orrr
#help-26
strong roost
glad to hear it
vital dragon
glad to hear it
and the four is actually positive right bc i always feel like i get that wrong
but in the og it’s given as a negative bc if it (in the equation) was negative it would multiply by the -2/3 and become positive right??
or am i yapping
strong roost
if h is negative then x-(-h) = x+h
strong roost
ye
strong roost
that's a cubic
vital dragon
huh
strong roost
look at the form for the original problem
strong roost
yeah
waxen flame
the question is a little vague, but very likely you should model his revenue depending on the price he sets
ornate magnet
In qstn 33 if i write r wrt CM and then differentiate it wrt time will i get Velocity of P wrt CM ?
topaz sinewBOT
In qstn 33 if i write r wrt CM and then differentiate it wrt time will i get Vel...
drifting swift
,rccw
thorny flameBOT
topaz sinewBOT
@ornate magnet Has your question been resolved?
pearl fog
which one is considered a function?
topaz sinewBOT
which one is considered a function?
pearl fog
i think its b but i cant like verify its correct or not
also sorry to the guy that was talking here
mellow venture
do you know what the condition is for something to be a function?
pearl fog
sorry for late response, but the domain has to only have 1 codomain, no more no less
digital pollen
I’m studying for an exam and I need help working out these problems
topaz sinewBOT
I’m studying for an exam and I need help working out these problems
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
pearl fog
!status
topaz sinewBOT
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
Don’t know where to start
I’ll start with how do I work out the square root property
topaz sinewBOT
@digital pollen Has your question been resolved?
topaz sinewBOT
@digital pollen Has your question been resolved?
vestal totem
I’m studying for an exam and I need help working out these problems
show your work
digital pollen
I don’t have work. Not sure what to even do
vestal totem
then perhaps go study first
go read on how to solve linear equations in two variables
i believe they're all pretty easy
digital pollen
I am studying
Trying to find someone who can explain square root property or any of those problems so I can go practice them
I was looking to find someone who might be able to explain in a way I’ll understand it
vestal totem
aight let's see
i have no clue what in the hell the square root property refers to
however
i know how to solve it
it's pretty simple
$3\left(x-4\right)^2=15$
thorny flameBOT
Percy
vestal totem
$(x-4)^2=15/3 \Rightarrow (x-4)=\pm \sqrt{5} \Rightarrow x=4 \pm \sqrt{5}$
thorny flameBOT
Percy
vestal totem
I just googled
the 'square root property' is just that $x^2=y \Rightarrow y=\pm \sqrt{x}$
thorny flameBOT
Percy
vestal totem
@digital pollen
nimble crown
so I'm following through an online video and at this part for completing the square, he says "the -4 is influencing the 1 in the bracket so we have to offset it by adding a 4 on the outside" (paraphrased) what does he mean by this? and isn't the 4 also multiplied by the bracket so you can't subtract it
topaz sinewBOT
so I'm following through an online video and at this part for completing the squ...
nimble crown
I know the idea of the original complete the square where when you add the number at the end and then add the negative of that number because you techincally just added a number from nowhere
like this but how does this logic apply to that?
flat kindle
$-4(x^2+2x)=-4(x^2+2x+1-1)=-4(x^2+2x+1)+4$
thorny flameBOT
WhereWolf(ping if needed)
flat kindle
yes the -1 in the bracket becomes +4 outside
nimble crown
but if you multiply the bracket, don't you need to do the whole thing?
oh, factorised
but then how does -4 and 4 then cancel out each other?
flat kindle
first no one said we must expand everything at once
flat kindle
but then how does -4 and 4 then cancel out each other?
the +1 and -1 cancel each other inside the bracket, we multiplied -4 to -1 cause we don't need the -1
flat kindle
yes
nimble crown
I get that we multiplied -4 and -1 because we don't need / want the -1
but theres still the -4
wait
no nevermind
that doesn't matter I forgot the kept it
ok that answers my questions then
jade thunder
I’m pretty sure $\int\frac{1}{\sqrt{(x-a)^2-b^2}}, dx$ is on an integration table
thorny flameBOT
Frosst
nimble crown
it is but this is one of those more harder cases
becaue the bottom would be a quadratic
jade thunder
**Frosst**
The bottom can always be factored into this form
Because that’s just the vertex form
Of your quadratic
nimble crown
yea which is what the video is going through yea I get it
nimble crown
I'm extremely confused how a domain of 0<= x <= pi/6 has sin and cos stop at pi
nimble crown
did the teacher do this because thats the part we only need?
lapis raft
topaz sinewBOT
indigo wren
did the teacher do this because thats the part we only need?
No
topaz sinewBOT
✅
topaz sinewBOT
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Available help channel!
warm lark
Is there a comprehensible proof for the uniqueness of fourier transform for someone who never studied fourier transform but need it for proving equivalences of definition of multivariate normal distribution? (pdf definition is equivalent to characteristic function definition)
topaz sinewBOT
Is there a comprehensible proof for the uniqueness of fourier transform for some...
@warm lark Has your question been resolved?
warm lark
<@&286206848099549185>
topaz sinewBOT
@warm lark Has your question been resolved?
waxen locust
i can't understand why, if we substitute 2^x for y, 2^(2x) = y^2
cursive thorn
2^(2x) can be written as (2^x)^2 using exponent rules
autumn plaza
hello
drifting swift
,calc 0.17*60
thorny flameBOT
Result:
10.2
10.2 mins round up to 11?
drifting swift
yes since you don't quite have 50 million bacteria after exactly 10h10m
robust cradle
hi
topaz sinewBOT
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
two friends gave me two different awnsers
i dont know where to begin
my teacher keeps refusing to help me
for like everything
versed cairn
do u know the propety of angles within lines?
robust cradle
Adjacent?
robust cradle
ok
versed cairn
here <4 and <5 are adjacent to each other
which means <4 and <5 are equal , rest u can do pretty sure
robust cradle
which means <4 and <5 are equal , rest u can do pretty sure
i need to make an equation?
versed cairn
yeah seems correct
topaz sinewBOT
@robust cradle Has your question been resolved?
robust kayak
topaz sinewBOT
bold nebula
tan(θ) = BE/OE
robust kayak
yes, so it would be BE
bold nebula
= AD/OD
bold nebula
yes
topaz sinewBOT
robust kayak
.reopen
topaz sinewBOT
✅
robust kayak
to find sec
it would be 1/cos
so
OE/OD
but I don't know how to proceed from there
nvm I found it
.close
trim kelp
"For which real numbers can the expression be interpreted?"
topaz sinewBOT
"For which real numbers can the expression be interpreted?"
trim kelp
The tranalation may not be right idk
sturdy oracle
Remember that sqrt(a) means that a >= 0
neon iron
what does it exactly mean by "coplanar vectors"? suppose we have 3 coplanar vectors a and b. does this imply that both of the vectors lie in on plane completely?
topaz sinewBOT
what does it exactly mean by "coplanar vectors"? suppose we have 3 coplanar vect...
neon iron
or their tips are in the same plane?
odd jacinth
it means they are linearly dependent
take 3 vectors a, b, c
and consider the plane which direction is vector a and b, and which contains a point A
then A+c belongs to the plane iff c = xa+yb for some x, y
it's in this case that we call them coplanar
it is equivalent to say you could "fit" all three vectors in a same plane as long as you move their "ends" without changing the vectors
neon iron
it is equivalent to say you could "fit" all three vectors in a same plane as lon...
oh that makes sense, tysm
.close
topaz sinewBOT
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Available help channel!
digital pollen
I need help with these problems
topaz sinewBOT
I need help with these problems
drifting swift
have you been able to use the rational root thm in previous exercises?
topaz sinewBOT
@digital pollen Has your question been resolved?
digital pollen
have you been able to use the rational root thm in previous exercises?
Yes
drifting swift
right
you can use it again here
your polynomials are cubic and so are guaranteed at least one real root
btw there's no reason to wait until the bot pings you lol
@digital pollen do you want to be pinged for every message?
digital pollen
Lol sure. I’m studying in between this assignment
drifting swift
i mean im not forcing you
drifting swift
there is just an expectation that if you open a help channel you're there to talk to whoever comes around to help
yeah ok so
digital pollen
Got it
drifting swift
find that one real root, factor the thing accordingly, and you're left with a quadratic
and quadratics can be solved with a variety of methods
digital pollen
Ok let me see if I can try it for #41
I’m not sure how to factor it. Wouldn’t the GCF be 1?
drifting swift
rational root theorem, remember?
you find a root first
then you will get a factor out of it
digital pollen
then you will get a factor out of it
Ok so the real solution is 2
drifting swift
,calc 8 - 8 * 4 + 25 * 2 - 26
thorny flameBOT
Result:
0
ok yeah checks out
that means you have (x-2) as a factor
figure out the other one
digital pollen
@drifting swift
drifting swift
ok yeah there are not
have you been taught anything about complex numbers? or is that completely new and foreign territory for you somehow
digital pollen
I’ve been introduced to them
drifting swift
ok right
so then like, seeing a negative number under a square root (given the right context) doesnt scare you, right
digital pollen
Oh autocorrect
drifting swift
when you see a negative number under the square root, write sqrt(-n) as sqrt(n)*i
drifting swift
Oh autocorrect
a tool of the devil that is better when turned off
digital pollen
Haha exactly
digital pollen
when you see a negative number under the square root, write sqrt(-n) as sqrt(n)*...
Ok that makes sense
How do I know which numbers will get me the right answer?
digital pollen
Like say sqrt(-2) was a solution but only paired with i so it would be sqrt(2)*i but how do I prove that?
digital pollen
No hang on let me see if I can word it better
So the way I used rational root theorem to find that 2 was a solution right? I found 2 by using synthetic division
drifting swift
no, synthetic division is how you did two things: (a) confirm that 2 is indeed a root, and (b) factorize the cubic into the product of (x-2) and a quadratic
digital pollen
So my question is, how do I find the complex solution? Do I use rational root theorem?
drifting swift
no
digital pollen
Ok
drifting swift
again, what's left is a quadratic equation
maybe if you could show me your work, i could write it out for you explicitly so as to help bring this down on the abstraction ladder
but the quadratic equation can and should be solved with any method you know of that applies to quadratic equations
digital pollen
Ok I think I understand
drifting swift
in particular (but if it REALLY doesn't sit right with you at all, then this is not mandatory) the quadratic formula can be used to solve this quadratic equation
digital pollen
I’ll show my work then write it out as a quadratic equation
drifting swift
the fact that you can use the quadratic formula has NOTHING to do with the provenance of the quadratic equation to which you're applying it.
but also please don't confuse the words "quadratic equation" and "quadratic formula".
digital pollen
Yes I am most familiar with solving quadratic equations using the quadratic formula
drifting swift
ok right so like
i'll assume you did the synth div correctly
you now have the equation x^2 - 6x + 13 = 0
digital pollen
So I have x^2 -6x +13 = 0
digital pollen
Ok
drifting swift
ping me once you have the work written out ig
drifting swift
ok now what's sqrt(16)
digital pollen
4
My answer is the one that’s boxed
It’s a bit confusing because I ran out of space
drifting swift
My answer is the one that’s boxed
right ok
i mean you could simplify that to 3 ± 2i
digital pollen
.close
neon iron
Prove that vector ML is parallel to the bases of the trapeze
topaz sinewBOT
Prove that vector ML is parallel to the bases of the trapeze
neon iron
ive been battling htis for a GOD DAMN 3 HOURS
clever verge
ok for parrellel vectors there cross product is 0.
define an arbitrary trapazoid on a euclidean plane and simply show that the cross products must =0
topaz sinewBOT
@neon iron Has your question been resolved?
topaz sinewBOT
@neon iron Has your question been resolved?
neon iron
.close
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Available help channel!
undone flicker
topaz sinewBOT
topaz sinewBOT
@undone flicker Has your question been resolved?
topaz sinewBOT
proud bear
i put it here to not annoy people
drifting glen
Ah, unfortunately, pure DEs isn't really my strong suit
proud bear
proud bear
Ah, unfortunately, pure DEs isn't really my strong suit
is this something you could help with a bit more?
i think i computed the fourier cosine series
its pretty ugly but, i did it
but not sure what to do to apply to part b
drifting glen
In a bit, my keyboad is boken ight now and its eally annoying
proud bear
no worries ahhaa
topaz sinewBOT
@proud bear Has your question been resolved?
lucid lion
I am struggling with chain rule and with how to determine the difference between the inside and outside function
topaz sinewBOT
I am struggling with chain rule and with how to determine the difference between...
wintry sonnet
chain rule?
lucid lion
here is the problem
wintry sonnet
ahhh wait
lucid lion
the answer according to the textbook is 12x^3(5-x^4)^3
I don't understand how they got there...
So the chain rule is the outside function evaluated at the inside function unchanged times the derivative of the inside function correct?
wintry sonnet
hm wait ah
lucid lion
so here's how I did it.
the outer function f=x^3
f prime is 3x^2
g of x the inner function is 5-x^4
the derivative of that is g prime which is 4x cubed
I then plugged that into the chain rule formula
so that gives me 3x^2(5-x^4)(4x^3)
wintry sonnet
we know that dy/dx = dy/du × du/dx
so let u= 5-x⁴ let y = u²
now differentiate,
du/dx = -4x³
dy/du = 2u
now apply dy/dx,
dy/dx = 2u × -4x³
wintry sonnet
and then just sub in u = 5-x⁴
lucid lion
so is that another way of wording chain rule?
wintry sonnet
yes
empty sail
the derivative of that is g prime which is 4x cubed
No, it's -4x^3
wintry sonnet
easier one
lucid lion
okay
empty sail
so that gives me 3x^2(5-x^4)(4x^3)
And you were close here, you just needed to simplify it
empty sail
Multiply the terms
lucid lion
okay so how would I go about doing that?
empty sail
Multiplication is commutative
wintry sonnet
to check, you can just diff like normal one
y= (5-x⁴)³
dy/dx = (3) × (5-x⁴)² × (-4x³)
empty sail
a * b = b * a
lucid lion
would I use product rule?
empty sail
Why?
lucid lion
so wait yeah I would be finding the second derivative and that's not what i'm trying to do
empty sail
Multiplication is commutative
a * b = b * a
wintry sonnet
empty sail
You can move the terms around and multiply 3 and -4x^3
lucid lion
so hold on give me a second I'm going to work this out
wintry sonnet
the other side is using the formula
wintry sonnet
the other side is using the formula
,rotate
thorny flameBOT
wintry sonnet
we know that dy/dx = dy/du × du/dx
so let u= 5-x⁴ let y = u²
now differentiate,...
but if youre supposed to solve using chain rule, u can just use this
easy for you to understand and more clear
lucid lion
ah okay. That makes sense give me a second to simplify the terms in the other way however
wintry sonnet
okay sure
empty sail
so that gives me 3x^2(5-x^4)(4x^3)
Also I just realized that you put 3x^2 which is wrong
lucid lion
so that means I got the outside function wrong and it's derivative?
empty sail
The derivative is right
It's just that with chain rule, you plug the inner function back in
lucid lion
oh
empty sail
In place of the variable that's in the outer function, that you used
lucid lion
so it would be 3(5-x4)^3)^2(5-x^4)(4x^3)?
or am I missing something?
@empty sail
I think I got it
12x^3(5-x^4)(4x^3)
<@&286206848099549185>
topaz sinewBOT
@lucid lion Has your question been resolved?
severe marsh
help pls
twin atlas
Why dis wrong
glossy granite
topaz sinewBOT
glossy granite
i need help computing this
frail dove
Try making the numerator into the form a^n
glossy granite
heres what i did
but in my tutorial i notted down 6/5
the difference in mine and theres is the starting term for them was 2
but i think it should be 2/3
glossy granite
Try making the numerator into the form a^n
yup, i think i did that in my picture to get the ratio
frail dove
Shouldn't a=-2?
glossy granite
how tho?
isnt it
(-2)^2/3^1
oohhh
starting index is 0
i was doing one
omg
glossy granite
Shouldn't a=-2?
thank you for that XD
i just needed to talk out my problem and i got it
works now thank you 👍
.close
topaz sinewBOT
glossy granite
.reopen
topaz sinewBOT
✅
neon iron
you can do that with an alternating series 
?
glossy granite
you can do that with an alternating series <:e_blue_shocked:935946298346070047> ...
yeah i guess
just need to pull out a 2
to get the powers to match
then its a geometric series
.close
wary pecan
topaz sinewBOT
wary pecan
This is my third attempt at a similar question, I just don't really understand it.
The first answer is getting me with the number of years since 1990
C=36x+???
drifting swift
how did you get 36 as the slope?
drifting swift
yes the slope is 9
so you know C = 9x + b, and you know that when x = 8 (in 1998), C = 175
use this to find the y-int
wary pecan
103?
drifting swift
asking me? or second-guessing yourself
drifting swift
well show how you got it
i'd rather you not get too complacent on external answer validation
wary pecan
175=9(8)+b
72
175-72 = b
103 = b
drifting swift
ok, so which part of this work do you doubt?
the multiplication of 9 by 8, or the subtraction of 72 from 175?
wary pecan
less of individual calculations, more regarding that I did the correct steps
drifting swift
well you did do the correct steps yes
bc you did find the value of b
anyway yeah C = 9x + 103 should be your equation
wary pecan
alright, thank you
ok I think I got the rest
I'll keep the chat open for a minute or so and then submit it or ask another question
got it
tysm!
.close
topaz sinewBOT
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Available help channel!
grand shoal
topaz sinewBOT
flat kindle
turn them to factorial
cyan creek
does this server also help with physics questions?
topaz sinewBOT
does this server also help with physics questions?
sweet shard
does this server also help with physics questions?
some basic ones yea. #old-network for harder physics questions usually
cyan creek
this shouldn't be hard
i know that friction = coefficient x Normal force but im not sure what the normal force here is. is it just m1gcostheta?
wait no i think ig ot it
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
quiet oxide
topaz sinewBOT
tough cargo
I think I see how to solve it, or at least 2/3rds of the steps
First u square $x +y +z$
thorny flameBOT
992qqoloy
tough cargo
Solve for $xy + xz + yz$
thorny flameBOT
992qqoloy
tough cargo
Then cube $x + y + z$ and hopefully u can solve for $xyz$
thorny flameBOT
992qqoloy
tough cargo
I haven't checked out the curbing part tho
rich bison
a³+b³+c³-3abc= (a+b+c)(a²+b²+c²-ab-bc-ca)
topaz sinewBOT
@quiet oxide Has your question been resolved?
quiet oxide
but what does abc = ?
topaz sinewBOT
@quiet oxide Has your question been resolved?
young tinsel
topaz sinewBOT
young tinsel
I really don't understand this problem.
Can I have some assistance.
I tried drawing a diagram and am stuck between.
Can someone tell if I am going in the right direction? I'm basically assuming that she is at the end of the shore and runs down a little bit and then swims at angle to the child distance swam.
its an application of derivatives problem
please help me someone so stuck.
topaz sinewBOT
@young tinsel Has your question been resolved?
sterile wave
yes, I think your direction is right. Let's assume lifeguard run x m and swim y m to find the quickest path to reach the child
so the time = x/8 + y/3, right?
and you also get the the relation between x and y.
so you can replace y with x
and finally, taking the derivative of both sides of the equation, you can get infor x = ?
untold forge
Julie has 3.10 in change, only 50 cent and 20 cent pieces and the total number of coins is 11, how many coins of each type does she have?
topaz sinewBOT
Julie has 3.10 in change, only 50 cent and 20 cent pieces and the total number o...
untold forge
*urgent
<@&286206848099549185>
I just need help writing out the equations, word questions like these are so annoying
minor vapor
Use unknowns to represent the amount of each coins
minor vapor
What do u hv
minor vapor
And?
untold forge
uh
minor vapor
Julie has 3.10 in change, only 50 cent and 20 cent pieces and the ---(1)
total number of coins is 11, how many coins of each type does she have? ---(2)
minor vapor
What do u use to represent 50 and 20 cents respectively?
minor vapor
So..?
untold forge
310 = 50x + 20y?
minor vapor
Yep
untold forge
Ohhhh
Ok i can do the rest
That was the only part i was struggling with
Ty
.close
short olive
I have a sphere of radius (rm) and a number of spheres (n) that must fit inside the sphere m, what is the radius of the spheres (rn)? I would need them to be arranged spherically
topaz sinewBOT
I have a sphere of radius (rm) and a number of spheres (n) that must fit inside ...
@short olive Has your question been resolved?
nimble crown
could someone help explain to me how that trig turns into 3cos^2(theta)
nimble crown
versed cairn
sqrt(9(1-sin^2 theta))
(sqrt 9)(sqrt (1-sin^2 theta)
3 (sqrt cos^2 theta) (as sin^2 theta + cos^2 theta = 1)
3cos theta
nimble crown
where did the 1/2 go?
versed cairn
1/2?
versed cairn
yeah
versed cairn
np
nimble crown
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
junior stratus
Let $x(t)=a(t)+ib(t)\in \mathbb C^n$ be a complex-valued solution of the system $x'=Ax$, where $A$ is a real matrix. Show that $a(t)$ and $b(t)$ are solutions of the system. Any hints are appreciated.
topaz sinewBOT
Let $x(t)=a(t)+ib(t)\in \mathbb C^n$ be a complex-valued solution of the system ...
thorny flameBOT
sunside
drifting swift
show $\overline{x}(t)$ is also a solution
thorny flameBOT
Ann
junior stratus
show $\overline{x}(t)$ is also a solution
hmm, thank you for the hint. If $\overline{x}(t)$ is a solution, do you mean that $$\frac12 x(t)+\frac12 \overline{x}(t)=a(t)$$ would also be a solution, or were you referring to something else?
thorny flameBOT
sunside
drifting swift
yes
junior stratus
yes
just how do I show $\overline{x}(t)$ is also a solution? I do not know what $Aa(t)$ and $Ab(t)$ are...
thorny flameBOT
sunside
topaz sinewBOT
@junior stratus Has your question been resolved?
drifting swift
just how do I show $\overline{x}(t)$ is also a solution? I do not know what $Aa(...
you can just take conjugates of both sides and know that A is a real matrix and thus its own conjugate
junior stratus
.close
astral temple
topaz sinewBOT
astral temple
So I've missed a couple lectures
I can't seem to find anything on this in my textbook (Kreyzig, advanced engineering mathematics 10th ed. international).
Nothing I find on google is proving very helpful, any tips on what to look up or where to start would be much appreciated
topaz sinewBOT
@astral temple Has your question been resolved?
astral temple
<@&286206848099549185>
topaz sinewBOT
@astral temple Has your question been resolved?
astral temple
.close
half field
topaz sinewBOT
half field
Can someone guide my mistake??
clear lodge
the mistake would be
px^2 = 2
that simply should not be there.
Everything else is correct
half field
the mistake would be
px^2 = 2
the x is the coordinate is 1 isnt it ?
half field
that simply should not be there.
Everything else is correct
how bout part (b) ?
clear lodge
the x is the coordinate is 1 isnt it ?
the x coordinate is any real.
You're given the gradient, p
it might help if you rename it
let's call 1/y = A
x^2 = B
thus, you have:
A = pB + q
with your variables now being A and B
so you got a straight line of slope p and y-intercept of q
for part (b), you're basically being told:
Is the point (B, A) = (4, 10) in the line A=pB+q?
or in other words.
If p=2 and q=3 (since you already calculated them), would 1/y = 10=A and x^2=4=B satisfy the equation?
half field
or in other words.
If p=2 and q=3 (since you already calculated them), would 1/y...
so 1/10 = 2(4)^2+3 ?
half field
yea
half field
oh no
clear lodge
see that the line is not graphing with x and y
it's graphing with 1/y (your new variable A) and x^2 (your new variable B)
with your new variables, they ask for a point, on the new variables
half field
i should find new y = mx + c ?
clear lodge
no
you're simply not calling your variables x and y this time
see, this is why i teach my students to never memorize the letters, but to understand what they mean
your first graph is easy:
y=1/(2x^2+3)
that's what you're accustomed to
the SECOND graph is the line:
y=2x+3
however, they are simply not CALLING the variables y and x
half field
however, they are simply not CALLING the variables y and x
okay
half field
your first graph is easy:
y=1/(2x^2+3)
how this 2x^2 you turn to 2x as the second graph ?
clear lodge
the second graph would be using what i'm calling A and B
topaz sinewBOT
@half field Has your question been resolved?
dusty valve
practice competition problem, im trying to understand why my solution is wrong:
need a sec to post it
topaz sinewBOT
practice competition problem, im trying to understand why my solution is wrong:
...
dusty valve
near panther
Wdym by 4 even and 5 odd
near panther
For the 10s digit you can have 0, 2, 4, 6, 8 so wouldn’t there be 5? Unless you mean something else
dusty valve
the first division is for the hundreds places
but yea for the 10s place i wrote 5 in the next branch
near panther
What does the 4 even 5 odd column mean then
I thought it was like first column is 100s then next is 10s then next is 1s
dusty valve
that was a split of the hundreds column
because i was looking for combinations of two digits that were both odd or even
topaz sinewBOT
@dusty valve Has your question been resolved?
near panther
Oh so it’s 40 for the top since 4x5 + 4x5
Ok I think I get it now I was confused because I though you wrote 105 and 15 instead of 10s and 1s
half field
topaz sinewBOT
half field
Can somebody teach me this part ?
topaz sinewBOT
@half field Has your question been resolved?
half field
<@&286206848099549185>
native raptor
Area of the sector of a circle is
πr^2 * x/2π
where x is the angle subtended by the sector at the centre.
here,
r = 1.8
x = π/4
there's 4 of these sectors so,
4 * (πr^2 * (π/4)/2π)
= 4 * (π(1.8)^2 * 0.125)
= 4 * 1.272348
= 5.09
now, your shaded region excludes that small circle in the middle, so we have to subtract that area
same formula, except this time, r = 1
4 * (π(0.5)^2 * 0.125)
= 4 * 0.098175
= 0.393
subtract area of the small circle sectors from the area of the bigger sectors,
5.09 - 0.393 =~ 4.7
that's the area of the shaded part
@half field can you do the rest by yourself?
half field
same formula, except this time, r = 1
the small circle radius not 0.5 ? thats diameter for 1
half field
ah nvm
half field
4 * (π(0.5)^2 * 0.125)
= 4 * 0.098175
= 0.393
how does 0.125 came from ?
native raptor
how does 0.125 came from ?
π/4 divided by 2π
if radians are confusing
π/4 = 45 degree
2π = 360 degree
45/360 = 0.125
native raptor
π/4 divided by 2π
you can just put this in your calculator and get the same result
the shaded part are the holes in the brooch
so we subtract them from the area of the whole circle
area of the whole circle = π(2.2)^2 = 15.2
subtracting the shaded part from the whole circle,
15.2 - 4.7 = 10.5
Area of brooch = 10.5 cm
depth = 1mm = 0.1 cm
therefore, volume = Area * Depth = 10.5 * 0.1 = 1.05 cc
that should be the answer
half field
4 * (π(0.5)^2 * 0.125)
= 4 * 0.098175
= 0.393
When I find the small circle why don't use πr² directly?
half field
π/4 = 45 degree
2π = 360 degree
45 deg is like 1/8 sector of the circle
native raptor
45 deg is like 1/8 sector of the circle
yea, and 1/8 is 0.125
native raptor
When I find the small circle why don't use πr² directly?
our sector areas only consider the blue parts of the smaller circle
and the whole small circle is the red outlined in red
see how there are still white regions? if we used pi r^2 directly, we would take those into account too
which we don't want, we only want the blue parts of the smaller circle, that's why we used the sector formula again and multiplied it by 4
does that make sense?
half field
ooh
native raptor
our sector areas only consider the blue parts of the smaller circle
I did a poor job but if this were accurate,
the small circle would be half blue half white
so using the whole circle area would mean you're taking twice of what you need to take
half field
I did a poor job but if this were accurate,
the small circle would be half blue ...
its okay i can imagine this
the radius 1.8 is only the line silver color right ?
not counted from the blue
native raptor
Im sorry I don't quite get what you mean
the radius 1.8 is from the centre to the edge of the shaded region
the pink line there is 1.8
and the pink line till the red outline is 0.5
half field
(n+1)! = ?
n(n-1)!
native raptor
so, your 2nd line is kinda wrong
half field
oh okay
native raptor
n(n-1)!
uh, no, Check what I wrote
hmm
3! can be written as 3*2!
any number's factorial can be written as that times the factorial of it's previous number
the previous number is gotten by subtracting 1
so, the antecedent number of n+1 is n
hence (n+1)! is (n+1)n!
does that make sense?
half field
yup
native raptor
oh my bad it's not wrong.. my eyes are tired sorry
you just arranged it differently
half field
so n = 0 or n = 5 yea
alright thank you
topaz sinewBOT
@half field Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
topaz sinewBOT
lucid moat
This is the correct contrapositive right
I’m not dumb right
How does the absolute value signs affect the proof? How does it change from just a = b?
<@&286206848099549185>
potent urchin
You could also have a = -b
lucid moat
You could also have a = -b
wdym
potent urchin
This is the correct contrapositive right
But yeah that's correct
potent urchin
But indeed |3| = |-3|
still nacelle
Yeah that looks right
still nacelle
I think the last paragraph is a bit confusing. I would rather say “since (n, k)€Z and kn=1, |k|=|n|=1, then
|b|=|an|=>|b|=|a| (((OR))) |a|=|bk|=>|a|=|b|”
Excuse my use of the Euro
potent urchin
Also the first line of your proof should say "it's enough to prove that if a | b and b | a then |a| = |b|"
or something along those lines
topaz sinewBOT
@lucid moat Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
undone flicker
If three points are given, is there any direct formula to find the circle equation?
topaz sinewBOT
If three points are given, is there any direct formula to find the circle equati...
undone flicker
Points are (2,2), (9,9) (x,0)
topaz sinewBOT
@undone flicker Has your question been resolved?
ionic oar
$x^2 + y^2 + 2gx + 2fy + c = 0$
thorny flameBOT
NEON
topaz sinewBOT
Available help channel!
tough void
hello i need help to find out how much is in somfing like "how much wahter is in a pool thats 5 x 5 x 5 meters big
topaz sinewBOT
hello i need help to find out how much is in somfing like "how much wahter is in...
versed cairn
well find the volume of the shape
tough void
well i know that i just dont know how to do them
versed cairn
hello i need help to find out how much is in somfing like "how much wahter is in...
5x5x5 meters big means that length of 1 side of the cube is 5meter
volume = "length^3"
tough void
so i just multiply all the numbers and the number i geht is the volumen?
so L in wahter?
mint raft
you will get the volume in m^3
mint raft
dose that aplly to evry lenght so if i have 13 x 2 x 8 meters?
you get it from multiplying
13 meters x 2 meters x 8 meters
mint raft
yes
tough void
and thats the volumen?
mint raft
yes, the answer is 208 m^3
tough void
ohhh now i geht it
and how was it with liters again?
so how do i find it out in liters
tough void
...
okey so i got that now
i just need to remember it
waht is my main problem
but thank you and @versed cairn alot
.close
untold forge
Uh I remember seeing this in a video somewhere but dont remember...
Prove that the sum of all natural numbers (1+2+3+4+5+6+...) = -1/12, accepting that the distributive law works for infinite sets of numbers
vital relic
Who has assigned you this question
cinder sigil
Who has assigned you this question
must be a physics prof
golden mesa
prove it and i'll give you a million dollars
topaz sinewBOT
@untold forge Has your question been resolved?
untold forge
prove it and i'll give you a million dollars
Lol
Can anyone help me then?
Im thinking just say x equals the set.. say a = (1-1+1-1+1-...) forever
and if y = (1-2+3-4+5-6+7-...) forever
If you can figure out A, you can figure out y and hence x
But the distrubutive law probably doesnt work for infinite sets of numbers so this wouldnt be true normally but it is explicitly stated in the question
So say 1-a = 1-(1-1+1-1+1-...)
You can distribute the 1 on the right side
so it just becomes A again, since its infinite
so 1-a=a
a=1/2
Alright now i think i might be able to do it
Hmm
2y=a
just realised
y= 1/4
s-y would be (4+8+12+...) which is just 4s 😆
s-y = 4s
s- 1/4 = 4s
s = -1/12
Pretty simple
Ok
.close
neon iron
this is a bit of an odd question
topaz sinewBOT
this is a bit of an odd question
neon iron
ionic oar
Ah yes a classic
neon iron
envision this circle in the yz plane, is it possible to verify that $\dd {\vb E_y}$ will always be equal to $0$ other than like, "it looks like it"?
thorny flameBOT
ionic oar
dEy won't be 0
neon iron
E_y will be
neon iron
mistake on my end
ionic oar
you can set up a polar integral i think right
You can just integrate it regularly
You'll have the integral of an odd function from -a to a or whatever
And that would be 0
neon iron
oh cool okay
although another question is kinda confusing me
A nonconducting disk of radius $R$ has a uniform positive surface charge
density $\sigma$. Find the electric field at a point along the axis of the disk a
distance $x$ from its center. Assume that $x$ is positive.
its pretty much similar to the one above i think lol
thorny flameBOT
ionic oar
you'd integrate the field of elemental rings for this one yes
No component shenanigans
neon iron
also
what does "a nonconducting" imply here even
like ik what it means
but what is the meaning of including it
ionic oar
If it were conducting all the charge would repel and appear on the surface
It would effectively become a ring
ionic oar
vale heath
let x and y be vectors
topaz sinewBOT
let x and y be vectors
vale heath
there isnt a difference between x.y and |x.y| is there
golden mesa
x.y can be negative
topaz sinewBOT
shrewd crow
<@&286206848099549185>
ive tried too many times and i keep getting it wrong
.reopen
golden mesa
get a new channel, this one will close
young prawn
vale heath
😶
vapid hawk
.reopen
topaz sinewBOT
✅
vale heath
😮💨
vapid hawk
but now whose channel is this...
vale heath
guys the channels in my name; unless u were the last user dont re open
just ask ur question
first .close tho
vapid hawk
do u have any question?
vapid hawk
ah wait you closed it, sorry for re opening. i thought it was closed mistakenly
please close it, again apologies
vale heath
.close
hollow void
can someone explain how i can approach the second objective? what does it mean by calculus techniques?
topaz sinewBOT
can someone explain how i can approach the second objective? what does it mean b...
hollow void
i asked my teacher on kinda how to answer it and he said this
how do i use calculus techniques to find a range??
this is application of derivatives btw
potent silo
Hello @hollow void, depending on the value c, you can have a different amount of stationary points and a different amount of roots. You first need to tell every possible outcomes for these two numbers
hollow void
Hello <@706411907351052328>, depending on the value c, you can have a different ...
yes i have them :D
potent silo
Cool! Can you tell me what you got?
potent silo
Ok, so Part B asks you to prove all of it mathematically. Is the question clear?
hollow void
yes with calculus techniques