okay now whats the scaling factor from length to length
#help-10
minor belfry
i mean it should be three
three is correct
dense tinsel
oh wait
minor belfry
for the length to length
dense tinsel
yes
minor belfry
it should be 10 * 3^3
dense tinsel
what was your plan
minor belfry
length to length is 3x
dense tinsel
yes sir
minor belfry
3:9
10:x
because ur comparing length to length for 3:9
but since the 10 is a volume
u need to do the cubed ratio
mighty thunder
Oh, you're saying it's 270 cubed cm?
minor belfry
exactly
dense tinsel
wait a second
mighty thunder
Interesting
minor belfry
10 * (3^2)
mighty thunder
Actually, take the cube root this time of your answer
dense tinsel
can't we do proportions
minor belfry
proportions are if u are comparing the same unit type
minor belfry
but because u are doing length vs volume
u need to do the equivalent scaling
length is 1d
volume is 3d
hence why u cube or cuberoot
dense tinsel
would it be 64/27
dense tinsel
yeah to get ratio
minor belfry
so what do u do to 64/27
dense tinsel
^2?
minor belfry
u do cube root
mighty thunder
4/3 would he the cubes
dense tinsel
13.32
minor belfry
thats ur scaling factor for length
minor belfry
cube root
minor belfry
volume
minor belfry
yes
dense tinsel
but why are we cubing? aren't we going up, not down?
dense tinsel
sorry, why are we cube rooting
warm shaleBOT
dense tinsel
and not cubing
minor belfry
and not cubing
because u are comparing volumes
dense tinsel
bro what im tripping so hard
mighty thunder
Remember in this problem we cubed to find the volume
In this one, we are given the volume, so by algebraic processes, we would take the cube root
dense tinsel
do you guys realize im only in 10th grade
mighty thunder
I'm in 11th
dense tinsel
this world is brand new to me and im slowly losing my sanity
minor belfry
its alright
dense tinsel
alright wait so
minor belfry
ur both doing great
dense tinsel
what do we do with 4/3
mighty thunder
In 10th grade, I was teaching myself calc
minor belfry
times by ur length
minor belfry
In 10th grade, I was teaching myself calc
damn ahaha
minor belfry
4/3 * 6
dense tinsel
right ok
mighty thunder
When you take the cube roots of the volumes,
You get 3/6 and 4/x
minor belfry
^^
dense tinsel
writing this shit down holup
mighty thunder
"Volumes" and lengths respectively
dense tinsel
x = 8?
dense tinsel
ok wait
minor belfry
i recommend u draw up squares and cubes
and compare the values
minor belfry
itll help u understand what ur doing
mighty thunder
Think about it as
27x^3 and 64x^3
dense tinsel
alright
im done
i dont want to see this school subject until monday afternoon
which is when my math class is
mighty thunder
Lol
mighty thunder
Your welcome
dense tinsel
@minor belfry
minor belfry
its all good bro
shell hill
Solve sin (theta+60)= -0.75 for 0⁰<= theta <= 360⁰
obtuse pebbleBOT
Solve sin (theta+60)= -0.75 for 0⁰<= theta <= 360⁰
shell hill
I got the answer but it's wrong apparently 🥲
theta+60= arcsin -0.75
theta+60= -48.59
theta= -108.59
theta= -108.59+180 ?
warm shaleBOT
Requested by shikhargupta1207
median dome
ok nvm
shell hill
why + 180?
The angle in 3rd quadrant?
shell hill
why?
median dome
also there will be 2 solutions
shell hill
I got the other solution its 360- 108
shell hill
so wouldn't you add 360?
I just calculated that and it gives the same answer as 360-108.59
Whats the other solution
median dome
draw the unit circle, should make things easier
rancid hedge
Do i start by seeing how i could turn those constants with the t into a fraction where the t is the denominator and its negative so that the fraction becomes zero.
obtuse pebbleBOT
Do i start by seeing how i could turn those constants with the t into a fraction...
rancid hedge
.close
manic sparrow
need some help with electromagnetism
obtuse pebbleBOT
need some help with electromagnetism
manic sparrow
here is the formula for magnetic flux ΦB=BAcos(Θ)
B is magnetic field, A is area
and cos theta is the angle....parallel to magnatic field and the coil or someting idk
if i increase B, A or change the angle, it will result in induction
idk if induction will increase or decrease if i do lets say cos 70
vs cos 0
brazen gorge
cos(0) is 1
manic sparrow
uh huh
brazen gorge
and that's the maximum value that cos(x) can have
so cos(70) must be less that that
manic sparrow
so if its cos 70, it will be less than 1?
brazen gorge
yep
manic sparrow
but what does less angle mean in this context
brazen gorge
at cos(90) it will be 0
manic sparrow
is the confusing part, will emf induction be higher or lower
brazen gorge
but what does less angle mean in this context
not less angle, the value of cosine is smaller
what's Faraday's law
relating emf and flux
$\varepsilon = -N \frac{d\Phi}{dt}$
warm shaleBOT
artemetra
brazen gorge
looks familiar?
brazen gorge
yes
manic sparrow
oh i guess we just input the values
brazen gorge
yep
next crescent
where am i going wrong ?
obtuse pebbleBOT
@next crescent Has your question been resolved?
next crescent
<@&286206848099549185>
next crescent
.close
scenic thicket
(sin(x)+cos(x))^2=4sin(x)cos^2x+1
obtuse pebbleBOT
(sin(x)+cos(x))^2=4sin(x)cos^2x+1
sage geode
!status
obtuse pebbleBOT
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 solved first part and put it all on one side and don't know what to do next
sage geode
Could you show your work?
scenic thicket
sin^2x+2sinxcosx+cos^2x-4sinxcos^2x-1=0
sage geode
Right, and what's sin^2(x) + cos^2(x) equal to?
scenic thicket
1
sage geode
So that will cancel out with the -1
Leaving you with 2sin(x)cos(x) - 4sin(x)cos^2(x) = 0 and sin(x)cos(x)(1 - 2cos(x)) = 0
Can you do the rest?
scenic thicket
THANK YOU SO MUCH
obtuse pebbleBOT
@scenic thicket Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
unique tendon
obtuse pebbleBOT
timid silo
$$\begin{pmatrix}
1 & c & 11\
c & 16 & f\
\end{pmatrix}$$
warm shaleBOT
unique tendon
Okay so that's the augmented matrix
timid silo
first question asks us to eliminate the L2
any ideas
take note we can multiply L1 by any scalar
unique tendon
take note we can multiply L1 by any scalar
Hmm this might be a dumb question but why is that
timid silo
Hmm this might be a dumb question but why is that
remember your row operations
where you did R2 -> 3R1 + R2 for example to eliminate an entry in Row 2
timid silo
where you did R2 -> 3R1 + R2 for example to eliminate an entry in Row 2
arbitrary example*
unique tendon
Hmm yeah okay
Ok so I don't understand what exactly they are asking to eliminate
Do they want us to eliminate C?
timid silo
the term involving the x in the second equation
timid silo
Do they want us to eliminate C?
yes
unique tendon
Okay so can we first multiply L1 by C
timid silo
good
timid silo
Okay so can we first multiply L1 by C
write the row operation properly
L2 -> ?
timid silo
what did you do
unique tendon
I multiplied by C
timid silo
ah multiplied by c, yh you do that on the side, we wont be changing L1 we'll be changing L2 with that multiple
timid silo
when you had
1 2 4 5
3 1 1 3
for example how would have gone to eliminate the second row
@unique tendon still with me?
unique tendon
Yess i am
unique tendon
Ok so first
Ah my wifi is so baaad
Ok so we do 3R1-R3
Or -3R1+R2
@timid silo
timid silo
@unique tendon okay how would that work here
obtuse pebbleBOT
@unique tendon Has your question been resolved?
verbal niche
how do i check my work for this?
obtuse pebbleBOT
how do i check my work for this?
@verbal niche Has your question been resolved?
timid silo
this channel is now occupied, create a new one
unique tendon
Ooh
obtuse pebbleBOT
@verbal niche Has your question been resolved?
glossy basalt
you can check by noticing that
2(1,0,-1)+3(2,1,3)=(8,3,7)
obtuse pebbleBOT
@verbal niche Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
grizzled gulch
any idea to solve this xd?
obtuse pebbleBOT
any idea to solve this xd?
grizzled gulch
I need the slope of the line which crosses (x1, y1) and (x2, y2)
also AB is equal to AC
obtuse pebbleBOT
@grizzled gulch Has your question been resolved?
obtuse pebbleBOT
@grizzled gulch Has your question been resolved?
obtuse pebbleBOT
@grizzled gulch Has your question been resolved?
obtuse pebbleBOT
@grizzled gulch Has your question been resolved?
tiny seal
any idea to solve this xd?
since AB = AC, we know
$\sqrt{(x_2 --\frac{10}{7})^2 + (y_2 - 11/7)^2}=\sqrt{(x_1--\frac{10}{7})^2+(y_1-\frac{11}{7})^2}$
warm shaleBOT
Cycadellic
tiny seal
we also know that $y_2=-\frac{3}{4}x_2+\frac{1}{2}$ and $y_1=-\frac{4}{3}x_1-\frac{1}{3}$
warm shaleBOT
Cycadellic
tiny seal
finally, we know that
$\frac{y_2-y_1}{x_2-x_1}=\frac{y_2--2}{x_2-1}$
warm shaleBOT
Cycadellic
tiny seal
from these four eqautions, you can find the four points
then the line is easy to solve from there
grizzled gulch
I will try to solve by that way💀
tiny seal
I will try to solve by that way💀
It looks more complicated than it really is
grizzled gulch
xd
tiny seal
Its probably better if you solve for a variable from that and then plug that into another equation
tiny seal
also AB is equal to AC
This part is what makes it so tedious
grizzled gulch
Yeah 😢
tiny seal
I think if you can use trigonometry, the equations will be much easier to work with
grizzled gulch
which one?
tiny seal
All of them
They can be turned into right triangles, which would then share two side lengths
grizzled gulch
I'm seeing that the inclination angle of the line I want is a part of the other lines
so I maybe It could help me
tiny seal
finally, we know that
$\frac{y_2-y_1}{x_2-x_1}=\frac{y_2--2}{x_2-1}$
If you can find the angle and then convert to slope with arctan, then that should allow you to solve x2 and y2 from this
tiny seal
**Cycadellic**
And this
grizzled gulch
alright 🫡
tiny seal
**Cycadellic**
You can solve all of it without this, if you do it using that angle, actually
Supposing you can actually find it
tiny seal
I need the slope of the line which crosses (x1, y1) and (x2, y2)
Oh wait, i misread
I thought you wanted everything
grizzled gulch
I've just realized the two lines given make an 90° angle xd
grizzled gulch
my bad 😔
obtuse pebbleBOT
grizzled gulch
Thank you so much btw @tiny seal
obtuse pebbleBOT
Available help channel!
nova yew
i need help solving dont know where to start or what to do
obtuse pebbleBOT
i need help solving dont know where to start or what to do
native inlet
say BD is x, right?
native inlet
if BD is x, and you know DA is one of the sides of the square what is BA? 
nova yew
yes
nova yew
ba = x + 4
nova yew
4
native inlet
what is AC?
nova yew
12
native inlet
what is BD?
nova yew
x
native inlet
Now, since $\bigtriangleup BDE\sim\bigtriangleup EFC$ is follows that $\frac{BD}{DE}=\frac{BA}{AC}$
warm shaleBOT
PajamaMamaLlama
native inlet
right?
nova yew
yes
native inlet
this is just ratios, it's just saying we scaled the triangles
nova yew
wow
native inlet
now plug in your known values :)
native inlet
well you did your ratios right, right?
obtuse pebbleBOT
native inlet
i got it right
you're a fast learner, some people need a second explanation on ratios :)
obtuse pebbleBOT
Available help channel!
nova yew
<:catthumbsup:614540188747563008>
ty
nova yew
ima start this one
im a bit confused
so
why wouldn't it be 1/3
can someone help
candid yarrow
why wouldn't it be 1/3
The different pieces have different area
nova yew
native inlet
$(S_{ideratio})^2=A_{rearatio}$
warm shaleBOT
PajamaMamaLlama
pale crown
After visiting the Titanic, Captain Brain and Mr. Pinky are taking the Alvin submarine back to the surface of the water. They start 1800 meters below the surface of the water, and ascend at 58 meters per hour. Note: under the water is a negative number.
Write an equation to model this situation (use m for meters and h for hours)
obtuse pebbleBOT
After visiting the Titanic, Captain Brain and Mr. Pinky are taking the Alvin sub...
jaunty rover
Do you want an expression for their depth at a given time?
pale crown
trying to find an equation, sorry i havent done algebra in over 16 years
pale crown
correct. the wording got me off
jaunty rover
oh
okay
now
they ascend at 58 metres per hour
so in one hour they get 58 metres above
so their depth now is -1800 + 58
did you understand till now?
pale crown
following
jaunty rover
okay
so in 2 hours they ascend 58 * 2 metres
can you tell me in t hours how much will they ascend?
pale crown
i got 31.03
pale crown
correct
jaunty rover
not a value
so we take a general case
at a time t hours
they will have ascended 58 * t metres
right?
pale crown
right
jaunty rover
yes
so their depth at a time t is
-1800 (initial depth) + 58t (the distance they ascended in that much time)
pale crown
so an hour later, they would be at -1742... is suppse i could use that to find the slope 😄
jaunty rover
we already have the equation
obtuse pebbleBOT
jaunty rover
okay
obtuse pebbleBOT
Available help channel!
mental onyx
Is this true?
obtuse pebbleBOT
Is this true?
tiny seal
Use definition of derivative
$\frac{d(f+g)}{dx}=\lim_{dx\rightarrow 0}\frac{f(x+dx)+g(x+dx)-f(x)-g(x)}{dx}$
warm shaleBOT
Cycadellic
tiny seal
You should be able to get this into df/dx + dg/dx from here
mental onyx
For this quest is this how it supposed to be done?
tiny seal
Yeah
mental onyx
Alright thank you!
obtuse pebbleBOT
@mental onyx Has your question been resolved?
bleak eagle
what are the line coordinates for the projective line determined by the xz-plane?
obtuse pebbleBOT
what are the line coordinates for the projective line determined by the xz-plane...
bleak eagle
I know i can do the cross product of two projective points to find the line coordinates for other projective lines, so can i just take two random points on the xz-plane and calculate their cross product?
tiny seal
what are the line coordinates for the projective line determined by the xz-plane...
What do you mean “projective”
tiny seal
Oh, mb i have no clue
bleak eagle
no worries
tiny seal
i can pull out the definition from my book if necessary
You could and i may be able to help
Who knows
obtuse pebbleBOT
tiny seal
nah its good ill try to figure it out, but thanks \
There are others on this server who could certainly help
obtuse pebbleBOT
Available help channel!
static patio
Write a mathematical formula in your report giving the probability that a
k-mer at a fixed position in the original genome does not contain any mutation
in the mutated version for some value of p (the formula will use parameters k
and p).
obtuse pebbleBOT
Write a mathematical formula in your report giving the probability that a
k-mer...
static patio
genome is just a string consisting of letters A,C,G,T and k-mer is a subsequence of length k
$Pr(p,k) = (1-p)^k$
warm shaleBOT
Michal
static patio
is it correct?
candid yarrow
genome is just a string consisting of letters A,C,G,T and k-mer is a subsequence...
can you give an example?
obtuse pebbleBOT
@static patio Has your question been resolved?
static patio
can you give an example?
AACGTTACTG
AACG is kmer of length 4, ACGT is another kmer of length 4
obtuse pebbleBOT
@static patio Has your question been resolved?
obtuse pebbleBOT
@static patio Has your question been resolved?
candid yarrow
AACG is kmer of length 4, ACGT is another kmer of length 4
What would a mutation be?
static patio
What would a mutation be?
Single letter can change to one of the remaining 3
candid yarrow
Write a mathematical formula in your report giving the probability that a
k-mer...
What is the original genome?
Can you send a picture of the original question
drifting wraith
there's missing context, "the mutated version", or what p means
so take a screenshot or photo, that would help
static patio
there's missing context, "the mutated version", or what p means
p is probability for single letter to get mutated
static patio
What is the original genome?
You can consider arbitrary genome
drifting wraith
yeah that's correct then
static patio
In this task we want to evaluate if Jaccard similarity on a full set of k-mers is a
suitable measure of sequence similarity. To this end, we will use randomly mutated
genomes for different values of mutation probablity p. We will consider 1-p as the
true genome similarity (the percentage of bases that were conserved) and see if
the Jaccard similarity is in some way related to this value.
- Write a mathematical formula in your report giving the probability that a
k-mer at a fixed position in the original genome does not contain any mutation
in the mutated version for some value of p (the formula will use parameters k
and p).
This is entrie problem statement
gray tapir
how can i find the limit of this series B(n)
obtuse pebbleBOT
how can i find the limit of this series B(n)
gray tapir
anyone?
warm canopy
write out the first few terms of the series
warm canopy
okay then use the hint to get a closed form for B(n)
gray tapir
thats what i dont understand
warm canopy
what dont you understand
gray tapir
how do i get the closed form like you said using the hint given
warm dome
how do i get the closed form like you said using the hint given
Your closed form is supposed to look like the hint
So that you can apply the hint to get the limit
gray tapir
Your closed form is supposed to look like the hint
i am aware, but idk how to get there is what my problem is
warm canopy
also your expression for B(n) should be $\sum_{i=1}^n \frac{1}{(-2)^{i+1}}$
warm shaleBOT
ΣΑCu
warm canopy
not with an n as the indexing variable but with an i
gray tapir
right, thanks
warm canopy
then you might find it useful to write $(-2)^{i+1} = (-2)\cdot(-2)^{i}$
warm shaleBOT
ΣΑCu
warm dome
i am aware, but idk how to get there is what my problem is
Notice that for each consecutive term, you just add another term to the sequence. That’s why a sum is the best way to write it
warm dome
also your expression for B(n) should be $\sum_{i=1}^n \frac{1}{(-2)^{i+1}}$
I think you should add -1/2 before the sum, no?
warm dome
but its defined for 0 < x < 1
Then write it that way
warm canopy
possibly, i was just copying their expression
warm dome
but its defined for 0 < x < 1
Define the right x such that you have x^i. It’s possible
Though more complex that I originally thought, I will admit
gray tapir
writing the (-2)^(i+1) using the hint is my only difficulty
warm dome
Well the -2 is part of a fraction
And the enumerator is 1
So you could write (-1/2)^i for a start
One -1/2 can be factored out
The problem is that the sign switches for each i
For every odd i you have negative x, for each even I you got positive x
gray tapir
For every odd i you have negative x, for each even I you got positive x
yea correct
warm dome
So choose a sum for the even and a sum for the odd parts i suppose
So write one sum with 2i
And one with 2i-1
Change the n up a bit too. One for even one for odd n
For the odd numbers we have -2 multiplied
And then the same as the even numbers
gray tapir
im sorry but i dont seem to understand it
warm dome
Yeah my messages are all over the place
$$\sum_{i=1}^{2n}(-x)^i=\sum_{i=1}^n(-x)^{2i-1}+\sum_{i=1}^n(-x)^{2i}$$
warm shaleBOT
FirstNameLastName
warm dome
@gray tapir makes sense?
$$\sum_{i=1}^{2n}(-x)^i=-x^{-1}\sum_{i=1}^n(x^2)^{i}+\sum_{i=1}^n(x^2)^{i}$$
warm shaleBOT
FirstNameLastName
warm dome
$$\sum_{i=1}^{2n}(-x)^i=(1-x^{-1})\sum_{i=1}^n(x^2)^{i}$$
warm shaleBOT
FirstNameLastName
warm dome
$$\sum_{i=1}^{2n+1}(-x)^i=???$$
warm shaleBOT
FirstNameLastName
warm dome
@gray tapir try to take it from here
warm dome
1/2
Your expression for B(n) should be $-\frac{1}{2}+\sum_{i=1}^n \left(-\frac{1}{2}\right)^{i+1}$
warm shaleBOT
FirstNameLastName
warm dome
Which is the same as $-\frac{1}{2}\left(1+\sum_{i=1}^n \left(-\frac{1}{2}\right)^{i}\right)$
warm shaleBOT
FirstNameLastName
gray tapir
yea i think im going to drop maths
warm dome
yea i think im going to drop maths
What’s confusing you? The sums?
gray tapir
how are we using the hint here
gray tapir
so the hint still calls for a positive x value right?
gray tapir
but what about the negative sign
gray tapir
**FirstNameLastName**
so what role does finding this play?
gray tapir
x^2 is between 0 and 1
so 0.25 in this case?
warm dome
so what role does finding this play?
So far we’ve found the limit as n is strictly even
We need to show that the limit is the same for the odd numbers for n
Otherwise we don’t know if the sequence diverges
warm dome
so 0.25 in this case?
Yes
gray tapir
so the sum until 2n is found, so the +1 will just be the original thing added?
warm dome
so the sum until 2n is found, so the +1 will just be the original thing added?
The +1 is so we have the sum for any odd number of s
gray tapir
yea i get that
gray tapir
**FirstNameLastName**
but when simplifying this, we add a +1
warm dome
It will increase one of the sums by one more element
warm dome
I think it should be the odd numbers +1
So the sum from i=1 to n+1
Because then we have $x^{2(n+1)-1}=x^{2n+1}$
warm shaleBOT
FirstNameLastName
warm dome
So we’ve added the element we wanted to add
gray tapir
$$(1-x^{-1})\sum_{i=1}^{n+1}(x^2)^i$$
warm shaleBOT
daddyirani
warm dome
No cause we’re only adding one to the odd numbers, not the even numbers
warm dome
**FirstNameLastName**
Consider this one here
warm dome
**FirstNameLastName**
Or better yet this one
gray tapir
do you mind doing a quick voice chat?
warm dome
Can’t do that rn sorry
gray tapir
alright no worries
warm dome
$$\sum_{i=1}^{2n+1}(-x)^i=\sum_{i=1}^{n+1}(-x)^{2i-1}+\sum_{i=1}^n(-x)^{2i}$$
warm shaleBOT
FirstNameLastName
warm dome
Can you figure out why this is the case?
warm dome
**FirstNameLastName**
.
gray tapir
to get the odd values
warm dome
Yes
And be aware that we’re adding only one to the odd numbers
Because we’ve only added 2n+1 to the sum
Which is odd
gray tapir
now should this be simplified further?
warm dome
Yes
warm shaleBOT
daddyirani
gray tapir
$$\sum_{i=1}^{2n+1}(-x)^i=-x^{-1}\sum_{i=1}^{n+1}(x^2)^{i}+\sum_{i=1}^n(x^2)^{i}$$
warm shaleBOT
daddyirani
warm dome
Correct
Now you could rewrite the odd sum such that it goes from 1 to n, not n+1
You see how we could do that?
If you don’t then that’s fine too
We can solve it either way
What we need now is to take the limit of the two sums
And see if they approach the same value
gray tapir
as n tends to $\infty$
warm shaleBOT
daddyirani
warm dome
Yes
gray tapir
the even sum approaches 0
warm dome
the even sum approaches 0
No
We’ve converted the expressions in such a way that you can apply the hint
Control result, as I can’t be as active rn: -1/3
gray tapir
No worries I'm going to have lunch as well
obtuse pebbleBOT
@gray tapir Has your question been resolved?
obtuse pebbleBOT
fervent cradle
yeah it's pretty easy to go from one to the other
cos(t) = sin(t - pi/2), remember
so if you get the Rsin(t + a) form that's just the same as Rcos(t + a - pi/2)
yes
sin(t) = cos(t + pi/2)
no it does
no
-3pi/2
?
it has to be /2
not /4
wait am i dumb
hang on hang on
wait i'm stupid!
nononono
ignore everything i said
sin(t) = cos(t - pi/2)
cos(t) = sin(t + pi/2)
oh god
i need to die now
shame
dishonour upon my family
ok ok the way to think about is that cos is like pi/2 ahead of sin
so you need to add pi/2 to the sin one
to get to cos
?
wdym
i mean, sorta
otherwise you have to switch the formula around i should think
it'll be different
vocal warren
yo
vocal warren
i need a bit of helo
if 6x+2y= 160
then how do you find x
if x+y = 50
<@&286206848099549185>
timid silo
Start by trying to eliminate y from the equation
Make the coefficient of y same in both equations
vocal warren
and how do i proceed with that?
timid silo
Subtract both equations
vocal warren
so 6x-2y=160-2y?
timid silo
No
Make the coefficient same
You have to remove y from the equation
Ok let's try another way
Isolate y in the first equation
What do you get?
vocal warren
6x-2
timid silo
When I said isolate y I meant Y= something
timid silo
When I said isolate y I meant Y= something
In this form
vocal warren
im not sure i follow
vocal warren
ok
timid silo
First subtract 6x from both sides in the first equation
vocal warren
2y=160-6x
timid silo
Now divide both sides of the equation by 2
vocal warren
y=80-3x
vocal warren
x+80-3x=50
timid silo
Ok
vocal warren
/14 sry
timid silo
Wait
vocal warren
You have to multiply by 2
oh yeah myb
6x+36-14x/14=9
=26-8x/14=9
26-8x=126
-8x=100
x=12.5
timid silo
=26-8x/14=9
Wrong
vocal warren
=26-8x/14=9
36-8x/14=9
timid silo
6x+36-14x/14=9
Upto ghis point it's right
timid silo
36-8x/14=9
That's wrong
vocal warren
5x+36=9?
timid silo
No
vocal warren
i thought we divide the term as a whole
vocal warren
but dont we divide it as a whole
timid silo
On both sides
Then subtract
vocal warren
oh
timid silo
And sorry if the response takes time
vocal warren
but why are we not including 6x
timid silo
My internet is not good
vocal warren
np your responses are rapid
timid silo
but why are we not including 6x
Because only the y value is divided by 14
The y value that we put in the equation, remember?
timid silo
Now try it again
timid silo
np your responses are rapid
That's good as it sometimes take a while for the msg to go
vocal warren
6x+36-x=9
timid silo
36 is still divided by 14
vocal warren
ok myb
timid silo
No problem
vocal warren
6x + (36 -14x)14=9*14
timid silo
6x + (36 -14x)14=9*14
(36-14x)
It was already divided by 14
So when we multiply by 14
It cancel out
vocal warren
6x + 504 -190 = 126
vocal warren
It was already divided by 14
so it reveals original value?
timid silo
No
vocal warren
96*
timid silo
No
timid silo
Ok
timid silo
lol dumb mistake
It's ok
vocal warren
ok
timid silo
On the right hand side there was 126
timid silo
And on the left there was 36-70x
timid silo
18-7x/7
It's equal to 14 y
And it's 18 - 7x = 14y
Put the value of x
Which is 9/7
vocal warren
18-7x/14
timid silo
Why is there a x
timid silo
thats the value of y right
Yes
vocal warren
which is x/2
timid silo
Yeas
timid silo
This method is called substitution
timid silo
No problem
timid silo
Good luck!!
timid silo
Np 👍
vocal warren
.close
woeful fulcrum
obtuse pebbleBOT
woeful fulcrum
violet sentinel
hi there
woeful fulcrum
idk what i did wrong
violet sentinel
what have you tried so far?
ah
lol
So I would take a step back and relabel everything. Looks like you skipped a few steps and that might be why you're getting confused.
We will need to use the chain rule to differentiate with the volume. Do you see why?
We have dV/dt, we have the radius, but we need the growth in terms of dr/dt. So how can we do that?
woeful fulcrum
i used the chain rule but did i use it wrong?
do i need to find r'(t) instead of r(t)
violet sentinel
no but it might help to explicitly write this stuff out. For example, you write r(t) but what you meant was dr/dt.
woeful fulcrum
confusion
violet sentinel
The issue you have is that you did something wrong. You multiplied your radius by 2 when in fact you were supposed to squre it
you'll get a unit of cm^2 that way
you tried to square root one side, but you can't do that; you have to square root both sides.
violet sentinel
But you don't need to square root at all
woeful fulcrum
well i was confused because how do i get dr/dt in the equation then
oh
so radius isnt constant
ohhhhhhhh
i think i see
i confused radius being constant just cuz of it saying find the rate when radius is 2cm
violet sentinel
$\frac{dV}{dt} = 4\pi r^2 \cdot \frac{dr}{dt}$
$\\ 2 \frac{cm^3}{sec} = 4 \pi (2 cm)^2 \cdot \frac{dr}{dt}$
$\\ 2 \frac{cm^3}{sec} = 16 \pi cm^2 \cdot \frac{dr}{dt}$
$\\ \frac{2 cm}{16 \pi sec} = \frac{dr}{dt}$
$\\ \frac{1 cm}{8 \pi sec} = \frac{dr}{dt}$
warm shaleBOT
MellowDramaLlama
violet sentinel
i confused radius being constant just cuz of it saying find the rate when radius...
No worries it happens 🙂
woeful fulcrum
okok i got the first part right
im gonna ignore the rest and try to solve on my own and see if get the same answer
violet sentinel
My only suggestion is to label things as derivatives (either with Newton or Leibniz notation)
like I did above
violet sentinel
so dr/dt is better than r'(t)
either or as long as you remember!. When dealing with chain rule I prefer Leibniz so you know what variables your differentiating with respect to.
boreal spear
Let $(X,\mathcal{T})$ be a topological space and let $(Y,d_Y)$ be a metric space. Let $f_n:(X,\mathcal{T})\to(Y,\mathcal{T}_{d_Y})$ be a sequence of continuous functions. Let $x_n$ be a sequence of points of $X$ converging to $x$. Show that if the sequence $(f_n)$ converges uniformly to $f$, then $(f_n(x_n))$ converges to $f(x)$.
obtuse pebbleBOT
Let $(X,\mathcal{T})$ be a topological space and let $(Y,d_Y)$ be a metric space...
warm shaleBOT
jsidind810
boreal spear
Does it suffice to show that $f$ is continuous?
warm shaleBOT
jsidind810
boreal spear
Since this theorem in Munkres:
Showing $f$ is continuous would mean showing that given any $x\in X$ and $\varepsilon>0$, there is a $\delta_\varepsilon >0$ such that $d_X(x,y)\Rightarrow d_Y(f(x),f(y))<\varepsilon$.
warm shaleBOT
jsidind810
boreal spear
But what is the metric of $(X,\mathcal{T})$?
warm shaleBOT
jsidind810
boreal spear
<@&286206848099549185>
warm canopy
a topological space need not have a metric in general
warm canopy
you'll have better luck asking in #point-set-topology or #advanced-analysis
boreal spear
They’re going to kick me out because im asking a question
warm canopy
? the channels are for questions
boreal spear
.close
woeful fulcrum
obtuse pebbleBOT
woeful fulcrum
confused
ill post my work in a sec
i was confused when m^3/m^3 happened cuz i need m/sec
theres somethign wrong but idk what
pine barn
Well your using the wrong value for h
woeful fulcrum
OH
pine barn
You have to find the ratio between h and r :p so both of those values are wrong
woeful fulcrum
yeah i see
so 10m is irrelevant in this question
me when i dont read the question entirely 🤦♂️
pine barn
It's 2m when the hight is 10m
pine barn
So you find the ratio to find what r is when h is 3m
severe reef
im pretty sure in this problem the radius of the cylinder is constant
you only have to worry about h
woeful fulcrum
logically i think if like water is leaking from a cylinder the radius doesnt change
but idk
pine barn
Oh yeah, I'm thinking of cones
woeful fulcrum
okay
severe reef
check your differentation of V
woeful fulcrum
so i just repeat what i did before with 3m right
severe reef
why did that h remain there?
woeful fulcrum
instead of 10m for h
severe reef
$d(Pir^2 h)dt = Pir^2*dh/dt$
warm shaleBOT
Radiation 𝕏
severe reef
why is the h removed?
it isnt removed
woeful fulcrum
so instead of h(dh/dt) it just becomes dh/dt?
severe reef
yes
woeful fulcrum
ok
severe reef
tell me one thing, d(3x)/dx
whats this
its just 3 d(x)/dx or 3 right?
same goes here
woeful fulcrum
so
im doing the problem rn on paper
one sec
so would the answer be 4/4pi m/sec?
the only thing im confused on is why i didnt use 3m for height at all when solving
@severe reef
OHHHHHH
i see another mistake
since its leaking the rate would be -4m^3/sec as well
not positive?
severe reef
yeah
dv/dt=-3
and i suggest you to not worry about the units that much
math will take care of that for you
severe reef
-4 my bad
severe reef
because the rate of change of height in this case is independent of the current height h