#help-39
stoic imp
you didnt show how you got the orthogonal complement of T
nor the orthogonal complement of S
we can compute it together
let v =(x1,x2,x3,x4)
T = <(-1,1,0,0),(4,0,1,1)>
v . (-1,1,0,0) = 0
i) -x1+x2 = 0
ii) 4x1+x3+x4=0
i) -x1+x2 = 0 <==> x1 = x2
ii) 4x1+x3+x4=0 <==> x3 = -x4 -4x1
(x1,x2,x3,x4) = (x2,x2,-x4-4x2,x4)
T orthogonal is = <(1,1,-4,0),(0,0,-1,1)>
stoic imp
you prolly did a mistake when finding the orthogonal complement of T because the dimension of T orthogonal + T should give the whole space R^4
plush dagger
Hmm hold up
stoic imp
dim(T)+dim(T perp) = dim(R^4)
stoic imp
since T and T perp are complementary subspaces and both are subspaces of R^4 their dimensions should sum up to R^4
Also you didn't show how you got that basis for S
plush dagger
let v =(x1,x2,x3,x4)
I like this approach more
stoic imp
yeah is using the standard dot product for a vector v = (x1,x2,x3,x4)
stoic imp
I mean we need to compute the orthogonal complements correctly
stoic imp
also is impossible W is dim 1 because it has nontrivial intersection with the orthogonal complement of S and the orthogonal complement of T
stoic imp
yeah now I need to find basis of S
when we have basis of S we can compute the orthogonal complement of S
i) 4x1 + x2 - x4 = 0
ii) x1 + x3 = 0
ii) x1 + x3 = 0 <==> x1 = -x3
plush dagger
Yes
stoic imp
i) 4x1 + x2 - x4 = 0 <==> x4 = 4x1+x2
x4 = 4x1 + x2 <==> x4 = -4x3 + x2
(x1,x2,x3,x4)=(-x3,x2,x3,-4x3 + x2)
S = <(-1,0,1,-4),(0,1,0,1)>
plush dagger
Perfect
stoic imp
let v = (x1,x2,x3,x4)
i) v . (-1,0,1,-4)=0
i) v . (-1,0,1,-4)=0 <==> -x1+x3-4x4=0
ii) v .(0,1,0,1)=0 <==> x2 + x4 = 0
I am trying to find orthogonal complement of S
plush dagger
I am trying to find orthogonal complement of S
And got it?
plush dagger
S = <(-1,0,1,-4),(0,1,0,1)>
After having that it shouldn't be hard
stoic imp
-x1 + x3 -4x4 = 0 <==> x1 = x3 - 4x4
i) x1 = x3 - 4x4
ii) x4 = -x2
plugging ii) in i)
x1 = x3 + 4x2
(x1,x2,x3,x4)=(x3+4x2,x2,x3,-x2)
orthogonal complement of S is = <(1,0,1,0),(4,1,0,-1)>
plush dagger
Not -4?
stoic imp
I plugged ii) in i)
at first it was x1 = x3 -4x4
but then it became
x1 = x3 + 4x2
because ii) say that x4 = -x2
plush dagger
Yep
stoic imp
,, W \subset S + T \ W \ne S + T \ W \cap S^{\perp} \ne {0} \ W \cap T^{\perp} \ne {0}
jolly parrotBOT
xbz
stoic imp
this are the conditions subspace of R4, named W has to comply
plush dagger
So you're done?
stoic imp
well
We know W has at least one vector from the orthogonal complement of T and one vector at least from the orthogonal complement of S
and we know W is not a basis for S + T
but W is entirely contained in S + T
first let's find a basis of S + T
plush dagger
Okay
stoic imp
sorry I was in the toilet
stoic imp
ok good
plush dagger
And you don't need me anyway you're good
pearl pondBOT
@stoic imp Has your question been resolved?
pearl pondBOT
@stoic imp Has your question been resolved?
midnight haven
can anyone help me with calc 1
pure rapids
can anyone help me with calc 1
!occupied
pearl pondBOT
can anyone help me with calc 1
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
pearl pondBOT
@stoic imp Has your question been resolved?
pearl pondBOT
@stoic imp Has your question been resolved?
summer sundial
stoic imp
Its intersection of vector subspaces
stoic imp
S = <(-1,0,1,-4),(0,1,0,1)>
T = <(-1,1,0,0),(4,0,1,1)>
,w rref {{-1,1,0,0},{4,0,1,1},{-1,0,1,-4},{0,1,0,1}}
jolly parrotBOT
stoic imp
S+T=<(-1,1,0,0),(4,0,1,1),(-1,0,1,-4)>
T orthogonal = <(1,1,-4,0),(0,0,-1,1)>
orthogonal complement of S = <(1,0,1,0),(4,1,0,-1)>
,w rref {{1,1,-4,0},{0,0,-1,1},{1,0,1,0},{4,1,0,-1}}
jolly parrotBOT
jolly parrotBOT
stoic imp
,w rref {{-1,1,0,0},{4,0,1,1},{-1,0,1,-4},{0,1,0,1}}^T
jolly parrotBOT
stoic imp
,w rref {{1,1,-4,0},{0,0,-1,1},{1,0,1,0},{4,1,0,-1}}^T
jolly parrotBOT
stoic imp
,w rref {{4,1,0,-1,0},{1,0,1,0,0}}
jolly parrotBOT
stoic imp
i) x1 + x3 = 0
ii) x2 -4x3 -x4 = 0
x1 = -x3
x2 = 4x3+x4
(-x3,4x3+x4,x3,x4)
(-x3,4x3+x4,x3,x4)=x3(-1,4,1,0)+x4(0,1,0,1)
S = <(-1,4,1,0),(0,1,0,1)>
T = <(-1,1,0,0),(4,0,1,1)>
S + T = <(-1,4,1,0),(0,1,0,1),(-1,1,0,0)>
,w NullSpace[{{-1, 4, 1, 0}, {0, 1, 0, 1}}]
jolly parrotBOT
stoic imp
(x-4y, -y, x, y) = x(1,0,1,0) + y(-4,-1,0,1)
S n T = <(4,0,1,1)>
S perp = <(1,0,1,0),(-4,-1,0,1)>
S = <(-1,4,1,0),(0,1,0,1)>
T = <(-1,1,0,0),(4,0,1,1)>
,w Nullspace [{-1,1,0,0},{4,0,1,1}}]
jolly parrotBOT
stoic imp
(-x-y,-x-y,4x,4y) = x(-1,-1,4,0) + y (-1,-1,0,4)
T perp = <(-1,-1,4,0),(-1,-1,0,4)>
S n T = <(4,0,1,1)>
S perp = <(1,0,1,0),(-4,-1,0,1)>
S = <(-1,4,1,0),(0,1,0,1)>
T = <(-1,1,0,0),(4,0,1,1)>
S + T = <(-1,4,1,0),(0,1,0,1),(-1,1,0,0)>
,w rref {{-1,-1,4,0},{-1,-1,0,4},{1,0,1,0},{-4,-1,0,1}}
jolly parrotBOT
jolly parrotBOT
stoic imp
there is something off
Sperp n T perp I found it correctly
but when I try to look up the intersection between Sperp n Tperp with S+T the vectors are linearly independent
wtf man
there is something that I am missing
T perp = <(-1,-1,4,0),(-1,-1,0,4)>
S n T = <(4,0,1,1)>
S perp = <(1,0,1,0),(-4,-1,0,1)>
S = <(-1,4,1,0),(0,1,0,1)>
T = <(-1,1,0,0),(4,0,1,1)>
S + T = <(-1,4,1,0),(0,1,0,1),(-1,1,0,0)>
dim(S+T) = dim(S) + dim(T) - dim(SnT)
dim(S+T) = 2 + 2 - 1 = 3
,w rref {{-1,4,1,0},{0,1,0,1},{-1,1,0,0},{1,0,1,0},{-4,-1,0,1}}
jolly parrotBOT
stoic imp
(S + T) n S perp = <(-4,-1,0,1)>
,w rref {{-1,4,1,0},{0,1,0,1},{-1,1,0,0},{-1,-1,4,0},{-1,-1,0,4}}
jolly parrotBOT
stoic imp
T perp = <(-1,-1,4,0),(-1,-1,0,4)>
S n T = <(4,0,1,1)>
S perp = <(1,0,1,0),(-4,-1,0,1)>
S = <(-1,4,1,0),(0,1,0,1)>
T = <(-1,1,0,0),(4,0,1,1)>
S + T = <(-1,4,1,0),(0,1,0,1),(-1,1,0,0)>
a(-1,-1,4,0)+b(-1,-1,0,4) = c(-1,4,1,0)+d(0,1,0,1)+e(-1,1,0,0)
(-a-b,-a-b,4a,4b)=(-c-e,4c+d+e,c,d)
,, \begin{cases} -a-b=-c-e \ -a-b = 4c + d \ 4a = c \ 4b = d \end{cases} \ \begin{cases} -a-b + c + e=0 \ -a-b -4c - d = 0 \ 4a -c = 0 \ 4b -d = 0 \end{cases}
jolly parrotBOT
why is math so hard anyways?
stoic imp
,w rref {{-1,-1,1,0,1,0},{-1,-1,-4,-1,0,0},{4,0,-1,0,0,0},{0,4,0,-1,0,0}}
jolly parrotBOT
stoic imp
,, \begin{cases} a + \frac{5e}{32} = 0 \\ b - \frac{17e}{32} = 0 \\ c + \frac{5e}{8} = 0 \\ d - \frac{17e}{8} = 0 \end{cases}
jolly parrotBOT
why is math so hard anyways?
stoic imp
(a,b,c,d,e) = (-5e/32, 17e/32, -5e/8, 17e/8, e)
a(-1,-1,4,0)+b(-1,-1,0,4) = c(-1,4,1,0)+d(0,1,0,1)+e(-1,1,0,0)
stoic imp
**why is math so hard anyways?**
e is free
we can choose e = 32
and then (a,b,c,d,e) = (-5, 17, -20, 68, 32)
-5(-1,-1,4,0) + 17(-1,-1,0,4)
(5,5,20,0)+(-17,-17,0,68)
(-12,-12,-20,68)
(-6,-6,-10,34)
(-3,-3,-5,17)
T perp = <(-1,-1,4,0),(-1,-1,0,4)>
S n T = <(4,0,1,1)>
S perp = <(1,0,1,0),(-4,-1,0,1)>
S = <(-1,4,1,0),(0,1,0,1)>
T = <(-1,1,0,0),(4,0,1,1)>
S + T = <(-1,4,1,0),(0,1,0,1),(-1,1,0,0)>
T perp = <(-1,-1,4,0),(-1,-1,0,4)>
S n T = <(4,0,1,1)>
S perp = <(1,0,1,0),(-4,-1,0,1)>
S = <(-1,4,1,0),(0,1,0,1)>
T = <(-1,1,0,0),(4,0,1,1)>
S + T = <(-1,4,1,0),(0,1,0,1),(-1,1,0,0)>
v = a(1,0,1,0) + b(-4,-1,0,1) , a generic vector of Sperp
v = (a-4b,-b,a,b)
a generic vector of S + T
(a-4b,-b,a,b) = c(-1,4,1,0)+d(0,1,0,1)+e(-1,1,0,0)
(a-4b,-b,a,b) = (-c-e,4c+d+e,c,d)
,, \begin{cases} a - 4b + c + e = 0 \ -b - 4c-d-e = 0 \ a -c = 0 \ b - d = 0 \end{cases}
jolly parrotBOT
why is math so hard anyways?
stoic imp
,w rref {{1,-4,1,0,1,0},{0,-1,-4,-1,-1,0},{1,0,-1,0,0,0},{0,1,0,-1,0,0}}
jolly parrotBOT
stoic imp
(a,b,c,d,e) = (-3/10 e, 1/10 e, -3/10 e, 1/10 e, e)
(a-4b,-b,a,b) = c(-1,4,1,0)+d(0,1,0,1)+e(-1,1,0,0)
a(1,0,1,0) + b(-4,-1,0,1) = c(-1,4,1,0) + d(0,1,0,1) + e(-1,1,0,0)
(-3/10).(e,0,e,0) + (1/10).(-4e,-e,0,e) = (-3/10).(-e,4e,e,0) + (1/10).(0,e,0,e) + e(-1,1,0,0)
(-3).(10e,0,10e,0) + (-40e,-10e,0,10e) = (-3).(-10e,40e,10e,0) + (0,10e,0,10e) + e(-1,1,0,0)
(-30e,0,-30e,0) + (-40e,-10e,0,10e) = (30e,-120e,-30e,0) + (0,10e,0,10e) + (-e,e,0,0)
e(-30,0,-30,0) + e(-40,-10,0,10) = e(30,-120,-30,0) + e(0,10,0,10) + e(-1,1,0,0)
e(-30-40,-10,-30,10) = e(30-1, -120 +10 + 1, -30, 10)
e(-70,-10,-30,10) = e(29, -109, -30, 10)
v = (-7, -1, -3, 1)
T perp = <(-1,-1,4,0),(-1,-1,0,4)>
S n T = <(4,0,1,1)>
S perp = <(1,0,1,0),(-4,-1,0,1)>
S = <(-1,4,1,0),(0,1,0,1)>
T = <(-1,1,0,0),(4,0,1,1)>
S + T = <(-1,4,1,0),(0,1,0,1),(-1,1,0,0)>
,w rref {{-7,-1,-3,1},{-1,4,1,0},{0,1,0,1},{-1,1,0,0}}
jolly parrotBOT
stoic imp
a(-1,-1,4,0) + b(-1,-1,0,4) = c(-1,4,1,0) + d(0,1,0,1) + e(-1,1,0,0)
,, \begin{cases} -a-b+c+e = 0 \ -a-b-4c-d-e = 0 \ 4a-c = 0 \ 4b -d = 0 \end{cases}
jolly parrotBOT
why is math so hard anyways?
stoic imp
,w rref {{-1,-1,1,0,1,0},{-1,-1,-4,-1,-1,0},{4,0,-1,0,0,0},{0,4,0,-1,0,0}}
jolly parrotBOT
stoic imp
i) a = -3/16 e
ii) b = 7/16 e
a(-1,-1,4,0) + b(-1,-1,0,4) = c(-1,4,1,0) + d(0,1,0,1) + e(-1,1,0,0)
a = -3
b = 7
-3(-1,-1,4,0) + 7(-1,-1,0,4)
(3,3,-12,0) + (-7,-7,0,28)
(-4,-4,-12,28)
(-2,-2,-6,14)
(1,1,3,-7)
T perp = <(-1,-1,4,0),(-1,-1,0,4)>
S n T = <(4,0,1,1)>
S perp = <(1,0,1,0),(-4,-1,0,1)>
S = <(-1,4,1,0),(0,1,0,1)>
T = <(-1,1,0,0),(4,0,1,1)>
S + T = <(-1,4,1,0),(0,1,0,1),(-1,1,0,0)>
,w rref {{-1,4,1,0},{0,1,0,1},{-1,1,0,0},{1,1,3,-7}}
W = <(1,1,3,-7),(-7,-1,-3,1)>
,, \textbf{Guys I have this subspaces: } \ \mathbb{T}^{\perp} = \langle (-1,-1,4,0), (-1,-1,0,4) \rangle \ \mathbb{S} \cap \mathbb{T} = \langle (4,0,1,1) \rangle \ \mathbb{S}^{\perp} = \langle (1,0,1,0), (-4,-1,0,1) \rangle \ \mathbb{S} = \langle (-1,4,1,0), (0,1,0,1) \rangle \ \mathbb{T} = \langle (-1,1,0,0), (4,0,1,1) \rangle \ \mathbb{S} + \mathbb{T} = \langle (-1,4,1,0), (0,1,0,1), (-1,1,0,0) \rangle \W \cap T^{\perp} \ne {0} \ W \cap S^{\perp} \ne {0} \ W \ne S + T \ W \subset S + T
jolly parrotBOT
why is math so hard anyways?
stoic imp
,, \textbf{Guys I have this subspaces: } \ \begin{align} \mathbb{T}^{\perp} &= \langle (-1,-1,4,0), (-1,-1,0,4) \rangle \ \mathbb{S} \cap \mathbb{T} &= \langle (4,0,1,1) \rangle \ \mathbb{S}^{\perp} &= \langle (1,0,1,0), (-4,-1,0,1) \rangle \ \mathbb{S} &= \langle (-1,4,1,0), (0,1,0,1) \rangle \ \mathbb{T} &= \langle (-1,1,0,0), (4,0,1,1) \rangle \ \mathbb{S} + \mathbb{T} &= \langle (-1,4,1,0), (0,1,0,1), (-1,1,0,0) \rangle \ \mathbb{W} &= \langle (1,1,3,-7), (-7,-1,-3,1) \rangle \end{align} \ \textbf{How do I prove the following conditions hold? } \ \begin{align} \mathbb{W} \cap \mathbb{T}^{\perp} &\ne {0} \ \mathbb{W} \cap \mathbb{S}^{\perp} &\ne {0} \ \mathbb{W} &\ne \mathbb{S} + \mathbb{T} \ \mathbb{W} &\subset \mathbb{S} + \mathbb{T} \end{align}
jolly parrotBOT
why is math so hard anyways?
stoic imp
.close
pearl pondBOT
stoic imp
.reopen
pearl pondBOT
✅
stoic imp
,, \textbf{Guys I have this subspaces: } \ \begin{align} \mathbb{T}^{\perp} &= \langle (-1,-1,4,0), (-1,-1,0,4) \rangle \ \mathbb{S} \cap \mathbb{T} &= \langle (4,0,1,1) \rangle \ \mathbb{S}^{\perp} &= \langle (1,0,1,0), (-4,-1,0,1) \rangle \ \mathbb{S} &= \langle (-1,4,1,0), (0,1,0,1) \rangle \ \mathbb{T} &= \langle (-1,1,0,0), (4,0,1,1) \rangle \ \mathbb{S} + \mathbb{T} &= \langle (-1,4,1,0), (0,1,0,1), (-1,1,0,0) \rangle \ \mathbb{W} &= \langle (1,1,3,-7), (-7,-1,-3,1) \rangle \end{align} \ \textbf{How do I prove the following conditions hold? } \ \begin{align} \mathbb{W} \cap \mathbb{T}^{\perp} &\ne {0} \ \mathbb{W} \cap \mathbb{S}^{\perp} &\ne {0} \ \mathbb{W} &\ne \mathbb{S} + \mathbb{T} \ \mathbb{W} &\subset \mathbb{S} + \mathbb{T} \end{align}
jolly parrotBOT
why is math so hard anyways?
autumn trellis
cursive flare
I feel like I've seen this question being asked a month ago
cursive flare
ask in #latex-help next time
but you can look it up in detexify
swift nymph
Oops
stoic imp
I was thinking of multiplying the vectors from S = <(-1,4,1,0),(0,1,0,1)> with
let v = (x1,x2,x3,x4)
for example like this:
i) v . (-1,4,1,0) = 0 ==> -x1 + 4x2 + x3 = 0
ii) v . (0,1,0,1) = 0 ==> x2 + x4 = 0
and then, seeing if the vectors from W = <(1,1,3,-7), (-7,-1,-3,1)> satisfy the equations i) and ii) , if one of the vectors satisfy the equations i) or ii) that would mean W = <w1,w2> either w1 or w2 is contained in S perp
for example if you evaluate w2 = (-7,-1,-3,1) in equation i) and ii) you get
i) 7 -4 -3 = 0 ==> 0 = 0
ii) -1 + 1 = 0 ==> 0 = 0
so w2 intersects with the orthogonal compĺement of S
we can do the same for the vectors from T,
iii) v . (-1,1,0,0) =0 ==> -x1+x2 = 0
iv) v . (4,0,1,1) = 0 ==> 4x1 + x3 + x4 = 0
stoic imp
,, \textbf{Guys I have this subspaces: } \ \begin{align} \mathbb{T}^{\perp} &= \langle (-1,-1,4,0), (-1,-1,0,4) \rangle \ \mathbb{S} \cap \mathbb{T} &= \langle (4,0,1,1) \rangle \ \mathbb{S}^{\perp} &= \langle (1,0,1,0), (-4,-1,0,1) \rangle \ \mathbb{S} &= \langle (-1,4,1,0), (0,1,0,1) \rangle \ \mathbb{T} &= \langle (-1,1,0,0), (4,0,1,1) \rangle \ \mathbb{S} + \mathbb{T} &= \langle (-1,4,1,0), (0,1,0,1), (-1,1,0,0) \rangle \ \mathbb{S}^{\perp} \cap \mathbb{T}^{\perp} &= \langle (4,1,0,-1) \rangle \ \mathbb{W} &= \langle (1,1,3,-7), (-7,-1,-3,1) \rangle \end{align} \ \textbf{How do I prove the following conditions hold? } \ \begin{align} \mathbb{W} \cap \mathbb{T}^{\perp} &\ne {0} \ \mathbb{W} \cap \mathbb{S}^{\perp} &\ne {0} \ \mathbb{W} &\ne \mathbb{S} + \mathbb{T} \ \mathbb{W} &\subset \mathbb{S} + \mathbb{T} \end{align}
jolly parrotBOT
why is math so hard anyways?
stoic imp
,w det {{1,1,3,-7},{-7,-1,-3,1},{-1,-1,4,0},{-1,-1,0,4}}
jolly parrotBOT
stoic imp
,w det {{1,1,3,-7},{-7,-1,-3,1},{1,0,1,0},{-4,-1,0,1}}
jolly parrotBOT
stoic imp
,w det {{1,1,3,-7},{-1,4,1,0},{0,1,0,1},{-1,1,0,0}}
jolly parrotBOT
stoic imp
,w det {{-7,-1,-3,1},{-1,4,1,0},{0,1,0,1},{-1,1,0,0}}
jolly parrotBOT
stoic imp
dim(W)=2
dim(S+T)=dim(S)+dim(T)-dim(SnT)
dim(S+T)=2+2-1=3
dim(W) < dim(S+T)
2 < 3
,, 2 \ne 3
jolly parrotBOT
why is math so hard anyways?
pearl pondBOT
leaden topaz
pearl pondBOT
Available help channel!
forest gull
x | 5 | 8 | 10 | 20
y | 6.4 | 4 | 3.2 | 1.6
inverse direct or neither
torn sky
I just would like to know if my approach here is valid
pearl pondBOT
I just would like to know if my approach here is valid
torn sky
Tried my best to recreate it as good as possible in paint lol
pearl pondBOT
@torn sky Has your question been resolved?
pearl pondBOT
@torn sky Has your question been resolved?
torn sky
Should I rephrase?
shadow stag
I just would like to know if my approach here is valid
ye it is valid
you have to plug it back in and verify that it works though
torn sky
ye it is valid
Ah alright, thanks for the clarification
shadow stag
because in general, you may get extraneous solutions
like technically you would also get x=-10 but plugging it in doesnt give a valid equation
torn sky
I've noticed with some of the other tasks indeed, where I got that x = -1, but that would work of course if log10(-1)
Yeah exactly, alright
On another note maybe
If we have 2lg(x)-5lg(x)+6 = 0
Generally with equations, if we substract or add we add to the whole number so we could substract 6 from each side to get 2lg(x)-5lg(x) = -6, but with multiply/divide/root/powers, we have to do that to each term, correct?
I'm not sure why I suddenly got that error in my brain, but it suddenly didn't make sense that I substracted only 6 from 1 term
shadow stag
you are always doing your operation to do the whole expression on each side
and with addition and subtracting, that is equivalent to just doing it to a single thing from each side
torn sky
and with addition and subtracting, that is equivalent to just doing it to a sing...
Okay, so what I said is valid as we would essentially just add or subtract 6 from the final number?
Whereas those other operations do something with 1 value, thus we have to do with with each term
shadow stag
whenever you have an equation of the form [expression1] = [expression2], always imagine performing an operation on the whole expressions
and then from there you decide whether you use associativity or distributivity
shadow stag
Okay, so what I said is valid as we would essentially just add or subtract 6 fro...
what do you mean subtract rom the final number?
torn sky
what do you mean subtract rom the final number?
So lets say we have what I said earlier, 2lg(x)-5lg(x)+6 = 0, we could in theory subtract or add 6 on both sides, which would just add or remove a 6 from the end product, in this case it makes sense to subtract 6, but if we were to multiply both sides with 2 we would do that with each term, like 2(2lg(x)-5lg(x)+6) = 2*0, where as add or subtract basically adds a new term
I hope that explains a bit what I got confused with?
shadow stag
yeah you can think of it that way
pearl pondBOT
pearl pondBOT
Available help channel!
graceful spruce
What did I do wrong ? Find area And perimeter
pearl pondBOT
What did I do wrong ? Find area And perimeter
rose robin
What did I do wrong ? Find area And perimeter
area of the circle and rectangle is wrong
you also didn't add it right for the perimeter
the individual parts seems right though
rose robin
you didn't divide by 2 there
graceful spruce
you also didn't add it right for the perimeter
How?
It’s 17,13
M
Ok got it right
rose robin
It’s 17,13
yup, should be that
graceful spruce
Can anyone tell me all measurements?
Meter
Hekto
Centi
etc.?
urban sun
just google
graceful spruce
just google
Why when converting cm^2 to m^2 you have to divide by 100 and 100?
@urban sun what’s corner line?
graceful spruce
What what corner line?
In a square, the corner line is 15 cm find the area
verbal whale
Why when converting cm^2 to m^2 you have to divide by 100 and 100?
Because 1 cm = 1/100 m
verbal whale
In a square, the corner line is 15 cm find the area
What is the corner line?
graceful spruce
Because 1 cm = 1/100 m
But why dtwice?
graceful spruce
What is the corner line?
Idk… I’m asking you
verbal whale
But why dtwice?
Because you're squaring them !
brisk steeple
It's not magic
urban sun
do you know what ^2 means
brisk steeple
It's just directly said
urban sun
cm x cm
graceful spruce
I think corner line is the yellow line
brisk steeple
1m^2 = 1m * 1m = 100cm * 100cm = 10^4 cm^2
1cm^2 = (1/10^4)m^2
graceful spruce
It's not magic
Stop with the attitude, I’m not your friend.
urban sun
Stop with the attitude, I’m not your friend.
you're literally asking elementary problems
urban sun
im convinced you are a troll
graceful spruce
Then don’t talk to me.
urban sun
ye
brisk steeple
Ok
pearl pondBOT
graceful spruce
You failed all subjects.
Quiet it down, Timmy.
Yeah right your grade is 1.
Lol
You’re so funny
You can’t even calculate it
graceful spruce
.close
pearl pondBOT
graceful spruce
You’re gonna fail at your life.
verbal whale
<@&268886789983436800>
graceful spruce
This dude is real enemy of everyone’s enemy.
modest tartan
Bro wha going on?
graceful spruce
Your whole personality is the definition of rude.
unborn abyss
both of you shut up
perhaps you'll take a class at uni that teaches you how to be nice
when you do, you can come back here
mild berry
<@&268886789983436800> i saw what happened why has andrzej not been banned too
graceful spruce
Stop going on alt.
graceful spruce
Because I was attacked first.
unborn abyss
<@&268886789983436800> i saw what happened why has andrzej not been banned too
was less egregious and he wasn't the aggressor
graceful spruce
Im allowed to defend myself.
unborn abyss
having said that you should just call mods
graceful spruce
*having said that* you should just call mods
I don’t want to disturb you.
mild berry
was less egregious and he wasn't the aggressor
He attacked other ppl
For helping him
How does that make sense
W moderation
unborn abyss
I don’t want to disturb you.
i'm already disturbed. just call mods in the future
mild berry
Ur just gonna allow this guy to have a false sense of authority over people helping him
He told some fella to chop chop
And to shut the fuck up and calling ppl worm
And thats allowed
Nice
brittle pebble
ngl, andrzej pasts msg is a bit rude lmao
verbal whale
Stop with the attitude, I’m not your friend.
Also this, why did you attack Meolve like that??
mild berry
Also this, why did you attack Meolve like that??
Thats what im saying
unborn abyss
yes, i was looking into those and was going to talk to him in private about that but yall have forced my hand
pearl pondBOT
Available help channel!
mild berry
Then i get banned for backing my fellow mathematicians against an absolute master of evil
brittle pebble
Then i get banned for backing my fellow mathematicians against an absolute maste...
How does this relate to maths STAY ON TOPIC id:customize
graceful spruce
@mild berry Also stop being invested in this, it’s not concerning you.
verbal whale
They had attitude.
Not at all. It's your (incorrect) interpretation
mild berry
It concerns me i see serious failure of moderation and egregious behaviour
unborn abyss
ugh. @graceful spruce yes your behaviour today has been very rude. please remember that helpers are volunteers. the main reason i'm not currently banning you is because this seems to be your first day here and you can learn
i see you editing posts btw
brittle pebble
the fact that he is new implies that he is most likely a troll
mild berry
He joined months ago
graceful spruce
ugh. <@1184625819432267819> yes your behaviour today has been very rude. please ...
Thank you, otherwise there’s a mod here that would definitely ban me.
mild berry
Is blud tripping
brittle pebble
Thank you, otherwise there’s a mod here that would definitely ban me.
💀
mild berry
Nice edit bro
graceful spruce
the fact that he is new implies that he is most likely a troll
Sure buddy, I need math help, but yall started to act in my channels.
mild berry
Even he agrees he should be banned
graceful spruce
Even he agrees he should be banned
No, im saying I’ve seen people getting banned for sending a sticker in #discussion
unborn abyss
however, i think you can take a break from here for a bit. stay on topic in help channels. i'm closing this. don't talk about this anymore. if you encounter rudeness don't fight back just call mods. is2g
graceful spruce
Or sending a meme video in a help channel.
brittle pebble
i jsut saw this channel and just went to ur pasts msg and just think its a bit dumb that 2 ppl got banned and not him
unborn abyss
.close
pearl pondBOT
graceful spruce
however, i think you can take a break from here for a bit. stay on topic in help...
I’ll, also keep an eye of these alts.
unborn abyss
I’ll, also keep an eye of these alts.
i'm also muting you for a few hours fwiw. please come back when you can be nice.
pearl pondBOT
Available help channel!
sharp smelt
prove If $\sup(A) < \sup(B)$, show their exists an element $b \in B$, that is an upper bound for $A$
jolly parrotBOT
ƒ(Why am. I here)=I don't Know
sharp smelt
By definition $sup(A)$ satisfies the two following conditions: It' s an upper bound of $A$, and if any other upper bound exists , it's greater than $\sup(A)$.$\sup(B)$, too, must be an upper bound of $B$, and if any other upper bound exists , it must be greater than $\sup(B)$.
\
Let such an upper bound in $B$ not exist. Thus if there's no element in $B$ satisfying $\sup(A) \leq b$, it must be that $sup(A) > b ; \forall b \in B$. Thus $sup(A) \geq sup(B)$, which contradicts the given condition. Thus our assumption must be wrong, and such an upper bound in $B$ exists
jolly parrotBOT
ƒ(Why am. I here)=I don't Know
pearl pondBOT
@sharp smelt Has your question been resolved?
sharp smelt
<@&286206848099549185>
autumn trellis
By definition $sup(A)$ satisfies the two following conditions: It' s an upper bo...
yeah that works. you can also take (sup (A) + sup(B))/2 which will be in between sup A and sup B. since it is smaller than sup B there is an element of B say b that is greater than or equal to (sup (A) + sup(B))/2 , so it is an upper bound for A
south inlet
Hmm, and that would be the direct proof ?
should be
pearl pondBOT
sharp smelt
.reopen
pearl pondBOT
✅
sharp smelt
I have to show this isn'ttrue if $sup(A) \leq sup(B)$
jolly parrotBOT
ƒ(Why am. I here)=I don't Know
sharp smelt
I was thinking $A=[0,1]; B=(0,1)$
jolly parrotBOT
ƒ(Why am. I here)=I don't Know
spare lark
**ƒ(Why am. I here)=I don't Know**
Well here sup(A) = sup(B) = 1 no ?
sharp smelt
Well here sup(A) = sup(B) = 1 no ?
ywah, but there's mo element in b, that's an upper bound for A
spare lark
Ah you was checking what happen when <= ?
sharp smelt
yes
spare lark
Interesting
sharp smelt
That was the next subquestion
spare lark
Ok ok then great counterexample
Which
Works with any x,y since you set A = [x,y] and B = (x,y)
y > x
And non empty
I believe
rare scaffold
A=B=(0,1) also works
sharp smelt
Can I close this channel now
lapis stone
Hi
pearl pondBOT
pearl pondBOT
Available help channel!
old oriole
Im so confused.. i know it seems easy but im struggling 😭
pearl pondBOT
Im so confused.. i know it seems easy but im struggling 😭
random ermine
old oriole
Ive tried stuff 😭
nimble osprey
random ermine
what's the slope of 3x+y=-7
old oriole
I have absolutely no idea
random ermine
also what r the options on the right
old oriole
Its just for a math lib
random ermine
what's the slope of y = 2x
random ermine
what's the slope of y = 2x
what's y(1)
old oriole
what's the slope of y = 2x
Would it just be 2?
random ermine
yes
random ermine
y = 3x?
old oriole
3?
old oriole
Ohh
random ermine
it's still 3 the +2 doesn't matter
old oriole
Oh
random ermine
cuz if u shift it up and down it's the same slope
+2 is just shifting up by 2 units
old oriole
Ohh
random ermine
m
old oriole
Im so bad at this im sorry
random ermine
we did m=2 and m=3 before
random ermine
what's the slope of 3x+y=-7
can u write this in that form
pearl pondBOT
@old oriole Has your question been resolved?
calm wing
what?
picture on the way?
let x be the original price
17% were discounted and now it's 340
so $x-0.17x = 340$
jolly parrotBOT
artemetra
jolly parrotBOT
Result:
28220
Result:
409.63855421687
artemetra
calm wing
you are still supposed to divide by 83
not multiply
what?
how many percent what
210% of 3000?
ah
yes
yes
divide 52425 by 0.85
,calc 52425/0.85
jolly parrotBOT
Result:
61676.470588235
,calc 52425*1.25
jolly parrotBOT
Result:
65531.25
yeah no
calm wing
Result:
```
61676.470588235
```
it's this one
yes, except it's 0.75 in the end
so here we have x-0.25x = 52425
we get 0.75x = 52425
oh cool icelandic
indeed
yep
well 52.425 isn't 25% of the original price, it's 100%-25% = 75% of the original price
this is why you use 75
jolly parrotBOT
Result:
6.9230769230769e+5
,w 225000/0.325
jolly parrotBOT
calm wing
yep
pearl pondBOT
pearl pondBOT
Available help channel!
stone imp
pearl pondBOT
stone imp
I’m so lost
plush bramble
do you know the length of the right side in this picture
sharp condor
It's 2x
stone imp
Huh
sharp condor
4x - 2x
sharp condor
Cuz u got the 2x on the right and 4x on the left
sharp condor
Oh I shoudve mentioned I already did A
Do a and then split the picture into 2
Like a square and a rectangle
stone imp
Wdym
stone imp
Yes
lusty merlin
Idk the words in englihs
Do you know how to find area of this?
pearl pondBOT
pearl pondBOT
Available help channel!
pearl pondBOT
pine jay
What do you think?
What do you know about the hypotenuse of a right angle triangle compared to its other sides?
?
Answer my question
pearl pondBOT
pine jay
Bruh
valid peak
don't be rude to helpers. either way I'm assuming this is a mute evasion #help-20 message
same picture
pearl pondBOT
Available help channel!
desert solar
$(z-1)(z-3)(z+5)(z+7)=297$ determine the sum of the roots of the equation
jolly parrotBOT
Bob Pancakebutter
pearl pondBOT
@desert solar Has your question been resolved?
warm current
$(z-1)(z-3)(z+5)(z+7)=297$ determine the sum of the roots of the equation
!status
pearl pondBOT
$(z-1)(z-3)(z+5)(z+7)=297$ determine the sum of the roots of the equation
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
warm current
How did you get this?
toxic fractal
show said calculations?
desert solar
$(z-1)(z-3)=z^2-3z-z+3=z^2-4z+3$
jolly parrotBOT
Bob Pancakebutter
pearl pondBOT
desert solar
.reopen
pearl pondBOT
✅
desert solar
$(z+5)(z+7)=z^2+7z+5z+35=z^2+12z+35$
jolly parrotBOT
Bob Pancakebutter
toxic fractal
okay. And why did you split those?
desert solar
$(z^2-4z+3)(z^2+12z+35)=297$
storm hatch
It may be a good idea to start factorising $297$
desert solar
okay. And why did you split those?
I put together
toxic fractal
It may be a good idea to start factorising $297$
i believe that to be unneeded
jolly parrotBOT
BananabrainJoe
pale frost
After some calculations you get here
brave sluice
maybe the LHS will be 4 integers
nevermind it's not
pale frost
Then apply Vieta's formulas and you are done !
toxic fractal
maybe the LHS will be 4 integers
you had a lot of faith on that considering 297 is 3*3*3*11
storm hatch
$$297=11\times3^{3}=(-9)(-3)(3)(1)=(1)(3)(9)(11)$$ then immediately $4$ and $-8$ are solutions
brave sluice
when i factored it, i saw that it was not
jolly parrotBOT
如月あやみ Kisaragi Ayami
jolly parrotBOT
BananabrainJoe
light helm
there's no real need to expand anything
jolly parrotBOT
BananabrainJoe
pale frost
brave sluice
i gave up too quickly
desert solar
**BananabrainJoe**
This Is the final sol?
light helm
as you aren't required to find the individual roots, just the sum
pale frost
Did I do well? @light helm
storm hatch
noting that z-1, z+7 and z-3,z+5 form pairs that are centered at $z+2$, just let $y=z+2$ and let the formula for difference of two squares take it from there
it's this simple
brave sluice
ayami do you claim there are only 2 zeros?
light helm
note that in vietas formula, sum of roots (for degree 2+) isn't dependent on the constant term
toxic fractal
it does require you to expand to get the first and second terms tho
jolly parrotBOT
如月あやみ Kisaragi Ayami
light helm
e.g consider the sum of roots for
x^2 + 2x + 7 = 0
x^2 + 2x + 13 = 0
x^2 + 2x - 3 = 0
x^2 + 2x + 5 = 0
x^2 + 2x = 0
pale frost
note that in vietas formula, sum of roots (for degree 2+) isn't dependent on th...
But I find correctly
jolly parrotBOT
BananabrainJoe
light helm
yes
jolly parrotBOT
BananabrainJoe
pale frost
Isn't it correct to do the exercise like this?
light helm
you could, but I'm hinting at a trick that can do it much faster
pale frost
I also think I've found another way
storm hatch
Noting that $z-1, z+7$ and $z-3,z+5$ form pairs that are centered at $z+2$ we let $t=z+2$ and thus $$(z-1)(z-3)(z+5)(z+7)=(t-3)(t-5)(t+3)(t+5)=(t^{2}-9)(t^{2}-25)$$\$$=t^{4}-34t^{2}-72=297$$\If you now move everything to the left hand side and factor like a piece-of-cake quadratic you get $$\Rightarrow(t^{2}-36)(t^{2}+2)=0\Rightarrow t={\pm 6,\pm\sqrt{2}i}$$. Plug this back into $t=z+2$ and all four zeroes appear right in front of your eyes like magic.
light helm
that the sum of roots of
(z-1)(z-3)(z+5)(z+7)=297
will be the same as
||(z-1)(z-3)(z+5)(z+7)=c||
||(z-1)(z-3)(z+5)(z+7)=0||
and the roots of that and subsequently their sum can be determined quite easily
desert solar
z=-8,4,-2+i√2,-2+i√2?
pale frost
You can do it like this too
storm hatch
**如月あやみ Kisaragi Ayami**
basically my solution but you used a harder to see substitution
pale frost
@light helm right?
storm hatch
-8 is the correct answer
you dont have to seek validation from a moderator every step of the process
desert solar
The sol Is -8!!!!
pale frost
Sorry
storm hatch
icic im just wondering why youre being pinged so much here lol
light helm
yes, the sum is -8,
but my point is that this exercise doesn't actually require you to expand everything and/or solve the original equation
pale frost
And how is it done?
light helm
i've already mentioned above
pale frost
that the sum of roots of
(z-1)(z-3)(z+5)(z+7)=297
will be the same as
||(z-1)(z-...
This ?
light helm
yes
light helm
yes
light helm
sum of roots in
P(z) = 0
is -b/a
constant term doesn't affect that
storm hatch
oh yeah, since the zeroes are symmetrical about some C shifting the graph up and down doesn't affect their total sum
makes sense
pearl pondBOT
pale frost
@light helm One last question, but how did you know if you could use viete if you didn't expand first?
light helm
you have a polynomial
timber parrot
crimson bloom
The drawing shows a rectangle 𝐴𝐵𝐶𝐷, in which side 𝐵𝐶 is 4 cm long.
On the sides of the rectangle, points 𝐸 and 𝐹 are marked, and segments 𝐸𝐹 and 𝐹𝐶 are drawn so that two identical triangles 𝐸𝐴𝐹 and 𝐹𝐵𝐶 are created. In both triangles, angles of the same measure 𝛼 are marked. Segment 𝐴𝐸 is 3 cm long.
Calculate the area of rectangle 𝑨𝑩𝑪𝑫. Write down the calculation.
plush bramble
did you try using similar triangles to get an equation for the length of AF or FB
crimson bloom
its impossible to do that if i dont have another side...
@plush bramble
<@&286206848099549185>
plush bramble
its impossible to do that if i dont have another side...
I said an equation not solve for
tall mural
The drawing shows a rectangle 𝐴𝐵𝐶𝐷, in which side 𝐵𝐶 is 4 cm long.
On the...
EAF and FBC are congruent to each other.
crimson bloom
i know..
tall mural
that's all the information you need
crimson bloom
but like i need other sides?
tall mural
what does EAF being congruent to FBC imply?
crimson bloom
i know what it is
tall mural
but like i need other sides?
and you know those two triangles are congruent
crimson bloom
but i need to know what x will be
WHAT am i finding?
i only have 2 sides that are the same
tall mural
but i need to know what x will be
what is the x you're talking abt?
tall mural
since EAF and FBC are congruent to each other, then EA = FB = 3 cm and AF and BC = 4 cm.
tall mural
thse are congruent?
the triangles are congruent
tall mural
so yes EA = FB
crimson bloom
i forgot that i can rotate the triangle
tall mural
so you know BC, you can find AF and BF and AB = AF + BF, then you'll have all the information you need to find the area of ABCD
crimson bloom
then what now?
tall mural
EA / CB = EA / FB
and it should be EA/FB = AF/CB
tall mural
since EAF and FBC are congruent to each other, then EA = FB = 3 cm and AF and BC...
refer back to this
tall mural
so you know BC, you can find AF and BF and AB = AF + BF, then you'll have all th...
and this
jolly parrotBOT
crimson bloom
48 cm^2
tall mural
3 cm / FB = AF / 4 cm
as I've mentioned before, this is unnecessary since you are dealing with congruent triangles and not similar ones
crimson bloom
so its EAF and FBC
tall mural
since EAF and FBC are congruent to each other, you can find FB = EA = 3 cm and AF = BC = 4 cm.
so AF + FB = 7 cm = AB
since you have AB and BC now, you can find the area of ABCD = 28 cm²
tall mural
so its EAF and FBC
yes those two are congruent to each other
jolly parrotBOT
Result:
1.3333333333333
river lodge
What is the expected value for the number of siblings just by looking at this graph?
terse patrol
"The expected value is the mean of the possible values a random variable can take, weighted by the probability of those outcomes."
so sum up $\sum_s P_s * s$
jolly parrotBOT
Adum
river lodge
"The expected value is the mean of the possible values a random variable can tak...
but how would u do it without calculations
just by looking at the graph
would it be the average of 0 and 2 since they are the same
so approx 1
terse patrol
wherever the mean of the distribution falls basically, so yeah 1, but slightly to the right because of the extra 0.03
river lodge
i see, ok
but also, if we were to use calculations, how would it work?
like how exactly do u do "greater than 3"
0(0.36) + 1(0.25) + 2(0.36) + 3(0.03) ... and then?
terse patrol
I would just estimate with 3*0.03 for the tail, but you cant get an exact answer without knowing the full distribution
river lodge
I would just estimate with 3*0.03 for the tail, but you cant get an exact answer...
i see, alright okok
thanks for ur help
.close
pearl pondBOT
pearl pondBOT
Available help channel!
buoyant garnet
One message removed from a suspended account.
pearl pondBOT
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buoyant garnet
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jolly parrotBOT
Kenzo
buoyant garnet
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plush bramble
Missing dr or Delta r
buoyant garnet
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jolly parrotBOT
Kenzo
buoyant garnet
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pearl pondBOT
@buoyant garnet Has your question been resolved?
buoyant garnet
One message removed from a suspended account.
plush bramble
You just need to calculate the two volumes and subtract them
Volume of sphere of radius a = (4π/3) * a^3
versed mica
what riemann said
buoyant garnet
You just need to calculate the two volumes and subtract them
One message removed from a suspended account.
versed mica
🤔
jolly parrotBOT
Kenzo
versed mica
what
plush bramble
I don't know what "did" means
buoyant garnet
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plush bramble
You have to explain your work
versed mica
huh
buoyant garnet
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versed mica
lol
buoyant garnet
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One message removed from a suspended account.
One message removed from a suspended account.
One message removed from a suspended account.
versed mica
🤔
versed mica
brother are you even reading the same question
buoyant garnet
One message removed from a suspended account.
buoyant garnet
brother are you even reading the same question
One message removed from a suspended account.
buoyant garnet
One message removed from a suspended account.
plush bramble
Volume of sphere of radius a = (4π/3) * a^3
This is volume
versed mica
One message removed from a suspended account.
$SA = 4\pi r^2$
jolly parrotBOT
knief
plush bramble
One message removed from a suspended account.
How did you get from volume to this
versed mica
$r = a \to r = a +\Delta r$
buoyant garnet
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jolly parrotBOT
knief
buoyant garnet
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buoyant garnet
**Kenzo**
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One message removed from a suspended account.
versed mica
not the same question at all
buoyant garnet
One message removed from a suspended account.
versed mica
One message removed from a suspended account.
they didn’t even take the derivative
just delta r = 1, since 13-12 =1
buoyant garnet
One message removed from a suspended account.
jolly parrotBOT
knief
buoyant garnet
One message removed from a suspended account.
versed mica
🤔
buoyant garnet
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versed mica
and a sitting out there
buoyant garnet
One message removed from a suspended account.
versed mica
you differentiated V for some reason
buoyant garnet
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One message removed from a suspended account.
One message removed from a suspended account.
versed mica
not yet
buoyant garnet
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versed mica
you don’t?
buoyant garnet
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buoyant garnet
you don’t?
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jolly parrotBOT
Kenzo
buoyant garnet
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plush bramble
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This should be a instead of 10 and Delta r instead of 0.05
Then expand and simplify
buoyant garnet
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plush bramble
Wut
buoyant garnet
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plush bramble
(a+b)^3 = (a^2 + 2ab+b^2) * (a+b)
jolly parrotBOT
Kenzo
plush bramble
(a+b)^3 = (a^2 + 2ab+b^2) * (a+b)
Keep multiplying
buoyant garnet
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jolly parrotBOT
Kenzo
buoyant garnet
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jolly parrotBOT
Kenzo
buoyant garnet
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buoyant garnet
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jolly parrotBOT
Kenzo
buoyant garnet
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plush bramble
Yea just cancel and you're done
buoyant garnet
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buoyant garnet
Yea just cancel and you're done
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jolly parrotBOT
Kenzo
buoyant garnet
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brave sluice
(4/3)pi
buoyant garnet
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buoyant garnet
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buoyant garnet
from here, you could:
factor out (4/3) pi
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brave sluice
i don't know i haven't read the question in detail
buoyant garnet
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brave sluice
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this doesn't mention the values of a and delta r
buoyant garnet
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buoyant garnet
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brave sluice
how does your book describe "linearization"?
buoyant garnet
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brave sluice
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i see this one but i don't understand
buoyant garnet
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brave sluice
ah
buoyant garnet
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brave sluice
but the derivative where? at a=10?
buoyant garnet
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brave sluice
ah
i think i understand
you had taken the derivative of the volume earlier, right?
what did you get
buoyant garnet
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plush bramble
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This is just the linear Delta r approximation
buoyant garnet
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brave sluice
yes
buoyant garnet
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buoyant garnet
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brave sluice
the process seems correct to me
buoyant garnet
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brave sluice
in order to find the value of the derivative at a
wait
that's the answer to the first question
buoyant garnet
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brave sluice
delta r is meant to be small, so whether you plug in a or a+delta r, it should yield approximately the same value for the derivative
buoyant garnet
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brave sluice
in order to find the rise
the derivative is rise / run
so you multiply by the run, which is delta r
buoyant garnet
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brave sluice
you're welcome
buoyant garnet
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pearl pondBOT
pearl pondBOT
Available help channel!
knotty prism
I'm taking AP Calc and we were learning about related rates. I wanted to know if I'm on the right track? I have no clue what I'm doing lol
pearl pondBOT
I'm taking AP Calc and we were learning about related rates. I wanted to know if...
@knotty prism Has your question been resolved?
knotty prism
No it has not yet
warm current
I'm taking AP Calc and we were learning about related rates. I wanted to know if...
How did you get r=h/5? math doesn't seem right there
pearl pondBOT
knotty prism
.reopen
pearl pondBOT
✅
knotty prism
Could u explain what steps I did wrong?
warm current
Could u explain what steps I did wrong?
Well, when h is 20, r should be 5, right? If you say that r=h/5, then i simply ask you what is 20/5?
warm current
With that minor correction, you can now express V as a function of h. Then, to relate their rates, you differentiate both sides of your equation with respect to t
knotty prism
So for volume I got V=1/48(3.14)(h^3)
3.14 would be pi ofc
But im not sure what the nexts steps are, that's where I'm confused
mystic bison
if it makes you feel any better related rates is by far the hardest topic in that class
warm current
(Until you get to integral calculus then have fun)
warm current
Would the next step be like dv/dt = 3/48(3.14)(h^2)?
Very very close
knotty prism
(Until you get to integral calculus then have fun)
Oh heck no😭
warm current
h is a being considered a differentiatiable function of t. You can call it h(t). So for RHS, you need chain rule
knotty prism
Would it look like this?
warm current
Would it look like this?
warm current
For the next step would I move to the other side to set the equation to zero?
You simply need to now solve for dh/dt
knotty prism
You simply need to now solve for dh/dt
Could u explain this step please? I'm not sure what u mean
warm current
Would it look like this?
You have dh/dt as the only unknown in your last equation. It's just algebra now to solve for it