So you can solve for its legs
#help-23
mint spindle
Would I half the 50 for the angle? So 25 degrees in the right triangle
split ether
Yes
mint spindle
Alright, so I have the radius and height but what’s the formula for the surface area of a cone? Like Google gives me a long thing with a square root but surely there’s an easier to remember formula or something?
split ether
It's just $\pi r^2 + \pi r l$ where $l = \sqrt{r^2 + h^2}$
flat frigateBOT
A Lonely Bean
split ether
If google gave you this then no you can't simplify this
mint spindle
Ok that first one makes more sense- Google gave me which is the same thing but makes less sense at first glance
split ether
**A Lonely Bean**
Yeah I prefer to write it this way since it's more intuitive
Since it's just base area + lateral area
ebon heath
Where did the integral of 2 1(big f thingy)-1 change into 4 1(big f thingy)0?
safe radishBOT
Where did the integral of 2 1(big f thingy)-1 change into **4** 1(big f thingy)*...
calm bridge
even function
final halo
Since your function is even (symmetric around the y axis) the area from -1 to 1 is twice the area from 0 to 1
calm bridge
range?
calm bridge
bounds
static token
hello guys
safe radishBOT
hello guys
static token
can i multiply the question to make it easier to do the quadratical formula
obtuse leaf
yup
static token
is it right
obtuse leaf
why not dont be scared bro its just those loser math laws
static token
yeah I'm actually just trying to help my friend but i want to make sure im right
thanks ig
.close
hexed geyser
i need help on items 10-16
G8 laws of exponents
safe radishBOT
i need help on items 10-16
G8 laws of exponents
hexed geyser
starting with number 10
x³y⁴
x²y⁷
fickle yew
When you divide, you subtract exponents with same base. When you multiply, you add the exponents with same base.
Sample: x^2 times x^3 = x^2+3 , x^3 divided by x^2 = x ^3-2
hexed geyser
so all the variables become x?
fickle yew
Nope, it's only applicable to the ones with the same variable. In that case, you have to repeat the same process if theres another variable
hexed geyser
so what will the answer of the fraction look like with two different variables
fickle yew
For example in number 10, you have 2 variables present, x and y
hexed geyser
yea?
fickle yew
They'll just be side by side with each other.
If the other variable has a negative exponent, you have to put it in the denominator
Example y^-1 = 1/y
hexed geyser
so it would be
xy⁷
xy⁹
?
fickle yew
x^-2 = 1/x^2
hexed geyser
Example y^-1 = 1/y
does that only apply for the negative exponent rule?
fickle yew
it's y^4-7
hexed geyser
ohhh
fickle yew
Yesyes you put negative exponent in the denominator
hexed geyser
il do that with both sides?
fickle yew
Yes
fickle yew
The first one, it's correct
fickle yew
Yess
fickle yew
To the other items, just take note of pemdas rule and order of operations
It's essentially the same process
safe radishBOT
fickle yew
welcome🤗
safe radishBOT
Available help channel!
safe radishBOT
@upbeat peak Has your question been resolved?
upbeat peak
<@&286206848099549185>
upbeat peak
???
safe radishBOT
@upbeat peak Has your question been resolved?
upbeat peak
Is where AF and BE meet a 90° angle?
Yes
minor ore
Ok then lets call angle EBA x
What is EBC?
In terms of x
Are you here?
@upbeat peak
upbeat peak
Yes sorry
upbeat peak
<@774598612100317205>
I was busy
minor ore
Ok now youre free?
upbeat peak
1 min
minor ore
Ok
upbeat peak
In terms of x
90-x
upbeat peak
90 90 x-90 and f
minor ore
90-x not x-90
upbeat peak
Oh yes my vas
minor ore
What does that equal to
upbeat peak
360=270-x
lean otter
i think we can prove the angle DAF and ABE equal
minor ore
Yes simplify a bit
minor ore
i think we can prove the angle DAF and ABE equal
We are doijg right now
lean otter
then we can prove the triangle abe equal to triangle daf
upbeat peak
Yeah
lean otter
so angle PAB + ABP = 90
and DAF + PAB = 90
then PBA = DAF
minor ore
What is angle AFC in terms of x then?
lean otter
sry if my english is bad
upbeat peak
What is angle AFC in terms of x then?
let me think
lean otter
we have: ADF = BAE = 90
AD = AB (ABCD is square)
DAF = ABE (has proved)
=> Triangle DAF = ABE
=> AF = BE
is that right? anything wrong?
upbeat peak
mmmm
upbeat peak
What is angle AFC in terms of x then?
idk
minor ore
90+x
upbeat peak
that is what I thought
minor ore
360=90+90+(90-x)+(90+x) so the x cancels out and we have 90+90+90+90=360
Now we have angle AFC what is angle AFD
upbeat peak
I have a lesson rn sorry
minor ore
Ok
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@upbeat peak Has your question been resolved?
static finch
what does the double vertical line mean? In this example
safe radishBOT
what does the double vertical line mean? In this example
static finch
I assume it is not simply a sum notation, but rather some kind of an operation on the vector w
is it a modulus of this vector?
static finch
its called a norm
so it is the same as a modulus? Based on what I can see it is the same term. Thank you!
peak estuary
yes
static finch
.close
wraith prism
safe radishBOT
wraith prism
can anyone tell me in easy way to remember these 3 terms
safe radishBOT
@wraith prism Has your question been resolved?
slate heart
safe radishBOT
plucky elk
like I ain got all dayy
!volunteers
safe radishBOT
like I ain got all dayy
Helpers are just people volunteering their time to help you. Be polite.
slate heart
Helpers are just people volunteering their time to help you. Be polite.
I'd be polite if I'd completed this stuff an hour ago
plucky elk
I'd be polite if I'd completed this stuff an hour ago
you only asked your question <20 minutes ago
also still not a good reason to be rude and entitled
slate heart
you only asked your question <20 minutes ago
buddy im here for help with my math
bro thinks I know how long an hour is
plucky elk
buddy im here for help with my math
then wait and follow the rules
plucky elk
bro thinks I know how long an hour is
is that what you need help with? 1 hour = 60 minutes
worthy hemlock
is that what you need help with? 1 hour = 60 minutes
60 minutes = 3600 seconds
plucky elk
60 minutes = 3600 seconds
,calc 60 * 60
flat frigateBOT
Result:
3600
correct
worthy hemlock
is that what you need help with? 1 hour = 60 minutes
1 hour = 1/24 days
safe radishBOT
@slate heart Has your question been resolved?
safe radishBOT
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Available help channel!
teal gate
safe radishBOT
teal gate
not sure if i did either right
im p sure i got the graph right but i have no idea how to do the second one i just kind went for it :p
safe radishBOT
@teal gate Has your question been resolved?
teal gate
<@&286206848099549185>
oak urchin
yes.
kind fractal
https://cdn.discordapp.com/attachments/1132355987651694622/1148733517358968842/I...
Hello, (x-4)(x-2) is not a function. It's part of the procedure when you find the intersections of the parabolas
yeah your graph is correct, so follow it. You have 3 different intervals here
kind fractal
https://cdn.discordapp.com/attachments/1132355987651694622/1148733517358968842/I...
state the intersections here so the intervals are clearer
each of these intervals have a top function and a bottom function
teal gate
ohhhh so i solved for the first interval
kinda
just for the bounds
which would be 4, 2
kind fractal
ok those are the intersections of the parabolas
the first interval from the left would go from x=1 to ...
teal gate
2? ish
kind fractal
yes
kind fractal
so those are the bounds for the integral
(first integral)
when calculating are, the integrand is top - bottom
do the same for the other regions
teal gate
so the bounds for each three respectively are 2 and 1, 4 and 2, and 5 and 4
teal gate
do the same for the other regions
idk what the integrals would be though im stuck there
kind fractal
idk what the integrals would be though im stuck there
it's top function - bottom function
follow your shetch
teal gate
follow your shetch
so the first one would be int2,1 (x^2-6x+10)dx - int2,1 (-x^2+6x-6)dx
flat frigateBOT
ELeonardo
kind fractal
?
teal gate
yeah
kind fractal
ok
teal gate
sorry idk how to do that
kind fractal
well you usually write it all in the same integral
teal gate
so like int2,1 (x^2-6x+10) - (-x^2+6x-6)dx
kind fractal
yes
kind fractal
yesss 👍🏽
safe radishBOT
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Available help channel!
honest mortar
how do I interpret this x|x≠2
safe radishBOT
how do I interpret this x|x≠2
buoyant shadow
maybe it's a set that has everything except 2
if it's {x|x≠2}
i guess it can;t be that without {} so no need to guess
buoyant shadow
right, so it's a set that has no 2, but has everything else
U \ {2} in other words
honest mortar
so ≠ means the number can't be used?
buoyant shadow
no it measn not equals
teal gate
hey!
teal gate
im pretty sure i found a, i have the integrals for b setup (hopefully) i just have no idea if i got a right or my setup for b right and any help would be great
ill send a pic of my work <3
tardy mango
im pretty sure i found a, i have the integrals for b setup (hopefully) i just ha...
(a) mostly correct, but don't forget the region in the third quadrant too
teal gate
(a) mostly correct, but don't forget the region in the third quadrant too
the question only asks for the first quadrant so thats all i did
tardy mango
ok hello discord decided to die
a is fine
for b these two should be switched
y=x makes a larger solid than y=x^3
also I don't think you need the third integral
but I could be wrong
safe radishBOT
@teal gate Has your question been resolved?
teal gate
ohhhh
uhmmm
why wouldnt i need the third
or idk
thanks tho
wait yeah when u reflect over a point that isnt touching i think id need to have the r(3)
is there anyway someone else can look at it to see if the third integral is needed
safe radishBOT
teal gate
.reopen
safe radishBOT
✅
teal gate
can someone look at it when u have a chance!
safe radishBOT
@teal gate Has your question been resolved?
nimble tartan
Hey I was hoping someone could help me with these concepts. They're from an economics textbook but this discord is more active than the econ one and it's pretty much all math.
safe radishBOT
Hey I was hoping someone could help me with these concepts. They're from an econ...
nimble tartan
I was hoping someone could help me with the difference between strong monotonicity monotonicity, and local non satiation
in principle I get the definitions
but, say we have a vector of two goods. if we assume strong monotonicity, then y>=x means y is preferred to x
this condition implies monotonicity, and local nonsatiation
so say we have two bundles (x_1, x_2) and (y_1, y_2)
let x = (1, 1) and y = (1, 1+e/2) for any e>0
as far as I understand the definitions, y would be preferred to x under strong monotonicity AND under local nonsatiation, but not under monotonicity
sorry I should mention that squiggly > is a binary relation
safe radishBOT
@nimble tartan Has your question been resolved?
safe radishBOT
@nimble tartan Has your question been resolved?
final halo
well what does >> mean
nimble tartan
a vector is strictly larger to the other vector
final halo
based on what?
nimble tartan
[1 , 1 , 1] >> [0, 0, 0] but [1,0,0] is not >> than [0, 0, 0]
safe radishBOT
Available help channel!
winter whale
x^x^3 = 36
safe radishBOT
x^x^3 = 36
opaque bolt
$x^x^3 = 36$
flat frigateBOT
Jatin
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
opaque bolt
x^x^3 = 36
its x to the power x to power 3 or x to power 3x
winter whale
The first one
lean otter
write it as (x^x^3)^3 = 36^3
then try msking both sides of the form y^y for some y each side
quasi bison
@winter whale do you mean $(x^x)^3$ or $x^{(x^3)}$? these are not the same.
flat frigateBOT
Ann
opaque bolt
i was asking OP, not you.
wht?
quasi bison
i was asking OP what they meant. i was not asking you, @opaque bolt.
opaque bolt
i alrdy asked whats the que he said me that only
opaque bolt
safe radishBOT
@winter whale Has your question been resolved?
desert juniper
how are you allowed/expected to solve it? what's the syllabus that you're currently on?
opaque bolt
how are you allowed/expected to solve it? what's the syllabus that you're curren...
its a algebra que ig
i have a soln but dont know it right or wrong
desert juniper
i do have an exact solution, but i want to know what he is expected to do
opaque bolt
<@774859580899196938> Has your question been resolved?
cross or GG
desert juniper
we're not supposed to give the answer directly
opaque bolt
dm ?
winter whale
Here
opaque bolt
u got it right?
desert juniper
that would be correct
winter whale
This was an Olympiad question
desert juniper
the way i solved it initially would not be accepted on the olympiad :3
winter whale
Well regardless yall ggs
opaque bolt
I was just asking yall
u testing helpers
winter whale
💀
desert juniper
what, you dont like being tested to keep sharp?
opaque bolt
anyways if its done the .close?
winter whale
.close
dull sequoia
ok so i need some help clarifying these wack ass words in logic:
A only if B means A => B
A if B means B => A
A if and only if B means A <=> B
A unless B means A => B
are these right?
safe radishBOT
ok so i need some help clarifying these wack ass words in logic:
A only if B mea...
dull sequoia
mostly just the only if and unless parts
static flame
A only if B means B has to happen for A but B can happen without A
A if B means A has to happen for B but A can happen without B
A if and only if B means if one or the other condition is satisfied, the other condition must exist, so in that way it’s “bidirectional”
A unless B means A happens in all scenarios except those where B happens
but still if you think of them as A —> B and B—> A it makes more sense why if and only if could be an arrow pointing in both directions
desert juniper
So you want to translate the plain english to logic, correct?
The first three would be somewhat right (you'd use A -> B, B -> A and A <-> B in logic usually, the double line usually is used in maths because typically assumes that you already come from true statements)
The fourth one would be:
¬B -> ¬A
wet pecan
The first three would be somewhat right (you'd use A -> B, B -> A and A <-> B in...
Isn't not B -> not A the same as A -> B
I think fourth is (not A only if B) i.e. (not A -> B)
static flame
Yeah you’re right
safe radishBOT
@dull sequoia Has your question been resolved?
dull sequoia
I think fourth is (not A only if B) i.e. (not A -> B)
so A unless B means B => A?
no wait that's not right
not B => A
you can't win unless you finish first
you didn't finish first => you cant win
hmm that's true
normal cloud
I asked this question earlier but the anwser we came to as a conclusion was wrong
safe radishBOT
I asked this question earlier but the anwser we came to as a conclusion was wron...
normal cloud
MelMetal was helping me i think
normal cloud
yea the anwser is 17496
omds
im so sorry
i literally came in to check the anwser
and i remembered it wrong
then i checked my work
because im driving
ahh
harsh parcel
4 x 6 x9 x9 x9 is right
normal cloud
so sry
harsh parcel
i didnt
normal cloud
its right
safe radishBOT
safe radishBOT
Available help channel!
elfin badge
Well in the above question the cylinder cut's the another one and my teacher told me that the sphere is obtained and the projection will be circle But I think that we will get cylinder as a cutted region what do you think about the answer
safe radishBOT
Well in the above question the cylinder cut's the another one and my teacher tol...
lethal musk
,rotate
flat frigateBOT
elfin badge
<@&286206848099549185>
safe radishBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
elfin badge
Ok sorry about that I was a little impatient
sweet mica
elfin badge
Well I know the projection is cylinder
But I am talking about the cutted region whether it is cylinder or sphere
But both the 3d shapes have same projection and that is circle
<@&286206848099549185>
now I can use this tag right
rich meteor
safe radishBOT
@elfin badge Has your question been resolved?
elfin badge
No
safe radishBOT
@elfin badge Has your question been resolved?
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Available help channel!
red talon
safe radishBOT
red talon
is this correct
glad gyro
strange glade
safe radishBOT
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@strange glade Has your question been resolved?
craggy trout
I dont understand why this evaluates to b and not d?
safe radishBOT
I dont understand why this evaluates to b and not d?
haughty fern
show ur work
craggy trout
There was no work really. I just used theorem 1 here
calm bridge
those are not theorems.
calm bridge
I dont understand why this evaluates to b and not d?
also, use a trig sub here
x = (3sinu)/2
craggy trout
those are not theorems.
What would be the right thing to call them?
calm bridge
What would be the right thing to call them?
generalised results/formulas
haughty fern
There was no work really. I just used theorem 1 here
there u have -1 before u , in ur task u have -4x
its not same
craggy trout
Ah, my bad
flat frigateBOT
dopediscorduser
craggy trout
Like this?
safe radishBOT
@craggy trout Has your question been resolved?
dusky harbor
Hello. Calculus questoin, I got confused by this "prove" question.
flat frigateBOT
HqppyFeet
dusky harbor
there
I didn't fully understand how to proceed with this. I made it so that z=x+yi and w=a+bi
thereafter the conjugates of these two would be \bar{z}=x-yi and \bar{w}=a-bi... but what
twin jetty
How would you express z+w in (...)+i(...) form?
twin jetty
You could, but it's easier if you keep things in Cartesian form
forest sorrel
can someone help lol
twin jetty
z + w = x + iy + a + ib = (x + a) + i(y + b)
dusky harbor
can someone help lol
bruh this is OCCUPIED, go to the Math Help AVAILABLE channels (they are actually caps, im not yelling)
twin jetty
z + w = x + iy + a + ib = (x + a) + i(y + b)
If you take the complex conjugate of this, you'll find a familiar result
dusky harbor
z + w = x + iy + a + ib = (x + a) + i(y + b)
Oh this makes sense. Ah I should've known
thank you ❤️
twin jetty
No worries! It's easy to overthink proofs
dusky harbor
.close
safe radishBOT
safe radishBOT
Available help channel!
faint hazel
hi i need help with math can i send it here?
safe radishBOT
hi i need help with math can i send it here?
spare forum
yes
earnest mica
Start by calculating the side lengths in each right angled triangle starting from the biggest one the one with 36,39
faint hazel
but i don't understand how
earnest mica
Using pythagorean theorem
earnest mica
I don't think i know any other ways no
safe radishBOT
@faint hazel Has your question been resolved?
spare forum
for this youre gonna need the Pythagorean theorem, which states:
c^2 = a^2 + b^2
c is the longest side of the triangle (the hypotenuse) and its opposite to the right angle
a & b are the two other sides which are next to the angle
spare forum
careful we said c is the side opposite to the right angle
in this case we can see that the side opposite to the right angle (c) is 39, so you just have to solve for a
faint hazel
So I got the answer of the largest triangle wrong?
spare forum
yeah you need to solve for a since you have c already
again c is the longest side and is opposite to the right angle
faint hazel
Start by calculating the side lengths in each right angled triangle starting fro...
But
Is it right now?
nvm
it s not
spare forum
yes!
spare forum
you gotta repeat it a few more times but its the same thing just different numbers
now using the new a = 15 side you continue with the next smaller triangle as rosa said
and remember to check which side is the c side for the next triangle 😉
faint hazel
faint hazel
Ohhhh yeaaa
Sorry
I forgot
Okayy nice, Thank you very much. @spare forum and @desert pivot
But I have one more task that I don't understand
desert pivot
But I have one more task that I don't understand
with u
faint hazel
I need to calculate the ABC of a triangle
a) Angle sizes
b) Edge lengths
c) And the inside of the triangle
faint hazel
But how do you do solve it?
faint hazel
Where is x?
desert pivot
x =13
faint hazel
I don't understand
desert pivot
faint hazel
How did you get the answers?
faint hazel
the total of angels = 180
I need bc angle, ac angle and ba angle
spare forum
what Ali or Alj im not sure is saying is that the three angles A B C when added are equal to 180 degrees, so
A + B + C = 180
then we substitute the equations for A B and C in there, solve for x and youre good to go from here :)
also for the sides you use the pythagorean formula again but this time solving for y
faint hazel
But how do you know that angle A is 53
spare forum
so in the formula A + B + C = 180 substitute all the info of the picture in there and solve the equation for x
then plug in that x to the individual formulas for A B and C to find them
chrome berry
safe radishBOT
chrome berry
I thought average velocity is slope
chrome berry
i tried the first one
where it'd be (2,28) and (3,54)
then did slope formula of
54-28 / 3-2
got 26, it wasnt right
stray socket
It's asking for the 3s starting from t = 2
So you need to find the slope between t = 2 and t = 5
chrome berry
So find slope with (2,28) and (5,102)
ah okay got it
@stray socket could you explain this one please?
I thought it'd be (x+h) (or a+h) bc 1 = a
With that problem, it leads me confused onto this one also
safe radishBOT
@chrome berry Has your question been resolved?
chrome berry
1 = 1^13
sorry just seeing this
(x)^13?
hmm thats right but that makes no sense ot me
stray socket
$\lim_{h\to 0}\frac{(x+h)^{13} - x^{13}}{h}$
flat frigateBOT
Umbraleviathan
chrome berry
What does x =
1
stray socket
So what the function, and where is it evaluating its derivative at?
chrome berry
(x)^13
stray socket
Same deal. 16 = 2^4
chrome berry
Same deal. 16 = 2^4
I dont understand
rather I get how theres 16
got it
okay thank you
.close
random rivet
how do i do 14
safe radishBOT
how do i do 14
azure horizon
If the cosine of theta is root 3 / 2, then you can use the inverse cosine of root 3 / 2 to find theta
lilac patio
do you know your unit circle?
lilac patio
look up the unit circle
random rivet
look up the unit circle
lilac patio
cos is x sin is y for the ordered pairs
random rivet
cos is x sin is y for the ordered pairs
can u rexplain
lilac patio
there's ordered pairs for specific angles
random rivet
yes
random rivet
yes
random rivet
ouhh
lilac patio
so for 30 degrees
random rivet
x
random rivet
sin30 is 1/2
how did yk it was that one
lilac patio
it tells you
lilac patio
cos150 is also sqrt3/2 yes
random rivet
😭
lilac patio
in your problem it says theta is from 0-90
safe radishBOT
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Available help channel!
lean otter
safe radishBOT
safe radishBOT
@lean otter Has your question been resolved?
outer robin
don't you have it written correctly there?
lean otter
don't you have it written correctly there?
Ik but it’s asking for a single surd
<@&286206848099549185>
outer robin
buddy I think that's a single surd unless you're looking for sqrt(288)
lean otter
buddy I think that's a single surd unless you're looking for sqrt(288)
Yes
That
Is the answerkey
How to get that
outer robin
when you went from sqrt(4) * sqrt(3) = 2* sqrt(3)
you converted sqrt(4) to 2*sqrt(1)
sqrt(1) = 1
so to put something back under that root sign (forgetting what it's called right now)
you'd square it
i.e. 2 = sqrt(2^2) = sqrt(2 * 2) = sqrt(4)
so do you see what doing the same to 12 would look like?
safe radishBOT
@lean otter Has your question been resolved?
lean otter
Wait i still@dont get it
outer robin
sqrt(288) = sqrt (2 * 144) = sqrt(2) * sqrt(144) = sqrt(2) * sqrt(12 * 12) = sqrt(2) * sqrt(12^2) = sqrt(2) * 12
@lean otter
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@lean otter Has your question been resolved?
frail trench
What mistake did I do in tryna solve for x
safe radishBOT
What mistake did I do in tryna solve for x
empty gyro
I can't read your last line
rocky ferry
how did you get from -5x + 42 = 12 to 5x=54
cobalt acorn
Factor 4x^2-27x-40 = 0. Answer is (x-8) (4x+5) = 0 at least without fully solving it's the answer. My question is why isn't it (2x and (2x since 4 is factorable by 2 and 2
safe radishBOT
Factor 4x^2-27x-40 = 0. Answer is (x-8) (4x+5) = 0 at least without fully solvin...
quasi bison
well you could write it as (2x - 16)(2x + 5/2) but that is a lot uglier
cobalt acorn
well you could write it as (2x - 16)(2x + 5/2) but that is a lot uglier
Can you explain why it's x and 4x instead of 2x and 2x
I had another question where 6x^2 was 6x and x instead of 2x and 3x
So I need to understand why
quasi bison
it's entirely a matter of convenience and desire for integer coefficients, nothing more..
i really don't know what else to say, sorry.
cobalt acorn
Ok well thanks for trying I still didn't understand but thanks
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lean otter
sqrt(288) = sqrt (2 * 144) = sqrt(2) * sqrt(144) = sqrt(2) * sqrt(12 * 12) = sqr...
Oh okay thanks
oak ledge
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oak ledge
Hello I have put images of my working and the answeri
I would like to know where the sin(X) went
sinful grove
u-substitution while integrating sin(x)e^(-cos(x))dx
u = -cos(x) du = sin(x)dx --
y = (e^u)du = (e^u) + C = e^(-cos(x)) + C
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choufleur
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wise sky
.reopen
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amber timber
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September 1 enjoyer
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September 1 enjoyer
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amber timber
,rotate
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amber timber
I have no idea what to do from here
sinful grove
You can cancel (s+t)
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wraith prism
I didn't understand the argument
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I didn't understand the argument
wraith prism
They should use [] bracket?
wind stream
well if both endpoints are included, it wouldn't be a function anymore
wind stream
For example, with their first definition, if it were to be [-pi, pi], Arg(-1) could be pi or -pi
And then again, this wouldn't make Arg(z) a function at all
wind stream
that's not what bijectivity is...
what I'm saying is that for z=-1, the function Arg would have two outpus if the range were [-pi, pi]
Bijectivity on the otherhand says that every element in the codomain can be mapped to
and to be clear, the definition of "function" that I'm talking about here is a single-valued function
wraith prism
Yes i was thinking that the function should get one value only
Okay so another question is (0,2π]
Why are we using two different terms for range?
wind stream
two different terms for range?
Can you specify what these are? Since I don't understand what you mean by "different terms"
wind stream
we actually do. Generally, the defintion for principal argument will output values in the interval of (-pi, pi]. But you can also use another definition that suits your preference.
But of course, be consistent with it
like they said
...there is no general convention about the definition of principal value...
wind stream
I don't think I get your question
Are you asking if we can find what the range of f(theta) = e^(itheta) is or...
wraith prism
I meant can we not find a range of this function?
Pr interval for this function like period?
@wind stream
Period of it?
,w period of e^(i thita)
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wind stream
is this a file that you are trying to send?
wraith prism
In the file it is just euler formula
wind stream
alright, so you are asking about the range of e^(itheta) = cos(theta) + isin(theta)?
it's not really something that has a "range"
it's not really a function that outputs anything, just an equality that is true
wraith prism
I see
wind stream
if you are asking about the function f(theta) = e^(itheta) for real values of theta however. This function outputs complex numbers that has magnitude of 1
wraith prism
,w range of arctanx
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wraith prism
Why are we using interval (-π,π] it should be (-π\2, π\2]?
wind stream
I don't see why it should be (-pi/2, pi/2]
wraith prism
Is it not arctan (y/x)
wind stream
no, generally Arg(z) != arctan(y/x) for z = x+iy
you will see why this is a problem for complex numebrs that lie in the second and third quadrant on the complex plane
and of course, evidently through your wfa search
wraith prism
I can't search for it
Can you please do it for me?
So that i can visualise
Thanks for that complicated part explanation
wind stream
Iirc, there is a MathStackExchange for this discussion
wraith prism
Please provide that link
wind stream
oh wait nvm, it's not that
There was one where they had a derivation for it
oh well. Can't find it.
Anyway, the derivative is as simple as considering cases. The first obvious one is complex numbers that is in first and fourth quadrants. Meaning their real parts is positive. And these numbers have argument ranging from (-pi/2, pi/2)
Then, the second case if for numbers that are in second quadrant, these have arguments ranging (pi/2, pi], Hence you want to add pi, giving you arctan(y/x) + pi
And similarly, you have a case for complex numbers in the fourth quadrant
Then consider the cases where z is (pure) imaginary as well, since this is the case where the real part (i.e x) is 0
You actually don't need to specify that Arg(z) is undefined for x=y=0. This is already implied if you don't specify it
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magic tusk
how to simplify to simplest form
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how to simplify to simplest form
magic tusk
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Dyssrupt
calm bridge
use the first one.
calm bridge
yeah
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karmic glacier
Hello
karmic glacier
If I were to use the integral formula for finding the length of a curve
To solve for y(x) = 2 + 5x^3/2, for 0 ≤ x ≤ 10
Would I just integrate the 5x^3/2 then apply the limits to find the solution
so for example 7.5x^1/2 into the formula
sqrt(1+(7.5x^1/2)^2))
sqrt(1+(7.5(10)^1/2)^2))-sqrt(1+(7.5(0)^1/2)^2))
little venture
You integrate the whole expression, not just the stated derivative.
karmic glacier
So I would sub u for 1+(7.5x^1/2)^2)?
little venture
You are trying to solve $\int_{a}^{b}\sqrt{1+\left(\frac{15}{2}\sqrt{x}\right)^{2}}dx$
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Chixen
little venture
I guess u sub would work
little venture
Try $\frac{p}{q}$ instead
flat frigateBOT
Chixen
little venture
or $\sqrt{x}$
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Chixen
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karmic glacier
Anyways, all I wanted to know was weather I could just sub the limits in at that point or weather u needed to be subbed in
karmic glacier
Yeah, sorry if I phrased it badly
So I'm on the right track with it being u = 7.5x^1/2?
little venture
Yeah that for 1+ that.
karmic glacier
oh?
little venture
There’s a square
karmic glacier
u = (1+7.5x^1/2)^2?
little venture
No, where is the square in the integral?
karmic glacier
To solve for y(x) = 2 + 5x^3/2, for 0 ≤ x ≤ 10
From here?
2 + 5x^3/2 should equal 7.5x^1/2 when integrated no?
dropping the power of 3/2 infront of the number (5x) and then reducing the power by 1
tepid walrus
Sending this again cause I forgot to say "no" to the bot >_> Basically, new to complex analysis, cauchy residue theorem and whatnot. Tried this integral, and the result I get is not the same as wolfram's. So I need help understanding what I did wrong. Don't hesitate to ask me to clarify bits of the image as it's not very good :)
safe radishBOT
Sending this again cause I forgot to say "no" to the bot >_> Basically, new to c...
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pseudo scroll
Sending this again cause I forgot to say "no" to the bot >_> Basically, new to c...
You'd probably have better help in the advanced channels
tepid walrus
Oh perhaps yeah
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native robin
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native robin
how to do part D
outer robin
what did you get for (c) ?
native robin
what did you get for (c) ?
yes since B is diff so B is cont and (B(4)-B(1))/(4-1)=2.5 by MVT
outer robin
so the function for chloe's velocity between 0 and 2 is te^(4-t^2)) and you can use MVT to get B for that interval
then you use an equality and solve for t in chloe's equation
and see if that t is within the range
native robin
dont i have to find if there is a t such that B(t)=C(t)
outer robin
using the intermediate value theorem
yeah
if you plug in values of 0, 1, and 2 into C(t)
then you can see the values of B(t)-C(t) and see if they would go through 0
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tacit cosmos
How do you integrate
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How do you integrate
tacit cosmos
1/x?
tacit cosmos
But we solved this in reverse, like how are we supposed to know we start from ln f(x)
solid shell
But we solved this in reverse, like how are we supposed to know we start from ln...
Consider how one function in the integrand is the derivative of the other
One of the first integration methods we learn is a great tool for that situation
fleet tendon
When you do u-substitution
what do you do?
You solve for u'
then obtain du
then how do you plug that back in the integral?
in particular, what is du
solid shell
$\int{\frac{f'(x)}{f(x)}}dx$, let $u=f(x)$ and $du=f'(x)dx&, $\implies \int{\frac{1}{u}}du$
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lexitorius
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fleet tendon
👆
tacit cosmos
Oh
fleet tendon
Do you understand now?
fleet tendon
Cool
tacit cosmos
Got it thanks
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clear mist
Using interval notation, describe the set of all numbers x such that |x^2 + 8x| > 8
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Using interval notation, describe the set of all numbers x such that |x^2 + 8x| ...
clear blade
write it as two inequalities without the absolute value
if you’re unsure on how to do this, think about how you would do it for |x| > a
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orchid glen
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bold ferry
speed = distance / time
orchid glen
Ok
I understood that part
This is supposed to be Solve inequalitys, and I’ve literally got no Idea what to do with this one question
bold ferry
speed = distance / time
well try to apply this
you are given the distance and the time
and I guess they want an inequality, so it would be speed >= distance / time
as it says at least 250 miles
orchid glen
Im sorry I have a smooth brain, Ima need a tiny bit more help
orchid glen
Everything, I only got 2 numbers to work with, and it’s telling me to find the average speed with only those 2 numbers
bold ferry
yeah
do you understand that the speed of something is equal to its distance divided by time?
like your car
drives at speeds in km per hour
(or miles per hour)
bold ferry
:/
bold ferry
do you understand that the speed of *something* is equal to its distance divided...
so is this a no?
orchid glen
Its a No
bold ferry
what part do you not understand
orchid glen
Never mind im sorry for wasting your time