Try the same proof if instead of 1/2, you use 1/3 or 3/4
#help-38
zinc ginkgo
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lethal valve
can anybody help
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can anybody help
lethal valve
please @ im gonna get some wateer
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lethal valve
anybody
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dusk dock
https://i.gyazo.com/11a5d5d8ea4083260d7b6d73ea62b043.png
What makes this true?
digital bison
for positive x, $x = (\sqrt x)^2$
solid kilnBOT
Zybikron
dusk dock
for positive x, $x = (\sqrt x)^2$
Could you elaborate? I understand the validity of your statement, but I'm failing to make the connection to the problem at hand. My algebra skills could use some work.
digital bison
what's $\frac{\sqrt x}{(\sqrt x)^2}$?
solid kilnBOT
Zybikron
dusk dock
$\frac{\sqrt x}{(\x}$
solid kilnBOT
2003 Volkswagen Jetta
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digital bison
right, but $x= (\sqrt x)^2$
solid kilnBOT
Zybikron
dusk dock
ohhh I see we are canceling one out.
digital bison
so $\frac{\sqrt x}{x}=\frac{\sqrt x}{(\sqrt x)^2}$
solid kilnBOT
Zybikron
digital bison
yeah,
median iron
when you sub in y^2 + 1 for the x^2 why dont you put it in brackets and how do you know whether or not you sub it into brackets
median torrent
You do sub it in with parentheses
But in this case
Because all that was happening around it was addition
You could drop the parentheses without affecting the outcome
Your rule of thumb should be to always sub in with parentheses
(Note that subtraction is technically addition )
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wraith hinge
I don't know how to start this I already got it wrong like 2 times
hallow spruce
how have you been coming across your incorrect answers?
wraith hinge
I've tried multiplying then divide but I forgot what we start off from my lessons
hallow spruce
suppose it was just for 1 year instead of 5
if $3500 is invested for 1 year earning 14.5% interest, how much would be in the account at the end?
wraith hinge
$4542 ?
hallow spruce
how are you getting that?
wraith hinge
oh wait 3514? I just divided 1 the multiplied 14.5- or idk im using my phone calculator
hallow spruce
it's not 3514
wraith hinge
Oh
hallow spruce
having a compound interest rate of 14.5% means that and the end of the compounding period (which is 1 year in this case), 14.5% of the principal is added into the account
wraith hinge
Ohh okay I think I understand it now
hallow spruce
if $3500 is invested for 1 year earning 14.5% interest, how much would be in the...
so then can you answer this?
wraith hinge
4007?
solid kilnBOT
Result:
4007.5
close enough
wraith hinge
so is that the first one right?
hallow spruce
no that's my example
wraith hinge
oh
hallow spruce
the first question has a time horizon of 5 years
wraith hinge
Oh okay okay I got it thank you!
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icy pelican
How do I factor a^2 + 2a +1? Factoring a^2 + 2a is very easy, its : a (a + 2) but the +1 is whats throwing me off
icy pelican
How do I factor out : $a^2 + 2a +1$
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Snaggii
lilac rain
long basin
That's the basic perfect square trinomial
tepid rock
yeah.
icy pelican
$a^2 + 2a + 1 = a^2 + a + a + 1$
solid kilnBOT
Snaggii
marble wharf
do you know the expanded form of (x+y)^2 ?
icy pelican
im not sure
idk the +1 just makes this so much more difficult than it has to be, ima just ask my teacher to explain this
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fickle helm
fickle helm
Why is it defined like that?
zinc ginkgo
you have a channel. close one
fickle helm
For example if there exists a f(x) greater than both f(a) and f(b) in the interval a to b then wouldn’t there also be a point x between a to b that maps f(x)
digital bison
For example if there exists a f(x) greater than both f(a) and f(b) in the interv...
not necessarily
f(x) = x
for x from 0 to 2, there isn't a value that maps to 3.
Also, close your other room.
fickle helm
But 3 doesn’t lie inside the interval you just gave? So what is the relevance
Let me draw an example of what I mean
digital bison
3 is the y value, the interval is on the x values
zinc ginkgo
For example if there exists a f(x) greater than both f(a) and f(b) in the interv...
how does this contradict intermediate value theorem?
light crystal
I'm thinking the same. Maybe their incoming example will explain things.
digital bison
they're not talking about contradicting it. They're wondering why it's defined so that y* is between f(a) and f(b)
I think
fickle helm
fickle helm
they're not talking about contradicting it. They're wondering why it's defined s...
Yes this is what I meant
digital bison
sure. that's true.
but it's not true for every function.
f(x) = x
find a value outside of f(0) and f(2) that has an x between 0 and 2 map to it
fickle helm
Yes it doesn’t apply to every function, but what I drew is never wrong though
digital bison
ok
light crystal
The theorem is not saying that f(x) cannot take values outside of f(a) or f(b). It's just guaranteeing for any values between f(a) and f(b) there is some corresponding x in a < x < b that corresponds to that particular value of f(x).
zinc ginkgo
"intermediate" is relative to the value of the function at the endpoints. you can generalize it to min(f) and max(f) to get the extreme value theorem
you'll probably learn that next
fickle helm
I see, I was just wondering what is the point of the intermediate mean value theorem if you already have the mean value theorem
Actually wait
zinc ginkgo
you can use both IVT and EVT to prove MVT
light crystal
It's important to know that a continuous function takes on all it's values between it's minimum and maximum for example.
It's relied upon in the proof of Rolle's theorem which is used to prove the MVT.
zinc ginkgo
Isn’t this the mean value theorem?
nope
zinc ginkgo
https://en.wikipedia.org/wiki/Extreme_value_theorem
that's this
light crystal
Your book calls it Theorem 2 and mine calls it theorem 7 haha.
zinc ginkgo
funny that they give a name to IVT but not EVT
light crystal
I don't even get IVT lol.
zinc ginkgo
Isn’t this the mean value theorem?
"mean" implies some sort of average is being taken.
zinc ginkgo
there's no averaging going on here
light crystal
The MVT is so overpowered, it actually needs nerfing when I think about it.
digital bison
The MVT is so overpowered, it actually needs nerfing when I think about it.
i heard they're going to patch it in Calc 4.0
light crystal
The more I read my book the more crazy such a surprisingly simple thing is.
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twilit gorge
Hello! Trying to understand what derivatives are.
I know that by definition it is limit of (f(x+h)-f(x))/h with h approaching to zero - and I understand that it is the line "touching" the (x;f(x)) point on given function. But what I don't understand is that why is it only the slope of that function, i.e. why is that it is not the slope-intercept form kx+b but only the k. What am I missing?
Thanks!
plain slate
well because change in y / change in x is gradient
and that's basically what (f(x+h)-f(x))/h is
twilit gorge
well because change in y / change in x is gradient
Yes, but isn't it a line? Why can we just throw away the x and the b from it?
plain slate
no
all the derivative does is just find the gradient of the tangent line to that point
it's not the actual line
limber herald
For mean, let's say I have the table
28-30 31-33 34-36
189 91 120
cunning fable
Can someone tell me how to express $u_1,\ u_2$ in basis of $v_1$ and $v_2$
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Kedi
vapid crypt
Kedi , How you could me answer about problem with quadrilaterals
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lone comet
I was asked to take this and turn it into a linear then solve for linear and bernoulli I tried it but not sure if i am write. Please help me
light crystal
Show the question, please.
lone comet
I sent it with it as a PDF but the question is XDY +YDX = 0
but my teacher says it can be solved with both I belive maybe not Bernoulli's because I cant see away to have a extra y^2 on the other side of the equation
light crystal
I didn't see a question that made sense to me.
lone comet
sorry not really a question he just asked to solve it like a linear equation and I wanted to know if my steps made sense into turning it into a linear equation.
make it into a linear sorry to be confusing but kinda hard to explain
digital bison
where did the x on the right side come from?
light crystal
xdy + y dx = 0 is the same as x dy/dx + y = 0, dy/dx + (1/x) y = 0.
It can be solved as a separable equation or using a integrating factor.
lone comet
I was not sure if that was a legal move or not but I was trying to dispose of the X next to the dy/dx to make it a linear equation and I though it would just divde to the other side
that makes a lot of sense because it fitst the forumla perfect I just dont understand that like how you did the algebra to get there
@light crystal
light crystal
Which stage of the algebra?
lone comet
well in my head If i do it i think subtract the ydx to the oppiste side
then get XDY=-YDX
then divide by DX
DY/DXY=-Y
light crystal
I think I know the confusion.
lone comet
XDY/DXY=-Y
light crystal
Is it how the quotient of differentials of dy and dx become the derivative dy/dx?
lone comet
I can see that just how are you getting x*y or (1/x)y
light crystal
Start with xdy + y dx = 0 and divide by xy for xy ≠ 0.
$\frac{\dd{y}}{y} + \frac{\dd{x}}{x} = 0$.
solid kilnBOT
stabulo
light crystal
Oh. Sorry went on my own tangent in my head.
Just divide by x
$\dd{y}+ \left( \frac{\dd{x}}{x}\right)y = 0$.
solid kilnBOT
stabulo
light crystal
Using the memory aid* of dividing by dx to get dy/dx + (1/x)y = 0. *There's more complicated reasons why it is allowed.
lone comet
so you can divde by x and it flips the x and y
light crystal
Just divide xdy + y dx = 0 by x, what's so difficult?
lone comet
I see now I do not know how I didnt see it before
very obvious solution but still the linear diff eq formula is DY/DX P(X)Y=Q(X) so how would I get an X on the other side to manipulate it into that equaiton if it is possible.
lone comet
yeah that what I was looking is that not a linear?
light crystal
Obviously dy/dx + (1/x)y = 0 is linear. Set P(x) = 1/x and Q(x) = 0.
lone comet
I see I did not know I could solve with Q(x) to 0 i thought it was mandatory to have an x on the Q(X) side.
Ok so then I will use the eqation you have given to me and solve from there with 0 as Q(x) thank you
light crystal
Q(x) just means Q(x) is a function of x which means for each value of x corresponds one and only one output value Q(x).
Q(x) = 0 satisfies this.
lone comet
perfect thank you helps a lot to know that. I will be on my way now again thank you
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dire kraken
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tepid junco
why is b=7x^2 and not (x^2)/7
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why is b=7x^2 and not (x^2)/7
snow jackal
In decarts law of signs, what if one of the terms has an coefficient as zero ?
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silk jungle
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silk jungle
cos = 1, and cos = -1/5
but -1/5 doesn't exist on the unit circle
and cos = 1 only exists at 0 and 2pi no?
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wraith hinge
hihi i need some help uhh
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hihi i need some help uhh
trim lichen
so far so good
wraith hinge
but then im confused what to do next because 20 cant go into 16
my teacher said
something something multiply 3 into 20
find factors of 60
that go into 16x
trim lichen
what you do next is recognize that this is a quadratic equation.
and that there was no explicit instruction to use any particular method to solve such equations
trim lichen
so why not just throw the quadratic formula at this and not give yourself headaches
wraith hinge
im not sure what youo mean 💀
trim lichen
you need to solve the equation 3x^2 + 16x + 20 = 0
wraith hinge
si
trim lichen
i am suggesting that you do this via the quadratic formula
wraith hinge
i dont think she wants us to do that
since shes been teaching us stuf like factor by grouping
trim lichen
were you explicitly instructed against it?
wraith hinge
and stuff
i think she would rather me understand the concept in the way shes teaching it
so she knows i understand
trim lichen
you are not answering the question
wraith hinge
no
trim lichen
right
wraith hinge
how would i put it into the quad form then
trim lichen
that means it is perfectly okay to use the quadratic formula
3x^2 + 16x + 20 = 0
recall the formula itself
trim lichen
yes
wraith hinge
ok
lament jewel
wow nice graphic
trim lichen
also do not forget that x=0 is also a solution of the original equation
lament jewel
its not that bad (╯°□°）╯︵ ┻━┻
lament jewel
yes
it sometimes gives 2
or 1
or 0
well actually not 0
depends on how u look at it
0 in R
wraith hinge
would a be 3
lament jewel
you need to solve the equation 3x^2 + 16x + 20 = 0
this the eq?
yes then
b 16
c 20
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near spade
i dont know where to even start with this
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i dont know where to even start with this
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near spade
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shrewd ridge
you know water will be pumped 200 ft and you know how much
the units is the hardcore part though 
i must be missing something huge though, i don;t get how you would do it with calculus
near spade
i dont get how i would calculate it through any mean
unless the work required to fill it is the same as the work required to empty the water tower?
shrewd ridge
i would assume you raise all the water by 200 ft
it doesn't matter how much it falls after that
how much water to pump: 2/3 pi × 1000 ft³
how high: 200 ft
near spade
using W=integralF(x)dx
shrewd ridge
uh no i meant to know the volume of the sphere
object's energy is m×g×h, you raise the object, the h grows
the work is how much the energy grows
am i being hyper stupid?
near spade
object's energy is m×g×h, you raise the object, the h grows
idk my teacher didnt teach it very well so
shrewd ridge
ok
near spade
she just said that work = force x distance
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wraith hinge
What is 1/(a+b)
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What is 1/(a+b)
stark bison
It's 1 divided by the sum of a and b?
wraith hinge
Yes
stark bison
Is there anything given?
wraith hinge
Even thought it's true what are the ways to get there
Any identity?
@stark bison
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wraith hinge
Let F(x) = [f(x)]^2 + [f'(x)]^2 ; F(0)=6 ; f(x) is thrice differentiable such that |f(x)| =<1 for x in (-1 , 1) ; then prove that there is no point of local maxima of F(x) in (-1,1) ; also prove that for some c in (-1,1) , F''(c)=<0 and F(c) >= 6
this question was done in class by our math teacher and i couldnt understand it whatsoever. i straight up dont know what happened so i have no intial thought process to give [ please explain thru Lagrange's Mean Value Theorem and Rolle's Theorem]
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Let F(x) = [f(x)]^2 + [f'(x)]^2 ; F(0)=6 ; f(x) is thrice differentiable such th...
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wraith hinge
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wide gyro
A quarterback throws a football from a height of 6 feet with an initial velocity of 20 feet per second.
The height, h, of the ball at time t seconds can be represented by the equation h(t) = -16t2 + 20t + 6.
If the ball is caught at 2 feet, how long is the ball in the air? (help please)
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twin stone
How do you do this? I got confused after the second line.
split chasm
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glossy sandal
hi, this is algebra 1. i cant seem to remember how to solve the number of solutions, i just need a little assistance with these graphs.
smoky slate
by equation or by graph?
smoky slate
ok so when they intersect at one place there is one solution
if they are parallel there are no solutions
and if they overlap there is an infinite amount since they never seperate
smoky slate
intersect is when they cross paths
glossy sandal
sorry
smoky slate
its alright
glossy sandal
thank you!
smoky slate
np
glossy sandal
how would i solve the number of solutions with a system
also how do i solve for a variable and THEN get the number of solutions
<@&286206848099549185>
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grizzled agate
A right-circular cone of radius r cm contains a sphere of radius 12 cm. If the height of the cone is h cm, express h in terms of r
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A right-circular cone of radius r cm contains a sphere of radius 12 cm. If the ...
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grizzled agate
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proper plume
hey
proper plume
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sharp tundra
why is this wrong?
i did it exactly the same way as the example but it still won't accept the answer
sharp tundra
Maybe they want it sorted?
tried every permutation of formatting and it’s still wrong
shrewd ridge
find 3 more
lean falcon
there's 8 of those
u sure?
lean falcon
they are not primes
sharp tundra
||you're missing 6, 22, 33||
thought it was just asking for primes
shrewd ridge
never said that anywhere
barren kayak
Hey guys, so im coding a discord bot for a game using python, in this game you basically have structure "recipes" and resources. The bot receives a list of the materials the user has and the structure he wants to craft and is meant to calculate the most efficient way to craft. I dont know how to calculate it though because its too complex for simple math. The problem is the following:
1 circuit board = 3 silica, 1 metal
The structure costs 150 glue, 200 circuit boards, 400 metal, lets imagine the user has 5000 metal, 4000 glue, 7000 silica and 700 circuit boards
Now you might have noticed, if the user crafts too many circuit boards, there wont be metal itself left, if the user doesnt craft circuit boards the user can barely craft any structures. What I currently do is check how many structures can be crafted if we dont craft circuit boards, and how many can be crafted if we do, its better than not checking at all but I would like this to be as efficient as possible.
For short, I want to figure out how to make the maximum amount of structures with or without crafting more circuit boards with the materials given.
Is there any algorithm / math that can be done for this?
Thanks alot for any help
shrewd ridge
I don't understand this
either you can;t craft your list, or you can
what's there to do
you mean there are alternative recipes for the same product?
barren kayak
well, its about figuring out how to make the MOST of them
like, say we have 4000 metal, 6000 glue, 7000 silica and 30000 circuit boards, there would be no reason to craft circuit boards because if we did, we would be missing metal for the structure itself
I dont know its weird to explain lmaoo
trim lichen
sounds like some kind of linear programming problem
shrewd ridge
the problem is it doesn't
you just subtract the 150, 200, 400 and when you run out of circuit boards you start subtracting the materials for it instead, and then you run out
and you know how many structures you can build
no choices
barren kayak
ooooooo
yea, so I sort of just simulate as if I was crafting them myself
just keep making them 1 by one, and when out of circuit boards craft enough for 1 more
shrewd ridge
yes, and the bot can tell me how many structures i can build
but i don;t need his advice on how
barren kayak
well, its just so you can craft all circuit boards at once you know, and then craft the structures later
because it takes some time
but thats game related, I guess
shrewd ridge
aah
severe cargo
Math
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severe cargo
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dense breach
Can you set up some equations using the midpoint theorem thing?
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main olive
guys
main olive
help
near remnant
What
main olive
A quartic function in the form f(x) = ax^4 + bx^3 + cx^2 + dx + e is such that the coefficients of the quadratic and linear terms are 10 and –18, respectively. Additionally, f(0) = 9 and x = 1 is a root of multiplicity of 2. What is the value of (a + b)?
I made a system of equations and got (a,b)=(1,-2). Is this correct?
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north wigeon
A group consisting of 28 aggressive zombies triples in size every hour. Which equation matches the number of zombies after 7 hours?
civic oracle
A group consisting of 28 aggressive zombies triples in size every hour. Which eq...
this is just geometric sequences no?
so 28 * 3^n-1
so 28 * 3^8-1
61236
north wigeon
this is just geometric sequences no?
its Match Exponential Equation and Context
options are Z=3(1+28)
7
Z=3(28)^7Z=3(28)
7
Z=28(1 + 3)^7Z=28(1+3)
7
Z=28(3)^7Z=28(3)
7
civic oracle
whats the 7 for
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wraith hinge
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wraith hinge
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wraith hinge
im not sure how I should start with this
ripe minnow
@wraith hinge
wraith hinge
<@456226577798135808>
yeah?
ripe minnow
how much of the substance is left at no time passed?
wraith hinge
wait no
ripe minnow
how much is left?
ripe minnow
0% of the substance remains?
wraith hinge
wat
ripe minnow
100% of the substance remains, which is represented as 100
now, it asks you for the half-life, right?
ripe minnow
the initial value is the value at t= 0 right
yes
100 * e^0 = 100 × 1
= 100
-percent of the substance left
wraith hinge
50
wraith hinge
so then you have 50 = 100×e^kt
kt?
ripe minnow
you can simplify it to 1/2
ripe minnow
so whatever that likely 6-digit-long decimal number is
wraith hinge
then ln(1/2) = kt
wraith hinge
and ln(1/2)/k = t right
ripe minnow
yep
wraith hinge
i see
ic ty
i was having trouble understanding what i was supposed to input into the equation
ripe minnow
that's also a general formula you can just apply if you dont wanna do the algebra
wraith hinge
I'm currently writing a paper on decomposing piano chords through the fourier transform, to find the appropriate frequencies that make up chords. So I recorded an audio file of myself playing a chord, and found the equation for said chord. I'm confused as to what my next step should be to transform this into the frequency domain.
chilly mauve
a
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zinc ginkgo
I'm currently writing a paper on decomposing piano chords through the fourier tr...
section 3.3 - 4.3. equation 11 looks like what you need to compute next
https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=1142&context=jhm#:~:text=The Fourier transform is used,chord that is being played.
thorny trout
hints/suggestions?
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wraith hinge
wraith hinge
verify if cotx-1/cotx+1=1-sin2x/cos2x
subtle lava
what have you tried?
wraith hinge
i did cosx/sinx-1/cosx/sinx+1
then
i put on same denominator
so i got cosx-sinx/sinx/cosx+sinx/sinx
then
i removed the denominator sinx
i got cosx-sinx/cosx+sinx then idk
subtle lava
$\frac{cotx-1}{cotx+1}=\frac{\frac{cosx}{sinx}-1}{\frac{cosx}{sinx}+1}=\frac{cosx-sinx}{cosx+sinx}$
solid kilnBOT
Max..
subtle lava
so this so far?
wraith hinge
yes
frozen plover
Do you know what the formulae for cos 2x and sin 2x are?
subtle lava
in terms of single angles
frozen plover
Try to use those definitions to manipulate that fraction
wraith hinge
cos2x is 2cos²a-1 or 1-sin²a or cos²a-sin²a
subtle lava
yeah
wraith hinge
Do you know what the formulae for cos 2x and sin 2x are?
yes
solid kilnBOT
Max..
subtle lava
what can we multiply top and bottom by to get this?
wraith hinge
by cosx+sinx ?
subtle lava
close
wraith hinge
ah cosx-sinx ?
subtle lava
ah cosx-sinx ?
yep, you can use difference of two squares formula
then expand the top and manipulate it to try get the numerator we are after
wraith hinge
how i do
subtle lava
how i do
?
$\frac{cosx-sinx}{cosx+sinx}=\frac{cosx-sinx}{cosx+sinx}\times\frac{cosx-sinx}{cosx-sinx}=\frac{(cosx-sinx)^2}{cos^2x-sin^2x}$
solid kilnBOT
Max..
subtle lava
then i do cos²x-2cosxsinx+sin²x?
yep and simplify
subtle lava
note with these questions it's useful to look at both the LHS and RHS of the identity your trying to prove
subtle lava
2cosxsinx is the same as 2sinxcosx ?
yep
wraith hinge
so its cos²x+sin²x= 1 so 1-sin2x
subtle lava
yep
subtle lava
cosa*cosa is the same as 1-sin²a ?
yep
trim joltBOT
@wraith hinge Has your question been resolved?
wraith hinge
@subtle lava i have a question
i have 1+tana*tan2a in denominator is the same as 1+2tan²a/1-tan²a ?
or @frozen plover
frozen plover
$\frac{\tan a \times 2\tan a}{1 - \tan^2 a}$
wraith hinge
this is the same as 1-2tan²a/1-tan²a ?
solid kilnBOT
NEONPerseus
frozen plover
Is this what that is?
wraith hinge
you forgot the 1-
1-tanax2tana/1-tan²a
but the 1- is not in the fraction is near
like this
@frozen plover like this
frozen plover
$1 - \frac{\tan a \times \tan 2a}{1 - \tan^2 a}$
solid kilnBOT
NEONPerseus
wraith hinge
yes
frozen plover
And your question was?
wraith hinge
and my question is if this is the same as 1-2tan²a/1-tan²a
frozen plover
What intuition did you use to arrive to that 
wraith hinge
**NEONPerseus**
no its 2tan(a)* sorry
wraith hinge
.close
steel trellis
I have the following figure of the picture with the points A(0,0) B(12,0), C(12,12) D(0,12) and E(7,12).
The first exercise is to prove that the Straight EB could be described by the function y = -12/5x + 144/5
The second to calculate the area of the triangle APD if the triangle DPE has the area 28
The third to calculate the area of the triangle APD if the triangle DPE is isosceles
I am able to solve the first exercise by taking the points E and B and to make a calculation to the given function
The second exercise would be solved by me by subtracting the area of the three other triangles of that of the square and getting that way the area of the triangle DPE. For that I would first calculate the height of the triangle DPE and subtract it of 12 to get the height of the triangle APB
But the last exercise is unsolveable for me as for the current moment. Idk if im just dumb but I dont know any way how the given information are enough.
steel trellis
For reference on the second exercise the area of the triangle APD would be 62
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@steel trellis Has your question been resolved?
young swift
For reference on the second exercise the area of the triangle APD would be 62
So move p to a point on eb where it makes it isocoles
Or where ED=EP
Then since you will know all 3 sides, you can find the area
Or you can find an angle in it
steel trellis
that means where e to p is 7
even though I still dont understand the exact way, I will try it
steel trellis
So move p to a point on eb where it makes it isocoles
Ah and may you check my solution above?
ty
steel trellis
even though I still dont understand the exact way, I will try it
got it I think
P has to be (5|x)
young swift
Your answer for the second looks right
steel trellis
after calculating x I have the exact point for p
But I still don't have the hight...
height
young swift
So what point did you get for p
steel trellis
9,912
ah no
estimated 9,91267
wait
and thats the height
of DPA
Which means 12 * 9,91 * 1/2 = 59,46
which is the area of DPA
young swift
Yup
wraith hinge
which equation would I use to solve this?
trim joltBOT
which equation would I use to solve this?
young swift
Which one is oposite over hypotonuse
wraith hinge
sin?
young swift
Yup
steel trellis
You can use sin sentence
young swift
Use that
steel trellis
sin(24°) = 19/x
steel trellis
seem to be
young swift
Yup
broken cave
Correct
broken cave
which equation would I use to solve this?
You can use the sine law here $\frac{19}{sin 24°}=\frac{x}{sin 90°}$
solid kilnBOT
𝓐𝓡𝓝𝓐𝓑 𝓟𝓐𝓛
wraith hinge
correct?
trim joltBOT
@wraith hinge Has your question been resolved?
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candid radish
You use the division method
In a way, there are a few good videos for this.
Yes.
delicate bobcat
prime factorization
200704 | 2
100352 | 2
50176 | 2
25088 | 2
12544 | 2
6272 | 2
3136 | 2
1568 | 2
784 | 2
392 | 2
196 | 2
98 | 2
49 | 7
7 | 7
1
candid radish
You could also do that, there are many methods
wraith hinge
these correct?
trim joltBOT
these correct?
wraith hinge
<@&286206848099549185>
wooden birch
1 and 2 are both correct
trim joltBOT
@wraith hinge Has your question been resolved?
wraith hinge
1 and 2 are both correct
what about the others??
wooden birch
you didn't solve the others
How can I verify your answers then lol
nvm you did I am blind
sorry
wraith hinge
😂
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wooden birch
4- correct
5- correct
6- correct
very quick check but I think so
also you forgot to answer 3 lol
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Available help channel!
hearty spruce
i’m trying to find x, im completely lost on how to go about it
south latch
2 sinx cosx = sin(2x)
that's an identity you need to memorize in this course
...if this is trig or precalc
(or higher)
use that.
also, note that -sin(w) = sin(-w) because sine is an odd function
use that too
@hearty spruce
hearty spruce
ahh gotcha, thanks ! i didnt think to use those idenities for some reason
south latch
there's an alternative that just uses factoring
sinx(1 + 2cosx) = 0
but the other way is
sinx = sin(-2x)
arcsine both sides.
...
wait.
hearty spruce
sinx(1 + 2cosx) = 0
this one makes the most sense to me yeah
hearty spruce
haha all good, thanks!
south latch
nevermind, ignore me
we all been there
inland orbit
Too much math, not enough sleep
south latch
x + 2 pi k = 2(x + 2 pi k)
0 = x + 2 pi k
x = - 2 pi k
x = 2 pi k s.t. k in Z (?)
I'm missing half of these though
2pi k + x = 2x or 2pi k + (pi - x) = 2x (?)
x = 2pi k or x = pi(2k + 1)/3 ???
what's the traditional route give
sin(x) = 0 ---> x = pi*k
cos(x) = -1/2 ---> x = 4pi/3 + 2pi*k, x = 8pi/3 + 2pi*k
completely different
I'm an idiot
inland orbit
x + 2 pi k = 2(x + 2 pi k)
0 = x + 2 pi k
x = - 2 pi k
x = 2 pi k s.t. k in Z (?...
Did you steal my mistake? shouldn't that be -2?
sin(x) = sin(-2x)
x + 2pi k = -2x + 2pi j
south latch
¯_(ツ)_/¯
wolfram says my two constant values in the cosine solutions are off by a factor of 2
oh no
it's the same
they just delivered answers in a form that are symmetric over x = 0
whereas I'm all about that sweet, sweet unit circle
south latch
Did you steal my mistake? shouldn't that be -2?
I should have negated the interior but I did other things wrong too
inland orbit
I would have never even thought to solve it that way honestly
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@hearty spruce Has your question been resolved?
south latch
I would have never even thought to solve it that way honestly
I must be doing it wrong though
I saw a problem a couple of days ago that was required to be solved something like this
but I keep messing it up
@hearty spruce yes, just do what you are expected to do, and factor
the identities are fine
the trouble comes when I am trying to find intersections for functions that differ only by wavelength
which is what sin(x) = sin(-2x) is
...that and it's flipped over y axis
maybe that's part of the trouble
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trail ingot
try drawing a picture 🙂
haiii c:
do you have a guess for what the answer is?
do you think f(x) could be greater than 10 for any x?
random citrus
f might not be increasing
Seems like maybe you have the right idea
Ok this doesn't make grammatical sense
But you shouldn't assume f is increasing
What do you think the answer is?
We can prove it after that
Yea ok
Suppose BWOC there exists an x* in the interval such that f(x*) > 10
Try to get a contradiction using MVT
By way of contradiction
Under what we've supposed, x* is fixed
We want to show such an x* can't exist
I don't think the absolute value around f' is required in the question?
trail ingot
me neither
random citrus
Use 0 and x* as endpoints for MVT
Btw try to visualise the set up, or draw it because it helps immensely
And view the derivative as slope of tangent
What
Nop
Do you mean x*?
What's f(x*) bigger than?
From what we've assumed
random citrus
Suppose BWOC there exists an x* in the interval such that f(x*) > 10
^
No
f(x*) > 10 but x* <= 10
So this can't be true
I'm using the star btw because it's fixed
2nd part is not true
Unless you can reason to it somehow to get that very contradiction
How exactly
The MVT allows you to relate the value of the derivative to the value of the function itself
Pretty much nothing else that's not derived from MVT does this
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south latch
domain is every value of x that can produce an output without problems.
is there any value of x here that would cause a problem
?
it is.
oh wait
no
you got it backwards a little
see?
you wrote it wrong
and you don't understand
if x is negative, you are safe
because the inside is positive
but if x is bigger than 2, the inside is negative
that's a problem for even roots
so x is good as long as it is in (-inf, 2]
(2 is inclusive, hence the square bracket)
since we can take roots of zero. that's just 0
$x \in (-\infty,2]$
solid kilnBOT
Disorganized
south latch
if you have a graph of something
imagine "squishing it" against the x-axis.
you read in all the points from left to right
you went right to left
if there is a hole or a gap in the graph, it will be pressed against the x-axis also, and you need to follow those easy rules
same goes for the Range: "squish" the graph against the y-axis and read in the points from bottom to top
always most-negative to most-positive.
near spade
I did everything correctly up to this point - I don't understand what happened to the +1 in the numerator of the first fraction?
inland orbit
1/2 is a constant. It got absorbed into the C
near spade
1/2 is a constant. It got absorbed into the C
oh so all constants just become part of C in integrals?
ok
inland orbit
You don't have to do that
But yeah. C is an unknown constant. Now it's greater by 1/2, but it's still just an unknown constant
hollow pebble
What’s your question…
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night zodiac
Don't troll
hollow pebble
<@&268886789983436800>
night zodiac
<@&268886789983436800>
stable siren
pearl robin
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pearl robin
how does second to last step go to the last step
trail ingot
i think just cancelling (4x)^2s
or maybe um
(4x)^2/2s
yea that
or if you imagine factoring out (4x)^2/2 from the numerator and the denominator and cancelling, that might be easier to see
@pearl robin does that help?
pearl robin
or if you imagine factoring out (4x)^2/2 from the numerator and the denominator ...
how would you factor out (4x)^2? from a series? is that allowed
trail ingot
yea, with power series you can do a lot of things like you would with finite sums of things
other types of series you might run into trouble, but power series are very safe to play with generally
pearl robin
yea, with power series you can do a lot of things like you would with finite sum...
hmm could i just divide each term by x^2? to get the same answe
trail ingot
yep, that also works
pearl robin
yep, that also works
wait why is it x^2 btw i watched a video but that's not the largest degree so why x^2 ?
trail ingot
all the other fractions will go to 0 as x goes to 0
like 4x/3 for example
and another nice thing about power series is you can take limits termwise
so the limit will be (1-0+0-...)/(-1-0+0-...)
that's why cancelling the x^2s makes it nice
pearl robin
so the limit will be (1-0+0-...)/(-1-0+0-...)
ah so cancelling x^2 which is the first term just makes the others go to 0 except first term
so that finds the limit?
trail ingot
yep
wise heart
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inland orbit
What even is E? It must have been defined earlier.
inland orbit
Uh, maybe? There are 24 numbers there, so I guess you could put them in a 4x6 matrix
But, you'd kind of be guessing on how to arrange the entries
Is there any more context to this?
wise heart
I can't find anything else about what e is or how I could solve it
south latch
I can't find anything else about what e is or how I could solve it
this is your homework. You must have called something "E" in your notes or earlier in the text or something
wise heart
I don't... As I was saying, I am 97% sure it is the 85, 27... string of numbers
south latch
What does "post" mean?
wise heart
it is a discussion
south latch
Ok
For each column of E^-1 (which is what I think that is supposed to be)
Multiply on the left by B^-1
Then concatenate all the columns
The "solution" is the cypher for that result
You only have 24 characters so I guess only 23 letters are being used?
wise heart
It would have to be
south latch
Good news is there are only 6 matrix multiplications to do
"Only"
Do you have a program to do this for you?
wise heart
I have a graphing calc that can
south latch
Ok
wise heart
how would E be arranged? I know 4x6 but what order would the numbers be
south latch
I am wondering myself
Because the row length doesn't match if E is the encoded message
Idk I guess take the values 4-at-a -time row-wise
Let those be the vectors
Or...
Down each column from left to right ?
2 columns making a 4x1 vector?
wise heart
I am doing across each row right now
if that doesn't work then I guess down and then over to the right 1 column is what ill do next.
You cant get a inverse of "E" if you go across the line and down.
south latch
Forget what I said about E^-1 that's probably not correct terminology
That's what I'm talking about
There's 24 values in E or E^-1 or whatever that is
That's divisible by 4 regardless of whether you take values rowwise or columnwise
If one way fails the other should succeed
wise heart
Oh I might see, let me try it really quick
TO DECODE A MESSAGE
-
Take the string of coded numbers and multiply it by the inverse of the matrix that was used to encode the message.
-
Associate the numbers with their corresponding letters.
south latch
It's rowise for sure
The first 4 values as a column vector output a column where each value is in {1,...,27}
wise heart
Can you provide a example using the problem, I am still completely lost.
wise heart
Most likely spaces, I think 0 is a space and 1 is A
wise heart
south latch
Or maybe it just predates me
wise heart
No, this is the last discussion until the midterm and everything after that is sets and unions and junk
south latch
K. There you go.
wise heart
I feel safer with Peddle to the Metal than RAWHIDE TO LEATHERNECK lol
wise heart
would you mind sending me or explaining to me how you got E? or is it the one you posted above?
lol
wise heart
18,1,23,8
9,4,5,0
20,15,0,12
5,1,20,8
5,18,14,5
3,11,0,0
is this E?
wise heart
Got it , thanks.
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Available help channel!
karmic dragon
I think this might be very simple but i’m not sure how to work it out
turbid spruce
for a non-prime natural number $m$ where you can write $$m=p_1^{r_1}\cdot p_2^{r_2}\cdot \dots\cdot p_n^{r_n},$$ then the number of positive factors of $m$ is $$(r_1+1)(r_2+1)\dots(r_n+1)$$
note that $p_1, p_2,\dots, p_n$ are primes
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@karmic dragon Has your question been resolved?
candid sequoia
if function was y= x^2 and x was -1 what would y be
trim joltBOT
if function was y= x^2 and x was -1 what would y be
trim lichen
just plug it in