hidden heart
just try the same one
#help-0
lone heartBOT
@supple tundra Has your question been resolved?
supple tundra
.close
zenith olive
hi
lone heartBOT
quiet crow
Who is near here form 2
lone heartBOT
Available help channel!
bright reef
lone heartBOT
bright reef
How do I even approach it?
I have dealt with finding h(x) where x = a
but not sure why i have a function
as my x
split oriole
use chain rule
raven rover
^^
raven rover
You have a composition of functions
You’re looking for the derivative of a composed function
bright reef
h'(x) or h(5x^4)
dy/dx of h'(x) is 1/xln(2) but wouldn't that make it the 2nd derivative?
but it's asking for h(5x^4)
glass lichen
you want to find $\dv{x}h(5x^4)$
ocean sealBOT
Mosh
glass lichen
h'(5x^4)*(20x^3)
recall chain rule
bright reef
there edited
glass lichen
recall power rule
glass lichen
and you know what h'(x) is
bright reef
there
glass lichen
and you know what h'(x) is
.
bright reef
h'(5x^4)*(20x^3)
so our answer will be:
log_2 (5x^4) * (20x^3):?
glass lichen
yes.
glass lichen
.close
bright reef
.close
lone heartBOT
lone heartBOT
Available help channel!
vernal shore
How do I enter the solution to the system of equations below
vernal shore
placid zinc
lone heartBOT
Available help channel!
alpine sable
lone heartBOT
alpine sable
A friend gave me the answer for each, but i need the steps to solve each item
Answers:
a) 5π/4, 7π/4
b) 4π/4, 10π/4
split oriole
Answers:
a) 5π/4, 7π/4
b) 4π/4, 10π/4
10 pi/ 4 is not in 0 to 2pi
this option is not right
alpine sable
10 pi/ 4 is not in 0 to 2pi
What do you mean tho??
split oriole
theta should be between 0 to 2pi but 10 pi/4 is not in this range
so 10pi/4 is not right
for this question
alpine sable
Ok, so that was wrong. But how are they solved??
split oriole
your friend know about its values or may be he\she has chart of these values
first is like find $\theta$ if $\sin(\theta) = \frac{-1}{\sqrt{2}}$
ocean sealBOT
Solution
alpine sable
So, -1√2/2...???
Wait, before moving on, the values of theta must be between 0 and 6.3, right??
I tried sin^-1(√2/2) = -45 = (-1π/4)
And then sin(-1π/4) = -0.0137...
I gues this is wrong
alpine sable
**Solution**
So... -45???
split oriole
I tried sin^-1(√2/2) = -45 = (-1π/4)
-pi/4 is also not in range
alpine sable
-pi/4 is also not in range
Yeah...
split oriole
but you can make it
alpine sable
By finding its absolute value...??
split oriole
By finding its absolute value...??
okk, do you know where sin x is negative ( in which quadrents)
alpine sable
Quads 2 and 3...??
split oriole
Quads 2 and 3...??
yup
so just p + pi/4 and 2pi - pi/4 ( i am taking pi and 2pi because sin will not change )
5pi/4 and 7pi/4
alpine sable
π + π/4 = 5π/4 like that??
split oriole
yesss
alpine sable
I tried sin^-1(√2/2) = -45 = (-1π/4)
So, i have to show this first
alpine sable
π + π/4 = 5π/4 like that??
and then this
split oriole
yes you can
alpine sable
so just p + pi/4 and 2pi - pi/4 ( i am taking pi and 2pi because sin will not c...
Why is pi/4 positive in the first solution? Is it bcus
π - (-π/4)????
split oriole
Why is pi/4 positive in the first solution? Is it bcus
π - (-π/4)????
beause you want 1/sqrt(2) which is possible at pi/4 and you are in 3rd quadrent so pi+pi/4
teal frigate
can someone explain why x-x0 gives the vector in green? I thought subtracting a vector just meant going in the opposite direction, so I thought x-x0 would just get you back to the origin, i draw a depiction of this in red and blue
teal frigate
the only way i could go close to reconciling this is by drawing x+x0 and then flipping the direction like this
but i still dont get the exact vector which is supposedly x-x0 (in green on the original image)
lone heartBOT
@teal frigate Has your question been resolved?
lone heartBOT
teal frigate
.reopen
lone heartBOT
✅
teal frigate
<@&286206848099549185>
jagged imp
go to another channel. this one is taken.
alpine sable
Ok
teal frigate
go to another channel. this one is taken.
are you talking to me?
jagged imp
no. someone posted over your question
but they deleted their messages after i said to move
teal frigate
okay
lone heartBOT
@teal frigate Has your question been resolved?
inland frigate
lone heartBOT
lone heartBOT
@inland frigate Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
sage epoch
how do you work this problem with cos^2?
lone heartBOT
how do you work this problem with cos^2?
sage epoch
frozen python
sage epoch
like 1-(cosx)(cosx)/5x?
ocean sealBOT
MattDog_222
eager fern
lone heartBOT
jagged imp
you don't.
sick fable
lone heartBOT
Available help channel!
exotic dust
How much would you save in interest (over the life of the loan) on a 15-year mortgage at 2.5% if you reduced the amount you borrowed from $325,000 to $200,000?
brittle abyss
Im not to educated on this but would it be like this: (325,000x(1.025)^(15)) - (200,000x(1.025)^(15)) = diffrence
money x interest ^ time
zenith compass
$[\lim_{{(h_1,h_2)}\to\ (0,0)}\frac{1}{\sqrt{\frac{1}{h_1^2}+\frac{1}{h_2^2}}}]$
ocean sealBOT
Trenton
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
zenith compass
Can anyone tell me why this limit tends to zero?
lone heartBOT
@zenith compass Has your question been resolved?
zenith compass
<@&286206848099549185>
$\lim_{{(h_1,h_2)}\to\ (0,0)}\frac{1}{\sqrt{\frac{1}{h_1^2}+\frac{1}{h_2^2}}}=0$
ocean sealBOT
Trenton
zenith compass
How to show that?
lethal stump
ok @zenith compass so i've never done limits like these before so i may be wrong but i think i got it so here's my soln?
from here its pre obvious to see that c approaches zero as h1 and h2 approach zero
but i may be wrong
lethal stump
ty 😁
zenith compass
lethal stump
i was pre sure i recognized that formula from somewhere so i just fiddled around with right triangles until i got something
zenith compass
Actually the problem is from proving differentiability
zenith compass
i was pre sure i recognized that formula from somewhere so i just fiddled around...
Ya this idea is genius
lethal stump
oh thats coool
zenith compass
.close
solar merlin
how do i solve a second order diff eq that isn't equal to 0? i have the mark scheme, and i got $e^{-x}(A\cos(2x)+B\sin(2x))$ in my solution, but apparently the answer is $e^{-x}(A\cos(2x)+B\sin(2x))+\textbf{10}$
ocean sealBOT
ALIAS
boreal prawn
slender marten
how do i solve a second order diff eq that **isn't equal to 0?** i have the mark...
Solve the related homogeneous differential equation first. Find a particular solution, by any means, and the general solution will the addition of the two.
solar merlin
could you clarify that, please? i'm not exactly sure what you mean, particularly with the "addition of the two" step
slender marten
A particular solution is the term used for the any solution which satisfies the actual differential equation.
I'm not sure how much stuff you know about differential equations to guide further guidance.
Are you aware of complementary functions and particular solutions?
rapid verge
lone heartBOT
rapid verge
how would u answer this
supple tundra
my friend
rapid verge
hello
supple tundra
u just have to add it
rapid verge
what so 10/5h?
rapid verge
u just have to add it
on mathway the answer is different
gray isle
how would you simplify something like
$$\frac12 + \frac13$$
ocean sealBOT
ℝamonov
supple tundra
on mathway the answer is different
shouldn't be using bots yet to solve your problems
rapid verge
**ℝamonov**
find lowest common denominator
that would be 3/6 + 2/6 = 5/6
@gray isle
gray isle
apply the same idea to your question
rapid verge
so add a h
rapid verge
so 40/5h + 2h/5h
lethal stump
yea
rapid verge
then cant that be 2(20 + h) / 5h
lethal stump
yea
but like
factoring a 2 out isn't really gonna do much
its helpful in most instances to factor stuff out
rapid verge
so it can be 40 + 2h / 5h aswell
lethal stump
yea
rapid verge
ok thankyou so much
lethal stump
np np
rapid verge
.close
tepid mauve
Can anyone help me to find the inequality that I circled
lone heartBOT
Can anyone help me to find the inequality that I circled
tepid mauve
I already found the equation but the answer key says x+2y<4
So do I just move my 2 to the left? Then i move my -x to the left?
But where do you get 4? So i also multiply 2 with 2?
tepid mauve
Ohhh okay thanks
I also noticed that if i have -x, i always move it to the left, why is that?
balmy warren
Just nicer to deal with positives rather than negatives
fickle cliff
Where did the m+n in the denominator go?
lone heartBOT
Where did the m+n in the denominator go?
cunning trout
The (m+n) went to the other side of the equation and multiplied by zero hence got it’s value as zero.
slate kayak
lone heartBOT
slate kayak
How do i give an equation of a plane from O(0,0,0) that goes through the 3 normal vectors
The 3. Normal vectors are (1,-1,-1) and (1,1,-3) and (2,-1,-3)
fringe token
You can construct a plane with three points
pure anvil
lone heartBOT
alpine sable
Are all denominators of LHS equal
Don't think so.
pure anvil
Yo the last a3an-2 should be there
alpine sable
I think it should be
a1 an
a2 a n-1
a3 a n-2
a4 a n-5
...
an a1
alpine sable
Yo the last a3an-2 should be there
Yep.
pure anvil
Don't know
alpine sable
The problem looks interesting. Might give it a try after 5 minutes.
pure anvil
Okie
alpine sable
Don't know
I think you should try partial decomposition and then add up the first and last terms.
1/a1an = x/a1 + y/an like this. When you will have a lot of them like
1/a1 + 1/an + 1/a2 + 1/an-1 + ... + 1/an + 1/a1
Actually then
Nah, decomposition won't be useful if we add lol.
pure anvil
Wait I tried it
oak perch
Are all denominators of LHS equal
You pair those 1/a_k+1/a_n-k on the right hand side
oak perch
$\frac{1}{a_{1}+a_{n}}(\sum_{1\leq k \leq n}\frac{1}{a_{k}})= \frac{1}{a_{1}+a_{n}}(\sum_{1\leq j \leq \frac{n}{2}}(\frac{1}{a_{j}}+\frac{1}{a_{n-j}})= \sum_{1\leq j \leq \frac{n}{2}}
\frac{1}{a_{j}+a_{n-j}}(\sum_{1\leq j \leq \frac{n}{2}}(\frac{1}{a_{j}}+\frac{1}{a_{n-j})=\ sum_{1\leq j \leq \frac{n}{2}}\frac{1}{a_{j}a_{n-j}}$
ocean sealBOT
Cogwheels of the mind
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
pure anvil
.close
lone heartBOT
lone heartBOT
@alpine sable Has your question been resolved?
rigid smelt
what have you tried?
lone heartBOT
@alpine sable Has your question been resolved?
gusty gyro
6/n * 5/(n-1) = 1/3
30 / n(n-1) = 1 / 3
n(n-1) = 90
n^2 - n - 90 = 0
Q.E.D.
The first line is probability of taking two orange candies in a row with respect to the taken out candy
gusty gyro
@alpine sable you here?
misty bobcat
how to show isomorphism between these groups ?
lone heartBOT
how to show isomorphism between these groups ?
marsh rapids
Don't think there is one. R is uncountable but Z^2 is, so there can't be a bijection
misty bobcat
Don't think there is one. R is uncountable but Z^2 is, so there can't be a bijec...
I think exactly same.
do you think that is enough to show this ?
marsh rapids
By contradiction is quite obvious. If there is one, you have a bijection from R to Z^2. But Z^2 is countable so you have a bijection from Z^2 to N. By composing them, you have a bijection from R to N (or a subset of N or an injection, depending on your definition for countability). However R is not countable, so that can't be.
misty bobcat
can I ask you what is the difference between (Z,+)x(Z,+) and (ZxZ,+)
?
because, im not able to imagine it
marsh rapids
Assuming that + is the usual addition (i.e. no shenanigans), there shouldn't be any
As the addition for a product group is done component wise
misty bobcat
ok thanks a lot
oak perch
I see, I am not trustworthy
marsh rapids
I see, I am not trustworthy
RIP
lone heartBOT
@misty bobcat Has your question been resolved?
marsh rapids
Just to be sure about definitions: a maclaurin series is a taylor series centered around 0 rather than any point right ?
Then sometimes Maclaurin is better because the formula is nice, sometimes Taylor is better because because of convergence reasons
Maclaurin series are just not as general as taylor series. They're nice for functions like sin, cos and exp, but sometimes they suck. Like if ask you to approximate sqrt(300), well... I let you compare both methods
Turns out the Maclaurin series isn't even defined because sqrt has no derivative at 0
but the linear approximation at x=289 is really good
You can do a series at any point, and locally (assuming it's well defined) it will work well. The problem is "locally", some functions lead to only a radius of convergence, then a taylor series is much better if you can compute some special values
you can do it at 0 yes
it's very nice at 0 because cos has a nice development at 0
how have you defined a taylor series
that's not a definition
a taylor series is the generalization of the local approximation of a function by its tangent line or parabola
a taylor series always has a center. Look at the definition you have. The center is the point where you can guarantee the approximation to be exact
the area around the center is the area around which the approximation is going to be the best
Here the order 2 approximation of cos and order 1 approximation of ln produces a really good parabola
That's not math, that's physics. That's basically saying "I know how it is at that point, but I don't know how it behaves, so I'm just going to assume nothing else happens"
that is correct, but the interpretation is based on physics liking t=0
the mathematical reason is you have no reason to prefer 0, it depends on the situation
t=2.52 and you approximate centered at 0 ? Look at the function dude
just approximate at the next root
there's no wrong and right. When comparing approximations, there's only better and worse
In practice when you want to approximate using Taylor polynomials, we choose the center such that:
- It's a convenient point where we already know the value and the formula is nice (otherwise it is not simpler to approximate)
- It's close enough to the value we want to approximate, so that we still get a good approximation
marsh rapids
Maclaurin series are just not as general as taylor series. They're nice for func...
Hence the example of x=289 to approximate sqrt(300)
approximations is a game of intuition
Do you think the information you have at 0 is appliable to what happens at t=2.52 ?
intuition
The function literally goes to -inf and comes back before reaching t=2.52. What information do you expect to carry over that trip ?
how good an approximation does that look ?
Doing approximations is like doing physics: it requires intuition
it requires an understanding of the function
ok can you easily compute an order 2 approximation for the function centered at 2.5 ? Obviously not using anything that would be about as hard or harder as just computing f(2.52)
Wdym "do" ?
center at 2.52 ?
ok what's the first step to center at 2.52 ?
I mean what's the first term you need to compute for your function/approximation ?
do you understand the point of taylor series ?
If you can plug the function into WA you don't need an approximation
solve what ?
That's precisely why you approximate
also in contexts where there is no calculator
yes please do, this is clearly trivial
Clearly a simple solution to your physics problem. Easy to deduce properties of this function looking at that formula
I frankly don't know if this is incompetence, bad faith or a lack of understanding
do you see how Taylor series are useful ?
avoids that hell of a formula
just slap an error term at the end of the approximation, and say "I did the approximations such that it's small enough for our purposes"
marsh rapids
you got || normally, where did it go ?
another reason to use an approximation I guess
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
wet pulsar
I just have a quick question
lone heartBOT
I just have a quick question
wet pulsar
In my textbook Markov matrices all row elements add to 1
And on YouTube a MIT professor is saying all columns add to 1
The book is a probability book and the YouTube lecture is a linear algebra video
I’m not good with linear algebra do I’m not sure if it even matters which way you do things
gusty gyro
As for my knowledge there is differences in schools, some teach to work with columns, some with rows. Just stick to your learnings and don't mix up the relative positions of some operations.
I feel like didnt say anything useful, so wait till somebody helps
lone heartBOT
@wet pulsar Has your question been resolved?
vital crown
I’m not good with linear algebra do I’m not sure if it even matters which way yo...
It does not. But you should make it clear what your vectors are. Are your vectors row vectors or column vectors?
If the transition matrix is written $P_{ij}$ from state $i$ to state $j$, where $i$ refers to the row index and $j$ is the column index, then it is clear row elements should sum to 1.
In this case, if columns also sum to $1$ then the matrix satisfies a very special property, but I don't think that is what you are asking about here so it doesn't matter
ocean sealBOT
pepper
vital crown
"it is clear" = "if you follow Kolmogorov axioms of probability"
sinful gorge
A booklet wants me to differentiate the following.
I got dy/dt = 36t^2.
The booklet however says that the answer is: 72t^2
What did I do wrong?
undone hinge
is that $y=1\cdot 18t^2+22\cdot 4$ ?
ocean sealBOT
Big xdddd
sinful gorge
Yes
undone hinge
formular is : $f(x)=x^n\to f'(x)=nx^{n-1}$
ocean sealBOT
Big xdddd
undone hinge
so if you differentiate that you get 36t
sinful gorge
Oh yeah I forgot that one step.
Regardless I think I solved the problem now. Those dots are actually decimal points instead of multiplication symbols apparently
.close
hollow robin
9x-7i>3(3x-7u)
lone heartBOT
9x-7i>3(3x-7u)
hollow robin
pls
lone heartBOT
@hollow robin Has your question been resolved?
lone heartBOT
@hollow robin Has your question been resolved?
final thorn
whats the correct way to prove a number is equal to another number sorry for the bad phrasing
merry depot
is there context for this question?
merry depot
what does the << mean?
see #❓how-to-get-help to open your own channel
final thorn
i need to show that (1/root(10)) = (1/10)(root(10)) without using a calculator
merry depot
So you want to look at rationalizing the denominator
sleek finch
see <#488120190538743810> to open your own channel
oops didnt notice it was occupied
merry depot
i need to show that (1/root(10)) = (1/10)(root(10)) without using a calculator
here are a couple of examples of rationalization.
The idea is to basically multiply your denominator by a factor that turns it from a radical (or a root) into an integer (or fraction). Then multiply that by top and bottom
final thorn
so id end up with (1 root(10) / root(100))?
neat sierra
lone heartBOT
neat sierra
This only shows that the sequence converges right?
But it doesnt converge to 0
please pin me if u answer
tacit arch
But it doesnt converge to 0
What do you mean. You calculated the limit and it's zero
neat sierra
The question asks also to find the value it converges to
I found the limit, which means I know that the sequence is convergent, I still dont know where it converge to
unless it's 0 as well?
dreamy glade
isn't that the value it converges to
neat sierra
I wasn't sure if that were the case, so Im just asking that
dreamy glade
mb mb
neat sierra
<@&286206848099549185>
little drum
unless it's 0 as well?
?
what exactly did you mean to do when you calculated "limit of a_n as n tends to infinity"?
neat sierra
There is a theorem that said if limit exists at infinity then the sequeunce is convergent, if it doesnt exist, then its divergent
so i calculated the limit of an as n tends to infinity to see if it converge
unless my notes was wrong?
little drum
nope.
I hope this enlightens you a bit
when is a sequence called convergent
-> A sequence is "converging" if its terms approach a specific value as we progress through them to infinity.
neat sierra
ohh, i see. So it converge to 0 in this case
little drum
Yes it does
thin urchin
lone heartBOT
thin urchin
Just want to make sure I set everything up correctly before I move on
thin urchin
Yes so inf - inf
alpine sable
Which would leave you with 15x(1) - 15x
alpine sable
Which would be inf-inf right?
Yep
thin urchin
Ok so is my setup and evaluation correct?
And then I think I have to divide the numerator and denominator by the highest power of x in the denominator
alpine sable
Ok so is my setup and evaluation correct?
Yh aslong you've multiplied correctly it's fine but isn't really necessary for this questions
thin urchin
Oh I mean I'm sure they will teach us a shortcut eventually but they are teaching us this method first
I still have inf- inf in the numerator
alpine sable
225x(e^(2/x) - 1)
alpine sable
No clue tbh
thin urchin
<@&286206848099549185>
cobalt ledge
atomic stirrup
lone heartBOT
@thin urchin Has your question been resolved?
grave shoal
someone help me please im begging😕😢😭
lone heartBOT
someone help me please im begging😕😢😭
@grave shoal Has your question been resolved?
grave shoal
<@&286206848099549185>
analog mica
want to do the first or second page?
grave shoal
the second page please
lone heartBOT
@grave shoal Has your question been resolved?
lone heartBOT
@grave shoal Has your question been resolved?
feral bridge
Hello
feral bridge
Someone was kind enough to help me with a problem, but I lost internet connection.
Could someone explain it for me please?
I have 2 static numbers. 5 and 10. I want to increase 5 slowly over the course of a week, or any set length of time, to reach 10.
So as soon as an event happens we start at exactly 5. Then every second we increase a little towards 10.
As we get further in time, it increases the more the number goes up each second.
So then on day 7, or any other set time frame. It reaches its cap and stays at 10
lone heartBOT
@feral bridge Has your question been resolved?
proud patrol
cost price of an article sold for $335 at a profit of 15%
lone heartBOT
cost price of an article sold for $335 at a profit of 15%
buoyant kayak
• After 15 minutes, feel free to ping @Helpers.
• Show your work, and if possible, explain where you are stuck.
jovial valve
isnt it just $335 x 85%
jovial valve
yeh
lone heartBOT
buoyant kayak
isnt it just $335 x 85%
don't do people's work for them
lone heartBOT
Available help channel!
trail fern
lone heartBOT
trail fern
what does the squiggly line denote here?
both variables are vectors
is the squiggly line just saying "gradient of vector" instead of just "gradient"?
alpine sable
lone heartBOT
alpine sable
i answered this question and the instructions from the module said i need a graph for to represent my answer
problem is i dont know how
does this question even have one
.close
candid agate
What is the distance from any point (x,y) to the point (2,0)?
buoyant kayak
distance formula
candid agate
😭
ocean sealBOT
Alexis Loveraz
ocean sealBOT
a disappointing son
lone heartBOT
@candid agate Has your question been resolved?
dawn star
lone heartBOT
buoyant kayak
• After 15 minutes, feel free to ping @Helpers.
dawn star
Sorry
sleek osprey
Yup!
dawn star
Mhm
buoyant kayak
so what exactly don't you understand
dawn star
I didn't see it
buoyant kayak
dawn star
So do I get help or not
buoyant kayak
read the formula given
.
buoyant kayak
it tells you exactly what you need to determine
.
buoyant kayak
(they also underlined)
.
buoyant kayak
so what exactly don't you understand
.
dawn star
.
oblique spire
.
merry coral
$$2/8 = 1/4$$
ocean sealBOT
Chunkin
merry coral
💀
dawn star
.close
pure anvil
lone heartBOT
storm grotto
How did they simplify this step?
lone heartBOT
How did they simplify this step?
tacit arch
(a-b) / c = a/c - b/c
storm grotto
Wouldn’t it be 1 - 2/n^2 if you did that?
I can’t tell if it’s a typo or if I’m missing something
brazen patrol
Yeah i think its a typo
what textbook is this?
maybe we can find the errata online
Strang?
This looks like Stewart 8 e
8th edition
storm grotto
Rogawaskis calculus for AP second edition
tacit arch
Yea typo
brazen patrol
What page is this?
storm grotto
What page is this?
Page 539
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
any tips on how to prove $\bar{A} \in \overline{P(A)}$ is false
ocean sealBOT
mahmooz
alpine sable
huh
brazen patrol
oh
lol
of course
so you're trying to show that the complement of A is not in the complement of the powerset of A?
alpine sable
ye
brazen patrol
well
you can try to show that the power set is closed under complement
after that, it should make sense
alpine sable
what do u mean by closed under complement
brazen patrol
so
if you have A, P(A) being the powerset, then for all B in P(A), show that B-bar is in P(A)
B-bar is the complement of B
If you can show this, then by definition of complement, A-bar can't be in P(A)-bar
lone heartBOT
@alpine sable Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
turbid harbor
hi so i am studying le control system design and i swerved uni at 18 (now 27 :D) and i have basically forgotten some basic maths concepts which can trip me up
such as here: not sure how setting s=1 and then s=s helps us get to 1=Pb + Ra
and 0=P+R
I know about comparing coefficients for powers of X but super confuseed what the heck happened here 😂
turbid harbor
whhich is funny because i completely understand the next lines about inverse laplace 😂
lone heartBOT
@turbid harbor Has your question been resolved?
lone heartBOT
@turbid harbor Has your question been resolved?
lone heartBOT
@turbid harbor Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
crude birch
How fundamental theorem of calculus connects integration and differentiation?
crude birch
From what I understand it connects area under the curve and anti-derivative.
lone heartBOT
@crude birch Has your question been resolved?
crude birch
<@&286206848099549185>
raw fractal
The first fundamental theorem says that $\frac{d}{dx}\int_a^x f(t) : dt = f(x)$. That is the link between the definite integral and the derivative.
ocean sealBOT
PhenomPlasma
raw fractal
In words, the rate of change of the area under the graph is equal to the height of the graph.
The second fundamental theorem says that $\int_a^b f(x) : dx = F(b) - F(a)$, where $F$ is any antiderivative of $f$.
ocean sealBOT
PhenomPlasma
raw fractal
In words, the area under the graph is the difference in the value of the antiderivative at the two endpoints.
crude birch
In words, the rate of change of the area under the graph is equal to the height ...
Doesn't this mean that differentiation of anti-derviative will lead to original function?
raw fractal
That's not what it says. Differentiation of the antiderivative is always the original function. That's the definition of antiderivative. What it says is that the function $\int_a^x f(t) : dt$ is an antiderivative of $f(x)$.
ocean sealBOT
PhenomPlasma
crude birch
I see. But what about d/dx part?
raw fractal
It says the derivative of that given integral is equal to f(x). Which by definition means that the given integral is an antiderivative of f(x).
crude birch
Does f(x) is original function?
raw fractal
Yes.
alpine sable
The average age for which maximum cases occurred is ?
lone heartBOT
The average age for which maximum cases occurred is ?
@alpine sable Has your question been resolved?
alpine sable
<@&286206848099549185>
zenith compass
Since 23 is the largest, the group 35-45 and 45-55 is desired one
Can u find the average age?
lone heartBOT
@alpine sable Has your question been resolved?
hoary crest
is it true that if i multiply two or more functions, the graph of the resulting function is the union of the graphs of the initial functions?
zenith compass
It depends how u “multiply”
If u set the RHS to be 0, that is kinda obviously true
zenith compass
is it true that if i multiply two or more functions, the graph of the resulting ...
I know you are talking about something like (Ax+By+C)(Dx+Ey+F)=0
But we usually don’t say multiply function is the union of the functions
The condition is to set the RHS to be 0
Otherwise the multiplication makes no senses
But if you set one side to be 0 and multiply all the nonzero sides and set them equals to 0
Then as long as the functions are well-defined, the desired graph is literally the “union” of the function
@hoary crest can I answer your question?
hoary crest
Otherwise the multiplication makes no senses
it does sometimes
even if rhs isn't zero, there is some rule about multiplying idk
alpine sable
$$ 10*2^{x+1}=50
lone heartBOT
$$ 10*2^{x+1}=50
alpine sable
well that didn't work
what's the prefix
anyway how do I even go about solving this for x
gray isle
try simplifying the equation first
slender gull
$$10×2^{x+1}=50$$
Is that your question?
ocean sealBOT
Sakata Yaksha
alpine sable
yes
slender gull
Alright so first of all, you could do a lot of things here.
First one seems fairly obvious.
Simplify without doing anything to that 2^{x+1}
alpine sable
I tried doing 2^x+1=5 but idk where to go from there
slender gull
Right, have you studied logarithm?
alpine sable
yeah a bit
alpine sable
the book says I should do this without a calculator lol
slender gull
Yes, I said take log you don't need a calculator for that.
gray isle
you can keep your results in exact log form
slender gull
Yeah.
alpine sable
the task wants me to compare the values of multiple results
I don't understand how I can do that with the log forms
slender gull
You still get a decent idea.
remote granite
lone heartBOT
https://www.chegg.com/homework-help/questions-and-answers/1--lifetimes-light-bul...
@remote granite Has your question been resolved?
odd aurora
lone heartBOT
odd aurora
i tried working out the midpoint, timesing by the freq for each then dividing by the total freq but it didnt work
any help?
<@&286206848099549185>
tall hearth
i tried working out the midpoint, timesing by the freq for each then dividing by...
why did it not work?
odd aurora
no idea, im pretty sure it shouldve
austere root
<@&286206848099549185>
The weekly transportation expenses of Grade 11 HUMMS students are
normally distributed with a mean of ₽500 and a standard deviation of ₽50.
a. How many percent of their transportation expenses are over ₽600? 36.65%
b. How many percent of their transportation expenses are below ₽400?
c. What is the probability that their transportation expenses are between ₽400
to ₽600
d. What is the sum of the probabilities below ₽400 and above ₽600?
lone heartBOT
lone heartBOT
Available help channel!
warped salmon
Hello, I would like to calculate the variance of a random variable but an having trouble extrapolating to a larger time scale.
Say I have a normally distributed variable X with Var[X]=a. X is say the change in value of something after a time delta of dt. I want to determine what the variance of a new random variable Y is that is the change in value after a time delta of 2*dt
warped salmon
I thought that this would be as simple as Var[Y] = Var[2X] = sqrt(2)*Var[X] but my model is falling apart. I think it is because I am not manipulating the underlying distributions correctly
I am calculating the variance of a lognormally distributed variable
This is a simulated stock price
doing a walk with geometric brownian motion
You can see that I am calculating the returns of the asset at each timestep and calculating the std. I am correcting for the fact that this volatility is observed at a higher fidelity than once every unit timestep by dividing by sqrt(dt).
I can tell this is incorrect because I am using the volatility to price some options -> the options should make no money to be fair -> but the options are making money. This means I am overestimating the volatility on my adjusted timeframe
The next reasonable adjustment is rather to calculate std(a)/dt but I don't see why I would divide by dt and not sqrt dt given the explanation I have above for my variance.
$$ shortreturn^{1/dt} = longreturn $$
ocean sealBOT
demo
warped salmon
from nor on short return = sr and long return = lr
$$ var[lr] = var[sr^{1/dt}] = var[exp(ln(sr)/dt] $$ from wikipedia
ocean sealBOT
demo
floral quail
Okay, so given that µ = 23.26 and σ = 4.10, find the probability out of 10 samples, that at least 4 of them have a mass greater than 25kg.
floral quail
I tried solving this by calculating the probability of them being over 25kg via a Normal Distribution
M~N(23.26, 4.10) then** P(M>25) = 1 - P(M<25) = 0.3352**
So if **0.3352 **is my calculated probability of them being over 25kg
I can now use a Binomial Distribution to calculate the probability of at least 4 of them
**Y~B(10, 0.3352) **where P(Y>=4) = 1-P(Y<=3)
I got **0.5541 **but the answer is 0.4469
Could anyone see where i've gone wrong?
floral quail
Eh......?
one sec
alr i redid it and I got precisely 0.552962702004
23.26 and 4.1 are just from the mark scheme which differed slightly from mine since i didnt round earlier
noble sinew
And it gives 0.4470… as final
Like I said
floral quail
Okay ive got 0.335640617297 on my calculator now
So that's ^ the probability of getting over 25kg
oh shoot
i've got it now
thanks
.close
fast cloak
lone heartBOT
fast cloak
Is it fine?
lone heartBOT
@fast cloak Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
rough yoke
I just had a couple questions about power series
lone heartBOT
I just had a couple questions about power series
rough yoke
so when finding the IOC
and taking the ratio test of a complex series that isn't just Ar^n
if the ratio test goes to 0
the radius of convergence is infinite right?
if the ratio converges to a finite number then I put the part with X between -1 < x < 1 and test endpoints
but what happens if it diverges
noble sinew
Wdym with not Ar^n
lone heartBOT
@rough yoke Has your question been resolved?
wild shard
lone heartBOT
wild shard
why is it true that b^2 can divide n^2 given a and b and coprime
lone heartBOT
@wild shard Has your question been resolved?
lone heartBOT
marsh rapids
why is it true that b^2 can divide n^2 given a and b and coprime
look up Gauss's lemma/theorem
lone heartBOT
Available help channel!
fierce prairie
A major appliance store is considering purchasing vacuums from a small manufacturer. The store would be able to purchase the vacuums for $86 each, with a delivery fee of $9,200, regardless of how many vacuums are sold. If the store needs to start seeing a profit after 230 units are sold, how much should they charge for the vacuums?
fierce prairie
I've thought of one equation: y = 86x + 9200 where x is the number of vacuums they buy and y is total cost
but idk how to incorporate the profit after 230 units sold
winged rock
Its not a profit of 230
You want to know how much to sell 230 vacuums for to match the total expenses
fierce prairie
yeah typo
fierce prairie
hm okay that actually makes sense but
the question asks to set up an augmented matrix
so like whaa..
wouldn't you need 2 equations?
<@&286206848099549185>
lone heartBOT
@fierce prairie Has your question been resolved?
alpine sable
can anyone help me on 7
lone heartBOT
can anyone help me on 7
sudden hinge
,rotate
ocean sealBOT
sudden hinge
or are you allowed to solve this using the inverse trig functions
probably not right
alpine sable
we can solve it in any way
teacher said as long as work is shown
i have formula for it
but i dont know how to start
sudden hinge
can you show the formula
ocean sealBOT
sudden hinge
so let's start by using the last formula for tan(2x)
alpine sable
ok
alpine sable
i think
sudden hinge
we have the value for cos(theta)
the pythagorean identity, which is sin^2(theta) + cos^2(theta) = 1, gives us a way to find sin(theta)
tan(theta) = sin(theta) / cos(theta)
sudden hinge
oh then you can already calculate tan(theta)
sudden hinge
that looks correct
alpine sable
ya but idk what to do next
sudden hinge
tan(theta) = sin(theta) / cos(theta)
plug the values in there for sin(theta) and cos(theta)
you should get a nice fraction
$\tan\theta = \frac{\sin\theta}{\cos\theta} = \frac{3}{5} \cdot \frac{5}{-4}$
alpine sable
why do we multiply it
ocean sealBOT
Navix
sudden hinge
I just took the reciprocal of cos theta
sudden hinge
yes thats correct
but we have sin(theta) / cos(theta) = (3/5) / (-4/5) = (3/5) * 5/(-4)
alpine sable
oh so we flip to multiply
sudden hinge
exactly
fractions inside of fractions usually dont look good
now you can simplify the expression
sudden hinge
the 5's cancel
alpine sable
oh so just 3/-4
sudden hinge
yep
alpine sable
and i am done?
sudden hinge
so the last formula
of your sheet
tan(2x) = ...
$\tan(2\theta) = \frac{2 \tan(\theta)}{1 - \tan^2(\theta)}$
ocean sealBOT
Navix
alpine sable
so the top will be 6/-4?
sudden hinge
or -3/2
alpine sable
did i do it wrong
alpine sable
why is it not negative
alpine sable
oh
sudden hinge
like (-2)^2 = 4 not -4
alpine sable
oh ok
sudden hinge
16/16 - 9/16 = ?
alpine sable
7/16
alpine sable
we multiply again right
alpine sable
14/-48
sudden hinge
now simplify the fraction and you're done
alpine sable
7/-24
thank you
on the paper it says i should have got 24/7
what part was wrong
sudden hinge
hmm
alpine sable
oh wait i did it wrong
instead of 16/7 i put 7/16
ya that was it
thank u
/close
.close
lone heartBOT