rocky tusk
and remember it’s not sin(x^2)
#help-36
terse folio
yup
terse folio
and that's any arbitrary function?
^2 literally means to multiply something by itself, so i'd assume so
final saddleBOT
final saddleBOT
Available help channel!
lament portal
The question is: does the permutation (first picture) determine the element in the second picture in an order 4 determinant... im not sure what its even supposed to mean, I know that the a31... is just different elements of a matrice (the numbers are row and column) but what does the permutation have to do with it?
final saddleBOT
The question is: does the permutation (first picture) determine the element in t...
lament portal
the correct answer is that its false
desert mantle
they are talking about the leibnitz formula for the determinant
$\det(A) = \sum_{\pi\in S_n} \operatorname{sgn}(\pi) a_{1,\pi(1)} a_{2,\pi(2)}\cdots a_{n,\pi(n)}$
soft zealotBOT
Denascite
desert mantle
have you seen that formula before?
final saddleBOT
@lament portal Has your question been resolved?
lament portal
dont think so,
well not in this state, but we did it with the leibniz formula,
i just dont know what should be done with the permutation
desert mantle
well if not like this, then how
you are supposed to check whether you get the term on the right if you plug the permutation into $\operatorname{sgn}(\pi) a_{1,\pi(1)} a_{2,\pi(2)}\cdots a_{n,\pi(n)}$
soft zealotBOT
Denascite
desert mantle
at least thats what I assume they want
lament portal
well if not like this, then how
this is basically how we did it, so Im a bit confused how this would apply to permutation
odd sleet
Let $X_1, ..., X_n$ be independent random variables with distribution $Pois(2)$. $Y ~ N(0,1)$. For what $f(n)$ does following hold:
$$\lim_{n \rightarrow \infty}P(\sum_{i=1}^n X_i > f(n)) = P(Y > 1)$$
final saddleBOT
Let $X_1, ..., X_n$ be independent random variables with distribution $Pois(2)$....
soft zealotBOT
szahu420
odd sleet
So far my reasoning is $\sum_{i=1}^n X_i = X ~ Pois(2n)$ since they are independent
soft zealotBOT
szahu420
odd sleet
I also know that $P(Y > 1) = 1 - \Phi(1)$
soft zealotBOT
szahu420
odd sleet
not a clue where to go from here tho
I got the equation $\lim_{n \rightarrow \infty}\frac{2n^{f(n)}}{e^{2n}f(n)!} = 1 - \Phi(1)$
soft zealotBOT
szahu420
final saddleBOT
@odd sleet Has your question been resolved?
odd sleet
<@&286206848099549185>
floral nova
Your limit isn't quite right because you are trying to calculate the probability your sum of poisson random variables is greater than f(n). So there is going to be an infinite sum in there too.
Either way, this is going to make a very difficult equation to work with. The approach you should take is to think about the problem in terms of the central limit theorem. Rescale your probability so that it converges to a normal distribution, then rescale that normal so that it reflects P(Y>1).
chrome fiber
final saddleBOT
chrome fiber
heeelllpppppp
chrome fiber
how many inches is one feet
12
frail vigil
it looks like you dont have enough information
<@&286206848099549185>
DE is smaller that AC but we dont know how much smaller
chrome fiber
yeah, idk is there a theorem than can help me with that?
modest birch
yeah you do have enough information
you are told that "the crossbar DE is attached at the midpoints"
so try to figure out the relationship between the length of DE and the length of AC
chrome fiber
how tho
frail vigil
so try to figure out the relationship between the length of DE and the length of...
you cant
you could measure the image
chrome fiber
so try to figure out the relationship between the length of DE and the length of...
de and ac are parallel
chrome fiber
you could measure the image
yeah but this lesson is kinda based on proofs, just learned the mid seg theorem
frail vigil
what that
modest birch
de and ac are parallel
and? the lengths
frail vigil
that AC and DE are parallel?
chrome fiber
modest birch
what does this say about the lengths
chrome fiber
and? the lengths
AC is 4 1/2
chrome fiber
y are you multiplying by 2
modest birch
as I said, do you know how long the crossbar is now?
chrome fiber
no?
knotty bear
We saw early on that 100 pennies, dimes, and quarters cannot total $5.00. Show that
they can total $4.99, and find all five combinations of coins that achieve this total (careful
that all your numbers of coins are non-negative!).
chrome fiber
oh u know i think ik what to do now
modest birch
what does the theorem that you posted say about the length of the crossbar?
knotty bear
We saw early on that 100 pennies, dimes, and quarters cannot total $5.00. Show t...
any one can solve it?
chrome fiber
what does the theorem that you posted say about the length of the crossbar?
its 1/2 it
modest birch
its 1/2 it
half of what
chrome fiber
DE is 1/2 AC
modest birch
okay so how long, in inches, is the crossbar, given the information in the problem?
frail vigil
We saw early on that 100 pennies, dimes, and quarters cannot total $5.00. Show t...
take a separate help channel
chrome fiber
okay so how long, *in inches*, is the crossbar, given the information in the pro...
27 inches
so yeah its long enough
27 is less than 30
modest birch
and there's your answer
also I told you absolutely nothing you didn't know already or couldn't read in the question
flint roost
find x
strange pike
is the circle part of the picture?
flint roost
yes it is
strange pike
tbh idk
flint roost
<@&286206848099549185>
severe hawk
flint roost
AT is tangent
stoic temple
AT is tangent
use angle subtentended at centre = 2 times that at cicrumference
flint roost
.close
vital crag
Yes
nocturne rune
Any idea how to proof this?
Tldr: show than if Lim a_n = a_infinity => Lim σ_n(a)= a_infinity
final saddleBOT
Any idea how to proof this?
Tldr: show than if Lim a_n = a_infinity => Lim σ_n(...
nocturne rune
final saddleBOT
@nocturne rune Has your question been resolved?
storm spruce
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odd rivet
105pi/2 is in its most simplified form
you cant simplify 105/2 because 105 is an odd number and pi is irrational
storm spruce
you cant simplify 105/2 because 105 is an odd number and pi is irrational
And how come they simplified 91pi/2
odd rivet
because $\frac{91}{2} = 45 + \frac{1}{2}$ usally if you can express your answer with 1 addend you would wanna do that
soft zealotBOT
tobi
storm spruce
Omg
I just need the answer but idk how to say it
91pi/2 was 44 3pi/2
And I have to do the same thing with 105pi/2
Please I’ve been trying to find the answer for the past hour
Please
Someone
@odd rivet
odd rivet
And I have to do the same thing with 105pi/2
do you know what $\frac{104}{2}$ is?
soft zealotBOT
tobi
storm spruce
52
odd rivet
91pi/2 was 44 3pi/2
$91\frac{\pi}{2} \neq 44 \frac{3 \pi}{2}$
soft zealotBOT
tobi
soft zealotBOT
tobi
storm spruce
So it’s 1pi/2
odd rivet
So it’s 1pi/2
$91\frac{\pi}{2} \neq 44 \frac{3 \pi}{2}$
soft zealotBOT
tobi
soft zealotBOT
tobi
odd rivet
$91\frac{\pi}{2} = 91 \cdot \frac{\pi}{2} = \frac{91 \pi}{2} = \pi \cdot \frac{91}{2}$
storm spruce
What?
soft zealotBOT
tobi
odd rivet
$e^{ix} = \cos(x) + i \sin(x)$
soft zealotBOT
tobi
odd rivet
do you know the value of $e^{i \frac{\pi}{2}}$
soft zealotBOT
tobi
odd rivet
you should however know the value of $\cos(\pi/2) + i \sin(\pi/2)$
soft zealotBOT
tobi
odd rivet
ye your answer should be correct
final saddleBOT
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foggy fable
does e^x grow faster then n!?
final saddleBOT
does e^x grow faster then n!?
foggy fable
I think the order of fastest growing was
ln(x)
x^p
a^x
x!
x^x
formal trail
remember than n! is just a constant here
foggy fable
remember than n! is just a constant here
can I also ask how can he come up with by dividing with x
like I see it works after it
being done
but coming up with it
is harder
formal trail
a common trick when you have limits involving powers of x is to divide numerator and denominator by the highest power (counting powers inside roots as fractional, e.g. $\sqrt{x^3+1}$ would count as 3/2
soft zealotBOT
cloud
foggy fable
oh
I didn't knew that
oh wait I think I knew that trick
to calculate horizontal asympotote
I guess I just didn't thought about it then
formal trail
yes, this is basically just asking for the horizontal asymptote
foggy fable
ye I just not used to being asked like this
usually used to asked about calculate the horizontal asympotte
final saddleBOT
@foggy fable Has your question been resolved?
terse plover
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.close
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green onyx
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green onyx
Can someone help me with this im not sure where to start
idk what it means by center of mass
sweet summit
An object’s center of mass, sometimes also called the center of gravity, can be thought of as the point where the total mass of an object or a system can be treated as a point mass.As far as a formula goes, it's:
$$ \frac{1}{M}[m_1x1 + m_2x_2 + m_3x_3] $$
Where $M$ is the total sum of the mass, and each $m_n$ is a mass and $x_n$ is the corresponding distance
soft zealotBOT
MellowDramaLlama
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
sweet summit
it doesn' t just have to be 3 points, I only did that because you have 3 masses here. BUT, the rule can be applied for many more points if you have them
for a line like this, think of a plank of wood where you have weights at certain distances. The center of mass is where you can place the wood and weights and it'll have equilibrium balance
like this
final saddleBOT
@green onyx Has your question been resolved?
sweet summit
So in your case your center of mass would look like this:
green onyx
So in your case your center of mass would look like this:
right
sweet summit
so then it'd just simply be 3kg
not quite
green onyx
oh wait
sweet summit
it's close to 3kg but it's a decimal value
sweet summit
nah no conversion needed. It says the distance is in meters already
green onyx
so then if not 3
what would i put
like not asking for answer
but
how to find the decimal value
sweet summit
**MellowDramaLlama**
Compile Error! Click the <:errors:504266556054962196> react...
Follow this formula here. Here M = 2 + 5 + 3, m1x1 = (2)(1), m2x2 = (3)(3), m3x3 = (5)(4)
green onyx
hmm
im not sure i understand the formula
sorry im a beginner to this
i understand m = 2 + 5 +3
does that mean 10 is multipled by 1 x1
sweet summit
do you know what a weighted average is?
green onyx
faintly
sweet summit
this is basically a weighted average.
in fact, it's not basically a weighted average, it is a weighted average
sweet summit
yeah no problem
basically what it means is that you take the sum of each point and each point is multiplied by it's respective distance
then you divide by the total mass
green onyx
hmmm
final saddleBOT
final saddleBOT
✅
sweet summit
hate when it does that lol
green onyx
Agreed.
green onyx
How do i solve for multiplying its "respesctive distance?"
sweet summit
so m1 * x1 = (2)(1) = 2
sweet summit
so m1 * x1 = (2)(1) = 2
LIke this 🙂
it's just each individual mass multiplied by it's distance, then summed all up
green onyx
hmm
so m2 would be
m2 * x2
would it equal 1
oh duh
its multiply
not divide
OHHHHH
I actually got 20 in my notes earleir so i did it right
sweet summit
ugh hold on
sweet summit
lol thanks, just practice though! 🙂
green onyx
Thanks, that's what this is
I failed 9th grade math
So this is my remedial summer school practice
That I'm getting a headstart on
So that I can reattempt 9th grade
sweet summit
hey you're good my dude
I went back to college at 25 and started back at college algebra
and I gradauted with a math degree 🙂
totally possible to catch up
green onyx
Wow
I hope
I am much better at language arts and reading.
Math has always been my downfall, but, that is why I am trynig to try more.
green onyx
and I gradauted with a math degree 🙂
Congrats btw
may i ask of your assistance for more
sweet summit
yeah absolutely! If anything math will help you problem solve, and that's worth its weight in gold. You don't have to love math but getting some practice in it will do wonders for everyday life skills
and thank you!
yeah go ahead
green onyx
most problems I think I know the answer already, but just want a pair of second eyes
green onyx
yeah absolutely! If anything math will help you problem solve, and that's worth ...
yes
So I'm thinking this would be -v
Since its at the bottom
of the rotating disk
sweet summit
oh this is my achilles heel lol. I'm terrible at physics
but what you say makes sense to me
green onyx
oh this is my achilles heel lol. I'm terrible at physics
ha
sweet summit
I went into CS instead 😛
green onyx
Yes i'm specifically practicing physics
becuase that was the weakest
of all my math last year
physics and algebra was my weakest
green onyx
But I think it has to do with the direction of rotation
It seems to be rotating counterclockwise
i mean
clockwise
sweet summit
yep!
sweet summit
so your intuition seems correct
green onyx
So for this one
mm
I believe it would be V
because im thinking its linear
velocity
and it would stay same on edge
green onyx
so your intuition seems correct
💟 .
sweet summit
yeah that sounds correct too
it's not rtational, just translational
like sitting in a car
green onyx
Yeah
sweet summit
part of Newton's law "an object in motion stays in motion" and the difference of the force is just the mass
green onyx
part of Newton's law "an object in motion stays in motion" and the difference of...
Exactly
This one im confused
i set up 0.35 m/s over 0.15 m
and as a result 7/3
but is that it
i feel like there is another step
idk if is hould convert to deicmal or not
sweet summit
given the units of the answer that makes sense.
hmm not sure. the decimal for that would be 2.3333333... so 7/3 is more precise
green onyx
hmm not sure. the decimal for that would be 2.3333333... so 7/3 is more precise
alright
final saddleBOT
@green onyx Has your question been resolved?
woeful oasis
woeful oasis
rustic sinew
!status
final saddleBOT
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
stark apex
am i doing it right or worng?
rustic sinew
can you check if B is correct?
Looks good
rustic sinew
am i doing it right or worng?
It should be (a-3)x^2 -7x +2 on that line I believe
stark apex
oh ok
dense garnet
How can I verify that the following series diverges? $$\frac{\log 3}{3}+2\frac{\log 4}{4}+\frac{\log 5}{5}+\frac{\log 7}{7}+2\frac{\log 8}{8}\ldots.$$ It is the real part of $$\sum_{n=2}^\infty \frac{\log n}{n}+i^n\frac{\log n}{n}.$$
final saddleBOT
How can I verify that the following series diverges? $$\frac{\log 3}{3}+2\frac{\...
soft zealotBOT
Philip
dense garnet
Or converges, I'm not sure.
odd rivet
How can I verify that the following series diverges? $$\frac{\log 3}{3}+2\frac{\...
use the fact that $\sum_{n=1}^\infty \frac{1}{n}$ diverges
soft zealotBOT
tobi
dense garnet
use the fact that $\sum_{n=1}^\infty \frac{1}{n}$ diverges
yes, but how can I rewrite the series above in terms of a sum?
odd rivet
also known as the harmonic series
viscid stag
brother
y=mx+b
make the denominator the same
times them
and find the infinite range
odd rivet
$\frac{\log 3}{3}+2\frac{\log 4}{4}+\frac{\log 5}{5}+\frac{\log 7}{7}+2\frac{\log 8}{8}\ldots > \sum_{n=3}^\infty \frac{\log n}{n}$
soft zealotBOT
tobi
viscid stag
no thats wrong
odd rivet
what was the original sum
odd rivet
do you know when a complex series converges?
lyric summit
this is from Spivak's Calculus, Chapter 27
i wrote you above, you use classical comparisom test
dense garnet
when its real and imaginary parts converge, the series converges, but I'm unsure if the comparison test applies here because certain terms cancel
lyric summit
when its real and imaginary parts converge, the series converges, but I'm unsure...
you were talking only about real part, werent you ?
dense garnet
yes
lyric summit
so real part is deifnitely divergent series, but
if you cope with convergence of complex series, then you shud study behaviour of module
module of the general term
but also we have theorem, that complex series is convergent iff when both parts real and imaginary are convergent
dense garnet
but the harmonic series does converge if you remove all terms with a digit 9 in them, so therefor I'm a little hesitant to apply the comparison test because my series above has certain omissions, e.g. it's missing log6/6 and log10/10 etc.
@odd rivet @lyric summit
lyric summit
but the harmonic series does converge if you remove all terms with a digit 9 in ...
harmonic series 1/n is always and ever divergent
mayeb you talk ab anharmonic series?
dense garnet
lyric summit
that is something different, sorry
it is not harmonic
harmic series, we call: Dirichlet series of order p =1
that is so famous divergent series
dense garnet
.close
final saddleBOT
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Available help channel!
crisp wharf
If the distance between the points (2√3, y) and (4✓3, 1) equals 4, what is the value of y?
Does this question allows two solutions for y? My reasoning:
final saddleBOT
If the distance between the points (2√3, y) and (4✓3, 1) equals 4, what is the v...
pale oracle
If the distance between the points (2√3, y) and (4✓3, 1) equals 4, what is the v...
you mean y?
use the distance formula!
crisp wharf
I am still typing the reasoning wait a minute :-:
pale oracle
;-;
?
Pi can you just upload a picture of your work if you really want to show it?
if you're having a hard time, you problem just made an algebraic error
crisp wharf
I did it by head that is why I'm typing
pale oracle
I did it by head that is why I'm typing
please don't do that
the time for that is over
this is Algebra
crisp wharf
The equation to find the distance between two points is: ✓((Xb - Xa)² + (Yb - Ya))², that being the case:
Xb = 4√3, Xa = 2√2
Yb = 1, Ya = y, therefore:
✓((4✓3 - 2✓3)² + (y - 1)²) = 4,
✓(12 + 1 - 2y + y²) = 4,
y² - 2y + 13 = 16
So, here we have a quadratic formula
Such equation implies in y² - 2y - 3 = 0
Quadratic formulas usually have two solutions, doesnt it?
Using the quadratic formula we arrive at the solutions: -3 and 1
Oops
3 and -1*
pale oracle
ok so it looks roughly correct at the start
crisp wharf
And, if substituting the y in the two points formula by both solutions in quadratic formula, the result will be 4
pale oracle
you can make this problem simpler by noticing that you can begin by squaring both sides
$D^2 = 16 = (4\sqrt{3} - 2\sqrt{3})^2 + (1-y)^2$
soft zealotBOT
Melvin Eugene Punymier
crisp wharf
Thank you to correct my error
pale oracle
$16 = (2\sqrt{3})^2 + y^2 - 2y + 1$
crisp wharf
Now I've noticed I swaped 1 and y
soft zealotBOT
Melvin Eugene Punymier
pale oracle
$16 = 12 + y^2 - 2y + 1\
16 = y^2 - 2y + 13\
y^2 - 2y -3 = 0$
soft zealotBOT
Melvin Eugene Punymier
pale oracle
hmm
crisp wharf
Yes a quadratic formula
pale oracle
you got it from here?
crisp wharf
As stated in my solution (despite the mistake, I typed under pressure you know)
crisp wharf
you got it from here?
Yes
pale oracle
As stated in my solution (despite the mistake, I typed under pressure you know)
that's ok it's just hard for me to read non-written and non-latex equations so I kind of tune out
crisp wharf
quadratic equations has always two solutions for x, doesn't it?
pale oracle
I can't process it so easily
pale oracle
quadratic equations has always two solutions for x, doesn't it?
yes. "Fundamental Theorem of Algebra"
crisp wharf
I did the quadratic equation, the result is 3 and -1
So, y has indeed two solutions?
lyric summit
There is also a geometric interpretation to know before calculating that there will be two points in the solution. If you draw a circle with a radius of 4 and a center at the second given point, this circle is intersected by the line x = 2sqr(3) in two places.
crisp wharf
I wont type the quadratic equation sorry :-:
lyric summit
pale oracle
"every polynomial equation of degree n with complex number coefficients has n roots, or solutions, in the complex numbers."
put another way, "there are n soultions to an n-degree polynomial"
crisp wharf
For the moment I have a zero background with plane geometry, I'm just seeing the basic formulas because I have an exam about that in 2 weeks
But I'm also studying plane geometry :-:
lyric summit
For the moment I have a zero background with plane geometry, I'm just seeing the...
it's ok, to find exact values, you do as Melvin showed you
pale oracle
So, y has indeed two solutions?
yes, but you can test the solutions if you are unconvinced
crisp wharf
I tested for both 3 and -1 and it did alright
pale oracle
there will be certain contexts and certain equations where one solution will not make sense or not actually be defined
pale oracle
I tested for both 3 and -1 and it did alright
cool. @lyric summit was trying to show you that both points are on the circle.
(right?)
crisp wharf
The original question was:
If the distance between the points (2√3, y) and (4✓3, 1) equals 4, then y can be:
a) 1
b) 0
c) -1
d) -2
I went to complicate it a bit more because my mind works like that 😭
pale oracle
The original question was:
If the distance between the points (2√3, y) and (4✓3,...
I don't think you complicated it
you just didn't give multiple choice answers
crisp wharf
When I see a question like that, and some Idea comes to my mind, I like to think about the idea
;-; logically I do this when I'm not doing an exam
pale oracle
that's good
crisp wharf
Thank you very much for the explanations of you both, you both helped me a lot to clarify my ideas
.close
hollow iron
That isn't a question you should ask here
kindred trench
oh
hollow iron
simply googling it would give you the answer
kindred trench
mb
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thorny lava
help pls
lament geode
do you know how to do separable differential equations?
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@thorny lava Has your question been resolved?
wet topaz
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celest crane
They calculated the Force in the horizontal direction times the distance travelled.
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rose ravine
hello
rose ravine
can anyone help me solve this one
rose ravine
like 0,1,2,3,4?
viscid fossil
Yep
Every integer is either 0 1 2 3 4 mod 5
So just find 0^5, 1^5,... mod 5
With some clever trickery you can verify this without even doing any real multiplication
rose ravine
h;ow does that prove a^5== a (mod 5) tho?
rose ravine
sorry i still dont rlly understand 😭
so is it like asking
to prove that all a^5 is equal to a mod 5?
foggy minnow
There's only 5 cases to check
what do the 3 straight bars mean
vital surge
what do the 3 straight bars mean
congruence
viscid fossil
When you reduce an integer modulo 5, you have 5 possibilities: 0,1,2,3,4. So it suffices to check only these 5 cases. So just find 0^5, 1^5,... and so on, mod5
foggy minnow
congruence
that doesn't make sense, mod 5 would only return 0,1,2,3,4 so 5^5 would not equal 5mod5
vital crag
that doesn't make sense, mod 5 would only return 0,1,2,3,4 so 5^5 would not equa...
Yes it does
If you don't understand modular arithmetic, open your own channel
viscid fossil
that doesn't make sense, mod 5 would only return 0,1,2,3,4 so 5^5 would not equa...
Mod isn't a function
It's an algebraic structure
foggy minnow
😭 nvm then i thougt 5 mod 5 is 0
foggy minnow
5^5 = 0?
foggy minnow
oh the WHOLE equation is mod 5 ok nvm then lol
rose ravine
can i ask why you do 0^5,1^5…?
viscid fossil
Sure
So let's say you take any number.
Divide it by 5.
Then take the remainder.
What numbers can you have as the remainder?
rose ravine
0,1,2,3,4
how does that prove congruence tho?
just to make sure what would you define congruence as
rose ravine
5
viscid fossil
So if we prove congruence for every number mod 5, then we have proven the statement for all integers
rose ravine
can you explain congruence? i don’t think i fully get it
viscid fossil
If a = b (mod 5), then a and b have the same remainder when you divide them by 5
rose ravine
so if a equals 0-4?
final saddleBOT
@rose ravine Has your question been resolved?
lament geode
Try this: every integer can be expressed in the form 5k, 5k+1, 5k+2, 5k+3, or 5k+4. These are the "a"s (ie. remainder 0, 1, 2, 3 or 4).
Next, expand the first "a": a^5 = (5k)^5 = 5^5 k^5 and take mod 5, do you get 0?
Yes. so we know a^5 = a mod 5 in THIS case where the remainder is 0.
Now you just have to prove the other 4 cases!
rose ravine
Next, expand the first "a": a^5 = (5k)^5 = 5^5 k^5 and take mod 5, do you get 0?
how do you get 0 though? couldn’t 25k^5 % 5 be any number?
lament geode
how do you get 0 though? couldn’t 25k^5 % 5 be any number?
its actually 5^5 * k^5, but either way we know the term out front has a 5 in it, so 5^5 k^5 % 5 = 0
rose ravine
its actually 5^5 * k^5, but either way we know the term out front has a 5 in it,...
wait duh that makes sense lol
so it’s the same logic just repeated for all the remainders?
lament geode
yes
I convinced myself that for (5k+1)^5 i really just need to look at the 1^5 since everything else will have a multiple of 5
rose ravine
I convinced myself that for (5k+1)^5 i really just need to look at the 1^5 since...
sorry wdym
whole halo
consider expanding (5k + 1)^5
(5k + 1)(5k + 1)(5k + 1)(5k + 1)(5k + 1)
the only way youre going to multiply this out without a 5 being in there is doing 1 * 1 * 1 * 1 * 1
any other choice would be like 1 * 1 * 5k * 1 * 5k or 5k * 1 * 1 * 5k * 5k which would multiply by 5
k here is an integer though
so those 5s cant be prevented
rose ravine
so it’s divisible by 5 ?
whole halo
what's divisible by 5
are you reading the * as a +?
I dont know what you mean by "it"
final saddleBOT
@rose ravine Has your question been resolved?
hollow spindle
Can someone help me with part b please?
final saddleBOT
Can someone help me with part b please?
tiny gorge
final saddleBOT
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
@hollow spindle Has your question been resolved?
slender sable
final saddleBOT
slender sable
limits and continuity should be used
just tell me how to do it
ivory vessel
take the limit of both sides
and see if both the limit and the value given at the point in question are equal
if they are, they are continuous at a given point
slender sable
and see if both the limit and the value given at the point in question are equal
how do i make them equal
can u provide a written/typed solution
final saddleBOT
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 halo
how do i make them equal
- write out the limit
- write the value 1/5
- write an = sign between them
whether the equation turns out true or not will tell you if its continuous at x=2
slender sable
im not asking for a solution for my hw, it's a friend who is struggling and she's doing the thing in advance
we haven't done this in our class yet
slender sable
1. write out the limit
2. write the value 1/5
3. write an = sign between them
w...
i see
ivory vessel
my point still stands
severe cove
im not asking for a solution for my hw, it's a friend who is struggling and she'...
maybe get her to try her best at first and send what she has and we can help with where it went wrong
slender sable
my point still stands
ye u r right
slender sable
maybe get her to try her best at first and send what she has and we can help wit...
okay, I'll ask her to send a picture and we'll act accordingly
final saddleBOT
@slender sable Has your question been resolved?
verbal steppe
What is primitive function to $f(x)=\frac{2}{(1-3x)^2}$
final saddleBOT
What is primitive function to $f(x)=\frac{2}{(1-3x)^2}$
soft zealotBOT
Merineth
soft zealotBOT
Merineth
whole halo
do a u-sub u = 1-3x
you can always u-sub u = mx + b without much consequence
once you do that, youll see the rule that you can apply
verbal steppe
$2u^{-2}$
soft zealotBOT
Merineth
verbal steppe
Like that?
soft zealotBOT
matt07734
whole halo
remember the steps for u-sub
verbal steppe
I don’t remember this at all 😔
whole halo
its right there on the sheet
you have to do a bit of trickery
and by that I mean "multiply by -3/-3"
I realize now you likely dont call this process u-sub if the name of the process is right there on the sheet
whole halo
you can go through this process by multiplying by -3/-3
the -3 in the numerator will act as g'(x)
the 1/-3 can be moved out of the integral
verbal steppe
But which is my g(x) and which is my g’(x)?
verbal steppe
Sorry..
whole halo
**matt07734**
what you get will look like the thing on the right, where u(x) = 1 - 3x
u(x) and g(x) are the same thing
we call it u-sub because we do this with u and with leibniz notation in the America(™)
for you, f(x) = 2x^-2 and g(x) = 1 - 3x
then g'(x) would just be a -3
multiply by -3/-3
the -3 in the numerator will act as g'(x)
the 1/-3 can be moved out of the integral
what you get is:
,,\int2(1-3x)^{-2}\dd{x}\
\int\frac{-3}{-3}2(1-3x)^{-2}\dd{x}\
\frac1{-3}\int2(1-3x)^{-2}(-3)\dd{x}\
t=1-3x,\dd{t}=(-3)\dd{x}\
\frac1{-3}\int2t^{-2}\dd{t}
soft zealotBOT
matt07734
verbal steppe
Sorry but that is too hard to understand
Is this the way it’s solved?
$2\int (u)^{-2} dx \implies 2 \int -(u)^{-1} \implies -\frac{2}{u}\ u=(1-3x), \frac{du}{dx} =-3 \implies du = -3dx$
soft zealotBOT
Merineth
verbal steppe
Do I substitute u back now? But with the added -3(1-3x) ?
split acorn
**Merineth**
your notation is wrong. replace dx with du appropriately to integrate u with respect to u.
final saddleBOT
@verbal steppe Has your question been resolved?
verbal steppe
Where do you mean?
split acorn
yes, that's correct.
verbal steppe
That one was easy since du =
dx
Not entirely sure what Im supposed to write at du
Should it say 3du/2
final saddleBOT
@verbal steppe Has your question been resolved?
verbal steppe
This is really hard to grasp
What about something like this?
I just replace dx with what I get from the equation?
split acorn
you skipped some steps, but yeah you get the idea
soft zealotBOT
Merineth
verbal steppe
I didn’t get the right answer but it is close?
So maybe I did something wrong somewhere and they work together
Ooh I cancel out x^2 from du before I find the integral
.close
glad steeple
when i have this peicewise function and need to find out whether this function is continous and differenciable.
Do I need to work with the definition of differenciability?
or can I just take the derivative of each part and plug in 1?
final saddleBOT
when i have this peicewise function and need to find out whether this function i...
loud sundial
Continuity: Show that $$\lim_{x \to 1^{-}} f(x)=\lim_{x \to 1^{+}} f(x)=f(1)$$ Differentiability: Show that $$\lim_{x \to 1^{-}} f’(x)=\lim_{x \to 1^{+}} f’(x)=f’(1)$$
soft zealotBOT
Civil Service Pigeon
final saddleBOT
@glad steeple Has your question been resolved?
vivid birch
final saddleBOT
vivid birch
idk where to start
loud sundial
What does De Moivre’s theorem state
vivid birch
De Moivre's Theorem states that the power of a complex number in polar form is equal to raising the modulus to the same power and multiplying the argument by the same power. I don't know what this means tho
loud sundial
Do yk what polar form is
vivid birch
z = r cos(theta) + i r sin(theta)
loud sundial
Do yk how to convert to polar form
vivid birch
x=rcos(theta) and y=rsin(theta). Replace x and y with those
weak vortex
Ok suppose you have a complex number z = r(cosθ + isinθ)
This is known as the polar form of a Complex Number where r = |z| which denotes the modulus of the complex number z
The De Moivre's Theorem states:
(r(cosθ+isinθ))^n = r^n(cos(nθ) + isin(nθ))
The proof is from Euler's notation
which is z = re^(iθ)
raise that to the nth power
and you will obtain the relation
vivid birch
can you show me how to use that to solve the problem? It would be helpful to actually see that in action
weak vortex
can you show me how to use that to solve the problem? It would be helpful to act...
do yk how to find the argument of a complex number?
vivid birch
no
weak vortex
no
Consider the argand plane which is the plane plotted between Imaginary part of a complex number and real part of the same
It's like the X-Y plane but Y axis is Im(z) and X axis is Re(z) where z is any complex number
Suppose a complex number z = a+ib
In the Argand Plane, it is located at the coordinates (a,b). Draw a line from the origin joining this point.
Thus a straight line is obtained with slope m = b/a
Hence for any complex number arg(z) = tanθ = Im(z)/Re(z)
For this problem arg(z) = -1
Or, tanθ = -1
vivid birch
i see
weak vortex
Hence θ = -π/4
Or, z = sqrt(2)e^(-iπ/4)
now just use de-moivre
And express z^10 in polar form
vivid birch
hm
I'm still having some trouble. Let me make sure I'm doing this correctly. This is what I have right now
I feel like I'm missing a part tho
@weak vortex could you walk me through it? I'm having trouble with it
vivid birch
where does the sqrt2 come from?
vivid birch
so the steps are: find the modulus(in this case sqrt2 because sqrt(a^2+b^2)), then raise that modulus by whatever exponent. Then get theta. Once you have theta just put it in polar form. The image above is the part I'm stuck on. How do I solve that?
weak vortex
so the steps are: find the modulus(in this case sqrt2 because sqrt(a^2+b^2)), th...
You find the modulus first, then the arguement or θ . Then write it in polar form or, z = r(cos θ + isin θ )
Then raise it by the exponent in the problem
weak vortex
yes
vivid birch
yes, the image I just sent is the part I'm stuck on. How do I solve from here?
weak vortex
yk cos(-θ) = cosθ (since it is an even function)
and sin(-θ) = -sinθ (since odd)
then use trigonometry
vivid birch
sorry but can you please walk me through solving it? I'm not getting it
like, show me the steps of it being solved please
weak vortex
sorry but can you please walk me through solving it? I'm not getting it
so [sqrt(2)]^10 is what?
2^5
that is 32
vivid birch
ok, what about the other part of the equation? That's the part I'm having trouble with. how do I apply the exponent to the cos and sin
weak vortex
ok, what about the other part of the equation? That's the part I'm having troubl...
That is where De-Moivre's Theorem comes to play
Use the definition
weak vortex
Ok suppose you have a complex number z = r(cosθ + isinθ)
This is known as the po...
This one
weak vortex
where do I go from here tho? Do I simplify it to -pi/2?
there won't be pi/2
But -5pi/2
which is still easy to deal with
As its just 2pi+pi/2
vivid birch
yeah thats what I meant. -pi/2 = -5pi/2 for this on the unit circle. I was just simplifying it because it made more sense to me that way
weak vortex
I see
vivid birch
so would the final answer be -32i?
weak vortex
Yes
vivid birch
.close
final saddleBOT
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Available help channel!
chrome hemlock
if i have this
final saddleBOT
if i have this
tawny halo
wth
dense coral
what are k, a, and b?
chrome hemlock
a and b are vectors
tawny halo
is it ka dot kb
this looks better
dense coral
is it ka dot kb
I don’t fully remember, but i thought it was actually ka dot b?
chrome hemlock
i dont htink so
dense coral
don’t take my word for it though, I may be wrong
dense coral
okay yeah lol
dense coral
you mean scalars?
dense coral
you mean scalars?
if you mean “are scalars the same as vectors” the answer would be no
scalars are described by (or just are) single numbers
vectors need to be described by many numbers, and in this case, have a magnitude and direction
chrome hemlock
.close
lavish iron
How do I find the expected value of a random variable with a piecewise pmf? can the expected values of the seperate cases simply be summed?
final saddleBOT
How do I find the expected value of a random variable with a piecewise pmf? can ...
lavish iron
or is it the product, because the cases are mutually exclusive?
barren hound
weighted average of the cases probably
lavish iron
well what if the weight of one of the cases is 0
i know that the variable is supposed to be zero-inflated, but because the weight of the P(X=0) case is 0, it doesn't contribute to the total at all
glass mica
,help
soft zealotBOT
A brief description and guide on how to use me was sent to your DMs!
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glass mica
$$ \int \frac{6dx}{xln(7x)} $$
soft zealotBOT
Zalamancer
glass mica
now i have $$ 6 \int \frac{1}{xln(7x)} dx $$
soft zealotBOT
Zalamancer
glass mica
do i use the u-sub for this?
glass mica
$$ \int \frac{6dx}{xln(7x)} $$
final saddleBOT
$$ \int \frac{6dx}{xln(7x)} $$
soft zealotBOT
Zalamancer
glass mica
now i have $$ 6 \int \frac{1}{xln(7x)} dx $$
soft zealotBOT
Zalamancer
glass mica
do i use the u-sub for this?
vital surge
yep
glass mica
okay
barren hound
try zooming out and substituting something bigger
glass mica
try zooming out and substituting something bigger
like xln(7x)?
soft zealotBOT
hayley!
barren hound
these are your options for u sub
glass mica
these are your options for u sub
i feel like ln(7x) would better now
what i did, does not seem right
barren hound
sometimes it takes multiple tries, even for me
glass mica
sometimes it takes multiple tries, even for me
i got this error
i added c and it says incorrect
barren hound
,w d/dx(6/ln(7x))
soft zealotBOT
barren hound
yeah looks like you did something wrong
glass mica
yeah looks like you did something wrong
i really can't get it right
soft zealotBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
glass mica
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final saddleBOT
Commands:
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glass mica
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final saddleBOT
Commands:
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glass mica
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Commands:
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glass mica
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Commands:
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glass mica
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final saddleBOT
Commands:
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glass mica
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barren hound
what are you trying to do with that command
glass mica
idk i thought it was stuck on the screen
nvm i don't think someone can really go through it step by step
.close
final saddleBOT
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Available help channel!
old dust
anyone know how i would start with this one?
final saddleBOT
anyone know how i would start with this one?
whole halo
anyone know how i would start with this one?
find the area of one white region by cutting like this
final saddleBOT
@old dust Has your question been resolved?
old dust
find the area of one white region by cutting like this
thanks that tip helped me get it!
final saddleBOT
whole halo
np
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jade sierra
Can someone remind me why
final saddleBOT
Can someone remind me why
jade sierra
$\frac{d}{dx} \int_1^x csc^2tdt = csc^2x$
soft zealotBOT
🌸 Katsune
jade sierra
When there is a d/dx * int, does that just mean the derivative cancels the integral?
tranquil pine
fundamental theorem of calculus
tranquil pine
more practical?
tranquil pine
,,
\dv x\int_a^x \m ft \dd t = \bm[\bigg]{\dv x}{\m F x - \m Fa} = \bm[\big]{\dv x}{\m F x} = \m fx
soft zealotBOT
tranquil pine
it's by definition that the derivative is the inverse of the integral then
jade sierra
Okay so it just cancels it out then
What is the significance of the limits of integration then for something like this
Why is it int_1^x but the end is just csc^2(x)
What happened to the 1?
tranquil pine
well F(1) is a constant yes?
jade sierra
It's like a cancelation but it also removes the constants then
so what if it was like d/dx int_1^x csc^2tdt + 1
final saddleBOT
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.
tranquil pine
if this is trailing off from something
tranquil pine
It's like a cancelation but it also removes the constants then
u should really just review up the fundamental theorem of calculus tho. It's the reason we have a unified calculus even
jade sierra
Ohhh.... okay... ig. I'm really just looking for a simplistic explanation for what solution is when I see d/dx * int(f(x))
tranquil pine
just f(x)
tranquil pine
also don't say f(x) you should be saying f(t)
jade sierra
And only variable limits remain?
prisma lantern
final saddleBOT
twilit galleon
2 and 6 result in 1/0 and -1/0, hence creating a vert. asy. there
so its 4 for that reason
and (x-3)(x-5) create asy. there
twilit galleon
sure
prisma lantern
twilit galleon
you need to pick an interval where there are no vert. asy. or holes
prisma lantern
Do I just simplify the denominator?
twilit galleon
yeah
still viper
if we have lim x-> t f(x) = b, lim x-> t g(x) = c, where c>b and f is continous strictly decreasing while g is continuous strictly increasing then how do we justify that f(x)=g(x) at some point in (b,c)?
or is this necessarily true
final saddleBOT
if we have lim x-> t f(x) = b, lim x-> t g(x) = c, where c>b and f is continous ...
still viper
i think its intuitive and can be proven using an indirect application of IVT(?)
warm ether
id say you have the right idea
still viper
id say you have the right idea
would we have to introduce something like epsilon?
hybrid heath
I think IVT is sufficient, just need a tiny bit of cleverness
still viper
do we consider an interval like [b, infity)
hybrid heath
x interval or y interval?
still viper
y interval
and then consider (-infinity,c]
and then use IVT on this then use IVT again on (b,c)
hybrid heath
Okay, you have $f :\bR\to\bR$ is continuous and strictly decreasing, $g :\bR\to\bR$ is continuous and strictly increasing, $\lim_{x\to t}f(x)=b$, $\lim_{x\to t} g(x)=c$, $c>b$, and you want to show that there is some $x\in(b, c)$ such that $f(x)=g(x)$?
soft zealotBOT
SWR
hybrid heath
Do I have that all correct?
still viper
yeah
hybrid heath
Correction: $y\in(b, c)$ such that $f(x)=g(x)=y$
soft zealotBOT
SWR
still viper
yes
hybrid heath
If $f,g$ are continuous, why bother with the limits? Why not just say $f(t)=b$ and $g(t)=c$?
soft zealotBOT
SWR
still viper
oh wait i think its not continuous over R
one second
im trying to apply the concept from a totally different problem so the phrasing needs to be careful
so x is continous over (a,t)
does that even make sense
hybrid heath
!xy
final saddleBOT
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 heath
does that even make sense
No. Please show original problem
still viper
wwait i just realized this application doesnt make sense
i have to do it again
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runic fern
Studying for grade 12 data management exam , couple road blocks throughout my exam review, looking for a little help!
final saddleBOT
Studying for grade 12 data management exam , couple road blocks throughout my ex...
marsh temple
!da2a
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No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
runic fern
so when i ask i’m referring to these questions
question 11
is what i’m stuck on jus now
marsh temple
which one is question 11?
sifting through all of those papers (half of them being sideways) doesn't look fun
runic fern
how many ways can 8 people be ordered if dan must sit next to nick
marsh temple
generally the best way to approach these types of problems is to start by treating dan and nick as one person
so if dan and nick merge into danick, how many ways can you order this new group?
runic fern
7
marsh temple
7 people yes, so 7! ways to order them
runic fern
ok ill try that
marsh temple
we aren't quite done
runic fern
just 7 factorial then