which is a word i just made up btw
#help-10
short spruce
tardy epoch
hemisphere area should be (4 pi r^2) / 2
short spruce
claiming it as my own
obtuse pebbleBOT
@grave kestrel Has your question been resolved?
grave kestrel
So if the book is wrong then how should I solve it
halcyon tulip
πr²h is volume
tardy epoch
is it using 22/7 to approximate pi wtf
What do you mean approximation. It's exact! #im-from-year-500-bc
upbeat dawn
It could be misprinted
grave kestrel
So I am supposed to find the surface area of the shape by adding the surface area of cylinder and surface area of hemisphere?
halcyon tulip
What do you mean approximation. It's exact! #im-from-year-500-bc
They do approximate like this in middle school
halcyon tulip
So I am supposed to find the surface area of the shape by adding the surface are...
Yes
inland valve
obtuse pebbleBOT
forest sinew
thats what id do
the youre just graphing in a plane
and dont solve them explicitly
if it can be avoided
graph them using your head
like clearly x=0 giving 0 =y² +3z² is a single point and not a curve
inland valve
its a single point?
forest sinew
yea
inland valve
i thought you can try solving for z but it ended with negative root
i didnt know what to do there
inland valve
yea
its hard for me to do it in my head
im way too used to 2 dimensional graphinh
and i just try to make it perpendicular
forest sinew
im way too used to 2 dimensional graphinh
so fantastic news is it is 2 d graphing 
we can do through
do you see how z=0 gives x=y^2?
inland valve
yes
forest sinew
and that this solution lays in the xy plane?
which makes it like 2d graphing
only a little skewed
inland valve
wait when i rewrite it would it jut be the same graph? 
i think that was my mistake
inland valve
and that this solution lays in the xy plane?
yes
inland valve
only a little skewed
yeah what im understanding is draw it in 2-d and try to place it perpendicular to each other
warm shaleBOT
inland valve
no sadge at me
forest sinew
same graph?
inland valve
yeah what you showed me here
inland valve
ok so its best to set every component to 0 right?
forest sinew
one by one, yea
theres three intersecting planes
so the hope is you get three curves
and together they sort of form a picture
forest sinew
hmm okay
so lets start with x=0
x=0 gives -y^2+5z^2+25=0
do you recognize this?
inland valve
forest sinew
no
inland valve
no?
inland valve
T_T
forest sinew
you dont need any numbers
just these shapes
you get these common forms like
x^2 + y^2 = 1
inland valve
x=0 gives -y^2+5z^2+25=0
why is this a hyperbola?
forest sinew
x^2 - y^2 = 1
inland valve
oh
forest sinew
so first, well isolate the constant and make it positive
inland valve
do i have to memorize those?
inland valve
5z^2-y^2= c
inland valve
ohh...
forest sinew
it avoids the axis which has the - before it
inland valve
but i have to memorize every shape?
forest sinew
i would memorize these two
in this general way
but you dont have to
they just come up often
especially hyperbola, and it has an untuitive shape
inland valve
T_T
forest sinew
its not immediately evident like
-y^2 + 5z^2 + 25 = 0
its not immediately clear to me what this looks like
forest sinew
so you memorize a form
forest sinew
there is no good way to make this explicit
as in like
y= something
or z=something
its just a curve that involves variables
like it makes more sense to write a circle as x^2 + y^2 = 1
than $y = \pm \sqrt {1 - x^2}$
warm shaleBOT
jan Niku (Shuri for Honorable)
inland valve
yeah ig
forest sinew
so all you need to memorize
two things squared
minus between them
equals a positive constant
forest sinew
$y^2 -5z^2 = 25$
inland valve
okok
forest sinew
this was it right
warm shaleBOT
jan Niku (Shuri for Honorable)
inland valve
uh 5z^2 -y^2 = -25
forest sinew
its a hyperbola, and it avoids the axis attached to the negative
forest sinew
uh 5z^2 -y^2 = -25
they have to equal a positive constant
inland valve
oh
forest sinew
well really really they have to equal one
inland valve
oh righ
forest sinew
but i wouldnt worry about that immediately
forest sinew
just make sure its positive
inland valve
okok
forest sinew
okay, so this hyperbola avoids which axis?
inland valve
x?
forest sinew
yea, something like that
inland valve
okok let me try the xy plane and zx plane with that chart you gave
forest sinew
,w 3d plot y^2-5z^2=25
warm shaleBOT
forest sinew
forest sinew
😮
forest sinew
,w 3d plot 25x^2-y^2+5z^2+25=0
warm shaleBOT
forest sinew
yea you can kind of think like
forest sinew
nothing i can do about that
you have two hyperbolas right
in the other planes
so you got these hyper fellas that are trying to avoid that axis
is how i interpret
inland valve
yyeah
forest sinew
but
you can reason through like
square is positiv
so negative square is negative
two negative squares is def negative
so them equalling a positive is never gonna happen
id say u got it 😄
inland valve
yeah
forest sinew
if you want to get your sketches more accurate
inland valve
im just worried i come across more complicated shapes
forest sinew
you can learn conics with a little more precision
inland valve
yeah
inland valve
calc 3
forest sinew
youre going to learn them at some point anyways
if you have the study time to do it
theres not very many of them
inland valve
1 chapter section each day
inland valve
it moves too fast
inland valve
before the shapes, it was vectors
forest sinew
it will all make sense
inland valve
PDE?
inland valve
T_T
forest sinew
partial differential equations
inland valve
sounds difficult
forest sinew
it will make everything in calc iii make sense
inland valve
forest sinew
just memorize and cheet sheet
inland valve
forest sinew
if u get one
inland valve
no cheatsheet i think
forest sinew
ask your teacher how precisely u have to draw these
inland valve
i have to memorize everything
forest sinew
fwiw they dont get too complicated
since it requires a lot of reasoning to do anything without an incredible amount of symmetry
forest sinew
it really is
forest sinew
i mean
my visual sense is garbage
in my head i cant see things
i sure as heck cant draw them
forest sinew
calc iii is garbage but just crush it
its a low point for sure
ODE is great
PDE is great
lin alg is great
pretty much every math class after that is great
except stats 1
inland valve
im taking lin alg with calc 3 rn
so painful
T_T
it sort of coincide in during the vectors portion but at the same time parametric equations still confuses me
inland valve
except stats 1
LOL yeah
i took stats last semester it made no sense to me
its just pure memorization
forest sinew
i have to sleep
inland valve
okok
thorn vigil
Can someone give a hint how to do this, I just thought by IVT there is a $x_0 \in [a,b]$ so that $f(x_0)(b-a) = \int_a^b f(x) dx$ but then tried a couple of things to no success
obtuse pebbleBOT
Can someone give a hint how to do this, I just thought by IVT there is a $x_0 \i...
warm shaleBOT
Anticipation
brittle swan
$\exists c_1, c_2 \in (a, b), f(c_1) (b - a) = \int_a^b f(x) dx, f'(c_2) = 0$
warm shaleBOT
Chromium
brittle swan
thorn vigil
is that the hint?
thorn vigil
ive tried doing this: so
say $f(x_0)(b-a) = \int_a^b f(x)$ is the IVT point for integral, then there is $c_1 \in (a,x_0)$ and $c_2 \in (x_0, b)$ so that $f'(c_1) = \frac{\int_a^b f(x)}{x_0-a}$ and $f'(c_2) = \frac{\int_a^b f(x)}{b-x_0}$
warm shaleBOT
Anticipation
thorn vigil
but the problem is b-x_0 or x_0-a can be bigger than a quarter, maybe this helps (whenever its smaller or equal quarter we're done)
bright stag
occupied channel, don't just come asking wherever.
obtuse pebbleBOT
@thorn vigil Has your question been resolved?
stuck owl
Uh I got 2 instead of 4 by splitting [a,b] by argmax f
thorn vigil
Uh I got 2 instead of 4 by splitting [a,b] by argmax f
ur referring to my question?
stuck owl
yes
thorn vigil
so u got a counterexample?
also argmax not necessarily exist cuz f isnt continuous?
stuck owl
f is differentiable so continuous
stuck owl
ah and I was drawing pictures for f≥0 as well .-.
thorn vigil
its ok i can ask prof or others
if the thread gets locked too long someone can just release it
brittle swan
if the thread gets locked too long someone can just release it
you can ping helpers
thorn vigil
right thanks <@&286206848099549185>
thorn vigil
Can someone give a hint how to do this, I just thought by IVT there is a $x_0 \i...
question is here
raven spire
$$\int_a^b \frac{1}{2}\abs{f'(c)}(x - a) \dd x \overset{?}{\geq} \int_a^b f(x) \dd x$$
warm shaleBOT
Ansh
raven spire
I really dislike these smartass IVT questions smh ._.
obtuse pebbleBOT
@thorn vigil Has your question been resolved?
stuck owl
I have some intuition. f is at most
warm shaleBOT
@stuck owl
glossy yew
Excuse me
timid silo
obtuse pebbleBOT
timid silo
Will my final equation to work out the time taken by each of them to wash the car be this:
warm shaleBOT
Nightsky
timid silo
Anticipable enough, no one will answer as usual.
raven spire
Anticipable enough, no one will answer as usual.
Lol
leaden ibex
Assumption is the mother of all failures.
timid silo
> Assumption is the mother of all failures.
Well, I'm not assuming here, I'm speaking from experience.
raven spire
$x(x - 60) = 72 \implies x^2 - 60x = 72$ $$\implies x^2 - 2\cdot 30x = 72$$ $$\implies x^2 - 2\cdot 30x + 30^2 = 72 + 30^2$$ $$\implies (x - 30)^2 = 30^2 + 72$$
warm shaleBOT
Ansh
timid silo
I'm not asking for the solution..lol.
timid silo
**Nightsky**
I'm asking whether or not this will be the final equation.
raven spire
🤔
timid silo
Well, I haven't tried, I just spoke from my Intuition.
Because I'm confused.
If they work together, the time taken to wash the car should be less than the time taken by either of them Individually.
So you must divided here?
leaden ibex
What if, instead of trying to intuitively guess the right equation, you derived it?
That way you can be sure it is correct too!
leaden ibex
Let x be the time it takes Kenneth to wash the car alone ( as you did I presume)
First we need to determine what happens when both of them wash the car together
warm shaleBOT
Nightsky
leaden ibex
Yep
timid silo
First we need to determine what happens when both of them wash the car together
Hmm..
The time taken will be less?
leaden ibex
Well of course, but we don't know by how much
we only know it will take 72 minutes
In this type of task, it is usually best if you look at the speeds of the people
Kenneth's speed is 1/x cars/min
Mario's speed is 1/(x-60) cars/min
timid silo
Kenneth's speed is 1/x cars/min
How?
timid silo
Oh yes.. my bad.
warm shaleBOT
Nightsky
\begin{gather*}
\frac{1}{x} + \frac{1}{(x-60)} = 72
\end{gather*}
timid silo
?
leaden ibex
Not quite.
timid silo
What happens to their speeds?
Increases?
leaden ibex
but almost
leaden ibex
Increases?
In exactly what way
timid silo
In exactly what way
What do you mean?
leaden ibex
This one person's speed is a, and the other one's is b. So their speed together will be
timid silo
a + b?
timid silo
Now we do.
leaden ibex
But we also do from the task. When they both work together, they take 72 min to finish the car
And that's your equality
timid silo
So what will be our final equation?
warm shaleBOT
Nightsky
timid silo
This?
leaden ibex
1/x is Kenneth's speed
1/(x-60) is Mario's speed
And added together they must add up to their speed together
timid silo
And added together they must add up *to their speed together*
What does this mean?
leaden ibex
well what is their speed working together (finishing a car in 72 min)
timid silo
1/72?
leaden ibex
yep
timid silo
Ah! I see... thank you so much!
leaden ibex
There might be other ways, but this one will work great for most tasks of this type
timid silo
What other ways are possible?
leaden ibex
At this time I couldn't tell you.
leaden ibex
,w 1/x + 1/(x-60) = 1/72
warm shaleBOT
leaden ibex
,w x(x-60) = 72
warm shaleBOT
timid silo
Well.. the answer is 'no' then.
leaden ibex
No, as you see you'll get a solution
But it won't make sense
That would mean Kenneth can finish a car in 24 minutes
but Mario is actually hindering him
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
@rugged kite hey so i watched the videos but i don’t get why we are in 4dimensions
obtuse pebbleBOT
<@!193692307453771776> hey so i watched the videos but i don’t get why we are in...
timid silo
rugged kite
Well, you have two dimensions for the input (the complex plane), and two dimensions for the output (yet again, the complex plane)
So in theory, you'd need four dimensions to graph it properly
timid silo
Well, you have two dimensions for the input (the complex plane), and two dimensi...
oh so this in input and output?
timid silo
like you'd do with y=f(x)
but there we only show the output
rugged kite
The inputs are represented by a line in a normal graph
the x-axis
Here the inputs are represented by a plane
rugged kite
Well, if you have 1 dimension for the input + 1 dimension for the output (normal graph), you need 2 dimensions total
Which is what happens, you draw 2d graphs
compact shadow
The real part of output is the third dimension, and imaginary part of output is denoted by color
timid silo
yea ik why the curvy thing then
rugged kite
Yeah, in theory you'd need 4 dimensions, but since that's not something we can visualize, so color is used
rugged kite
yea ik why the curvy thing then
define "curvy thing"
rugged kite
Yeah
The complex numbers are described by x+iy
So if you want to look at every possible input, you need to look at every possible value of x and y
Which takes a whole plane to do
(but if you have a way to show it with a single line, by all means tell me)
timid silo
damn i still don’t get it
rugged kite
Let's start with normal graphs again
timid silo
okay!!
rugged kite
The point of a graph is to show the output of the function for every possible input
timid silo
hm
rugged kite
here's a sample graph
So, we want to show what the function's value is for any value of x
timid silo
yea
rugged kite
So we must have some way to represent what the function's input is on the graph
Here's, it's done with the x-axis
timid silo
mhm
timid silo
yea
rugged kite
And then, the y-axis represents the output
timid silo
yep
rugged kite
Now let's go to complex numbers
We still want to represent the function's value at every point
that is, we want to be able to represent f(x+iy) for every real x and y
because that describes every single complex number
timid silo
that is, we want to be able to represent f(x+iy) for every *real* x and y
that’s 3d right
rugged kite
Not so fast
timid silo
hm
rugged kite
So, instead of the x-axis, to describe the input you need to show both x and y
(no relation to the x and y of a normal graph, there are only that many letters i can use)
timid silo
why
rugged kite
Every complex number can be written z=x+iy
On a normal graph, you need the x-axis to be able to point at a horizontal position and say "lookie, here, it represents the value of f(2)"
or f(1), or f(whatever)
timid silo
mhm
rugged kite
But here, you also need to be able to point at something and say "lookie, here it represents the value of f(x+iy)"
x+iy being some complex number
be it f(1) or f(i) or f(256-35i), whatever
timid silo
isn’t i imaginary and 1+i complex?
rugged kite
Not quite
the complex numbers are all the numbers that can be written x+iy
That includes the real numbers (take y=0), as well as the imaginary numbers (take x=0)
timid silo
but 1+0i is 1 is 1 complex too then?
rugged kite
So imaginary and real numbers are just specific kinds of complex numbers
Indeed
Real numbers are a part of the complex numbers
timid silo
ooh
rugged kite
Anyway, from the description of the complex numbers i just gave, it would be really convenient to be able to spot both x and y on the inputs
Because if you know x and y, you know x+iy, so you know the input
timid silo
but x+iy is just x+iy
rugged kite
What do you mean by that
timid silo
idk
rugged kite
Okay, on second thought this series might have not been the best recommendation
My apologies
rugged kite
I think it's more targeted towards people who have already manipulated complex numbers
So I'll just fall back on the good old and reliable Khan Academy
timid silo
oh no
rugged kite
They have this playlist on the introduction to complex numbers, that starts off very gently with imaginary numbers. Take it step by step if you need to, because there are many videos in this playlist
timid silo
khan academy can get really hard because i’m not english
timid silo
german
rugged kite
I see
timid silo
even tho u wanna do math in english
so i mostly learn on discord cuz i can ask questions
rugged kite
Well, you can always try to look up introductions to complex numbers in German if you want
It's a common topic, I'd be shocked to learn there are no comprehensive introductions to it
timid silo
can u show me how? cuz videos ain’t so fun :p
rugged kite
i honestly just typed "complex number introduction" in youtube and found something that looked long enough
"komplexe zahlen erklärt" could do the trick
search it on google if you don't want videos, whatever floats your boat
timid silo
can i dm u for questions?
rugged kite
If you really get stuck one something you can try, but I'm not going to be available very often
(actually, past this weekend, basically never for the coming month)
So yeah
rugged kite
Just getting used to the concept and learning what you can do with them, in general
timid silo
yea i know some stuff ig
like *i rotates 90°
and magnitude and angle
and e^it = cost + isint, even tho i don’t know why
rugged kite
found this playlist in german https://www.youtube.com/playlist?list=PLLTAHuUj-zHgrAfietLRb01pO1mtji8qn
what you're interested in is called the "trigonometric form", and its full generality it's the "polar form", but for now, take it slow
anyway, i have to go
lethal kelp
Hello every one, i have this question i need to study this for tomorrows exam please help
obtuse pebbleBOT
Hello every one, i have this question i need to study this for tomorrows exam pl...
timid silo
Hello every one, i have this question i need to study this for tomorrows exam pl...
Lhoptal ig
lethal kelp
?
plain owl
Before that check whether you really get 0/0 form
timid silo
We do ig
plain owl
Rationalisation is enough
Note your numerator = 2(x-3) and in denominator (x²-9)=(x+3)(x-3)
sharp grotto
Hello everyone, can someone help me with this problem
obtuse pebbleBOT
Hello everyone, can someone help me with this problem
@sharp grotto Has your question been resolved?
faint brook
obtuse pebbleBOT
faint brook
compact shadow
I use A’ to denote A bar
3,A(A’+B)=AA’+AB=A(1-A)+AB=A-AA+AB=AB
2,=A(1-B)+AB(D+1-D)+A’C’D’+A’BC’=A+ A’C’D’+A’BC’
faint brook
faint brook
I use A’ to denote A bar
3,A(A’+B)=AA’+AB=A(1-A)+AB=A-AA+AB=AB
2,=A(1-B)+AB(D+1...
can you show the steps
compact shadow
We already know that AA’=A(1-A)=A-A=0 so
a)=AB+A’B’+(AB)’=1+A’B’, so a) is weird,cause I showed it’s equal to 1+A’B’ not 1
b) =AA’B’B’+BB’A’A’=0+0=0
compact shadow
can you show the steps
If those are not steps, then what was I writing?
faint brook
i dont know about 3a 4a,b but you are wrong at 2a
compact shadow
It said simplify, I don’t know how simple it should be
compact shadow
Okay mine is the third line from bottom
I don’t see why A+AB=A holds, that implies AB=0, which isn’t generally the case…
elfin belfry
It’s a ring, with characteristics 2, and x^2=x for all x
Oh
compact shadow
x bar=1-x=1+x
elfin belfry
I thought this was a logical expression
What is this topic called?
Abstract algebra?
compact shadow
I don’t know, I only know that Jacobson calls it one to one correspondence between Boolean lattices and boolean algebras
compact shadow
No idea in 2a how he got the last three steps, that all require that AB=0, I didn’t see where it was given…
obtuse pebbleBOT
@faint brook Has your question been resolved?
toxic elm
can someone help me with this question plz?
obtuse pebbleBOT
can someone help me with this question plz?
chilly tundra
lucid flame
try choosing some values of sin(x) that you know and plot them
timid silo
that's if you want to do it irl
if not you could just plot it into desmos or other graphing calculator
toxic elm
if not you could just plot it into desmos or other graphing calculator
how to draw the graph in an exam
leaden ibex
Determine some special points of sinx
Like where its relative extrema are
And where it crosses 0
You know what it looks like
boom
No one will ask you to accurately plot sinx
you only need a sketch
unique solstice
When people draw sin with vertical slopes at the zeroes
unique solstice
chilly tundra
you probably also want to label the axis
leaden ibex
and a scale
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
wintry stream
can someone pls help me with this
obtuse pebbleBOT
can someone pls help me with this
wintry stream
i dont know what to do
gloomy valve
First draw the region in the xy-plane
obtuse pebbleBOT
@wintry stream Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
wintry stream
First draw the region in the xy-plane
obtuse pebbleBOT
wintry stream
so its kind of like a cake shape right
like smaller layer on top->bigger layer on bottom
gloomy valve
Yeah a truncated cone
obtuse pebbleBOT
@wintry stream Has your question been resolved?
runic holly
how do i get a_2019
obtuse pebbleBOT
how do i get a_2019
runic holly
.close
obtuse pebbleBOT
runic holly
sorry shen
obtuse pebbleBOT
Available help channel!
timid silo
Does anyone know if this true or false
obtuse pebbleBOT
Does anyone know if this true or false
timid silo
I can’t find anything in the textbook
true rain
So do you know u-substitution?
hybrid gull
So do you know u-substitution?
Wouldn't you need the integrand to be $g(h(x)) , h'(x)$ instead of $g(h(x)) , h(x)$ for that?
warm shaleBOT
Shen
true rain
oh fuck true
worthy comet
Wouldn't you need the integrand to be $g(h(x)) \, h'(x)$ instead of $g(h(x)) \, ...
thats the whole point of this question
timid silo
Wait what?
timid silo
I see that
But it’s like my brain keeps telling me it’s false
But I’m not sure
Like I did the u substitution
Anyone?
worthy comet
But it’s like my brain keeps telling me it’s false
then try to think of some examples where it goes wrong (constant function are always good for a start)
worthy comet
yes, its false. Of course you should think about it so long that you either have a counterexample or a proof for it
timid silo
@worthy comet
Can u check some?
Of my answers
Or anyone is this one good?
I feel pretty confident on it
Anyone?
timid silo
Does anyone know if this true or false
Wait this one is true
I just redid it
Im pretty sure they both true
Is that right @alpine raven ?
cedar lichen
That's not a supported assumption. I could name many functions that's not constant on some interval (a, b), yet h(a) = h(b)
alpine raven
yea I know
timid silo
So is it false then @cedar lichen I really don’t get it
cedar lichen
Yeah. Let b = 2, a = -2, g(x) = x, and h(x) = x². h(2) = h(-2), and ∫x²*x² dx = ∫ x⁴ dx is nonzero on that interval
cedar lichen
Consider the integral of 1/x² from -1 to ∞. Does that diverge?
timid silo
Yes
cedar lichen
What about the integral of 1/x² from 1 to ∞?
cedar lichen
Rotates to infinity?
timid silo
Moves to infinity
cedar lichen
Elaborate
timid silo
Like the domain and range would | o goes to oo
cedar lichen
What
The integral of 1/x² from -1 to ∞ diverges thanks to the asymptote at x=0.
But what about the integral of 1/x² from 1 to ∞? Does that diverge or converge?
timid silo
Converge
cedar lichen
Is -1 < 1?
timid silo
Yes
cedar lichen
Then we've found a counterexample
cedar lichen
This one true?
This is false
timid silo
Okay so they both false?
cedar lichen
Yep
timid silo
So this one is it good @cedar lichen
cedar lichen
Dunno, I don't feel like evaluating that
cedar lichen
Take the derivative of the RHS and see if you get the integrand
timid silo
Which I didn’t
So I’m pretty sure it’s false
These true or false ones really trip me up 🙁
cedar lichen
It's false. You'll see that the derivative is not the integrand
timid silo
Thx ur a life saver
This one also false?
I used this identity for it @cedar lichen
Arcsin(x) + arccos(x) = pi/2
cedar lichen
Yep
timid silo
This one is true? @cedar lichen
cedar lichen
Is this a test?
timid silo
No
cedar lichen
Yeah, it's true.
timid silo
Tests are in person for me
This is just hw
But for the true or false ones we get one try 🙁
How about this one @cedar lichen
cedar lichen
Use IBP
timid silo
Ibp?
We haven’t learned that I don’t think
I divided the integral
And then did the geometry
cedar lichen
It's integration by parts
cedar lichen
It's true
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
winter gazelle
hey does anyone know how to solve this further to find r, R and λ?
obtuse pebbleBOT
hey does anyone know how to solve this further to find r, R and λ?
@winter gazelle Has your question been resolved?
winter gazelle
<@&286206848099549185>
obtuse pebbleBOT
@winter gazelle Has your question been resolved?
hot sonnet
hey does anyone know how to solve this further to find r, R and λ?
Hello, I think that you can get R=r from equations 1 and 2
Are all these 7 equations independent? I mean, does any of these come from a previous one?
limpid saffron
Can I get help on this
limpid saffron
.reopen
obtuse pebbleBOT
✅
hybrid gull
Can I get help on this
What have you tried?
Know that for however many times the ball has bounced, it will bounce just 70% as high as the previous bounce
Starting at 100 m -> 0.7 • 100m = 70m -> 0.7 • 70m = ?
etc.
hybrid gull
What does that represent?
limpid saffron
Wait I think I got it
70+48+34+24+16+11 ~~ 205.88
Times 2 is 412 rounded up
Nvm I was looking at the wrong question
I got that one already
.close
spiral void
obtuse pebbleBOT
spiral void
the grammar isn't that good but
a) 3.5
b) 7?
c) idk
I need help with c)
2c) is what is the expected value of the product of two dies
I also need help with 2c)*
obtuse pebbleBOT
@spiral void Has your question been resolved?
obtuse pebbleBOT
@spiral void Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
coarse yacht
how do i write a quadratic equation in standard form
obtuse pebbleBOT
how do i write a quadratic equation in standard form
gloomy trellis
ax^2+bx+c = number
olive token
Simplify 2a - [3a + {4a - b - 2a -(a -2)} - b]
obtuse pebbleBOT
Simplify 2a - [3a + {4a - b - 2a -(a -2)} - b]
cold thistle
Start with the inner-most parenthesis
You can distribute a -1 over the terms inside
obtuse pebbleBOT
@olive token Has your question been resolved?
warm shaleBOT
Andreww
flat anvil
Why u-sub?
Oh ik why
Expand the square and then
Yeah remember 2sin(x)cos(x) = sin(2x)
warm shaleBOT
Andreww
flat anvil
Then let u = 2x
And remember sin^2 + cos^2 = 1
So do you know how to do it now?
Not cos^2(2x)
Just cos^2 of x
Also please do \sin not just sin
It makes it not italics
Also for derivatives
$\dv{y}{x} \dv[n]{f}{x}$
warm shaleBOT
Brontochad (Shuri for honorable)
flat anvil
You can use this shortcut
warm shaleBOT
Andreww
frozen willow
obtuse pebbleBOT
frozen willow
Where am I going wrong?
tardy epoch
you incorrectly applied l'hopital at the second equal sign
frozen willow
you incorrectly applied l'hopital at the second equal sign
Infinity/0 is indeterminate form no?
tardy epoch
Infinity/0 is indeterminate form no?
source?
frozen willow
I’m asking
tardy epoch
look it up in your text/notes
frozen willow
you incorrectly applied l'hopital at the second equal sign
Is infinity time infinity form always just infinity?
short spruce
you cannot use lhopitals unless you have a form of inf/inf or 0/0
even if you were to have another indeterminate form, lhopitals only accepts those two
frozen willow
even if you were to have another indeterminate form, lhopitals only accepts thos...
Thanks for the notice
frozen willow
Is infinity time infinity form always just infinity?
and yeah, it seems so
Thanks guys
.close
past solar
Hello need a little help, Just starting to work on geometry, How do you find the area of the crust with this information?
Thanks.
obtuse pebbleBOT
Hello need a little help, Just starting to work on geometry, How do you find the...
royal basin
@past solar have you made any progress so far or are you stuck not knowing how to begin?
past solar
I don't know where to begin with honestly.
past solar
Thats pi r²
royal basin
okay, good.
so now
if you knew the radius of the whole pizza, and the radius of the pizza without the crust, would you be able to find the area of the crust?
past solar
Yes
royal basin
okay
denote the inner radius (w/o crust) by $r_1$ and the outer radius by $r_2$. can you write down what the area of the crust would be in terms of those?
warm shaleBOT
Ann
royal basin
it'll be important later.
past solar
Ok ok
tardy epoch
if you know the radius is z and the height is a the volume is pizza
royal basin
@tardy epoch thanks for this utterly unhelpful comment
past solar
denote the inner radius (w/o crust) by $r_1$ and the outer radius by $r_2$. can ...
Area of the whole pizza - Area of the circle without the crust = Area of the crust
past solar
Sorry, English is not my first language, If you mean by outer radius, Do you mean the radius of the crust only circle?
(R1+R2)²pi - (R1)²pi
royal basin
no, when i say outer radius i mean the radius of the entire pizza
with the crust
center to edge
so it would be $\pi r_2^2 - \pi r_1^2$
warm shaleBOT
Ann
past solar
no, when i say outer radius i mean the radius of the entire pizza
Oh ok, I see
past solar
Ok
royal basin
look at the triangle that i drew
royal basin
where are you getting that from?
past solar
6 is the hypotenuse of a triangle
royal basin
and why are you just claiming out of hand that this is a right triangle?
just because it appears right does not actually make it right.
past solar
just because it appears right does not actually make it right.
Yeh I just tested it, It's an irrational number
royal basin
......
what
what on earth did you "test"
sounds like you ignored everything i just said
are you going to go off to do your own thing or should i continue trying to explain how to do this problem
past solar
are you going to go off to do your own thing or should i continue trying to expl...
Continue please.
past solar
Yes I can see it
royal basin
do you understand why the angle i marked as right is indeed right?
past solar
Yes I can understand
royal basin
what's x?
royal basin
...
i asked for the meaning, not the value.
but yes, the sides are r2, r1 (lowercase!!!!) and 3
royal basin
area = pi(r2^2 - r1^2) = pi * 3^2 by pythagoras.
gilded root
I need to get this out of fraction form
obtuse pebbleBOT
I need to get this out of fraction form
obsidian isle
Multiply top and bottom by conjugate
obtuse pebbleBOT
@gilded root Has your question been resolved?
weak coral
(3^2018-3^2016)/(3*3^2015)
obtuse pebbleBOT
(3^2018-3^2016)/(3*3^2015)
obtuse pebbleBOT
@weak coral Has your question been resolved?
obsidian isle
@weak coral still need help on this?
obtuse pebbleBOT
@weak coral Has your question been resolved?
cinder badge
can someone teach me how to solve the sin question on a TI inpsire CAS?
obtuse pebbleBOT
can someone teach me how to solve the sin question on a TI inpsire CAS?
cinder badge
would that be how u do it?
this guy got this answer but idk how ot get that answer on calculator
strange stump
Hello
vernal sky
Just type 12sin35 to find x?
warm shaleBOT
CatHashira
cinder badge
no im asking how to put it on a cas the question
vernal sky
There's a sin button
cinder badge
let me try rn one sec
quaint minnow
this works, assuming your calculator is in degree mode
quaint minnow
Just input sin(35) * 12
but yes it’s much easier to just evaluate this
timid silo
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!