indigo estuary
Ok I get it now
#help-26
topaz sinewBOT
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turbid linden
where does the z table comes from
topaz sinewBOT
where does the z table comes from
@turbid linden Has your question been resolved?
topaz sinewBOT
@turbid linden Has your question been resolved?
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wintry kestrel
how would one do this?
topaz sinewBOT
how would one do this?
winter egret
P(t) = rho_in * (r * t) + P_0
because r*t is the volume of the polluted water that has flown in by time t
so rho_in * (r * t) is the amount of extra pollution that has poured in by time t
ok no I didn't notice there's also water leaving the tank
wintry kestrel
P(t) = rho_in * (r * t) + P_0
would this be the solution?
winter egret
Yeah you need to notice that the volume of the setup remains constant
wintry kestrel
yuh
winter egret
would this be the solution?
I don't think I can read that handwriting sorry also I'm really hungry so I'll give up on this problem sorry for being very useless
wintry kestrel
I don't think I can read that handwriting sorry also I'm really hungry so I'll g...
lmao no worries thx
brazen inlet
topaz sinewBOT
brazen inlet
Question 30
I assume I need to use trig identities here with u sub
I know the derivative of csc(x) is -cscxcotx but idk how I can use that here
tawny spade
Can you cancel something first
nimble garnet
cot yeah
tawny spade
It becomes cos/sin²
brazen inlet
Cos/sin
tawny spade
Whats csc
brazen inlet
1/sin
tawny spade
Whats cos/sin * 1/sin
mortal spear
Where’s the new csc from
wdym new csc?
topaz sinewBOT
@brazen inlet Has your question been resolved?
golden wraith
L, B, P, M are playing UNO. There are 108 cards, 4 cards of +4. Everyone will have 5 cards when the game started. What are the chances that L getting 4 cards of +4 when the game started. I got the solution of 176851/1071819 but not sure so im here double check
topaz sinewBOT
L, B, P, M are playing UNO. There are 108 cards, 4 cards of +4. Everyone will ha...
golden wraith
thank you
My work here is :
Tổng số cách Long có thể bốc các lá bài là: 108*107*106*105*(104)/(120) = 111469176
Tiếp theo, để tính số cách mà trong 5 lá anh ta bốc có đúng 1 lá +4 và 4 lá khác, ta sẽ tính số cách chọn 4 lá khác từ số lá còn lại trong bộ bài (104 lá) và nhân với số cách chọn 1 lá +4 từ số lá còn lại trong bộ bài (4 lá +4).
Số cách chọn 4 lá khác là: 104*103*102*101/(1*2*3*4)= 4598126
Số cách chọn 1 lá +4 là : 4 cách
Cuối cùng, để tính xác suất, ta chia số cách có thể bốc được 4 lá +4 cho tổng số cách anh ta có thể nhận được 5 lá từ bộ bài UNO.
Xác suất của việc đó xảy ra là: 4598126*4/111469176=176851/1071819 xấp xỉ 16.5%
sr its Vietnamese but it is translated to :
The total number of ways Long can draw the cards is: 108*107*106*105*(104)/(120) = 111469176
Next, to calculate the number of ways in which among the 5 cards he picked, there is exactly 1 +4 card and 4 other cards, we will calculate the number of ways to choose 4 other cards from the remaining cards in the deck (104 cards) and multiply by the number How to choose 1 card +4 from the remaining cards in the deck (4 cards +4).
The number of ways to choose 4 other cards is: 104*103*102*101/(1*2*3*4)= 4598126
The number of ways to choose 1 +4 card is: 4 ways
Finally, to calculate the probability, we divide the number of ways he can draw 4 cards +4 by the total number of ways he can get 5 cards from the UNO deck.
The probability of that happening is: 4598126*4/111469176=176851/1071819 approximately 16.5%```well
You've probably played Uno
before
so does it seem reasonable that in 17% of your games, you get all +4 cards in your starting hand?
In approximately 1 in 5 games, you'd get all of the best cards in the game, of which there are only 4 in the deck
in your starting hand
doesn't seem plausible to me
winter egret
The first observation you can make is that you can assume that Long gets dealt their cards first
because it obviously doesn't affect the probabilities which order you deal the cards in
Then you can think about how many hands there are that contain all of the +4 cards
Note that in such hands, you have 4 +4 cards and 1 random card
golden wraith
ik
winter egret
Then you can divide that by the total amount of different hands which is nCr(108, 4)
and the result should probably look something like this
golden wraith
um i thought it should me ncr(108,5)
winter egret
The Binomial command is Mathematica's way of saying nCr
golden wraith
Then you can divide that by the total amount of different hands which is nCr(108...
i meant this msg
winter egret
oh yeah sorry that was a weird typo, that should indeed be nCr(108, 5)
golden wraith
so you are caculating like 104/ncr(108,5)
right?
I would like to see why it is a 104
winter egret
there are 104 different options for the fifth card in someone's hand
if they start out with 4 +4 cards
golden wraith
there are 104 different options for the fifth card in someone's hand
so what would it do with the ncr(108,5)
erm
nvm
i got it
thanks
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topaz sinewBOT
golden wraith
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topaz sinewBOT
✅
golden wraith
wait
can i ask again. Considering we are also giving the cards to the others
so what
nvm still got it
thanks
.close
topaz sinewBOT
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glad token
ok so
why is 0!=1 ?
topaz sinewBOT
ok so
why is 0!=1 ?
ivory sorrel
uh
ivory sorrel
ok so
why is 0!=1 ?
One way is that it's just convient to define it that way
glad token
One way is that it's just convient to define it that way
that dont solve my question '-'
winter egret
You often have factorials in the denominator, and if 0! was defined as 0 then you'd run into trouble
ivory sorrel
that just explains why it's defined that way though
worthy quiver
hmmm...
ivory sorrel
https://www.reddit.com/r/math/comments/s5ixpc/why_the_factorial_of_0_is_always_1/ this thread may help
winter egret
There's probably some euler gamma function argument for 0! = 1 that's probably the most convincing
normal tapir
(n+1)! = n!(n+1), evaluate this at n = 0 to see the result. And we choose this as a base case for the definition because it shows up a lot and is extremely useful to let this be the convention
winter egret
But at the end of the day, no one's forcing you to use the factorial of zero. You could just treat it as undefined in your own math and not really miss out on anything
Probably eventually you'll realize that 0! = 1 is just convenient to have
glad token
Probably eventually you'll realize that 0! = 1 is just convenient to have
Probaly eventually we will just use calculators
winter egret
Calculators follow rules programmed in by mathematicians and engineers
they're not the highest mathematical authority
we are
math is our little delusion
and lots of people like to imagine that 0! is 1 for some pretty compelling reasons
Maybe a loose philosophical argument for 0! being 1 would be that the argument of the factorial function is generally interpreted in an "additive" sense
Like counting for example is just you adding +1 over and over
And 0 is the additive identity element
however the output of the factorial function is a product
and in a product setting, 1 is the identity element
so maybe you'd expect one identity to get mapped to another identity or something
But idk if that actually makes sense or if that's just me being crazy
topaz sinewBOT
@glad token Has your question been resolved?
austere yew
topaz sinewBOT
austere yew
Where to start
tawny spade
With the difference of squares on the bottom
tawny spade
Hmmm
Maybe turn the top into a (cos²a+sin²a)²
By addind and subtracting to complete the square
lunar vault
can someone teach me hypothesis testing??
austere yew
Maybe turn the top into a (cos²a+sin²a)²
I think we can do a square + b sqaure form also
tawny spade
Probabky
We just need the top to become 3+cos4a
We finished the sec2a
Outside the brackets
austere yew
Maybe turn the top into a (cos²a+sin²a)²
I turned it into that
tawny spade
What do you have now
austere yew
4 tines 1 - sin square 2a
austere yew
tranquil stirrup
acoustic grove
Whats up
austere yew
Yes
austere yew
Yes
austere yew
1
austere yew
Huh
acoustic grove
4(a²+b²)
austere yew
I did a square plus b square form
acoustic grove
That would turj into 4a²+ 4b²
austere yew
Oh
acoustic grove
And a²+b² does not = (a+b)²
austere yew
And a²+b² does not = (a+b)²
I did -2ab also
austere yew
acoustic grove
Im lost my brain is too fried lololol
Sorry
@helper
<@&286206848099549185> tag in
neon iron
What's the question?
austere yew
Question
copper swallow
well i tried solving both LHS and RHS
LHS i got 4cos^2 A
though i cannot solve the RHS
the RHS ig needs to be solved further
topaz sinewBOT
idle crypt
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idle crypt
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ok so trying to figure this question
found the equation for arc length which im assuming r=4
topaz sinewBOT
Available help channel!
toxic stirrup
how would i do this?
topaz sinewBOT
how would i do this?
toxic stirrup
starting with part i
golden blade
,,\frac{1}{1-x} = \sum_{n=0}^{\infty} x^n \text{ for } \abs{x} < 1
thorny flameBOT
𝔸dωn𝓲²s
toxic stirrup
how would i use that to find 1/(x-2)(x-3)?
golden blade
You can multiply by 1-x
toxic stirrup
$\frac{1-x}{(x-2)(x-3)}$?
thorny flameBOT
talk_less
golden blade
Not 1-x cancels out
toxic stirrup
hm
golden blade
But this seems honestly like a too easy approach
the next step would be to divide now by (x-2)(x-3) obviously
BUT
i got it
You use partial fraction decomposition
,,\frac{1}{(x-2)(x-3)} = \frac{A}{x-2}+\frac{B}{x-3}
thorny flameBOT
𝔸dωn𝓲²s
golden blade
YOu sure?
toxic stirrup
1/(x-3)-1/(x-2)
toxic stirrup
yes
golden blade
What could you do forexample
golden blade
what happens if you factorize -3
toxic stirrup
-3(-x/3+1)
toxic stirrup
but
toxic stirrup
so it becomes this:
$\frac{-1}{3}\sum_{n=0}^{\infty}{(\frac{x}{3})^n}$?
thorny flameBOT
talk_less
golden blade
yes for what radius?
toxic stirrup
1
golden blade
$-\frac{1}{3}\sum_{n=0}^{\infty}{ \left (\frac{x}{3}\right )^n}$ for $\abs{\frac{x}{3}} < 1$
thorny flameBOT
𝔸dωn𝓲²s
golden blade
Now the same approach for the other fraction!
toxic stirrup
And then I also do the same for the other fraction?
So it will become a sum of two summations?
golden blade
yes
golden blade
Actually it makes more sense the one that is smaller
because if you take the one larger
the one series might converge while the other diverges
golden blade
Was it integration or differentiation lemme think
Ok here a hint
and then integrate
golden blade
**𝔸dωn𝓲²s**
Integrate the series and use this afterwards
Denoting it g(x)
Yea that should do it, good luck!
thorny flameBOT
𝔸dωn𝓲²s
toxic stirrup
Integrate the series and use this afterwards
So I integrate 1/(1-x) and multiply by x?
golden blade
**𝔸dωn𝓲²s**
You integrate this
Without the x part
Outside
,,x\underbrace{\sum_{n=1}^{\infty} nx^{n-1}}
thorny flameBOT
𝔸dωn𝓲²s
thorny flameBOT
talk_less
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
toxic stirrup
Now differentiate 1/1-x and you finished
that would be 1/(1-x)^2
not sure how this all comes together
thorny flameBOT
𝔸dωn𝓲²s
golden blade
@toxic stirrup
topaz sinewBOT
@toxic stirrup Has your question been resolved?
golden blade
You integrated wrote in a closed form and then differentiated
Giving you the initial series in other terms not pun intended lmao
toxic stirrup
lol
topaz sinewBOT
@toxic stirrup Has your question been resolved?
toxic stirrup
nothing at the moment
i jsut want to keep the channel in case i get another question
i still have to write this all down
toxic stirrup
thanks
neon iron
No problem
golden blade
@toxic stirrup What do you need help with
neon iron
<@996044212158083084> What do you need help with
He doesn't rn
@toxic stirrup you should close this
golden blade
Oh I see you helped him
neon iron
Yep
toxic stirrup
im actually a little confused about something
neon iron
Yes?
toxic stirrup
**𝔸dωn𝓲²s**
we differentiate 1/(1-x) but integrate sum(nx^(n-1))
thorny flameBOT
𝔸dωn𝓲²s
golden blade
We can tell that it will have to do with the geometric series but the problem is the factor n
So in order to get rid of that n
we would have to divide by n somehow
and that would be if we integrated the series in the first place with x^n-1
So we do this
thorny flameBOT
𝔸dωn𝓲²s
golden blade
We want it to write it in a closed form, ok?
And notice when you integrate this n will cancel
toxic stirrup
right
golden blade
$g(x) = \sum_{n=1}^\infty nx^{n-1} \implies \int g(x) \dd x = \int \sum_{n=1}^\infty nx^{n-1} \dd x = \sum_{n=1}^\infty \frac{\cancel{n}x^{n-1+1}}{\cancel{n}} + C$
$$G(x)= \sum_{n=1}^\infty x^n + C$$
We integrated both sides
toxic stirrup
right
thorny flameBOT
𝔸dωn𝓲²s
thorny flameBOT
𝔸dωn𝓲²s
golden blade
We can make it start at n = 0 but we need to subtract the first term so that the equality remains
and now we use our beloved geometric series formula
thorny flameBOT
𝔸dωn𝓲²s
golden blade
And now we want to somehow substitute g(x) with a closed form
We have G(x) the antiderivative of g(x) so that's why we differentiate
toxic stirrup
ah
thorny flameBOT
𝔸dωn𝓲²s
golden blade
**𝔸dωn𝓲²s**
Back to here
golden blade
**𝔸dωn𝓲²s**
Actually here
thorny flameBOT
𝔸dωn𝓲²s
golden blade
That is it
I get that it is difficult to find the how to start
it's important to define the steps and the goal and how to get there
toxic stirrup
right
golden blade
are there any questions, still?
topaz sinewBOT
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outer parrot
How do I turn a magnitude + bearing angle into a vector with i + j components
outer parrot
i'm in igcse mechanics 1
Forces P and Q act on a particle, P has magnitude 7N due north
resultant force of P and Q is magnitude 10N acting due 120 degrees bearing
what is the vector of resultant force R
meager tangle
Draw a diagram. You should be able to break your line into a horizontal and vertical component to make a right-angled triangle
The magnitude will be the length of the hypotenuse
And you use the bearing to get an angle inside the triangle
Then basic trig will get you the horizontal and vertical components
outer parrot
Draw a diagram. You should be able to break your line into a horizontal and vert...
i only have the hypontenuse and how do i use the bearing to get angle?
im stuck trying to determine angle inside the triangle
outer parrot
lets see
meager tangle
7 you don't need to do anything to since it's already vertical
But we want to split the 10N into horizontal and vertical parts
So since it's on a bearing of 120, that means it's 30 degrees beneath the horizontal
outer parrot
So since it's on a bearing of 120, that means it's 30 degrees beneath the horizo...
oh right i forgot how bearings work
its 30 under horizontal
okayu lets see
next step
meager tangle
So now you have a right-angled triangle with hypotenuse 10 and an angle of 30 in there
So you can find the vertical and horizontal parts using 10sin(30) and 10cos(30)
outer parrot
So you can find the vertical and horizontal parts using 10sin(30) and 10cos(30)
i have done that
usign basic tig
next?
meager tangle
So now you have the two parts into vertical and horizontal parts
So add then together
There's only one horizontal bit, so you're going 5rt(3) right
Which is the i part
Then you have 7 up but 5 down, so overall you have 2 up
Which is your j part
outer parrot
So now you have the two parts into vertical and horizontal parts
so now R = 5sqrt3 i - 5j
R - P = Q
outer parrot
q = 5sqrt3i + 2j
outer parrot
now to get the bearing of Q itself?
meager tangle
Wait can I double check the question
Do they give you P and Q?
Or do they give you P and the resultant
outer parrot
Do they give you P and Q?
just p
meager tangle
And you have to find Q
meager tangle
ah okay
Then yeah so R = 5sqrt3 i - 5j, P = 7j, so since P+Q = R, Q = R-P = 5sqrt(3)i - 12j
outer parrot
magnitude of Q = 14.8
outer parrot
Then yeah so R = 5sqrt3 i - 5j, P = 7j, so since P+Q = R, Q = R-P = 5sqrt(3)i - ...
yup
now to get bearing of q
meager tangle
Then if they ask for it as a vector, imo 5sqrt(3)i - 12j is enough
outer parrot
Then if they ask for it as a vector, imo 5sqrt(3)i - 12j is enough
nope they want that as a bearing
meager tangle
But if you want magnitude then do pythagoras yeah
And if you want bearing, draw a diagram and use tan-1
And add as many 90 degrees as you need
outer parrot
godbless
ans + 90 = 144
correct answer
so to sum it up the steps are to draw a diagram and use the bearing to get angle below horizontal then split components
then r - p = q
then use components of q to make a right angle
and find angle below horizontal using basic tig
tysm
meager tangle
yup, although it might not always be below horizontal
Could be in any of the four quadrants, so you judge how far round it is
outer parrot
yup just add the quarters
meager tangle
ye
topaz sinewBOT
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fast mesa
Calculate GBM exit time expectancy
topaz sinewBOT
Calculate GBM exit time expectancy
fast mesa
(GEOMETRIC BROWNIAN MOTION)
fast mesa
Hey!
fast mesa
None of the above
sleek haven
wym
vital relic
@sleek haven read the rules
sleek haven
vital relic
stop using other peoples channels
sleek haven
oh mb
vital relic
sleek haven
sorry
vital relic
please clear the chat
fast mesa
HI @vital relic , You know anyone with a PHD in probabilities?
fast mesa
Well GBM is a specific formula
topaz sinewBOT
@fast mesa Has your question been resolved?
topaz sinewBOT
@fast mesa Has your question been resolved?
unkempt niche
I have a question
topaz sinewBOT
I have a question
unkempt niche
in scenerios like this in number (b)
the answer is 36499-20750
here the max value we use is 36499
cause if we use 36500
it becomes 37000 when rounded
so my question is
then there are also some questions
when we are asked to state the upperbound
so in which cases can we use the upperbound value and where can we not?
like here
even though 35.5 becomes 36 we still state it as an upperbound
so when do we state use the boundary value for maximum and when do we not
topaz sinewBOT
@unkempt niche Has your question been resolved?
topaz sinewBOT
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steady copper
Good day! I am kind of stuck in this part. Can u help pls?
topaz sinewBOT
Good day! I am kind of stuck in this part. Can u help pls?
neon iron
Good day! I am kind of stuck in this part. Can u help pls?
subtract C and then solve for y
neon iron
remember though when you subtract C since we don't know its value there is still a C on the other side
steady copper
Can it be simplified further though?
steady copper
Is <#903430335474331698> ur classmate? Lol
Hehe
neon iron
I wouldn't bother simplifying it further
subtract C, cross multiply, divide by the x part
should get y = -1/(5sin(X)+C)
steady copper
How did you transfer the -1 numerator to the other side?
topaz sinewBOT
@steady copper Has your question been resolved?
prime stump
Can someone please help me I don't understand distributive property
prime stump
I have a test tmrw but I don't understand it
Here's my work and the brackets are the actual answers
My professor solved the answers but I don't understand how he came to that conclusion
May I please have some assistance?
keen venture
Can we focus on one that really confused you?
prime stump
Okay
neon iron
^^ also take a picture with better lighting
keen venture
I think that one says
(-5)(a - 6) + 2a?
prime stump
Yes
keen venture
I can see one mistake. You distributed the -5 into the +2a
But the +2a isn't being multiplied by the -5, so it shouldn't have been included
That second line should read:
(-5)(a) - (-5)(-6) + 2a
prime stump
Why isn't the 2a being multiplied?
keen venture
It WOULD be multiplied if the original question were:
(-5)(a - 6 + 2a)
Notice the position of the brackets matters here
prime stump
Okay
keen venture
(-5)(a - 6 + 2a)
The 2a should be distributed into
(-5)(a - 6) + 2a
The 2a should not be distributed into
prime stump
Let me try the equation again
I got a different answer
I got 27a
<@&286206848099549185>
Can someone help me
.close
topaz sinewBOT
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old plover
topaz sinewBOT
old plover
Could I plz get some help w/ 3b?
terse nest
use the auxiliary rectangle provided in the graph
the asymptotes of a hyperbola will pass through opposite corners of that rectangle, and the center
old plover
the asymptotes of a hyperbola will pass through opposite corners of that rectang...
Idk how to put it into general form
terse nest
do you know the how to get the a and b of the equation
terse nest
Is there any way u could solve it on paper and, like, send it to me?
no sorry, ill have to walk you through the problem
well if you have a hyperbola like this
terse nest
just by looking at the auxiliary rectangle, you can find the values of a and b by measuring the lengths of the rectangle
like that
once you got a and b, you can now write the general equation
its an hyperbola that opens left and right so you are.going to use
old plover
its an hyperbola that opens left and right so you are.going to use
Yeah
terse nest
,,\frac{x^2}{a^2}-\frac{y^2}{b^2}=1
thorny flameBOT
Renz
terse nest
subbing the values of a and b will give you the standard form
oh its general form lol
but you will have to do this first anyway
after figuring out the standard form, you can just multiply everything by a²b² and move everyone to the left, making it a general form
old plover
after figuring out the standard form, you can just multiply everything by a²b² a...
Hold on, lemme try that
Is this right?
For the standard form?
thorny flameBOT
Renz
terse nest
so its just that when you distribute the powers
so just multiply both sides by 4 then move everybody to the left
terse nest
yep
old plover
Thx sm
dark dagger
hello I need help with a problem
topaz sinewBOT
hello I need help with a problem
dark dagger
sin[cos^-1(-2/30]
-2/3
I am lost because in the notes for my calc class only examples were using the cancellation property
so I have no example to go off of for this homework question
pallid silo
Wait let me try this one
dark dagger
okay thank you
pallid silo
√5/3
dark dagger
how did you come to that answer?
pallid silo
Wait let me send you the picture
dark dagger
okay thank you
dark dagger
kk
dark dagger
Calc 1
for college
i have no setup for this though which is odd nothing in the notes to how you got that equation
dark dagger
I am assuming so, but I took trig last semester and I did not have this in those notes either
pallid silo
Okay
dark dagger
I appreciate your help a lot
pallid silo
But you should learn how to solve every type of questions
dark dagger
okay I will
dark dagger
Cali
pallid silo
Cali?
pallid silo
united states
Ooohhhh that's why
pallid silo
India
pallid silo
would that equation work for a sin and tangent problem as well
Yeah
topaz sinewBOT
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steel geyser
im doing 10x^2+6x=3 and i know the answer is -3 +,- square root 39
over 10
limpid linden
do you know the quadratic formula
steel geyser
yes
limpid linden
-b +,- square root -b^2 +4ac over 2a
x=(-b+,- sqrt(b^2 -4ac))/2a
rearrange the equation first
steel geyser
-6 +,- square root -6^2 + 4(10)(-3) over 2(10)
limpid linden
u might be wrong
steel geyser
ok
limpid linden
k
steel geyser
oh wait give me a sec
ok im back yeah i used the right one on paper but still dont get the right answer
limpid linden
how do i get to the -3 +,- square root 39
do you know how to simplify surds
steel geyser
probabyl not
limpid linden
damn
steel geyser
how do i do that
limpid linden
alright lets just do the working out first
steel geyser
kk
steel geyser
yup
steel geyser
yes
limpid linden
alright now you simplify it
steel geyser
its 36 + 120 right
limpid linden
yes
limpid linden
yes
steel geyser
k thats as far as i got before confusion
limpid linden
the thing that they have done now is to change the sqrt 156
ill give you a brief explaination
steel geyser
ty
steel geyser
ok
limpid linden
and sqrt 4 =2
steel geyser
yes
steel geyser
yes
steel geyser
yes
limpid linden
wait my bad
steel geyser
oh
steel geyser
ok
steel geyser
its alright
limpid linden
so x=-6+,- 2sqrt39 all over 20
divide everything by 2
steel geyser
ohh
limpid linden
np
steel geyser
.close
topaz sinewBOT
limpid linden
hope it made sense
steel geyser
yeah you helped tons
limpid linden
👍
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balmy spruce
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ivory sorrel
Can you differentiate this?
balmy spruce
$\int_{0}^{x}{xf(t)}{\dd t}=x\int_{0}^{x}{f(t)}{\dd t}$
thorny flameBOT
pirateking0723
ivory sorrel
and then solve the resulting ODE
balmy spruce
**pirateking0723**
now i differentiate using product rule no ?
balmy spruce
Can you differentiate this?
the question wants me to differentiate
chilly cedar
Oh
balmy spruce
idk if there is a solution manual somewhere but i dont have one
normal tapir
now i differentiate using product rule no ?
Yes
balmy spruce
no
balmy spruce
Shouldn't it be F'x = xF(x)
thats the full question in fact
ivory sorrel
huh
ivory sorrel
that feels off
chilly cedar
Actually the integration part would get removed since u r differentiating both sides
balmy spruce
Actually the integration part would get removed since u r differentiating both s...
i am differentiating but using product rule
the first time i will be differentiating x
thorny flameBOT
pirateking0723
balmy spruce
They should be lower case f
ah yes
normal tapir
that feels off
You had the exact same question earlier
balmy spruce
?
so here if I try the same thing i get $\int_{0}^{x}{f(u)}{\dd u}=\int_{0}^{u}{f(t)}{\dd t}$
thorny flameBOT
pirateking0723
balmy spruce
now i can just replace x with u and u with t ?
balmy spruce
**pirateking0723**
or is this just not a true equality
I did this by first expanding f(u)(x-u) then splitting the integral after that differentiating both sides
the RHS will leave the inner integral
balmy spruce
**pirateking0723**
LHS will leave the integral on LHS here +xf(x)-xf(x)
I mean $\frac{\dd}{\dd x}\int_{0}^{x}{uf(u)}{\dd u}=xf(x)$ by FTC right ?
thorny flameBOT
pirateking0723
balmy spruce
whats that
chilly cedar
Uhm
It's like
Definite integrate
Limit : from a to b
F(x) dx
Then it's equal to
F (a+b-x) dx
Use the bot for more clarity
balmy spruce
$\int_{a}^{b}{f(x)}{\dd x}=\int_{a}^{b}{f(a+b-x)}{\dd x}$
thorny flameBOT
pirateking0723
chilly cedar
On the rhs
balmy spruce
**pirateking0723**
RHS of this or of the one in the question above it directly
balmy spruce
so here if I try the same thing i get $\int_{0}^{x}{f(u)}{\dd u}=\int_{0}^{u}{f(...
so there or here
chilly cedar
RHS of this or of the one in the question above it directly
Q above directly
topaz sinewBOT
@balmy spruce Has your question been resolved?
balmy spruce
<@&286206848099549185>
topaz sinewBOT
@balmy spruce Has your question been resolved?
light valley
why doesn't the negative value of the dx itself create the negative area?
light valley
when integrating the curve
lone nest
dx is always the x at the right end of an interval minus the x at the left end. So it is positive even where the x's you subtract from each other are themselves negative.
(Assuming a somewhat standard development of one-dimensional Riemann integrals).
topaz sinewBOT
@light valley Has your question been resolved?
broken atlas
topaz sinewBOT
broken atlas
is there a particular equation for me to use?
abstract wadi
You could find how long it'll take for both bells to ring together again in minutes and then see what time it's then.
Think LCM for that.
abstract wadi
There is nothing left anymore. You're already done.
broken atlas
ok
abstract wadi
Whatever the time is then.
broken atlas
Ok, thanks
topaz sinewBOT
@broken atlas Has your question been resolved?
topaz sinewBOT
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boreal jasper
Where did the (az+b) come from?
topaz sinewBOT
Where did the (az+b) come from?
normal tapir
$(z-z_1)(z-\bar{z_1})$ is a second degree polynomial, $2z^3 - 7z^2 +16z -15$ is a 3rd degree
thorny flameBOT
chebyshev's infinite pee norm
normal tapir
what should be multiplied to the second degree polynomial to obtain an an arbitrary 3rd degree polynomial
boreal jasper
But where's that "a" coming from ?
normal tapir
it's to account for the leading coefficient of the z^3 term which is 2
if i only did (z-z1)(z-z2)(z-z3) my leading coefficient would be 1
topaz sinewBOT
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plucky pulsar
topaz sinewBOT
plucky pulsar
Why is the triangle with sqrt(2) a right triangle?
mint crescent
from the 45 deg angle, the highlighted arc is 90 deg
which makes this a right angle
mint crescent
from the 45 deg angle, the highlighted arc is 90 deg
Inscribed angle theorem is how you get this
mint crescent
which makes this a right angle
Then use the fact that central angle = measure of the subtended arc
topaz sinewBOT
@plucky pulsar Has your question been resolved?
plucky pulsar
Then use the fact that central angle = measure of the subtended arc
Thank you so much!
topaz sinewBOT
@plucky pulsar Has your question been resolved?
night wharf
topaz sinewBOT
night wharf
here is the problem i need help understanding work the teacher provided
here is the work he provided but i dont understand 2 things 1
wwhy does the 2 not multiply out wwith each iteration of the terms if it is being multiplied and my second question is what is happening for part 2
of the question
any help exsplaining this would be very helpful thank you in advancee
.close
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neon iron
@night wharf You need to be more patient.
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rough vapor
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rough vapor
is -x a horizontal flip?
craggy haven
thorny flameBOT
teacup kitten
topaz sinewBOT
@rough vapor Has your question been resolved?
foggy bloom
foggy bloom
can someone tell me if this is correct?
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Available help channel!
tulip snow
tulip snow
can someone help with this, so far ive gotten (h,k) = 0
and c = 5squareroot91
so they should stand 10squareroot91 feet apart
grim sable
topaz sinewBOT
@tulip snow Has your question been resolved?
tropic zephyr
I don't understand anything
topaz sinewBOT
I don't understand anything
tropic zephyr
I need to find center of mass for y
teal gust
you know the formula for finding centre of mass?
for that you just need the y coordinate of A
for B and C, the y coordinate is zero since they lie on the x axis
teal gust
for that you just need the y coordinate of A
is this where your doubt is
tropic zephyr
is this where your doubt is
This is what I know
$$ y_{cm} = \frac{m_A y_A +m_B y_B + m_C y_C}{m_A +m_B +m_C}$$
thorny flameBOT
Unknown
teal gust
This is what I know
$$ y_{cm} = \frac{m_A y_A +m_B y_B + m_C y_C}{m_A +m_B +m_C...
do you know what ya,yb, and yc are ?
tropic zephyr
But don't know what are the right values
tropic zephyr
Well from a previous example I did its the y position of that certain mass
teal gust
yeah
can you tell their y positions
from just looking a thte figure
just for b and c
tropic zephyr
This one is different though because it's like a triangle
teal gust
just for b and c
?
tropic zephyr
For B id say 0 and for C I'd say 0
tropic zephyr
That's literally what I did and the answer was wrong
teal gust
the y coordinate here is essentially the perpendicular distance of that point from the x axis
meaning
the height
of A
teal gust
That's literally what I did and the answer was wrong
o
you didnt do that tho
im getting the answer as 4
tropic zephyr
This what I did before making this help
Channel
teal gust
is the height 10?
tropic zephyr
For A to me Id say yes but I'm probably mistaking something
tropic zephyr
I wouldn’t have known to see it’s a right triangle
teal gust
i mean
you need the perpendicular distance
so youd need a right angle to the base (x axis)
somewhere
tropic zephyr
So the original 10 was a diagonal distance im assuming
teal gust
ye
tropic zephyr
I got4
teal gust
try it
tropic zephyr
It worked. But im still unsure of the next part of this problem finding moment of inertia
teal gust
send it
tropic zephyr
teal gust
whast the formula of MOI that you know
tropic zephyr
I know $$I=mr^2$$
But sometimes it's $$ \frac{1}{2} mr^2$$
thorny flameBOT
Unknown
teal gust
when is it sometimes 1/2 mr^2 ?
teal gust
I know $$I=mr^2$$
But sometimes it's $$ \frac{1}{2} mr^2$$
ye just use the first one here
tropic zephyr
I think for a thin cylinder
teal gust
I think for a thin cylinder
right
mr^2 is for usually point masses
where their shape doesnt matter
here we've got that
so just use mr^2
you know what m is
now all you need to figure out is r
tropic zephyr
is it going to involve that triangle again from earlier