i think there isnt any easier way
#help-38
foggy wharf
earnest granite
yea I think that's it
did your teacher say you are not allowed to use a calculator ?
foggy wharf
in home im free to use but during exam i cant
earnest granite
I get that but I don't think that in the exam it's going to have bad numbers
earnest granite
you're welcome
foggy wharf
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proven steppe
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proven steppe
oh its sinx
orchid wagon
yes
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frozen plume
Hello, given a coin with a radius of 1 cm. How far do you need to hold the coin from your eye to completely cover the moon with it? Distance moon to earth = 380.000km and radius of moon = 1737.4km?
frozen plume
My question is how would you calculate that? I already know that you could do tan(x) = r_coin / distance <-> distance = r_coin / tan(x)
but how do you calculate tan(x)?
frozen plume
mhm
frozen plume
and from there how do you get to d?
ty already for your reply!
@grim sequoia
couldnt you also just say: r_coin / d = r_moon / 3.8e5?
grim sequoia
and from there how do you get to d?
$$ \tan x = \dfrac{0.01}{d}$$
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grim sequoia
couldnt you also just say: r_coin / d = r_moon / 3.8e5?
yes but youll get stuff in kilometers
i converted to meters
pretty sure the answer is ≈ 2.18 meters
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frozen plume
pretty sure the answer is ≈ 2.18 meters
yeah perfect alos got that
thank you very much! @grim sequoia
dapper blaze
Hi
dapper blaze
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quick hound
is there an easier way to solve this?
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rough goblet
partial fraction decomp?
rough goblet
what about it
sharp spindle
a³-b³ I am assuming
sharp spindle
how do i do this
Just look for identities ig
quick hound
okay i think ih ave it in my notes
oh its justthis
ok i can do the rest thnak guys
ok
i got stuck on (x+2)/(x^2+x+1)
any help
i need to integrate that
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proud pecan
to convert it to quadratic form
Hey, i am new here. Can i ask you what is 1 0 0 -1 and lower part is? And how it is useful? How it is calculated and stuff?
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earnest breach
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earnest breach
Is there a step I'm missing?
Here's what I did. I set F_x and F_y equal to each other and solved for x and y separately
rugged latch
i see two linear equations of two variables each
isnt it just solving a system?
u shd prolly get numerical values for x and y
yea
just solve that system @earnest breach
just like how u would solve something like: x + y = 5, x - y = 6
earnest breach
just like how u would solve something like: x + y = 5, x - y = 6
I would just solve them like I would any system of linear equations. Set them equal to eacother, and solve for x or y no?
rugged latch
ok sure u can set them equal. but ultimately, if u get one variable in terms of the other, u have to sub back in into one of the equations
for example
$x + y - 5 = 0 \newline x - y - 6 = 0 \newline \therefore x+y-5 = x-y-6$
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Stephen
rugged latch
then u solve for a variable and plug back in to get the value of the other variable
earnest breach
hmmm
Like in this case I could solve for x and then y
and then sub in x back into one of the equaitons right?
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Stephen
rugged latch
try to solve this by elimination
rugged latch
yep
earnest breach
x = 80/24
rugged latch
np
earnest breach
I think I just forgot that I could eliminate one of the variables tlike that from algebra
appreciate the walk through
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elder musk
Any idea at which step I did a mistake with calculating the determinant here? The solution is -12, but I somehow got 76 with Sarrus
elder musk
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brittle pier
is there a way to solve this using binomial dist. ?
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is there a way to solve this using binomial dist. ?
hallow spruce
Indeed
brittle pier
Ok cause the problem had asked to list out all possible outcomes but that seemed quite tedious
hallow spruce
Well there's only 16 so it could be worse
hallow spruce
How would you use BD for this?
Start by constructing your binomial random variable
brittle pier
Start by constructing your binomial random variable
Would it be T = 4 ? and F = 4?
and you add the two together
P(T=4) + P(F=4)
hallow spruce
Yes
brittle pier
Oooo ok cool
Also whats a quick way to determine how many total outcomes?
My english is not super good so I have a hard time figuring it out sometimes
hallow spruce
Each question has 2 answers and there are 4 questions, 2^4 = 16 total outcomes
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summer ferry
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summer ferry
is this the right way of differentiating 25ln(2x)
rugged latch
yea
summer ferry
right so had to apply chain rule on the 2x right?
rugged latch
yea
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frozen prism
i am conflicted with the info i am given, is this in row echelon form or not
slow dawn
A matrix is in row echelon form if:
All rows having only zero entries are at the bottom
The leading entry (that is, the left-most nonzero entry) of every nonzero row, called the pivot, is on the right of the leading entry of every row above
frozen prism
A matrix is in row echelon form if:
All rows having only zero entries are at th...
so is this in row echelon form?
slow dawn
should be yes
slow dawn
some sources say every pivot / leading should be 1
frozen prism
and which source should i follow
slow dawn
but usually thats only for reduced row echelon form
frozen prism
damn now i am confused as hell
slow dawn
"Some texts add the condition that the leading coefficient must be 1[3] while others require this only in reduced row echelon form."
frozen prism
ok thanks... guess i will ask the professor
but at least now i know why the answers are conflicting
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tardy hemlock
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brittle pier
Could someone help me figure out how to solve this question?
viscid flower
Could someone help me figure out how to solve this question?
What you want is Bayes rule or Bayes theorem
brittle pier
What you want is Bayes rule or Bayes theorem
Since these are all given in the problem, so I would just plug and solve for missing values?
last rune
Do you have P(no crash)?
brittle pier
Yes i got 0.7125
shrewd ridge
they gave it as part of the data though
you don;t need anything at all
it's 1- 0.15
brittle pier
Where?
shrewd ridge
they said (crash | no alcohol) is 0.15, so you know (no crash | no alcohol) is 0.85
brittle pier
How did you conclude to that?? 😭
shrewd ridge
i subtracted from 1
brittle pier
how did you know that so quickly though?
I was using all sorts of formulas and everything
Is that just a thing? P(A'|B) = 1 - [P(A|B']
brittle pier
without the second '
so in the context of this problem
P(no crash | no alcohol) = 1 - P(crash | no alcohol)
shrewd ridge
certainly
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rotund moth
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tepid hamlet
would you know how to find sin x and cos x?
rotund moth
tepid hamlet
,rotate
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tepid hamlet
you can use sin(2x) = 2sin(x)cos(x)
and cos(2x) = cos^2(x)-sin^2(x) identities and then use that triangle you drew to find sin x and cos x
rotund moth
Should I use sqrt(119) as a side for the triangle?
tepid hamlet
you drew the triangle somewhat off actually, remember tangent is opposite over adjacent
rotund moth
Yeah but I don’t know what I’m doing wrong with the drawing?
tepid hamlet
your theta is not the right angle
tepid hamlet
theta is never the right angle
rotund moth
That’s right. Thanks
tepid hamlet
so what is the length of the hypotenuse?
rotund moth
13
rotund moth
12/13 is sin (x) and cos (x) is 5/13
tepid hamlet
pay attention to signs, 2nd quadrant meaning what?
rotund moth
Negative x, and positive y
rotund moth
Negative sin and positive cos?
tepid hamlet
remember cos is just the function giving you the x values of the points on unit circle and sin is just the function giving you the y values on those points
sooo
rotund moth
Cosine would be a negative value and sin would be positive?
tepid hamlet
ya
you can always think of the signs of cos \ sin in various quadrants as having same signs as x / y values there
-
- in 1st, - cos + sin in 2nd, - both in 3rd, +cos and -sin in 4th
cause x = cos theta and y = sin theta
you learned cos and sin in terms of the unit circle right?
tepid hamlet
so good to keep this idea in mind, the geometric interpretation of cos sin, all that it's saying is that if you take that angle theta, and you see what point on the unit circle goes with it, the coordinates of that point are (cos theta, sin theta)
so you can see where sin^2 + cos^2 = 1 comes from, that's just simply pythagorean theorem applied to that right triangle, since the unit circle has radius 1 (the hypotenuse of the triangle)
rotund moth
I understand now
tepid hamlet
12/13 is sin (x) and cos (x) is 5/13
so anyway now yeah you have - cos and + sin and you can use the whole sin(2x) = 2 sin x cos x thing and just plug in the values on the right to get sin(2x)
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wraith hinge
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wraith hinge
Can someone help me with k
charred trail
just need to simplify it?
wraith hinge
I’ll give u an example 3(x-4) is 3x-12
charred trail
okay yeah so you are just expanding the brackets sure
so k is: -ab(a^2+b^2). we distribute the -ab, and then simplify, recognising that (a^m)(a^n) = a^(m+n), and so on
wraith hinge
So a^2 is 1+2 that’s how they got 3? As a replacement
charred trail
yes so the first term is (-ab)(a^2), and because a = a^1, we get that (-ab)(a^2) = -ba^3
we do a similar process for (-ab)(b^2)
charred trail
haha dont slack over spring break 🙂 lol
charred trail
any order is fine, multiplication and addition are commutative, i.e. x+y = y+x and xy=yx, so order doesnt matter if that is what your question is
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wraith hinge
any order is fine, multiplication and addition are commutative, i.e. x+y = y+x a...
Then how do ik to put -a3 b-ab3
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amber ivy
Ok so say you have (2x^2) * (x+2) you would multiply 2x^2 into each term into the second so (2x^2) * (x) + (2x^2)*(2)
and then you would get 2x^3 + 4x^2
@wraith hinge
main olive
$\int\sqrt{t^2+t^4}\dd{t}$
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Jash
autumn trout
trig sub
autumn trout
what did you learn
main olive
what did you learn
u sub ibp etc
autumn trout
so try a u sub
main olive
with what
main olive
so try a u sub
u=?
gaunt harness
this requires a double usub
tough tusk
Im trying to do inflation with over 5 years and im confused. do i add the yearly expenses and the inflation together to get the expenses after 5 years with inflation?
tough tusk
neat slate
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neat slate
Hi guys, for the next part am I able to bring the ^2 out in front of the lim?
strong zinc
Hi guys, for the next part am I able to bring the ^2 out in front of the lim?
Would your result change if you do or don’t?
sacred sapphire
<@&268886789983436800>
tribal jetty
sorry i still rather eating mcdonodlsw
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round galleon
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round galleon
i help needis
needism of help
helpmeism
helpuism
anyways
what do i do with 2x-2? now knowing that x+5=3x-4
mystic veldt
what's the question asking for? x?
round galleon
yep
mystic veldt
these vertical sides are given equal, so you just equate them and find for x
round galleon
these vertical sides are given equal, so you just equate them and find for x
wait so thats it?
mystic veldt
i guess so
i mean those double strikes are used to indicate that these 2 sides are equal
so this should be it
round galleon
x+5=3x-4, subtract 5 and 3 both sides …-2x=-9 divide then i get 4.5
round galleon
so this should be it
so i do nothing with 2x-2 then?
mystic veldt
only if they've asked you to calculate length of tha side
otherwise there is no need
round galleon
oh ic ty
mystic veldt
np
round galleon
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quasi apex
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quasi apex
I need to prove that these sequences either converge or diverge
using epsilon-N proofs
I know the first one diverges because the limit does not exist
but i'm struggling with the actual proof
cedar moss
@quasi apex this sequence is either 1 or 3 for all n, right?
cedar moss
Yes
The idea here is this
You want to say that for every real number L, the sequence does not converge to L, right?
quasi apex
i need to do this using the epsilon delta definition of divergence
$\forall M > 0, \exists N > 0$ s.t $n > N \implies a_n > M$
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aguaman
quasi apex
i have no idea where to even begin with this proof
cedar moss
What's the negation of epsilon N?
cedar moss
Yeah that'll vaguely be how the quantifiers go
To be exact
a_n -> L means, for all eps there is some N such that |a_n - L| < eps for all n≥N
a_n fails to converge to L if there exists some eps such that for all N, there exists n≥N with |a_n - L| ≥ eps
cedar moss
It's not even "instead" so much as, it's just unwrapping negation through quantifiers
cedar moss
**aguaman**
Oh wait I just read this more carefully
This is not the definition of divergence
This is when a sequence diverges to infinity
cedar moss
Sure. So the idea conceptually is this
For every L, we either have L is not equal to 1, or L is not equal to 3
If L is not equal to 1, the fact that we have infinitely many 1s kills convergence. If L is not equal to 3, having infinitely many 3s kills it
How does this look formally?
Well, assume L≠1. Then pick epsilon = |1-L|/2. Then for any N, we pick some even number n ≥ N. Then |a_n - L| = |1-L| = 2eps > eps
quasi apex
so my proof so far is
Assume L != 1, choose epsilon = |1 - L|/2
we have
|a_n - L| >= epsilon
|2-(-1)^n - L| >= epsilon
@cedar moss what should I do from here
cedar moss
|2-(-1)^n - L| >= epsilon
This is for n even in particular. So there is no N such that |a_n-L| < eps for all n≥N. Since I can always find one for which that's false
On the flip side, if L=1, then I take eps = 1. Then for all odd n, |a_n-1| = 2 > eps
So in particular, there is no N such that the distance is less than eps for all n≥N
wraith hinge
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wraith hinge
this problem is so confusing 😭 i don’t even know where to start
ik the concepts of similar triangles
but like how do i even set this up
frozen plover
what two triangles are similar in this case?
wraith hinge
okay so we got
that top little triangle
and then the whole triangle itself
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slow owl
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last rune
when does \sqrt{x+2} have real solutions?
knotty locust
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heady gulch
Can anyone tell me where I went wrong with this? I’m trying to Laplace transform cos(t) between 0 and pi
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whole coral
.on that third line, cos(pi) is -1, so you should have e^{-pi * s}/s there, but think that's the only thing?
wraith hinge
is there a name of a function of this shape? i swear i remember something like this
wraith hinge
Like something similar to a Haar wavelet
this can be expressed in heaviside functions of course but i really think there is some name to this general shape
scarlet escarp
hard sigmoid?
looks like a sigmoid in general and it seems "hard" is the denotation for sharp here
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sour talon
any idea how to right this as Taylor Young 's formula for x0 = 0
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any idea how to right this as Taylor Young 's formula for x0 = 0
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worthy dove
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thorn sparrow
they should be a insert equation in the insert tab of whatever app youre on
just paste this into the equation box there
umbral maple
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umbral maple
from this graph I have to give it in interval notation
The answer is [-4,0] U [1, infinity) but I don’t understand why they picked those two parts of the graph instead of let’s say the part before -4 or the part between 0 and 1
quick tusk
The answer is [-4,0] U [1, infinity) but I don’t understand why they picked thos...
When you do "interval notation", you need to define what the interval represents. For example, it could be the interval where the y value is greater than 10, negative, increasing, etc. In this case, the interval appears to be when the y value is negative.
So you're missing info, "I have to give it interval notation" can't be done without saying something like "where the y value is positive" (for example).
umbral maple
I got the graph from f(x) = 4x-3x^2-x^3
quick tusk
yeah but what do you want your "interval notation" to represent
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raw rapids
hello, I just need someone to explain how to get tan^2x(1-sin^2x) in this image.
burnt mulch
Factor out tan^2 x
raw rapids
thank you, but can you give me like a breakdown
I'm really confused how to factor them
burnt mulch
$\tan^2 x \cdot 1-\tan^2 x \cdot \sin^2 x=\tan^2 x(1-\sin^2 x)$
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Civil Service Pigeon
burnt mulch
Idk how to make it clearer tbh
raw rapids
oh okay! I just need to know how to factor them..
rugged latch
$a-ab = a(1-b)$
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Stephen
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scarlet hawk
Can anyone help me with partial derivatives?
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scarlet hawk
I need to find the profit maximizig output level
Do i get this level by deriving R(q) and C(q)? And then doing R’(q) - C’(q) ?
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quick hound
how do i do this witohut calculator?
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how do i do this witohut calculator?
quick hound
i did the uh
this sub
with the 1+cos(2x)=2cos^2(x) substitution
and its just like
i cant calc this without calculator
any ideas?
leaden glacier
with the 1+cos(2x)=2cos^2(x) substitution
U can open cos² 4x like that
And subsitutde cos2x as u
And -2sin2xdx would be du
It should get simpler
Oh wait no
My bad
Cos²4x would become 8x if u do that right
Then yeah write cos²4x as (cos8x+1)/2 and multiply sin2x into it and apply the half angle formulae for sin2xcos8x and regular integration for sin2x
That should do
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quick hound
Then yeah write cos²4x as (cos8x+1)/2 and multiply sin2x into it and apply the h...
yeah thats what i did
but i cant do like
sin10x without calculator
ill try the usub
i think that can work
ohh
wait
yeah
wait
how
quick hound
Then yeah write cos²4x as (cos8x+1)/2 and multiply sin2x into it and apply the h...
u know how to do this without calc?
is there any way to make it not like cos8x
wraith hinge
change cos²4x to (2cos²2x -1)²
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fathom light
Help me please.
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wraith hinge
Help me please.
c = 2a - 3a³
int (0 to a) 2x - 3x³ - c = 0
2 equations 2 unknowns
wraith hinge
represent what
fathom light
to solve these equations together
wraith hinge
simplify the integral first
fathom light
$\int[2x-3x^3]$
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ElPanaArturo
fathom light
$\int[x^2-\frac{3x^4}{4} + c]$
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ElPanaArturo
wraith hinge
u should add that x to c aswell
wraith hinge
c = 2a - 3a³
int (0 to a) 2x - 3x³ - c = 0
this c
fathom light
why
wraith hinge
if u integrate 2x - 3x³ - c
u get x² - 3/4x⁴ - cx
wraith hinge
should be -cx
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ElPanaArturo
fathom light
$a^2-\frac{3a^4}{4} - ca=0$
wraith hinge
=0 yes
wraith hinge
c = 2a - 3a³
int (0 to a) 2x - 3x³ - c = 0
use this
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ElPanaArturo
wraith hinge
change c to 2a - 3a³
wraith hinge
**ElPanaArturo**
here
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ElPanaArturo
fathom light
$-\frac{3a^4}{4} -a^2+3a^4=0$
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ElPanaArturo
fathom light
$\frac{9a^4}{4} -a^2=0$
solid kilnBOT
ElPanaArturo
wraith hinge
a>0
wraith hinge
from this
solid kilnBOT
ElPanaArturo
fathom light
$a^2(\frac{9a^2}{4} -1)=0$
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ElPanaArturo
fathom light
$a=0, a=\frac{2}{3}, a=-\frac{2}{3}$
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ElPanaArturo
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cloud grail
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cloud grail
plz help
delicate belfry
Draw a line that is perpendicular to the lines.
late flume
yep
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brave pagoda
This is a rule. Those 3 angles add up to 360 if upper and lower lines are parallel
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lapis blade
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lapis blade
hi can someone help me use polar coordinates and squeeze theorem to solve this
I get really confused on how to use squeeze theorem when dealing with these kind of limits
I am not even sure if im supposed to use polar coordinates or not btw i just plugged this into a calc and it said you should
lapis blade
ok so why is the original function greater then 0?
blissful bison
module, can you see it ?
lapis blade
I have done trig in a while so its prob somethign to do with that
yes i can see your attachment
blissful bison
k, good)
lapis blade
I can see that the upper bound is going to 0 but why is the lower bound greater then 0 or equal to
lapis blade
Yes I am just confused why the lower goes to 0
blissful bison
lim 0 = 0
lapis blade
ok
blissful bison
no need to use polar coords here, it wud be too much
lapis blade
ok thank you!
blissful bison
yw)
blissful bison
ok thank you!
also remember that if in the product one factor tends to zero and the other is bounded, then the entire product tends to zero
lapis blade
ok this is really good to know ty
lapis blade
Ok so since sin goes to 0 and arctan is bounded that means that the upper is 0 and the lower is 0 so it is 0?
blissful bison
yes)
because:
and if you add sinus on both sides, then lower and upper goes to zero as you said
lapis blade
ahh ok wait i see because then you can set both to 0
blissful bison
yes that is squeeze theorem
but knowing this fact i told you before, we knew it even without it
lapis blade
gotcha
exotic pumice
!help
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whole flower
when I set this integral with respect to x the area i get is 8, but with respect to y i get a decimal number thats way larger than 8
whole flower
kinda stuck idk where I went wrong
wraith arch
the area that you shaded there is incorrect
notice that it’s bounded by x=-1 and x=1
wraith arch
yep
your integral bounds should be a little different now
since the right and the left function changes when y=1
wraith arch
i still get the same result tho
can you show me your final integral expression
whole flower
whole flower
can you show me your final integral expression
oki
wraith arch
ywyw
whole flower
calc 2 fried my brain and its just the third week lol
whole flower
i hope so haha
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zinc raft
-16(1)^2
What do I do first?
1^2 = answer
Answer times -16
Or
-16 times 1 = answer
Answer ^2 = answer
?
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dqvidutzul
spiral socket
or $(-16\cdot1)^2$
solid kilnBOT
dqvidutzul
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ripe topaz
-16(1)^2
What do I do first?
1^2 = answer
Answer times -16
Or
-16 times ...
exponent first
true aurora
i'm opening this channel en behaf of lana since i lost acces to the channel for some reasons, @wintry crater, can we please continu over here ?
wintry crater
i'm opening this channel en behaf of lana since i lost acces to the channel for ...
hello!
yes please haha im not sure what happened
true aurora
.close
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potent bone
yes please haha im not sure what happened
the channel got closed because you deleted the original message
true aurora
.reopen
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✅
potent bone
#help-22 message here's the previous channel
true aurora
alright, can you please send your calculs again?
wintry crater
true aurora
,rotate
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true aurora
oh ok
wintry crater
but how does that affect the right hand side?
true aurora
the pi * cos(pi*y) should end up under in the answer
wintry crater
why?
true aurora
i'm still looking for the why, but that's the answer my calculator gave me
wintry crater
ah okay because im also confused if pi cos (pi y) - dy/dx -2xy -x^2 dy/dx =0 is the differentiated bit
how does that part end up underneath?
true aurora
because $\frac{d \sin(\piy(x))}{dx}=\pi\frac{d y}{dx}\cos(\piy(x))$
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nico
wintry crater
why have u done y (x)?
true aurora
because i solved it using implicit derivation
wintry crater
yes me too but idk where that came from
ive done it wrong ofc haha but im just a little confused
true aurora
no you did good
it's just by using implicit derivation, you say by default that y is a fonction of x, that's why i wrote y(x) you make it clear that y is a function of x
wintry crater
Is this the final answer?
wintry crater
the one above
true aurora
indeed
wintry crater
yaaaay!!! thank you nico!!!
if i put in say (2,1) would i write that last bit as pi cos ( pi * (1)(2))?
true aurora
you would write simply pi cos ( pi * (1) )
wintry crater
so the x is just there after we differentiate theres no real value to it?
wintry crater
unless you need to find the y using the function there was before differencing
mmm okay thank you so much for your help ^^
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terse portal
hi
tribal jetty
if r=1 or r=-1 by trial and error the whole expression = 0
so (r-1)(r+1) = r^2+1 are factors of it, then you can try to divide everything by that
tribal jetty
nevermind im dumb asf
terse portal
lol so how is it then?
terse portal
if r=1 or r=-1 by trial and error the whole expression = 0
bro what do u mean even here xD?
terse portal
it does not say anything important
it just says this is a solution for the diff which is by r=+-i and where r^2+1 is a factor (F-s)
@tepid hamlet bro can u help me with this one?
tepid hamlet
!xy
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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.
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terse portal
nope
terse portal
wait wrong one lol
bro i know the information instead of giving me a lecture u can teach me the math where i need help lol
tepid hamlet
reading comprehension:
Please do not ping or DM individual users about your question.
but now you ping me a 2nd time?
tribal jetty
idk in your defense it has already been 15 minutes
tepid hamlet
idk in your defense it has already been 15 minutes
it wasn't the 15 minutes part that was relevant it was this: "Please do not ping or DM individual users about your question."
tribal jetty
my bad
tepid hamlet
just common courtesy, don't ping random individuals just because they answered a question of yours a previous day, why is this so difficult?
floral sinew
am bad at math can i get help please (=
terse portal
am bad at math can i get help please (=
create the help bar up there bro not here
floral sinew
id ont know how server works its my first time am sorry
tribal jetty
sorry I don't know the other division 'syntax'
notation idk
by trial and error r = 1 is a solution
so we must be able to rewrite the expression as factors(r-1) = 0 to just plug r=1 so it becomes 0
(r^4+r^3-r^2+r-2) = factors(r-1)
factors = (r^4+r^3-r^2+r-2)/(r-1)
then you continue factorizing ok
terse portal
why factors with r-1?
i think the way u have done it is wrong mate
becuase idk what it is called in english
tribal jetty
r-1 is a factor because r=1 is a solution
terse portal
but how do u know from the beginning that r=1 is a solution?
tribal jetty
trial and error
terse portal
and how do u do that?
terse portal
bro its okay thx for the shot u giving
but i think there is a another way we need to approach the question to solve it
tribal jetty
prob
terse portal
.close
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viscid spear
are the following statements correct?
- if a graph is not planar, it is not planar after adding a node
- if a graph is not planar, it is not planar after adding an edge
- if a graph is not planar, it is not planar after replacing an edge with a node and edges to both original nodes
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are the following statements correct?
* if a graph is not planar, it is not plan...
@viscid spear Has your question been resolved?
edgy willow
are the following statements correct?
* if a graph is not planar, it is not plan...
yea those are all true, they don't help you draw it on a plane
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grand sable
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grand sable
what did i do wrong
rugged latch
10(2) + 22 = ?
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grand sable
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lapis star
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wooden hamlet
How do we do this if we only have one side
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How do we do this if we only have one side
wooden hamlet
I know we would do a2+b2=c2
scarlet escarp
have you heard of the law of sines? if not, have you heard of a 30-60-90 triangle?
wooden hamlet
have you heard of the law of sines? if not, have you heard of a 30-60-90 triangl...
Yea I know the second thing
scarlet escarp
well look at the angles you have
one is 90, the other 60
what must the last one be
wooden hamlet
How would that help us find sides tho
scarlet escarp
because the side ratios are well known for a 30 60 90 triangle
so if you know one, you know all of them
wooden hamlet
But isn’t that only angles and not sides?
scarlet escarp
yes, but a 30 60 90 triangle has well known side ratios as well as the angles
wooden hamlet
What’s a side ratio sorry
scarlet escarp
like if you know one side, you can deduce the rest
scarlet escarp
the hypotenuse, yeah
scarlet escarp
do you know the formula for area of a triangle?
scarlet escarp
b*h/2
wooden hamlet
Nope def not
scarlet escarp
base * height / 2
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trail ingot
@scarlet escarp
austere zealot
I get confused at manipulating logic operations, when there's more than one statement involved
austere cedar
You're trying too hard to make it symbolic
You can explicitly say what you mean in English
"Consider the case that x ∈ A. Since A ⊆ C, this implies x ∈ C"
scarlet escarp
<@217089972933623808>
austere cedar
Then eventually "since both cases lead to x ∈ C, A U B ⊆ C"
gusty quarry
Help
gusty quarry
Confused with 3f
Specifically the instructions where it asks to reduce to ref
The process doesn’t bother me but I’m confused what matrix I’m using to do that with
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.close
late hound
what's the derivative of e^e^x
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what's the derivative of e^e^x
scarlet escarp
what have you tried
scarlet escarp
yes
blazing dawn
It's sketch asf
late hound
It's sketch asf
?
left oriole
if you don't know, why are you typing in rvce's doubt channel?
late hound
Then take the log
@hereis this valid?
blazing dawn
It's totally valid.
scarlet escarp
yes, but you'd be using implicit differentiation
if you're not familiar with that, just use the chain rule
left oriole
it's one line if you use the chain rule, what's the concern?
late hound
yeah
late hound
explain
late hound
okay...
scarlet escarp
[y = e^{x^x} \implies \ln y = x^x]
solid kilnBOT
maximo
late hound
that makes sense
scarlet escarp
though again, do you know implicit differentiation?
late hound
yes
scarlet escarp
ok
late hound
but I'm not sure how to deal with the x^x
blazing dawn
late hound
what's the difference?
scarlet escarp
one is e^(x^2) the other e^(x^x)
anyway, now we have
ln(z) = xln(x)
and ln(y) = x^x
we want to find y'
late hound
oh ok
scarlet escarp
so we do implicit diff. on the second equation there
which gives y'/y = (x^x)'
or y'/y = z'
let me know if you are lost
late hound
um
blazing dawn
That's why I used f(x)
blazing dawn
y is a function of x
scarlet escarp
ln(z) = xln(x)
and ln(y) = x^x
y = e^x^x
so ln(y) = x^x
then we just say z = x^x
late hound
okay I see
scarlet escarp
so ln(z) = ln(x^x) = xln(x)
and we have our two equations
ln(y) = x^x = z
and ln(z) = xln(x)
late hound
yeah
scarlet escarp
if we want y', we implicitly dif.
y'/y = z'
so y' = z' * y
but now we need z'
so you implicitly dif. the second equation
ln(z) = xln(x) -> z'/z = ln(x) + 1
or z' = (ln(x) + 1)z
scarlet escarp
sure
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merry zodiac
Y=2x+sinx is bijective
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Y=2x+sinx is bijective
merry zodiac
How to check it will be one one and onto
blazing dawn
How do you know it's one one?
left oriole
check its derivative
blazing dawn
Given?
merry zodiac
No we just need to check
merry zodiac
check its derivative
2+cosx
merry zodiac
How do you know it's one one?
We just need to check
merry zodiac
Derivative is continuous
merry zodiac
And one one?
merry zodiac
I guess no