#help-36
proud igloo
soft zealotBOT
proud igloo
If I sqrt I introduce an abs(x)
worthy wren
final saddleBOT
final saddleBOT
Available help channel!
gentle zephyr
guys I have another question
final saddleBOT
guys I have another question
ornate tree
yes plz
gentle zephyr
- Dada la funcion
$$f(x,y) = \begin{cases} \frac{x^2\sin(y)}{\frac{1}{3} (x^2 + y^2)} &\text{ si } (x,y) \neq (0,0) \ 0 &\text{ si } (x,y) = (0,0) \end{cases}$$ (a) Hallar todos los $v \in \mathbb{R}^2$ de norma 1 tales que $\pdv{f}{v}$ $(0,0) = 3\$
soft zealotBOT
Renato
gentle zephyr
,align f(x,y) &= \begin{cases} \frac{x^2\sin(y)}{\frac{1}{3} (x^2 + y^2)} &\text{ si } (x,y) \neq (0,0) \ 0 &\text{ si } (x,y) = (0,0) \end{cases} \ D_{\vec v} f(x,y) &= \lim_{h \to 0} \frac{f(x + hv_1, y + hv_2) - f(x,y)}{h} \ D_{\vec v} f(0,0) &= \lim_{h \to 0} \frac{f(0 + hv_1, 0 + hv_2) - f(0,0)}{h} \ D_{\vec v} f(0,0) &= \lim_{h \to 0} \frac{f(hv_1,hv_2) - 0}{h} \ D_{\vec v} f(0,0) &= \lim_{h \to 0} \frac{\frac{(hv_1)^2 \sin(hv_2)}{\frac{1}{3} \cdot \left[ (hv_1)^2 + (hv_2)^2\right]} - 0}{h} \ D_{\vec v} f(0,0) &= \lim_{h \to 0} \frac{3(hv_1)^2 \sin (hv_2)}{h \cdot \left[ (hv_1)^2 + (hv_2)^2 \right]} \ D_{\vec v} f(0,0) &= \lim_{h \to 0} \frac{3 \cdot h^2 \cdot (v_1)^2 \sin (hv_2)}{h \cdot \left[ h^2 \cdot (v_1)^2 + h^2 \cdot (v_2)^2 \right]} \ D_{\vec v} f(0,0) &= \lim_{h \to 0} \frac{3 \cdot h^2 \cdot (v_1)^2 \sin (hv_2)}{h \cdot h^2 \cdot \left[ (v_1)^2 + (v_2)^2 \right]} \ D_{\vec v} f(0,0) &= \lim_{h \to 0} \frac{3 \cdot (v_1)^2 \sin (hv_2)}{h \cdot \left[ (v_1)^2 + (v_2)^2 \right]} \ D_{\vec v} f(0,0) &= \lim_{h \to 0} \frac{3 \cdot (v_1)^2}{(v_1)^2 + (v_2)^2} \cdot \frac{\sin(hv_2)}{h} \ D_{\vec v} f(0,0) &= \lim_{h \to 0} \frac{3 \cdot (v_1)^2 \cdot v_2}{(v_1)^2 + (v_2)^2} \cdot \frac{\sin(hv_2)}{hv_2} \ D_{\vec v} f(0,0) &= \lim_{h \to 0} \frac{3 \cdot (v_1)^2 \cdot v_2}{(v_1)^2 + (v_2)^2}
soft zealotBOT
Renato
gentle zephyr
like I found all the directional derivatives of f(0,0)
the issue is that, idk how to finish the exercise
like strictly speaking we need to equate this to 3?
worldly mesa
Remember your result
worldly mesa
like strictly speaking we need to equate this to 3?
Yes
gentle zephyr
Yes
the issue is that there are like many possibilities dude
and like how do I solve this equation
this is like equivalent to, solve for $x \in \mbb{R}$ and $y \in \mbb{R}$ $$\begin{cases}x^2 + y^2 = 1 \ xy^2 = 1 \end{cases}$$
worldly mesa
2 equations 2 variables
soft zealotBOT
Renato
gentle zephyr
2 equations 2 variables
dude this is tuff
you know what I mean?
y^2 = 1 - x^2
x(1 - x^2) = 1
x - x^3 = 1
the fuck is this dude
,w solve x - x^3 = 1
soft zealotBOT
gentle zephyr
@worldly mesa u here?
worldly mesa
Yes
gentle zephyr
dude problem is fucked up
you looking at this?
I am not even joking dude
this shit was in last semester midterm exam
I wouldve just shit my pants right there, I cant finish this shit? you know what I mean? @worldly mesa
gentle zephyr
I would get 0 points if I do that
its either exercise complete or incorrect
is it possible to solve for v1, v2?
@worldly mesa ideas?
worldly mesa
No
gentle zephyr
fuck my life dude
worldly mesa
Some equations don't have nice solutions
I tried rechecking your work and didn't find and mistakes
gentle zephyr
dude wtf is wrong with this professor
it doesnt make any sense to give an exercise without any possible solution
,w x * y^2 =1
soft zealotBOT
drowsy epoch
v1²+v2²=1 is actually wrong
We divide by the norm so to work with the unit vector version
gentle zephyr
yes
drowsy epoch
There should be infinite many solutions since we always normalize the vector but the directions is invariant
gentle zephyr
what?
drowsy epoch
(1,1), (2,2) etc. all maintain the same direction
gentle zephyr
,, D_{\vec v} f(0,0) = \frac{3 \cdot (v_1)^2 \cdot v_2}{(v_1)^2 + (v_2)^2} = 3 \ D_{\vec v} f(0,0) = \frac{(v_1)^2 \cdot v_2}{(v_1)^2 + (v_2)^2} = 1
drowsy epoch
If we choose v2=1 for example then you should acquire v1 easily
Really it could be any value as long as it's fixed
soft zealotBOT
Renato
gentle zephyr
Really it could be any value as long as it's fixed
can u elaborate
gentle zephyr
If we choose v2=1 for example then you should acquire v1 easily
why are u picking random v2
drowsy epoch
Because we always normalize the vector
So there is always a family of vectors that are a solution
drowsy epoch
Again, for example whether we picked (1,1), (2,2), (π,π) etc. it doesnt matter
they all get normalized and become the same unit vector since they all have the same direction
gentle zephyr
,w (x^2 * y)/(x^2 + y^2) = 1 where (x,y) = (pi, pi)
soft zealotBOT
drowsy epoch
I cant read Spanish but I am also certain it says some and not the vector v
drowsy epoch
,w (x^2 * y)/(x^2 + y^2) = 1 where (x,y) = (pi, pi)
dude it was an example unrelated
gentle zephyr
Hallar todos los v en R2 de norma 1 tales que partdialdiv{f}{v} (0,0) =3
Find all the v in R2 of norm 1 such that partialdiv{f}{v} (0,0) = 3
gentle zephyr
dude it was an example unrelated
like, there is something I am not understanding here
how am I supposed to find all the vectors such that the partial derivative of f wrt v at (0,0) is 3?
gentle zephyr
I cant read Spanish but I am also certain it says *some* and not *the* vector v
well, I think I am not supposed to actually find v1, v2 themselves
like, it says all right?
Find all the v in R2 of norm 1 such that partialdiv{f}{v} (0,0) = 3
in other words, I think this is good enough
like, IDK how to solve for v1, v2
you say they have to be fixed, but I dont get it
drowsy epoch
Ok but then you can still find one vector
drowsy epoch
Just fix one variable
It's like solving a system of one equation but two variables
One will depend on the other
(v1,v2)=(v1,f(v1))
gentle zephyr
whats your idea?
,, D_{\vec v} f(0,0) = \frac{3 \cdot (v_1)^2 \cdot v_2}{(v_1)^2 + (v_2)^2} = 3 \ D_{\vec v} f(0,0) = \frac{(v_1)^2 \cdot v_2}{(v_1)^2 + (v_2)^2} = 1
soft zealotBOT
Renato
gentle zephyr
also we are loosing solutions if we fix one
drowsy epoch
You basically get a quadratic in v1 but I would just set v2=1 and then solve for v1
Then all solutions are all multiples of (v1,1)
multiples
drowsy epoch
Yeah
gentle zephyr
then I get
(v1^2)/(v1^2 + 1) = 1
and then theres clearly no solution
because
v1^2 = v1^2 + 1
we get 0 = 1
gentle zephyr
my bad
v1^2 * 2 = v1^2 + 4
2v1^2 - v1^2 = 4
v1^2 = 4
v1 = +- 2
(v1,v2) = (+-2, 2)
,w (x^2 * y)/(x^2 + y^2) = 1 where (x,y) = (2, 2)
soft zealotBOT
gentle zephyr
dude what
drowsy epoch
Ok but my assumption was still off
gentle zephyr
what assumption, that it works for any fixed (k,k) = (v1,v2)?
drowsy epoch
The best is to solve this as a quadratic in y
gentle zephyr
how
gentle zephyr
where did you got that from
soft zealotBOT
gentle zephyr
what
drowsy epoch
Just bring everything to one side
drowsy epoch
Apply the quadratic formula
gentle zephyr
oof
drowsy epoch
Your solutions are then in the form (x,y)=(x,±f(x))
drowsy epoch
Multiples was wrong initially because just because (2,2) was a solution doesn't mean it's the line (a,a) might also just be a point on another of the infinite lines
gentle zephyr
gentle zephyr
The thing is if x=y=0 then we would get 0/0
is not a solution then
drowsy epoch
Multiplying both sides by the denom already assumes x and y isn't 0
drowsy epoch
Yes
gentle zephyr
dude
(v1,v2) = (2,2) is not possible either
like the norm is not 1
you follow?
drowsy epoch
Bro
The norm is not 1
Unit vector means u/|u|
Dividing by the norm makes it unit
gentle zephyr
ok, my bad
drowsy epoch
and that norm can be any positive number
gentle zephyr
lets continue then
how to solve this quadratic, is the trivial solution (0,0) possible or not?
shit is getting so nasty
drowsy epoch
how to solve this quadratic, is the trivial solution (0,0) possible or not?
no
It's never a unit vector
gentle zephyr
wdym?
drowsy epoch
What I said
gentle zephyr
you talking about the trivial or in general
drowsy epoch
(0,0)
gentle zephyr
fuck bro this exercise is fucked up
drowsy epoch
we omit it
gentle zephyr
dude I need help with this quadratic
drowsy epoch
directional derivatives only apply for unit vectors, (0,0) is never a unit vector
drowsy epoch
dude I need help with this quadratic
it's just algebra
gentle zephyr
fuck my life bro
drowsy epoch
Ok now thats it y=...
Now write it in set notation and you should be good
{(x,y) in R^2 : y=...}
gentle zephyr
jajaj fuck this prof mate, idk whats his problem
this quadratic with two variables always makes me uncomfortable
this should be it
drowsy epoch
Yeah, afaik
You could also possibly state the domain for x
1-4/x² >= 0
So to not get off points
gentle zephyr
drowsy epoch
You can solve for x
drowsy epoch
gentle zephyr
gentle zephyr
x² >= 4 => |x| >= 2
oh, right
drowsy epoch
think
drowsy epoch
you dont need for all
gentle zephyr
?
drowsy epoch
?
gentle zephyr
what do you mean?
drowsy epoch
you write the for all quantor and then dont know what i mean by for all
drowsy epoch
because you have (x,y) such that
drowsy epoch
What you wrote on the right is a trivially true statement, but we just write the conditions
drowsy epoch
ye I might be tripping
yes
gentle zephyr
I appreciate it dawg, this one was a hardone
like, at least for me, im new to directional der
drowsy epoch
you didnt even know quadratic equations lowkey
gentle zephyr
and I fucking hate this quadratic with two thingies
drowsy epoch
gentle zephyr
<:DGworryRabbit:1047043098066300948>
😂
I am still in the learning phase
but yeah I got like less than 2 weeks b4 my exam so I might need to practice more of this
I appreciate it dawg
I think this is solved
.close
final saddleBOT
final saddleBOT
Available help channel!
steady wraith
final saddleBOT
final saddleBOT
@steady wraith Has your question been resolved?
velvet pecan
Hello, how would you setup an inequality relation base on the available information here ?
one more hint, ''non-congruent" is the key to the puzzle. Think about the special triangle SSA case
cerulean radish
okay
cerulean radish
question
ornate tree
yep
cerulean radish
say we have f(x) = sin(x)/x and we wanna find if its continuous at x=0
if we input the values in directly, we can see that f(x) = 0/0, which is indeterminant
cerulean radish
but if we use l'hopitals
right and left side become 1
so f(0) becomes.... 1?
so, it agrees to one condition of continuity, but not the other
what is it then
because limit as x approaches 0 for f(x) is clearly not equal to f(x)
🤔
plucky rover
Continuity at a point where the function isn't defined...
Means that the left limit is equal to the right limit
plucky rover
It depends on convention really
cerulean radish
Wdym
plucky rover
Some profs say continuity requires the function to be defined at the point and the limit equal the value
Some say LHL = RHL is enough if the function isn't defined
plucky rover
Some say LHL = RHL is enough if the function isn't defined
Because in this case you can define the function at that point to be the limit
cerulean radish
so when we're graphing that function
what exactly are we supposed to do at x=0
u cant really graph something if its undefined there
versed crater
what exactly are we supposed to do at x=0
A hole
And we denoted that with an open circle as said above
versed crater
At (0, 1)
cerulean radish
So it says that its not exactly defined there
But
but ye
Hmmmmm
Are there any other functions that behave similarly
cerulean radish
wow
versed crater
4sin(x)/x
cerulean radish
i suppose so
versed crater
I’m very creative I know
cerulean radish
😭
bleak granite
(1-cosx)/x
cerulean radish
Even x/x works
Ur right
X/x at if
like
x = 0
is undefined
but limit is1
due to lhopitals
versed crater
No
versed crater
The limit is 1!!
cerulean radish
Yes
versed crater
Look at it again
cerulean radish
Limit is 1
versed crater
Are yoy sure it’s 1
bleak granite
is undefined
it's a removeable discontinuity, so it's a hole
a function like 1/x has a non-removable discontinuity at x=0
cerulean radish
it's a removeable discontinuity, so it's a hole
interesting
bleak granite
so it is an asymptote, not simply a hole
versed crater
You can’t make f(0) something and turn it continuous
cerulean radish
for 1/x, its undefined, definetely, and u cant use lhopitals since its not 0/0 or inf/inf
bleak granite
for 1/x, its undefined, definetely, and u cant use lhopitals since its not 0/0 o...
and in fact, the limit (as x->0) DNE
versed crater
All the previous examples you could put f(0) as some particular value and then f would then be continuous
That’s what we mean by removable
Cos you could remove the hole if you plugged it up with some value
For 1/x nothing you plug in for f(0) will make it continuous at 0
cerulean radish
and in fact, the limit (as x->0) DNE
true
cerulean radish
For 1/x nothing you plug in for f(0) will make it continuous at 0
Correct
cool
frosst can i ask wyf
final saddleBOT
steady wraith
Hello, how would you setup an inequality relation base on the available informat...
oh yeah uh
idk why i keep asking a question and forgetting i asked it
final saddleBOT
Available help channel!
blissful echo
I’ve done everything else, but I’m confused on the last line
final saddleBOT
I’ve done everything else, but I’m confused on the last line
bleak granite
well from the line above that you have cos^2sin^2 in -1/16(z^2-1/z^2)^2 and you expressions for z^2 and 1/z^2 in terms of costheta and sintheta
final saddleBOT
final saddleBOT
Available help channel!
craggy plank
final saddleBOT
craggy plank
What's the mistake in this code? Language: Java
it says { is expected, but I legit have no idea where to put this down
rare girder
is Main.java a valid name for a class in java?
opal plinth
Just remove .java
craggy plank
Just remove `.java`
Can that appear in the file name?
static oak
Ok I sent this last night but I fell asleep since it was nearly 2 am but could somebody just tell me what it is since I don’t have time to do it until 8 pm . I know e and f are wrong
final saddleBOT
Ok I sent this last night but I fell asleep since it was nearly 2 am but could s...
latent dragon
,rotate
soft zealotBOT
static oak
Yea
final tangle
how did you get 0 and -1?
do you know which part of the graph you should be looking at?
static oak
I’m not sure exactly but I thought I was looking at the lines towards the y axis
final tangle
ok, those would be the limits for x → 0^- and 0^+ which isn't what's being asked
here you want to consider what happens when x gets really big on the negative and positive sides
static oak
It’s either one of these
Or actually it’s any of them I don’t really know at this point
Because to could also be that other one starting at the orgin
Idk I’m really confused
static oak
It feels like it could be any of them at this point since they all go towards infinity
final tangle
for the other limits you looked around x = the specified number right?
e.g. for x→ 3^- you looked around what happens just to the left of x=3
static oak
Yea
But we don’t have an x that equals infinity that impossible
And they all go towards infinity
final tangle
wdym by "they"
static oak
All the lines
final tangle
well you don't care about all the lines
note my emphasis on x
for x → inf
you want to consider what happens when x gets really big (on the positive side)
you're focussing on places where y is -inf or inf
static oak
I’m confused since i thought. That’s what I’m looking out
final tangle
which isn't how you should be thinking about it
static oak
Then I don’t see any going towards X infinity wouldent that havw to be a straight line
final tangle
for x→ inf,
you should be focusing on the right side of the graph,
the left side doesn't matter for this
static oak
I dont understand how it can go towards x infinity but not y infinity
final tangle
if you were to extend that part, what would happen
static oak
it would make the graph bigger
Is it the one starting in the orgin? Because if so there is only one line and I need two
final tangle
you don't care about the origin
the first focus is the value of x
note for the other limits, you don't initially care about infinities,
the first focus is the value of x
and if the limit ends up being infinites, so be it
for x→3^-,
you didn't care abount anything not even close to 3
similarly for x→inf, you only care about what happens as x gets really big
static oak
So it’s the two farthest right and left ones
how would I know for the Ys for that if the left one is not zero?
final tangle
imagine extending the line
static oak
Sorry I have to go in like 7 minutes so I’m rushing
final tangle
based on what's present
static oak
So the answer is infinity?
static oak
Ok ty
ornate tree
Allie do you still need help?
static oak
Quick question when I have g(0)=1 which value is the x value and which one is the y value
final tangle
functionname(input) = output
input is represented on the horizontal axis,
output the vertical
junior token
so you could say 0 is the x value and 1 is the y value
final saddleBOT
@static oak Has your question been resolved?
exotic shale
hello
tired walrus
differentiation and integration
desert mantle
read the first paragraph?
what exactly are you expecting from us? its not like we know those notes
scenic walrus
https://tutorial.math.lamar.edu/Classes/DE/DE.aspx
learn calc 1 here and probably some integration techniques?
exotic shale
differentiation and integration
Only?
I saw it has basic stuff but also goes into heat wave equations
tired walrus
pdes and the like will come later
for these you need to know how to handle multivar functions calculus-wise
exotic shale
for these you need to know how to handle multivar functions calculus-wise
Ok
Thanks
.close
final saddleBOT
final saddleBOT
Available help channel!
vague anchor
4th guys🙏
ivory bear
,rotate
soft zealotBOT
ivory bear
Bro after Ann u r the one who always comes up for me
maybe
vague anchor
Yepp🙌
ivory bear
aasan h
ivory bear
ill send the soln in few moment sire
vague anchor
Oh now then u can feel relieved that competition is lesser
ivory bear
Then?
just 12thie rn
studying for mains
syllabus is non ending bro
feeling anxious
vague anchor
just 12thie rn
Bro I can tell ull do it
vague anchor
Most probably u would have seen the head
ivory bear
Bro I can tell ull do it
||dms me add krlu tumhe?||
vague anchor
||dms me add krlu tumhe?||
Freely
final saddleBOT
@vague anchor Has your question been resolved?
ivory bear
@vague anchor ??
vague anchor
Can anyone tell me my mistake here 😭
final saddleBOT
Can anyone tell me my mistake here 😭
final saddleBOT
thin cloud
final saddleBOT
Available help channel!
sonic falcon
How does this work?
final saddleBOT
How does this work?
sonic falcon
I don't understand this simplification of the exponents
Maybe there is another example which could help clear things up?
ivory bear
$e^{-{x_1}^{2}} \leq e^{-{x_2}^{2}}$
soft zealotBOT
Dhairya
ivory bear
Maybe there is another example which could help clear things up?
do you know logarithms?
sonic falcon
Actually wait I understand now
So for the inequality at the top to be true
The inequality at the bottom has to be true
ivory bear
The inequality at the bottom has to be true
yea
ivory bear
fine
sonic falcon
.close
ivory bear
Ty for help
i just typed out using latex
final saddleBOT
final saddleBOT
Available help channel!
cedar obsidian
in this problem i analysed that sand will move opposite to direction of flatcar => the thrust force is oppsite to motion of flatcard
final saddleBOT
in this problem i analysed that sand will move opposite to direction of flatcar...
cedar obsidian
my question is what velocity to assume of sand here with respect to ground
so that splitting velocity also includes in it
that is u
will it remain the same ie u
it goes back with velocity v then its velocity wrt ground becomes v + u?
old quarry
what is u
old quarry
how is kg/s unit of velocity
heady otter
well the initial x-velocity of the sand is 0
cedar obsidian
how is kg/s unit of velocity
but that is the rate of coming out
cedar obsidian
well the initial x-velocity of the sand is 0
everything is in motion
cedar obsidian
not the velocity
yes acutally
old quarry
it goes back with velocity v then its velocity wrt ground becomes v + u?
so how is mu in the velocity here..
cedar obsidian
there where do i utilize it
heady otter
stationary hopper no?
cedar obsidian
stationary hopper no?
but sand moves
old quarry
there where do i utilize it
u need to write an equation where u can write the mass as m + dm/dt
heady otter
yeah only in the y direction initially
old quarry
write a force equation
cedar obsidian
F= ma
cedar obsidian
mb i took it by mistake
old quarry
yea we can write it as that but it will get us nowhere
cedar obsidian
it should be ut
old quarry
have u studied force due to variable mass systems
cedar obsidian
if u kg is falling in per second then in t time it beomces ut
cedar obsidian
have u studied force due to variable mass systems
yes in case of rocket that is thrust force and the concept is same here
cedar obsidian
| F_t | = v_rel dm/dt
cedar obsidian
now can u tell me the rewritten force equation?
ma = v_rel * u
m = m_o + extra mass of sand
cedar obsidian
F - F_t = v_rel * u
old quarry
F - F_t = v_rel * u
hm isnt v_rel*u = Ft?
cedar obsidian
hm isnt v_rel*u = Ft?
i can't agree
old quarry
| F_t | = v_rel dm/dt
u literally wrote it right here
cedar obsidian
do you mean F_t = v_rel* u or Ft = v_rel * u
cedar obsidian
hm isnt v_rel*u = Ft?
here
old quarry
yes i meant F_t sorry..if i had put another underscore it wouldnt have shown properly
cedar obsidian
if its F_t = v_rel* u then i agree
cedar obsidian
ma = v_rel * ut
cedar obsidian
why F_t is being added
while the sand is moving backwards due to F wrt to flatcar
old quarry
yeah we will figure out the signs later
i just wanted to show u the equation
vectorially
cedar obsidian
okay
cedar obsidian
ok now can u tell me what F_t is
ma = m_o* a - (v_rel*u)
old quarry
everything correct except the m_o*a part
u cant write F as that
F is given to us in the question
cedar obsidian
m(dv/dt) = F _ (v_rel*u)
old quarry
yes !
cedar obsidian
now just integration
old quarry
now in this case lets take v_rel as v
old quarry
now just integration
yeah
cedar obsidian
okay
old quarry
u can proceed from here right
final saddleBOT
final saddleBOT
Available help channel!
final saddleBOT
👍 be careful also that m is not m_o
cedar obsidian
👍 be careful also that m is not m_o
ill keep it same
old quarry
can you tell me why i was doing such small mistakes in force sense
variable mass systems are kind of a tricky concept
cedar obsidian
can you tell me why i was doing such small mistakes in force sense
what do i need to practice for that to improve
old quarry
.close
final saddleBOT
old quarry
what do i need to practice for that to improve
just questions tbh
u can also read theory
cedar obsidian
what kind of specifically
old quarry
ye
cedar obsidian
ma is equal to v_rel dm /dt
then later how can we say ma = F + F_t
F_t = ma = v_rel dm/dt
old quarry
no
cedar obsidian
that was typo
old quarry
its still wrong..
old quarry
ma = F - (v_rel*u)
..
final saddleBOT
Available help channel!
cedar obsidian
m(dv/dt) = F - (v_rel*u)
final saddleBOT
m(dv/dt) = F - (v_rel*u)
cedar obsidian
is this correct
old quarry
yes
cedar obsidian
?
hybrid heath
Yes, it is correct
cedar obsidian
|F_t| = v_rel*u
ma = vrel*u
mdv/dt = vrel*u
then where does the given force in question goes
cedar obsidian
Hi
cedar obsidian
@old quarry r u here
That was F_net = F - F_t right?
I am getting v = F_t/m - u integral v_rel dt from 0 to t
Now v_rel is making problem
final saddleBOT
@cedar obsidian Has your question been resolved?
final saddleBOT
@cedar obsidian Has your question been resolved?
red leaf
help?
edgy mauve
help?
What have u tried
If distance double,u got to denote it as 2r
And if first charge is quadruple ,then it becomes 4Q_1
red leaf
If distance double,u got to denote it as 2r
i said that the new one increases by factor of 2.68
edgy mauve
Lemme check
red leaf
so?
edgy mauve
edgy mauve
i plugged in a random number for k
Y plug in random k has a constant value
But that's not needed to be plugged in,cuz both k and r² cancels out
red leaf
Y plug in random k has a constant value
But that's not needed to be plugged in,...
so the overrall equation would be?
edgy mauve
F_2=0.67F_1
red leaf
F_2=0.67F_1
so it would be .67?
edgy mauve
Yea
edgy mauve
.67 of initial force
edgy mauve
like the force? percentage?
Times
edgy mauve
.67 times of initial force?
Yes
red leaf
thanks
edgy mauve
Nw
final saddleBOT
@red leaf Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
twilit fern
Why not sin(60) = 2h/a?
final saddleBOT
Why not sin(60) = 2h/a?
ornate tree
Where did you get 2h from?
thin cloud
Cos(60)=2h/a
twilit fern
half of side a
ornate tree
h/a, yes. 2h/a, no
twilit fern
omg sorry
thin cloud
You might mistook tan and sin
final saddleBOT
final saddleBOT
Available help channel!
copper roost
In an urn there are 50 balls, some of which are yellow and some black. It is known that the number of yellow balls is greater than the number of black balls. A game of chance is played in which two draws with replacement are made. The probability of drawing balls of different colors is 0.4032.
final saddleBOT
In an urn there are 50 balls, some of which are yellow and some black. It is kno...
copper roost
can someone explain how you come to this solution
thin cloud
In an urn there are 50 balls, some of which are yellow and some black. It is kno...
What do we have to do...
thin cloud
Like where's the question
thin cloud
In an urn there are 50 balls, some of which are yellow and some black. It is kno...
I don't know what they say here but
It seems like p is the probability of drawing a ball black/yellow
thin cloud
If p is the probability of drawing a black ball
thin cloud
Then 1-p is the probability of drawing yellow ball
thin cloud
I mean
Okay
So without the fact that yellow balls are more than black balls
Both 0.28 and 0.72 could be the probability of pulling a black/white ball
I mean yellow
Agree?
@copper roost 
you here?
copper roost
<@419857529032409088> <a:thisissosad:591882643193331722> you here?
yo
im in the bus
copper roost
Both 0.28 and 0.72 could be the probability of pulling a black/white ball
yeah
copper roost
So let p just be the probability we pulling a yellow ball
okay
thin cloud
So the probability of drawing a black ball is 1-p
thin cloud
ok so how solve the bracets
Quadratic equation bro🥀
You should have known how to do it
ornate tree
:sobbing
final saddleBOT
@copper roost Has your question been resolved?
spring abyss
is it any faster to check continuity of wxy than to find both wxy and wyx?
final saddleBOT
is it any faster to check continuity of wxy than to find both wxy and wyx?
@spring abyss Has your question been resolved?
versed crater
well the first one is smooth
the 4th one is also smooth
the other ones you'd have to check manually
round cedar
hey, is the green step ok?
final saddleBOT
hey, is the green step ok?
runic tulip
Yes
rain sentinel
Hi, I don't understand why their is (7-8t) because I've expanded it with the -2
gentle barn
$\left(\frac{u}{v} \right)'=\frac{u'v-uv'}{v^2}$
soft zealotBOT
Good
ivory bear
Hi, I don't understand why their is (7-8t) because I've expanded it with the -2
there seems to be an issue with the differential scrawled on the VEEZU copy below
recheck it
rain sentinel
there seems to be an issue with the differential scrawled on the VEEZU copy belo...
What about on the book
rain sentinel
**Good**
This is what I did
But I've expanded the bracket ln(t) -2 (7-8t)
And I don't understand why the (7-8t) is still there
plucky rover
What is the function you're trying to differentiate
ivory bear
But I've expanded the bracket ln(t) -2 (7-8t)
first of all that is a blunder.
plucky rover
Bracket things properly
ivory bear
But I've expanded the bracket ln(t) -2 (7-8t)
ln(t)-2 is wholly multipled with the derivative of $7t-4t^{2}$
soft zealotBOT
Dhairya
rain sentinel
ln(t)-2 is wholly multipled with the derivative of $7t-4t^{2}$
It's (7-8t)ln(t)-2
rain sentinel
From the question
plucky rover
Cuz your question says lnt+2 but it becomes -2 on the next line
ivory bear
Cuz your question says lnt+2 but it becomes -2 on the next line
i was too wondering the same fact
plucky rover
!original Please show us the actual question
final saddleBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
ivory bear
!original Please show us the actual question
yes
edgy mauve
plucky rover
And v = ln(t)-2
plucky rover
No we are past this
edgy mauve
Oh it's "-"
rain sentinel
I'll show you what I'm confused at
plucky rover
That would be helpful yes
rain sentinel
I don't understand why the (7-8t) is still there
When it's been expanded with the -2
plucky rover
Cuz you can't really multiply it by ln t
So that's just the expression you end up with
edgy mauve
If u do want to expand u should be expanding (ln-2)(7-8t)
Not js the 2
plucky rover
Like you can make it 7 lnt - 8t lnt but that doesn't give you much
plucky rover
If u do want to expand u should be expanding (ln-2)(7-8t)
Not js the 2
Oh god damn it I thought she actually bracketed it this time
My bad for assuming
Please for the love of god use brackets
Wait no she has
edgy mauve
My bad for assuming
She did technically, but she used one (7-8t) within brackets and multiplied an extra one (7-8t)
Which i thought was the one but then there is another 7-8t at teh beginning
rain sentinel
I'm sorry?
rain sentinel
If u do want to expand u should be expanding (ln-2)(7-8t)
Not js the 2
But it's ln(t)-2
Even after I expand shouldn't the (7-8t) go
edgy mauve
edgy mauve
Even after I expand shouldn't the (7-8t) go
It's supposed to be something like this
edgy mauve
Even after I expand shouldn't the (7-8t) go
Yes it should and u didnt expand it the right way
Oh... i got what u did
Lemme rewrite
Whatver u did is right
edgy mauve
edgy mauve
You did lnt x 7 and then -2 x 7
Yes i expand it fully,u did it partially
Took me a while,sorry for the misunderstandings
Xavier was right all along
edgy mauve
This is what u did notice that 7-8t is in multiplied form with both lnt and 2
U expanded the portion with 2 but thw one with lnt stayed as it is
And that's y there is 7-8t
rain sentinel
Ah ok
rain sentinel
So you expanded it and then factorised it
edgy mauve
So you expanded it and then factorised it
I didnt factorize, js expanded in ny approach
The one of urs i js expanded it
Like (x+1)(x-2)
U can write that x(x-2) +1(x-2)=(x+1)(x-2)
That's how it was broken down
rain sentinel
So you're saying ln(t) x (7-8t) gives the same thing
As in it gives ln(t) (7-8t)
Or (7-8t) ln(t)
edgy mauve
Yes
edgy mauve
Or (7-8t) ln(t)
The same thing
final saddleBOT
final saddleBOT
Available help channel!
static oak
Is this correct
final saddleBOT
Is this correct
opal plinth
,rccw
soft zealotBOT
opal plinth
Assuming the graph continues downward on the left, then yes
static oak
Kk ty!
terse crypt
in the math server 🥀
static oak
Math sucks
I agree
final saddleBOT
@static oak Has your question been resolved?
static oak
I’m so confused how this has a slope of 2 . I found two points ( -3,-2),(-1,2) and then I did (2- -2)/(-1- -3) and I got (4/-4) which equals -1 but it’s a postive slope so it’s 1
final saddleBOT
I’m so confused how this has a slope of 2 . I found two points ( -3,-2),(-1,2) a...
ripe jewel
I’m so confused how this has a slope of 2 . I found two points ( -3,-2),(-1,2) a...
-1--3=?
final saddleBOT
@static oak Has your question been resolved?
next thorn
I’m so confused how this has a slope of 2 . I found two points ( -3,-2),(-1,2) a...
( -1) - (-3) is not -4, unfortunately.
a calculator is a human's bestfriend ❤️
next thorn
dw allie, I did 4-3 = -6 once 🤩
final saddleBOT
final saddleBOT
Available help channel!
minor summit
how to prove red having black
final saddleBOT
how to prove red having black
zenith cedar
,tex Is it $(n+1)! \le \left(\frac{n+2}{2} \right)^{n+1}$
soft zealotBOT
Triaengle
pliant shore
how to prove red having black
what's the original question?
presumably it's $n! \le \left( \frac{n + 1}{2} \right)^n$ right
soft zealotBOT
south
soft zealotBOT
snozzi
minor summit
yup
either n+1 to have (n+1)! on the right side or (n+1)/2 to have (n+1/2)^n+1 but first option is the nearest i believe
because on the right side we want (n+2/2)^n+1
minor summit
we want to prove n! =< (n+1/2)^n for all n in N*
ripe jewel
where is it going on
.
minor summit
it works for n=1 so we assume its true for a given n
pliant shore
we want to prove n! =< (n+1/2)^n for all n in N*
this way should be easier
if we can show that $\frac{(1 + \frac{1}{n + 1})^{n+1}}{2} \ge 1$ we're good
soft zealotBOT
south
ripe jewel
theres a much simpler way
minor summit
hm
minor summit
is it the same as proving $n! \le \left( \frac{n + 1}{2} \right)^n$
soft zealotBOT
snozzi
ripe jewel
Basically essentially yes but its much more straightforward
well
holdon lemme think
minor summit
we have to compare the right side with n^n then
ripe jewel
im not sure without paper and pencil now that im second guessing myself
because if the half
yeah nm sorry
minor summit
dwdw
pliant shore
yeah the inequality is in the wrong direction; you'd need to find something smaller than n!
minor summit
we want to prove $(n+1)! \le \left(\frac{n+2}{2} \right)^{n+1}$
soft zealotBOT
snozzi
minor summit
having $n! \le \left( \frac{n + 1}{2} \right)^n$
soft zealotBOT
snozzi
ripe jewel
induction sure
pliant shore
or maybe I overcomplicated it too, cause if you just divide
you're multiplying by (n + 1) on the LHS
oh wait that's the same idea actually
minor summit
induction sure
its already an induction
we actually want to prove $n! \le \left( \frac{n + 1}{2} \right)^n$
soft zealotBOT
snozzi
minor summit
by induction
but we need to prove for n+1
so
$(n+1)! \le \left(\frac{n+2}{2} \right)^{n+1}$
soft zealotBOT
snozzi
minor summit
right?
minor summit
you divide
pliant shore
the dividing one is actually a bit messy
minor summit
erm
pliant shore
**south**
it's better to use the fact that $(n + 1)! \le \frac{(n + 1)^{n + 1}}{2^n} \le \frac{(n + 1)^{n + 1}}{2^n} \cdot \frac{(1 + \frac{1}{n + 1})^{n+1}}{2} \cdots$
soft zealotBOT
south
final saddleBOT
Available help channel!
maiden raven
Hi, I came to ask for help on the factorisation of binomials and trinomials
craggy plank
Alright, can you post the questions?
maiden raven
Oh, I just wanted to ask for a quick method to break most down.
I don't have any questions right now
wise wyvern
how to factorise an expression highly depends on what the expression is
so it's hard to say a certain method that works everytime
vivid sierra
Q. 48
