difference between them are the same
#help-33
naive fox
naive fox
it is different because the second one is the wrong function. Notice that for the second one, you need to have $(4x+1)^{\frac{1}{2}}$ in the denominator and you will not have $\frac{1}{2}$
elfin berryBOT
naive fox
this is for the image that you sent and deleted
celest harbor
so i got $4 \sqrt{3}$, do i do anything since its $\frac{1}{9}\sqrt{3}$ above y=0?
elfin berryBOT
morphine_addiction
naive fox
I don't think you need to do anything as the boundary is set to be $0<x<20$ or $1 < u < 9$ already
elfin berryBOT
celest harbor
I don't think you need to do anything as the boundary is set to be $0<x<20$ or $...
apparently 4sqrt(3) is wrong
weak quartz
you need to subtract the area of the rectangle
celest harbor
ye i got $\frac{16\sqrt{3}}{9}$ which is correct
elfin berryBOT
morphine_addiction
celest harbor
thank you for the help
celest harbor
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tender ibex
The figure shows a flagpole erected in a vertical plane. At point A, the mast is hinged to the vertical wall. At point B, the mast is connected by a cable to the wall at point C. The distance |AC| = 4 m and the distance |AB| = 3 m (where m stands for metres). By varying the length of the cable |BC|, the angle θ made by the mast with the horizontal can be adjusted. The relationship between cable length and time t is given by |BC| = l(t). Determine the relationship between velocity dl/dt by which the length of the cable |BC| changes and the angular velocity dθ/dt. Note: the figure is not drawn to scale and the angle θ is expressed in radians.
marsh citrusBOT
The figure shows a flagpole erected in a vertical plane. At point A, the mast is...
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still temple
So I am meant to simplify [
S(t) = 19\6vt +4\dv[v]t-2\int_{-\infty}^t\6vt\dd t
]
where $\6vt = 55\6\cos{5t+44\degrees}$ and we assume the value of the integral at $t= - \infty$ is zero. Anyways, I did the following, where i am assuming the form $\6vt = A\6\cos{\omega t + \varphi}$:
\e{align*}{
19\6vt +4\dv[v]t-2\int_{-\infty}^t\6vt\dd t \Iff 19V + 4j\omega V - 2\4V{j\omega} &= V(19 +4j\omega +2j\omega) \ &=V(19+6j\omega) \ &= V(19+30j) \ &=35.5Ve^{57.7\degrees j}\ &= 35.5e^{35\degrees j}e^{57.7\degrees j} \ &=35.5e^{92.7\degrees j}
}
where $V$ is frequency domain representation of the sinusoid. I am not sure how to carry on with this now though?
marsh citrusBOT
So I am meant to simplify \[
S(t) = 19\6vt +4\dv[v]t-2\int_{-\infty}^t\6vt\dd t
...
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wooden tartan
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lean wedge
Ohh sorry
wooden tartan
I didn't understand what I have to do to find the right answer
shadow thorn
if you look at the top most left 3x3 square
consisting of 3 black squares and 6 white ones
wooden tartan
uhum
shadow thorn
its the same as the other 3x3 squares at each corner
look at the square at the third row and second colum
if i move it to the top middle
and repeat that pattern for the other 3x3 squares
i get a new 5x5 square with does not change when rotated 90 degrees
wooden tartan
You rotated the figure but it keep the same thing
shadow thorn
one sec
wooden tartan
ok
shadow thorn
imagine moving the square
squares
you get a new pattern
try calculating all the ways you can move around the squares
also
consider the other 2 black squares
the one at the top
and the other black one next to it at the bottom rigth corner of it
after that
consider adding black squares
ye this is a tough one
good luck
shadow thorn
just focus on this square
because the 5x5 grid is this square copied 3 times and rotated
shadow thorn
consider the other 2 black squares
acc ignore this logic
i thought you had to keep the same no. of black squares
just try to figure out all the possible ways to configure that 3x3 square
be careful about avoiding repetition
the no. of combinations of black and white squares in a 3x3 grid is 2^9
thats 512 so thats a lot
because there was some repetition
try to figure out where that comes from
@wooden tartan got it
shadow thorn
idk where the repetition comes from
wooden tartan
I think the answer is 128
shadow thorn
I think the answer is 128
would the question consider these to be the same
shadow thorn
hmm ya 2^7 = 128
shadow thorn
oh yaaa
wooden tartan
What do you think?
shadow thorn
that has to be the answer yes
wooden tartan
Nice
shadow thorn
hope i helped a bit
shadow thorn
you found the answer though
low oriole
marsh citrusBOT
low oriole
why did they not set y=k and x=k
only z=k
Like they found that on the xy plane, z = k is the ellipse. They found this by setting z = k.
They did that in this example too.
z = k --> found ellipse.
They found the traces in the yz and xz plane by setting x = k and y = k too.
So why did they not do that in the first example?
Ah I guess _ = k just indicates how it behaves on the third axis.
setting it equal to 0 just shows how it acts on the immediate plane
i see now.
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scenic peak
hi, i'm learning about the likelihood function for regression. suppose we have a degree 50 polynomial which perfectly fits the data points and a degree 1 line which doesn't capture the curve of the data. am i right to think that the parameters for the degree 50 would have a higher likelihood than the parameters for the degree 1?
marsh citrusBOT
hi, i'm learning about the likelihood function for regression. suppose we have a...
scenic peak
the degree 50 polynomial is likely to overfit if the data points actually came from, say a degree 4 polynomial with noise added. what do people usually do to control the degree of the polynomial?
versed pagoda
this broadly fits into model complexity
if your model is too complex (has too many parameters) then its likely to overfit to data
so typically you trade off degree with accuracy
and then use a validation set
to check for overfitting
ocean zenith
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muted kite
hello
muted kite
so i have a question about special relativity
wet holly
it was invented by Special Ed in 1995
muted kite
In special relativity, it is said that when an object is moving with a speed close to the speed of light an observer that is still with respect to said object measures its length as shorter than the object's length with respect to its frame of reference
lets say i have the coordinates of Xa' and Xb' of such object with respect to its frame of reference
its length is then L' = Xa' - Xb'
The question is then: can i get the coordinates Xa and Xb in the frame of reference of an observer that is still with respect to the object by using the following formulas:
Xa = γ(Xa' - vt)
Xb = γ(Xb' - vt)
because if i do, then L is equal to γL', which would mean that the length measured by a still observer is longer than the actual lenght of the object
where L is = Xa - Xb
i got it
apparently i was looking at the problem the wrong way
given the case that i have just explained
S is moving with respect to S' with velocity v
meaning that the length in S, which is moving, is bigger than the lenght in S' which is still
meaning then that the lengths in the frame of reference that is moving are always bigger than the lenghts in the frame of reference that is still
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brisk totem
Question 117 I have no idea how to solve this
marsh citrusBOT
Question 117 I have no idea how to solve this
lucid zenith
do you know what King's rule is?
brisk totem
No
lucid zenith
it's a rule for definite integrals
it states that $$\int_a^b f(x) dx = \int_a^b f(a+b-x) dx$$
elfin berryBOT
kheerii
lucid zenith
that's literally the only way to solve this
oh well you can derive this super easily
it's just a u-substitution, u=a+b-x
brisk totem
I’m not sure
lucid zenith
Question 117 I have no idea how to solve this
here substitute $u=a-x$
elfin berryBOT
kheerii
lucid zenith
what did you get?
lucid zenith
the denominator will have a plus
lucid zenith
also I think you meant integral from 0 to a
lucid zenith
sure that works
lucid zenith
now since this is a definite integral the variable u doesn't hold any significance
so you can change that to
x
brisk totem
Okay
elfin berryBOT
Nathan
brisk totem
Okay
lucid zenith
since the limits are the same the integrands will just be added
brisk totem
Okay one sec
$$\int^a_0 \frac{f(-x+a)+f(x)}{f(-x+a)+f(x)}dx$$
Uh
Okay
Like that?
lucid zenith
the dx is supposed to be outside the fraction
brisk totem
Yeah my bad
lucid zenith
$$\int_0^a\frac{f(a-x)+f(x)}{f(a-x)+f(x)} dx = \int_0^a 1 dx$$
elfin berryBOT
Nathan
elfin berryBOT
kheerii
brisk totem
Oh
Fair enough
Ok
I had another quick question though
Didn’t we abuse u sub when you let u be x again?
u had a meaning of x-a
brisk totem
I don’t understand
You said that after we u subbed you wanted to let u = x even though = x-a
lucid zenith
not u=x
it's more like you're transforming u to x
$$\int_a^b f(u) du = \int_a^b f(x) dx$$
elfin berryBOT
kheerii
lucid zenith
would you agree with this statement?
lucid zenith
Well if u=x then yes
why?
whatever our variable is, it doesn't matter
what's what I'm trying to tell you
you're integrating the same function within the same limits
a definite integral is just a number
the variable inside doesn't matter, so we can change it
the only reason we had to change it is so that we could add the two integrals
we could have just as easily changed the original integral into u and added them that way
brisk totem
But x is its own variable
You could say u=t=z=s that doesn’t matter
But x is already used
And u is literally defined as x-a
We can’t just say u=x now
lucid zenith
we are NOT saying u=x
okay what if I tell you to transform both integrals to some other variable
say y
$\int_0^a \frac{f(x)}{f(a-x)+f(x)} dx = \int_0^a \frac{f(y)}{f(a-y)+f(y)} dy$
elfin berryBOT
kheerii
brisk totem
Okay sure
lucid zenith
and $\int_0^a \frac{f(a-u)}{f(a-u)+f(u)} du = \int_0^a \frac{f(a-y)}{f(a-y)+f(y)} dy$
elfin berryBOT
kheerii
lucid zenith
now can we add them together?
brisk totem
now can we add them together?
Yes
lucid zenith
that's the same as what I did
I just reused x for convenience, since the variable really doesn't matter in a definite integral
but I get why it confused you
brisk totem
**kheerii**
So what’s next after this
lucid zenith
we converted them both to y right?
brisk totem
We converted the right one to y
The left one is u
y=x
u=a-x
Mv they equal
Nvm
so how do we add them @lucid zenith
brisk totem
How?
marsh citrusBOT
@brisk totem Has your question been resolved?
gloomy fossil
I need help with lhopital
marsh citrusBOT
I need help with lhopital
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still temple
I need help with lhopital
you need help with applying the rule ? to a specific question or in general ? or you want to know the proof ?
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celest harbor
did i intergrate wrong?
marsh citrusBOT
did i intergrate wrong?
celest harbor
celest harbor
ye
winter smelt
wait
when integrating 1/(2u+5)
that doesn't give you ln(2u+5)
it's 2/(2u+5) that integrates to ln(2u+5)
celest harbor
it's 2/(2u+5) that integrates to ln(2u+5)
oh ye i forgot to divide by the coefficient of u
winter smelt
oh ye i forgot to divide by the coefficient of u
or just break 20 = 2*10 and bring a 2 into the numerator
celest harbor
ye 10ln(9/7) is correct
winter smelt
cool
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still temple
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still temple
can anyone explain
high pine
yes
still temple
damn
this is so difficult
you need to see how you can reform it
so it's easier to use the rule
high pine
Believe that is not, it might be because you see it for the first time
It's very common "trick"
high pine
yes
You cannot use l'Hospital when you have [1/0]
inside the limit
It should be 0/0 or inf/inf
high pine
so it's 0/0 then
How? It's not.
still temple
no?
high pine
When we plug x = 10 directly into the fraction we'd get 1/0
log(10) = 1 (log with base 10)
high pine
x-10 = 10 - 10 = 0
still temple
and 1/0 doesn't exist
high pine
It's 1/0, in such a case I'd recommend examining sided limits
high pine
and 1/0 doesn't exist
Yea, but 1/0 doesn't necessarily mean that a limit doesn't exist
still temple
Yea, but 1/0 doesn't necessarily mean that a limit doesn't exist
okay
high pine
(and in your case they're not and this is why limit DNE)
still temple
can I ask one last question?
how would I need to do this one
you don't need to make it for me
but like
a quick analysis
of what to do
and what I can't do here
and why
high pine
mhm, surely l'Hospital wouldn't help
maybe try diving by e^x?
both the top and bottom
still temple
mhm, surely l'Hospital wouldn't help
why's that?
still temple
okay I get that
and what I could try to do it dividing both top and bottom by e^x
what would be the result of that?
high pine
look, I'll apply it for the top
still temple
okay
elfin berryBOT
Modus
still temple
bottom is almost the same
high pine
and it gives 1 - e^(-2x), right?
elfin berryBOT
Modus
high pine
do the same with the bottom part
high pine
Now you have:
elfin berryBOT
Modus
still temple
correct
high pine
And notice it's not indeterminate anymore
high pine
what's e^(-inf)
high pine
Then expalin how did you get -1? 🙂
still temple
I removed 1 in the upper and 1 in the lower bc they're the same? 😢
and then it's -1
high pine
It doesn't work that way.
high pine
Okay, first of all
Do you know why we only now plug "inf"?
And why we didn't do it at the beginning
high pine
Generally we should start from this point, when you deal with a limit you always try to plug a number into it, directly
and you see what you get
still temple
what is e^inf
high pine
e^inf is just inf, you are familiar with "e" number?
still temple
i kinda forgot
high pine
e equals about 2,72
still temple
it was this special number
high pine
therefore e > 1 and e^inf = inf
high pine
then what's e^-inf
still temple
- inf
high pine
or what's let's say 2^(-inf)? imagine calculating 2^-1, 2^-2, 2^-3, ..., 2^-10...
high pine
It's not -inf
still temple
1/inf
high pine
Finally, yes haha
still temple
sorry haha
high pine
That's fine
still temple
so e^-inf is 0
high pine
yeah, every number greater than 1 raised to -inf is 0
winged harness
still temple
this is why we did division
the division by e^x right?
still temple
Do not plug it into the original limit!
because we would get inf/inf if we plug it?
right?
high pine
That's right
high pine
Yes, when you obtain an indeterminate form you are supposed to do some stuff to get a result
high pine
Yeah
high pine
You're welcome.
still temple
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plush nacelle
@knotty trellis why do you mean by automatically or manually? I just meant that if we want to find the radius we can just use google maps and take a screenshot and then draw straight lines to find the distance. Wdym by drawing circles on GeoGebra ?
marsh citrusBOT
<@951190447185874994> why do you mean by automatically or manually? I just meant...
@plush nacelle Has your question been resolved?
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vivid tusk
a question on proving linear independence of the dual basis:
let V be our vector space, B = {v_1, ... v_n} its basis, and f_i(v_j) = \delta_{i,j} for each basis vector (so that the f_i are our coordinate functions/dual basis elements)
say we have scalars a_i s.t.
a_1*f_1 + ... + a_n*f_n = 0
the standard argument is evaluating this above null functional on each v_i and noticing each a_i is 0. is there another way? why not evaluate on a generic v in V? does the standard argument imply something else?
marsh citrusBOT
a question on proving linear independence of the dual basis:
let V be our vector...
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elfin berryBOT
Biggs
vivid tusk
and i got
elfin berryBOT
Biggs
vivid tusk
and im not sure if its possible to deduce a_i = 0 here
marsh citrusBOT
@vivid tusk Has your question been resolved?
slim spire
there's probably a way but it's all linear with =0 so might as well do the component vi's
vivid tusk
im more confused on how you can obtain "constant" values of a_i evaluating on specific vectors (basis here)
vivid tusk
**Biggs**
i thought of making n equations, each one evaluated on a different v_i, then summing with scalars as to make up an arbitrary v, but it leads me to this case too
vivid tusk
im more confused on how you can obtain "constant" values of a_i evaluating on sp...
the question is more "why can i use specific values to determine a_i rather than having to use arbitrary v"
slim spire
I think you'd need n different arbitrary ones to be able to conclude any 0's, so it'd be messy
but like in a sense applying it to an arbitrary one lets you split it up into n equations because of linearity and =0
vivid tusk
could you elaborate on how to split it into n different equations
sounds like what i need
hushed egret
the sum
a_1 f_1 + ... + a_n f_n
is an entire function V -> your field
and saying that it is = 0 means that at every point in V you could evaluate the function at
it will be 0
so of course you can choose where to evaluate
vivid tusk
because the value (of 0) is the same for everyone, whatever you get about the function for any choice of vector must be true for any other vector, so youre saying i might as well make a smart choice by choosing the basis vectors, on which the function is easy to evaluate on
is what youre saying
marsh citrusBOT
@vivid tusk Has your question been resolved?
tight turret
Which is better, Coq or Lean?
sonic palm
would this be a good example?
marsh citrusBOT
would this be a good example?
sand kindle
would this be a good example?
that's an example
(though no example can prove the statement)
sonic palm
(though no example can prove the statement)
so the statement is true?
sand kindle
so the statement is true?
if you want to prove the statement, you need to show it is true for ANY f
if you want to disprove it, you can show that it is false for some f
sonic palm
if you want to prove the statement, you need to show it is true for ANY f
i wanted to prove false
and chose my f as a counter example
sand kindle
you're saying the limit exists for f?
sonic palm
yes
sand kindle
what's the limit?
sonic palm
i mean the limit technically never reaches 2
proud ice
i mean the limit technically never reaches 2
nor does it reach 0
proud ice
no
marsh citrusBOT
@sonic palm Has your question been resolved?
proud ice
Im sorry do you think the question is true or false
are you asking if the given statement is true or false? What are your thoughts? It sounds like you think it's false?
sonic palm
I think the given statement is false.
proud ice
so you think the limit converges?
sonic palm
yes
proud ice
and what do you think it converges to?
proud ice
What do you mean by "$\lim_{x\to\infty} \cos x+1$ is bounded between 0 and 2" Did you mean that just $\cos x+1$ is bounded between 0 and 2?
elfin berryBOT
SWR
proud ice
Okay yeah, $\cos x +1$ is indeed bounded between 0 and 2. But what do you mean by "but never reaching 0 and 2"?
elfin berryBOT
SWR
sonic palm
because if we take the limit of cos(x)+1, it approches 2 but is not two. although cos(0)+1 = 2 but the limit approches 2
proud ice
because if we take the limit of cos(x)+1, it approches 2 but is not two. althoug...
take what limit? What is x approaching?
proud ice
$\lim_{x\to\infty} \cos x+1$ does not exist
elfin berryBOT
SWR
sonic palm
But then that doesn’t guarantee f(cosx+1) is dne
proud ice
But then that doesn’t guarantee f(cosx+1) is dne
why do you think that?
sonic palm
Because fx could be 0 for all x except at 2
proud ice
Because fx could be 0 for all x except at 2
f(x) could be 0 for al x except at 2, yes. But that does not imply your previous statement. In fact, it implies the opposite.
Are you familiar with the formal definition of a limit?
the epsilon-delta definition?
sonic palm
Yes
proud ice
Yes
Okay, so try proving your assertion using epsilon-delta definition of a limit to infinity
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plush saffron
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south smelt
What have you tried?
plush saffron
What have you tried?
i transformed this eq into dy/dx form
south smelt
And that gives you?
plush saffron
And that gives you?
varible seprable form ive benn stuck to integrate at last
south smelt
Okay, but you got $\dv{y}{x} = \frac{2x^2+2x+3}{x^4+2x^3+3x^2+2x+2}$ ?
elfin berryBOT
ℑμΤ𝛄𝛗θ
south smelt
or keep the dx on the other side, whichever you prefer
plush saffron
Okay, but you got $\dv{y}{x} = \frac{2x^2+2x+3}{x^4+2x^3+3x^2+2x+2}$ ?
yes
but how do i integrate ()dx ?
south smelt
partial fractions most likely, but it looks like a mess
Apparently you're supposed to notice that (1+x^2) is a factor of the denominator
I really don't know how you'd figure that out, but here you go
plush saffron
Apparently you're supposed to notice that (1+x^2) is a factor of the denominator
yeah but how do i have to notice that
south smelt
I'm not quite sure. Has this been given to you by a teacher? There's no way they just want you to trial and error until you find the right factor right?
the polynomial doesn't even have real roots
plush saffron
I'm not quite sure. Has this been given to you by a teacher? There's no way they...
nah this a question from entrace exam
for college
south smelt
Is the exam ongoing?
plush saffron
Is the exam ongoing?
nah
south smelt
Okay good
south smelt
I see I see
plush saffron
I see I see
is it hard for 12th grader ?
south smelt
I don't live in a country with that schooling system so I wouldn't know
plush saffron
I don't live in a country with that schooling system so I wouldn't know
but acc. to your country?
south smelt
I don't know what 12th grade corresponds to
plush saffron
I don't know what 12th grade corresponds to
high school
south smelt
See where I live we don't even do calc in highschool 
south smelt
**ℑμΤ𝛄𝛗θ**
So, if you want to, I suggest you ping @ helpers, and someone else might be able to explain the logic behind finding that factor of (1+x^2) in the denominator
Because I sure as hell can't see it
plush saffron
See where I live we don't even do calc in highschool <:shrugs:240813604469735424...
wait senior school sorry
plush saffron
So, if you want to, I suggest you ping @ helpers, and someone else might be able...
ohh thank you for your help 
plush saffron
<@&286206848099549185>
marsh citrusBOT
@plush saffron Has your question been resolved?
plain crescent
wait senior school sorry
I solved it but with using an integration calculator cause I don't know how to integrate this
it shows the steps tho
substitube x with -1 and equate it to -pi/4 and get the C, then substitute the x with 0 and add the value of C and you should end up with pi/2
plush saffron
substitube x with -1 and equate it to -pi/4 and get the C, then substitute the x...
i got that but didnt understand how to break the biquadratic
plain crescent
i got that but didnt understand how to break the biquadratic
Yeah sorry I'm not sure how
marsh citrusBOT
@plush saffron Has your question been resolved?
narrow bear
How do you get E(X)?
I understand 1., A was 4 - sqrt(2), but I have no idea how to get E(X)|
the answer is E(x) = 1.97 but how do i get there
marsh citrusBOT
How do you get E(X)?
I understand 1., A was 4 - sqrt(2), but I have no idea how...
narrow bear
ping if answering please
cloud field
ping if answering please
you know the formula for E(X)?
narrow bear
I don't know, I assumed it was taking the integral from its lower bound to upper bound but it wasn't that
cloud field
indeed you take the integral
narrow bear
Well when I did that I got 0.5 and the answer was 1.97
cloud field
you got your steps?
narrow bear
its on paper and its a bit messy so i used an online one and they also got 0.5
and this is answer key
cloud field
its on paper and its a bit messy so i used an online one and they also got 0.5
first thing, you forgot to multiply an x
second thing, you need to add it with the integral of the x(x-1) part
narrow bear
if I add it with the above integral it's 0.5 too since both have to add up to 1 to be continous
but what do ytou mean multiply with an x
cloud field
Yes, E[X] = sums of X * Y
like you said
E(X) = sum of xf(x)
but since this is continuous distribution, it will be the integral of xf(x)
narrow bear
but since this is continuous distribution, it will be the integral of xf(x)
Sorry but I don't understand what you mean
cloud field
Sorry but I don't understand what you mean
ok doesnt matter
the important thing is you need to use integrals correct?
narrow bear
yes
cloud field
ok what should you be integrating
narrow bear
in my head this is the integration i should be doing
but doing this gets me 0.5 so idk what to change about it
narrow bear
like this?
cloud field
yes
narrow bear
that gets me this which still isnt the answer (1.97)
cloud field
ok you got that
but thats not the entire distribution
you still have an x-1 right?
f(x) = x-1 for 1 <= x <= 2
you do the same thing with it
narrow bear
Oh ok I understand now thanks
marsh citrusBOT
marsh citrusBOT
Available help channel!
still temple
marsh citrusBOT
still temple
Greetings, im very confused about question 13, please help me to start
marsh citrusBOT
@still temple Has your question been resolved?
still temple
<@&286206848099549185>
brave spire
!status
marsh citrusBOT
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
ok
brave spire
lemme draw it real quick
the ellipse is the bullet btw
clearly after t=0, the ball will be acted by gravity
gaining a=-g
still temple
ok perfect
still temple
Ok'so let the ball reach h'
brave spire
exactly
still temple
they we shoot the bullet?
brave spire
so it takes
still temple
but the bullet also goes down due to gravity yes?
brave spire
but the bullet also goes down due to gravity yes?
Oh shit i forgot about that 🤦♂️
well it shouldnt be too tough
the premise remains the same
instead of considering h'
we consider h' + (d/(horizontal speed of bullet))*(vertical speed of bullet)
this should make sense
still temple
Why exactly?
brave spire
because d/horizontal speed is the time it needs to reach the ball horizontally
but in that time it will travel down as well
so the distance it travels down is the vertical speed * time
brave spire
btw u do know how to determine the horizontal speed yes? given its a vector of magnitude v
still temple
ok
brave spire
so ur distance for ball (d_b) = h' + d*(-gt)/v
$d_b = h' - \frac{dgt}{v}$
hopefully that isn't too confusing
(-gt = vertical speed, horizontal speed is given = v, h' because it needs to obviously travel that, and d is the horizontal distance for the bullent)
elfin berryBOT
rak³en
still temple
db is the distance for the ball to cover?
brave spire
db is the distance for the ball to cover?
yes
still temple
no
brave spire
what no
still temple
so the bullet moves down -1/2g(d/v)^2
brave spire
we shall apply second equation of motion as well
brave spire
so the bullet moves down -1/2g(d/v)^2
Huh?
still temple
please check again
still temple
Yes i calculated that for the bullet moving vertically down
fluid hinge
so the bullet moves down -1/2g(d/v)^2
it moved down with a = -g
still temple
that what i meant, sorry
fluid hinge
so the bullet moves down -1/2g(d/v)^2
this is the verticle distance of the bullet from the ground when it covered d distance
fluid hinge
yea
still temple
yes
fluid hinge
this is the verticle distance of the bullet from the ground when it covered d di...
am i right?
sorry not from the ground
from height h'
brave spire
eh sure ur right
still temple
vertically downward wrt to ground, yes
brave spire
**rak³en**
so this should be $d_b = h-h' - \frac{g}{2}\left({\frac{d}{v}}\right)^2$
fluid hinge
whts db?
brave spire
distance to be covered by the ball
fluid hinge
why h'??
elfin berryBOT
rak³en
brave spire
missed the h there
still temple
ok heres another' problem <:opencry:586078614865444865>
we can not shoot the bullet when the ball reaches h', because the ball will have much greater velocity and the bullet will miss because its initial vertical velocity is 0
brave spire
didnt i mention that alr?
still temple
Idk
still temple
This has to do something with relative velocity
still temple
ill ping if i solve it
i have solution but i dont understand shit and i think its probably wrong
fluid hinge
who said it collides at h'??
fluid hinge
Sorry my english is not very good
its okay
still temple
ill send
fluid hinge
ok
still temple
see if you can understand
fluid hinge
hmm
wait a min ill text you after finding the solution
i think im close
@still temple bruh the didnt mention anywhere tht d is small
still temple
Yes so we assume bullet moves down
fluid hinge
yes if we do tht then im getting the answer u sent - (d/v)^2
still temple
please send your solution
fluid hinge
the time take for the ball to reach the distance - time taken by bullet to reach the distance
fluid hinge
please send your solution
let me write it properly
still temple
The question is what time after the ball is dropped, gun should be fired
still temple
ok
still temple
,rotate
elfin berryBOT
fluid hinge
should i take a better pic?
still temple
$h-h'-\frac{1}{2} g \frac{d^{2}}{v^{2}}$
fluid hinge
h-(h'+(1/2)(g(d/v)²)) right
h-(h'-(1/2)(g(d/v)²))
@still temple dw i can understand the message
still temple
I give up.
fluid hinge
<@456226577798135808> dw i can understand the message
.
zinc condor
fluid hinge
why?
fluid hinge
hmm
still temple
Can u explain the last para?
fluid hinge
yea
so the time taken to cover the distance where the ball and bullet hit is this solution
still temple
Ohhh
fluid hinge
so the time taken to cover the distance where the ball and bullet hit is this s...
by ball
still temple
The wait time + time taken bullet to reach the point = time taken for the ball to reach the point
fluid hinge
The wait time + time taken bullet to reach the point = time taken for the ball t...
yea
so got it?
still temple
You're from India?
fluid hinge
h-(h'+(1/2)(g(d/v)²)) right
i scribbled the diagram to cross check again when u sent this msg
fluid hinge
You're from India?
yea
still temple
Classmate notebooks
echo elm
Hi
fluid hinge
Classmate notebooks
haha
still temple
Hello ali
echo elm
Do you need help
fluid hinge
@still temple so done right?
still temple
Yessir, thank you
fluid hinge
Yessir, thank you
btw r u preping for jee?
still temple
Yessir.
echo elm
Done already 👍
still temple
We on the grind
fluid hinge
haha me too
echo elm
Let me check
fluid hinge
i was air13
woah wth
stark trail
im oci now
still temple
i was air13
Bro is a shiny Pokemon 😭
fluid hinge
im oci now
r u for real? or kidding
stark trail
for real
stark trail
last
fluid hinge
any proof?
stark trail
my word
stark trail
im not revealing my identity here
still temple
Bhaiya do you solve doubts
stark trail
Bhaiya do you solve doubts
I ABCD=always be clearing doubts
fluid hinge
im not revealing my identity here
k
stark trail
air 13 on 2023 right
no
fluid hinge
im not revealing my identity here
ur identy is revealed over whole india why fear now?
still temple
I respect that.
fluid hinge
hmm
fluid hinge
no
which collage?
dont tell if u dont want to
@still temple i think u can close this channel
marsh citrusBOT
echo elm
I need help
echo elm
fluid hinge
tag helpers im heading out so cant help rn
echo elm
Ok
marsh citrusBOT
Available help channel!
polar forum
i need to find where $A\cup B=\varnothing$ but why is ㄱ wrong
marsh citrusBOT
i need to find where $A\cup B=\varnothing$ but why is ㄱ wrong
elfin berryBOT
R4F43L1006
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
limber marsh
I mean, if a b and c are variables, they could technically be 0 1 or 2?
Weird assumption to make though
I'd normally assume the first answer is right
Could you translate the last two?
polar forum
I mean, if a b and c are variables, they could technically be 0 1 or 2?
that's my thoughts but it says ㄱ is an answer
limber marsh
that's my thoughts but it says ㄱ is an answer
So it is right?
polar forum
So it *is* right?
it says so
limber marsh
Then all is fine in the world
You normally don't treat a b and c as variables
I was confused over why you were saying it was wrong
polar forum
@limber marsh but cant $A\cap B\neq \varnothing$
elfin berryBOT
R4F43L1006
limber marsh
Yes
Imma go use Google translate
Brb
Yep, the first answer is right
They're disjoint
polar forum
the question says to choose all where $A\cap B=\varnothing$
elfin berryBOT
R4F43L1006
polar forum
yeah but the answer say ㄱ,ㄹ
limber marsh
yeah but the answer say ㄱ,ㄹ
Which I agree with
Sorry, what exactly are you trying to ask?
polar forum
so i can treat a,b,c as not variaples
limber marsh
so i can treat a,b,c as not variaples
Yeah
polar forum
but theres a case a, b, c are varibles
limber marsh
Except unless they say they are
They're not
They're just letters
polar forum
ah okay 👍
limber marsh
I realize algebra brainwashed us all into thinking math is all numbers and letters only exist to be variables
But nah, letters can exist as just letters
And with set theory they most likely are just letters unless otherwise implied
polar forum
so then it will say 'for variables $a,\ b,\c$' if they are?
limber marsh
If they're doing variable things with them
They're variables, otherwise they're just letters
marsh citrusBOT
marsh citrusBOT
Available help channel!
still temple
why can both sides be subtracted by 2n
marsh citrusBOT
why can both sides be subtracted by 2n
vernal forge
why can both sides be subtracted by 2n
a bit more explicitly
n | 2n+1 -> 2n+1 = k*n for some k
so k*n-2n = 1
so (k-2)*n = 1
since n and k are integers, this is only possible if n = 1 and k = 3, or if n=-1 and k = 1
so $n=\pm1$
elfin berryBOT
artemetra
polar forum
$2n+1=nk$
$1=nk-2n=n(k-2)$
$\therefore 1\mid n$
marsh citrusBOT
still temple
.reopen
marsh citrusBOT
✅
polar forum
why?
still temple
i saw that you were typing mb
polar forum
no nvm 🙂
still temple
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
dim hedge
Given tetrahedron ABCD with 3AD+2AC+AB ≤ 18a and volume of V=6a^3. What is the distance between point A and plane (BCD)?
I figured out from this 6a^3 = (S_BCD * h_A)/3, i could infer this h_A = (18a^3)/(S_BCD) and i'm stuck in here at this point.
marsh citrusBOT
Given tetrahedron ABCD with 3AD+2AC+AB ≤ 18a and volume of V=6a^3. What is the d...
@dim hedge Has your question been resolved?
dim hedge
<@&286206848099549185>
marsh citrusBOT
@dim hedge Has your question been resolved?
dim hedge
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
visual storm
I needed to find the derivative. is this the right answer?
marsh citrusBOT
I needed to find the derivative. is this the right answer?
still temple
Whats tg
quaint elm
tangent
still temple
Tanx?
visual storm
tangent x
twilit grove
what happened to the denominator for the first term?
heady lark
we can use the derivative formula for division
heady lark
heady lark
yes
heady lark
were did you got the image
visual storm
from my book
heady lark
k
substute the values
when you substuting
be careful
as their is a sqrt
we have to take it as power 1/2
twilit grove
she already did that in her answer
@visual storm I think you're missing the denominator in your first term
twilit grove
i got (x^2+1)^2 as denominator
yes, it is the denominator for both terms
visual storm
so I can shorten the one in the numerator?
whole thorn
I needed to find the derivative. is this the right answer?
seems right to me
twilit grove
so I can shorten the one in the numerator?
what do you mean?
visual storm
in numerator we have 3 (x^2+1)
and in denominator we have 2
so we need to delete one from numerator or we cant?
twilit grove
you can if you want, but then you'll have two fractions
$\frac{x^2 + 1}{(x^2 + 1)^2} = \frac{1}{x^2 + 1}$. you didn't keep the factor in the denominator of the first term
elfin berryBOT
cwatson
visual storm
lost a little bit
visual storm
what is desmos