Set the sum to 0
#help-13
slow thicket
soft jay
Okay 👌
slow thicket
Cause that’s what stops it from accelerating
soft jay
Out of curiosity
If I then had to find the acceleration would I just do smth like this?
slow thicket
something like what
slow thicket
did you make up that problem
soft jay
No
slow thicket
cause in the question you asked before it is stationary
soft jay
Hang on
slow thicket
the whole reason we can set it to 0 is because it is not accelerating in the y direction
it is hanging
slow thicket
since we know a_y = 0, ma_y = 0 so sum(F_y) = 0
soft jay
This time I calculated the horizontal components and added them up
Then found what acceleration is using f/m
slow thicket
yes
soft jay
So it’s fine to have negative acceleration?
slow thicket
that just means its going in the negative direction
but your work is still relatively disorganized
stick with symbols
soft jay
Ity
slow thicket
its so much harder to mess up
soft jay
I suck at mechanics
slow thicket
you dont suck
soft jay
But thanks for all the help 🙏
slow thicket
no problem
soft jay
I didn’t manage to get into my course because of mechanics.
So I’m stuck here doing a foundation year lol 😂
.close
odd sierra
cedar kilnBOT
hallow quartz
just a small algebra mistake
u need to minus 5 from both sides
x=-5-3i
x=-5+3i
dire crag
remeber to .close if no more questions!
odd sierra
.close
opal perch
Hi everyone! I need help with this problem:
cedar kilnBOT
Hi everyone! I need help with this problem:
opal perch
First, I decided to split up the triangles to make it easier for myself to see
Then I came up with the equation:
PQ = (RT-RP) - QT
So then I started substituting:
PQ = (10-RP) - 5
So at this point, I needed to solve for RP.
I looked at that red triangle and since there is an angle being bisected, I decided to use the angle bisector theorem
So using the angle bisector theorem:
8/6 = (PT/10-PT)
80 - 8PT = 6PT
oh shit
i see where i went wrong
sorry
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
fallow parrot
Helllo?
fallow parrot
o thts how it works
F(x)=2x/x-1
The question is asking to find all asymptotes that we are doing in class
So i found the Vertical asymptote and horizontal asymptote
But the question is also asking to graph this rational function
Now would I just plut the VA x=1 and HA y=2
Draw the dotted lines and that would be the ened of it?
cedar kilnBOT
@fallow parrot Has your question been resolved?
merry tinsel
cedar kilnBOT
sharp kestrel
cedar kilnBOT
sharp kestrel
is this correct?
static fern
remember, $\tan \theta = \frac{\sin \theta}{\cos \theta}$...
wraith daggerBOT
FireBlazer
sharp kestrel
remember, $\tan \theta = \frac{\sin \theta}{\cos \theta}$...
so which part is incorrect
dire geode
so which part is incorrect
Are you just guessing?
static fern
if we divided both sides of the first equation by $\cos^2 \theta$, we would get $\tan^2 \theta + 1 = \sec^2 \theta$
wraith daggerBOT
FireBlazer
static fern
is that what we want tho?
sharp kestrel
Are you just guessing?
no
sharp kestrel
is that what we want tho?
yea?
static fern
we want $\cot^2 \theta$, not $\tan^2 \theta$
wraith daggerBOT
FireBlazer
sharp kestrel
yea thats what I got
I did sin^2(theta) + cos^2(theta) = 1
and simplified it down to
1 + cot^2(theta) = sec^2(theta)
static fern
1 + cot^2(theta) = sec^2(theta)
u got that from dividing both sides by $\cos^2 \theta$?
wraith daggerBOT
FireBlazer
sharp kestrel
u got that from dividing both sides by $\cos^2 \theta$?
yea
sharp kestrel
If you divide both sides by cos^2, what should you get?
tan^2(theta) + 1 = sec^2(theta)
obsidian coral
And is that what you want for the first question?
obsidian coral
then it turns into 1 + cot^2(theta) = sec^2(theta)
How
obsidian coral
No
You don't use multiple division steps like that
All you need is one single division step
tan^2(theta) + 1 = sec^2(theta)
If that is what you got when you divided by cos, is that what you want as an answer for the first problem?
brave pike
cedar kilnBOT
brave pike
how did they even do this
granite knoll
well what did they substitute?
brave pike
like it would be 4 [sin^2t*csc^t} no?
they multiplied the 4
but idk how they got rid of all the trig
granite knoll
oh actually, what is the csc equal to?
granite knoll
yea
brave pike
I hate these explanations
makes sense tho i see how they got there
thank you so much
.close
dim gust
I have what has to be an abnormally easy question around here. If I wanted to find out how many sets of 5 teams of 6 men could be made from a pool of 30 men, how would I do that?
dim gust
Not just the combinations of 6 men, but the combinations of 5 teams each containing six men, with no man on more than one team... I feel like I'm making this harder than it is
cedar kilnBOT
@dim gust Has your question been resolved?
fair geyser
you shuffle all 30
and divide into 5
and then you unshuffle the contents of teams and the order of teams
30! / 5! / 6! / 6! / 6! / 6! / 6!
so 11423951396577720
you can also think of it like
take the first person alphabetically
pick 5 more men
take the next unpicked person and repeat
29c5 × 23c5 × 17c5 × 11c5
same result
cedar kilnBOT
@dim gust Has your question been resolved?
worthy ridge
what did I get wrong here?
cedar kilnBOT
what did I get wrong here?
worthy ridge
could I not have just simplified the expression by linearity?
oh my
i forgot the brackets
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
Can someone help me I'm just kinda confused in this math solution
crimson sedge
how 8t^-1/2-12t^3/2dt turned into 16t^1/2-24/5t^5/2
drifting marlin
They applied the power rule for integration
drifting marlin
If you think it's necessary
drifting marlin
.close
jade stag
how can relative extrema happen at x_2?
cedar kilnBOT
how can relative extrema happen at x_2?
cedar kilnBOT
cedar kilnBOT
Available help channel!
wide ether
So a rational function doesnt has 0?
cedar kilnBOT
So a rational function doesnt has 0?
wide ether
f(x) / g(x) where g(x) cant be 0?
earnest socket
f(x) / g(x) where g(x) cant be 0?
this is where the function is defined
the zeros of the function are precisely the zeros of f(x) where g(x) is nonzero
wide ether
but how what if it is 0
wide ether
and
1/-1.5 = -0
-0.67*?
as in
there will be a munis right
minus*
minus sign
cuz -0.67 and 0.67 are confusing me nvrm i got it
also
R--{0} what does this mean
R here is relation
of function
.close
frail nacelle
Suppose η is random variable with the density function F . Prove that (Xt, t ≥ 0) exists
random process and find its one-dimensional
and bivariate distribution functions.
frail nacelle
cedar kilnBOT
@frail nacelle Has your question been resolved?
cedar kilnBOT
@frail nacelle Has your question been resolved?
frail nacelle
<@&286206848099549185>
cedar kilnBOT
@frail nacelle Has your question been resolved?
frail nacelle
Suppose η is random variable with the density function F . Prove that
random process
cedar kilnBOT
@frail nacelle Has your question been resolved?
crimson sedge
im mildly confused about how to approach that gcd(a,b) times lcd(a,b) = ab
crimson sedge
i thought i had an idea, but there are like many ways to prove this it hink
but i want to use divisibility
solar sun
it's quite simple, actually
say you want to find lcm(a, b)
it is the least number that is divisible by both a and b
now say gcd(a, b) = x
this means a/x and b are coprime (as all the common divisors have been erased by dividing a by common divisors with b), so lcm has to be divisible by ab/x (as it's div. by a/x and b)
in fact, it can just be ab/x, as it fits as an lcm, as both a/x and b/x are integers, so lcm = ab/x, which means gcd * lcm = ab
@crimson sedge
crimson sedge
sorry im reading thrpugh this! thank you
solar sun
yeah sure np
crimson sedge
it is the least number that is divisible by both a and b
this is the same as the least common multiple?
solar sun
this is the same as the least common multiple?
it is its definition lol
crimson sedge
i think its like ab / gcd(a,b) right?
solar sun
yeah lcm(a, b) is that
nimble verge
solar sun
crimson sedge
lmao? those look like anxiety meds
crimson sedge
now say gcd(a, b) = x
this means a/x and b are coprime (as all the common diviso...
is this like a WLOG for a and b
solar sun
is this like a WLOG for a and b
yep
crimson sedge
can we break this down even more
why do you start off by choosing to find the lcm(a, b)
solar sun
because it's meaningful to do that: it looks the weirdest in the equation
so we might wanna comprehend it rather than anything else
hence we want to prove lcm(a, b) = ab/gcd(a, b)
crimson sedge
also would i need to prove (as all the common divisors have been erased by dividing a by common divisors with b specifically
crimson sedge
in fact, it can just be ab/x, as it fits as an lcm, as both a/x and b/x are inte...
i think i understand this more than ```
this means a/x and b are coprime (as all the common divisors have been erased by dividing a by common divisors with b), so lcm has to be divisible by ab/x (as it's div. by a/x and b)
this is just the proof for that
you could also prove it by saying that if you remove any divisor from ab/x it will fail, but it's the same
solar sun
ok
crimson sedge
i suck at this math lol
solar sun
no problem lemme explain
a and b have some common divisors, right?
x is basically all of them
crimson sedge
yes i got that
solar sun
so if you remove x from both, they won't have any common divisors
but in fact you don't need to remove it from both, because if you remove it from one it'll be gone
look: a = x * p and b = x * q
wait brb
sorry about the coprime thing, it's quite confusing. not the point
crimson sedge
ehh im kinda the opposite at gifted in math
solar sun
look: a = x * p and b = x * q
so because of this we need lcm to be pqx, so it is divisible by both px and qx
crimson sedge
i sorta need to break down like everything unfortunately
solar sun
so because of this we need lcm to be pqx, so it is divisible by both px and qx
so
if remove any factor from pqx, it will look like pqx/m
so let's look at (pqx/m)/px and (pqx/m)/qx
they both have to be integers by the definition of lcm
so q/m and p/m are integers
but q and p don't have any common divisors, hence it's impossible
@crimson sedge yeah bruh I just forgot how to prove this
sorry that I didn't type it out later and left you confused
cedar kilnBOT
@crimson sedge Has your question been resolved?
lavish plank
cedar kilnBOT
lavish plank
unsure on what this means. taking limit
cedar kilnBOT
@lavish plank Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
jaunty mural
cedar kilnBOT
https://i.imgur.com/TucBVrt.png
jaunty mural
I want to move that minimum closer to the origin
while maintaining the overall... kindof shape
Like without making f(4) much closer to 0
hard to describe what im after 
===
f is a cost function for minimization, and I need the above shape with:
f(a) > f(b)fora <= 0, b > 0f(0)is the supremum off(a),apositive- The minimum as close to 0 as possible
jaunty mural
Like without making f(4) much closer to 0
so this wouldnt work cus this
Ask me for clarification 
so graphically, I like want to just squash the function between 0 and 1
autumn fox
How are you allowed to transform f 
jaunty mural
I want to end up with an analytic function
so the transformations should be continuous
and... not too complicated preferably?
===
But yeah, I was just asking here for ideas more than anything
I just can't think of how to do that squash
f(cbrt x) kindof works, but then the slope at the origin is infinite and I cant have that
kindof, not really tbh
jaunty mural
===
`f` is a cost function for minimization, and I need the above shape with:
- ...
====================
To give more details uh
The cost function should be infinitely differentiable.
It assigns a 'cost', and I want to punish values far from 0. In addition to that, I do not want negative values at all, so it should heavily punish negative x.
The function is a cost, so the larger the value, the higher the cost/punishment
===
I have an array of values I want to minimize the sum of the cost f(x_1) + f(x_2) + ...
jaunty mural
The problem with the green graph is that the minimiser software thinks it can't do much better at say f(4) because the slope is negligible
and my x_1's range from roughly [-2, 10]
https://i.imgur.com/MisXCaT.png
So any function with this shape fits the bill. I want the minimum as close to the origin as possible and the slope to be non-negligible for x < 10
ah found a solution
(repeatedly) applying h(x) = ln(x+1) to the input makes that slope flattening slow down
.close
cedar kilnBOT
jaunty mural
cedar kilnBOT
Available help channel!
turbid spoke
is x+y = 80?
cedar kilnBOT
is x+y = 80?
turbid spoke
o and then 40
gentle flower
2y + 2x = 80
y = 80/2 - 2x/2
y = 40-x
olive gorge
Pls help, a^2 + b^2 + c^2 = 2 prove: a + b + c =< abc + 2
cedar kilnBOT
Pls help, a^2 + b^2 + c^2 = 2 prove: a + b + c =< abc + 2
bright bridge
!status
cedar kilnBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
@olive gorge Has your question been resolved?
olive gorge
Pls help, a^2 + b^2 + c^2 = 2 prove: a + b + c =< abc + 2
granite knoll
!status
cedar kilnBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
latent bloom
@olive gorge your channel is here
olive gorge
Yea
latent bloom
Have you tried attempting the problem?
olive gorge
Yes
olive gorge
I tried to square it, but I didn't succeed
olive gorge
Could you show us your work?
I can’t find it
torn wren
I tried to square it, but I didn't succeed
What is a b and c
latent bloom
They're constants. Greaka wants to prove that the sum of the squares of a, b, and c are less than (abc +2).
torn wren
They're constants. Greaka wants to prove that the sum of the squares of a, b, an...
Real numbers ??? Positive numbers ??? Integers???
olive gorge
They're constants. Greaka wants to prove that the sum of the squares of a, b, an...
No I Wonna prove: a + b + c =< abc + 2
torn wren
Dude
We just can't approach a problem like that without knowing the nature of a,b and c
olive gorge
a,b,c - Materialized
torn wren
????
cedar kilnBOT
@olive gorge Has your question been resolved?
abstract narwhal
cedar kilnBOT
abstract narwhal
Any one plz
bright bridge
!status
cedar kilnBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
hollow timber
So do what you normally do for definite integrals then just find the values of a which is the smallest surely
Wait am I being an idiot
zenith sail
Wait am I being an idiot
If you are then so am I lol, that's what I would do
hollow timber
If you are then so am I lol, that's what I would do
K
cedar kilnBOT
@abstract narwhal Has your question been resolved?
cedar kilnBOT
@abstract narwhal Has your question been resolved?
oblique nymph
what is p? i dont understand the tables and how they wrote p for some of them
bright bridge
inland kraken
Gcd means greatest common divisor?
oblique nymph
how is the lcm of 1 and p, p
crimson sedge
helo
bright bridge
how is the lcm of 1 and p, p
it is
inland kraken
it's a prime number
modest lichen
how is the lcm of 1 and p, p
if p is prime
bright bridge
if p is prime
oblique nymph
ok so how is the gcd of p and 1 p
oblique nymph
but the gcd of 1 and 7 is 1
modest lichen
yes?
oblique nymph
ok wait i think im just confusing myself
oblique nymph
how is b x a of a = 1 and b = p, p
oblique nymph
doesnt it say that on the table on the roght
yes i see that now
modest lichen
how is b x a of a = 1 and b = p, p
where is that
modest lichen
first table is +?
modest lichen
😭
oblique nymph
just completely missed that
cedar kilnBOT
Available help channel!
true hatch
Bruh my retarted ass couldn't solve this question bruh
cedar kilnBOT
Bruh my retarted ass couldn't solve this question bruh
true hatch
pls help
bright bridge
!status
cedar kilnBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
glass oasis
you can split a^2b^2+a^2c^2+b^2c^2
true hatch
hmmmmm
glass oasis
ur right
true hatch
ummmm
true hatch
breh
glass oasis
i didn't have paper until now
oh for this you just show that b^2>bc
and same for a^2 and b^s
glass oasis
oh wait AM and GM would help here
true hatch
yea so bruh then how do i show b^2>bc
glass oasis
wait I don't think that works too
true hatch
-___-
glass oasis
Arithmatic and geometric progression
i'm also solving this along with you
and you are getting my thoughts raw
true hatch
hmmmm ok but im also under a time crunch as it's due tomorrow 💀
glass oasis
Arithmatic and geometric progression
this, use the fact that A>G
true hatch
alright
glass oasis
hmmmm ok but im also under a time crunch as it's due tomorrow 💀
lmao I also have my homework to do, but taking a break
but it's due in a couple of hours
true hatch
RIP
glass oasis
nahhh i'm fine, it's just discrete mathematics
true hatch
for compsci ?
glass oasis
for maths degree
true hatch
oooh nice
glass oasis
how about you?
true hatch
still in high school 🥲
lime scaffold
then can i just equate a^4>= a^2b^2
No you cannot
glass oasis
it's a direct prrof
glass oasis
No you cannot
yh we been through this
true hatch
oooh i finally got it
glass oasis
oooh i finally got it
yup
my answer too
(there's only 1 answer)
as far as i'm aware
lime scaffold
oooh i finally got it
How do you know that a^2(b^2+c^2) => a^2(2bc)
lime scaffold
Good
glass oasis
nw
true hatch
.close
boreal epoch
what
@steady anchor I don't think i understood your question right can you rephrase it
wraith daggerBOT
TheWhiteShadow
boreal epoch
what about them
if you show u1 is independent from u2 and vice versa what will you achieve from it?
steady anchor
so $au_1+bu_2=\mathcal{P}_2$
wraith daggerBOT
TheWhiteShadow
boreal epoch
sorry im not familiar P2 represents 2D?
steady anchor
therefore $span({u_1, u_2})=\mathcal{P}_2$
steady anchor
sorry im not familiar P2 represents 2D?
all 2nd degree polynomial
wraith daggerBOT
TheWhiteShadow
steady anchor
right
and since {u1, u2} is a subset of S, S is also a spanning set
yea i think that works
boreal epoch
ah okay this makes sense now i was confused with p2
steady anchor
for part b do we need to include all the elemtns?
boreal epoch
originally i thought you had to prove each u is independent
boreal epoch
for part b do we need to include all the elemtns?
seems like it
steady anchor
**TheWhiteShadow**
also does this work
boreal epoch
but you can make a matrix system equation out of each scalar before variables
modern compass
therefore $span(\{u_1, u_2\})=\mathcal{P}_2$
you're probably going to need 3 elements.
steady anchor
you're probably going to need 3 elements.
wait why
modern compass
P2 has dimension 3
steady anchor
but each elements are in the same dimension no?
boreal epoch
P2 has dimension 3
yes you beed 3x3 matrix
steady anchor
is that not how it works
boreal epoch
and show that it is independent
boreal epoch
first write down the 3x4 matrix
modern compass
pretty sure P2 is "up to degree 2" polynomials. Otherwise it isn't a vector space.
boreal epoch
and from there you have 2 possible 3x3 matrices
steady anchor
okay yea mb up to
boreal epoch
and from there you have 2 possible 3x3 matrices
actually there are more
but yeah get each scalar factor in front of each variable to build the 3x4 matrix
to prove if the 3x3 matrix of your choice is independent or not you either reduce the matrix with basic operations or find the determinant≠0
wraith daggerBOT
TheWhiteShadow
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
boreal epoch
1 1 1
2 -1 -2
5 1 1
-1 2 4
@steady anchor this is what you got
now from this 3x4 matrix you can make many different 3x3 matrices, try 3 first rows and find it's determinant
if it's determinant is different from 0 it means you have a independent matrix
after that for question B you can use the new matrix 3x3
after that if let's say your basis is
1 1 1
2 -1 -2
5 1 1
you do Ax=B
1 1 1
2 -1 -2 * X = [5 -2 0]
5 1 1
steady anchor
right cheers
cedar kilnBOT
@steady anchor Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
fringe escarp
cedar kilnBOT
fringe escarp
So for b i got 2.5 bacteria but that seems way to low but i dont know where i went wrong
cedar kilnBOT
@fringe escarp Has your question been resolved?
hexed ocean
You want to be integrating y with respect to time instead of .5y w.r.t. y, this of because y is the quantity you want to average (number of bacteria) and you are averaging over a time interval (so you integrate w.r.t. time)
dense helm
is there another way to solve this other than using lhopital?
livid hound
manipulation considering conjugates and factorisation of difference of two cubes
dense helm
should i start with the conjugate of numerator or denominator ?
lime scaffold
is there another way to solve this other than using lhopital?
In num take x^2 common from root
livid hound
conjugates / duifference of two squares to rationalise the sqrt(x+1) - 3
factorisation for difference of two cubes to rationalise the cbrt(x) - 2
dense helm
conjugates / duifference of two squares to rationalise the `sqrt(x+1) - 3`
facto...
i don't quite get the 2nd step here TT what should i do after this?
livid hound
factorisation for difference of two cubes to rationalise the cbrt(x) - 2
considering the factorisation for a difference of two cubes,
(cbrt(x) - 2) * (what) = something rational
lime scaffold
i don't quite get the 2nd step here TT what should i do after this?
The denominator is more complex now
crimson sedge
i am a little confused over it
cedar kilnBOT
i am a little confused over it
crimson sedge
if uve to take a above it becomes inverse
if u take a from number one its correct
if u do it from 2, why its not?
royal loom
Don't think of A inverse as dividing by A in the sense of actually putting it below B
do you remember that matrix multiplication is not the same from the left as it is from the right
When we have $Ax=B$
wraith daggerBOT
AustinU
royal loom
If we multiply both sides by A^-1 from the right we get
crimson sedge
my tutor has been teaching it this way
royal loom
$AxA^{-1}=BA^{-1}$
wraith daggerBOT
AustinU
crimson sedge
x = b/a
royal loom
See how the A and A^-1 can't cancel
because they aren't connected
So we have to multiply by A^-1 From the left
crimson sedge
it is
wraith daggerBOT
AustinU
crimson sedge
did you get my question
royal loom
Please speak in full sentences and properly articulate your confusion
crimson sedge
we are learning from this scenario
royal loom
I'll try to give you an explanation okay? please read it
crimson sedge
ok
royal loom
I think your confusion is coming from the fact that you don't see why matrix multiplication is different from the left than it is from the right. You are probably used to the fact that in normal algebra, a * b is the same as b * a. But, for matrices this is not always true. Make up 2 random 2x2 matrices A and B, and multiply them together first with A on the left and then with A on the right, see that the results are different? This shows you that AB is not the same as BA and you can't just interchange the positions of matrices in multiplication.
royal loom
So the real real real key point is ** Order matters for matrix multiplication **
crimson sedge
thank you so v much
wraith daggerBOT
AustinU
cedar kilnBOT
royal loom
yeah no problem
royal loom
thanks once again
I like trying to help with linear algebra when I can, so if you have more questions in the future you can feel free to DM me whenever!
cedar kilnBOT
Available help channel!
crimson sedge
I like trying to help with linear algebra when I can, so if you have more questi...
yay!
royal loom
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cedar kilnBOT
cedar kilnBOT
✅
crimson sedge
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cedar kilnBOT
dull oxide
Reopened to close 
cedar kilnBOT
Available help channel!
crimson sedge
Can a line (Not Lime Segment) be Defined as an arc of a circle with its radius at infinity
crimson sedge
And in the same way, can a point be defined as a centre of a circle with its radius as infinity
cedar kilnBOT
@crimson sedge Has your question been resolved?
dusty pasture
Can a line (Not Lime Segment) be Defined as an arc of a circle with its radius ...
Well, lines are mostly undefined and only has their properties inherited from axioms, so.... Not really, since no axiom implies as such, is there?
crimson sedge
But the staement isnt false either is it?
dusty pasture
But the staement isnt false either is it?
it is since lines are not defined at all in the first place
we only defined what can make lines, and what lines can represent and where they can appear, but not what exactly they are
vagrant hamlet
how do i do this question, I dont understand
cedar kilnBOT
how do i do this question, I dont understand
gritty galleon
3rd?
livid hound
which question
vagrant hamlet
3
gritty galleon
!status
cedar kilnBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1 i think?
vagrant hamlet
ye
gritty galleon
well, from question, what does the length of wire represent?
vagrant hamlet
ye
vagrant hamlet
ye
wraith daggerBOT
ItzKraken2
gritty galleon
write it out on paper and send a photo (if u can)
wraith daggerBOT
ItzKraken2
gritty galleon
**ItzKraken2**
can u find smthing to take common in this expression?
gritty galleon
**ItzKraken2**
can u rewrite this expression after taking out common
livid hound
its more convenient and also intended that you work in radians
gritty galleon
missing a bracket, after 2r
gritty galleon
its more convenient and also intended that you work in radians
well..I'd multiply both sides by 180 upong pi ig?
gritty galleon
wait 1sec
vagrant hamlet
okay
gritty galleon
$$ 2r({{\frac{\theta\pi}{360}} + 1}) = 80 $$
livid hound
yeh, or you could do that from here,
or just start with more simpler pre-established formula for arclength using for an angle in radians
gritty galleon
yeh, or you could do that from here,
or just start with more simpler pre-establi...
right..me stupid 😢
wraith daggerBOT
ItzKraken2
gritty galleon
**ItzKraken2**
well from this, can u obtain an expression for theta?
vagrant hamlet
gritty galleon
yk i think ramanov was right
vagrant hamlet
a
gritty galleon
if we consider theta in rad
then the formula for perimeter
is
$$ \theta*r + 2r = 80 $$
wraith daggerBOT
ItzKraken2
vagrant hamlet
i
gritty galleon
OH
vagrant hamlet
wait
gritty galleon
I AM DUMB
vagrant hamlet
i forgot my
gritty galleon
got it
vagrant hamlet
radius
gritty galleon
yeah
vagrant hamlet
ye
gritty galleon
$$ \theta = \frac{80-2r}{r} $$
vagrant hamlet
gritty galleon
well gg
vagrant hamlet
wha
gritty galleon
u made a mistake
vagrant hamlet
whaaa
gritty galleon
r*theta = 80-2r
vagrant hamlet
oh
gritty galleon
theta = 80/r - 2
vagrant hamlet
oh yea
wraith daggerBOT
ItzKraken2
vagrant hamlet
yay
gritty galleon
how do i do this question, I dont understand
well coming to area
vagrant hamlet
ye
gritty galleon
how do i do this question, I dont understand
also i cant help with part ii, since afaik only a function has a stationary point
gritty galleon
derivative
yeah, but how do u do that with a variable? i think its asking to find the derivative of the area function
gritty galleon
yeah
gritty galleon
np
vagrant hamlet
no
not yet
HAHAHA
the stationery point is r=20
ye
its correct
thank you
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visual nebula
can someone please recommend a good book for number theory as it is my weak spot ,
and also recommend a question practice source
cedar kilnBOT
can someone please recommend a good book for number theory as it is my weak spot...
@visual nebula Has your question been resolved?
visual nebula
.close
dusk finch
For every a,b in G, a○b is in G.
Would this be correct way of writing the statement above?
$\forall{a,b \in \mathbb{G}}, a \circ b \in \mathbb{G}$
wraith daggerBOT
MathIsAlwaysRight
dusk finch
how would it be written with parenthesis?
dull oxide
$\forall(a,b \in \mathbb{G})(a \circ b \in \mathbb{G})$
wraith daggerBOT
SWR
boreal falcon
cedar kilnBOT
bright bridge
hm
steel heart
!15m
cedar kilnBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
boreal falcon
!15m
Oh wait sry
I’m 3 min off
I thought it was 10 min
Can someone help tho pls
Anyone ?
Bruh
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quiet wind
Can you guys check if i did this correctly??
cedar kilnBOT
quiet wind
livid hound
You deleted your original post. The channel will abruptly close and possibly lock. (This is irreversible).
Please claim a new channel.
cedar kilnBOT
Available help channel!
crimson sedge
Given f(x) = x^3 - 3x. How many squares can be found if their points are located on the graph of f(x)?
crimson sedge
Seriously I need help because I have no idea what to do at first 💀
old pine
Is the domain R?
crimson sedge
They announced that the answer was 2
crimson sedge
Well, what function contain all the squares?
x^3 - 3x (I mean like it contains the points that make up the squares)
tropic oxide
uh wait what
crimson sedge
And I have to find the number of squares can be found
old pine
No, I was asking you that to understand what you have to do
what function have as values squares?
gritty viper
(geometric) squares with all points being on the curve
crimson sedge
Yeah that's right
tropic oxide
this looks pretty nontrivial to solve actually
or at least there's a lot of moving parts to it...
crimson sedge
this looks pretty nontrivial to solve actually
It's from a mock test in my province
old pine
what function have as values squares?
?
gritty viper
?
I have no idea what you're asking either
it really doesn't seem like there'd be any squares
old pine
I'm asking which function give you a square when you input a value x into it?
gritty viper
x^2
old pine
yes
tropic oxide
@old pine you have completely misunderstood the problem.
old pine
Isn't the problems asking for all the squares that are contained in the function x^3 - 3x?
crimson sedge
it really doesn't seem like there'd be any squares
But the announced answer was 2 and I have no idea tho, I also tried graphing by hand and only found 1 (didn't even know how to prove that was a square)
tropic oxide
there might be a square arranged roughly like this (finger drawing on a bus, so it's shaky)
crimson sedge
there might be a square arranged roughly like this (finger drawing on a bus, so ...
Yes I drew it like that
old pine
Ohhhh
crimson sedge
But there is another square idk what to do
crimson sedge
Hmm
tropic oxide
dunno
gritty viper
coordinates are (a,b) (b,-a) (-a,-b) (-b,a)
so we could try plugging those all in to y=x^3-3x and solving
tropic oxide
oh. for a square centered at the origin i guess that is so
crimson sedge
so we could try plugging those all in to y=x^3-3x and solving
😂 But that'd be too complicated
For me ig
gritty viper
,w b=(3b-b^3)^3-3(3b-b^3)
wraith daggerBOT
crimson sedge
hmm
crimson sedge
Can you tell me why this equation would be used tho @gritty viper
cedar kilnBOT
@crimson sedge Has your question been resolved?
junior timber
question 18
cedar kilnBOT
question 18
junior timber
how do I get the area without the height
hushed spoke
well you could in fact find out the height of the trapezium
and then go the common route
junior timber
trapezium?
runic garnet
trapezoid
junior timber
oh
runic garnet
Same
junior timber
but i dont know how to find the height
runic garnet
Hm idk if this is the easiest method, but try drawing lines down from the top base to the bottom base (perpendicular)
junior timber
yea thats what i did
runic garnet
Then u can use Pythagoras
runic garnet
Show me what u labeled the sides
junior timber
but its on both sides
junior timber
runic garnet
Good
runic garnet
Label ur unknown sides x and y, and height = h
Do this
junior timber
is x and y 4 and 9?
junior timber
ohh ok
runic garnet
So what’s x + y =
junior timber
5
runic garnet
Just do each individual triangle
runic garnet
Lol if u know just do it, don’t overcomplicate it, just do Pythagoras on one triangle and tell me what u get
Don’t let the variables confuse u
U don’t need to solve for anything
Just do the Pythagoras
junior timber
but what number do i use for the base
runic garnet
Use x as the base for the first triangle and y as the base for the second triangle
just apply a^2 + b^2 = c^2 to it
U don’t need to use a number
runic garnet
It’s fine lol, don’t solve for anything
Don’t find any value
Just do the Pythagoras
Just set it in the form a^2 + b^2 = c^2
runic garnet
i need two numbers to find the last one
Don’t
runic garnet
Yes exactly
Lol
Do that to the other
We are trying to get a system of equations for which we can solve for x and y
junior timber
yea
runic garnet
Now with the first 2 equations, get one equation with both x and y in it
x^2 + h^2 = 16
y^2 + h^2 = 25
Make one equation with both a “x^2” and “y^2”
runic garnet
?
runic garnet
That’s not an equation
Notice how both equations both have a “b”
Solve for “b” then see if u can go from there
junior timber
b = c - a
b = e - d
runic garnet
Now what can u do
To get a and d in the same equation
I’m trying to get u to understand the process
That’s the reason I’m using another example right now
runic garnet
y^2 + h^2 = 25
Now do that for these
junior timber
wdym by that
runic garnet
h^2 = 16 - x^2
h^2 = 25 - y^2
Set them equal to each
Equation 1 = equation 2 because both are equal to h^2
Have u ever done systems of linear equations before? This should be a relatively straightforward concept if you are doing geometric problems of this caliber
junior timber
ohh