#help-19
odd edgeBOT
south plume
set LHS to your initial definition of $a_n$: $a_n=2^n+5\cdot3^n$
clever fjordBOT
artemetra
lone zinc
.close
zealous basin
OPTIMIZATION PROBLEM
An offshore oil well is located 2km from the coast. The refinery is 4 kilometers down the coast. Installing the pipeline in the ocean is twice as expensive as on land. What path should the pipeline follow to minimize the cost?
zealous basin
Something like that, pls HELP
odd edgeBOT
@zealous basin Has your question been resolved?
zealous basin
what do you mean by "path"
trajectory
inner tulip
sorry can't be of much help on this one
zealous basin
ok
odd edgeBOT
@zealous basin Has your question been resolved?
zealous basin
<@&286206848099549185>
odd edgeBOT
@zealous basin Has your question been resolved?
exotic lance
OPTIMIZATION PROBLEM
An offshore oil well is located 2km from the coast. The re...
Hello
This is calculus, right?
Start by setting some variable x
What distance in this problem should be x? 🤔
exotic lance
yeah this diagram is much better to see which variable defines a path
odd edgeBOT
@zealous basin Has your question been resolved?
river yacht
odd edgeBOT
fair prism
Is this the right process to solving this type of question?
I believe your first step is wrong. It seems like you just moved the inverse to the right but idk any rule that would let you do that
river yacht
Yea im wasnt sure on how to even start this qeustion
i just assumed that adding an inverse on both sides
would cancel the inverse on the left side
how would you begin to remove hte inverse?
fair prism
$AA^{-1}=A^{-1}A=I$
clever fjordBOT
Haruno Haruka
fair prism
<@280588750373912576> sorry for the ping
No you kinda had the right idea before. You want to cancel out the entire left side. To cancel out (A^T+2I)^-1 we want to turn it into the identity matrix by multiplying it by (A^T+2I) (either side is fine in this case)
then from there you can solve for A
odd edgeBOT
@celest bay Has your question been resolved?
odd edgeBOT
@celest bay Has your question been resolved?
odd edgeBOT
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modest bronze
If u and v are linearly independent vectors and S is a set where x is orthogonal to at least u or v, what would that set look like?
modest bronze
Would it just be the zero vector?
odd edgeBOT
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odd edgeBOT
@modest bronze Has your question been resolved?
odd edgeBOT
@modest bronze Has your question been resolved?
odd edgeBOT
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full blade
I am currently trying to understand when a 1-form w = Σ w_i dx_i is exact.
I understand that the equation in the picture is sufficient enough. However does this need to work for any combination of i and j? so even if i = j?
low locust
well if i=j then both sides are the same
full blade
true. Okay makes sense. How would i integrate a 1 form if it is exact?
Just write an integral infront without differentials?
$\int w$
clever fjordBOT
derdotte
full blade
basically?
odd edgeBOT
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fair snow
I am confused regarding how to answer this.
If f'(x) and g'(x) exist and f'(x)>g'(x) for all real x, then the graph of y=f(x) and the graph of y=g(x)
A. intersect exactly once
B. intersect no more than once
C. do not intersect
D. could intersect more than once
E. Have a common tangent at each point of intersection
steel quarry
I am confused regarding how to answer this.
If f'(x) and g'(x) exist and f'(x)>...
What do you think?
odd edgeBOT
@fair snow Has your question been resolved?
fair snow
I am confused regarding how to answer this.
If f'(x) and g'(x) exist and f'(x)>g'(x) for all real x, then the graph of y=f(x) and the graph of y=g(x)
A. intersect exactly once
B. intersect no more than once
C. do not intersect
D. could intersect more than once
E. Have a common tangent at each point of intersection
fair snow
What do you think?
I'm thinking C because one is always growing bigger than the other.
zenith edge
What does it mean that f'(x) > g'(x) for every valid x, what does that mean for their antiderivatives F and G
zenith edge
I'm thinking C because one is always growing bigger than the other.
well yes this
Now try to visualize this with some random function, could you move those functions around to force them to intersect?
fair snow
I haven't learned antiderivatives.
fair snow
Now try to visualize this with some random function, could you move those functi...
Sure, by adding x/y offsets.
zenith edge
Then you don't know that they won't ever intersect
for any given pair of functions f and g
the antiderivatives are just f and g before derivation btw
Shouldn't have used that word in this context tbh, my bad. Better formulation is what it means for f(x) and g(x)
The fact that f always grows faster than g means that it could intersect g given that it "starts" below g
So F can catch up to G, but G can never catch up to F
Is this making sense?
odd edgeBOT
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odd edgeBOT
dim thorn
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dim thorn
I feel like I may not be understanding level surfaces
This seems too simple of an explanation to be right
Can somebody tell me if this is completely wrong and give me a little help?
Both 3 and 4
tardy lagoon
f(x,y,z) is not a line though
dim thorn
f(x,y,z) is not a line though
What would it be?
tardy lagoon
In 3D f gives each point in space a scalar value
and In 4D It is a 3D object embedded in 4D
dim thorn
dim thorn
In 3D f gives each point in space a scalar value
This graph above makes sense for this
tardy lagoon
no that's completely wrong
dim thorn
Oh lol
dim thorn
When I tried to graphed x + 5y + 3z it gave me an error
tardy lagoon
well you need 4 dimensions to graph it
dim thorn
well you need 4 dimensions to graph it
I don’t understand
tardy lagoon
you have 3 variables x,y,z
and you need a extra dimension for f
so you need 4 dimensions
like when you have f(x)=something
you need 1 dimension for x and 1 dimension for f(X)
dim thorn
you need 1 dimension for x and 1 dimension for f(X)
Right
So how would I enter that into the calculator? I’d assume f(x, y, z) would be that dimension then
old gull
dim thorn
what's the equation of the level curve?
f(x, y) = z
tardy lagoon
??
a level curve is when the function equal some constant
oh I meant level surface mb
so f(x,y,z)=a where a is some constant
dim thorn
so f(x,y,z)=a where a is some constant
So you’d set x + 5y + 3z equal to any constant?
Like just 1
tardy lagoon
yes then you get a level surface
and this time it is a plane
also slight issue with Q3. f(x,y)=x^2+y^2 is not a circle, rather the level curves are.
dim thorn
also slight issue with Q3. f(x,y)=x^2+y^2 is not a circle, rather the level curv...
Ah, yeah this makes sense now working through 4
I was initially under the impression f(x, y) is 2d and f(x, y, z) is 3d
Idk how I’m 7 weeks into calc3 lol
tardy lagoon
you need to work on your geometric understanding lol
tardy lagoon
umm no
dim thorn
Duck
dim thorn
Looks like a missile
dim thorn
Oooo ok so any level curve of the inside would have to be a circle
Cause like well it’s a missile
So any specific 2d part of it would be a circle
tardy lagoon
correct
tardy lagoon
sqrt(k)?
dim thorn
if f(x,y)=k then yes sqrt(k) is radius
Bruh isn’t this what I said earlier?
tardy lagoon
I was confused about what's k
dim thorn
I switched a to k cause it’s what we use in class mbmb
So for it to not be centered at the origin wouldn’t it be k = (x^2 + 1) + (y^2 + 1)
tardy lagoon
yea you are correct about that
dim thorn
dim thorn
yea you are correct about that
How does this look?
tardy lagoon
I mean you should explain what k is on your work
dim thorn
I mean you should explain what k is on your work
Maybe I’m a little confused on what k is?
I thought it was just a constant for the equation?
tardy lagoon
that's basically it
you should add something like "for the level curve f(x,y)=k, ..."
dim thorn
you should add something like "for the level curve f(x,y)=k, ..."
Okay, done. Gonna work a bit on 4 now.
odd edgeBOT
@dim thorn Has your question been resolved?
odd edgeBOT
Is this right
odd edgeBOT
@hasty wigeon Has your question been resolved?
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Available help channel!
late vessel
can u guya hwlp mw
odd edgeBOT
can u guya hwlp mw
late vessel
Its about Synthetic Division and I'm trouble to know the divisor
How can I turn 2x²+3 to be a divisor for 4x⁵ + 6x⁴ + 5x² - x - 10?
(This is synthetic division and I'm aware of the missing terms)
This is so disgusting, i hate math
<@&286206848099549185> plz help
yee yee ass server
.close
odd edgeBOT
odd edgeBOT
Available help channel!
dim thorn
odd edgeBOT
dim thorn
Where does my mistake lie here?
Im pretty sure this is wrong somewhere but I don’t know where
dim thorn
<@&286206848099549185>
odd edgeBOT
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dim thorn
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signal oar
Regarding Russell's paradox
odd edgeBOT
Regarding Russell's paradox
signal oar
We have that R = {X | X not in X} and the paradox is R in R <==> R not in R.
What does X not in X really mean though?
Wouldn't e.g. the set {1} be a possible candidate for X?
signal oar
it means that X is not an element of itself
Does a set that has the property X in X even exist?
viscid flint
sure
signal oar
It needs to be some never-ending one
viscid flint
yeah I mean sure as in "I can write something down but that's why it's a paradox"
signal oar
yeah I mean sure as in "I can write something down but that's why it's a paradox...
But isn't R in R just a false statement then?
Why must R be in R
signal oar
Not in ZFC as I remember
oh, alright
signal oar
Not in ZFC as I remember
Though, still, why must R be in R?
Or must it be not, it's just an assumption?
crisp wadi
Look up axiom of regularity, it has been introduced in order to avoid paradoxes like these
signal oar
I'd first like to find the intuition behind Russell's paradox though
crisp wadi
Though, still, why must R be in R?
We begin with the principle of no middle, one of these must be true: X is in X or X is not in X
signal oar
We begin with the principle of no middle, one of these must be true: X is in X o...
Yeah
crisp wadi
If X is in X, then it must satisfy the property that it has for its elements
Meaning X should not be in X
For X to be an element of X
But that's a contradiction
Alright then, let's now look at the case if X is not in X
If X is not in X, then X is in X by the definition of X
Which is also a contradiction
signal oar
Meaning X should not be in X
Wait
crisp wadi
Sorry I meant to say R instead of X
signal oar
If R is in R; then it satisfies the property for its elements X that (X not in X).
But why does that mean R should not be in R?
signal oar
Then yeah
crisp wadi
For all X in R, we have X not in X, right?
So, if R is in R, then we must have R is not in R
signal oar
So, if R is in R, then we must have R is not in R
If R is in R, then it's some set X not in X
Oh
Thank you!
How does the barber paradox follow out of this?
signal oar
You can define the barber as ‘one who shaves all those, and those only, who do not shave themselves.’ The question is, does the barber shave himself?
If the barber shaves himself, then he shaves someone who shaves himself. A contradiction
If the barber doesn't shave himself, then no one is shaving him, so he must shave himself (since he shaves everyone who don't shave themselves). Contradiction.
crisp wadi
Sounds like a similar thing to Russel's paradox
Yeah it looks almost the same
But without abstract concepts like sets lol
signal oar
We can't directly translate the barber as R or something though right?
Or X in X as "X shaves X"
crisp wadi
To provide an analogy, yes
signal oar
To provide an analogy, yes
Ah, yeah, seems like that would work approximately, lol
Thanks
.close
tardy blaze
odd edgeBOT
tardy blaze
explain this part please
errant jay
$\frac{1}{5+2\sqrt{6}} = 5 - 2 \sqrt{6}$ by rationalising the denominator
clever fjordBOT
Frog_Man
tardy blaze
Please explain in more detail
errant jay
$\frac{1}{5+2\sqrt{6}} = \frac{5-2\sqrt{6}}{(5+2\sqrt{6})(5-2\sqrt{6})} = \frac{5-2\sqrt{6}}{5^2 - (2\sqrt{6})^2} = \frac{5-2\sqrt{6}}{1} = 5 - 2 \sqrt{6}$
clever fjordBOT
Frog_Man
errant jay
this means that $\frac{1}{t} = \frac{1}{(\sqrt{5+2\sqrt{6}})^x} = \left(\sqrt{\frac{1}{5+2\sqrt{6}}}\right)^x = (\sqrt{5-2\sqrt{6}})^x$
clever fjordBOT
Frog_Man
mystic saffron
3³+3⁴+3⁵ = 3³(1+2+3²)
odd edgeBOT
3³+3⁴+3⁵ = 3³(1+2+3²)
mystic saffron
Where do you like get 3³(1+2+3²)
uh that's wrong
I don't know good English but what does faktorise mean
Is it not right?
static totem
it's a typo
static totem
yes
mystic saffron
Yeah how do you get from 3³+3⁴+3⁵ = 3³(133²??
mystic saffron
Hmm okay ill try
static totem
multiply by 3³ and you get 3³(1+2+3²)
mystic saffron
r 3³+3⁴+3⁵ / 3³?
Like that?
I still don't understand
I understand that but I don't understand how to get 3³(1+2+3²)
From that
I haven't learned algebra in school yet. Does this question need algebra?
My teacher says if I somehow show how to get 3³(1+2+3²) it's like A
Okay so I just follow that formula?
Is there any way to do it another way without algebra? Or no
Okay whatever
.close
mystic saffron
odd edgeBOT
static totem
looks right
hushed bobcat
Do you know what happens when you have a power to the power of something?
Laws of indices ^^
So for eg: what happens when you do (2^2)^2?
mystic saffron
uhh
mystic saffron
So for eg: what happens when you do (2^2)^2?
remind me ig
hushed bobcat
You multiply the powers
mystic saffron
yes
mystic saffron
If we have this
then?
hushed bobcat
If when you have a power to a power you multiply
Then in this case we also multiply
Hence the answer would be?
mystic saffron
uhm i don't follow
hushed bobcat
If when you have a power to a power you multiply
Are we alright with this?
mystic saffron
Are we alright with this?
yes we are
hushed bobcat
When you have a power on top of another power you multiply the powers
Similarly in this case we have a power on top of another power
mystic saffron
we multiple 2/3 with 6
mystic saffron
which is 4 right
mystic saffron
yep which is 4
hushed bobcat
Mhm
mystic saffron
so it will be 6 with exponet 4
hushed bobcat
Yh
mystic saffron
Or am I wrong on that?
i think you might be
i searched online as well i came across this
but i think im supposed to write it with radicals
so i tried coming here for
addtional help
hushed bobcat
Hm
mystic saffron
but the question was asking for the 6^2 / 9 specifically i think
mystic saffron
I’ve understood it now
share
hushed bobcat
Cassandra is saying 6^(6^2/3)
So this
They’ve typed it out weirdly
And hence
But we know the correct exponent is actually 12/3 = 4
In other words how can we change the 6^2/3 to make it into 4
Or how can we change 36/3 to make it = 4
@mystic saffron
mystic saffron
In other words how can we change the 6^2/3 to make it into 4
ah yes
mystic saffron
What multiplied by 4 = 36
9?
mystic saffron
mmm makes sense
hushed bobcat
That’s how we change it or what we replace with what Cassandra did
Hence the exponent 6^2/3 needs to be replaced with 6^2/9
Apologies if it’s confused you but it was typed out very weirdly
mystic saffron
Apologies if it’s confused you but it was typed out very weirdly
yeah i think it was a trick question
i do understand it now tho so that's all that matters
.close
odd edgeBOT
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Available help channel!
oblique jasper
odd edgeBOT
warm lark
@oblique jasper How many sides and angles does it tell you are congruent?
oblique jasper
idk tbh
neat dirge
odd edgeBOT
@oblique jasper Has your question been resolved?
keen matrix
A car is traveling at a speed of 80 km/h towards a 30-story building. Each story of the building is 5 m high. A fragment of the building breaks off from the top and falls to the ground. How much does the car need to decelerate to reach the building 2 to 5 cm before the fragment hits the ground?
odd edgeBOT
A car is traveling at a speed of 80 km/h towards a 30-story building. Each story...
@keen matrix Has your question been resolved?
odd edgeBOT
@keen matrix Has your question been resolved?
oak jewel
have gradient, just need help with b, finding the angle
[3:46 PM]
potent sphinx
We know that the gradient is the vector that points in the direction of maximum increase
odd edgeBOT
@oak jewel Has your question been resolved?
spark yarrow
Im not sure what to do for the next step here
odd edgeBOT
Im not sure what to do for the next step here
spark yarrow
Im using implicit differentiation to find dy/dx
cold sage
you needed to use the product rule
proud ibex
Keep in mind that y also has an x-dependence
spark yarrow
Ohh
cold sage
but after youve corrected that - the next step is to make dy/dx the subject, which you can do by rearranging and factoring
spark yarrow
Okay let me do the work and make sure i did it right
Should be right now, right?
.close
mystic saffron
odd edgeBOT
mystic saffron
I've never understand the why behind this
can anyone explain why p is inside and q is outside
merry finch
mystic saffron
i mean like
why is it not
sqrtp A^q
how is it simplified to the RHS
@merry finch
sharp oak
It doesn't matter if you put the p outside and q inside, for positive reals anyway
clever fjordBOT
Tushar
sharp oak
If you're including negative reals, then this question is scary and I don't like it.
zenith jasper
Are you asking why it's the qth root rather than the pth root, or are you asking why we can write the root and exponent in any order (for positive A)?
odd edgeBOT
@mystic saffron Has your question been resolved?
mystic saffron
It doesn't matter if you put the p outside and q inside, for positive reals anyw...
can u give me the latex code u use
for this
actually nvm
i have it
.close
last kindle
odd edgeBOT
plain lagoon
We have a chemistry server in #old-network
night raft
its apart of my math assignment
Can you reverse engineer the formula to isolate [H+]?
last kindle
Can you reverse engineer the formula to isolate [H+]?
wdym
night raft
We have pH=-log[H+], right?
night raft
That [H+] is the concentration of hydrogen ions
You’re given the pH
So you need to solve for [H+]
Does that make sense
night raft
You can do this ye
odd edgeBOT
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clever fjordBOT
xNiden
odd edgeBOT
last kindle
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verbal schooner
odd edgeBOT
verbal schooner
ok so i got
-1.36538313756
but it was wrong
so we derive cos(2x) right
= -2sin(2x)
plug in pi/6
cos(pi/3)
that gives the slope
-1.73205080756 (this is the slope i found)
then put it into the y - f(a) = m(x-a) formula
so what did i do wrong
mystic saffron
help mee
worldly robin
Lol
mystic saffron
im dum
grizzled tide
my brother in christ you know how to solve this
mystic saffron
i know its 1/4 but it says wrong
grizzled tide
its not 1/4
mystic saffron
i know
grizzled tide
whats the rise, and whats the run?
grizzled tide
really? the rise is 1? I dont see the graph going up at all
it goes up 1 unit for every 4 across it goes?
grizzled tide
vast dragon
The slope is going down
mystic saffron
HOLY CRAP
I QUIT MATH
WOW
vast dragon
-1/4
odd edgeBOT
mystic saffron
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vast dragon
@grizzled tide can u help me rq
mystic saffron
so -1/4 right
vast dragon
Ya
mystic saffron
.close
shell sorrel
a/b+c +b/c+d + c/d+e + d/e+a + e/ a+b > 5/2
odd edgeBOT
a/b+c +b/c+d + c/d+e + d/e+a + e/ a+b > 5/2
@shell sorrel Has your question been resolved?
toxic snow
barren elm
odd edgeBOT
Available help channel!
dapper glacier
i have a problem when the solution is provided, but i don't understand the solution
dapper glacier
#14
the screenshot is the solution
can someone explain how the test makers made the equation?
to be more specific, i'm talking about the equations for the series
(-4k-1)^2 + (4k+1)^2 and (-4k)^2 + (4k+2)^2
<@&286206848099549185>
odd edgeBOT
@dapper glacier Has your question been resolved?
dapper glacier
<@&286206848099549185>
odd edgeBOT
@dapper glacier Has your question been resolved?
wheat drum
Say I have the equation 2x = 10 mod 23, I've checked the multiplicative inverse of 2 mod 23 is 12, so x = (2^-1)*10 = 12*10 = 5 mod 23
My question is, does the 'natural' way of simplifying directly 2x = 10 into x = 5 work in all cases ? Or does it fail sometimes ?
shy smelt
radiant shell
odd edgeBOT
radiant shell
How do i even start w this question
like 2x+y = 6 and x^2 = 9 when x = 3, y = 0, so is it just the question?
i don't even know if im supposed to do chain rule
odd edgeBOT
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odd edgeBOT
radiant shell
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mystic saffron
When do I have to put a parenthesis when inserting a value and when do I not?
mystic saffron
I often mess this up and it leads to the entire question being wrong so what's the rule for this?
E.g. say I have a tangent equation with f'(u)*(x-u)+f(u)
And I want to put in -4u+3 for f'(U) ans -2u^2+3u+10 for f(U)
Where do I put a parenthesis and why?
low locust
you always put parenthesis around the entire thing you plug in
if its just a single number then this doesnt really matter so many people dont actually write the parenthesis down in that case
mystic saffron
if its just a single number then this doesnt really matter so many people dont a...
Hm
So here I'd do (-4u+3)*(x-u)+(-2u^2+3u+10)?
low locust
yes
mystic saffron
yes
Thank you
How about when it's a chain function?
Or actually rather
if it's u(x)*v(x)
Do I then do [(u'(x) * v(x))+(u(x) * v'(x))]
<@&286206848099549185>
low locust
do you mean if you want to plug (u(x)v(x))' into some other thing? yes
odd edgeBOT
@mystic saffron Has your question been resolved?
mystic saffron
do you mean if you want to plug (u(x)v(x))' into some other thing? yes
Yep
odd edgeBOT
odd edgeBOT
Available help channel!
austere rover
What happened here?
odd edgeBOT
What happened here?
austere rover
where did it come from?
is it like derivative of a power series?
also why did they differentiate it?
austere rover
can someone explain how they got h(X) to me
odd edgeBOT
can someone explain how they got h(X) to me
austere rover
I only know that 1000X is the revenue function
but getting the rest, I have no idea how
echo ginkgo
I only know that 1000X is the revenue function
no
1000X + 200(3-X) is the revenue
there's X computers you sell normally for $1k
echo ginkgo
the remaining computers (3-X) are regiven to the manufacturer for $200
that's where the 200(3-X) comes from
your store makes back some money with the unsold computers
@austere rover
odd edgeBOT
@austere rover Has your question been resolved?
sudden charm
Hello, Im having trouble with a problem: A number has 30 digits all of which are 0 or 6. can it be a square? I got that it has to end in an even number of zeroes and start with a 6.
sudden charm
if n ends with 10^2k, then 10^2k|n => n/10^2k is a square
and it clearly wont be cuz it ends with 6 and other digits are 0
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topaz stone
I need help with 9b (i) and (ii)
odd edgeBOT
@topaz stone Has your question been resolved?
neon ravine
if i put a 2x2 matrix in row echelon form, is that basically just the 2nd row becomes 00 and the first row remains the same?
green elm
the second row should be of the form [0, c] where c is some number (maybe zero, maybe not)
and the first row should be of the form [a, b] where a is nonzero
that's assuming that the first column contains a nonzero number
otherwise the first row will be of the form [0,a] where a is some number (maybe zero, maybe not) and the second row is [0,0]
neon ravine
so it's just the bottom left value that needs to become 0?
green elm
yes
more precisely, the rules are:
the first nonzero entry in any given row has to be to the right of the first nonzero entry in all the rows above it
gilded bluff
odd edgeBOT
gilded bluff
why does theta = 30?
drifting valley
theta is the angle ABD, and there's a theorem about angles inside circles (don't know the english name, look in your lesson) which says it's half the angle AOD
but since AOD is equilateral, each angle, including angle AOD, is 60°
so ABD, which is half of that, is 30°
wicked ledge
Maybe I'm misunderstanding these
odd edgeBOT
Maybe I'm misunderstanding these
waxen jay
i need help with math
wicked ledge
i need help with math
Sorry this channel's in use
waxen jay
kay sorry
wicked ledge
That's the answer but I don't really get it
I thought that the arrows were put in phase diagrams and their direction was based on whether du/dx was positive or negative before/after that point
But with sinx it'd have positive and negative?
sinu
tardy lagoon
?
from 0 to pi sin u is positive and from pi to 2pi sin u is negative
what's the issue here
wicked ledge
Oh my lord. I'm so sorry.
tardy lagoon
from 0 to pi sin u is positive and from pi to 2pi sin u is negative
thus right arrow between 0 and pi and left arrow between pi and 2pi
tardy lagoon
np
wicked ledge
.close
uneven turret
hi
uneven turret
if
3|2n+1 and 7|n-2
how many 2-digit n exist
I tried multiplying both sides or at some points right side by something but I could not find the answer
but I know it's easier to solve it with mod
but idk how to
.close
coral cloak
Resolve x in the interval [0;2pi]
Knowing that:
2cos(x)+sin(x)>1
Help needed once again ;-;
(Ping me)
coral cloak
.close
trail raft
I am supposed to simplify: (1/cosx) + tanx)(1/cosx) - tanx). and i am wondering if (1/cosx) - (sinx/cosx) will become 1-sinx/cosx or cosx/cosx. i say this because i don't know if 1-sinx becomes cosx in the same way 1-sin²x = cos²x
jovial cape
Hey
jovial cape
Wanted some help on this
I know how to know if y is a function of X with coordinates but not sure how to otherwise
Could yall help me?
mint abyss
Wdym "with coordinates"?
stark heart
https://i.imgur.com/UOdZCVv.png
Do you know what are the conditions that allow y to be a function of x?
odd edgeBOT
@jovial cape Has your question been resolved?
jovial cape
Do you know what are the conditions that allow y to be a function of x?
If each input has 1 output
jovial cape
Wdym "with coordinates"?
There was a similar question on the homework that used coordinates
stark heart
If each input has 1 output
Yeah that's correct
Like when it comes to the very first option do you think that it is a function or not?
jovial cape
Yeah that's correct
Like when it comes to the very first option do you think tha...
no
because there is 2 variables
or am i wrong?
errant heart
After doing all this how do i find the point c?
odd edgeBOT
After doing all this how do i find the point c?
@errant heart Has your question been resolved?
odd edgeBOT
@errant heart Has your question been resolved?
teal carbon
hello can someone help me with this
odd edgeBOT
hello can someone help me with this
teal carbon
xd
i got to this
-cot^2x times secx - secx + 2
i was thinking about factoring out secx like this
secx(-cot^x -1 but idk what to do with the +2
haughty scaffold
u did well by factoring out sec(x) on the left hand side, u can do the same with 2 on the right hand side as well before u bring anything over
well no lets do it differently
u can start off by bringing everything on the left hand side, then from (cotx)^2*secx-secx u can factor out a secx, from the 2-2(cotx)^2 u can factor out a -2, and then youll see that u have another common factor (cotx)^2-1
so now you can factor that one out as well and then youll have a multiplication equal to 0, so youll just set each of the parts equal to 0
teal carbon
hmm one sec let me work it out that way
teal carbon
u can start off by bringing everything on the left hand side, then from (cotx)^2...
i dont get this part
//u can factor out a secx, from the 2-2(cotx)^2
haughty scaffold
no yeah u factor out a secx from the expression before that part of the message, and from the next expression youll factor out a -2
like this
slightly different order on my notebook, but the idea remains the same
haughty scaffold
i just factored out a 2
haughty scaffold
yup
haughty scaffold
nw!
teal carbon
.close
nocturne belfry
I have I think a simple multivar question
odd edgeBOT
I have I think a simple multivar question
nocturne belfry
If im looking at two curves $$x^2 - y^2 = a^2$$ and $$xy=a$$, whats the process to showing that these two curves will always be orthogonal at a point of intersection?
clever fjordBOT
jan Niku
steel quarry
If im looking at two curves $$x^2 - y^2 = a^2$$ and $$xy=a$$, whats the process ...
You can show that one of them is the orthogonal trajectory of the other
obtain the differential equation to one curve, replace dy/dx with -dx/dy, and integrate once more
nocturne belfry
obtain the differential equation to one curve, replace dy/dx with -dx/dy, and in...
how do you mean? implicitly differentiate?
i have to apologize my multivar is horrible
steel quarry
I don't know any multivar, but what you're looking for is an orthogonal trajectory
steel quarry
how do you mean? implicitly differentiate?
yeah
nocturne belfry
yeah
im not sure i understand the process youre describing
why does this show what we want to show
hard field
you could skip the integration process
take the derivative of both and show the product of the gradients is -1
steel quarry
why does this show what we want to show
I'm unaware of a proof of this fact myself if that's what you wish for
hard field
take the derivative of both and show the product of the gradients is -1
taking the using implicit differentiation ?
nocturne belfry
assume ive never taken calc iii
do i just work with the LHS of each of these in constructing the gradient?
hard field
yes
the rhs would become 0 in both cases
for example the first one would become 2x dx - 2y dy = 0
nocturne belfry
i want to understand it because i need to write about it
its the motivation for a method of approximation of integrals
so i need to understand it
but i never took multivar 😳
hard field
dont need anything gradient vector based I think
nocturne belfry
for example the first one would become 2x dx - 2y dy = 0
i dont think this process gives the result we want here, if i did it right
but isnt the gradient defined as a vector?
hard field
I suppose so
nocturne belfry
I suppose so
how does whatever the process youre describing work out?
oh wait
i think i see
so in the one youd have $$2x-2yy'=0$$
clever fjordBOT
jan Niku
nocturne belfry
and the other $y+xy'=0$
clever fjordBOT
jan Niku
nocturne belfry
product in what sense?
nocturne belfry
how do you know
hard field
oh lawd , you're testing my fundamentals ;-;
nocturne belfry
oh, wait
i think i got you
@hard field okay so the products are negative 1
this would be like
hard field
this makes more sense to me geometrically than any math proof
hard field
their isnt much of a surface here
nocturne belfry
and we just rely on like negative reciprocal
negative reciprocal means perpendicular
i think i getchu
hard field
just a ~~ circle~~ BOWL THING extended through z I guess
nocturne belfry
a circle 
hard field
MY BAD
hard field
if level curve one has y' = m at a point
yes
I think this makes sense to me
at least
nocturne belfry
okay
i can learn more later
i do think you need to use vectors
taking the gradient of an equation doesnt make sense to me though
how do you get a gradient involved with a level set
hard field
Im not much use to you for fundamental questions I think, I only learnt general n dimensional gradient vectors weeks ago :D
nocturne belfry
would it really just be like x^2-y^2 = a^2 -> <2x, -2y>?
and then the other is
<y, x>
so 2xy-2yx 
okay
resolved
.close
odd edgeBOT
hard field
yes
nocturne belfry
thanks @hard field
hard field
thanks <@256906999348854795>
odd edgeBOT
Available help channel!
viscid sage
odd edgeBOT
viscid sage
line that divides a line or an angle into two equivalent parts
so 124 divided by 2
=62
haughty scaffold
yup
haughty scaffold
again, BD is a bisector
what does that tell us about the two angles marked on the photo
viscid sage
that it is half
haughty scaffold
ABD is 4x+4 and DBC is 6x-14 right?
viscid sage
yes
they have to equal the same thing
I did this but I dont think it is right
I looked it up and google said 9
Which is correct ?
each = 40
How do I do this ?
<@&286206848099549185>
odd edgeBOT
@viscid sage Has your question been resolved?
signal halo
How do I do this ?
Angle bisector means it splits it into two equal angles
If QS was the angle bisector than m<PQS=m<RQS
viscid sage
so they are both 75 ?
signal halo
Well we know PQS is 35
viscid sage
Correct
signal halo
So is it possible for RQS to be 35
viscid sage
no
viscid sage
is the bisector 70
signal halo
Yeah if the large angle was 70 then QS would be an angle bisector
signal halo
So let me phrase it like this
QS is an angle bisector if and only if the large angle is 70
viscid sage
I said it is true because it is in the middle idk if that is correct
signal halo
And is the large angle 70
signal halo
Yeah
signal halo
Do you know the midpoint formula
viscid sage
x1 x2 y1 y2?
viscid sage
which one do I label first ?
signal halo
(B/2, (a-4)/2) = (-5,-4)
signal halo
which one do I label first ?
Wdym
signal halo
The formula formula says
The coordinates of the midpoint are
((X1+x2)/2,(y1+y2)/2)
signal halo
No
First of all the y coordinate is always the one on the right
So (0,-4) would be x1,y1
And -5,-4 are the coordinates of the midpoint
signal halo
((X1+x2)/2,(y1+y2)/2)
Which are calculated using this^
signal halo
No
X2 and y2 are unknown
They are what we are trying to solve for
But we know the midpoint
signal halo
((X1+x2)/2,(y1+y2)/2)
So we know this is equal to (-5,-4)
So if we plug in x1 and y1 we can solve for x2 and y2
viscid sage
I dont understand the equation
signal halo
I dont understand the equation
Ok so
the midpoint is always ((x1+x2)/2, (y1+y2)/2) right
viscid sage
yes
signal halo
and they also tell us that the midpont is (-5,-4)
viscid sage
yes
signal halo
so (-5,-4) = ((x1+x2)/2, (y1+y2)/2)
this is saying that two points are equal
but for two points to be equal they need to have the same x and y values
so we can split this into two equations
-5 = (x1+x2)/2
-4 = (y1+y2)/2
we know x1 is 0 and y1 is -4
can you solve from there?
signal halo
no
theres no commas anymore
so we would have -5 = (0+x2)/2 right
and -4 = (-4+y2)/2
so how do we solve for x2 in the equation
viscid sage
-4 dividedd by 2 ?
signal halo
use this equation: -5 = (0+x2)/2
quartz pier
odd edgeBOT
quartz pier
this would be false right
because
1 2 | 3
1 1 | 1
1 2 | 1
1 2 | 3
0 -1 | -2
0 0 | -2
last row is 0 0 | -2 so it has no solutions
right
wooden python
yeah sure
quartz pier
alr ty and one more question identity matrix dimensions are always Z x Z where Z can be any natural number right
so 2 x 2, 3x3 , 4x4 but 4x5 wont be possible
it has to be the same
wooden python
that certainly is a choice of letter for denoting an arbitrary natural number
but yes identity matrices are always square.
odd edgeBOT
odd edgeBOT
Available help channel!
bold egret
Hi, so I have this trig equation: sinx + cosx = 1, when I square both sides I get some wrong result but when I multiply both sides by sqrt(2)/2 I get the correct result and I don't understand why
zenith tartan
post your original quesetion @bold egret
bold egret
Find roots of sinx + cosx = 1 that belong to the interval [0, 2pi]
When I square both sides I get a wrong answer
