viscid cobalt
thanks
#help-41
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cursive wasp
The answer is (iii) but how is it different form (i) or (ii)?
keen pawn
can I have a hint
amber waspBOT
can I have a hint
keen pawn
Induction doesn't seem like it will work here
Contrapositive maybe?
Contrapositve induction
$\abs{a_1+2a_2 \dots na_n} >1 \implies |f(x)|>|sin(x)|$
grizzled pagodaBOT
A dense set
keen pawn
Base case $|a_1| >1 \implies |a_1 sin(x)|> |sin(x)|$
\
Inductive hypothesis $|a_1|+2|a_2| + \dots+ n|a_n| >1 \implies a_1sin(x)+a_2sin(x)+ \dots+ a_nsin(x) >1$
\
It trivially follows that $|a_1|+2a_2+ \dots + (n+1)|a_{n+1}| >1$. It thus follows that $|a_1|sin(x)+|a_2||sin(2x)| + \dots + |a_{n+1}| |sin(nx)| > |sin(x)|$
However the issue is thid eosn't prove what I want
grizzled pagodaBOT
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keen pawn
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dusk ice
hi
dusk ice
i’m supposed to factor it, where do i go from here?
long abyss
you can apply the quadratic formula for the equation on the right to make more factors
long abyss
yes something like that
amber waspBOT
frank zealot
so the results gonna be x^2(x-result)(x+result)??
should actually be 12x² (x - result)(x + result)
small modification
dusk ice
should actually be 12x² (x - result)(x + result)
gotchuu ty
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vivid osprey
someone free to help me with sketching the premitive?
amber waspBOT
someone free to help me with sketching the premitive?
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split sail
help
split sail
how to do c
cos
if we have diameter
and we use distance formula
we have 2 unknowns
and we dont have
any sort of equation of a life for QS
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clever island
Let's consider D as center of circle, then Try to find S, and then DS is radius, when you have D and S, you can find slope, then it is easy to find equation of tangent. If something not clear, feel free to ask
subtle viper
We were told to show f:R²->R with f(v) = v1+v2² in the two euclidean metric spaces (R², d1) and (R, d2) is continuous, but I can't prove it
pallid canopy
Are you using sequential continuity or topological
Probably neither actually. Do you have to use eps-delta definition?
subtle viper
Are you using sequential continuity or topological
eps delta yes
we do use topological approaches mostly, but I'd prefer doing this proof rigurously
I do see that it can be expressed as the sum of two continuous functions which makes it continuous, but how does eps-delta apply here without disintegrating the function?
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@subtle viper Has your question been resolved?
pallid canopy
I imagine it's similar to proving x+c is continuous and c+x^2 is continuous for any constant c
Oh d1 is sqrt(x^2 + y^2) ?
That's a little harder
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weak zinc
The metric on R being the “standard” one (absval of the difference?)
kindred grail
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kindred grail
i know its completing the square but ive forgotten how to do it
and it is due in 11 minutes
fresh hatch
if you know the topic to use to solve a question just quick search it you will find how to solve the question
vestal hatch
,w expand 12-3(x+2)^2
grizzled pagodaBOT
vestal hatch
no
kindred grail
gosh
grizzled pagodaBOT
kindred grail
,w expand 16+3(x+2)^2
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reef tide
Does this equal 0 or 1?
amber waspBOT
Does this equal 0 or 1?
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reef tide
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reef tide
how do they get 8sqrt2?
i get that 4sqrt5*sqrt 5 simplifies to be 20, and sqrt10 becomes sqrt50, but how do they get 8?
yes
but isnt it then 4 x sqrt2 x sqrt25?
sqrt25= 5
cunning birch
supposed to be 4sqrt(50) = 4*5*sqrt(2) = 20sqrt(2)
reef tide
supposed to be 4sqrt(50) = 4*5\*sqrt(2) = 20sqrt(2)
a miscalculation?
cunning birch
most likely, it's very easy to verify this over and over
reef tide
haha okay
cunning birch
sqrt(5)-sqrt(10) = sqrt(5) [1 - sqrt2]
so 4sqrt(5)[sqrt(5)-sqrt(10)] = 20[1-sqrt2]
reef tide
i feel bad for my teacher but the answers for the revision is full of incorrect answers
reef tide
so 4sqrt(5)[sqrt(5)-sqrt(10)] = 20[1-sqrt2]
yeah
thank you so much for the help!!
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reef tide
hi i was wondering why they remove the ^2 on the 10 when they make it a surd?
pallid canopy
hi i was wondering why they remove the ^2 on the 10 when they make it a surd?
simplify
reef tide
isnt it divided by 4 though?
pallid canopy
$\sqrt{10} = 10^{1/2}$
grizzled pagodaBOT
riemann
storm lynx
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storm lynx
For 4a how do I approach the question?
shrewd elm
you want a matrix C such that Ca = 0 for every column of A, right?
storm lynx
Yes but would that imply C can be a 0 vector?
cunning birch
Yes but would that imply C can be a 0 vector?
you want Cx = 0 for ONLY x in U
so for x outside of U, probably shouldn't be 0
storm lynx
you want Cx = 0 for ONLY x in U
How do you turn those conditions into a matrix?
cunning birch
How do you turn those conditions into a matrix?
If you have a basis of U
say {a,b}
complete it into a basis of F^4 for example
{a,b,c,d}
you know Ca = 0, Cb = 0
and Cc and Cd different from 0
take for example Cc = (0,0,1,0) and Cd = (0,0,0,1)
so if you take M the matrix with columns a,b,c,d
CM = some matrix
with M invertible...
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odd torrent
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grizzled pagodaBOT
k
cunning birch
$d_n = \sum_{k=0}^n \frac{n + \sqrt{k}}{n^2 + k}$
try to write it as something that looks like sum(f(...))
oops wrong person to ping
@odd torrent
hint: d_n = 1/n sum (f(k/n^2))
odd torrent
you said something about integrals before you edited
but i haven't had them yet
we only used the sqeeze theorem on those kind of sequences
and i couldn't find the upper and the lower bounds
amber waspBOT
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1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
odd torrent
Hello <@254671304723005440>
hello
brisk leaf
Have you tried integration?
As n tends to infinity it can be treated as dx
Or you could try squeeze theorem
@odd torrent
odd torrent
Have you tried integration?
i havent had integrals on my calculus classes yet:/
odd torrent
Or you could try squeeze theorem
yeah that's what i tried but i couldnt figure out the upper and lower bounds
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vast crystal
Determine the Euler characteristic of the surface of a pretzel, the Klein Bottle, and Torus using for each two different sets of triangulations.
vast crystal
am i cooked
robust isle
might be easiest to work with an explicit polygonal model for each
vast crystal
yea but i just dont know how to draw those
robust isle
do you know a polygonal model for the torus?
vast crystal
maybe its better if i send an image of one ive seen before hold on
robust isle
vast crystal
thats it?
robust isle
yes
making sure you are careful about identifications
since the two a edges are the same edge
and all 4 vertices are the same vertex
vast crystal
and for two different sets of triangulations does that i mean i split it into more triangles?
vast crystal
oh that seems much easier than i thought
do you have images for the pretzel and klein bottle for me to use as well?
robust isle
here is a pretzel
genus 3 surface
either of these will give you the klein bottle
taken directly from hatcher
vast crystal
thank you very much sir you are a wonderful human being
robust isle
robust isle
vast crystal
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near flower
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near flower
i can only think of two possible points but i don't rly know how to get any of the values
mint nacelle
if you've made a sketch the below reasoning should make sense
one of the points is $z_3 + (z_2 - z_1)$
grizzled pagodaBOT
south's secret twin brother
mint nacelle
now instead of using the vector between z1 and z2
try using the direction vector between z1 and z3 instead
and change the point you add it to ofc
near flower
try using the direction vector between z1 and z3 instead
this might be wrong but can i do (z3-z1)+z2
mint nacelle
this might be wrong but can i do (z3-z1)+z2
yeah you can
mint nacelle
**south's secret twin brother**
but that's the same as this point
near flower
oh crap mb
mint nacelle
yeah so like now you should know how to get the other point
there's like two possible directions
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misty bobcat
Ok guys, very crude diagram, but lets say you have a paralleogram and you have a shaded area shown above like between the diagonals and a line from the midpoint M, what fraction of the area of the paralleogram is the area
misty bobcat
I was thinking it was 1/4th cause if u do it with a square its 1/4th and a square is a paralleogram
but i dont think thats thorough enough
misty bobcat
so then how tf do u do this
sterile nymph
What level of math?
misty bobcat
nothing past like gcse level
misty bobcat
ye its like base times height
sterile nymph
And for a triangle?
sterile nymph
Yes
misty bobcat
Like
sterile nymph
It is 1/4
sterile nymph
Yup,
misty bobcat
oh nice
sterile nymph
Though you'll want to be very explicit with your justification, that's the gist.
sterile nymph
The square method has a draw back
It only proves it is true for parallelograms that happen to also be squares.
sterile nymph
I would approach the problem by comparing two different diagrams.
In the top parallelogram, we have a triangle, the triangle has the same base and height as the full parallelogram.
In the bottom parallelogram, we have that green shades area is also half of the area of the parallelogram. This is because the total height of the two triangles is the total height of the parallelogram, and the bases are the same.
Actually, we only need the second
Because we can use the fact that the two triangles are congruent.
@misty bobcat ^
I was trying to be clever and not have to use it. But it does eventually need proving to be solid, so might as well at the first opportunity.
Use only the second diagram.
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kind hound
.
keen pawn
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keen pawn
So I have the curve. $y=x^4+cx^3+12x^2-5x+2$.
Let there be 4 points that lie on both the curve and line( $y=mx+c$
\
chosing a,b, b,c, c,d there are atleast 3 tangents with slope $m$ , by MVT.
\
so $m=. 4x^3+3cx^2+24x-5$.
\
We need this cubic to have 3 solutions, again, using MVT, two turning points.
\
so $12x^2+6cx+24=0$ needs to have 2 solutions
grizzled pagodaBOT
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grizzled pagodaBOT
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keen pawn
We still have to ensure that the cubic has 3 roots
like consider the following equation: $x^4+16x^3+12x^2-5x+2$
grizzled pagodaBOT
A dense set(Ping when reply)
keen pawn
,w graph x^4+16x^3+12x^2-5x+2
grizzled pagodaBOT
keen pawn
,w roots of x^4+16x^3+12x^2-5x+2
grizzled pagodaBOT
grizzled pagodaBOT
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full wharf
Hey so im stuck again
amber waspBOT
Hey so im stuck again
signal furnace
Hint: inscribed angle theorem
signal furnace
Yooo i got it 😛
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full wharf
Whys x 48 degrees too??
Is it cos their identical triangles?? (idk if they are)
Thank you once again civil service pigeon
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split sail
why isnt it
soft trench
how do i do 10b? im not sure where to start
primal escarp
omgg wrong server
split sail
Lol
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errant flint
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opaque haven
Qn : when a number divided by 15,18,20,27 it will give reminder 10. It is a multiple of 31. What least number add to this number so that it become a perfect square
opaque haven
i found lcm of this as 1350 . and it gives remainder 10. how do i find which (multiple of 1350 + 10 ) is divisible by 31?
sterile nymph
This is equivalent to finding some k such that 1350k = 21 mod 31
opaque haven
This is equivalent to finding some k such that 1350k = 21 mod 31
i don't undestand
sterile nymph
If you need 1350k + 10 = 31j then you have 1350k = 31j - 10 = 31(j-1) + 21
lusty saffron
...how did you get 1350?
sterile nymph
lcm of 15, 18, 20, and 27, apparently
lusty saffron
1350 isn't a multiple of 20
sterile nymph
true...
sterile nymph
yes, that is correct.
opaque haven
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royal seal
amber waspBOT
royal seal
Can anyone help me with this word problem,
I really suck at solving systems of equations
amber waspBOT
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@royal seal Has your question been resolved?
sterile nymph
@royal seal did you set up the systems of equations from the word problem?
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vague jewel
trying to understand this question and it's not really making any sense
vague jewel
i got part a right just by guessing
trying to set up the equation itself is this is what i have:
A(x)=(x/4)^2
I dont understand how to do the triangle bit
hollow salmon
Hmm, not sure why that first one is correct. It shouldn't be.
As far as the equation goes, if the length used for the square was x, what would the length of the remaining wire be for the triangle?
What a nonsensical question.
shadow stump
i'm guessing one of those was meant to say "triangle"
shadow stump
well if we are maximizing "total area" i would imagine that means the area of square and triangle together
vague jewel
i guess
however im not even sure on how to plug in the eq triangle formula into this
amber waspBOT
@vague jewel Has your question been resolved?
vague jewel
tbh i kinda just gave up on it
hollow salmon
By the logic of your answer in part a), you could say that 0 length would minimize the area.
Which is why I said it was a nonsensical answer.
vague jewel
yeah 0 doesn't work
hollow salmon
There's no constraint on the triangle which would suggest a correct answer for part b.
amber waspBOT
gloomy tide
yes it would? descending then ascending
full sand
yes it would? descending then ascending
local minimum means that if you walk a tiny step left to -3 and a tiny step right to -3 and f(-3-small number) > f(3) and f(-3+small number) > f(3) or am I confused?
oh its f`
split sail
the graph is f'
full sand
my bad
split sail
not f
no because it increase right after
ver ?
uh no
its horizontal when f' = 0
try to draw what would f looks like around 1
yes
and no
no
draw it
best way to understand is a draw
hm send a picture
same that f'(-3) or that f(-3) ?
yes
yes
aahhh okk
yes
np
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old drift
Let $f: \mathbb{R}^2 \rightarrow \mathbb{R}$ be differentiable, and $f(x,y) = 0$ whenever $x^2 + y^2 = 1$ Show that there is atleast one point $(x_0, y_0)$ such that
$\frac{\partial f}{\partial x}(x_0, y_0) = \frac{\partial f}{\partial y}(x_0, y_0) = 0$
grizzled pagodaBOT
Bean Man
nova niche
Just an idea: the set of all points with x^2+y^2<=1 is a compact subset of R² and f has to have a maximum / minimum if f is continuous?
old drift
Can I restrict f to the closed unit disk and fix arbitrary $x$ and $y$ so that
$f_x(y) = f(x, y)$ and $f_y(x) = f(x, y)$
And since they are continuous functions on a compact set then they attain their maximum and minimum.
Then use Rolle's theorem?
grizzled pagodaBOT
Bean Man
gloomy tide
not sure what you mean by fixing arbitrary x and y
old drift
I'm not sure how else to describe it, let $x$ be some point in [-1, 1], then $f_x(y) = f(x, y)$, is this not allowed?
I can be more specific and say let $x_0$ be arbitrary then $f_{x_0}(y) = f(x_0, y)$
and $y_0$ arbitrary so that $f_{y_0}(x) = f(x, y_0)$
And I know that both of these functions, by rolle's theorem have a point where the derivative is equal to zero. Let us call this point for $f_{x_0}$, $(x_0, y')$ and $(x', y_0)$
I'm not sure how to refine it to get the claim I'm looking for, or if it necessarily follows but that's the idea
grizzled pagodaBOT
Bean Man
old drift
I'm not sure if Rolle's theorem holds for $\mathbb{R}^2 \rightarrow \mathbb{R}$, so this is what came to mind
grizzled pagodaBOT
Bean Man
gloomy tide
oh ok i think i understand
might have been good to use a letter that wasn't x lol
maybe X
anyway
yeah that's the issue, isn't it - that you don't know if (x0, y') and (x', y0) are the same point
i don't know what theora you currently have access to, personally i'd reach for borsuk-ulam
old drift
Just an idea: the set of all points with x^2+y^2<=1 is a compact subset of R² an...
Is what I have what you were thinking?
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green salmon
How does this...
amber waspBOT
How does this...
green salmon
How does that go to that?
little widget
this what and that what?
vernal bobcat
Factorise a 2 from the numerator
amber waspBOT
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green salmon
Factorise a 2 from the numerator
huh
green salmon
hm
little widget
you can simplify with the denominator
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sleek zenith
$\int (x \sec(x) + \sec^2(x) (x \sin(x) + \cos(x))) e^x , dx$
grizzled pagodaBOT
Alex
sleek zenith
hi, i tried integrating this by parts
brave depot
Boy that is one ugly integral
molten shale
simplify first
sleek zenith
do u mean expanding?
sleek zenith
simplify first
I dont see how to do that
molten shale
yes expand
sleek zenith
this is a mess 
dull pike
Do not expand.
Rewrite sec in terms of cosine and the problem ends in one step.
$\frac{d}{dx} \left( f(x)e^x \right) = e^x \left( f(x) + f'(x) \right)$
$\int \left( \frac{x}{\cos(x)} + \frac{x \sin(x) + \cos(x)}{\cos^2(x)} \right) e^x , dx$
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Samuel
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candid estuary
amber waspBOT
candid estuary
how am i wrong
abstract canopy
candid estuary
but how am i wrong
latent nest
Were you supposed to just type 3?
quick ridge
h(t) = 6 find t, you did h(6)
quick ridge
yep
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vestal igloo
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vestal igloo
The answer here is 216, but I got 218
coz 87 num are divisible by 23 and 22 num are divisible by 88
then i just x 2?
lcm (23, 88)=2024 so no green
amber waspBOT
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vestal igloo
<@&286206848099549185>
amber waspBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
3
brisk leaf
Of different colours
vestal igloo
The answer here is 216, but I got 218
coz 87 num are divisible by 23 and 22 num ...
my soln
little widget
The answer here is 216, but I got 218
coz 87 num are divisible by 23 and 22 num ...
1495, 1496 are consecutive, first divisible by 23 and the other by 88
528, 529 are consecutive, first divisible by 88 and the other by 23
brisk leaf
1495, 1496 are consecutive, first divisible by 23 and the other by 88
528, 529 a...
These 2 pairs need to be subtracted
vestal igloo
1495, 1496 are consecutive, first divisible by 23 and the other by 88
528, 529 a...
how do i get these numbers
is there a shorter way
little widget
i just bruteforced to find these, idk about the math, sorry
brisk leaf
You could use the floor function and analyze from there on
vestal igloo
whats that
brisk leaf
It's like for numbers to be converted to integers
So floor(2.3) =2
Floor(3)=3
You could graph the thing
And see from there on
vestal igloo
np
brisk leaf
Ok I think I got an idea let's try it
So let's assume a number A which is divisible by 88
So let's assume A/88 = K
Where K is some integer
And let's assume a number B which is divisible by 23
So let's assume B/23 = Q
Q again being an intger
A=88K
B=23Q
we want that A - B or B-A should be 1
Let's go with first case
A-B = 1
88K-23Q = 1
Or
B-A = 1
23Q-88K=1
Now for Q the upper limit is 87
And for K it is 22
So Q-K<65
So 23Q - 23K < 1495
From 88K -23Q =1
23 Q = 88K-1
Substitute
88K- 1 - 23 K <1495
65K<1496 ; K< 24
And same can done for Q
88Q-88K<5720
65Q<5721 ; Q < 89
Compare and get answer
Same can be repeated for B-A=1
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fallen chasm
How do u do this?
amber waspBOT
How do u do this?
reef seal
sideways parabola opening up to the right, centered at the option you picked
what he said ^
fallen chasm
Ok but to find points where tangent line is vertical or when derivative is undefined, wouldn’t the denominator have to be 0?
Since the equation isn’t a fraction why isn’t the answer “the tangent line is never vertical”?
harsh fox
I think you can flip the graph, meaning swapping the position of x and y in the equation
and then find dy/dx=0
long abyss
or you can try finding dx/dy = 0 haha without having to flip the graph
harsh fox
or you can try finding dx/dy = 0 haha without having to flip the graph
yes:) flipping is for illustrative purpose
amber waspBOT
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harsh fox
Ok but to find points where tangent line is vertical or when derivative is undef...
Derivatives arent really defined by "division". It is the "limit" as the division get smaller. If you were to head straight into this derivavtive as dx/dy, you will find that its derivative is 1/+or-sqrt(x), which is not really a function. But as x approaches 0, this approaches +inf and -inf, which in the end is just the vertical line.
which is an undefined derivative, but the tangent line still exists
fallen chasm
Derivatives arent really defined by "division". It is the "limit" as the divisio...
Ok wait you said going into the derivative I’ll end up with 1/sqrtx. But I got 1/2(y-2)?? That’s why I chose (0,2) because when y=2, the denominator equals zero, thus undefined. Is this reasoning logical? 😭
reef seal
I'm not sure how you got 1/2(y-2), but if you solve the original for y, then you get y = plus/minus sqrt(x) +2. You only need to consider the positive version to see the vertical tangent. The derivative of the square root of x with respect to x is 1/(2sqrt (x)). See the screenshot
blue line is the positive branch of the horizontal parabola, purple line is the derivative
if you took the derivative with respect to y instead, you should get dx/dy = 2y - 4
I'm not sure you could do anything with that
harsh fox
Ok wait you said going into the derivative I’ll end up with 1/sqrtx. But I got 1...
1/+or-2sqrt(x) as jimmy said. Just make y the subject if you want to find dy/dx. (y-2)^2=x <=> +-sqrt(x)=y-2 <=>+-(x)^(1/2)+2=y. Take the derivative of that.
harsh fox
if you took the derivative with respect to y instead, you should get dx/dy = 2y ...
y=2 <=> dy/dx=2*2-4=0
reef seal
actually i guess dx/dy =0 precisely corresponds to the vertical tangent
yeah you right
thanks
fallen chasm
1/+or-2sqrt(x) as jimmy said. Just make y the subject if you want to find dy/dx....
Ohhhh I forgot squaring both sides is a thing
Ok yea idk how I got 1/2(y-2)
tytyy for all the help 😭
harsh fox
No problem, I think you just got the order of operation wrong somehow
fallen chasm
Lol yeaa I’m trynna do it again but I can’t get that answer anymore wierd
harsh fox
:)you dont need to try to relearn doing it wrong
hope that clears up any issue with the problem above
silent night
How do I enter this into WA
jovial oar
Does x! grow faster than e^x
amber waspBOT
Does x! grow faster than e^x
jovial oar
?
indigo cloud
x! grows each step with a factor of x (which gets bigger) and e^x grows each step with a factor of e
lime turret
Depends on the interval
honest dagger
amber waspBOT
@jovial oar Has your question been resolved?
median granite
how do i start?
amber waspBOT
how do i start?
prisma trench
how do i start?
u need to prove that both triangles are similiar
and then use the propotionality to it and ur good to go
median granite
so ratios?
median granite
DB is 5 and BE is 8 so CB should be BA* (5/8)?
median granite
prove the similarity first
okay
prisma trench
DB is 5 and BE is 8 so CB should be BA* (5/8)?
BA*8/5
amber waspBOT
amber waspBOT
Available help channel!
keen pawn
amber waspBOT
keen pawn
I don't know if I'm tripping here
would like my work checked
$EF = \sqrt{r^2-x^2}$
\
$BF = \sqrt{r^2-x^2+d^2+x^2-2dx}$
\
$ED = \sqrt{r^2-x^2} +l - \sqrt{r^2+d^2-2dx}$
This feels, off
HI !
cloud scarab
$EF = \sqrt{r^2-x^2}$
\\
$BF = \sqrt{r^2-x^2+d^2+x^2-2dx}$
\\
$ED = \sqrt{r^2-x^...
Last segment is probably ED, not EF
sage chasm
What i'm thinking here is to find the length ED in term of x and find the value of x when we are at the state of equilibrium
keen pawn
yea
keen pawn
Last segment is probably ED, not EF
huh
cloud scarab
You made a typo, no?
grizzled pagodaBOT
A dense set(Ping when reply)
keen pawn
What i'm thinking here is to find the length ED in term of x and find the value ...
Yeah, but minimising it doesn't give me the desired answer
keen pawn
$\frac{-2x}{2\sqrt{r^2-x^2}} + \frac{2d}{2 \sqrt{r^2+d^2-2dx}}=0$
sage chasm
Yeah, but minimising it doesn't give me the desired answer
did you take the derivative of ED ?
cloud scarab
He is trying to do that rn
sage chasm
ah yea
cloud scarab
Dense, you forgot a closing bracket in the first frac
grizzled pagodaBOT
A dense set(Ping when reply)
cloud scarab
Splendid
sage chasm
put them at the same denominator and solve for x ?
that looks very ugly to solve tho
proven vapor
how is x not dependent on W? I'm quite confused
sage chasm
$-x \sqrt{r² + d² -2dx} + d\sqrt{r²-x²} = 0$
grizzled pagodaBOT
Herels
keen pawn
yup, so we take one term to the other side and square it
sage chasm
$x \sqrt{r² + d² -2dx} = d\sqrt{r²-x²}$
cloud scarab
how is x not dependent on W? I'm quite confused
It does, kind of
BFD has length l
grizzled pagodaBOT
Herels
keen pawn
$x^2r^2+x^2d^2-2dx^3 = d^2r^2-d^2x^2$
grizzled pagodaBOT
A dense set(Ping when reply)
sage chasm
where that cube comes from
proven vapor
It does, kind of
BFD has length l
ahh okay I missed that
keen pawn
where that cube comes from
squaring both sides
keen pawn
I was trying to do this with pure mechanics
why 😭
keen pawn
**A dense set(Ping when reply)**
so yeah, we have a mess now
proven vapor
why 😭
I thought it might be doable
also I'm revising all my mechanics rn so I got a bit too cocky
sage chasm
$x² (r²+2d²) - 2dx^3 = d²r²$
grizzled pagodaBOT
Herels
cloud scarab
I was trying to do this with pure mechanics
Pure mechanics says that we should minimize the energy of W, which corresponds to maximizing ED
I think
proven vapor
Pure mechanics says that we should minimize the energy of W, which corresponds t...
I suppose that works yeah
I was just writing out all the forces and stuff
proven vapor
it got way too complicated
keen pawn
**Herels**
This ain't going to be pretty without the cubic formula
I guess vitaes may help
cloud scarab
,w factor -2x^3 + x^2 (r^2 + 2d^2) - d^2 r^2
grizzled pagodaBOT
keen pawn
oh, wait
sage chasm
,w solve x² (r²+2d²) - 2dx^3 = d²r²
grizzled pagodaBOT
Requested by herels
sage chasm
kek
keen pawn
,w solve x^2(a^2+2b^2)-2bx=b^2a^2
grizzled pagodaBOT
keen pawn
sage chasm
so you can factor out x-d
ahh
keen pawn
I forgot we can find roots by inspection 
sage chasm
so you can factor out x-d
hmm are you sure
proven vapor
yes
proven vapor
you have 2d^3 - 2d^4
all terms have power 4
sage chasm
yea i see
keen pawn
,w (x² (r²+2d²) - 2dx^3 - d²r²)/ (x-d)
sage chasm
let find it ourselves lmao
sage chasm
(x-d)(x²+Ax+B) = -2dx^3 + x² (r²+2d²) -d²r²
proven vapor
$2dx^2-r^2x-r^2d=0$
keen pawn
let's first see if $x=d$ is an inflection point
proven vapor
let's first see if $x=d$ is an inflection point
x=d is not possible physically, so
keen pawn
$x = \frac{r^2 \pm \sqrt{r^4+8r^2d^2}}{4d}$
proven vapor
r^2 d^2
keen pawn
we need x>0
grizzled pagodaBOT
A dense set(Ping when reply)
keen pawn
$x= \frac{r^2 +. r \sqrt{r^2+ 8d^2}}{4d}$
grizzled pagodaBOT
A dense set(Ping when reply)
proven vapor
**A dense set(Ping when reply)**
you should also probably check if this thing is less than d
it should be
cloud scarab
Double dropper sounds like a redstone component
keen pawn
lol
proven vapor
,w sqrt(r^2-x^2) + l - sqrt(r^2 + d^2 - 2d*x) at x=r/(4d) (r+sqrt(r^2 + 8d^2))
grizzled pagodaBOT
proven vapor
very nice
amber waspBOT
amber waspBOT
Available help channel!
ebon temple
a vase is formed by rotating the part of the curve y=2/x -1 between x=0.5 and x=2 about the y axis. find the volume of the base
ebon temple
on the diagram it also says it goes from y=0 to y=3 so i tried doing that but i got it wrong i think
how woud i do it if i have to rotate it about the y axis but it only gives me x coords
amber waspBOT
Available help channel!
terse wren
yo can somebody help me i will pay
amber waspBOT
yo can somebody help me i will pay
lavish wind
yo can somebody help me i will pay
What do you got?
terse wren
What do you got?
i txted ill show u
crude kite
yo can somebody help me i will pay
Do not offer money for doing homework assignments, and vice versa.
That's in the rules
amber waspBOT
@terse wren Has your question been resolved?
terse wren
`Do not offer money for doing homework assignments, and vice versa.`
That's in t...
man im sorry my dad passed nd im sick rn so i needed help
i do not recall the rules sorry
red oasis
send a picture of your assignment please
terse wren
ok
amber waspBOT
terse wren
.reopen
amber waspBOT
✅
terse wren
send a picture of your assignment please
my computer is dying but hold on i can send my login if u wanna see it ur self but i gotta go to my grandmas so my mom can work
terse wren
ok i will i gtg so she can goto work
mint nacelle
that sucks man
mint nacelle
ok i will i gtg so she can goto work
ok when you have access to your computer again just post your question
someone will always be there to help in this server
amber waspBOT
@terse wren Has your question been resolved?
mint nacelle
.close
pine glade
Hello
I have tried to solve this problem, but I cannot prove it.
I think that this question is wrong, but I want to ensure that
Chat gpt failed to solve it and even graphing the equation did not help.
y = x * arctan(x)
Prove that :
2xy = 2xy` + (1+x^2) y``
I would always get
2x^2 * arctan (x) = 2 + 2x * arctan (x)
rapid peak
what did you get for y' and y''?
amber waspBOT
@pine glade Has your question been resolved?
jovial cape
which part am i misunderstanding
amber waspBOT
which part am i misunderstanding
brisk leaf
Hello @jovial cape
I believe you have misunderstood the first statement
It's the same statement as statement 2
Just written in passive form
jovial cape
Hello <@663084908557893632>
hmm thats wrong as well
brisk leaf
No I mean
Both statement 1 and 2 are correct
They are saying the same thing
Only 2 statements are incorrect right?
brisk leaf
hmm thats wrong as well
jovial cape
Only 2 statements are incorrect right?
I dont know
OH
OK I TOTALLY MISUNDERSTOOD THE QUESTIONJ
jovial cape
Is 3,5 right?
i think its 4,5
because this is the definition of onto
which would be 3 i think
so 4 must be wrong
and 5 must be wrong
right?
brisk leaf
Yeah
I didn't even see those lol
I just saw the first options and immediately typed it
Sorry for that
pine glade
.reopen
jovial cape
i only got one attempt left 😭
jovial cape
im too scared to try
brisk leaf
Risk it
Every element does have image in codomain
But co domain should only contain images
It doesn't specify that
And d is wrong for obvious reasons
jovial cape
ok it was right 🙂
brisk leaf
Cool
brisk leaf
Sorry for that buddy
It's one thing getting your own stuff wrong
But getting some else's is just feels too bad
That's all for now?
@jovial cape
hexed lance
If log3(8)=a, then log9(64) is...
amber waspBOT
If log3(8)=a, then log9(64) is...
gloomy tide
you're going to need to apply some definitions and try some things here
here's a start
if $\log_38 = a$ then $3^a = 8$
grizzled pagodaBOT
hayley is stateside!!
hexed lance
yes im not sure where that gets me
hexed lance
do i have to rewirite the other log the same way?
gloomy tide
do i have to rewirite the other log the same way?
that might help yeah
hexed lance
I believe the answer is just a
id like to know how we get there
hexed lance
hexed lance
See if this makes sense
rly doesn't
hexed lance
how did you get that from multiplying it by one..
brisk leaf
The issue is how I multiplied by one?
hexed lance
that is a start for me yes
something i cant see why you did that and then got a whole diff thing
brisk leaf
I Mean a = a * 1
Which can be re write it as
a *2/2
Then just used the fact that
alogb = log b^a
2 log 8 is log 8^2
Which is log 64
hexed lance
im getting a bit confused, you did all that by multiplying a by a
basically
right?
brisk leaf
Cool
hexed lance
.close
amber waspBOT
brisk leaf
Ur welcome
thorn tapir
.close
amber waspBOT
Available help channel!
high dagger
can someone just tell me how this is meant to be solved? i think i can solve it but im not sure what order to do it in. I keep getting a scalar value when it wants a vector. the second image is what i got as my answer
high dagger
plugging anything into f(x,y,z) is going to give something in terms of x,y,z and then plugging in (3,1,2) would give a scalar so i must be doing something wrong
amber waspBOT
@high dagger Has your question been resolved?
pallid canopy
plugging anything into f(x,y,z) is going to give something in terms of x,y,z and...
f(x, y, z) returns a scalar. why do you think "it wants a vector"
show your steps how you got your answer
amber waspBOT
@high dagger Has your question been resolved?
slender hamlet
amber waspBOT
slender hamlet
please help
I made a few attempts but none gave me the right answer
all i need is the method
amber waspBOT
@slender hamlet Has your question been resolved?
slender hamlet
amber waspBOT
@slender hamlet Has your question been resolved?
opaque maple
can you share your work so far?
what do you have as the areas for each section ?
amber waspBOT
amber waspBOT
Available help channel!
long remnant
where did i go wrong
amber waspBOT
where did i go wrong
crimson cloak
where did i go wrong
nowhere?
cross out the x and divide everything by x on the bottom and top and you get the same thing
long remnant
cross out the x and divide everything by x on the bottom and top and you get the...
this is what is says for answer
crimson cloak
this is what is says for answer
cross out the x and that's what you get
split sail
this^ those answers are the same but one is more simplified than the other
long remnant
oh
long remnant
.close
amber waspBOT
amber waspBOT
Available help channel!
inner prawn
amber waspBOT
neat wind
nice name
coral wigeon
awful name
robust willow
W name
coral wigeon
fuck all of you then
neat wind
:(
inner prawn
so, i wanna know if it would work as well if instead of $(36a+b)(a+36b)$ it was $(2a+b)(a+2b)$
grizzled pagodaBOT
combinatorics hater
inner prawn
i think so, assuming WLOG the 2-adic valuation of a being less or equal of that of b
but idk
inner prawn
awful name
fuck you
coral wigeon
fuck you
inner prawn
$(\text{fuck you})^2$
grizzled pagodaBOT
combinatorics hater
coral wigeon
inner prawn
it really is
coral wigeon
neat wind
so, i wanna know if it would work as well if instead of $(36a+b)(a+36b)$ it was ...
I feel like the proofs should be fundamentally different
wooden bane
chill
neat wind
i.e. (2a + b)(a + 2b) is easier to prove than with 36