and pick two different deltas?
#help-33
gentle remnant
hazy lion
as long as your cases are exhaustive
hazy lion
yea
like
epsilon odd and epsilon even isnt exhaustive
but if epsilon is real, then irrational and rational is exhaustive
still temple
dtheta is nothing but just a small part of theta right ?
So why is not outside theta
marsh citrusBOT
dtheta is nothing but just a small part of theta right ?
So why is not outside ...
still temple
It should be inside theta no as it is small part of theta?
pure gull
It looks like they're just showing $\theta$ and $d\theta$ separately for clarity.
elfin berryBOT
jolimath
still temple
It looks like they're just showing $\theta$ and $d\theta$ separately for clarity...
Can u read this and rectify?
As in I have also read it but I am not sure about it
fervent rampart
$\theta$ is the angle position, whereas $d\theta$ is a small change in that angle
elfin berryBOT
cloud
still temple
$\theta$ is the angle position, whereas $d\theta$ is a small change in that angl...
Ohhhh
Not it makes sense
How about this tho
X and dx?
Same logic?
still temple
Same logic?
@fervent rampart
fervent rampart
yes
toxic remnant
Find the number of all onto function from the set {1, 2, 3, ... n} to itself.
marsh citrusBOT
@toxic remnant Has your question been resolved?
warped jay
Since both the domain and the codomain comprise of the same set , the functions between the two sets are forced to be one to one functions
Which means two values of the domain can't have the same result ,
Because if two values had the same result , one value of the codomain would be left behind . It's not possible to compensate for it as 1 single value of the domain can't connect with two values of the codomain
Now let's take the first value of the domain , it can correspond with another value of the codomain in n ways . Similarly , the next value of the domain and correspond with any value of the codomain in (n-1) ways , and soon , by the product rule , n(n-1)(n-2).... 1 = n!
mighty gyro
similar triangles?
elfin berryBOT
Wendy's Support guy #0193
still temple
**Wendy's Support guy \#0193**
this?
still temple
ae/fd = cd/db
we know this because the triangles are similar
still temple
**Wendy's Support guy \#0193**
if we substitute values we get this
the square
what?
if you put a square in a triange that splits it into two trianges it would be similar
think about it
if you scale up triange fdb it becomes the bigger triangle
yes
elfin berryBOT
dice
still temple
**dice**
we don't know that fd is 12]
yet
oh
nevermind
sorry
lol
then
we
can convert that to (x-12)(y-12)=144
whole compass
That's because EF and CD are parallel
still temple
so
whole compass
still temple
we know that
$\sqrt{x^{2}+y^{2}}=35$
elfin berryBOT
Wendy's Support guy #0193
still temple
and that
still temple
**Wendy's Support guy \#0193**
$\left(x-12\right)\left(y-12\right)=12\cdot12$
elfin berryBOT
Wendy's Support guy #0193
still temple
we could use subtitution
that prob would not work well
i don't know what to do from here
we're very close
yea
yea\
we are on the right track
if we graph both things we have right now we get the answer
yea
this just for making sure we don't do something incorrectly]
wait
$if the answer is 35\ +\ x+y$
elfin berryBOT
Wendy's Support guy #0193
elfin berryBOT
Wendy's Support guy #0193
still temple
we know it is 35+xy/12
so
we just need x and u
y
the only thing I can think of is guess and checking
which is bad
and not what we want
good idea
serene spoke
Hii
Is this the question ?
okkk
BF/AB = FD/AC
BD = √(BF² - 12²)
CD =12
AC² + BC² = 35²
BF/35 = 12/AC
Solve for BF and AC using the two equations
Bro i thibk its a quadratic so you will get two solutions only
serene spoke
Bro i thibk its a quadratic so you will get two solutions only
And just roots will interchange
Ah sry
BC = BD + 12
Now try to solve
Yeah
serene spoke
AC² + BC² = 35²
This equation
serene spoke
BF/35 = 12/AC
And this one
serene spoke
BD = √(BF² - 12²)
And this
Express BD in terms of BF
Then you will have two equations two variables
@still temple Are you solving ?
Why ?
Did i make a mistake ?
fallen sky
serene spoke
Ok see
Again
BF/35 = 12/AC
BC = BD + 12
and BD² + 12² = BF²
BC can be completely expressed in BF terms ^^^
Solve for BF and AC
Understood ?
What im trying to say
hmm
AC² + (√(BF²-12²) +12)² = 35²
,w solve x/35 = 12/y and y²+(√(x²-12²) + 12)² = 35²
Solution ^
BF == x and AC == y
We have two possible solutions as Thm mentioned
Take the positive values
I think you can do the rest
You can by expanding i understand it will be hard but still solvable
actually calculative approach
can you do the rest?
But ?
Yeah expand the sqaure
You will be left with a square root term
Move it to the other side
And square the eqn again
serene spoke
you have copy
velvet cedar
Even if you expand, you end up having to solve a quartic equation
serene spoke
Even if you expand, you end up having to solve a quartic equation
No not actually
velvet cedar
How so
serene spoke
It can be reduced to quadratic
velvet cedar
Ah you're right
serene spoke
I can deduce this observing the ± nature of roots
Now i dont have a pen and paper and the calculative approach must be taken by dice,
y² + x² + 2×12×√(x²-144) = 35 ²
Or y² + x² -35² = -2×12×√(x²-144)
Now square both side again
Replace y with x
Okk ?
(A + B)² = A² + B² +2AB
2AB part
🙂
Now solve
12² + x² -12² = A² + B² (part)= x²
^
serene spoke
In the second equation y² + (A+B)² = 35²
Now use and solve using formula
√(x²-12²) = A and 12 = B
Yes
ypu see the part under root
Take it to the other side of the equation
And keep all the non root parts on another side
Now square both sides
Yeah
Calculations on you bro
should i find a alternate approach ?
Yeah it will be big
serene spoke
should i find a alternate approach ?
?
You can solve it this way and its fine
I will be back after half n hour nd look for an alternate easier approach
Will dm you if can find ok
marsh citrusBOT
@still temple Has your question been resolved?
still temple
marsh citrusBOT
still temple
@ me please
merry pewter
what have you tried?
still temple
i gotta add two cases together
one where 8 is first no and one where its 7 or 9
but im stuck from there
<@&286206848099549185>
whole compass
Hey
@still temple
So 1st digit can have 3numbers
2nd digit can have any of the 4 numbers remaining
And then 3rd digit can have 3 numbers
And then 2
So 3x4x3x2x1
marsh citrusBOT
@still temple Has your question been resolved?
still temple
@whole compass
still temple
So 3x4x3x2x1
you arent accounting for the second case
you are only calculating the no of digits >40000
<@&286206848099549185>
whole compass
you arent accounting for the second case
Oh mb
I didn't see ut
So let's take first case
As
Odd number at first and last digit
So it can be 7 or 9 at 1st digit
still temple
yes
whole compass
So it can be 7 or 9 at 1st digit
And last can be one of the remaining and there is 1 too
So 2x2x( )
still temple
last one can either be 9 or 1
whole compass
So fill the remaining numbers
2nd place can have 3 numbers, 3rd place 2 numbers, 4th place 1 number
So it's 2x2x3x2x1
Same for next case but 1st digit is 8 only
Proceed then
still temple
isnt it 2x3x2x1x2
and 1x3x2x1x3
for odd and even cases first digit cases
respectively
marsh citrusBOT
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Available help channel!
sharp mauve
i dont get how they arived at (-2)^4?
marsh citrusBOT
i dont get how they arived at (-2)^4?
@sharp mauve Has your question been resolved?
marsh citrusBOT
Available help channel!
valid cape
February 2020 has 5 Saturdays. What is the closest year for February to have 5 Sundays?
marsh citrusBOT
February 2020 has 5 Saturdays. What is the closest year for February to have 5 S...
valid cape
id like to check my answer, which is 2032
the answer was arrived through a ton of thinking and i concluded that the year:
- must be a leap year
- must has Jan 1st as Thursday
but is this correct?
marsh citrusBOT
@valid cape Has your question been resolved?
royal creek
if Feb has 5 Saturdays, then the first of Feb first also be a Saturday, we know that this is true for 2020, and since we know that each successive year has the same date shifted forward by one day of the week (bar leap years which are two days) we can carry that forward until we get a multiple of 7 and the year is a multiple of 4, so we add on 28 years so the answer is 2048
valid cape
2048 isnt an option lol
royal creek
what are the options
valid cape
2024, 2028, 2032, 2036
oh cool i checked the calendar myself and 2032 is indeed correct
royal creek
oh waut i misread the question it was sunday not saturday
sudden skiff
marsh citrusBOT
sudden skiff
simple question, how do you get from the first to the second
winter smelt
write x = (x-4)+4, then split the fraction
sudden skiff
what do you mean sorry
winter smelt
$\frac{x}{x-4} = \frac{(x-4)+4}{x-4} = \frac{x-4}{x-4} + \frac{4}{x-4}$
elfin berryBOT
lgkoo
marsh citrusBOT
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pure quail
how do i do the part that looks like the graph of 1/x?
marsh citrusBOT
how do i do the part that looks like the graph of 1/x?
@pure quail Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
azure flare
can anyone assist me here please?
marsh citrusBOT
can anyone assist me here please?
azure flare
An hour before midnight, a body is found in a room where the temperature is constant. At that moment, the body has a temperature of 32.3°C. At midnight, the body temperature is 26.7°C, and by 1 a.m., it has dropped to 23.9°C. Assuming that the body temperature at the time of death was 37°C, what was the time of death?
We have to use Newton's law of cooling here but I don't know how to do it for this question
marsh citrusBOT
@azure flare Has your question been resolved?
azure flare
<@&286206848099549185>
@lilac delta
can u remove that
and when ur done removing that can u help me
:I
<@&286206848099549185>
An hour before midnight, a body is found in a room where the temperature is constant. At that moment, the body has a temperature of 32.3°C. At midnight, the body temperature is 26.7°C, and by 1 a.m., it has dropped to 23.9°C. Assuming that the body temperature at the time of death was 37°C, what was the time of death?
We have to use Newton's law of cooling here but I don't know how to do it for this question
fossil tide
just substitue the values
azure flare
yea but we dont have Ts
lilac delta
<@964645905330475079>
Ping mods in the future
azure flare
Ping mods in the future
oh right
fossil tide
wait lemme do it
lilac delta
We have to use Newton's law of cooling here but I don't know how to do it for th...
What is your definition for Newton's law of cooling
azure flare
What is your definition for Newton's law of cooling
So what I found is that To = 32.3 and that we have 2 equations and 2 unknowns but i havent been able to successfully reconcile them without creating an extremely complex equation
lilac delta
That's okay, what are the points we care about? As in, what are the temps at what times
That we know
azure flare
temp at t = 0 is 32.3, t = 1 is 26.7, t = 2 is 23.9
fossil tide
for surrounding temperature - room temperatur has to be taken?
azure flare
for surrounding temperature - room temperatur has to be taken?
no i believe we have to calculate surrounding temperature
fossil tide
right
azure flare
@fossil tide are you still trying 🥺
fossil tide
yesyes
fossil tide
it is
we keep trying though
im not sure about the surrounding temp 🥲
you're supposed to use dT/dt =K(t-t0)
azure flare
you're supposed to use dT/dt =K(t-t0)
yea so
ii tried to do some miracle shit with that formula
dT/dt = -K(T(t)-Ts)
for surrounding temperature i got 2.6°C after rigorous work and for K i found 0.166
fossil tide
oh
azure flare
but i dont know if they're correct values because when I try to calculate time
i get 0.88
fossil tide
do you know ans
azure flare
do you know ans
its 22:30
i think once we find time (which will be in hours, probably) we have to substract it with the begin value which is 23
but idk
azure flare
for surrounding temperature i got 2.6°C after rigorous work and for K i found 0....
and in any case i don't think we used the formula dT/dt to do this
fossil tide
is it like approx 22:30 or exact
azure flare
is it like approx 22:30 or exact
approx
fossil tide
yeah im getting the apporx value
azure flare
yeah im getting the apporx value
pls 🙏 how
fossil tide
so
robust verge
wait
i can do this
answer is sigmaboy
gdagtaaada
e
ee
e
e
e
e
e
ee
e
e
e
e
e
sorry
my autoclicker
turned on
😭
e
ee
e
ee
ee
ee
e
e
e
e
e
e
e
e
e
e
again
sorry
fossil tide
dT/dt=K(T-t0)
where T is the avg temp and t0 is surrounding temp
T=T1+T2/2
Now Body(Temp) at 11pm is 32.3
Body(Temp) at 12 is 26.7
Body(Temp) at 1 AM is 23.9
Dt/dt=32.3-26.7)/1=28/5
T=(32.3+26.7)/2=59/2
substituting,
28/5=K(59/2-t0)----eq1
for eq 2
We do the same thing but for the temperature differnce between 12 Pm and 1 am
we get 14/5=K(253/10-t0)
divide both of these equations you get t0 = 21.1 approx
now find K
you get K = 2/3
now to find the time at which the body died ,
we can do the following substitution
(37-32.3)/t=2/3(693/20-21.1)
we get t approx 30 minutes
since the body can't heat up after 11 PM
we must subtract and get 10:30 pm
@azure flare
azure flare
i think ima kill myself
azure flare
dT/dt=K(T-t0)
where T is the avg temp and t0 is surrounding temp
T=T1+T2/2
Now ...
are you allowed to take average temperature?
azure flare
shouldn't it be T = T1 + T2 + T3/3?
fossil tide
you first consider two temperatures
azure flare
why
fossil tide
idk why lol
azure flare
💀
azure flare
dT/dt=K(T-t0)
where T is the avg temp and t0 is surrounding temp
T=T1+T2/2
Now ...
Dt/dt=32.3-26.7)/1=28/5
T=(32.3+26.7)/2=59/2
what did u do here
azure flare
how did you get surrounding temperature though
how can you find out dT/dt without K or surrounding temp
fossil tide
dt/dt is just the temperatre diff with respect to time
dt=1
dT= diff of temp
you don't need K to find that
I got 2 equations , then divided them so I got rid of K
now im omnly left with surrounding temperature t0
plugging in the value of that i got k
marsh citrusBOT
marsh citrusBOT
Available help channel!
azure flare
HOLY SHIT
azure flare
@fossil tide I GOT IT BRO
I FUCKING GOT IT
OH MY GOD
YES
RAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAH
;CLOSE
.close
marsh citrusBOT
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signal nebula
marsh citrusBOT
signal nebula
need to prove C is on (15,0)
any hints as to what I can do to calculate C based on the graph and its measurements
fossil coral
I hate dutch
signal nebula
ik quite some geometry methods
signal nebula
I hate dutch
as do I dont worry
tight furnace
Ignore E, F, and D
signal nebula
Ignore E, F, and D
im afraid im still not seeing it, another small tip please!
tight furnace
Use similar triangles
signal nebula
good one, I see ABH ~ ACG, ill try to test with the similarity ratio's, thanks ill give it a shot
tight furnace
Np
tight furnace
Have you solved a system of equations before
signal nebula
euhm, probably but clearly not good at it or dont remember it
frankly i am not familiar with the term
let me google it
signal nebula
I just vaguely remember to prep it this way
signal nebula
yes
tight furnace
p = (2/3 * p) + 5
tight furnace
Yeah
signal nebula
p = (2/3 * p) + 5
3p = 2p + 15
p = 15
like this?
tight furnace
Yeah
tight furnace
Yeah but isn't p what you wanted to solve for
signal nebula
ah yeah ure right, exactly since that'd be the distance from A to C
nice nice, you just opened my eyes, thanks for this little step through process that was super helpful
I'll go watch some videos and do exercises on it, thanks!
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marsh citrusBOT
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lyric kelp
marsh citrusBOT
lyric kelp
Im not too sure where to start here
tight furnace
First, plug in b_n+1 and b_n
lyric kelp
First, plug in b_n+1 and b_n
and how do i get that? im lost at what this question asks me to find
marsh citrusBOT
tight furnace
np
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Available help channel!
lyric kelp
marsh citrusBOT
bleak thistle
it should be
elfin berryBOT
misha
lyric kelp
it should be
yeah its weird
elfin berryBOT
misha
marsh citrusBOT
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Available help channel!
gilded ember
marsh citrusBOT
obsidian trail
2-t=0 so t=2
tight nymph
Yeah e^(something real) can’t be 0
fossil tide
<@872491891407597598> I GOT IT BRO
xd : )
elfin berryBOT
faiyrose
gilded ember
marsh citrusBOT
marsh citrusBOT
@gilded ember Has your question been resolved?
marsh citrusBOT
floral fern
Does anyone has solution to this
marsh citrusBOT
Available help channel!
night bane
simplify tan(360⁰-θ) and sin(270⁰-θ)
marsh citrusBOT
simplify tan(360⁰-θ) and sin(270⁰-θ)
hard gull
there area formula for those
night bane
which formula?
hard gull
sin(A-B) and Tan(A-B) or u could use unit circle
night bane
do I put that in the calculator
hard gull
sin(a-b) = sinacosb - cosa sinb
wanton ferry
simplify tan(360⁰-θ) and sin(270⁰-θ)
$=tan(-(2\pi -\theta) = tan(\theta) $
night bane
I have but a really long time ago
hard gull
night bane
damn
can I ask another question instead?
A committee of four is chosen randomly from 6 men and 5 women, Find the probabilities that, the committee does not include and women
I remember it's something like combination
raven musk
**A committee of four is chosen randomly from 6 men and 5 women, Find the probab...
whats the probability, that the first person chosen isnt a woman?
glass anvil
**A committee of four is chosen randomly from 6 men and 5 women, Find the probab...
if
combination
ur finding total number of ways
if
probabilities
its <1
1/22
marsh citrusBOT
@night bane Has your question been resolved?
woven vigil
Fill in the blank by choosing a monomial so that the trinomial can be represented as the square of the binomial. Write the monomial in standard form in the answer field.
marsh citrusBOT
Fill in the blank by choosing a monomial so that the trinomial can be represente...
cloud field
(x+y)² = x² + 2xy +y²
compare this with your question and see what the middle term should be
woven vigil
compare this with your question and see what the middle term should be
2xy?
cloud field
yes
woven vigil
its not right
cloud field
well you need to know what x and y are
woven vigil
i don't understand
cloud field
ok dont worry
we first know that the first term and last term are both squares of something
so x² is 64a²
what should x be
marsh citrusBOT
@woven vigil Has your question been resolved?
marsh citrusBOT
@woven vigil Has your question been resolved?
woven vigil
he's not there
I do not know what to do
64a²
1/4b²
2ab?
8²
?
i don't know
elfin berryBOT
faiyrose
woven vigil
4²?
elfin berryBOT
faiyrose
woven vigil
a?
elfin berryBOT
faiyrose
woven vigil
0,125
woven vigil
Fill in the blank by choosing a monomial so that the trinomial can be represente...
help
.close
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ripe cypress
marsh citrusBOT
ripe cypress
This is what I’ve done so far, but I don’t know how to manipulate it further to change the signs
tulip marsh
for C i do not understand why we must put c(12) first and then add that to the integral
marsh citrusBOT
for C i do not understand why we must put c(12) first and then add that to the i...
cobalt sentinel
That’s the starting temperature
The integral gives us our change in temperature
Add those to get the ending temperature
tulip marsh
The integral gives us our change in temperature
yeah but thats why we are taking the integral to find the equation to then be able to plug in the limits.
y must we add our starting tempeture, we are solving for temp at t = 20
cobalt sentinel
The integral lets us find the change in temperature from t=12 to t=20
It doesn’t tell us where we started
tulip marsh
like what key words tells us to add starting tempeture in this problem
cobalt sentinel
No key words, just thinking about the problem rationally
wind whale
like what key words tells us to add starting tempeture in this problem
it's not about that, think of it as also putting the bounds for LHS
C(20)-C(12) = RHS
because you're integrating definitely but you can't only do it for one of the sides
wind whale
it's not C' anymore, you've integrated C' to get C for LHS
dC/dt = f(t) (rhs)
dC = f(t) dt
[C] (necessary bounds) = rhs
vast radish
A little confused on and this one i found where they intersect but not sure which points to use and how to correctly set it up
marsh citrusBOT
A little confused on and this one i found where they intersect but not sure whic...
@vast radish Has your question been resolved?
vast radish
nope thats it
The graph is correct i think but Im insure how cuz theres like 3 intersections
dawn niche
you need to use the polar graph
open kayak
Ah
silk sable
This may be a little helpful as well.
https://www.geogebra.org/classic/rrfg4un3
vast radish
theres a lot going on 
from the link
silk sable
Well, mine shows that the points of intersection occur at the same angles which is helpful.
vast radish
ok so how would I fit that into the problem?
silk sable
You will need to break it apart into separate integrals.
vast radish
oh ok so would it be like 1/2 the integral from 0 to pi/4 of 4^2 ?
for the first like part
silk sable
Yeah.
vast radish
@silk sable what would the 2nd and 3rd integrals be? would they be the same as the first just different intersections?
silk sable
They are symmetric to R1 and R2, respectively.
So you an just multiply R1 *2 and R2 *2.
vast radish
okok so 1/2 integral from 0 to pi/4 of (4)^2 * (4+2sin(4theta))^2 ?
silk sable
eh?
You don't need to integrate the sector of the circle. You can find that just by dividing the area by 8.
pi(4)^2/8 equals the area from theta=0 to theta=pi/4.
vast radish
okay why divide by 8? wouldnt it be 4 cuz its pi/4
silk sable
The sector from 0 to pi/4 is 1/8th of the area of a circle.
silk sable
Yes.
vast radish
alr then what about that last area on the end
silk sable
It's the same as the second region, just rotated.
vast radish
yea but its cut off right so wouldnt it be less
vast radish
sorry but im still kinda confused
silk sable
The two points of the curves intersect at theta=pi at (-4,0).
So the region is from 3pi/4 to pi which has the same area as the region from pi/4 to pi/2 becaus they are symmetric.
One moment, Desmos is better at portraying polar regions than Geogebra.
Those two green regions are equal areas.
silk sable
Don't know how to change the color of a region in Desmos, but the red and grey regions are also the same areas.
vast radish
so the regions from 0 to pi/4 and from pi/2 to 3pi/4 are the same
same thing with pi/4 to pi/2 and 3pi/4 to pi
and each region is 2pi
so then its just 8pi
silk sable
The regions bounded by the circle are 2pi + 2pi = 4pi.
The regions bounded by 4+2sin(4theta) are different.
silk sable
Looks good.
vast radish
😭 alr thanks so much i know it took a long time for me to get it but I appreciate the help
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marsh citrusBOT
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glass locust
This is a small doubt
marsh citrusBOT
This is a small doubt
merry seal
glass locust
I just fused
If integration if 2 is 2x
Then why is integration of R not Rx
We take R outside the integration
Nevermind got it what the fuck
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manic raptor
,w \int \frac{1}{2x\sqrt{9x^2 - 1}}
marsh citrusBOT
,w \int \frac{1}{2x\sqrt{9x^2 - 1}}
manic raptor
why i did wrong
elfin berryBOT
manic raptor
\begin{flalign*}
\int \frac{dx}{2x \sqrt{9x^2 - 1}} && \\
\intertext{let \(\sec{\theta} = 3x\), then \(x = \frac{\sec{\theta}}{3}\), and \(dx = \frac{1}{3} \sec{\theta} \tan{\theta} \, d\theta\)} \\
&= \int \frac{\frac{1}{3} \sec{\theta} \tan{\theta} \, d\theta}{2 \cdot \frac{\sec{\theta}}{3} \sqrt{9 \left(\frac{\sec{\theta}}{3}\right)^2 - 1}} \\
&= \int \frac{\frac{1}{3} \sec{\theta} \tan{\theta}}{\frac{2}{3} \sec{\theta} \sqrt{9 \left(\frac{\sec^2{\theta}}{9}\right) - 1}} \, d\theta \\
&= \int \frac{\frac{1}{3} \sec{\theta} \tan{\theta}}{\frac{2}{3} \sec{\theta} \sqrt{\sec^2{\theta} - 1}} \, d\theta \\
&= \int \frac{\frac{1}{3} \sec{\theta} \tan{\theta}}{\frac{2}{3} \sec{\theta} \tan{\theta}} \, d\theta \\
&= \int \frac{1}{3} \cdot \frac{1}{\frac{2}{3}} \, d\theta \\
&= \int \frac{1}{2} \, d\theta \\
&= \frac{\theta}{2} + C \\
\intertext{Since \(\sec{\theta} = 3x\), then \(\theta = \sec^{-1}(3x)\)} \\
&= \frac{\sec^{-1}(3x)}{2} + C
\end{flalign*}```Juan
frail pecan
.close
frail pecan
What was so funny in it
manic raptor
why are you closing my thread
frail pecan
Your what
manic raptor
get out of here
frail pecan
How old are u
icy lantern
Bro what is happening here
manic raptor
Bro what is happening here
my wolfram answer is different of my answer
icy lantern
```latex
\begin{flalign*}
\int \frac{dx}{2x \sqrt{9x^2 - 1}} && \\
\inte...
What’s your question?
manic raptor
haha
manic raptor
What’s your question?
up
my answer is different from wolfram answer
wondering what i did wrong
icy lantern
Ok I will check in a bit unless someone else can help you till then
manic raptor
aight ❤️
<@&286206848099549185> sorry i dont know if i can ping you guys, i need a quick help with this integral, just dont give me the same answer as wolfram do, btw if ping helpers is not for this, let me know
manic raptor
Are u sure they’re different answers?
mmm
still temple
perhaps if we look a little closer
manic raptor
yeah i did it in my whiteboard
still temple
😱
manic raptor
hypo = 3x
opossitive = \sqrt{9x^2 - 1}
andyancent = 1
tan = oposs...
OH
HAHAHHAAH
❤️
cobalt sentinel
manic raptor
thanks i just always evaluate my answer with wolfram
and if i dont get the same answer
still temple
LMAOO
manic raptor
i get frustrate
marsh citrusBOT
marsh citrusBOT
Available help channel!
azure flare
Could someone help me with this differential please?
marsh citrusBOT
Could someone help me with this differential please?
azure flare
I almost have the exact same answer but there are a few differences
for example for the negative integral of 1/x i have -ln(x), and when u raise it to e then it should just be -x right?
but apparently the answer is -1/x
cobalt sentinel
$\frac {dx}x = \frac {y \cdot dy}{1-y-\frac 1{y+1}}$
elfin berryBOT
azure flare
$\frac {dx}x = \frac {y \cdot dy}{1-y-\frac 1{y+1}}$
were u thinking of using partial fractions for this?
partial fraction decomposition
cobalt sentinel
lemme see if i can do it first, i just rearranged in terms of x and y
azure flare
ok
velvet cedar
for example for the negative integral of 1/x i have -ln(x), and when u raise it ...
e^(-lnx) is 1/x
(e^(lnx))^-1 = x^-1 = 1/x
or
(e^(-lnx)) = e^(ln (1/x)) = 1/x
azure flare
e^(-lnx) is 1/x
(e^(lnx))^-1 = x^-1 = 1/x
or
(e^(-lnx)) = e^(ln (1/x)) = 1/x
wtf how is e^(-ln(x)) = 1/x?
oh
elfin berryBOT
cobalt sentinel
i didnt do partial fractions
cobalt sentinel
i simplified this, did long division, then u-sub
azure flare
this is the answer lol
azure flare
i didnt do partial fractions
oh interestng
cobalt sentinel
yea hold on i gotta simplify more
cobalt sentinel
bruh i accidentally put a 'y' in the numerator here
cobalt sentinel
ok now i got a slightly closer answer, but its not the exact same
$e^{\ln x + C} = e^{\ln y} * e^{-\frac 1y}$
elfin berryBOT
cobalt sentinel
$Cx = u \cdot e^{-\frac 1u}$
elfin berryBOT
cobalt sentinel
this is the answer im getting
azure flare
$Cx = u \cdot e^{-\frac 1u}$
its irritating cuz if i had this excersise as an exam question
then i wouldn't really understand if what i have is correct because there's 2 U's there
and a general solution has just 1 u (or y)
oh well
thanks for your help
oh wait
cobalt sentinel
yea well if u want to get this in terms of 1 u, you need to product log (lambert W)
azure flare
yea well if u want to get this in terms of 1 u, you need to product log (lambert...
i think that may be too long
also
cobalt sentinel
this is the answer lol
but are u sure this is the right answer
im not seeing how to get C/x
azure flare
how do you know what sort of differentials these are? how do you know which ones are linear, exact etc
azure flare
but are u sure this is the right answer
yes, i believe you carried the negative sign to the u side
but if it was kept at the X side then it wouldve resulted in C/x
cobalt sentinel
i have no clue sorry, the most ive done with differential equations is just the separable ones from calculus 2
azure flare
i have no clue sorry, the most ive done with differential equations is just the ...
oh ok
thanks for your help
cobalt sentinel
np
azure flare
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
crystal apex
Using the diagram on the right, determine the displacement x(α) of the piston, taking the origin of the axis
axis (Ox) at the point where the volume is minimal and α = π. Hint: use the algebraic height y, the length z and the angle π.
length z and angle γ to help you when starting from x + z = b + R, but at the end these quantities should no longer
the formula.
Deduce the volume V = S × x variable between volume Vmin and volume Vmax as a function of α.
marsh citrusBOT
Using the diagram on the right, determine the displacement x(α) of the piston, t...
still temple
<@&286206848099549185>
can you not read?
crystal apex
can you not read?
read what ? I did'nt understand sorry
still temple
"After 15 minutes, feel free to ping <@&286206848099549185>."
crystal apex
"After 15 minutes, feel free to ping <@&286206848099549185>."
Sorry I didn't think
still temple
it's okay if they made the mistake once
mhm
but
the thing is
this is the third time
crystal apex
third time?
still temple
you have pinged helpers w/o waiting
crystal apex
you have pinged helpers w/o waiting
It's possible I didn't pay attention to what it write, I've seen people use it and no one pointed it out to me before you did.
no problem I know now
crystal apex
you have pinged helpers w/o waiting
I can now ?
marsh citrusBOT
@crystal apex Has your question been resolved?
crystal apex
<@&286206848099549185>
marsh citrusBOT
@crystal apex Has your question been resolved?
crystal apex
Using the diagram on the right, determine the displacement x(α) of the piston, taking the origin of the axis
axis (Ox) at the point where the volume is minimal and α = π. Hint: use the algebraic height y, the length z and the angle π.
length z and angle γ to help you when starting from x + z = b + R, but at the end these quantities should no longer
the formula.
Deduce the volume V = S × x variable between volume Vmin and volume Vmax as a function of α.
marsh citrusBOT
@crystal apex Has your question been resolved?
crystal apex
Nobody ?
marsh citrusBOT
@crystal apex Has your question been resolved?
devout oak
marsh citrusBOT
devout oak
It’s in French but basically I have to find the volume under the function z and above the rectangle R
If anyone can confirm my integral would be nice since there is no correction
.close
cosmic summit
Hii how do I do 2 a i
marsh citrusBOT
Hii how do I do 2 a i
cosmic summit
(How do I dialate y = x^2 y axis by 1/2)
tough star
just do x/2
marsh citrusBOT
@cosmic summit Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
marsh citrusBOT
elfin berryBOT
Tommy
whole compass
<@&286206848099549185>
elfin berryBOT
Tommy
digital hound
Does the Riemann rearrangement theorem have anything to do with uncountable infinite sets?
Consider the conditionally convergent series:
[
\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n} = 1 - \frac{1}{2} + \frac{1}{3} - \frac{1}{4} + \frac{1}{5} - \frac{1}{6} + \cdots
]
The terms (1, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{1}{5}, \frac{1}{6}, \ldots) are clearly infinite, and we can rearrange this series in any way we want to obtain any real number.
Does this mean the number of permutations of the terms of the series
[
\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n}
]
is uncountably infinite?
My assumption is that by rearranging the terms of the sum, we can get any real number. The number of permutations of a set with (n) terms is given by (n!). Let (P(S)) be the set of all permutations of a conditionally convergent sum (S). Then there exists a function (f) such that (f: S \to P(S)), but (P(S) \subseteq \mathbb{R}), so (S \subseteq \mathbb{R}).
elfin berryBOT
Tommy
marsh citrusBOT
marsh citrusBOT
Available help channel!
cunning trench
i have a question on 95, i think i got all the transformations but im really stuck on how to graph it?
marsh citrusBOT
i have a question on 95, i think i got all the transformations but im really stu...
@cunning trench Has your question been resolved?
cunning trench
<@&286206848099549185>
marsh citrusBOT
@cunning trench Has your question been resolved?
cunning trench
i almost figureed out how to graph sin but i js have one thing that i am having trouble with
its the shifting part, like ik for the problem im doing im supposed to go up 3 but how do i go right 2pi/3
marsh citrusBOT
@cunning trench Has your question been resolved?
marsh citrusBOT
@cunning trench Has your question been resolved?
earnest jay
i have a question on 95, i think i got all the transformations but im really stu...
You have to find your critical points and the start and end points
So for the crit. points you divide the period by 4, and critical points you set the inner sin function (2(theta)-2pi/3) equal to 0 which is your start point, and the end point is setting the same equation equal to the period, which is pi
The starting point should be pi/3, and the end point is 5pi/6
The critical points is how far you move each time
marsh citrusBOT
@cunning trench Has your question been resolved?
neon wharf
Help with this problem pls!
These are normal distributions btw
marsh citrusBOT
Help with this problem pls!
These are normal distributions btw
normal sky
!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
- I have begun but got stuck midway
I'm not sure what transformations to apply to L
normal sky
does it say find $P(M * 1.16 < 10^2)$
elfin berryBOT
chebyshev's infinite pee norm
elfin berryBOT
MegA_waTT
neon wharf
Apologies, that is a poor 2
neon wharf
does it say find $P(M * 1.16 < 10^2)$
I am writing a paper on Central Limit Theorem, and created two sampling distributions.
One of them follows a normal distribution (represented by random variable M).
The other follows a lognormal distribution because the data was skewed prior (say it is represented by random variable X)
I then did log(X) to produce a normal distribution, represented by random variable L
I would like to compare the two random variables, M and L
Which is why there is a 10^L
marsh citrusBOT
@neon wharf Has your question been resolved?
neon wharf
<@&286206848099549185>
marsh citrusBOT
@neon wharf Has your question been resolved?
marsh citrusBOT
@neon wharf Has your question been resolved?
marsh citrusBOT
@neon wharf Has your question been resolved?
manic raptor
can someone help me with this integral
marsh citrusBOT
can someone help me with this integral
@manic raptor Has your question been resolved?
safe badger
can someone help me with this integral
looks like a weird partial fraction
tall sun
marsh citrusBOT
tall sun
is this right
twilit grove
no
tall sun
wait why
fervent rampart
did you try both counterexamples?
twilit grove
(a + b)^2 = (a + b) * (a + b)
boreal rose
no, i thought what it was was common sense...
No no
Please expand cwatson’s expression
twilit grove
sure
crystal lintel
statement looks good to me
twilit grove
but it's good to just know what (a + b)^2 equals
tall sun
so 0+1 ) ^2
boreal rose
statement looks good to me
Lmao why you trolling 😭
crystal lintel
boreal rose
Good good
tall sun
i really fooled myself with that common sense thing
boreal rose
But please you should know that (a+b)^2 = a^2 + 2ab + b^2
tall sun
yeah that SHOULD be common sense
boreal rose
If you plug in non zero a and b
twilit grove
it is asking which one is the counterexample
twilit grove
right
crystal lintel
You’re good haha Dw
i was just being silly
twilit grove
so the third choice is the counterexample
tall sun
counterexample, is just the wrong version of something??
how would you get this without multiple choice
boreal rose
counterexample, is just the wrong version of something??
It’s like catching a bug
twilit grove
how would you get this without multiple choice
by expanding (a + b)^2
tall sun
sorry for my repeated foolishness 
boreal rose
sorry for my repeated foolishness <:flonshed:629835071465062410>
No problem!
tall sun
i would say im having a bad day but that is most days when it comes to brain stuff
boreal rose
Have a great night all of you
still temple
marsh citrusBOT
still temple
so I've determined that the unknown coordinate dotted with direction vector 1
must be the same unknown coordinate when dotted with direction vector 2
so would it be safe to assume that the dot product between direction vector 1 and the unknown coordinate
would be equals to the unknown coordinate in the second dot product?
just doing this to save steps but not sure if it's right, the only other way I can think of is guess and check but I assume that would take a lot of time
the other peice of information backing up this claim I'm making is that if the first direction vector dot product is equals to 0, that would automatically mean the second direction vector dot product would be 0 since 0 dotted with anything is 0
also just to clarify the unknown coordinate would be the direction vector
of P1P2
jovial lance
marsh citrusBOT
serene spoke
Bro
P = V I
Now since total resistance in both wires is same
i is same for both
But voltage in X And Y will be half of that in Z
So.answer is 1/2
whole compass
@jovial lance
serene spoke
Remember the statement voltage same in parallel and current same in series
jovial lance
total resistance is same, but wont voltage be half in resistor x
cuz its (v/2)^2 / r for x
lucid zenith
So.answer is 1/2
!nosols
marsh citrusBOT
So.answer is 1/2
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
serene spoke
total resistance is same, but wont voltage be half in resistor x
Yes
Thats what ive written
jovial lance
yh so it will be 4P
for resistor y, it will be 2p
what im trying to say is if you use the power resistance voltage formula, the answer is reversed for some reason, although i agree youre right
serene spoke
See potential dropp across x and y = potential drop across z
jovial lance
but we're just meausuring the power of x so wouldnt we only calculate the potential drop between x
serene spoke
So its clearly 1/2 no ?