
that isnt the answer indeed, i was stating
tall viper
average is given for all 14 frogs, you have values for 13 frogs, assume the 14th...
this.
fringe apex
average is given for all 14 frogs, you have values for 13 frogs, assume the 14th...
find the mean of the 13 then do what with the average already given
tall viper
so essentially ,
(2.3 + 1.9 + 2.0 + 2.4+2.5+3.0+2.7+2.6+2.5+2.4+2.3+2.1+2.4+x) / 14 = 2.35
solve for x
tall viper
find the mean of the 13 then do what with the average already given
mean of 14.
x (unknown ) will be your 14th entry
you have been given the mean of 14 frogs, you use that to find the value of 14th frog
fringe apex
how do I do that?
tall viper
alright, im sorry but i need to leave now, i hope i was helpful
tall viper
so essentially ,
(2.3 + 1.9 + 2.0 + 2.4+2.5+3.0+2.7+2.6+2.5+2.4+2.3+2.1+2.4+x) ...
this is how.
tall viper
so essentially ,
(2.3 + 1.9 + 2.0 + 2.4+2.5+3.0+2.7+2.6+2.5+2.4+2.3+2.1+2.4+x) ...
these are all the values from the table you sent
x being the 14th value that wasnt shown
alright, have a good day/ night
fringe apex
you too
topaz sinewBOT
@fringe apex Has your question been resolved?
fringe apex
so essentially ,
(2.3 + 1.9 + 2.0 + 2.4+2.5+3.0+2.7+2.6+2.5+2.4+2.3+2.1+2.4+x) ...
<@&286206848099549185> I'm not sure how to find X here
long forum
<@&286206848099549185> I'm not sure how to find X here
super easy , multiply 14 in both sides , and then solve
fringe apex
super easy , multiply 14 in both sides , and then solve
wdym by both sides?
long forum
wdym by both sides?
both sides of the equation
$$ (2.3 + 1.9 + 2.0 + 2.4+2.5+3.0+2.7+2.6+2.5+2.4+2.3+2.1+2.4+x) / 14 = 2.35 $$
thorny flameBOT
Quantum
long forum
in which grade do you study ?
long forum
what is that ? high school level ?
fringe apex
yes
long forum
bruh , then you should solve it , 5 6 graders can solve it easily
fringe apex
that has nothing to do with this, can you tell me how I'm supposed to get to 1.8?
long forum
what you got after multiplying 2.35 with 14
long forum
ok
long forum
that = 31.1
(- 31.1 not +31.1
fringe apex
(- 31.1 not +31.1
fringe apex
here
fringe apex
just gives this
long forum
can you show me the problem from where you got this
.
fringe apex
I did
fringe apex
alr
long forum
bruh you did a thing wrong
I said to add all the integers in left side , and the sum is 31.1
so answer is x = 32.9 - 31.1 = 1.8
long forum
so answer is x = 32.9 - 31.1 = 1.8
@fringe apex
fringe apex
wait 1 sec im confused
so 31.1 (the sum of the integers) - (2.35x14)
yep gives 1.8
gilded robin
assuming no air resistance does the actual mass of a particle affect the vertical acceleration of it, or is it always -g?
topaz sinewBOT
assuming no air resistance does the actual mass of a particle affect the vertica...
fiery badge
It's always -g
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dull mason
How to prove that The crossed lines AB and O1O2 make up a 90 degree angle
fiery badge
I mean... symetry or something
dull mason
yeah but i need to prove it, i dont know how...
fiery badge
Maybe try to define the positions of A and B in terms of 01 and 02
dull mason
I dont really understand what you are trying to say, i aint that good in english đ
dull mason
i thought O1A and A1B make up a triangle with AB, and from that i can tell that some of the angles are equal
dull mason
and look at it
2 triangles, and how does it prove that the angle is 90 degrees?
fiery badge
isn't there this thing about triangles
that sometimes they can
be
similiar
and when they're similiar
they have some properties
and stuff
dull mason
yeah there is, but i am not really sure..
fiery badge
Let C be the point of intersection, look at triangles AO1C and BO1C
look at them very closely
dull mason
they are the same
fiery badge
Aye, meaning they have the same angles
and we know ACB is 180°
so ....
This needs some more steps to be proven formally
like you gotta look at the other side with 02 as well
but you get the idea
dull mason
so this is enough to prove that the lines make up an 90 degree angle? Because i know a rule that the diameter divides the chord in half?
if its 90 degrees?
fiery badge
if you can prove that the triangles are similiar, it's enough
dull mason
perpendicular
fiery badge
now you gotta get to that
which you already kinda did, but need a bit more to get to it
formally
fiery badge
Is this for a grade or something?
dull mason
yeah, teacher said that the first one to prove this would get a 10/10 (European), and i really need that grade so my grades would rise
fiery badge
Yeah I assumed so, I can't solve it for you if it's for a grade, I can only nudge you along, which is what I did
dull mason
yeah but the point is i dont really get how does it prove that the lines crossed are perpendicular
with the triangles
fiery badge
The key is triangle similiarity, as I said
dull mason
well at this situation, isnt it not similiarity but like, equality?
because they are the same
i know, A01C B01C are equal, same with ACO2 AND BCO2
fiery badge
yeah congruence
dull mason
but like, does it really prove it?
sorry for asking thatt much, but how does it prove that the C is 90 degrees?
fiery badge
If you can prove that O1CA and O1CB are equal angles then you got your solution right there
since you know that BCA = 180°
dull mason
you mean the line BCA?
dull mason
yeah its 180 degrees
dull mason
1
fiery badge
soooooooo...............
dull mason
and they summed give 180...
but one triangle is 180 degrees?
fiery badge
I give up lol
dull mason
đŠ
topaz sinewBOT
@dull mason Has your question been resolved?
topaz sinewBOT
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dry rune
topaz sinewBOT
dry rune
5.c
turbid sable
!status
topaz sinewBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
turbid sable
what do you have now
dry rune
i connected the bottom part
turbid sable
right
turbid sable
so you know how you can change the order of adding an still get the same result like $(2 + 1) + 3 = 2 + (1 + 3)$
thorny flameBOT
MerryTacoGamerCat
turbid sable
the idea is the same with vectors
turbid sable
so you can add the first two vectors that meet at a 90 degree angle
turbid sable
yeah
turbid sable
then you add that vector to the remaining one
turbid sable
yes
turbid sable
dry rune
ahh i see
turbid sable
fr
dry rune
ok so the bottom part was 192N
and theta was 35.3 degrees
now what
is that all
192 N at a bearing of 75 degrees
dry rune
wait