apple is 1?
#help-42
autumn tusk
yeah
dull wagon
write out the whole thing
don't oversimplify the description to
answer is no.1
because i have nfi what you mean by that
autumn tusk
You have an expression a + b = c, where
a = c - b
b = c - a
c = a + b
If you eliminate the expression (a + b = c where a = c - b, b = c - a and c = a + b you get -2a - 2b + 2c = 0) and the given question (a + b = c) you get δ1. Then continue simplifying the expression with (a = c - b, b = c - a and c = a + b) . Every time you simplify the expression eliminate with the δ1, δ2,δ3 till infinity.
now?
autumn tusk
ok
listen
so
the
question
a+b=c
i gave the values of a, b, c
so
input the values of a,b,c
in the question
that is
δ1
dull wagon
still have nfi what you're getting at...
dull wagon
answer to what
you're still being extremely unclear in your explanation
you just ended up with an equivalent equation
autumn tusk
Substituting the values of a, b, c in the expression a + b = c you get [ (c - b) + (c - a) = (a + b) ] = -2a - 2b + 2c = 0, consider this solution as “Expression 1”. Now try to eliminate “Expression 1” and the given question (a + b = c), you get:
-2a - 2b + 2c = 0
a + b - c = 0
-3a - 3b + 3c = 0
Consider -3a - 3b + 3c = 0 as “Solution 1”
We know that “Expression 1” has different variables like a, b, c (-2a - 2b + 2c = 0), so now plug in the values of a, b, c in “Expression 1” you get [-4(c - b) - 4(c - a) + 4(a + b) = 0] = 8a + 8b - 8c = 0, consider this solution as “Expression 2”. Now eliminate “Expression 2” and “Solution 1 ” we get:
8a + 8b - 8c = 0
-3a - 3b + 3c = 0
11a + 11b - 11c = 0
Consider 11a + 11b - 11c = 0 as “Solution 2 ”
We know that “Expression 2” has different variables a, b, c (8a + 8b - 8c = 0), so now plug in the values of a, b, c in the “Expression 2” we get [8(c - b) + 8(c - a) - 8(a + b)] = -16a - 16b + 16c = 0, now consider this solution as “Expression 3”. Now eliminate “Expression 3” and Solution 2” we get:
-16a - 16b + 16c = 0
11a + 11b - 11c = 0
-27a - 27b + 27c = 0
It goes on till infinity
Hence, we get a series of -, -, + and -, +, +
We get -, -, + when we eliminate a greater even expression and a least odd expression of:
-ax - bx + cx = 0
ay + by - cy = 0
-az - bz + cz = 0 (-, -, +)
Where “x” is constant through the entire expression having the same value which is plugged in with a, b, c where a, b, c is greater even expression. “Y” is constant through the entire expression having the same value which is plugged in with a, b, c where a, b, c is lesser odd expression. And “z” is the constant value that we get after the elimination.
We get +, +, - when we eliminate a greater even expression and a least odd expression of:
ax + bx - cx = 0
-ay - by + 3c = 0
az + bz - cz = 0
Solutions for the given expression goes on like
-az - bz + cz = 0
az + bz - cz = 0
-az - bz + cz = 0
az + bz - cz = 0
…..
And so on
Hence, for the expression a + b = c where
a = c - b
b = c - a
c = a + b
dull wagon
and gave it a different name
autumn tusk
here
dull wagon
a = c - b
b = c - a
c = a + b
are all different forms of the original equation
doing substitution into itself like this will either yield a trivially true statement or something equivalent to what you started with
a + b = c isn't really a question
autumn tusk
yeah they are different forms of the original equation
it is
when u read the question fully
dumb!
.close
calm coralBOT
calm coralBOT
Available help channel!
thorny sorrel
thorny sorrel
why is this not -\sin\left(te^{-3t}\right)\left(-3t\right)\left(te^{-3t}-1\right)e
potent lotusBOT
cookie2
calm coralBOT
@thorny sorrel Has your question been resolved?
calm coralBOT
@thorny sorrel Has your question been resolved?
calm coralBOT
@thorny sorrel Has your question been resolved?
gentle peak
hello
dawn narwhal
hello
marsh agate
x² = 4. So x = +- sqrt(4) = +- 2
gentle peak
ye how is it xto the power of 2 =4?
marsh agate
just divide each side by 5
gentle peak
why's that
marsh agate
that it becomes x² = 4 ?
marsh agate
4x² = 8 ? Same, divide by 4, gives x² = 2, so x = +- sqrt(2)
marsh agate
4 divided by 2 - 10 = x=+0 sqr of 2?
what
gentle peak
wdym what
marsh agate
didn't understand a single part of that sentence
marsh agate
you don't divide by 2 numbers
marsh agate
then just say 4 / (-8)
gentle peak
so am i wrong or right
marsh agate
what are you trying to do
marsh agate
4x² = 8 ? Same, divide by 4, gives x² = 2, so x = +- sqrt(2)
I don't understand what you are doing with this equality
celest scarab
is this integration by parts no matter which way i go?
calm coralBOT
is this integration by parts no matter which way i go?
celest scarab
alpine stone
Unless you integrate with respect to y first and then x
opaque dune
I'd imagine integrating with respect to y first will give you the simplest path to the answer.
celest scarab
i thought so too
its still gonna be integration by parts tho isnt it?
its been a while lol..
alpine stone
No, rather u-sub
opaque dune
Yep. Just checked and it looks like a obvious substitution problem after that.
celest scarab
sad that I was going to attempt the usub off the rip but instead just overlooked it.
thanks guys
opaque dune
Should get e^(16) - 1 it seems from a quick calculation. The clue was the coefficient of the exponential being one degree lower than the exponential term.
celest scarab
oh darn
i misread the problem i think
you meant higher?
one degree higher right?
opaque dune
$\int_{0}^{2} 6x^2 e^{2x^3}\dd{x}$.
potent lotusBOT
stabulo
opaque dune
Notice the derivative of 2x^3 is conveniently 6x^2.
If u = 2x^3 then du = 6x^2dx so it quickly simplifies to
opaque dune
$\int_{0}^{16} e^u \dd{u}$.
potent lotusBOT
stabulo
celest scarab
like i said its been months since i've done integration
sad i forget it all so fast lol.
opaque dune
😢
celest scarab
i forgot the 6
in front of the problem when i wrote
so it threw me off completely lol
thanks again!
celest scarab
.close
vale valve
Anybody know how to answer this?
calm coralBOT
Anybody know how to answer this?
wise spire
what are conditions for two quadrilaterals to be congruent?
calm coralBOT
@vale valve Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
real stirrup
Hi I would like to know if I’m doing these problems correctly so far
real stirrup
this is my problem
https://www.youtube.com/watch?v=QaAQ-bKCUME&list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz&index=33 this is where im learning the material
calm coralBOT
@real stirrup Has your question been resolved?
calm coralBOT
@real stirrup Has your question been resolved?
calm coralBOT
@real stirrup Has your question been resolved?
calm coralBOT
@real stirrup Has your question been resolved?
calm coralBOT
@real stirrup Has your question been resolved?
wise spire
which problem?
wise spire
ok share it first
calm coralBOT
@real stirrup Has your question been resolved?
stark marlin
sharp canopy
Hi I would like to know if I’m doing these problems correctly so far
NO! You were not supposed to express solutions like that!
@real stirrup you here?
real stirrup
Yes I am
real stirrup
<@338255141235064846> you here?
I’ll be back later, I hv class
formal garnet
.close
loud pumice
a,b are coprime, solve for a+b without partial fractions
calm coralBOT
a,b are coprime, solve for a+b without partial fractions
wise spire
decompose each term
loud pumice
?
loud pumice
i cant use them Modus
wise spire
i mean for example, 7/3^2*4^2 can be rewritten as 1/3^2 - 1/4^2
loud pumice
i cant use them Modus
haven't done them
loud pumice
i mean for example, 7/3^2*4^2 can be rewritten as 1/3^2 - 1/4^2
still using pfd
well let's skip that nvm
new problem:
A number is said to be multiplicatively perfect if, by multiplying all its positive divisors, we obtain n ^ 2.
How many multiplicatively perfect numbers are there less than 100
.close
cerulean temple
Hey, I'm currently trying to learn thales' theorem. Could anyone explain it to me ?
royal salmon
Hey, I'm currently trying to learn thales' theorem. Could anyone explain it to m...
it's just that if there's an inscribed triangle with a right angle, the hypotenuse is the diameter
it's easy to see from this theorem
cerulean temple
it's just that if there's an inscribed triangle with a right angle, the hypotenu...
Hm, I see. I was mostly wondering about the way to prove it. I've heard that proving it is really long/complicated
royal salmon
as in that case, the angle would be 180, so the angle on the circumfernece would be 90
royal salmon
Hm, I see. I was mostly wondering about the way to prove it. I've heard that pro...
hm I don't think it's complicated
let me have a look
oh yeah I remember this proof
do you want me to just shhow you it or do you want a hint
cerulean temple
I'd prefer you showing me. I don't have any excercises to do it on, just trying to learn it
royal salmon
alright gimme a sec
cerulean temple
take your time
royal salmon
what are the sum of the angles equal to @cerulean temple
also they're isoscleles cus AO OC AND OB are all the radius
cerulean temple
what are the sum of the angles equal to <@931659740738646126>
shouldn't it be 180 degrees ?
cerulean temple
90 ?
cerulean temple
Oh yeah, one sec lets see
cerulean temple
in terms of alpha and beta
alpha + beta = 180 no ?
unless im missunderstanding it completely
cerulean temple
right angle ?
I do apologise if im getting this wrong, english isn't my native language so i might be getting half this stuff wrong :/
royal salmon
triangle AOC is isosceles, so angle CAB = angle ACO
angle ACO is alpha, as I labelled
so angle CAB is alpha
using the same logic what's angle CBA
cerulean temple
OCB ?
royal salmon
so angles in triangle ACB = 180 = alpha + (alpha + beta) + beta
180 = 2 alpha + 2 beta
do you see the final step to finish the proof?
cerulean temple
Sadly no
cerulean temple
Ohhhhh
royal salmon
QED
royal salmon
no problem
wise stag
Why is this wrong
wise stag
<@&286206848099549185>
calm coralBOT
@wise stag Has your question been resolved?
loud pumice
A number is said to be multiplicatively perfect if, by multiplying all its positive divisors, we obtain n ^ 2.
How many multiplicatively perfect numbers are there less than 100?
calm coralBOT
A number is said to be multiplicatively perfect if, by multiplying all its posit...
@loud pumice Has your question been resolved?
loud pumice
thanks bud
calm coralBOT
@loud pumice Has your question been resolved?
fossil juniper
hi
fossil juniper
If you know that Pr(E|H) is very high, then you find out E is true, does it logically follow that Pr(H) is very high?
calm coralBOT
@fossil juniper Has your question been resolved?
fossil juniper
do uk why u would say that?
amber bolt
i;m not a psychology expert?
fossil juniper
its not psychology
**When you’re translating an argument into symbolic language, what would happen if you replace one and the same variable with multiple sentences? **
<@&286206848099549185>
wise spire
"then you find out E is true" this phrase means nothing. whether an event happens or not doesn't change the probability
calm coralBOT
@fossil juniper Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
solar aspen
probability of 3 dices,addition of gained number is <7
calm coralBOT
probability of 3 dices,addition of gained number is <7
rustic osprey
honestly you may just want to figure out the cases in which the sum is less than 7, then divide that by the total number of possible combos (6^3 = 216)
solar aspen
if the first dice is 6,it fails
5 fails too
<7
not=
1: (4,3,2,1)
4,1,1
3,2,1
3,1,1
man this is annoying
too many probabilities
rustic osprey
man this is annoying
casework be like that sometimes
fair monolith
1 1 1
1 1 2
1 2 1
2 1 1
1 2 2
2 1 2
2 2 1
2 2 2
1 1 3
1 3 1
3 1 1
1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1
1 1 4
1 4 1
4 1 1
tell me if i missed any
solar aspen
about 112 and 121
are they the same?
it gives the same number in addition
but the second dice and third dice rolled different
fair monolith
assuming orders matter
fair monolith
1 2 1 means u get 1 on the first roll, 2 on the second roll, 1 on the third roll
solar aspen
but yeah
fair monolith
unless stated probably
solar aspen
its different on the host of the probability
fair monolith
cuz if it is "all dices are rolled on the same time" then orders dont matter
fair monolith
rolled at the same time
ahh ok, then ignore permutations
so just :
1 1 1
1 1 2
1 1 3
1 1 4
1 2 2
1 2 3
2 2 2
solar aspen
the only numbers are (1-4)
fair monolith
yes
solar aspen
(x+y+z)<7
fair monolith
ye
fair monolith
oh u're finding the denominator part?
solar aspen
oh u're finding the denominator part?
whats that
fair monolith
for the probability
so far u got P = 7/something
i assumed u were trying to find that something
solar aspen
im just trying to work out an equation that shows how the number affects the other numbers
idk if that's even possible
4,1,1
fair monolith
ohh
so like for example u roll a 1 on the first try
u want to figure out how the probability changes?
solar aspen
you must roll (1-4) on the second dice
but the second dice affects the number needed on the third dice
hurts my head
x=4 y=(1/6) z=(1/6)
x=3 y=(1/3) z=?
if y rolls a 2, z must get 1
but feels like its the same
just 2 and 1
lol
1 1
1 2
2 1
2 2
calm coralBOT
@solar aspen Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
winter hazel
does this hold for m=0? we cant use geometric series if m=0 right? also what if m>0, does this still hold? or is there anything we can use?
calm coralBOT
does this hold for m=0? we cant use geometric series if m=0 right? also what if ...
@winter hazel Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
copper stag
calm coralBOT
copper stag
Number 5
scenic valley
hi
coarse apex
Number 5
Purely imaginary means real part is 0
Just consider the real part to be 0 and see what you get
coarse apex
I feel like you should get a circle
copper stag
i got y squared - yi - 2y -2
is that the equation of circle?
@coarse apex
Or is that a semi circle assuming that the equation of the circle is x²+y²-2ax-2by-c XD
coarse apex
i got y squared - yi - 2y -2
How did you get that
coarse apex
I may have calcation error but the technique
No
They are not saying that Z is purely imaginary
It says that the whole function is purely imaginary
x is the real part of Z, not real part of (Z-2i)(zbar-1)
copper stag
Ignore the upper part
Its the circled one
Like this ?
Should i cross the the real part now ?
Oh wait maybe it
Should draw the circle then say that it only moves on the diameter of the circle (the one perpendicular to the x axis cz its imaginary)
copper stag
Lemme draw it for demonstration
coarse apex
Just equate that to 0
copper stag
Yea but then the imaginary part is an equation of two unknowns
coarse apex
Yea but then the imaginary part is an equation of two unknowns
So?
coarse apex
Oh ok then the radius and venter are unkown
Why do you think so
Do you know how to find the radius and center from the equation of a circle?
copper stag
No
copper stag
Oh i wait yes i get it -2ax and -2by calculate the coordinates of the center
C calculates the radius
Which is equal to redical a²+b²+r
X²+Y²-2ax-2by+c
coarse apex
Yes
fierce cradle
calm coralBOT
fierce cradle
I got -8 as my final answer.
Does that make sense?
I might’ve messed up I only learned it 2 days ago and I’m trying to understand
dull wagon
no, you've made some sign errors and some questionable decisions
like so many sign errors
x^2 - 8x + 15 factorises to (x-3)(x-5)
glacial junco
Sonny, you did some weird stuff after you got (x-3)(x-5)/(x-3)
dull wagon
there was no need for any of that sign manipulation and the invalid work that went with it
coarse apex
@fierce cradle what happened here
fierce cradle
there was no need for any of that sign manipulation and the invalid work that we...
I was trying to replicate the sign changes my professor made:
dull wagon
don't blindly do patch work
fierce cradle
I didn't I swear that expression could factorize and I needed to do sign manipulation
dull wagon
note that the reason the factored -1 out was because their coefficient of x^2 was negative
which makes it easier to factorise
the coefficient of x^2 was already positive, factoring out -1 like that is unwarranted
also note that you had
(x-3)(x-5) expanding out to
x^2 - 5x -3x +15
which is actually x^2 -8x+15
and not the x^2 **+**8x +15 you wrote below that
,W factorise x^2-8x+15
potent lotusBOT
fierce cradle
also note that you had
(x-3)(x-5) expanding out to
x^2 - 5x -3x +15
which is act...
shit i messed up
Was the rest of the process right besides the sign changes?
dull wagon
no
fierce cradle
oh
dull wagon
for some reason the minus sign in
(x-5) turned into a +
fierce cradle
for some reason the minus sign in
(x-5) turned into a +
Yeah, because I was trying to manipulate the signs of the expression because I thought I couldn't factor the original one out.
coarse apex
Yeah, because I was trying to manipulate the signs of the expression because I t...
What were you tryna factorise here
fierce cradle
O
dull wagon
there's valid manipulation and then there's changing stuff on a whim
fierce cradle
Yeah I'm sorry this was just a bad attempt
coarse apex
X-5 = X+δ
dull wagon
without the first sign screw up, you'd have
lim as x to 3 of (x-5)
at which point you can sub in x=3
fierce cradle
Thanks again you guys are great
calm coralBOT
@fierce cradle Has your question been resolved?
blissful quest
Could you please expand $/frac{−5x+9}{x^2 −3x+2}$ using partial fraction expansion, and the substitution method for solving or variables.
potent lotusBOT
kangaroo rat
blissful quest
Thanks!
calm coralBOT
@blissful quest Has your question been resolved?
wanton steppe
calm coralBOT
wanton steppe
What number is this
5.99E-03*x + 16.5
.00599x
right?
just weird how theres a 03
am I right
need some confirmation
prisma mango
just weird how theres a 03
E-03 is the calculator's way to do scientific notation
blissful quest
Could you please expand $/frac{−5x+9}{x^2 −3x+2}$ using partial fraction expansion, and the substitution method for solving or variables.
potent lotusBOT
kangaroo rat
wintry glacier
$\frac{−5x+9}{x^2 −3x+2}$
potent lotusBOT
Gijs
blissful quest
yes
calm coralBOT
@blissful quest Has your question been resolved?
blissful quest
https://www.symbolab.com/solver/partial-fractions-calculator/partial%20fractions...
what is this step
calm coralBOT
@blissful quest Has your question been resolved?
blissful quest
it makes it easier to work out
Can you do that for all partial fraction expantion
calm coralBOT
@blissful quest Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
faint sage
hi, how does it become the second equation?
calm coralBOT
hi, how does it become the second equation?
faint sage
this is right, yes?
mellow crater
this is right, yes?
yes, but it gives you nothing if you want to solve for x
faint sage
yes, but it gives you nothing if you want to solve for x
I don't understand
coral osprey
hi, how does it become the second equation?
Distribute x, collect x terms, factor out x
empty creek
can someone point me in the right direction for this?
calm coralBOT
can someone point me in the right direction for this?
empty creek
i don't really know what to do here
real sentinel
draw 2 triangles
empty creek
yea i got that far too
real sentinel
find 2 expressions for h
remote mural
can someone point me in the right direction for this?
does "vertically challenged" mean short
that's really funny if so
but yeah, just draw a triangle of all the distances first
empty creek
so that answer i am getting is 3806 feet
but i used tan
but if i do cot i get 4166(?)
probably a problem in approximations
but mount doom is 4500
hmmm
real sentinel
what 2 expressions did you get for h using tan
assuming you labelled the unknown horizontal distance as something like x or a
that's what i did at least
empty creek
what 2 expressions did you get for h using tan
x tan 16 = (5000+x)tan12
empty creek
so that answer i am getting is 3806 feet
i calculated more precisely and i got 4115
real sentinel
what did you get x as
empty creek
14362
real sentinel
im guessing you rounded things like tan 16 and tan 12 then
empty creek
yes
real sentinel
if you can it's probably a good idea just to leave them as tan 16 and tan 12 in your calculations
otherwise you won't get the exact correct answer
empty creek
the question instructs you to round to the nearest hundred so i guess it's 4200
real sentinel
it's 4100
real sentinel
or at least that's what i got
real sentinel
i got 4107
empty creek
i wonder where is it that it's going wrong
real sentinel
wait so the answers give 4500?
empty creek
the book doesn't provide answers
but mount doom from lotr which the question is very obviously reffering to stands at approx 4500 feet
real sentinel
i mean i wouldn't trust the textbook to use the actual height of mount doom
empty creek
that's truee ig
real sentinel
Well depending on how well you round the answers fall between 3800 and 4200 so clearly they're just assuming mount doom is 4100 feet
empty creek
i guess i can move on then
they should have given nicer values ngl
or atleast told the height of mount doom
real sentinel
agreed
real sentinel
np
empty creek
.close
random stratus
i don't get why $\frac{jz - j}{z-j} \in \mathbb{R} <=> (jz - j)(z(bar) - j^2) \in \mathbb{R}$
calm coralBOT
@random stratus Has your question been resolved?
random stratus
<@&286206848099549185>
calm coralBOT
@random stratus Has your question been resolved?
solar badger
Hi, any ideas how should I mathematically prove that Dijkstra works for digraphs where the only negative cost arcs are those leaving the source node?
calm coralBOT
Hi, any ideas how should I mathematically prove that Dijkstra works for digraphs...
@solar badger Has your question been resolved?
solar badger
<@&286206848099549185>
calm coralBOT
@solar badger Has your question been resolved?
calm coralBOT
@solar badger Has your question been resolved?
sleek plover
You have two possibilities :
-By induction : at every step of Dijkstra, you have the shortest path to the frontier
-By contradiction : consider a strictly shorter path and the first vertex that's different from Dijkstra
solar badger
You have two possibilities :
-By induction : at every step of Dijkstra, you have...
what do you mean by "the first vertex diff from Dijkstra"
sleek plover
You take P the path you get from Dijkstra and P' the other path. You take the first vertex of P' that is not in P
tepid snow
calm coralBOT
tepid snow
Why isn’t there the possibility that x belongs to A and x belongs to C
Or X belongs to B and x belongs to A
Is it because we don’t care about these cases since when belongs to A, it actually satisfies A union (B intersection C)
remote mural
both of those cases belong in the 1st case (x∈A)
calm coralBOT
@tepid snow Has your question been resolved?
drifting bison
Hi, I'm trying to parametrize this but I'm not quite sure how to do so
drifting bison
Kinda confused about the concept of parametrization in general
calm coralBOT
@drifting bison Has your question been resolved?
supple needle
I'm not sure how well I can help with that problem but I can help with understanding parametrization
I'm relatively new to it too
drifting bison
Sure, I mean anything helps
supple needle
Parametric equations you can think of as a list of functions for each variable
So they'd be written something like $\alpha(t) = (\text{Function of x}, \text{Function of y}, \text{Function of z})$
potent lotusBOT
B\infty
supple needle
All in terms of t, which I guess could be anything
So the function f(x) = x + 2 could be written
$\alpha(t) = (t, t + 2)$
potent lotusBOT
B\infty
supple needle
Where the first part of that is how x behaves, and the second part is how y behaves with respect to x
steel grail
Hi, I'm trying to parametrize this but I'm not quite sure how to do so
This set is a little weird to parametrize because it is a tube and not a one dimensional curve
supple needle
Given f(x) = x + 2, f(5) would be 7
As such, alpha(5) would yield (5, 7) which is the point on the graph of f(5)
drifting bison
This set is a little weird to parametrize because it is a tube and not a one dim...
Yeah, that's what I'm a bit confused about as well. This is for a multivariable calculus course I'm taking
Oh sorry, I should probably mention, the constraint given is that a,b > 0
steel grail
Are you directly asked to parametrize this or is this to solve a problem?
drifting bison
The first part is to directly parametrize it
And then the second part is to use the parametrize to calculate the surface area by taking a double integral
steel grail
Can you parametrize it with a single variable or is two variables allowed?
steel grail
It doesn't have to be two variables, it just wouldn't be a continuous parametrization (and probably not suitable for what you need to do, for integration) if it was a single variable
But to do 2 variables you could do theta from 0 to 2pi and t for the y, yeah?
Something like (a cos(theta), t, a sin(theta)) where 0 <= theta < 2pi and 0 <= t <= b
drifting bison
ahh, I see what you're saying
And then finding the surface area I would just take the double integral of r dr d theta with the bounds you mentioned?
steel grail
I'm also taking multivariable calculus right now, but my class hasn't gotten into double integrals yet. I am unsure, but that is probably right.
drifting bison
Oh ok gotcha
Yea, that parametrization seems right to me, but I'm still a bit iffy on parametrization as a whole
Thanks!
steel grail
good luck
drifting bison
.close
glass meadow
If y=x has been stretched parallel to the x axis by scale factor 2, will it be a stretch in y or x and what's the numbers be?
glass meadow
Like x/2 or whatever
calm coralBOT
@glass meadow Has your question been resolved?
calm coralBOT
@glass meadow Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
magic palm
hey boys
limber nacelle
Hello
This is a isosceles triangle
And
CD and FE are the median
I've to prove that CD = FE
By vector method
Anyone??
calm coralBOT
@magic palm Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
blazing umbra
is 1|3 true or 3|1 true
i forget the order....
humble ivy
| stands for the word "divides"
so you have 1 divides 3 and 3 divides 1, which one is true?
blazing umbra
1 divides 3
humble ivy
yes
calm coralBOT
calm coralBOT
Available help channel!
round drum
what test would I use to determine convergence / divergence
calm coralBOT
what test would I use to determine convergence / divergence
visual nimbus
comparison I guess
round drum
limit or direct
visual nimbus
wdym
round drum
limit comparison or direct comparison
visual nimbus
hmm idk, what I have in mind is doing a taylor expansion
round drum
o does ln(k)/ k^4 not work
long canyon
Right, but that's not enough on its own for convergence of the series.
What tests do you know so far?
round drum
uhh
visual nimbus
Spoiler ||D'Alembert ?||
round drum
i know all the important ones
root integral geo tele ratio pseries
limit comparison direct comparison
long canyon
I'd recommend limit comparison with 1/k^3.
round drum
but wouldn't the limit diverge
o wait
k^3 mb
but that lim approaches infinity though
i mean it approaches
0
sorry
but anyways
long canyon
Lim of ln(k)/k should converge
round drum
yea to 0
long canyon
Ah, you have the weaker version of the test.
L<inf means converge -> converge and 0<L means diverge -> diverge
You can use integral test, but it's a bit annoying.
long canyon
Or just ratio to 1/k^3, assuming you also don't have a bad version of ratio test. 🙂
round drum
o wait
couldn't i just
use a direct comparison to ln(k)/k^2
since that converges and is always more than ln(k+1)/k^4
we can say that ln(k+1)/k^4 converges
long canyon
K=1 is sad for the standard direct comparison, but you can remove finite inital terms
And yes, that should work.
long canyon
Integral?
round drum
oh then i might as well just use ln(k)/k and make it easy on myself
long canyon
If only that converged
round drum
doesn't it
long canyon
Does it?
long canyon
The original question should converge
Because direct comparison with diverge doesn't mean that the first one diverges
solar spruce
you can just compare it to (k+1)/k^4
round drum
yea i still don't know about maximo's cause that converges to 0 and i just feel like sticking to the test I was taught
L<inf means converge -> converge and 0<L means diverge -> diverge
but ye ln(k)/k^2 worked
uhh now the last question i got
is
how do i do any of this
i just need one example and i could probably figure out the rest
long canyon
This is a concept question, testing if you understand what's going on.
long canyon
Try plugging in sn in the first one.
round drum
lim n > infinity Sn = L
long canyon
Yep
round drum
wtf that's so simple
when i see things that short i usually think to myself
am i doing it right so
long canyon
The only one that could be troublesome is c
round drum
yea was just thinking that
round drum
woudln't that laos
also just be L
yea all i can think of is L
since Sn = Ak where k is just heading to infinity
solar spruce
yea i still don't know about maximo's cause that converges to 0 and i just feel ...
if you have two series, a and b, and the terms of a < the terms of b, then if b converges a must converge as well
since (k+1)/k^4 = 1/k^3 + 1/k^4 is a convergent series, and ln(k+1) < k+1 for sufficiently large k, ln(k+1)/k^4 < (k+1)/k^4
so the series for ln(k+1)/k^4 must converge as well
solar spruce
i understand
i was just saying how my example works
because im sure you've learnt about the direct comparison test before
round drum
yea you're talking about the direct comparison i was looking at my limit comparison
that's my bad
long canyon
also just be L
No, this is asking about an, not sn
round drum
yea i get that
since Sn = Ak where k is just heading to infinity that was my line of thinking
long canyon
Sn is importantly ADDING up all the infinite an
long canyon
It's not the most obvious thing, but you can write an = Sn-S(n-1).
round drum
wat
i gotta think about that for a sec
o i guess that makes sense
its the current sum - previous sum which just gives the current value
but is that the answer? sn-s(n-1)
long canyon
Yep. And now you can substitute like in a
round drum
wat
long canyon
Plug that in to the limit
round drum
mmmmm i don't think i can
long canyon
In part a, you did one of the two parts
Lim n-> inf sn =L
So how about lim n-> inf S(n-1)?
long canyon
Yes, you're right, but that doesn't get us very far.
The trick is to see that lim n-> inf is the same as lim (n-1) -> inf
round drum
yea i dont know how u see that
long canyon
So Lim n-> inf s(n-1) =L
It's a conceptual question
If you're taking a limit, it doesn't matter if the n is off by 1
round drum
but
long canyon
You'll still get all the components in the sum
long canyon
Because of the limit
Sn means "add up everything to the n term"
Sn-1 means "add up everything to the n-1 term"
round drum
o wait
i feel stupid
they just reversed it on me
for a series to converge
ak has to go to 0
long canyon
But if we now take the limit as n goes to infinity, theyre both "add everything up"
Yes, also that way. 🙂
What i went through above is an explanation of why that is true.
round drum
but
they wouldn't be the same amount of infinity would they
so that is like
tripping up my brain
long canyon
We aren't adding infinities or anything crazy
We're just adding up terms, in sequence
And when we take the limit, we add all the terms.
round drum
yea its just not clicking
cuz you're saying
it equals to 0
but
ok now my brain's in shambles
xd
let's not think about it anymore
ill just think of the reverse if i ever see this again
long canyon
okay
long canyon
fortunately not
long canyon
you got it
round drum
k im gonna need to give you my explanation of why that befuddles my brain though
the 2nd one
if you're adding infinite terms and then subtracting those same infinite terms without a term
how could that equal 0
wouldn't it be equal to that one missing term
long canyon
Without too much snark, because the terms that come later go to 0.
if you have the sequence 1/n, the terms go to 0.
Nevermind that the sum doesn't converge, you get telescoping, and the answer is just the "last" term
but if the sum does converge, this last term is 0.
long canyon
you're adding the wrong way?
long canyon
Sn = a0 +a1 +a2+ ... an
long canyon
the values of an approach 0
but lets focus on just Sn
The problem promises us that lim n -> inf Sn = L
round drum
yea
long canyon
so if we take S_100, it's getting close to L
round drum
uh huh
long canyon
and S_100000 and so on.
now think of S_(n-1)
We were promised that S_100 is close to L,
so S_(101-1) = S_100 is getting close to L
So S_(n-1) is also getting close to L
and formally, when we do the limit, we see that lim n-> inf S(n-1) = lim n-> inf Sn = L
because that -1 doesn't matter. We see all the same values of the sum, going off towards L, in the same order
we just see them "one term later", but they're all there.
round drum
my head hurts
so
in summary
i can do
s(n-some large number)
and it'd still be equal to L
long canyon
in the limit, yes
round drum
that does not sound intuitive in any way shape or form
but alright ill just take it at face value cause it does somewhat
make sense
thanks for the help
.close
calm coralBOT
barren prism
lmao it means signs and letters get mixed up
barren prism
it takes some time for me to actually read something correctly
calm coralBOT
lucid wedge
Bye!
<@&286206848099549185> how long does it normally take for a channel to be moved back to the available help channels
calm coralBOT
Available help channel!
thorny oar
uhh i need help
calm coralBOT
uhh i need help
leaden thunder
uhh i need help
leaden thunder
read this
calm coralBOT
@thorny oar Has your question been resolved?
regal obsidian
i'd do like that yes
potent lotusBOT
marc
glass heart
if it helps, imagine you have an antiderivative G of g
then int_x^y g(t) dt = G(y)-G(x) and this you can easily differentiate
glass heart
Well G(y) is constant with respect to x
So the derivative with respect to x is just 0
calm coralBOT
Available help channel!
hasty bluff
calm coralBOT
hasty bluff
Since it is second derivative
Then
it is open interval (), not closed [], correct?
However, for first derivative
Is it closed or open for the -1/2
regal obsidian
Is depends if, when you say increasing, is it strictly increasing or not ?
regal obsidian
So it's -1/2 included in the interval
regal obsidian
Got this difference ?
hasty bluff
I see then too
so that would also be
closed
and
<=/>=
What about here then thouh
Do I do <=/>= in that evaluation or no
i think i dont
right
regal obsidian
You let like that but on the vertical lines, you put a 0
So we know that you know that the function is equal to zero
hasty bluff
You let like that but on the vertical lines, you put a 0
sorry can you explain this better
regal obsidian
But idk if they do it this way in your country because i'm french
calm coralBOT
regal obsidian
But these are details
calm coralBOT
Available help channel!
jade summit
I need help at B, C, and D
calm coralBOT
I need help at B, C, and D
scenic quail
For B you want to substitute n for a term in the sequence. 3(1) +5 , 3(2) +5, 3(3) +5.......
jade summit
ah gotcha
so it would be 8, 11, 14, 17, 20, 23, 26
thanks
<@&286206848099549185> so i understand how to do B and D now.. i need help with C
wise spire
yeah
jade summit
and series is the total of all numbers in the sequence?
wise spire
actually, i now see that the series is a different one for D
jade summit
oh wait
D is actually also a series
now i am confused to do that too
Do i just have to identify all the numbers
in each terms
then add them all up
wise spire
yeah it would be easier since there are only 5
jade summit
C. 1 3 5 7 9 11 13 15
the sum of all is 64
that's how you answer it right
do i have to say it like Sn = 64
wise spire
yeah maybe
calm coralBOT
@jade summit Has your question been resolved?
calm coralBOT
jade summit
ty
calm coralBOT
Available help channel!
sterile island
how to find x for x/2 + x/3 =1?