I’m trying to get the bisector of the purple line and the X axis
#help-10
sinful mortar
It doesn’t seem to be working with the usual equation
lusty cedar
usual equation?
sinful mortar
((ax+by+c)/-sqrroot(a2+b2))-((ax+by+c)/-sqrroot(a2+b2)) =0
lusty cedar
umm
it is actually + and -
both are bisectors
one is of acute angle and other is of obtuse
sinful mortar
no worries
lusty cedar
do you have any issues now?
sinful mortar
yeah, because that’s what I thought
lusty cedar
hmm
sinful mortar
but it doesn’t seem to be right
sinful mortar
i’ll try that
lusty cedar
alr
sinful mortar
feeling like such a dum dum rn
stable apex
what should I look up for? sets and relations multiplication?
obtuse pebbleBOT
what should I look up for? sets and relations multiplication?
@stable apex Has your question been resolved?
stable apex
.close
proven zephyr
−6(3i)(−2i) @nocturne sun
obtuse pebbleBOT
−6(3i)(−2i) <@591872343320821763>
warm canopy
What's i²?
warm canopy
Right so 3 negatives total
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
formal musk
i think i know the answer to this but i just nedded a confirm
formal musk
would this be no intersection
royal basin
no
royal basin
ok so let's first try this
formal musk
ok
formal musk
line mn
formal musk
line MN
royal basin
- no, line MN is not the intersection of LMN and JON. point M does not lie in plane JON.
tranquil beacon
It might help to write out all the point on each plane identified and then see what points are in common for each plane
royal basin
i've highlighted plane LMN in red and JON in green
tranquil beacon
Since it's a rectangular prism there are going to be four points for each plane
royal basin
look at this again and tell me what their line of intersection is @formal musk
formal musk
line KN
royal basin
there we go
and now
line KN and plane LIJ intersect at a point.
what is that point?
refer to the diagram again.
formal musk
point K
royal basin
there we go
formal musk
ok thanks you
fierce tapir
Could anyone explain what this means? I tried to ask the teacher and he was overwhelming vague
obtuse pebbleBOT
Could anyone explain what this means? I tried to ask the teacher and he was over...
timid silo
q22 or 23?
valid crown
find x for every point
fierce tapir
Ohh
valid crown
though A should have possible answer 2
fierce tapir
I.... i still dont understand but ok
obtuse pebbleBOT
@fierce tapir Has your question been resolved?
feral sedge
Could anyone explain what this means? I tried to ask the teacher and he was over...
Do you know what domain of the func. is?
obtuse pebbleBOT
fierce tapir
Do you know what domain of the func. is?
Nope
feral sedge
domain refers to what value of x you can take for function such that f(x) makes sense
obtuse pebbleBOT
Available help channel!
feral sedge
For this question, it is certain that when x=-3, x=0, x=1, and x=2, y should have the corresponding value.
obtuse pebbleBOT
For this question, it is certain that when x=-3, x=0, x=1, and x=2, y should hav...
feral sedge
i.e. The answer is D.
fierce tapir
Thank you
obtuse pebbleBOT
@feral sedge Has your question been resolved?
feral sedge
.close
prisma python
Could anyone explain what this means? I tried to ask the teacher and he was over...
Btw why have you marked D for Q22
obtuse pebbleBOT
Btw why have you marked D for Q22
fierce tapir
Yes i think so
It is what it is, i was kinda looking for someone to explain so i could solve it myself but,. Its fine
prisma python
Yes i think so
Don't you think it's B ?
Anyways I accidentally opened this
.close
obtuse pebbleBOT
fierce tapir
Don't you think it's B ?
Buddy i cant do math because i havent paid attention sense 7th grade and im now in 11th. I have no clue
obtuse pebbleBOT
Available help channel!
zealous wagon
Heyo, anyone who knows a tad bit about Newton-Raphsons method.
I'm trying to utilize Newton-Raphson on a 2-variable function. So far all I've found on the internet is utilizing Newton-Raphson on a system of equations, but that's not what I'm trying to do. I'm trying to perform Newton-Raphson on one 2-variable function (also trying to know how to do this for n-variables)
I was thinking I should just calculate partial derivatives for all, then just evaluate them to find what I'm looking for. But I don't think this is correct. Any suggestions?
obtuse pebbleBOT
Heyo, anyone who knows a tad bit about Newton-Raphsons method.
I'm trying to uti...
@zealous wagon Has your question been resolved?
zealous wagon
Pretty much, yes.
frosty river
Simply apply Newton-Raphson
A single equation is a system of equations with one equation
brave bramble
So the problem is that the method doesn't extend well to a multivariable equation. You aren't really guaranteed to be getting closer to a zero if the tangent line changes direction
zealous wagon
Simply apply Newton-Raphson
I was thinking that instead of utilizing the function's derivative it would be a vector with all of the partial derivatives evaluated. So recursion would still happen and iterations can continue until f(x,y)=0
brave bramble
Instead consider something like gradient descent?
zealous wagon
So the problem is that the method doesn't extend well to a multivariable equatio...
Yes I understand this is a possibility. However for the sake of the exercise, we skip this concept.
zealous wagon
Instead consider something like gradient descent?
Hmmm could consider utilizing gradient descent as a formidable solution.
Okay that should be enough info for me to keep pushing with. Thank you so much for your help @frosty river @brave bramble!
.close
honest steppe
Hi, anyone here who can help me with triangle similarity? And finding a the length of an missing interger in parallel lines?
obtuse pebbleBOT
Hi, anyone here who can help me with triangle similarity? And finding a the leng...
honest steppe
I dont know if I can show an image, but only this question has stumped me in my online math
drowsy girder
You can send a picture
honest steppe
Alright I will
Its this one and one other
let me get a screenshot
its mostly this one though
drowsy girder
See if ratios of longest sides and shortest sides match
honest steppe
Okay
honest steppe
And for this one? ive done done fraction form etc I just dont get what to do
drowsy girder
$$\frac{11}{x} = \frac{13}{4}$$
warm shaleBOT
Pluton
drowsy girder
This would be my guess
honest steppe
okay so just solve this?
drowsy girder
Yes
honest steppe
okay thanks so much!
honest steppe
Ill see if it isnt ill probably be back
It was, thanks so much that was stumping me for days lol
.close
warm pivot
Help
timid silo
obtuse pebbleBOT
@warm pivot Has your question been resolved?
warm pivot
Would the line connecting to the chain middle coming down to the middle count as the radius or the diameter
timid silo
the green part is the radius
warm pivot
This would also count as an isosceles traingle?
timid silo
right angle triangle
warm pivot
the green part is the radius
And I am supposed to find that little red remaining correct?
timid silo
yes
warm pivot
Would Pythagorean theorem work here?
timid silo
yup
warm pivot
Isn’t the bottom of the traingle missing?
The right traingle specifically
Am I supposed to calculate both the bottom and the side
@timid silo
timid silo
we know the two red sides from the question. then we can find the green side using pythagoras. then subtract a radius to get the small part
the right angle is there because of tangency
timid silo
9 is correct
timid silo
yup
timid silo
no
warm pivot
Or would one of them count as an radius
timid silo
the chain is 9, the other is radius=15
warm pivot
2.5cm would be the answer
You are one smart person
Do you also know about surface area?
and converting volume to something I can work with
timid silo
at the top
long sinew
I would find one of the cubes surface area
And then multiply by 6
Unless theres a faster way
warm pivot
They gave me the whole volume of the object
long sinew
Ah
warm pivot
Which is 56cm
long sinew
Yes
warm pivot
And they want the surface area
long sinew
And there are 7 identica cubes
warm pivot
So converting volume to surface area I suppose
long sinew
You could say that sure
Find volume of one of the cubes first
That should be simple? Knowing they are identical
timid silo
it would be funny if there wasn't a cube in the middle and the question was a troll
long sinew
Lol true
warm pivot
I kinda forgot how volume works.
We ain’t even learn about this in class
And we have it on the final exam. (Dw I am working with a practice exam)
warm pivot
Oh okay
long sinew
So there are 7 cubes :)
warm pivot
I think 1.333 repeating
long sinew
Yes one cube
warm pivot
Or just 8
long sinew
Is your calculator on drugs
Alright
Now what is the side length of the cube?
Knowing its volume is 8cm^2
warm pivot
Idk. I know the length of one face
long sinew
Side length...
warm pivot
Would side length be the same as the base
long sinew
Volume of a cube = side * side * side
In other words
Side^3
Or if you think of it as area base * height its side^2 * side
warm pivot
Would using area x base work
warm pivot
4 x 2
warm pivot
Side length is 2
long sinew
Using area(face) * 5 since there are 5 surfaces on this cube (one of them is hidden)
So the area of one face is...?
warm pivot
There is 6 faces on a cube
long sinew
I just explained...
long sinew
So go ahead
warm pivot
Hmm
Thinking
We calculate the base of a cube and side length correct?
How do I convert from cube to face
long sinew
If you know side length of a square how would one find its area?
warm pivot
Times it by base
long sinew
Which is 2
warm pivot
Ok so 10
That is the area of one face? Or the cube
What would I do next
@long sinew
So area of each cube is 10
Times it by 6 since basically a whole cube is missing
Or we could include and subtract it as overlap
Would overlap be 30?
60-30
30cm^2 I think
timid junco
find the area of one of the faces and multiply it by how many faces there are
obtuse pebbleBOT
@warm pivot Has your question been resolved?
obtuse pebbleBOT
@warm pivot Has your question been resolved?
tardy epoch
Uhh there's a lot to go through. Can you just open a new help channel summarizing what you've tried and what you're stuck on now
warm pivot
.close
timid junco
what am I doing wrong here
obtuse pebbleBOT
what am I doing wrong here
hybrid gull
Send work - do you have an expression for f'(x)?
timid junco
sending rn
hybrid gull
👍
hybrid gull
Sorry looking over your work - appreciate your patience tho 👍
Looks good up until the very end
Check the last line and the second to last line (in the numerator)
timid junco
ohhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
I can't believe I've gone this far in arithmetic and still can't add and subtract
timid junco
I use calculator for everything now
I don't trust myself
thanks for the help
and everybody else you're helping XD
.close
obtuse pebbleBOT
hybrid gull
good luck 👍
dim rock
guys whats the meaning if $lim\delta x->0$
warm shaleBOT
Night Wølf
tardy epoch
Your channel's gonna close
tardy epoch
guys whats the meaning if $lim\delta x->0$
But also, read this
https://tutorial.math.lamar.edu/classes/calci/TheLimit.aspx
dim rock
But also, read this
https://tutorial.math.lamar.edu/classes/calci/TheLimit.aspx
thanks 🥲
like i understood its application but i am not sure about what it converts like is it delta x or delta y in my condition
obtuse pebbleBOT
Available help channel!
warm pivot
obtuse pebbleBOT
warm pivot
Would Pythagorean Theorm work?
tardy epoch
Try it
haughty echo
BPT would be simpler
warm pivot
Doesn’t work
haughty echo
How does that work
Similarity of triangles
warm shaleBOT
GG・Goof
warm pivot
Do I solve this?
tardy epoch
,calc pi * 13.8 ^2
warm shaleBOT
Result:
598.28490494964
Similar triangles
warm pivot
18.1?
obtuse pebbleBOT
@warm pivot Has your question been resolved?
warm pivot
I solved it
timid silo
obtuse pebbleBOT
timid silo
Can someone check my work?
I set x = t, solved for y, then plugged that into the second equation
I don’t think that that’s right though since I’d get a +/- after taking the square root of y
solar elm
There are five people of different height. In how many ways can they
stand in a line, so there is no 3 consecutive people with increasing height?
obtuse pebbleBOT
There are five people of different height. In how many ways can they
stand in a ...
solar elm
I know the total without removing cases is 5!/(5-5)! = 120 but how do I continue form here
zenith raft
hmm so you can call the heights 1, 2, 3, 4, and 5 (1 is shortest, 5 tallest) and count the number of permutations that have a 123, 234, or 345 in them
cursive scroll
the only cases that you have to avoid are: 1,2,3 | 2,3,4 | 345
zenith raft
haha
quaint glen
What about 135 for instance?
zenith raft
oh I read it as consecutive heights but that probably wasn't the right way
solar elm
yeh this is a hard one for me haha
it is consecutive heights i think
so like 2 3 1 4 5 is fine
solar elm
the only cases that you have to avoid are: 1,2,3 | 2,3,4 | 345
124 125 234 235 345 maybe?
quaint glen
If my interpretation is correct, no because it contains 145
zenith raft
There are five people of different height. In how many ways can they
stand in a ...
is this exactly how it was asked?
solar elm
is this exactly how it was asked?
yes
im thinking we need to avoid these
123 124 125 134 135 145 234 235 245 345
thats 10
zenith raft
I guess that would work, just be careful about double counting
solar elm
ok someone just posted the start of the answer
surely this question is worded weird
if it only wants 123 234 or 345
zenith raft
oh haha
solar elm
the f?
zenith raft
well that makes it easier
solar elm
im not reading this wrong right
zenith raft
is that the officially provided solution?
solar elm
yes
zenith raft
then yea... sounds like it was about consecutive heights
solar elm
yeh
zenith raft
do you need any help still?
solar elm
ye
right now im look at this
id be looking at slots for each
1 2 3 x x
x 1 2 3 x
x x 1 2 3
=3 * (2^2)
Then 3 diff ways it can happen so 123, 234 and 345
so its *3
therefor
120 - 36 = 84 ways?
zenith raft
almostttt
but two problems there I think
there are only 2 ways you can place the last two letters after you fix 1, 2, and 3
not 2^2
and the other thing is you are double counting like this
you are counting 12345 in your example, but you'll count it again when you count permutations that have a 345 in them
zenith raft
yea, not 11, 00, 10, and 01
solar elm
but normally I do number of unknowns ^ number of things that can go there
zenith raft
or 4s and 5s, whatever
solar elm
oh right
so its 5! - ((2+2+2) * 3) -1
120 - 18 - 1 = 101
actually 12345 is counted 3 times so i needs -2
so 100?
zenith raft
uhh can you show a little work, I didn't do it out lol
zenith raft
just showing the double/triple counting is fine, the rest I'm good with
solar elm
then we have
N N N x x
x N N N x
x x N N N
and also 123 234 345
So for 123 we have 2 + 2 + 2 different ways
so 6 * 3 = 18
so 102 ways now
now for double counting
12345 is counted in this 3 times, so we need to -2
100 ways
thats all i got so far
cursive scroll
say NNN is the case you're trying to avoid, and AB is the other two numbers
there is NNN AB and NNNBA
solar elm
yep
cursive scroll
ANNNB and BNNNA as well
solar elm
yep thats what ive done here
N N N x x
x N N N x
x x N N N
NNN A B and NNN B A 2 ways for each
this is actually the answer
but not sure how to fully do that
zenith raft
if you are unsure, you could write out all 18 permutations and see how many unique ones there are
solar elm
ok I got 14 different ways
23451 is a dupe its in there twice. so its 51234 twice. then 12345 three times
wait so the answer is 14?
zenith raft
maybe (but I didn't do it out)
obtuse pebbleBOT
@solar elm Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
obtuse pebbleBOT
royal basin
careful
it might do you some good to actually list out what the elements of X are
the backslash does denote set difference.
also, no, 20 ∉ X.
uppercase A.
Let X = {n ∈ N : 10 ≤ n < 20}
...
i didn't even ask you HOW MANY elements were in X
i asked you to write out WHAT THEY ARE
reading comprehension
right, so you need to make a set A of ten elements such that X \ A = {10, 12, 14}
for each number from 10 through 19 inclusive, ask yourself: does this number belong to A?
...
so many things wrong with what you just wrote
mostly style and wording things.
you could've said "the numbers 11, 13, and 15 through 19 must belong to A, while the numbers 10, 12 and 14 must NOT belong to A"
commas between the numbers.
but other than this, yes.
you know what P(X) is, right?
reading comprehension
math is case-sensitive
please do not mix lowercase x with uppercase X
it is annoying to have to correct that for the n'th time in a row
but yes {{}, {10}, {11}, {12},{13}} works for part c
no
ordered pairs, not two-element sets like you wrote
ok sure yes
you could try to prove that the only set satisfying the criterion in part (e) is X itself but doing so takes more work than is required of you
uh
are you FORCED to denote events relevant to the problem with specifically the letters A and B and nothing else?
so you tend to DELIBERATELY AVOID names that speak for themselves, huh?
that's bad programming style.
i would have named the set of all red cards R and the set of all face cards F.
think again
cards which are either red OR a face card.
what set operation corresponds to "or"?
.....................
many things wrong with what you just said.
first off there isn't really such a thing as addition of sets.
(except sometimes there is, but NOT in this context.)
second
"or" corresponds to UNION and you should've recognized that
the set of all cards that are red or faces is $R \cup F$.
warm shaleBOT
Ann
royal basin
you need to explain why $|R \cup F| = 32$.
warm shaleBOT
Ann
royal basin
WHY MAKE THIS SO OVER THE TOP COMPLICATED
IT'S JUST UNION IT'S JUST UNION IT'S JUST UNION!!!! OR MEANS UNION!!!!!!!!!!!!!!!!!!!!!!
the explanation they're looking for is $|R \cap F| = 6$, and thus $|R \cup F| = |R| + |F| - |R \cap F| = 26+12-6$
warm shaleBOT
Ann
royal basin
$R \cap F = {\heartsuit K, \heartsuit Q, \heartsuit J, \diamondsuit K, \diamondsuit Q, \diamondsuit J}$ if you want to be extra explicit
warm shaleBOT
Ann
royal basin
years of practice.
the point could've been gotten to faster.
it's a tricky question.
would not describe it as a trick question as such.
but given that you've specifically said you have never done proofs before in your life i think you'll have a hard time justifying why you have not missed any possibilities if you find any.
perhaps it would.
i would ask you to check for yourself but i doubt whether that'll go anywhere.
does it?
what are |A| and |C| in your example?
when A = B = C = {1,2}, that is
and what is {2, |A|, |C|}?
no
notation matters, sushi
as does reading comprehension
also x ≠ {x}
what's lowercase b?
so... you conclude from this that your example works?
you said B={1,2} but then when i asked you what {2,|A|,|C|} was you said {2}
.
"will work" is a property of a TRIO of sets (A,B,C) not of any individual set
yes, this one does work.
don't thank me for having yelled at and demeaned you for like an hour straight lmao
also we didn't even solve the problem, because we have not yet found ALL trios of sets (A,B,C) which satisfy the conditions of the problem.
i am however not looking forward to taking you through the somewhat grueling case work..
plus it would be a proof and you're allergic to those so
we could leave the problem unsolved yes
timid silo
The total of 3 numbers is 82, the numbers are x,y,z
if x : y = 2 : 3 and y : z = 4 : 7, find the xyz
obtuse pebbleBOT
The total of 3 numbers is 82, the numbers are x,y,z
if x : y = 2 : 3 and y : z =...
timid silo
thats 6th grade(i'm not 6th grade) math and i cannot solve it 
x + y + z = 82
x/y = 2/3
y/z = 4/7
Simultaneous eq.
what
?
I gave the equations the rest is basic algebra
i didn't get what you said...
somber mural
you have 3 equations relating to x y and z
they are all linear
you can solve them simultaneously
somber mural
$\frac{x}{y} = \frac{2}{3}$
warm shaleBOT
IntelligentCake
somber mural
how can you rearrange this so that there are no fractions
timid silo
3x+2y=0?
timid silo
2) x = 2y/3
3) z = 7y/4
Now replace these values in eq(1)
what is eq(1)
somber mural
do you know how to rearrange @timid silo
timid silo
the first equation wait
timid silo
do you know how to rearrange <@456226577798135808>
whats that
timid silo
- x+y+z = 82
- x/y = 2/3
- y/z = 4/7
somber mural
khan academy has good resources on it
timid silo
2) x = 2y/3
3) z = 7y/4
Now replace these values in eq(1)
so its 2y/3 + y +7y/4 = 82?
ys
i think i can solve it with this
hold on
the y=24
well
i found the answer as 16128
something is definetily wrong
8/12y + 12/12y + 21/12y = 82
41/12y = 82
y = 24
if x = 2/3y then x = 2/3 * 24 or 16
is that false?
@somber mural
timid silo
if x = 2/3y then x = 2/3 * 24 or 16
(2/3)y yes
u should get 16 if y = 24
timid silo
(2/3)y yes
u should get 16 if y = 24
but i get a way high number if i do that for all the numbers then find the xyz
i got 16128
16(the x)x42(the z)x24(the y)
its xyz
royal basin
what's the original problem
timid silo
what's the original problem
The total of 3 numbers is 82, the numbers are x,y,z
if x : y = 2 : 3 and y : z = 4 : 7, find the xyz
timid silo
The total of 3 numbers is 82, the numbers are x,y,z
if x : y = 2 : 3 and y : z =...
find xyz
value of x * value of y * value of z
24 * 16 * 42 should be answer whats wrong tho
timid silo
find xyz
value of x * value of y * value of z
24 * 16 * 42 should be answer wh...
the number is really high but i could ask to my teacher if i found it right or wrong
anyways thanks
.close
royal basin
8+12+21 = 41, so the numbers are 2*8, 2*12 and 2*21
obtuse pebbleBOT
royal basin
ok
timid silo
8+12+21 = 41, so the numbers are 2\*8, 2\*12 and 2\*21
i got the same numbers as this
16 24 42 nothing changed
royal basin
,calc 16 * 24 * 42
warm shaleBOT
Result:
16128
yeah then everything is working as intended
obtuse pebbleBOT
Available help channel!
deft ore
obtuse pebbleBOT
deft ore
i did this question and got
-2lnx +ln(x+1) +ln(x-1) +C
but the answer says something different
royal basin
,w d/dx (-2log(x) + log(x+1) + log(x-1))
warm shaleBOT
royal basin
it appears your answer is correct
deft ore
erm
royal basin
and perhaps this is an issue of the answer key writing it down in a different form
royal basin
$-2\ln(x) = \ln\paren{\frac{1}{x^2}}$
warm shaleBOT
Ann
royal basin
they just wrote the thing as a single logarithm. nothing else
lunar lagoon
obtuse pebbleBOT
lunar lagoon
how do we determine the homogenity
warm canopy
what precisely do you mean?
obtuse pebbleBOT
@lunar lagoon Has your question been resolved?
fresh nymph
Hi guys !
CONTEXT :
I need to find solutions for a point in space that is on three spheres. This should output two solutions as three spheres that intersect have two common points. This is a practical problem where you can consider that the two spheres always have a circle in common (they are not far apart from each other or inside each other or with a single point in common like just touching).
MATHS :
I have three points p1, p2, p3 and three distances d1, d2, d3. How do I find the coordinates for the two points A and B that are a distance d1 to p1, a distance d2 to p2 and a distance d3 to p3 ?
I get these 3 formulas :
(x - p1.x)² + (y - p1.y)² + (z - p1.z)² = d1²
(x - p2.x)² + (y - p2.y)² + (z - p2.z)² = d2²
(x - p3.x)² + (y - p3.y)² + (z - p3.z)² = d3²
But where do I go from there ? I could develop the powers but then I get some unknowns squared which I've never dealt with before in this kind of situation
obtuse pebbleBOT
Hi guys !
CONTEXT :
I need to find solutions for a point in space that is on thr...
@fresh nymph Has your question been resolved?
fresh nymph
<@&286206848099549185>
royal basin
i think some geometric insight might help
try looking at the plane spanned by p1, p2 and p3; the two points of intersection will lie along the line normal to that plane and passing through the circumcenter of the triangle p1p2p3
obtuse pebbleBOT
Available help channel!
turbid hamlet
how do you calculate trigonometry?
obtuse pebbleBOT
how do you calculate trigonometry?
turbid hamlet
im confused
proven zephyr
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
oh you meant calculate sin cos tan?
or triangle?
or angle?
turbid hamlet
all of them sorry 😭
turbid hamlet
how do i tell when i need to use sin , cos or tan ?
proven zephyr
to find angles
turbid hamlet
yep
proven zephyr
or missing sides in a right angled triangle
proven zephyr
,rotate
warm shaleBOT
proven zephyr
so basically.. sin is the ratio of hypotenuse to the opposite
turbid hamlet
oh
proven zephyr
if you're trying to find the opposite side, use sin
if you're trying to find the adjacent side, use cos
turbid hamlet
ohh
turbid hamlet
alrightt
proven zephyr
Sin = Opposite/Hypotenuse, Cos = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent or Sin/Cos
proven zephyr
sure
turbid hamlet
for example 5(m+y) = 4(m-3y) , how do i make m the subject?
proven zephyr
what do you mean by making m the subject
turbid hamlet
make m the subject of the formulae
proven zephyr
is y a variable or coordinate
turbid hamlet
variable
proven zephyr
oh ok i think i get it
turbid hamlet
okayy
turbid hamlet
thats the expanded right?
turbid hamlet
ohh
OH
thank you 😭
wait and one more thing srry 😭
how do you do simultaneous questions..
proven zephyr
?
turbid hamlet
wait nvm i remembered i could do it with the calculator
proven zephyr
ok?
turbid hamlet
thank you again
proven zephyr
np
turbid hamlet
.close
obtuse pebbleBOT
dreamy tinsel
I tried to solve it, but i failed sorry
timid silo
hi
obtuse pebbleBOT
@timid silo Has your question been resolved?
chilly trellis
wouldnt the first term be negative?
obtuse pebbleBOT
wouldnt the first term be negative?
obtuse pebbleBOT
feral sedge
@chilly trellis
Doesn't matter, If $-1<x<0$, then $0<1+x<1$.
Also, $x^2 + x^3 = x^2 (1+x)$.
$x^2 >0$, $0<1+x \Rightarrow x^2 + x^3 > 0$.
Continuing this process, $\dfrac{1}{1-x} > 0$.
Note that the geometric series $\dfrac{1}{1-x} = \displaystyle\sum_{k=0}^{\infty} x^k$ (The ans. is the last one) has radius of convergence of $x \in (-1, 1)$.
warm shaleBOT
kelvinchan9786
obtuse pebbleBOT
Available help channel!
formal musk
obtuse pebbleBOT
formal musk
how would u do this
restive ridge
• Show your work, and if possible, explain where you are stuck.
formal musk
i dont know how to set up the equation
restive ridge
what's the full angle
formal musk
for what angle?
formal musk
The whole angle for the problem?
formal musk
180 degrees.
formal musk
360 degrees.
formal musk
No not really.
Could you explain it?
Because I believe that could help me solve the problem.
Hello?
Can someone help me?
sour peak
obtuse pebbleBOT
sour peak
how can i find c2
c1 is 0.10
and i know that
y'(0) = 2
but idk how to derive this
because of the c1 and c2
sour peak
really and just add them back at the end?
warm canopy
d/dx(c*f(x)) = c*d/dx(f(x))
sour peak
since i found c1 earlier, would i plug c1 in then derive
so 0.10e^-2sqrt(5)t + c2te^-2sqrt(5)t
warm canopy
sure, makes no difference
you can leave it as c1 and put it in at the end if you want
solar trellis
Differentiate not derive
sour peak
.close
timid silo
can anyone help with b pls
obtuse pebbleBOT
can anyone help with b pls
heady coral
I'm currently writing a program to change the brightness of my laptop screen and I don't want it do do it linearly, so I would like to be able to provide profiles that contain brightness curves.
I'm looking for a parametric function over [0, 1] who's parameter(s) let me determine it's shape to look like/similar to the functions in my example.
I know that I could use exactly what I have in my example (excluding the circle segment)
fn curve(x, a) -> f32 {
match a {
..1 => {
1 - (1-x).pow(1/a)
},
1.. => {
x.pow(a)
},
}
}
However I don't feel that this is flexible enough as it doesn't allow for a circle segment for example.
obtuse pebbleBOT
I'm currently writing a program to change the brightness of my laptop screen and...
heady coral
@restive ridge don't tell them this isn't valid rust anymore 🕵️
I came up with a few more functions but those aren't nearly as flexible as the result I got above, so they are out.
<@&286206848099549185>
Is this question too advanced?
restive ridge
no idea what you're trying to do
heady coral
plug
$1-\left(1-x\right)^{\frac{1}{b}}$
and
$x^{b}$
into desmos and play with the slider for b between 1 and 10
warm shaleBOT
Hadis
tardy epoch
I'm currently writing a program to change the brightness of my laptop screen and...
you're just not specifying, in math terms, what you're trying to do.
heady coral
Because my math terms are rusty. But I can try.
I want a parametric function with these properties:
- f(0) = 0
- f(1) = 1
- f'(x) != 0 for x in (0,1)
- f(x) monotonously increasing for x in (0,1)
- f'(x) monotonous increasing for x in (0,1)
- f''(x) != 0 for x in (0,1) (unsure on this one)
I want the parameters of the parametric function to change the shape of the graph but keep those properties.
tardy epoch
f(x) = x^3 satisfies all of these
heady coral
It's not parametric
heady coral
$f_a(x)$
warm shaleBOT
Hadis
tardy epoch
what you described isn't parametric either
heady coral
Where?
tardy epoch
```
- f(0) = 0
- f(1) = 1
- f'(x) != 0 for x in (0,1)
- f(x) monotonously increa...
where is a here?
heady coral
I want a parametric function with these properties:
I did ask for a parametric function. I didn't know I had to specify the name of the parameter because I didn't even know if such a a function would need more than one parameter
Can you help me specify even more what I'm looking for?
tardy epoch
I did ask for a parametric function. I didn't know I had to specify the name of ...
it doesn't, e.g. x^3. so why do you want to incorporate a parameter a
$f_a(x) = x^{3/a}$ also works for $a > 0$
warm shaleBOT
riemann
heady coral
it doesn't, e.g. x^3. so why do you want to incorporate a parameter a
I'm currently writing a program to change the brightness of my laptop screen and I don't want it do do it linearly, so I would like to be able to provide profiles that contain brightness curves.
This was my use case
I want it to be very flexible.
heady coral
**riemann**
So this is worse than what I have already, even though it does match the properties I asked for
tardy epoch
$f_a(x) = x^{a/3}$ also works for $a > 0$
heady coral
Do you get what I'm trying to achieve?
tardy epoch
no because you're being descriptive in your asks
"provide profiles that contain brightness curves" is essentially meaningless
heady coral
It conveighs intent
timid silo
maybe it would help if you could draw some profiles and say that the family of curves has to include something that looks like them
tardy epoch
It conveighs intent
intent is meaningless if you can't translate it to implementation / math
heady coral
That's why I'm here!!
If I knew exactly how to phrase my problem completely in a mathematical way I'd have a much easier time solving it myself
heady coral
maybe it would help if you could draw some profiles and say that the family of c...
I'm looking for something that's not unlike Quadratic Bézier curves.
with P_0 = (0,0) and P_1 = (1,1) and P_3 = (1,0)
heady coral
Ah
So I want a quadratic bezier curve with P_0 = (0, 0), P_1 = (1, 1) and P_3 = (a, b) with a and b in [0, 1]?
heady coral
```
- f(0) = 0
- f(1) = 1
- f'(x) != 0 for x in (0,1)
- f(x) monotonously increa...
would that always satisfy these constraints?
tardy epoch
just generate it and plot it and see
heady coral
This is the most eccentric curve I can make with a Quadratic Bezier Curve
timid silo
are you like looking for a family of curves that limit to a right angle?
heady coral
If you mean the green curve then yes. My curve can't go beyond that
timid silo
but do you want it to get to that?
heady coral
That would be great.
timid silo
x^a works ._.
heady coral
But only if I can have everything in between the blue and the green curve in that image aswell
timid silo
well a can be irrational and very big...
timid silo
This is the most eccentric curve I can make with a Quadratic Bezier Curve
what if you multiply this curve by x^a
timid silo
it would make it limit to the right angle
heady coral
Not in a nicely uniform way.
If I just wanted to limit it to the right angle I could make it piecewise
timid silo
so you want it symmetric along the diagonal too?
timid silo
huh
heady coral
Depending on a parameter
timid silo
one parameter?
heady coral
any number of parameters
timid silo
oh ok
heady coral
Let's say a reasonable amount of parameters to deal with programatically.
This server doesn't get a lot of real world questions, right?
I can tell from @tardy epoch's confusion about my question especially.
I'm sorry I can't phrase it better, that's why I gave the use case for the parametric function I'm looking for.
timid silo
most of us arent engineers unfortunately
heady coral
i get that
timid silo
if you have a bunch of potential curves you like but there's something wrong with them, you could multiply them all together with different parameters so that you can adjust each thing seperately
heady coral
That's an idea that I haven't thought about
mmmmmh.
If I multiply two functions that mirror each other between the (1,0), (0,1) diagonal, do I get a function that is symmetric over that same diagonal?
If that was the case, that would basically solve my problem sufficiently
timid silo
mmmmmh.
If I multiply two functions that mirror each other between the (1,0), (0...
not sure, it makes sense but i cant prove it. try it and see ¯_(ツ)_/¯
heady coral
Oh my god my intuition is right for a bunch of functions that look like that
I don't need it to be true for all functions. Just the one's I can try
Thank you so much for helping me!
I'm 99% sure that's all that I needed
If I take f(x) and g(x) that are symmetric between that diagonal I can attatch weights to them and multiply them together
the flexibility of that resulting function is just huge
I call
.closed
tardy epoch
This server doesn't get a lot of real world questions, right?
#help channels are meant for homework, soooo no
heady coral
Yeah.
I asked here because it doesn't actually involve any uni level maths
High school maths turns out to be enough
tardy epoch
timid silo
throwback to the builder who wanted to know if he was being ripped off when buying building products from a company by asking us to compute an area of a weird shape
heady coral
I don't think my question is outside the realm of what a last year highschool teacher could give his students as homework
That's the way I read it,
homework-type
tardy epoch
your problem using high school math does not equate to you being able to explain it at that level.
tardy epoch
it takes effort to properly curate math problems
heady coral
here, you mean?
This would honestly have been a fun high school assignment if it was worded well.
Why is this thread not in available again?
.closed
Ah
.close
sour peak
in spring mass underdamped systems
obtuse pebbleBOT
in spring mass underdamped systems
sour peak
how do i find phi
like i dont understand where the phi comes from
.cloe
.closr
.close
grand carbon
i already got the horizontal asymptote but im not so sure about the intersection question ;-;
obtuse pebbleBOT
i already got the horizontal asymptote but im not so sure about the intersection...
main cedar
zenith raft
what if you let y = 0 and solve for x?
just from looking at it, there are values of $x$ that make $\frac{\ln(x-2)^2}{e^{x^2}}$ equal to 0 because that will happen whenever the numerator, $\ln(x-2)^2$, is 0, which is when $(x-2)^2 = 1$
warm shaleBOT
Spring
zenith raft
and you don't need to worry about 0s in the denominator cus e^(x^2) is positive for any x
@grand carbon
obtuse pebbleBOT
@grand carbon Has your question been resolved?
zenith raft
what if you let y = 0 and solve for x?
oh I actually forgot to mention, first you need that the horizontal asymptote is the line y = 0
grand carbon
oh I actually forgot to mention, first you need that the horizontal asymptote is...
ooh yes yes i actually got y = 0 as my horizontal asymptote
ok i’ll try that!
i solved for x and i got x = 3, 1
zenith raft
yep! that's right
obtuse pebbleBOT
grand carbon
.reopen
obtuse pebbleBOT
✅
grand carbon
ooh yay but does that determine like the intersection of the curve already? so the answer is “none of the choices” then?
zenith raft
wellll the points of intersection are (3,0) and (1,0)
zenith raft
yay, np!
grand carbon
.close
plush vapor
im doing my practice exam and these r the 3 questions im stuck on
obtuse pebbleBOT
im doing my practice exam and these r the 3 questions im stuck on
plush vapor
theres an answer key for them but the process to get the solutions is what im stuck on,
fierce lagoon
Okay, so the first one
You wanna use the expanded form, then condense
I'll highlight the roots
Gimmie a sec
plush vapor
alright no worries
fierce lagoon
I also wanna test this thing so
plush vapor
theres an answer key for them but the process to get the solutions is what im st...
4 = 3(x^2 - 2x - 10), 5 = (2, 8, 13, 4) and (-1.09, 1.73)
fierce lagoon
$$(x-{\color{lime}{(1+\sqrt{11})}})(x-{\color{magenta}{(1-\sqrt{11})}})$$
Hope this works
plush vapor
oh ok i was inputting it wrong
fierce lagoon
Oh wait hold on
warm shaleBOT
Umbraleviathan
fierce lagoon
Sorry I had to fix it @plush vapor
fierce lagoon
Well you just expand it
tardy epoch
$$(x-{\color{lime}{(1+\sqrt{11})}})(x-{\color{magenta}{(1-\sqrt{11})}})$$
man you really having fun with this new latex color discovery
fierce lagoon
man you really having fun with this new latex color discovery
Color
Wait hold on I just realized something
@plush vapor there might be an easier way
plush vapor
show me if u think there is
fierce lagoon
So what if I rewrote the roots as $$\frac{2\pm2\sqrt{11}}{2}$$
warm shaleBOT
Umbraleviathan
fierce lagoon
Then if you compare that to your quadratic formula
$$-b = 2$$
$$2a = 2$$
$$b^2-4ac = 44$$
warm shaleBOT
Umbraleviathan
fierce lagoon
I'm assuming your teacher wants it in standard form correct
plush vapor
yeah
plush vapor
yeah put that into the quadratic formula?
fierce lagoon
Well I just turned the roots into the result of a quadratic formula
I "unsimplified it"
So what would a and b be?
plush vapor
2
plush vapor
1
fierce lagoon
What would b be?
plush vapor
if -b = 2, b = -2?
fierce lagoon
Yeah
plush vapor
oh ok
fierce lagoon
So now what would c be?