atomic vortex
thats all right?
#help-28
devout valley
Well one of these should be removed at least
devout valley
Otherwise looks like all of them to me!
stable heart
thats a lot of emotes 
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crystal linden
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simple totem
what is your question?
stray oak
That’s my question
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frozen plover
Don't know how to do it
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Don't know how to do it
vast fossil
a and b are the roots of the function
vast fossil
Don't know how to do it
And, in this case, the function is supposed to change its sign around x = a, right?
frozen plover
Yes
vast fossil
But, the thing is, the same would happen around x = b
Unless the term (b - x) was squared
So, around x = b the function doesn't change its sign
frozen plover
Yes so it's not the last ok
vast fossil
And, given that x = b is located to the right of x = a (since a < b), we are left with the options A and D
The last thing that we need to account for is the leading coefficient of the polynomial
Is it positive or negative in this case?
vast fossil
Why A and D ?
The thing that they share in common with our requirements is that the function doesn't change its sign around the second root
frozen plover
Ok yes
vast fossil
A general tip on determining whether the leading coefficient is positive or negative given a graph would be to look at what happens on the far right part of its graph
If it tends to go upper and upper, then it's positive
And if it tends to go lower and lower, then it's negative
In this case, since the leading coefficient of (a - x)(b - x)^2 is negative (specifically, -1), we have to go with the option A
tulip beacon
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tame rune
What's the arithmetic meaning of the numbers: ${0},{1},{0},{1},{1},{1},{0},{0},{0},{6}$ ?
glossy valveBOT
Bunnings
onyx glen
what was the point of enclosing each one in its own set of braces 
tame rune
idk. i though thats how bot worked lol
onyx glen
also are you sure you meant "arithmetic meaning" as opposed to "arithmetic mean"?
tame rune
I dont remember the question properly. it was on a test
onyx glen
okay... "arithmetic meaning" is not a phrase typically used in math
so
do you know in general how to find the arithmetic mean of a set of numbers
tame rune
Is that a fancy way of saying find average of these numbers ?
onyx glen
yes, "average" is the everyday word for mean
tame rune
And that's how i lose numbers on my tests. Those fancy words annoy me.
one more thing
The locus of points with the same distance from two given distinct point is ? $//$
Whats locus of points ?
glossy valveBOT
Bunnings
onyx glen
the set of all points such that ___
where the blank is whatever goes after the word "locus"
in your case, the question could be rephrased in a less shitty way as:
"Fix two distinct points A and B. What is the set of all points which are the same distance from A as they are from B?"
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outer dust
the answer to this is C because n^n grows much faster then n! right?
olive locust
the answer to this is C because n^n grows much faster then n! right?
you can split it into 2^n/n^n and n!/n^n which is 0 for both which is easy to prove
undone hemlock
my son is x years old. in 5 years time, i will be twice his age and both our ages will be multiples of 10. the sum of our ages will be between 55 and 100. how old am i now?
undone hemlock
2(x+5) right?
static bramble
Technically true but probably not super helpful
undone hemlock
yea, im stuck now
static bramble
So the ages in 5 years will be, let's use new letters, u and v where:
u = 2v (or v = 2u, whichever you want)
u and v are both multiples of 10
55 <= u + v <= 100
The 2nd condition especially should make it very easy to check combinations of u and v
undone hemlock
oh ok
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storm nest
b.)
storm nest
I was plugging in my last line but forgot to include the - in -9/128 + 1/4
Yet I got the correct answer
I’m not sure how as the - needs to be Included
I think
I used a calculator
OOOOH
IM DUMB
I forgot to include the - in -1/128
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knotty marlin
Swapping the bounds for this integral:
$\int_{0}^{3} \int_{x^2}^{9} x^3 e^{y^{3}} dy dx$
$$0 \leq x \leq 3$$
$$x^2 \leq y \leq 9$$
Re-writing gives:
$$0 \leq x \leq 3$$
$$x \leq \sqrt{y} \leq 9$$
Why is implied that you use $\sqrt{y}$ and not $-\sqrt{y}$
fast peak
yes
rustic ibex
Calculate skillfully
How does this work
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Calculate skillfully
How does this work
hollow grove
Are you talking about 8?
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proven pine
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proven pine
Can someone help me with this exponential equation. I tried to transform things out and use substitution, but I ended up with a incorrect answer
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glacial pasture
if you expand the bracket and so some separations using exponent laws you can create a quadratic of the form $a\cdot 2^{2x}+b\cdot 2^x+c=0$ Ill leave a,b and c for you to determine, however you can then apply the quadratic formula to get values for $2^x$ and then x itself
glossy valveBOT
AℤØ
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proven pine
if you expand the bracket and so some separations using exponent laws you can cr...
Yeah dude, that is what I did, but the result is not what you expect
glacial pasture
$\sqrt{9-4\sqrt{2}}=2\sqrt{2}-1$
glossy valveBOT
AℤØ
proven pine
Oh, yeah, mb, I thought it was supposed to give a different result, so I assumed I did something wrong
Thanks
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shadow fractal
Does anyone know a good software or online calculator to solve a system of nonlinear simultaneous equations
summer steeple
https://atozmath.com/CONM/NewtonRaphson2.aspx
Maybe this, but its littered with ads…
You could also just program the newton algorithm yourself, shouldnt take too long
Or probably even wolframalpha
Shouldve been my first thought
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shadow fractal
Or probably even wolframalpha
Yea that was my initial guess but I've been getting absolutely nowhere with it its weird
It's for deriving a 3 point gaussian quadrature rule but the equations are an absolute nightmare to solve
summer steeple
I can check real quick in matlab
shadow fractal
If you don't mind? My programming skills are very limited hahaha
summer steeple
Does anyone know a good software or online calculator to solve a system of nonli...
Is that supposed to be (x_2)^3 in line 4?
shadow fractal
Yes my bad
shadow fractal
No idea 😦 Im guessing I must be missing a trick
summer steeple
Kinda not getting anything
shadow fractal
Kinda not getting anything
Same here, I may call it a day and sleep on it and give it a go again tomorrow
shadow fractal
Kinda not getting anything
Thank you so much for your help
summer steeple
np but now i kinda want to get the value, for 0,0,0,0,0 its pretty close
But it could just be that the function is somehow bounded in a way that there is no solution
shadow fractal
That seems to be the result I've been getting using wolfram alpha and the online link you suggested with the modified Newton method
summer steeple
Well that sucks
Huh. I played around with the initial guess and now my program is stuck in the while loop
Aaaand nan again
Uh i got something
(1.6826,-1.1111,1.8285,0.6761,-0.4034)
For (w0,w1,w2,x0,x2)
With tolerance of 0.001
Seems as though this function has extremely bad behavior.. kinda lucky
Exact for about 9 digits
summer steeple
There are probably more solutions but this function is so janky
summer steeple
Was this from trial and error with different initial guesses?
Yea had a bit of luck
summer steeple
But there should be more solutions right?
Or is this a problem with a unique solution?
shadow fractal
I'm actually not quite sure to be honest
I've been asked for just one there wasn't really an inplication that it was a unique one
summer steeple
It's for deriving a 3 point gaussian quadrature rule but the equations are an ab...
Oh i see
I kinda recognize the identity used
Yea should be unique
shadow fractal
Perfect we're in business then!
summer steeple
But arent the weights just calculated by the zeroes of the legendre polynomial?
shadow fractal
I believe so yea
Well I don't know what to say thank you so much for your help you're a life saver!
summer steeple
np :)
undone wagon
If I have a differential equation A•dwdx = B•dydz, where A and B are constants, can I take the double integral of both sides and say that A•w•x = B•y•z?
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reef grotto
I am so genuinely confused by what chatgpt is trying to show me here can anyone help clarify?
I don't understand the reason why you would zero index this equation.
a(i, j) = (i - 1) * N + j
^ here
reef grotto
a(i, j) = (i - 1) * N + j
This operation calculates the difference between the current row number (i) and the first row. Since we are using 1-indexed row numbers, we subtract 1 from i to make it zero-based. This step helps us determine how many rows come before the current row.
Isn't the current row already attributed for by the current row number? Why do I need to zero index it?
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lone cobalt
Can someone tell me where I went wrong
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lone cobalt
<@&286206848099549185>
tiny notch
I have this problem
"Ilan and Justin are competing in a math competition. They work independently and each has the same two problems to solve. The two problems take an exponentially distributed amount of time with mean 20 and 30 minutes respectively (or rates 3 and 2 if written in terms of hours). (a) What is the probability Ilan finishes both problems before Justin has completed the first one. (b) What is the expected time until both are done?
i'm not sure how to go about part (b) I'm thinking along the lines of the total time to solve the problem + probabiility Ilan finishes first * time it takes Justin to finish + probability Justin finishes first * time it takes Ilan to finish
bitter orbit
Try to figure out the expected value of the maximum of the completion times of each one
So ILan's time is
$I = I_1 + I_2$
And Justin's
$J = J_1 + J_2$
bitter orbit
Let $T = \max{(I,J)}$
glossy valveBOT
Max Hetfield
bitter orbit
Find $\mathbf E[T]$
glossy valveBOT
Max Hetfield
tiny notch
So just finding the expectation of the maximuim between two hypoexponential variables?
That sounds very nasty...
bitter orbit
So just finding the expectation of the maximuim between two hypoexponential vari...
Yes
It's not that bad
I mean
To find the CDF of T
tiny notch
We can probably utilize CDfs maybe?
bitter orbit
$P(\max(I, J) <t) = P(I \and J < t) $
tiny notch
$P(max(I,J) \leq t) = P(I \leq t) P(J \leq t)$>
bitter orbit
And as they are independent
glossy valveBOT
heheitsop
bitter orbit
$P(max(I,J) \leq t) = P(I \leq t) P(J \leq t)$>
Yeah
tiny notch
and then just differentiating that and then applying definition of expectation
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golden obsidian
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onyx glen
!status
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What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
2
ik that
you can get the semi circle
which is 31.4
but then
idk
@onyx glen
??
torn jolt
its ez right
golden obsidian
wdym
golden obsidian
yeah but
torn jolt
breh area of a semicircle 1/2pi r^2
golden obsidian
oh
torn jolt
i did pi*r^2
so r=5cm
golden obsidian
ye
torn jolt
22/7*5^2
slim pollen
120 + pi * 5 * 5
slow wraith
Wdym
torn jolt
120 is area of rectangle
golden obsidian
120 is area of rectangle
how did u get that
slow wraith
you don't have to do that
golden obsidian
then i did 2.5 x pi
torn jolt
u have the answer to this??
slow wraith
because you know the diameter of the smecircles combined is 10
golden obsidian
u have the answer to this??
huh
torn jolt
how did u get that
radius is 5 so 22-5+5
slow wraith
therefore the length of the rectangle should 22 -10
golden obsidian
because you know the diameter of the smecircles combined is 10
so the
semi circles
are
31.4
?
slow wraith
no
golden obsidian
combined
golden obsidian
where u getting 22/7
slow wraith
pi(5)^2 is the area of the semicircles combined
torn jolt
bestie pi is not 22/7
...
slow wraith
pi(5)^2 is the area of the semicircles combined
which is 25pi
golden obsidian
pi(5)^2 is the area of the semicircles combined
oh i forgot to square
torn jolt
fine if u do pi as 3.14*5^2
golden obsidian
so pi x 25
slow wraith
yeah
torn jolt
so pi x 25
78.5
slow wraith
yeah
golden obsidian
yes
slow wraith
then simply add the area of the rectangle
slow wraith
which is 12 * 10
torn jolt
how u get 120
10*12
torn jolt
which is 12 * 10
bro i hab a doubt can u solve??
golden obsidian
10*12?
slow wraith
10 times 12
slow wraith
yeah
golden obsidian
we got 12 by subtracting 22 from the sum of both semicircle radius
im lost
torn jolt
let me do this in my notebook first
k
ocean lark
Rationalise the LHS's denominator by multiplying the numerator and denominator it by its conjugate. I would rather you do this in a new channel though, since James still seems to be confusewd.
slow wraith
okok
ocean lark
That's what I'm saying!
slow wraith
so
torn jolt
what about my question
...
slow wraith
we know that the radius of the semicircles is 5
golden obsidian
yes
slow wraith
so we found their areas
golden obsidian
yes
slow wraith
approx 78.5
golden obsidian
yes
slow wraith
now we need to find the area of the rectangle
amber kindle
2 semicircles on the side of a rectangle
so you can calcualte it as a circle and a rectangle
diameter 10
slow wraith
if we remove the semicircles from the rectangle, you would have to subtract 22 -10
amber kindle
is the semi circle
wdym how far
amber kindle
yep yep
slow wraith
because each semiricle occupies 5 cm of the total length
amber kindle
but there are semicricles on the sides
torn jolt
slow wraith
yeah
torn jolt
...
torn jolt
solve this plss
slow wraith
lol
golden obsidian
solve this plss
cant u go to another channel
amber kindle
no
torn jolt
cant u go to another channel
idk how to
amber kindle
he told u
torn jolt
:/
torn jolt
cant u go to another channel
u understood?
golden obsidian
nah
torn jolt
brehhhh
golden obsidian
its a semicircle, the diameter is 10
yh
amber kindle
do you agree the dotted grey lines are the radius as well?
slow wraith
because we know that the diameter is 10
golden obsidian
oh
slow wraith
for both semicircles
golden obsidian
so they are 5
slow wraith
yeah
slow wraith
correct
amber kindle
thats rectangle correct
golden obsidian
+78.5?
amber kindle
now add those semicircles back
slow wraith
yep
amber kindle
78.5?
golden obsidian
ok thanks
amber kindle
pi * 5^2
slow wraith
which is 25pi
golden obsidian
bruh sorry for making this long
slow wraith
nono
golden obsidian
but thanks
slow wraith
it's fine
torn jolt
torn jolt
but thanks
phew
torn jolt
i made this shit ;-;
golden obsidian
lmaoo
slow wraith
oh wow
torn jolt
I rationalised the fraction
k u got any answe?
slow wraith
so if you multiply the fraction by the conjugate, you get (14-6sqrt5)/-11
torn jolt
9/11 and 19/11
slow wraith
if I am not wrong
slow wraith
9/11 and 19/11
ok
torn jolt
im literally 8th
torn jolt
india...
slow wraith
can u send the pic of the problem again
torn jolt
slow wraith
ok wait a sec
torn jolt
k
torn jolt
uhh
slow wraith
oh alright
slow wraith
damn
slow wraith
I am thinking
torn jolt
;-;
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golden obsidian
should i close it
slow wraith
yeah
golden obsidian
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slow wraith
bye
warped tundra
bruf i need help
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torn jolt
Why 0+0i is both purely imaginary and purely real?
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Why 0+0i is both purely imaginary and purely real?
vast fossil
Cuz real and imaginary parts are both 0
Recall:
Purely real <-> Imaginary part is zero
Purely imaginary <-> Real part is zero
That makes 0 + 0i identify as both
torn jolt
HMMM
0 is a very sus no
It is neither negative or positive
It is both purely imaginary and purely real
If it is purely imaginary it shouldnt exist in the real world
If its purely real it should exist
AAAAAAAA
ocean lark
Can you tell me what it means for a number to "exist in the real world"
vast fossil
If it is purely imaginary it shouldnt exist in the real world
The implication is false as you can see
torn jolt
Numbers belonging to R
vast fossil
There is a purely imaginary number in the set R
torn jolt
Uh
ocean lark
mb when you said "exist in the real world" i thought you were getting philosphical, not meaning literally \in \bR LOL
eternal goblet
Numbers are all made up concepts
vast fossil
What?
torn jolt
As far as i know its like wait 1 min
torn jolt
Its like this
vast fossil
Right
eternal goblet
torn jolt
Yes
eternal goblet
Where did you learn this?
eternal goblet
Whole number
torn jolt
Which involved this
vast fossil
Yeah what's "whole" btw?
torn jolt
So all real numbers are complex
vast fossil
So all real numbers are complex
Yes
torn jolt
Yeah what's "whole" btw?
Whole number
vast fossil
Isn't a whole number the same as an integer?
eternal goblet
Yeah what's "whole" btw?
Natural + 0 in some textbooks, otherwise just natural numbers
Yes, natural numbers have 0
torn jolt
So all real numbers are complex
But all complex numbers ≠ real numbers right
vast fossil
Ofc
torn jolt
But all complex numbers ≠ real numbers right
*correction
eternal goblet
Negative is not in whole
vast fossil
This is how a proper subset works indeed
torn jolt
But what should be the place of 0 here
eternal goblet
You are confusing it with "0 is not negative nor positive"
vast fossil
Wdym?
torn jolt
But what should be the place of 0 here
Should it be in complex world or real world?
Or is it that boundary i made
Between complex and real
vast fossil
It's everywhere except naturals 
torn jolt
Oh yessss imaginary
eternal goblet
Complex does contain real
eternal goblet
It's everywhere except naturals <:sully:651816820122189834>
eternal goblet
0 is natural
vast fossil
That is controversial
torn jolt
torn jolt
So is like this hmm
vast fossil
Why are reals inside imaginary
torn jolt
AAAA Hhow and wheress sshould i put it then
eternal goblet
AAAA Hhow and wheress sshould i put it then
The previous one was correct
vast fossil
It is impossible to illustrate with Venn diagram
torn jolt
vast fossil
Except you could instead illustrate {0} and {ai, a in R*}
vast fossil
And say that the union of those two is the set of imaginaries
eternal goblet
It is impossible to illustrate with Venn diagram
I guess you can draw a rectangle then divide it into 2, one in real and one is imaginary
And then put all the set you have into real numbers
eternal goblet
vast fossil
Sure, except 0 isn't in the "imaginary" here
torn jolt
0 being the connecting link between the two
torn jolt
Hmm also is it z or c to represent complex no ?
vast fossil
You use Z for complex numbers?
vast fossil
Btw that implies that 0 isn't in the integers
vast fossil
Hmm also is it z or c to represent complex no ?
It is usually denoted with C
torn jolt
You use Z for complex numbers?
Small z as my book uses it too
vast fossil
<:sully:651816820122189834>
Told you, the only thing you can do is make the set look disjoint on the diagram
torn jolt
But if i do then i dont include 0 in imaginary
vast fossil
Except you could instead illustrate {0} and {ai, a in R*}
I suggest doing this
torn jolt
Oh hmmm
vast fossil
R* means all reals except 0 iirc
torn jolt
But in short
0 is omnipresent
Except in natural numbers
Also why dont we compare imaginary nos with each other hmmm?
Is it just a rule?
Or is there a significance behind it?
vast fossil
We would need to know whether i is positive or negative
Let's assume i > 0 and see if any contradictions appear
i > 0
Multiply both sides by i
i^2 > 0 (the inequality sign does not change as i is positive)
-1 > 0 ?
Okay, let's now try i < 0
Multiply both sides by i
You still get i^2 > 0 (the inequality sign changes because i is negative)
So -1 > 0 again
torn jolt
vast fossil
You can't compare i with 0 -> You can't compare complex numbers in general
torn jolt
I kinda get it
As it doesnt matter how many imaginary friends you have
At the end
I will be alone
😃
vast fossil
Re(imaginary) = 0 indeed
torn jolt
But can imaginary be compared with non imaginary?
vast fossil
Still no
torn jolt
I don't even think the guy is still here anwyas
... i came back
@slow wraith u there??????????
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short siren
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dusk forge
In my introductory group theory class the assignment asks: "Draw a figure in the plane that has exactly 7 symmetries." is it not just a heptagon? I'm just confused about what it means "in the plane". Thanks in advance
onyx glen
in the plane means it should be a flat figure and not something three-dimensional or higher
dusk forge
in the plane means it should be a flat figure and not something three-dimensiona...
ahah Thanks
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torn jolt
D_7 has 14 elements tho?
dusk forge
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dusk forge
7 unique symmetries
torn jolt
symmetries should include rotations in this context, right?
onyx glen
if you go with a plain heptagon then it also has reflection symmetries in addition to rotations
there is a way to remedy that, namely by adorning the heptagon with some modification that breaks reflection symmetry but keeps the rotational kind
dusk forge
symmetries should include rotations in this context, right?
I think you're correct
Yep makes sense
Thanks again Toby and Ann!
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mossy crystal
For statistics, I think I'm failing to understand the question
Its 4 marks, but if the p-value is 0.035 and the significance level is 2.5%, surely 0.035 > 0.025 and that's all you need to do
viral maple
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viral maple
i am simply having a hard time figuring out what this question wants
its very hard to read
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fierce roost
I just don't know what to do for this one
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I just don't know what to do for this one
hollow sable
,rotate cco
glossy valveBOT
hollow sable
use PoP
twilit leaf
The instructions say you cant
hollow sable
oh
fierce roost
yeah im kinda confused at what to do lol
twilit leaf
Here: whats the radius of the circle?
Then draw the radius to D
Then draw a segment from the circles center to C
You have two right triangles
hollow sable
but isn’t that quadratic formula
fierce roost
I don't know what the radius is : /
hollow sable
that’s what I thought but you’ll have an x^2 term
twilit leaf
Draw a radius to B
fierce roost
Ohhhh yeah sorry missed that
hollow sable
What is pop?
power of a point
safe trench
,w power of a point
glossy valveBOT
fierce roost
I got root 13
fierce roost
Angle D is definitely a right angle when you draw in the radius, correct?
twilit leaf
Yes
twilit leaf
Ok now use triangle COX to find CX
twilit leaf
Yeah then add AX to get AC
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tired summit
So im trying to solve a hill cipher demo for extra credit for this class...
tired summit
I know that the solution is a message that is converted to numbers using just the trivial pattern A = 1, B = 2, etc...
I know that the encryption key is a 3x3 matrix that starts with the word "CONFIDENTIAL"
eternal goblet
hill?
tired summit
So I have that A = [[C,O,N],[F,I,D],[E,N,T]] (where each letter is a variable with it's encrypted result), and that B = [[6,9,4],[5,14,20],[9,1,12]]
C = 195
O = 153
N = 48
F = 99
I = 78
D = 24
E = 228
N = 191
T = 70
I = 97
A = 103
L = 54
Am = Matrix([[F, I, D],[E, N, T],[I,A,L]])
Bm = Matrix([[6,9,4],[5,14,20],[9,1,12]])
The cipher result is given, so that's why I know what CONFIDENTIAL is after encryption
granite finch
what is the problem?
tired summit
Yeah. So this is what I thought initially
that AB = X, so B = A^-1 * X
what do I need to add?
eternal goblet
that AB = X, so B = A^-1 * X
nothing
tired summit
that AB = X, so B = A^-1 * X
This unfortunately doesn't seem to work
eternal goblet
i mean
if you have a 3x3 * 3x1, you will get a 3x1 vector
so encrypt every 3 letters in a column vector
if you want to multiply the vector before, you would need 1x3 * 3x3 = 1x3
you understand what I mean?
eternal goblet
how to find inverse matrix?
tired summit
I'm not sure how legible that is
eternal goblet
do you know how to find multiplicative inverse of modular
say you have 2x = 1 (mod 3), can you solve this?
eternal goblet
tired summit
well I can solve it, but not through some formula or process
eternal goblet
ah in matlab here is the code
tired summit
So where do I apply this?
eternal goblet
,w 2281^-1 (mod 26)
tired summit
I have 676/2281 ... so I turn that into 676 / (2281^-1) % 26?
eternal goblet
yeah
glossy valveBOT
tired summit
what happened to the numerator here?
eternal goblet
what happened to the numerator here?
https://www.khanacademy.org/computing/computer-science/cryptography/modarithmetic/a/modular-inverses
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rustic wagon
why is -8/6 = 4/3 but -6/10 is -3/5
why does it not keep its negative value
rustic wagon
ik thats a elementary question but im just shit at fractions lmfao
crystal raven
rustic wagon
yeah thats what i thought
but i got the question wrong somehow lol
i thought when its - -8/6 it would by kept
dusty scaffold
if you're negating something twice then the negatives cancel out
dusty scaffold
...ok wait now i've lost track of what the question was and what you answered
stiff wagon
Can someone help me on this problem
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Can someone help me on this problem
stiff wagon
fleet briar
so 18*sinxcosx(pheta)/64sec^3(pheta)
how did you get sin(theta)cos(theta)
$\tan = \frac{\sin}{\cos}$
glossy valveBOT
doctor99268
glossy valveBOT
doctor99268
stiff wagon
Would it be?
fleet briar
Would it be?
you havent even done the integration
and no
i literally said it wouldnt be that
how did you get sin(theta)cos(theta)
since when does tan^2(theta) = sin(theta)cos(theta)
stiff wagon
since when does tan^2(theta) = sin(theta)cos(theta)
Im sorry, would it be
fleet briar
Im sorry, would it be
yh
now
to integrate it
you can see that
you can use integration by inspection
because you can see that cos(theta) is the differential of sin(theta)
so this is reverse chain rule
stiff wagon
you can use integration by inspection
I have never heard of this? Is it known by another term
fleet briar
I have never heard of this? Is it known by another term
if you want
you can also use subsitution for this
u = sin(theta)
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vapid sierra
is this trying to be silly or did i not read the chapter enough
vapid sierra
like is part a anything other than "we are using a different letter to represent the index"
solemn grotto
looks silly lol
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outer dust
shouldnt the answer be pi/2?
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shouldnt the answer be pi/2?
quiet stirrup
The limits of integration and answer are wrong, but it's not pi/2 either
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outer dust
no? but is the antiderivatives still arctan(u)?
quiet stirrup
The antiderivative of 1/(1+u^2) is arctan(u), yes. Plus a constant but that doesn't matter here.
The confusion that made me do a double take is that because the limits of integration are wrong, you wouldn't split this up into two integrals when done correctly, which is probably where you are getting pi/2 but I don't know what you did
tacit eagle
this is my answer at the bottom (correct.)
but how is this answer also correct (1-ln(x^11))/x^12 ?
hallow walrus
$log_a{(b^c)} = c\cdot log_a{b}$
glossy valveBOT
kheerii
hallow walrus
so $11 \ln(x) = \ln{(x^{11})}$
glossy valveBOT
kheerii
obtuse condor
Yes
hallow walrus
yes
tacit eagle
so i guess it still applies
hallow walrus
but usually in calculus you only ever deal with the natural log
obtuse condor
Yep
hallow walrus
hence you will see in many places just the notation log(x) with no base as a replacement for ln(x)
hallow walrus
since log(x) makes more sense regarding complex numbers
obtuse condor
Isn't it?
hallow walrus
logx has a base 10 right
well
obtuse condor
since log(x) makes more sense regarding complex numbers
Yep
hallow walrus
depends on the context
obtuse condor
depends on the context
Well true
hallow walrus
but usually it just means ln
teal aurora
its so weird before joining this discord i never saw people refer to log_10 as log
but apparently its taught a lot
hallow walrus
I don't see the significance of log_10
obtuse condor
In some cases
teal aurora
maybe its just a country thing
hallow walrus
unless you're doing some math regarding number of digits
teal aurora
cause was always ln for me
obtuse condor
unless you're doing some math regarding number of digits
Yes
On that case also it's self understood
logx=10
x= 10^10
But it changes then like
Logx_2 = 10
Where
x=100
So it depends on context
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sleek quest
@old edge how do add 3?
You can turn this into
m = (101+9-3a)/(3-a) = 101/(3-a) + 3
sleek quest
Also, don't ping random people
they were helping me previously
they added 3 to the equation
not sure if that works
sleek quest
where did the +9 come from
old edge
and 110 = 101 + 9
old edge
so I said:
(110-3a)/(3-a) = (101 + 9 - 3a)/(3 - a)
= 101/(3-a) + (9-3a)/(3-a)
= 101/(3-a) + 3
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dense edge
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dense edge
are all 3 of these expressions equal?
nova basin
1 and 3 are, 2 is ambiguously parenthesised
grave elm
Im not sure about the second one, it could be interpreted as (ln(1+2x))^(x^2)
I assume (1+2x)^x^2 = (1+2x)^(x^2)
dense edge
1 and 3 are, 2 is ambiguously parenthesised
what do you mean? x^2 could be confused for an exponent of ln rather than the argument?
dusty scaffold
it's not clear if it's $\ln((1+2x)^{x^2})$ or $(\ln(1+2x))^{x^2}$
glossy valveBOT
bee
dense edge
so I can only bring an exponent to the front of the log if that exponent is **inside ** of the argument?
therefor only 1 and 3 are equal
and 2 is not equal
dusty scaffold
1 and 3 are equal
dense edge
interesting..
dusty scaffold
for 2 it's ambiguous what it means
dense edge
ya, that makes sense. the argument i like a jail cell
dusty scaffold
you would need to decide which of the two possibilities it is before it's equal or not equal to anything
dense edge
what is this term, "ambiguous", in math?
hot herald
unclear, open to interpretation
dusty scaffold
i just mean "ambiguous" in the normal way
"unclear"
there are multiple possible ways you could interpret it
grave elm
what is this term, "ambiguous", in math?
more than 1 ways to interpret it
dense edge
unclear, open to interpretation
it's not clear though?
dense edge
i thought all math was clear haha, with how we write it
dense edge
even this silly exercise is clear, with order of operations
dusty scaffold
well when maths is done properly it's entirely clear
but it is possible to write things in standard notation that parse ambiguously, you just shouldn't
hot herald
it really isn't
dense edge
it really isn't
how should it be written instead?
hot herald
with sufficient parentheses as needed