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lone tangle
how is this equal to 1?
marsh citrusBOT
how is this equal to 1?
lone tangle
according to my understanding "complex" = "conjugate of complex" only when z is purely real
this is the question
viscid sky
PW xD?
lone tangle
yea lol
past maple
how is this equal to 1?
Since $\dfrac{7z_2}{5z_1}$ is imaginary, we can write $\dfrac{7z_2}{5z_1} = ki$ for some $k\in\mathbb{R}$. Then use the identity $|a+bi| = \sqrt{(a+bi)(a-bi)}$:
$$\dfrac{|2+3\tfrac{z_2}{z_1}|}{|2-3\tfrac{z_2}{z_1}|} = \dfrac{|2+3\cdot\tfrac{5k}{7}i|}{|2-3\cdot\tfrac{5k}{7}i|} = \dfrac{\sqrt{(2+3\cdot\tfrac{5k}{7}i)(2-3\cdot\tfrac{5k}{7}i)}}{\sqrt{(2-3\cdot\tfrac{5k}{7}i)(2+3\cdot\tfrac{5k}{7}i)}} = 1$$
viscid sky
yea its mod so both will be equal
elfin berryBOT
d
lone tangle
in general | z | = | z̅ | for any complex no. ?
past maple
Yes
viscid sky
yes
viscid sky
Chu#ya banane ke liye diya h
lone tangle
Since $\dfrac{7z_2}{5z_1}$ is imaginary, we can write $\dfrac{7z_2}{5z_1} = ki$ ...
oh ok gotcha
thanks!
woeful rivet
Hello, is this correct?
marsh citrusBOT
Hello, is this correct?
woeful rivet
marsh citrusBOT
@woeful rivet Has your question been resolved?
woeful rivet
<@&286206848099549185>
oblique falcon
.
woeful rivet
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marsh citrusBOT
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inner delta
answer should be D yes?
inner delta
<@&286206848099549185>
marsh citrusBOT
@inner delta Has your question been resolved?
main idol
answer should be D yes?
!show
marsh citrusBOT
answer should be D yes?
Show your work, and if possible, explain where you are stuck.
marsh citrusBOT
@inner delta Has your question been resolved?
teal kernel
marsh citrusBOT
teal kernel
help
tall pewter
!status
marsh citrusBOT
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
shell granite
The larger angle is the one facing the taller side
teal kernel
The larger angle is the one facing the taller side
it says explain tho, how should i explain it
man this is hard
shell granite
Maybe just say because it's facing the tallest side ig
teal kernel
Maybe just say because it's facing the tallest side ig
alrr thankss
wb question b
wait
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still temple
marsh citrusBOT
still temple
could someone explain the process of this pls
hazy idol
Those are the two rules now watch
elfin berryBOT
SkyTwX
still temple
oh
why does my screenshot go further
to make it with a 1 in numerator
whats the point of that part
dont i want whereu ended it instead
hazy idol
dont i want whereu ended it instead
You don't want anything, it's just to see how you can manipulate this kind of expression. It is very important to be fluent and to know what you can do and what you can't do
elfin berryBOT
SkyTwX
hazy idol
See? You should be able to do things like that if needed
marsh citrusBOT
@still temple Has your question been resolved?
still temple
You don't want anything, it's just to see how you can manipulate this kind of ex...
do u think flashcards is the best way to know
hazy idol
do u think flashcards is the best way to know
No, just remember the two rules
hazy idol
**SkyTwX**
Rule one: negative exponent is simply a denominator
Rule two: multiplying with same basis "a" is given by adding the exponents
hazy idol
And so one.. You need to know the two rules and to practice a lot, that's it
still temple
And so one.. You need to know the two rules and to practice a lot, that's it
where can i practice
do u know a place i mean
hazy idol
where can i practice
Idk my friend
I just took the first link I could find on Google
https://www.matesfacil.com/english/secondary/solved-exercises-powers.html
marsh citrusBOT
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random nymph
"Interpret the geometric relationship."
|z+i|=<1
marsh citrusBOT
"Interpret the geometric relationship."
|z+i|=<1
stoic saddle
is z real or complex?
random nymph
i is complex 😉
knotty trellis
not an answer to ann's question
random nymph
I have No idea
spark otter
Then z should be complex in any case
random nymph
i is complex No?
spark otter
Yes it is
First step : write z = x+iy and square both sides of the inequation. Deduce something about the point (x,y) compared to the point (0,1)
random nymph
What
spark otter
What part do you not understand?
random nymph
Can you use simple words
spark otter
Ok
Let z be any complex number
That means we can write it as z = x + iy, where x and y are real numbers, right?
spark otter
Then, z+i = ?
random nymph
<=1
spark otter
First of all, that's not true because z+i is complex
spark otter
Radius of what?
spark otter
Yes I know, but I'm asking if you know what else do we need
random nymph
Absolut belopp is a circle with a its own center
random nymph
Yes I know, but I'm asking if you know what else do we need
X+iy +i im assuming?
spark otter
X+iy +i im assuming?
That's where i was going towards
random nymph
Module?
spark otter
And you wrote x+2iy instead of x+i(y+1)
random nymph
And you wrote x+2iy instead of x+i(y+1)
I dont get it
spark otter
So you already knew that this meant that z is in a disk?
random nymph
Where does 1 come from
random nymph
So you already knew that this meant that z is in a disk?
I can tell its a circle Yeah? Or sorry its the center point.
(X+iy)i
spark otter
So |z+i| <= 1 means that z is in the disk of center ___ and of radius ___
random nymph
Why
random nymph
Yup
spark otter
Ok so that's it
random nymph
But that’s the same as x+2iy
spark otter
But that’s the same as x+2iy
You're telling me that 2iy is the same as i + iy ?
spark otter
i² is -1
spark otter
So an imaginary number, i+iy, is the same as a real number -y ?
random nymph
No
random nymph
That’s 2i y
spark otter
Or is that multiplication
Yes
spark otter
There we go
So getting back from the beginning, what is the center of the circle if |z+i| <= 1 ?
random nymph
I dont know
spark otter
Hint : |z+i| represents the distance of z to the center of the circle
random nymph
Because x is still unionen
spark otter
No need for that
random nymph
Hint : |z+i| represents the distance of z to the center of the circle
I know from the origo
spark otter
So the center of the circle is at distance 0 from itself
random nymph
Wait why is x disregarded
spark otter
Wait why is x disregarded
z = x+iy so it is not
random nymph
Intresting. Im guessing because it has No real number in that form
random nymph
i(1+y)
spark otter
Nonono forget about that sorry
random nymph
Z is iy
spark otter
Let's be quicker
Nono forget about x and y for a bit
What is the only complex number z that verifies |z+i| = 0
spark otter
Yes
random nymph
Is that its root
spark otter
So the center of the circle is -i
spark otter
So we finished
"|z+i| <= 1" means that z is on the disk of center -i and of radius 1
random nymph
Why Did we do =0
spark otter
To find the center
random nymph
That would mean the radius is 0?
spark otter
The center is at distance 0 of itself
spark otter
That would mean the radius is 0?
No, the radius is 1
random nymph
Oh shit
random nymph
z is a complex number?
random nymph
What made you think of 0
Did you force the equation to know its distance of 0
@spark otter
spark otter
Well it's just about finding the center of the circle
If |z+i| is the distance of z to the center of the circle
Then plug z = center
And so you have distance of 0
grand aurora
any geometry helper :v
marsh citrusBOT
any geometry helper :v
smoky plover
Find BP or PQ with LOC and then find BQ with LOS
marsh citrusBOT
@grand aurora Has your question been resolved?
grand aurora
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knotty salmon
hollow sparrow
hi you still have an open channel at #help-34 . Can you work there or close that channel first? Otherwise close this one. We don't allow more than one channel open at a time
knotty salmon
hi you still have an open channel at <#908075848752590918> . Can you work there ...
Sorry, people left so I went to another
.close
marsh citrusBOT
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Available help channel!
jolly sigil
marsh citrusBOT
jolly sigil
I emailed my professor about this but why would you draw a tree diagram?
why not just a venn diagram?
tight furnace
A tree diagram lets you choose one condition first
tight furnace
so, the second bill depends on the first bill (that is, it is easier to predict the second bill outcome given the first bill outcome then the other way around)
jolly sigil
I thought it would just be a intersection problem
A and B must occur
not
like what's the prob that they pay the second month given that they paid the first month
There's like certain words I'm looking for and it didn't seem like a conditional prob
I'm still unsure about the tree diagram.
Like would I make two nodes
one where they pay the first and one where they don't pay
marsh citrusBOT
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frank eagle
Consider the DE $\frac{\mathrm{d}x}{\mathrm{d}t}=t\tan x$ with initial value $x(0)=\frac\pi{6}$. \
-
Find the solution. \
-
Describe the region in which the solutions are defined.\
marsh citrusBOT
Consider the DE $\frac{\mathrm{d}x}{\mathrm{d}t}=t\tan x$ with initial value $x(...
elfin berryBOT
sunside
frank eagle
We see that $x=k\pi$ is a solution for $k\in\mathbb Z$. So suppose $\tan x\neq 0$, then rearranging and writing $\tan x=\frac{\sin x}{\cos x}$ we have $$\frac{x'\cos x}{\sin x}=\frac{\mathrm{d}}{\mathrm{d}t}\log(|\sin x|)=t.$$ Integrating, we obtain, $$\log(|\sin x|)=\frac{t^2}{2}+C$$Now, how do I get rid of the absolute values here?
elfin berryBOT
sunside
red gulch
What are the values of x
frank eagle
What are the values of x
0<x<pi and pi<x<2pi
red gulch
if that's the case what are the values of sin(x)
frank eagle
well, for those intervals I stated, we have 0<sin(x)<1 and -1<sin(x)<0 respectively
red gulch
Well if 0 < x < pi, then 0 < sin(x) < 1 and so on that interval |sin(x) | = sin(x)
frank eagle
indeed
red gulch
On the interval pi< x < 2pi, then we know sin(x) < 0, and so we can't remove the absolute values or else we would be evaluating log(b) for a negative b, for which log is not defined
So there must be some issue with your intervals
frank eagle
I think one has to argue about something with uniqueness of solution, if the initial value is x=pi/6, then x will always remain positive, right?
red gulch
Possibly, I'm not too familiar with ODE's I'm afraid what I said is all I'll be able to offer
Maybe someone else may know more
frank eagle
.close
timid ice
Just want to be sure. The limit as x approaches 2 from the right is DNE, yes?
lyric bay
No
timid ice
Is it -2 then
lyric bay
The definition of a limit is where the graph/function is heading to
lyric bay
Is it -2 then
Yeah great!
timid ice
So when I see a point on the x value I’m looking at, but there’s two open circles on the x value at different y coordinates, it’s not DNE?
lyric bay
Open circles are called "holes" btw
The value from left and right can be different
However, the limit at a specific value can not exist if the left and right limits are different
timid ice
Okay. So look at the values of the hole’s graph (line/segment) on the right side, in this instance
Thanks!
.close
still temple
what were the steps to simplifying and solving a limit that has a fraction involved?
marsh citrusBOT
what were the steps to simplifying and solving a limit that has a fraction invol...
marsh citrusBOT
@still temple Has your question been resolved?
marsh citrusBOT
@still temple Has your question been resolved?
still temple
as first step i would simpify it.
thats exactly what i need to know how to do
i can do it when its like
the foil methood
but i dont know where to start when it comes to fractions
spark siren
you have a difference of two fractions in the numerator. write this as one fraction.
jade iron
do the reciprocal now
spark siren
sorry. no. what is the common denominator in $\frac{1}{3+h}-\frac{1}{3}$?
elfin berryBOT
ThM
spark siren
do the reciprocal now
does not make sense as long as the first step is wrong.
jade iron
does not make sense as long as the first step is wrong.
I see, didn't look at the previous comments
still temple
hm
still temple
sorry. no. what is the common denominator in $\frac{1}{3+h}-\frac{1}{3}$?
so would it just be h? it doesnt make sence to me since technically there arent common denominator as long as h is there
spark siren
$\frac{1}{3+h}-\frac{1}{3}=\frac{-h}{3(3+h)}$
elfin berryBOT
ThM
spark siren
so would it just be h? it doesnt make sence to me since technically there arent ...
yes, and therefore you have to do some operations to get a common denominator. i think you should practice such calculations.
still temple
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marsh citrusBOT
marsh citrusBOT
Available help channel!
misty crest
is this correct? ( this is for no. 5 )
marsh citrusBOT
is this correct? ( this is for no. 5 )
hard gull
yeah , negative sign cancels out
late geode
poor notation
hard gull
u are left with 5+7
hollow oracle
poor notation
?
misty crest
okaaay thank youuu
late geode
$$(x^2-4)(3)$$
represents the product of $(x^2-4)$ and 3, which is NOT what you want. \
same issue with the \ $w(-3)$, and even worse the fraction line is invisible
elfin berryBOT
ℝam()n()v
misty crest
so.. what did i do wrong here ;-;
hard gull
what he is trying to say is write it like this
x^2 -4
as x = 3
3^2 - 4 and so on
so that its easily understandable
late geode
you could instead write something like
$$(x^2-4)\eval_{x=3} + \br{\frac{3x+2}{x+2}} \eval_{x=-3}$$
elfin berryBOT
ℝam()n()v
hard gull
or like that
misty crest
okaaay, thank youuuu
i'm not sure what i'm going to do here...
do i simplify the like terms?
late geode
what's with the extra multiplication by x to the numerator and denominator
misty crest
oh i just put the x sign there as reference
late geode
this is similar to the notation issue i mentioned before
and here you actually DID multiplication that you shouldn't have
$\br{\frac hf}(x) = \frac{h(x)}{f(x)}$
elfin berryBOT
ℝam()n()v
late geode
which is $$\frac{6x^2-24}{x^2-4}$$
elfin berryBOT
ℝam()n()v
late geode
and this can be simplified further
misty crest
oh i don't need to distribute the x;-;?
late geode
there's NOTHING to distribute
h(x) is NOT the product of h and (x)
h is NOT 6x^2 - 24
f(x) is NOT the product of f and (x)
f is NOT x^2 - 4
misty crest
so i'll just invalidate the (x) in the scenario?
late geode
no
late geode
!help
marsh citrusBOT
Please read #❓how-to-get-help
royal blaze
bruh i dont wanna read allat
late geode
well read it if you want to get help
failure like insisting on asking here will most likely go ignored
royal blaze
aight
misty crest
no
from the lessons of my prof, he keeps distributing all these stuff and i keep getting confused on what i should distribute or not ;-; so what must i do
late geode
it may resemble "distribution", i wouldn't describe it as such
misty crest
then what should i do with the x? nothing?
late geode
no
give this a read
there's a whole chapter on this type of stuff
understand the notation
misty crest
okayyy thank you
green crag
Given $E_m^a = {x \in [0, 1] \colon \abs{f_m(x)} < a}$, how do I show $\bigcap_{k=1}^{\infty} \bigcup_{l=1}^{\infty} \bigcap_{m\geq l} E_m^{\frac{1}{k}}$ is equal to $x \in [0, 1]$ such that $f_m(x) \to 0$ as $n \to \infty$? I can kind of describe the unions/intersections and have that correspond to convergence on the right but I'm unsure of how to make that justification more rigorous.
marsh citrusBOT
Given $E_m^a = \{x \in [0, 1] \colon \abs{f_m(x)} < a\}$, how do I show $\bigcap...
elfin berryBOT
endrev
marsh citrusBOT
@green crag Has your question been resolved?
green crag
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marsh citrusBOT
@green crag Has your question been resolved?
marsh citrusBOT
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frank eagle
Basic question probably, but consider the equation $$|\sin x| = |A|e^{\frac12 t^2}.$$ Here $x$ is the dependent variable and $t$ is the independent variable. I would like to solve for $x$, but I'm unsure if I can remove the absolute value signs. Does it follow from this equation that $A$ has to have the same sign as $\sin x$?
marsh citrusBOT
Basic question probably, but consider the equation $$|\sin x| = |A|e^{\frac12 t^...
elfin berryBOT
sunside
pine ravine
You can redefine something as C to include both positive and negitive elements
allowing you to remove the abs sign
frank eagle
You can redefine something as C to include both positive and negitive elements
how would you do that?
frank eagle
ok 🙂
pine ravine
See during the end where I redefined k
It should be +/- e^c but hopefully that makes sense
the constant takes out the need for the abs
frank eagle
the constant takes out the need for the abs
hmm, ok, thank you for replying, I will have to think on this some more. It feels kind of strange for a constant to be able to "absorb" that plus minus sign, but it's apparently possible
whole sleet
DE is just "kind of like this"
sweet quail
still temple
You have to open your own help channel.
This one is currently occupied by someone else.
Try sending your message in #help-31 (a channel that is currently unoccupied which you can use )
still temple
marsh citrusBOT
still temple
is this odd, even, odd
I lost the answer keys, thats why I need just a confirmation so Im not doing it wrongly
sorry
Even: $f(x) = f(-x)$
Odd: $f(x) = -f(-x)$
replace f(x) with your functions and check for yourself
elfin berryBOT
Brandon H#1125
still temple
I used that rule to check for myself
and those are the answers I obtained
I want to make sure the processes of using those rules are done correctly
Yeah, it seems as though you're correct
ok thanks
it seems like you got some energy to do the checking work
.close
marsh citrusBOT
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meager gull
marsh citrusBOT
meager gull
in question 3 no C
how did he know it was a sphere and a cone?
and how did he get the limits of the theta integration?
marsh citrusBOT
@meager gull Has your question been resolved?
still temple
marsh citrusBOT
merry plaza
I dont understand how 1 works at all
marsh citrusBOT
I dont understand how 1 works at all
merry plaza
supposedly zZeta is suppoed to represent the line
on the complex plane
but how can the real part of it just stay constant?
merry plaza
then Re(z) = -c makes sense right? <@393206199979606026>
yes
rocky sapphire
and you know how multiplying by a complex number is like rotation?
merry plaza
yea u add the arguments
rocky sapphire
you can think of zeta_0 doing that
rotating the straight line
so you get the right slope for l
do you know how to prove (1) algebraically?
rocky sapphire
and where do you go from there
usually when you want to prove something like that
its easy to just replace all the complex variables with x+iy and simplify everything
try doing that for z,zeta_0 and calculating Re(zZeta_0) and see if you can choose a zeta_0 so you get the equation for l
marsh citrusBOT
Available help channel!
still temple
I dont get this at all
marsh citrusBOT
I dont get this at all
supple yarrow
Where did they get the 4?
what is u1 here?
like a1?
like first term?
what is U1?
still temple
Its progression and sequence
So We need to find the Comkon different and first ter no
still temple
Ya
summer trench
$S_{n}=\frac{n}{2}(2a+(n-1)d)$
elfin berryBOT
yajatk07
still temple
Where did the 2aa comw from?
summer trench
thats the arithmetic prog. sum formula
summer trench
you have 2 eq, and 2 unknown, simply solve it using substitution
supple yarrow
\
yeh
see
they first used the Sum of all terms formula
then they found 1st tern that is A1 or U1
supple yarrow
you have 2 eq, and 2 unknown, simply solve it using substitution
bruh
summer trench
Find the value of- $$\tan{\theta}.\tan(60^{\circ}-\theta).\tan(60^{\circ}+\theta)$$
marsh citrusBOT
Find the value of- $$\tan{\theta}.\tan(60^{\circ}-\theta).\tan(60^{\circ}+\theta...
elfin berryBOT
yajatk07
desert socket
show work
summer trench
i dont have a mobile
but i did some simplification
after
just multiplied them and tried to use any other identity
desert socket
do you know tan(3x) formula?
summer trench
yep
desert socket
well, it is quite hard to get you to that with no knowledge of your progress
just use difference of squares formula in numerator and denominator
summer trench
alright, ill try using that
desert socket
$\tan\left(3x\right)=\frac{3\tan x-\tan^{3}x}{1-3\tan^{2}x}$
elfin berryBOT
B-eard
summer trench
yeah
desert socket
$\tan x\cdot\frac{\left(\tan60-\tan x\right)}{\left(1-\tan60\tan x\right)}\cdot\frac{\left(\tan60+\tan x\right)}{\left(1+\tan60\tan x\right)}$
elfin berryBOT
B-eard
desert socket
See the (tan60+tanx)(tan60-tanx)
you can write it as tan^2 60-tan^2 x
similarly for the bottom onw
summer trench
wait
summer trench
oh
desert socket
Notice that is the same thing
marsh citrusBOT
marsh citrusBOT
Available help channel!
random sphinx
i couldnt define a^2, what should i do
marsh citrusBOT
i couldnt define a^2, what should i do
still temple
Try a^2=b
random sphinx
i got -6
still temple
So a^2=-6
random sphinx
ok thanks
here's another one im struggling with
i'm supposed to type the numerator from the fraction at then end and it was 7, but ig it's wrong 🤷♂️
still temple
i'm supposed to type the numerator from the fraction at then end and it was 7, b...
Subtract the degree of denominator from degree of nominator
It is 2
So multiply x+3 with x^2 and substract from nominator
Do it again until there aren't any terms with x in numerator
still temple
Me too found -7
wooden grotto
May someone help me with this?
marsh citrusBOT
May someone help me with this?
marsh peak
What's your question?
Ah
Well, if you look over each step
You will notice that every type of step is valid
Except for dividing both sides
Dividing both sides (or anything in general) by what number is not allowed?
wooden grotto
Dividing both sides (or anything in general) by what number is not allowed?
The flaw occurs in the 4th step, right? The common factor (b−a)(b−a) is canceled from both sides. However, if a=ba=b as stated in the beginning, then (b−a)=0(b−a)=0. Dividing both sides of an equation by zero is undefined, making this step invalid...
marsh peak
Yes
sterile rock
wooden grotto
Yes
I'm now being asked this:
So, aside from the obviously false first claim 2=1, each other step is valid when read from bottom to top, right?
marsh peak
Yeah
marsh peak
I've seen many people say that multiplying both sides by 0 is invalid; Sure, it doesn't do anything useful, but, it yields the equations 0 = 0
Which is true
And anything implies true
proper zodiac
The question is now asking about the proof from bottom to the top
marsh peak
that way you can literally prove 2 = 1
I am saying that "a = b implies 0 * a = 0 * b"
Not the converse
undone bane
oh understood
open kayak
I've seen many people say that multiplying both sides by 0 is invalid; Sure, it ...
If we start from a true statement a \neq b, then multiplying both sides by 0, we'll have 0 \neq 0.
Why would we consider an operation like that valid?
Shouldn't the operations we perform preserve the truth value of the equation?
If we define a "step" to mean that
proper zodiac
1 != -1 but 1² = (-1)²
Some operations only go one way, and make unequal things equal and that's fine
open kayak
If we start from a true statement a \neq b, then multiplying both sides by 0, we...
Ah, the last sentence is false, yeah, then multiplying by 0 should be fine
marsh citrusBOT
Available help channel!
waxen heron
marsh citrusBOT
waxen heron
The overall outcome will be something that is satisfying E and F which is EF. I do not know how to relate this to this $B_\Omega$
elfin berryBOT
13wrc
waxen heron
so here the event of E is B_Omega and the reduced sample space of P_f(E) is now F . We should look for all the instances of B_omega now in F to compute P(E|F).
marsh citrusBOT
@waxen heron Has your question been resolved?
final trail
Why is my answer not correct:
0 -1
-1 0
My work:
cos(-pi/2) -sin(-pi/2) * 1 0 = 0 1 * 1 0
sin(-pi/2) cos(-pi/2) 0 -1 = -1 0 0 -1
ancient slate
wait you wrote it in that order?
ancient slate
Yeah that would make sense
Here's the deal
Suppose the input of the transformation is called x
Let's call the rotation part Rot, and the reflection part Ref
The problem says you rotate x first. So that Rot(x)
Then the problem says you reflect the result of that
So Ref(Rot(x))
You had the order wrong
final trail
Oh, so:
1 0 * 0 1
0 -1 -1 0
ancient slate
Yes!
It's one of those things that you need to be careful with, especially since matrix multiplication is not commutative
The order REALLY matters
final trail
I see
ancient slate
try it out
glacial lynx
Why is it not 25πh for the first part but 5πh²??
marsh citrusBOT
Why is it not 25πh for the first part but 5πh²??
open plume
how did you get 25πh for the first one? show us some work so that we can better assist you.
glacial lynx
Been trying to get a picture
glacial lynx
how did you get 25πh for the first one? show us some work so that we can better ...
I don't see how there is supposed to be an x with the r, which I'm assuming has to be the case since there is a x^2 with the r in the answer
Ping me if you respond
marsh citrusBOT
@glacial lynx Has your question been resolved?
glacial lynx
<@&286206848099549185>
I'm using the circle formula with disk method to get the hemisphere volume
marsh citrusBOT
@glacial lynx Has your question been resolved?
marsh citrusBOT
@glacial lynx Has your question been resolved?
marsh citrusBOT
@glacial lynx Has your question been resolved?
glacial lynx
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
lethal bridge
i don’t get what the question is asking
marsh citrusBOT
i don’t get what the question is asking
lethal bridge
Where’s my function??
undone bane
h(x)
lethal bridge
but there’s nothing there to differentiate
undone bane
f'(1) is given
f(1) is given
g'(1) is given
g(1) is given
what else do you need?
lethal bridge
But those are all the values I substitute in therefore there’s no where to put x = 1?
Unless it wants me to set the derivative = 1
stoic saddle
you are told exactly what f(x), g(x), f'(x) and g'(x) all are at x=1
tf else do you want
lethal bridge
idk
stoic saddle
well it’s
f’g - fg’ / g^2
missing parentheses
lethal bridge
stoic saddle
$h'(x) = \frac{f'(x)g(x)-f(x)g'(x)}{g(x)^2}$
elfin berryBOT
Ann
lethal bridge
basically what I said 
stoic saddle
you substitute x=1 in here it is really not as complicated as you are making it.
lethal bridge
okay yeah I get it now lol
For part i
What does it mean find the values a and b so that it is smooth?
undone bane
$h'(x) = \frac{f'(x)g(x)-f(x)g'(x)}{g(x)^2}$
missing parantheses in denominator
undone bane
waterbeam can
lethal bridge
woah flame
stoic saddle
waterbeam can misread a lot of shit on purpose
lethal bridge
not ON purpose
stoic saddle
much like anybody else who may be maliciously minded
lethal bridge
am not maliciously minded
undone bane
lethal bridge
ok never mind I get the smooth part. So do I just differentiate the parabola function for I)
stoic saddle
you will need that yes
you want y'(0) = 1.2 (the slope of line RO) and y'(30) = -1.8 (the slope of line PQ)
lethal bridge
y’ = 2ax + b
stoic saddle
solve for a and b this way
lethal bridge
you want y'(0) = 1.2 (the slope of line RO) and y'(30) = -1.8 (the slope of line...
Why do we do this for RO and PQ
stoic saddle
read the problem
you want the slope of the parabolic part to match that of the straight parts at the juncture points x=0 as x=30
undone bane
the hint is given in the question
lethal bridge
read the problem
Where does it say x=0?
stoic saddle
the straight line sections must be tangent to the parabola at O and at P.
stoic saddle
y'(0) is the slope of the tangent to the parabola at x=0
we want this tangent to coincide with RO
therefore we set that slope equal to that of RO
to repeat myself for what i think is the third time
stoic saddle
||inb4 the fluorescent ceiling light of your understanding blinks off again and you have to ask again||
lethal bridge
Not gonna happen
stoic saddle
hopefully not.
stoic saddle
yes
lethal bridge
So if 30m is the horizontal distance from p to the y axis how does y’(30) help why not y’(0) again?
lethal bridge
||inb4 the fluorescent ceiling light of your understanding blinks off again and ...
So anyways
stoic saddle
So if 30m is the horizontal distance from p to the y axis how does y’(30) help w...
ugh
stoic saddle
y'(0) is the slope of the tangent to the parabola at x=0
starting from here, replace "0" with "30" and "RO" with "PQ"
lethal bridge
y’(30) at x=30?
undone bane
sigh
undone bane
y’(30) at x=30?
yeah
undone bane
lethal bridge
stoic saddle
y’(30) at x=30?
i mean i didn't ask you to abridge my statement THAT far
lethal bridge
so I got y’(30) = 60a + b
Sounds right
so I need to find the values of a and b,
do I solve for a in y’(30)
since y’(0) gives me b?
stoic saddle
you know 60a+b = -1.8
stoic saddle
and you know b
stoic saddle
ann's presence is necessary for you
it's unfortunate
lethal bridge
it's unfortunate
stoic saddle
sully dyssrupt not me
undone bane
lol
lethal bridge
a = -1/20
Coolio so that’s part i done
For part ii) do I put the parabola into vertex form or something
I haven’t practiced much with the vertex stuff how do I do that
undone bane
find the x coord of vertex
undone bane
From the y = ax^2 + bx part?
yeah
lethal bridge
I can just
Bypass this using
f’(x) = 0
oh so genius
2ax + b = 0
Hm okay not sure what to do now
What if I make the vertex of the parabola = 30
Does that do anything
undone bane
you found the vertex?
lethal bridge
yeah 2ax + b = 0
lethal bridge
you found the vertex?
Isn’t that the vertex
unborn condor
You're given 2 line segments and a parabola arc
You're told that the transition needs to be smooth
transition being smooth requires:
a) the limit from each side at the point of transition is equal
b) the function is defined at that point
c) the value of the function and the limits are the same
d) the limit of the derivative from each side at the point of transition is equal
unborn condor
not really, since he's not done
lethal bridge
Well dats part i) and it’s alr done
undone bane
lethal bridge
not in a and b
How can I find the value of the vertex if I’m not given a or b
unborn condor
you ARE given a and b.
It's on part (i)
lethal bridge
I thought those were the values for the derivative at RO and PQ
lethal bridge
The derivative of PQ
undone bane
really?
unborn condor
that's problem data, -1.8
undone bane
a is the derivative?
lethal bridge
Yeah
unborn condor
bruh
undone bane
ok @stoic saddle please
unborn condor
ann hasnt been around 20 mins, it's safe to assume she is busy
stoic saddle
hhrgh
lethal bridge
oml
undone bane
your senses back now?
lethal bridge
your senses back now?
My senses is that is the derivative at x=30 to the line PQ
undone bane
ahmm
lethal bridge
What else could it be
unborn condor
you said part (i) is done, Dyss?
undone bane
it was
unborn condor
If so, can i condense the results of part (i)?
lethal bridge
the derivative is 2a(30) + b
no it’s a = -1/20
undone bane
atleast what he said
unborn condor
Okay. I'm gonna do the problem properly from the start to the end of part (i).
Data:
Slope of RO: 1.2; It's equal to derivative of function at x=0
Slope of PQ: -1.8; It's equal to derivative of function at x=30
O: (0, 0)
P: (30, unknown)
function: ax^2 + bx
derivative: 2ax+b
f'(0) = 1.2 = b
f'(30) = -1.8 = 60a+b
-3 = 60 a => a = -1/20
Function: (-1/20)x^2 + 1.2
Now, i'm told this is how far you got so far. Correct? understood until here?
@lethal bridge
lethal bridge
I didn’t get the function: -0.05x^2 + 1.2 part but everything else yes
unborn condor
-0.05 = -1/20
lethal bridge
can we keep it in fraction 
unborn condor
yes you can
lethal bridge
So what happens when we put values a and b into y = ax^2 + bx
unborn condor
you dont put values on a and b.
You were given a set of conditions.
Those conditions are only satisfied if a = -1/20, AND b = 1.2, simultaneously
since those conditions are only satisfied for a particular value of "a" and "b", your parabola has those values of "a" and "b". In other words, you know the exact parabola
lethal bridge
What’s -x^2/20 + 1.2 then isn’t that what you did?
lethal bridge
What’s -x^2/20 + 1.2 then isn’t that what you did?
How did you get that?
@unborn condor
unborn condor
Okay, step by step then. The first four lines i've wrote under the picture is data from the problem
The next line is just copying again the function
First step:
You have the function f(x) = ax^2 + bx; That's the parabola that you want to find
You compute the derivative, f'(x) = 2ax + b
First condition: it needs to be smooth on the origin.
Slope of RO must be equal to slope of the parabola at the origin.
Slope of the parabola at the origin is the derivative at x=0
So 1.2 = f'(0) = 2a*0 + b = b
So b = 1.2
You have the first parameter of the parabola
Second condition: it needs to be smooth at x=30.
Slope of PQ must be equal to slope of the parabola at x=30
Slope of the parabola at x=30 is the derivative at x=30
So -1.8 = f'(30) = 2a*30 + b = 60*a + 1.2
So -3 = 60*a
So -1/20 = a
You now have the other parameter of the parabola
with this, you have both parameters of the parabola, so you have the parabola.
If we graph it, we have this (now, to scale):
you can see the sketch you had was pretty decent
tracking so far?
lethal bridge
Yes I get that
unborn condor
Okay, so (i) is done. You got a and b.
(ii): You're asked for the vertical distance from the vertex , V, to P.
Step 1: Get V
Step 2: Get P
Step 3: Get the vertical distance
Do you know how to get the vertex of a parabola?
lethal bridge
Well I know we can take f'(x) = 0 to find the max/min which is the vertex
lethal bridge
ok
$y'\left(x\right)=2ax+b=0$
and im just guessing i put the values for a and b in idk why but i guess thats what you should do
$y'\left(x\right)=0\ ⇒2\left(-\frac{x^{2}}{20}\right)x\ +\ 1.2\ =0$
elfin berryBOT
water beam
lethal bridge
$y'\left(x\right)=0\ ⇒\ -\frac{2x^{3}}{20}+1.2$
elfin berryBOT
water beam
lethal bridge
is this right?
it doesnt look right
@unborn condor
wait
i did something wrong lol
i didnt put a correctly
$y'\left(0\right)\ =\ 2\left(-\frac{1}{20}\right)x+\frac{1}{2}=0$
elfin berryBOT
water beam
lethal bridge
$y'\left(0\right)=-\frac{x}{10}+\frac{1}{2}=0$
elfin berryBOT
water beam
lethal bridge
this should be better
unborn condor
where does that 1/2 come from
also, if you say y'(0), you cannot have an x anywhere, cuz x=0
elfin berryBOT
water beam
lethal bridge
$x=12$
elfin berryBOT
water beam
lethal bridge
is that right?
unborn condor
That's the x coordinate of the vertex.
You can also compute the x coordinate of the vertex of a parabola in the standard form (ax^2 + bx + c = 0) as:
Xv = -b/2a
However, that is not the vertex. You need the Y coordinate too for that, Yv. Do you know how to compute that one?
lethal bridge
i think i forgot how to do that
@unborn condor isnt it just $y=2\left(-\frac{1}{20}\right)12+1.2$
elfin berryBOT
water beam
lethal bridge
this still open?
yes
now you have opted to volunteer to take over
you are trapped here
forever
undone bane
i pass
also you found the x coord of the vertex
and y too
just calculate the distance now
undone bane
**water beam**
and no it is not
vertex coords satisfy the eqn of parabola, not the slope
lethal bridge
i thought you were smart and already got y
wtf
"i thought you were smart"
wowwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwwww
undone bane
undone bane
vertex coords satisfy the eqn of parabola, not the slope
.
lethal bridge
no its chinese
undone bane
you aint sm-
undone bane
lethal bridge
undone bane
shush now
lethal bridge
then give me y value now
undone bane
vertex coords satisfy the eqn of parabola, not the slope
.
lethal bridge
vertex coords satisfy the eqn of parabola, not the slope
thatdoesnt help me
undone bane
hmm
the point lies on the parabola
you found the x coord of the point
now that x coord will give y when you plug it in the equation of parabola
lethal bridge
oh my goshness
thats illegal
you cant do thatt
$y=-\frac{1}{20}\left(12\right)^{2}+1.2$
elfin berryBOT
water beam
lethal bridge
@undone bane
undone bane
yeah
lethal bridge
yeah
um actually i was testing you
and you got it wrong!!!!!!!!!
get pranked
it should be
$y=-\frac{1}{20}\left(12\right)^{2}+1.2\cdot12$
elfin berryBOT
water beam
lethal bridge
$y=\frac{d}{dx}\left(\frac{d}{dx}\right)\cdot\frac{d}{dx}\left(\frac{d}{dx}\right)=7.2$
yes?
elfin berryBOT
water beam
undone bane
i just saw the ^2 term and said ok
lethal bridge
i just saw the ^2 term and said ok
wow
how do i find the distanceeeeeeeeeeeeeeeeeeeeeeeee
using the vertex corrrrrrrrrrrds
wheres my formula for that
undone bane
no formula
lethal bridge
bruh
undone bane
its just the difference between the y coords
undone bane
you see that dotted line?
lethal bridge
you see that dotted line?
And it doesn’t have y coord measurement
undone bane
what should be the eqn of that line?
lethal bridge
what should be the eqn of that line?
a straight line?
undone bane
i asked the eqn
lethal bridge
im not sure
undone bane
it passes through P and is a straight line
so every point on that line will have the same?
marsh citrusBOT
@lethal bridge Has your question been resolved?
marsh citrusBOT
@lethal bridge Has your question been resolved?
carmine scroll
marsh citrusBOT
carmine scroll
Please how should i go about this
marsh citrusBOT
@carmine scroll Has your question been resolved?
carmine scroll
<@&286206848099549185>
grizzled portal
what i would do is first solve for α & β
marsh citrusBOT
@carmine scroll Has your question been resolved?
shut bear
\textcolor{blue}{Furthermore}, the product of any \textit{epsilon-function} with any other function that is simply bounded is also an \textit{epsilon-function}. For instance, the limit value of an arbitrary function (g(x)) which is not an epsilon-function is
[
g(x) = 2x + x^3 + n^2 + \frac{1}{3}n^2 + 10x^5 + 10^n \qquad \lim_{x \to 0}{(g(x))} = 10^{n} + \frac{4n^{2}}{3}
]
However, if we take the product of an epsilon-function with (g(x)), we see
[
\lim_{x \to 0}{(\ln(1 + x) \cdot g(x))} = 0
]
marsh citrusBOT
\textcolor{blue}{Furthermore}, the product of any \textit{epsilon-function} with...
elfin berryBOT
SimonWin
shut bear
Is this correct statement?
marsh citrusBOT
@shut bear Has your question been resolved?
shut bear
Nope
marsh citrusBOT
@shut bear Has your question been resolved?
shut bear
Nope
marsh citrusBOT
@shut bear Has your question been resolved?
shut bear
Nope
upper timber
Is this correct statement?
Yeah ln|1| is 0 so the product limits to 0 if that’s what you’re asking
shut bear
Yeah ln|1| is 0 so the product limits to 0 if that’s what you’re asking
I just meant if what i wrote is correct
But it seems as you're saying yes?
shut bear
Yeah ln|1| is 0 so the product limits to 0 if that’s what you’re asking
like the product of an epsilon function and any abritrary function will be an eisilon function
upper timber
No idea mate sorry
marsh citrusBOT
@shut bear Has your question been resolved?
marsh citrusBOT
@shut bear Has your question been resolved?
devout mauve
what even is an epsilon function supposed to be
if its just a function that goes to zero as x goes to zero, then this follows by the squeeze theorem
tender mantle
marsh citrusBOT
tender mantle
Thanks Ann. Then one and only vector method works