Look up how to draw these hypercube projections on paper - the pattern is pretty easy to pick up, actually
#help-0
warped frost
knotty sleet
There'd be 8 '3d faces'
frigid moon
I see. The author (Gilbert Strang) didn't even mention these definitions so im having trouble. I still don't understand what a 3d face is, every face appears to 2 dimensional to me.
knotty sleet
They just mean the cubes that border the hypersphere
heady solar
hey ok so i have this problem i need to confirm my solution can anyone help me?
warped frost
They just mean the cubes that border the hypersphere
This is a very good way of conceptualizing it
knotty sleet
😄
Cause imagine you had a line segment, that'd be a 1d cube, then you have 0d points which border it
For a 2d cube (which is a square), you have 1d cubes (line segments) which border it
And so on
warped frost
Yeah, exactly
frigid moon
I see.
warped frost
Probably a good way to explain it to laypeople too
frigid moon
Well it is a poor question in my opinion especially given the fact the he did not define any of this in the chapter.
warped frost
Yeah, if Strang didn't give you any prior intuition to work on, that might not be an ideal question
knotty sleet
I remember once my teacher asked us what's the minimum number of matchsticks to create four equilateral triangles
warped frost
But I also think he was writing his textbooks for a certain student body - I think his original one was meant to be used for his course at MIT
knotty sleet
And everyone was like, 9 ofc but then he was like, aha! but you didn't consider a tetrahedron!
Idk I just found that quite cool
frigid moon
Yes you are right @warped frost perhaps ill only consider doing questions that have relevance to me
knotty sleet
You can also think about how other platonic solids generalise to higher dimensions
frigid moon
My question is, what books do I learn 4d from then?
warped frost
My question is, what books do I learn 4d from then?
So, that's a pretty broad question - it depends on your background
I know I picked up on these things when I tackled material focusing on simplicial complexes after a course in Topology
but there's also much friendlier ways to approach it
frigid moon
hmm I see. I guess I'll just have to google as I go along with the intention of only solving the problem at hand
alpine sable
In the year 2016, the total number of metric tons of copper produced in the world was 495,000.
Each year since, the total number of metric tons of copper produced has increased on average by about 3.25% over the amount produced the previous year.
Which function models the total number of metric tons of copper produced in the year that is x years since 2016?
c(x)=2010(3.25)^x
c(x)=495,000(1.0325)^x
c(x)=495,000(0.9675)^x
c(x)=495,000(1.325)^x
reef sinew
2nd one
4th is for 32.5%
3rd is for a decrease in copper
1st is just straight up nonsense
heady solar
<@&286206848099549185>
sleek gyro
@heady solar check your work, are you considering the action of G on the set or the action of U
hint: ||orbit-stabilizer||
heady solar
is that the inverted axis of the action of my cock on your ass?
queen nova
is that the inverted axis of the action of my cock on your ass?
what
heady solar
ok so you caught me cheating
he's my math teacher
he caught me cheating
cause you didn't answer my question in time
and now i'm gonna fail math
and i'll never be a dj
and i'll have to go back to the rice fields
F in chat bois
ripe jasper
knotty sleet
Use the rational root theorem
ripe jasper
what is it?
lilac lantern
do you want an explanation?
viscid cove
yes
open elbow
I don't understand
If a_n = n! / (2n)! then a_n+1 = (n+1)! / (2n+1)! no ?
so (a_n+1)/a_n = (n+1)/(2n+1)
knotty sleet
You need to replace n with n+1
open elbow
it's not what I do ?
viscid cove
i hope you understand now
thanks, i understand
lilac lantern
thanks, i understand
no problem :)
knotty sleet
A_n+1 is (n+1)!/(2n+2)!
open elbow
yes
but you don't understand
What I show you is not a_n+1
is a_n+1 / a_n
someone can help me pleas ?
ripe jasper
@open elbow What is the question?
open elbow
I have [(n+1)!/(2n+2)!] / [n! / (2n)!]
I want this :
But I found that :
(n+1) / [ (2n+2)n!]
knotty sleet
but you don't understand
Yes I know, you didn't cancel it out correctly
😅 Just check your working
ocean sealBOT
Happiness
little sky
<@&286206848099549185>
open elbow
$\frac{(n+1)!}{(2n+2)!} * \frac{(2n)!}{n!} = \frac{(n+1)!}{(2n+2)(2n+1)(2n)!} * \frac{(2n)!}{n!}$
ocean sealBOT
le J
ocean sealBOT
Happiness
knotty sleet
<@!321696814787067905> check <#496785905474994186>
What's happening?
knotty sleet
Wait what's [10]
ripe jasper
mod 10
knotty sleet
Ah
...there's always the plug in and bash
If you just try 1, 3, -3, -1
Cause you've shown they're coprime so X has to be one of those four
Or maybe multiply by x
Then x^2+2x-x=x(x+1)=0[10]
And so x+1=0[10] as required
@ripe jasper
ripe jasper
Then x^2+2x-x=x(x+1)=0[10]
how
knotty sleet
If you multiply by x on both sides
ripe jasper
sides of?
ripe jasper
how did u get that?
knotty sleet
https://cdn.discordapp.com/attachments/496785905474994186/845802889889054730/436...
Of this equation
ripe jasper
If you multiply by x you get this $2x^5+x^2-x = 0 [10]$
ocean sealBOT
Happiness
knotty sleet
how did u get that?
It's a well known fact which essentially says and number to the power of 5 has the same units digit as itself
You can show it with case bash or fermats little theorem
knotty sleet
Yh it's quite useful
knotty sleet
Also for e.g. if you need to determine remainders of very high powers
Um I'm not sure, I would write it out quickly but I'm actually about to go to bed
knotty sleet
It's a well known fact which essentially says and number to the power of 5 has t...
You can probably find it online by searching this
knotty sleet
Oh thanks Mosh
glass lichen
First one is the string proof
knotty sleet
Anyway yh after that you can factorise LHS and since X=/=0[10] then you know it had to be -1
Cause it's a quadratic
ripe jasper
@glass lichen I don't see the proof?
knotty sleet
But anyway I would probably just plug in the four values
glass lichen
read the article
knotty sleet
It's quicker than trying to be clever
ripe jasper
which segment?
glass lichen
any, but the article suggests that the string proof requires least math knowledge
under combinatorial proofs
knotty sleet
Hope I was being reasonably clear..😅
ripe jasper
Hope I was being reasonably clear..😅
ty
floral jungle
i know what g'(x) is but for part d, how does g'(2x) = -1?
shouldn't it be undefined since you are dividing by 0 if you plug in 0 for x
glass lichen
g'(0)=-1
vast cobalt
g'(0)=-1
floral jungle
oh is it because for every other value of n, it's 0?
glass lichen
they plugged in x=0
floral jungle
yeah
glass lichen
and in a polynomial, all the terms are non-negative integer powers of x
so the only thing that remains at x=0 is the constant
floral jungle
oh i think i get it
leaden sail
How do you get 2 <= n <= 43 from 2^n < n^8 ?
Do I have to check the numbers one by one?
ripe jasper
fallow meadow
Do I have to check the numbers one by one?
after some initial n's, 8lg(n)-n is a monotonically decreasing function so you can do a binary search instead
leaden sail
So you still have to do it semi manually?
Isn’t there an easier way?
alpine sable
what am i doing wrong here
im fairly sure E and F are correct
ive tried swapping b and c and still doesnt work
magic lichen
try rewriting each equation in the standard form for a sphere, then figure out what the X, Y, and Z translations and scales are, then it should be easier to match to the pictures
alpine sable
yeah i did that
i cant even make out properly the green and blue sphere
what are the coords of the center
magic lichen
Looks difficult to discern. Might need to use process of elimination instead
Could be the perspective but the blue appears to be at z = -1.
alpine sable
hmm im not sure how thats possible
rocky dock
,w (2x + 1)^2 + 4 = 0
ocean sealBOT
alpine sable
got it thx
alpine sable
can i get some help pls 
i understand that im trying to find WX but i cant do it while managing to fullfill UV/UZ=WX/WY
wary stream
i understand that im trying to find WX but i cant do it while managing to fullfi...
What is UZ compromised of?
And WY?
alpine sable
ummm
no so basiaclly this is what i understood right
im supposed to find WX right
and then
somehow
its supoposed to equal to 2/5 = WX/WY
so like
xy is 7
so WY would equal 7+x
and wx is just the X
wary stream
So you should end up with something like $\frac{2}{5} = \frac{x}{x+7}$
ocean sealBOT
dldh06
alpine sable
hmm
hidden horizon
**dldh06**
this is correct
wary stream
Cross multiply, get x on one side constants on the other
wary stream
why cross multiply
How would you get rid of the denominators?
You must be new, don't tell the answers. Let the person solve it themselves
hidden horizon
You must be new, don't tell the answers. Let the person solve it themselves
ohh
sorry
wary stream
And if they have trouble you check their work
hidden horizon
sorry i wont do it again sorry
wary stream
Because the purpose is a learning process. If you the answer straight away, most people will trust your answer and just copy it down @hidden horizon
hidden horizon
@wary stream my apologies
alpine sable
OHH
it makes sence
i get what u meant
since its division
we wanna get rid of it
so we multiply
hidden horizon
yeahh
wary stream
You tagged the wrong person but you're new, it's understandable
wary stream
so we multiply
Exactly
alpine sable
okok
so i got
well no wait
how would ik which to put after the = or does it not matter
wary stream
Getting rid of the denominators is the same as cross multiplying with like 1 to 2 less steps
wary stream
how would ik which to put after the = or does it not matter
Doesn't matter, as long as x is on one side, and constants on the other
hidden horizon
how would ik which to put after the = or does it not matter
order dosent matter coz it will be an equation anyway
wary stream
When you cross multiply x will be on both sides, but then get x on one side and constants on the other
alpine sable
Doesn't matter, as long as x is on one side, and constants on the other
.
one side messed me up lmaoo
2x+14=5x
alpine sable
isolate x basically?
hidden horizon
yeah
alpine sable
14=3x?
wary stream
Yes
hidden horizon
yes
wary stream
Now find x
alpine sable
x=4.7
hidden horizon
cool u got it !
wary stream
Exactly
alpine sable
but thing is lmaoo
i was getting that aswell but when i try to put it in with the umm
OH WAIT
SO
OOOOOO
okok brain clicked
thank you humans smmm
hidden horizon
cool bruh tc
crude furnace
spare sage
@crude furnace are u here
alpine sable
https://cdn.discordapp.com/attachments/830987746897559582/845773318324879380/Capture.PNG
where tf did he get the -5 from
also if you can please explain the whole thing i been stuck on this for days
spare sage
hm
ok so w is the distance the dude walked and b is the distance he traveled by bus
(in kilometers)
he traveled w kilometers at 5 kilometers per hour
so how long would it take?
to travel the walking distance
wary stream
https://cdn.discordapp.com/attachments/830987746897559582/845773318324879380/Cap...
Not sure why he chose to multiply by -5 but you can do 5 too, you get the same answer
spare sage
yeah
-5 seems unnecessary
it basically just comes down to getting the equations w/5+b/60 = 1.5 and w+b = 35
then you can solve however you like
wary stream
Canceling the denominators
spare sage
do u understand the equation w/5+b/60 = 1.5
wary stream
Simplying
spare sage
like how it came about
wary stream
Isolating w
alpine sable
not really
wary stream
All the same thing
spare sage
alright
so the dude walks from his home to the bus stop
the distance is w km and his speed is 5 km/h
how many hours would it take for that portion of the journey?
alpine sable
how would i know 
crude furnace
<@!626941839378874389> are u here
yes
spare sage
distance is speed*time right
alpine sable
yes
alpine sable
distance is speed*time right
wait is that a science formula or math
i seen it in science i think
spare sage
well its applicable to both
wary stream
how would i know <:CatCry:763793655412031538>
We're creating a system of equations using the given info
spare sage
so if youre moving at 5 km/h and youve moved w kilometers, then the time taken is w/5 hours
because rearranging distance=speed*time gives time=distance/speed = w/5
alpine sable
mhm
spare sage
(be careful with units)
so it took w/5 hours to travel the walking distance
now we apply the exact same logic to the bus part
he traveled b kilometers at 60 km/h
how long would it take?
alpine sable
total?
spare sage
no just for the bus part
alpine sable
yes
spare sage
so whats the distance for the bus part
alpine sable
60km..?
alpine sable
oh
spare sage
so if the distance is b km and the speed is 60 km/h then by time = distance/speed the time taken for the bus part is b/60 hours
so if the time taken for the walking section is w/5 hr and the time taken for the bus section is b/60 hr then whats the total time
alpine sable
1.5 hours
spare sage
yes but in terms of the variables
if it takes w/5 hr for the walking section and b/60 hr for the bus section then the total time is simply the sum of these times
which is w/5+b/60
alpine sable
2 hours
spare sage
so this is where the equation comes from
we also have another equation, w+b = 35
do you see where that comes from?
alpine sable
yes
spare sage
ok
alpine sable
the walk distance and the bus distance
spare sage
so we're basically solving the system of two equations
do u know how to do that in general
with systems of equations
alpine sable
not well
spare sage
alright
there are several ways
i think substitution works best here
so all the ways basically do the same thing, they first get rid of one variable and solve an equation involving the other variable
then u plug in the value for the variable u just solved into one of the original equations and solve for the second variable
heres an example
what we want to do is isolate a variable
meaning rewrite one of the equations so one side of the equation has only one variable and nothing else
alpine sable
yea
alpine sable
where do you get the 5 from tho
spare sage
now u get w+b/12 = 7.5
im simply multiplying both sides of the equation by the same number, which keeps both sides still the same
alpine sable
hm okay
spare sage
i chose 5 because i want to get rid of the denominator of w
spare sage
yeah
alpine sable
spare sage
so after we get w+b/12 = 7.5 we can rewrite this as w= 7.5 - b/12
alpine sable
mhm
spare sage
but now we remember the other equation
w+b=35
instead of w in the second equation we can plug in 7.5 - b/12
since the 1st equation has proven that w and 7.5 - b/12 have the same value
spare sage
youll get used to it eventually lol
yeah exactly
youve got it
now all we have to do is isolate b
alpine sable
then solve for b
spare sage
precisely
so we have 7.5 + 11/12 b = 35
or 11/12 b = 27.5
now if we solve for b by multiplying both sides by 12/11 we get b = 30
spare sage
now the final step
alpine sable
now to solve for w
spare sage
we go to the equation w + b = 35
since we already know b is 30, we just plug that in and get w + 30 = 35
and thus we find w = 5
and thats it
alpine sable
thanks a lot
spare sage
np
@crude furnace sorry i gtg now
i will come back eventually
or maybe u can ask someone else in the mean time
winter flare
heyy
Find an polar equation for the curve represented by the cartesian equation
<@&286206848099549185>
indigo jetty
do you know how to transform x and y into polar form?
lone heartBOT
winter flare
rsin theta = 2
woeful pulsar
please wait 15 minutes before helpers ping
winter flare
Sorry
woeful pulsar
it should be quite similar, the only difference is making r the subject probably
winter flare
indigo jetty
yeah, that's making r the subject
so maybe for your case, make r the subject for all the questions
or r^2
winter flare
can you explain me how she made that?
indigo jetty
👍
gray isle
consider a different route where you factor 2 out of the numerator and consider the sum of two cubes
gray isle
there is a special factorisation for the sum of two cubes
if you don't know it, consider looking it up
viscid cove
<@&286206848099549185> I need help with this
viscid cove
I think 15?
jaunty jasper
When the numbers add up to at least seven
jaunty jasper
How did u get that number
viscid cove
I counted the different numbers that reach a sum of 7 or greater
wheat sedge
Can someone help me with this question
"Prove that that the sum of all angles at the vertices of a n point star is (n-4)x180 degrees"
viscid cove
did I count incorrectly?
viscid cove
okay
wheat sedge
<@&286206848099549185>
"Prove that that the sum of all angles at the vertices of a n point star is (n-4)x180 degrees"
I tried to think of the possible ways to solve and ended up in none.
Can someone help me with this?
hidden horizon
<@&286206848099549185>
"Prove that that the sum of all angles at the vertices o...
it can be done by angle chasing
wheat sedge
Can u please explain?
lone heartBOT
woeful pulsar
<@&286206848099549185>
"Prove that that the sum of all angles at the vertices o...
maybe try drawing a diagram? though there might be a problem in the sense there are many ways to draw a n point star
hidden horizon
maybe try drawing a diagram? though there might be a problem in the sense there ...
or else , he can draw a circle around the star
hidden horizon
as angle subtended at centre is double than that of any point of circle , arcs will measure from 2a , 2b , 2c...2n
so 2(a+b+c+.....n) = 360
u can proceed further by this idea
cheers
wheat sedge
Thanks dude
hidden horizon
np
pliant rapids
Can anyone help me on a)(iii) and b) questions?
hidden horizon
Can anyone help me on a)(iii) and b) questions?
for a(iii) , check whether ABC is right triangle (it most prolly will be)
orthocenter of right triangle is midpoint of hypotenuse
normal lance
Find the slope by y2-y1 / x2-x1
woeful pulsar
Find the slope by y2-y1 / x2-x1
brackets
normal lance
And C as a mid points
normal lance
brackets
What brackets it direct to solve
You can find m and coordinate of C and then
Medians
woeful pulsar
What brackets it direct to solve
remember to include brackets to group your math properly
woeful pulsar
Can anyone help me on a)(iii) and b) questions?
also write your $x_1$ with subscript to make sure it's not ambiguous
ocean sealBOT
Elερραnt118
normal lance
Meadian are cut on the mid-point of the corresponding line segment
All mid point coordinates
pliant rapids
ok thank you very much
celest hollow
Hey guys i have some qns on summation n sequences n series
Is this correct?
Is this also correct
woeful pulsar
yeah 2n is a constant that can be taken out
woeful pulsar
Is this also correct
looks reasonable
celest hollow
okay thanks!!
pliant rapids
for a(iii) , check whether ABC is right triangle (it most prolly will be)
it isn't a right triangle
stoic lance
woeful pulsar
basically find the lattice points P on x=6 and x=-6 such that the [distance between (3, 4) and P] <= 4
gritty drift
??? please i need the answer
strong furnace
As long as they are allowed on discord
jagged imp
woeful pulsar
erm... might want to stop using discord until you turn 13
silver bay
^^
woeful pulsar
since bots can potentially record your messages here
silver bay
yeah thats against TOS
woeful pulsar
yeah we'll have to remove you from here, come back next year
gritty drift
lol
woeful pulsar
<@&268886789983436800>
woeful pulsar
might want to pick a less active channel
fading zephyr
we do it
woeful pulsar
btw this is probably the most interrupted channel, if you have a long question pick a less active channel
silver bay
yeahh will do
harsh acorn
asks for the area of the colored shapes one by one
I get 54, 120 and 90
I just want to check
oak chasm
@harsh acorn Looks good.
@alpine sable What's the formula for volume of a rectangular prism?
late tundra
l×b×h
sly mantle
👢
fading zephyr
oak chasm
@alpine sable As adithyan said, it's length times width times height.
So, multiply those together.
What do you get?
ionic jewel
dont even help him he spammed all the channels
silver bay
i think someone else is getting helped in questions-1 so im gonna put this here:
the L is the laplace transform btw
spare fern
Just use the definition of laplace transform
silver bay
i know, im kinda having trouble with the integration tho tbh :/
here lemme write out the definition just to make sure i have it right
$$\int_{0}^{1} t^{2}e^{-st}dt + \int_{1}^{2} (t-1) e^{-st}dt + \int_{2}^{\infty} 1e^{-st}dt$$
ocean sealBOT
oreo
silver bay
does that look right?
spare fern
Looks correct
silver bay
okay thanks
so
i would try integrating by parts for the left hand thing right
is there like a faster way to do this
spare fern
No
silver bay
because it takes me like 5 minutes each and i have way too many of them 
rip
$$\int_{0}^{1} t^{2}e^{-st}dt = - \frac{t^{2} e^{-st}}{s} - \int_{0}^{1} -\frac{2t e^{-st}}{s}dt$$
does that look right?
im not sure what to do with the right hand side now though
spare fern
Yeah, it is
ocean sealBOT
oreo
silver bay
it should be that right
silver bay
thanks
so ill try expanding it further
and yeah idk how to do the bar to show evaluating at the limit
like the vertical bar
so i kinda just left it out
$$\int_{0}^{1} t^{2}e^{-st}dt = - \frac{t^{2} e^{-st}}{s} - \left\frac{2te^{-st}}{s^2} - \int_{0}^{1} \frac{2 e^{-st}}{s^2}dt\right$$
ocean sealBOT
oreo
silver bay
does that look right?
silver bay
im confused, when did i do that?
silver bay
$$\int_{0}^{1} t^{2}e^{-st}dt = - \frac{t^{2} e^{-st}}{s} - \left(\frac{2te^{-st}}{s^2} - \int_{0}^{1} \frac{2 e^{-st}}{s^2}dt\right)$$
ocean sealBOT
oreo
silver bay
i had parentheses there
integrating the e^-st gets rid of the negative right
so then this should be right?
spare fern
Yeah looks correct
(I just did it in my head though)
pliant rapids
for a(iii) , check whether ABC is right triangle (it most prolly will be)
but is this angle 90 degree?
silver bay
Yeah looks correct
(I just did it in my head though)
oh lol
it was the same thing i sent earlier
but you told me to check my signs
so i guess its right?
god this is gonna take forever i have 30 of these
spare fern
Just compute the integral then we can verify the result
spare fern
god this is gonna take forever i have 30 of these
You don't have to do the computation everytime
Just use the results from previous questions
hybrid patio
Does anyone know how to solve this?
glossy tendon
Does anyone know how to solve this?
do you know how to get the circumference of a circle?
alpine sable
when you're doing combinatorics in a circle, and say 3 people had to sit next to each other at all times out of 6 people, would it be 4!/4
vale wigeon
@alpine sable channel occupied please move
hybrid patio
3/4 of 2 pi r?
hidden horizon
Does anyone know how to solve this?
it will be 3pi.r/2 + 20mm
glossy tendon
Assuming that that forms a 90 degree angle
hybrid patio
it will be 3pi.r/2 + 20mm
yeah i got that, but i dont know why I have to add the extra 20 mm
glossy tendon
for those two straight line
hidden horizon
i.e 30pi+20 mm put value of pi and there u go
hidden horizon
yeah i got that, but i dont know why I have to add the extra 20 mm
coz u hv to find perimeter
perimeter means length of boundary
silver bay
Just compute the integral then we can verify the result
i ended up getting $$\frac{(-e^{-s} (s^2+2s+2) + 2)}{(s^3)}$$ for the whole thing
ocean sealBOT
oreo
spare fern
,w integral of t²e^{-st} wrt t from 0 to 1
hybrid patio
coz u hv to find perimeter
oh ok ty
oak chasm
,w integral of t^2 e^(-st) dt from 0 to 1
ocean sealBOT
Requested by Chai T. Rex#7323
spare fern
,w integral of x²e^{-xt} from 0 to 1
silver bay
,w integral t^2 e^(-st)dt from 0 to 1
oak chasm
Strangely, it has the answer if you click the refine query online link: https://www.wolframalpha.com/input/?i=integral+of+t^2+e^(-st)+dt+from+0+to+1.
ocean sealBOT
Requested by oreo#0999
alpine sable
yeah sometimes it happens
spare fern
Yeah
alpine sable
i have seen that happening before
silver bay
ok so i guess i was right
yay
1/3 of one of 30 questions done
im gonna be up all night
oak chasm
Reported the bug.
spare fern
Chai (Tea) doing god's work
silver bay
fr
hybrid patio
Anyone know how to solve this problem?
vale wigeon
what's troubling you here?
deep field
i found the perimeter, but I dont know how to solve for the area
Do u know the formula for area of a circle and a triangle?
hybrid patio
yep for area its is pi r sqaured divided by 2 because it is a semi-circle, and for triangle it is 1/2 x b x h
vale wigeon
yeah and you have 8 semicircles and 8 triangles here
all the triangles are the same, and all the semicircles are the same
if you can find the area of one of the semicircles, and the area of one of the triangles, then finding the area of the whole shape is easy
vale wigeon
the additive principle for areas is more useful than you might think
deep field
Yes
indigo minnow
the arcs AB and CD add up to 120 deg. length of segment AB is 5 and the length of segment CD is 3.Find the radius of the circle.
ocean sealBOT
Chai T. Rex
indigo minnow
then?
deep field
Then u have 3 unknowns and 3 equations. You should be able to solve that
indigo minnow
Then u have 3 unknowns and 3 equations. You should be able to solve that
how would I solve it if I dont know measure of arcs here
hybrid patio
Hi, for the previous question this was the answer, though i got 285.84, im not sure what is right
hybrid patio
Anyone know how to solve this problem?
this was the previous question
hello?
anyone?
glossy tendon
anyone?
I think what you did is 3^2 pi / 2 to get the area of semicircle which is 14.137... and you rounded it down to 14.13 and multiply it by 8 which is 113.04
glossy tendon
Hi, for the previous question this was the answer, though i got 285.84, im not s...
what they did here is. Since 8 semicircles is 4 circles, they computed the area of one circle and multiply it with 4
What differs from your solution to their solution is the rounding issue
But for me the more correct one is 285.9
desert kernel
I have no idea how to get rid of the 2
ocean sealBOT
Chai T. Rex
desert kernel
Here’s what I got at the moment
oak chasm
@desert kernel First, notice that the powers of three are very similar.
desert kernel
Alright
ocean sealBOT
Chai T. Rex
desert kernel
Ok
oak chasm
What do you get?
oak chasm
No.
desert kernel
Oh
oak chasm
The left side has the wrong power.
Note that the power you're dividing by is less than the original power of the left side.
So, you should have a positive power on the left side after division.
desert kernel
Ok
oak chasm
Second, 27 should be divided when you divide the entire right side.
oak chasm
Closer. What's 27 as a power of 3?
desert kernel
3?
oak chasm
3^3
desert kernel
Yea
ocean sealBOT
Chai T. Rex
desert kernel
Is it the same thing
desert kernel
4-5x?
oak chasm
Right.
ocean sealBOT
Chai T. Rex
hybrid patio
But for me the more correct one is 285.9
oh ok ty, now i understand
pine lake
U guys done?
alpine sable
A hand of 5 cards is dealt from a standard deck.
What is the probability that it contains 4 queens
oak chasm
@desert kernel No problem.
@alpine sable OK, so how many ways are there to get 4 queens in a hand of 5?
alpine sable
<@456226577798135808> OK, so how many ways are there to get 4 queens in a hand o...
4!?
4!
oak chasm
Nope.
alpine sable
5!?
oak chasm
You know what 9C8 means?
oak chasm
Right.
So, 4C4 is the number of ways to choose 4 queens out of 4 queens.
And 48C1 is the number of ways to choose 1 card out of the 48 nonqueen cards.
Does that make sense?
alpine sable
well, that would be assuming that the order of the queens doesn't matter
right?
theres the diamond, hearts, spades and clubs
oak chasm
Right.
So, the number of ways to get 4 queens and 1 other card is 4C4 times 48C1.
What's the number of ways to pick 5 random cards?
alpine sable
52P5
so it would be
4C4 * 48/ 52P5
assuming that order of queens doesn;t matter
otherwise it would be 4! x 48/52P5?
oak chasm
Nope.
alpine sable
what d you mean
oak chasm
52P5 means order of the 5 cards matters.
52C5 means it doesn't.
On top, you have order of the cards not mattering because we used C.
On bottom, you should also have order of the cards not mattering.
oak chasm
OK?
oak chasm
No.
oak chasm
Right.
alpine sable
i don't understand
why doesn't 4! x 48 /52P5 work
there are 4 options for the first spot, 3 for the second, 2 for the third and four for the fourth if we want a queen
times that by the remaining cards, and we have 4! x 48
divided by the total number of ways you could pick 5 cards out of 52 cards
@oak chasm
sacred palm
is graph theory offtopic on this server ? I really need help but dont know where to find any
oak chasm
@alpine sable That also works.
oak chasm
You just need to have order mattering or not the same way on the top and bottom.
You can't mix them.
alpine sable
yeah
oak chasm
No problem.
ocean sealBOT
Chai T. Rex
oak chasm
Either one.
alpine sable
that doesn't provide the same value though
oh nevermind
they are assuming different things
yep.
gotcha
thanks!
ocean sealBOT
Chai T. Rex
oak chasm
There. That's how to do it with P.
You need to multiply by 5 to choose a place for the nonqueen card.
sacred palm
My question is about graph theory
So i'm trying to make a Path Finding Algorithm that return the shortest path possible between 2 points (in time or in distance)
But it also need to take in account a battery that is used to travel a distance
There is also Charging Stops that allows you to fill up your battery but takes 10 extra minutes
It looks a lot like a Dijkstra's algorithm but i can't figure out how to keep track on the Charging Stops
Like for example here a dijkstra algorithm would return the path on the top but it wouldn't be feasible and we would lose track of the one with the charging stop bellow
I also found a document on internet giving a pseudo code for this exact problem but it is very heavy and I don't understand how it works exactly
alpine sable
hmm
slim coyote
how do i find the angles of an irregular quadrilateral with no given angles (all sides are given)?
oak chasm
@slim coyote You know how you can take a square and push the top to the right to get a parallelogram?
slim coyote
yeah
oak chasm
So, that's a quadrilateral where the sides don't determine the angles.
oak chasm
If you fix one of the angles, though, you can get the other three.
iron hollow
Hi guys, can anyone help me with this please, we have two different answer I don't know which one is the right one
Basically the question is this:
An ant is starting from the point R going in the direction of the arrow.
At each intersection it have an equal chance to go in any of the three directions.
What are the chances for it to land on point E at the 4th intersection
I found that it can go in any direction on first intersection so
3/3 then I found in can go in two of the path so 2/3 and then only towards point E so 1/3
Which gives me 3/3 * 2/3 * 1/3
≈ 0.222
oak chasm
So, the first intersection is always C?
iron hollow
Yep
oak chasm
Yes, I think you're right.
3/3 will get you one closer.
From any point, 2 of the paths will get you one closer.
Then From any point, only 1 of the paths will get you to E.
iron hollow
Alright thanks 
main gate
I have this question: ```
A linear sequence has first term 7+12√5
The term-to-term rule is: add 9–2√5
One term of the sequence is an integer.
Work out the value of this integer.
``` I think I need the formula n = a+(n-1)d, where n is the nth term, a is the first term, d is the distance between terms.
So I have n = 7+12√5 + (n-1)(9–2√5) but I don't know what to do from here.
Could anyone help?
gray isle
whether your term is an integer depends on whether it has a "sqrt(5)" term
consider how many times 2sqrt(5) goes into 12sqrt(5)
alpine sable
Hi guys
I have a 3d vector (3,2,5) + m(10, 5, 0), which is the path of plane 1
and I have another point (0,0,1)
plane 2 flies from (0,0,1) and has speed of 18, so in which direction should I fly to intersect with plane 1?
I don't get this, aren't there multiple directions plane 2 can go in in order to intersect with plane 1 since plane 2's speed is higher?
alpine sable
<@&286206848099549185>
@alpine sable is the question you typed complete? There is no information about the speed/position of plane 1
well speed is just sqrt(10^2+5^2) and startpos of plane 1 is (3,2,5)
Wait isnt that the equation of a line you gave
which equation
The vector
yeah its a 3d line
Yeah so it is not necessary that the plane starts at (3,2,5)
It can start at any point on the line
And I m not sure about how you found out the speed too
wdym plane
at m = 0, the line starts at (3,2,5)
ocean sealBOT
sullen nova
How to turn that into standard ellipse formula?
alpine sable
the speed, which is the distance it traveled over the next unit is sqrt(10^2+5^2)
alpine sable
wdym plane
The vector line r = a + mb means a line passing through a and parallel to a vector b
Doesn't mean 'starting point' is a itself... m is some real number
alpine sable
,w plot ((x+3)^2+y^2)^(1/2)+((x-3)^2+y^2)^(1/2) =10
Use definition of ellipse
sullen nova
what
alpine sable
The locus of all points whose sum of distance from two points (focii) is same
That's the definition of ellipse... Any point on it say p has the sum of distance from both focus as a constant
sullen nova
ye
alpine sable
ok https://media.discordapp.net/attachments/830131406415331418/845980611859447828/unknown.png can anyone help
sullen nova
And how to turn that into a standard equation?
alpine sable
And the formula you gave is basically is the sum of distance of a point (x,y) from (-3,0) and (3,0) equals 10
So the focus is at -3 and 3
alpine sable
Find the points it cuts the x and y axis at
Simply put x 0 then y 0
It will give the length of semi major and semi minor axis
Aka a and b in standard formula
yep, i understand that
but given that 3d line of plane 1, how do you find the direction plane 2 has to go in to intersect it
alpine sable
but given that 3d line of plane 1, how do you find the direction plane 2 has to ...
Infinite solutions tbh with all the information you gave. It can cut at any point on the line if no time+position of plane 1 is specified
sullen nova
and how to do that?
alpine sable
For eg put y = 0 it will give the point at which the curve intersect the x axis. The equation will be ± (x + 3 + x - 3) = 10
So the ellipse cuts x axis at (-5,0) and (5,0)
So 2a = 10
a = 5
Similarly you can find the y axis intercept by putting x= 0 in equation and it will give b
sullen nova
and what is b?
sullen nova
Can you find b for me?
sullen nova
I want to be a Therapist but mom wants me be an Engineer.
alpine sable
Lol sounds like india
paper parrot
$$ f(x) = e^(\frac{x}{2}+2) $$
junior thorn
is this channel busy?
ocean sealBOT
andrewFTW8
paper parrot
how do i use maclaurin transform but have x^4 in the series?
stone cypress
can someone help me with this
1.The image of point A (−3, −2) is mirrored about the x-axis and then the image on the y-axis is ...
2.If the image of the point P (−2, −3) is reflected on the x axis then the image is reflected on the line y = 4, then the image is ...
3.reflection of the curve y = x ^ 2-4 to the line y = -5 gives the curve ....
4.The image of point B (10, −8) if reflected on the y-axis then continues to be reflected on the line x = −2, then the image is ...
5.The line 2x − 5y + 6 = 0 is reflected against the line x = 2 then continued with the line y = −1, then the equation for the image of the line is ...
6.Point A (2, −5) is mirrored against y = −3 then the result is mirrored back against y = 4, the image of A is ...
7.Point A (−5,8) is mirrored against the line x = 4 then reflected on the x-axis, then the image is ...
8.The image of point B (10, −8) if it is reflected on the y-axis then continues to be reflected on the line x = −2, then the image is ...
9.The image of the line y = −3x + 3 by reflection on the x-axis and followed by the line y = x is ...
10.The image equation 2x-y = 4 reflected on the x-axis is ...
sullen nova
,w ((x+3)^2+y^2)^(1/2)+((x-3)^2+y^2)^(1/2) =10
ocean sealBOT
sullen nova
,w simplify ((x+3)^2+y^2)^(1/2)+((x-3)^2+y^2)^(1/2) =10
ocean sealBOT
bold token
guys is the formula of variance in a population, and in a sample the same?
ocean sealBOT
junior thorn
,w solve \Gamma\frac15
ocean sealBOT
junior thorn
,w simplify \Gamma\frac15
ocean sealBOT
paper parrot
5
paper parrot
69
paper parrot
69
paper parrot
2
trim schooner
ok
junior thorn
savage
spark shadow
woeful sleet
I'm trying to graph a function to compare two systems. But I'm having a hard time figuring out how to write the function for one of them.
We start at x,t=(-9,0). Then, there's no change until t=19. At which point, x'=7/4 until t=27. x'=0 until t=55, x'=7/4 until t=63, and continues in this cyclic manner. So obviously, I could draw this out by hand on paper and figure out what I'm looking for, but it would be really nice to just be able to enter it as a function on desmos.
And I feel like I'm missing something obvious that I probably learned 10 years ago, but can't figure how to write it.
proud burrow
@spark shadow Answer is C
sweet mural
nicely done
cosmic cypress
can someone help me with this one? i don't know how to solve parametric inequalities and really dk where to start
c is a constant, more specifically a positive constant, while v is between -c and c
(yes, c is the speed of light)
hexed viper
Solve for what
void heron
hey
sullen nova
hammer?
void heron
i need help with this question
sullen nova
@alpine sable Diagonal
sullen nova
no problem
void heron
sooo anyone?
alpine sable
The volume of a cubical box is 474. 552 cubic metres. Find the length of each side of the box.
sullen nova
@void heron
alpine sable
help
The volume of a cubical box is 474. 552 cubic metres. Find the length of each side of the box.
void heron
<@!606927200536494111>
yes
ocean sealBOT
sullen nova
@void heron
alpine sable
@sullen novathanks
deep field
Where?
sullen nova
Where what?
deep field
<@!804196898923741235> What are you trying to say?
Why did u ask this?
sullen nova
You were typing
deep field
No I wasn’t
sullen nova
I saw it
deep field
I just left something written in regard to some previous question but never pressed enter