#help-28

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torn jolt
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By hamilton on A^2021

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If I can show the trace of A also is 0

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The problem is done

summer jacinth
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So that would mean $A^2 - trace(A)A = 0$ so either A is the zero vector or the trace of A is zero. Either one would mean the other is also true.

glossy valveBOT
summer jacinth
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well i guess you could have the matrix $\begin{bmatrix} 1 & 0\ 0 & 0\end{bmatrix}$

glossy valveBOT
summer jacinth
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I'm sorry man this has me stumped

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remote nest
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I have this set {1,2,3,4} and the relation from the set R={(4,4),(3,3),(1,4)}
So, the problem is to determine if the relation is symmetric, asymmetric, or antisymmetric.
The answer was antisymmetric which is I understood why but it should also be asymmetric too since (1,4) is an elemnt in the relation but (4,1) is not.

remote nest
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am i missing something?

remote nest
lament rock
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You are correct that the given relation is both antisymmetric and asymmetric. A relation is antisymmetric if it satisfies the property that for all elements a and b in the set, if (a,b) is in the relation, then (b,a) is not in the relation. In this case, the relation contains the pairs (4,4), (3,3), and (1,4), and it does not contain the pair (4,1). Therefore, the relation satisfies the antisymmetry property.

A relation is asymmetric if it satisfies the property that for all elements a and b in the set, if (a,b) is in the relation, then (b,a) is not in the relation, and (a,a) is not in the relation. In this case, the relation contains the pairs (4,4) and (1,4), but it does not contain the pair (4,1), and it does not contain any pairs of the form (a,a). Therefore, the relation also satisfies the asymmetry property.

Therefore, the given relation is both antisymmetric and asymmetric. It is possible for a relation to be both of these types at the same time, because the definitions of antisymmetry and asymmetry are not mutually exclusive.

remote nest
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thank you now my confusion is gone

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torn jolt
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Translation
Make a separate drawing for each question.
6p 4 In parallel projection, draw a tetrahedron with edges of 6 cm.

4p 5 Draw a second tetrahedron at 4 such that all corners of the bases form a regular hexagon.

Due to corona I have lacked a large amount of education, especially at maths, and I have zero clue how to do this. I managed to draw the tetrahedron, but I have no clue how to do the rest. the picture of the tetrahedron I sent is how my teacher told me to draw it, but I cannot find how to connect that with a second tetrahedron it can make a regular hexagon.. help would be dearly appreciated!

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torn jolt
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<@&286206848099549185>

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@torn jolt Has your question been resolved?

torn jolt
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..

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@torn jolt Has your question been resolved?

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@torn jolt Has your question been resolved?

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@torn jolt Has your question been resolved?

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sharp seal
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i feel like im super close to getting this but i just dont know what to do about the 3 under the du

stiff minnow
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Find an equation of the line perpendicular to y=2/3x+5 that passes through the point (7.-10) If possible, write the equation in slope-intercept form.

hollow herald
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or add/subtract... whatever you wanna do

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as long as it doesn't have a relation with the variable you're integrating with respect to(in this case "u")

stiff minnow
sharp seal
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so like could i take the 3 outside the integral like

hollow herald
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yes good job!

sharp seal
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ah ok! thank you!

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slender surge
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hello

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slender surge
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does marginal dependencies work when P[(A & B) ^ C] = P(A & B) x P(C)

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leaden roost
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leaden roost
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Can anyone help me how to figure these?

jade lynx
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hi

leaden roost
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Hello

hollow wharf
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What part are you stuck on?

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@leaden roost Has your question been resolved?

brisk obsidian
leaden roost
brisk obsidian
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One moment, I'm making a graph that will hopefully explain it better.

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Where the graph exists on the x-axis will be the domain.

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And because there is an empty circle at (4,-4), that means x=4 is not inclusive in the domain.

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So the domain exists from [-4, 4) as indicated by the vertical orange lines.

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For 1), to determine the Domain, imagine vertical lines that intersect the x-axis. Where they intersect will be the domain.

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To determine the Range, imagine horizontal lines that intersect the y-axis Where they intersect will be the range.

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native wolf
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“Bill bought 38 1/2 feet of wire fencing to put around his blueberry plants. He cut the wire into several pieces, each one measuring 5 1/2 feet. How many pieces of wire did he have after making the cuts?”

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native wolf
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<@&286206848099549185>

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fresh cypress
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What is the reason of these coefficients in the general formulae for dirichlett regularization of a summation?

fresh cypress
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So, Basically

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I've been trying to find the general formulae for the dirichlett regularizations of various summations

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These are all the formulae

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My question is, where do we derive the coefficients and constants we get here?

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They must have a source from somewhere

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and where do we get these from?

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It would help me out a lot

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thank you

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@fresh cypress Has your question been resolved?

fresh cypress
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<@&286206848099549185> Can one of you help me out perhaps?

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@fresh cypress Has your question been resolved?

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@fresh cypress Has your question been resolved?

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@fresh cypress Has your question been resolved?

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torn jolt
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guys i have an assumption that a matrix that has 2 linear dependent columns already has a determinant of 0 ? am i correct?

fast peak
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yes

torn jolt
# fast peak yes

also here at this matrix which clearly has rank 4 it asks me what dimension does the solution space have?

flint moon
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what is this

fast peak
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or just explicitly calculate the solution space

torn jolt
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i don't even know what that is, i am a cs freshmen

fast peak
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rank(A) + dim(ker(A))=n

potent acorn
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stop hijacking help lobbies

torn jolt
fast peak
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yes

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do you know what ker(A) is?

torn jolt
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no

torn jolt
fast peak
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ker(A) = {x: Ax=0}

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is the solution space of Ax=0

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and the solution space of any system Ax=b always has the same dimension as the kernel ker(A)

torn jolt
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the solution space of Ax=b

fast peak
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if anything that's a solution

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the solution space is a set

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which in this case only contains this vector

torn jolt
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so what do i need to do to get the kernal and the dimension

fast peak
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if a set only contains one vector then it has dimension 0

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otherwise like I said, rank-nullity

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you know rank(A)=4

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and n=4

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so dim(ker(A))=0

torn jolt
fast peak
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yes

torn jolt
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that's it?

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so 10x10 with rank 8 has a dimension of 2?

fast peak
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dimension of solution space, yes

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you can also word it as dim(column space) + dim(solution space) = n

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cause the first part is exactly what the rank is

torn jolt
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ah ok nice thx

fast peak
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surprises me that you don't know that theorem

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super nice theorem

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slender pond
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Can someone help me with question 4c please

wide sundial
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Well since you have a * b = 0

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Either a or b or both = 0

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Does that help?

slender pond
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Not really I think my school taught how to answer this question differently

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I’m supposed to use sin^2X + cos^2X = 0

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Or sinX/cosX= tanX

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But I’m not sure how I can use it to answer this

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Trig identities

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This is what I have done

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idle crow
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I'm trying to solve for all real solutions to the D.E below. I get that the roots of the charistic equaiton are $r = \pm 2i$, which should hten give me that the homogenous solution is $y_h = A\cos(2x)+Bi\sin(2x)$, however, this includes complex solutions as well

glossy valveBOT
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Chippotle Maths

idle crow
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The answer for the homogenous part is $y_h = A\cos(2x)+B\sin(2x)$

glossy valveBOT
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Chippotle Maths

idle crow
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But why?

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It feels like htey just crossed out i from the equation,,,

spice orchid
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because of identities like $\cos (\theta) = \frac{e^{i\theta} + e^{-i\theta}}{2}$

glossy valveBOT
idle crow
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Ahh, ocmpletly forgot about those! I'll try it again with the identities instead of just answering with the standard form

spice orchid
idle crow
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Will read that as well

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Thank you, ΣAC!

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I consulted my textbook as well as the website above. I still do not understand why one can simply do this. In my textbook they did the following manipulation

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Where $B = i(C_1-C_2)$. This means that $B$ is complex unless $C_1 - C_2 = -i$ (its conjugate, think that's the name in English)

glossy valveBOT
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Chippotle Maths

idle crow
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I tried using some of Euler's identities for cos and sine as well but can't really seem how to derive a formula where the answer is $Acos(2x)+Bsin(2x)$ where both $A$ and $B$ are real

glossy valveBOT
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Chippotle Maths

idle crow
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I fully understand the textbook's derivation of the formula... but that formula is only correct when B is complex... or am I mistaken?

idle crow
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ahh now it clicked.... really tired so it didn't even cross my mind that B can be complex with Im(B) = 0, oopsie!

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white willow
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can someone help me understand this question? we never learned this in class at all.

white willow
wild sleet
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like there's a red box and a blue box

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and it asks the proportion of numbers in a box

white willow
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ohhh okkk i c

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ty ty

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signal osprey
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Please don't occupy multiple help channels.

signal osprey
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how do I do these three bc im clueless

atomic blade
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Use your trig identities and then factor

signal osprey
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how

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can u walk me through it

atomic blade
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The easiest one is gonna be number 52

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Take the arccosine of both sides

signal osprey
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if you do them for me ill give you ten bucks

atomic blade
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I'm not doing them for you

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And also 10 bucks only 💀

signal osprey
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twenty?????

atomic blade
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I ain't doing them for you

signal osprey
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bruh

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can you help me i have no idea how arccosines work

atomic blade
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Refer to your unit circle

signal osprey
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idk how triangles work

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what is the unit circle

atomic blade
signal osprey
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so how do i do that

atomic blade
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(cosine, sine)

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Each coordinate point

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Find which points have the x-value of -sqrt(3)/2

signal osprey
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so i just plug each one in

atomic blade
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Well you have to look at the angles each point corresponds

signal osprey
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yes what about them

atomic blade
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That's what the arccosine outputs

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I gtg btw

signal osprey
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no

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dont leave me

atomic blade
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You can google what arc stuff first

signal osprey
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please

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i have no one

atomic blade
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I'll leave you this with:

Google to do to arcsine, arccosine, arctangent

Learn u-sub

Look at your trig identities

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If you excuse me I have to eat

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verbal musk
#

$$T = \Bigg{ \begin{pmatrix} x \ y\z\end{pmatrix} : -y \le x \le y\Bigg} $$

verbal musk
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is this a subspace????

glossy valveBOT
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please request a new nickname

verbal musk
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hint is that T is a cone in R3

outer moth
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Is it not?

verbal musk
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idk man

outer moth
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@verbal musk

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Smartass hahahahah

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I think it is tbh

verbal musk
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i did all the addition and stuff but i cant even visualize it

outer moth
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Wait oh

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Its -y

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Nah there should be subspace

vague kayak
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I will leave determining if scalar multiplication is closed to you

verbal musk
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ahh ok

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-y <= x <= y

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so -ay <= ax <= ay

vague kayak
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Precisely

verbal musk
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alright bet

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and the zero vector is obvious

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minor gazelle
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Need help

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slate zenith
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then ask for it

light sonnet
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• Show your work, and if possible, explain where you are stuck.```
minor gazelle
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Need help

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Juss trying to find out if these are true or not

waxen cloud
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true, true, false

minor gazelle
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Thx

waxen cloud
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well I think so...

minor gazelle
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Boy

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Are you serious right now

waxen cloud
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yeah yeah, you do 400 times 6 hours

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and it equals 2400

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so they will make 2400 bicycles in 6 hours

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gentle smelt
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gentle smelt
#

I could use some help with this

waxen cloud
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6,7543?

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basically, you need to put the numbers in the equation?

gentle smelt
waxen cloud
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so you put E0 which is 10^4,4 at the bottom and E which is 3,4*10^14 at the top

gentle smelt
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If so how did you get it

waxen cloud
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using a calculator

gentle smelt
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Oh that’s simple

waxen cloud
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can you use one or you can't use one for this exercise

gentle smelt
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I don’t have a graphing calculator so it doesn’t give me a similar answer

waxen cloud
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no you don't need a graphic calculator

gentle smelt
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Did you get 67,543

waxen cloud
gentle smelt
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Oh I see

waxen cloud
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yeah?

gentle smelt
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Why did you do 3.4E14

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Is it because 10 is similar to e

waxen cloud
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well E means Exp which is like doing (3,4*10^14)

gentle smelt
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Oh ok

waxen cloud
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its just faster

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but you can use either

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so what would be your answer

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?

gentle smelt
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Ya I figured it

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6.8

waxen cloud
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good job

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torn jolt
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torn jolt
#

doing part a and wondering where I went wrong

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So first

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i got

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$W = 9800\pi r^2 d$

glossy valveBOT
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hibyehibye

torn jolt
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I calculated r to be

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$r = 4-\frac{x}{2}$

glossy valveBOT
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hibyehibye

torn jolt
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so i got

hearty prairie
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no

torn jolt
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$\int_{0}^{8} 9800\pi (4-\frac{x}{2})^2 x dx$

glossy valveBOT
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hibyehibye

torn jolt
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I'm going top down

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could anyone help me see where I went wrong

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I calculated r by doing

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$\frac{4}{8} = \frac{r}{8-x}$

glossy valveBOT
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hibyehibye

torn jolt
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actually

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,w integral from 0 to 8 of 9800pi((4(8-x))/(8))^2x dx

glossy valveBOT
torn jolt
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gives me the correct answer

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so i went wrong simplifying r

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$\frac{4(8-x)}{8} = r$

glossy valveBOT
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hibyehibye

torn jolt
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$\frac{32-4x)}{8} = r$

glossy valveBOT
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hibyehibye

torn jolt
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$4 - \frac{x}{2}= r$

glossy valveBOT
#

hibyehibye

torn jolt
#

huh

#

,w integral from 0 to 8 of 9800pi(4-x/2)^2x dx

glossy valveBOT
torn jolt
#

,w is (4(8-x)/8) = 4-(x/2)

glossy valveBOT
torn jolt
#

wat

torn jolt
torn jolt
#

im actually so lost

#

,w is (4(8-x))/8 = 4-(x/2)

glossy valveBOT
torn jolt
#

,w integral from 0 to 8 of 9800pi((4(8-x))/(8))^2x dx

glossy valveBOT
torn jolt
#

,w integral from 0 to 8 of 9800pi(4-x/2)^2x dx

glossy valveBOT
torn jolt
#

,w expand (4-x/2)^2

#

,w expand ((4(8-x))/(8))^2

torn jolt
#

ok im even more confused now

verbal musk
#

bruh wtf

#

how are they the same but different lol

torn jolt
#

i got 0 clue what im doing wrong

#

imma make new thread

#

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spice pond
#

why is this wrong

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spice pond
#

this is the answer so i assume i missed a 1/2 somewhere but idk where

gritty rose
#

3rd line from top

#

You're missing a factor of 2 from one of the squared substitution identities

spice pond
#

OHHH

#

mb

#

tysm <3

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worthy dock
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worthy dock
#

how to do 17.b)

#

I’ve done this so far

deft zodiac
#

,rcw

glossy valveBOT
deft zodiac
#

hi

worthy dock
#

hi

deft zodiac
#

what dont u get

worthy dock
#

whats the question mean i dont get what to do

deft zodiac
#

,w graph y=x^3

deft zodiac
#

so

#

P moves along that at some rate

#

aka

#

dx/dt=5

#

u want to find

#

dy/dt

#

when x=1

#

for b u wanna find

#

(dy/dx)/dt

#

ok im heading off to buy stuff

worthy dock
#

o

#

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rich mesa
#

How many subsets of {1, 2, . . . , n} have no two successive numbers?

rich mesa
#

Why is the answer n-k+1 above k

indigo ore
#

Well, this is not the answer, k means nothing here

deft zodiac
#

:0

torn jolt
#

;0

topaz valley
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native wolf
#

“Joyce is making cookies. The recipe calls for 1.25 cups of sugar to make one dozen cookies. How many cups of sugar will she need to make three dozen cookies?”

native wolf
#

Then they just give me this, “1.25/3 = x/3”

torn jolt
#

Weird are you sure it's not 1.25 = x/3 or sth

#

Or in that case it means 1.25=x so find 3x=

native wolf
#

My bad.

#

So it’s 1.25/1 = x/3.

torn jolt
#

Yeah

#

Find x and you're done

native wolf
torn jolt
#

You can multiply by 3 each side and it's basically done

deft zodiac
#

amaze

native wolf
#

So 1.25 times 3?

torn jolt
#

Yeah

native wolf
torn jolt
#

Yeah that's the answer i mean it makes sens with your question right

#

She need 3 times more ingredients for 3 times the result

native wolf
#

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crystal leaf
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sacred fog
#

what do you need help with

crystal leaf
#

This

#

Two tasks

#

I don't know how to do them my sis too

sacred fog
#

don't expect us to put more time into helping you than you spent at asking your question

#

"I need help with this" isn't gonna cut it. you have to tell us what part you're struggling with / have trouble understanding for us to be able to help you >.<

crystal leaf
#

I don't know hot to even start this two tasks that why i need help

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@crystal leaf Has your question been resolved?

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@crystal leaf Has your question been resolved?

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slate shell
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onyx glen
#

@slate shell which of these best describes your confusion?

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
slate shell
#

I expanded and got 4x-3xi-y-6yi-3=0

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@slate shell Has your question been resolved?

rocky vale
slate shell
rocky vale
#

and the entire complex number is equal to 0

#

which means the real and imaginary parts are both equal to 0

slate shell
#

so then do I solve both equations simultaneously?

rocky vale
#

That should work

slate shell
#

ok great thanks

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tall tendon
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tall tendon
#

I got 11149 to be the most reasonable but it's wrong

#

I don't know what I am missing since I logically eliminate smaller options

onyx glen
#

,w 20 smallest primes greater than 10000

hollow herald
onyx glen
#

alright so

hollow herald
onyx glen
#

clearly we must have a-b make up the first two digits and a+b the last three

#

or actually maybe it's one and four but that would require c to be at least 11000

#

actually. hm.

#

10xxx is ruled out. bc this way a-b is even (being 10), so a+b is even and c will be even too

#

so that's no good

#

11003 works, doesn't it?

#

a-b=1, a+b=1003

hollow herald
#

11 concatenated with?

#

oh :o makes sense... well, that's that then: 11003

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@tall tendon Has your question been resolved?

tall tendon
hollow herald
tall tendon
#

Oh actually yeah I got it

hollow herald
#

oh, sorry Ann, didn't mean to ping

onyx glen
#

it's fine

tall tendon
#

Thank you

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glacial tiger
#

Hello...

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glacial tiger
#

I need some help on a few math problems.

gritty rose
glacial tiger
fallen bone
#

What does it mean to be an x-intercept?

glacial tiger
#

The x-intercept is where a line crosses the x-axis.

fallen bone
#

Where does the line cross the x-axis in the diagram drawn?

glacial tiger
#

(0,-2)?

#

<@&286206848099549185>

stray schooner
#

You need in the first equation to define x proportionally to y ( you need to have x = ...y)
Then on the second equation you change the value of x with the value that you found earlier and now there is only one unknow so you can solve the equation normally

glacial tiger
#

But x proportionally to y is going to be x/2 - 7, right?

stray schooner
#

I don't quite understand where you get x/2 -7 but what I'll do is
x + 2y = 7
x = 7 -2y

glacial tiger
#

Oh, yeah. Sorry, I divided by 2 then subtracted by 7.

#

So, now we know that x = 7 - 2y, how would we find the second equation?

stray schooner
#

Now you change the value of x with what you just found so with the example you will get:
2(7-2y) + 2y = 13
Then you just solve the equation

glacial tiger
#

Oh, ok. Though I do have another question before I close this...

#

How do you become a helper?

stray schooner
#

I don't exactly remember exactly where it is but in the first salon ( in the introduction category) there is somewhere a bot that let you chose what role do you want

#

And you can choose helper

glacial tiger
#

Thanks!

#

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glacial tiger
#

.reopen

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glacial tiger
#

Does anyone helper know when you get tagged?

#

nevermind

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errant lion
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torn jolt
#

integral of sin^3(x) cos^2(x)

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torn jolt
#

how would I integrate this?

#

i got it 🙂

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finite bluff
#

anyone familiar with inertia moments

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#

Please don't occupy multiple help channels.

finite bluff
#

Ixx?

errant lion
#

hello

errant lion
finite bluff
#

hi

#

so Ixx is this

#

right

errant lion
#

let me check

finite bluff
#

so for this

errant lion
finite bluff
#

im asked to find Ixx for each section

#

so Ab and EF have no y or z

#

so its Ixx is zero

errant lion
#

yep

finite bluff
#

for Bc and DE

#

integral is this

errant lion
#

yeah

#

and then CD

finite bluff
#

im confused by

errant lion
#

what?

finite bluff
#

as y remains constant

errant lion
#

true

finite bluff
#

answer says its 0.015

#

any clue

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@finite bluff Has your question been resolved?

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old sapphire
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old sapphire
#

im trying to find the sum using this table

#

it looks like e^x where x=5 but i dont know how to account for the (n+1)! if that was the case

stable heart
#

you can change it to $\sum_{n=1}^\infty\frac{5^n}{n!}$ and adding the first term

glossy valveBOT
#

Duh Hello

stable heart
#

or, subtracting it in this case

#

$\sum_{n=1}^\infty\frac{5^n}{n!}=\sum_{n=0}^\infty\frac{5^n}{n!}-\frac{5^0}{0!}$

glossy valveBOT
#

Duh Hello

old sapphire
#

so that would be e^5-1?

stable heart
#

yea

old sapphire
#

thanks dude

#

i tried something like that but got 5e^5-1

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hollow badger
#

Hey

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hollow badger
#

Go ahead lol

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dense arrow
#

i was wrong because i said this does not have a hole, how does this have a hole at (0, 15/2) if there is no same term at the numeriator and denominator?

dense arrow
#

;close

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fathom terrace
#

Did I draw #30 correctly?

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tight glen
#

which one?

#

ohh

glossy valveBOT
tight glen
#

not to scale so sure

#

its good

wise knot
#

Need help

tight glen
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@fathom terrace Has your question been resolved?

fathom terrace
#

Like does it need to be cut by a diagonal r smth

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hot mango
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hot mango
#

whatttttttttttttt

#

im going insane

brisk obsidian
#

Are you using a website?

#

It's possible you may have exceeded the required precision.

light sonnet
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@hot mango Has your question been resolved?

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verbal silo
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@verbal silo Has your question been resolved?

verbal silo
#

<@&286206848099549185>

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@verbal silo Has your question been resolved?

dense jungle
# verbal silo

Ok so in essence your question is saying you've got a bottle of x percentage wine and y percentage wine how can we get to z percentage wine

#

As long as z is between x and y it's reasonable that this is possible

#

So let's set the values to something simple

#

We've got 0% and 100%, how many litres of each to get to 50%?

verbal silo
#

500ML !!!!

dense jungle
#

Ok now how did you get there

verbal silo
#

i don't understnad how to really set up the algebra for it

dense jungle
#

I'll give you a hint, you used the average when you just found that value

#

Can you think of how to write that in terms of x y and z in the example i just gave you?

verbal silo
#

don't know

dense jungle
#

So you've got 0% and 100%

#

Let's assume we use one part of each

#

The formula for an average is the sum of your values divided by the total amount of values

#

When you got 50% you essentially did 0 + 100 / 2

verbal silo
#

yes?

dense jungle
#

So now let's say we mix 2 parts 100% and 1 part 0%

verbal silo
#

maybe x+y/2 = z?

dense jungle
#

But you usually don't have equal parts

dense jungle
verbal silo
#

50%

dense jungle
#

Imagine you are mixing paint

#

If you are mixing white and black 2 parts white 1 part black will be lighter than 1 part white 2 parts black

verbal silo
#

mhm

dense jungle
#

So the proportion when you are mixing matters

#

Do you have a different answer to the percentage of 2 parts 100% and 1 part 0% mixture now?

verbal silo
#

ohh 66%?

dense jungle
#

Yes

#

Can you write out the equation to get to 66?

verbal silo
#

100 + 100 +0 / 3 = 66?

dense jungle
#

Yes

#

Ok now let's say i have 75% solution, how many parts 0% and how many parts 100% do i need to get there?

verbal silo
#

4 parts 100% 1 part 0

#

3 parts 100% one part 0%

dense jungle
verbal silo
#

let y=0%, x=100% , z = 75%
3x + y / 2 = z?

dense jungle
#

Yes, now that you understand the problem I'll explain what your teacher wants you to be doing

#

You set the sum of solution 1 and solution 2 to the total amount of liquid

#

And then make a second equation involving the percentages

#

And solve because you've got two equations now

#

Make sure you don't rely too hard on formulas though, a strong intuition is far more useful than being able to spew xs and ys

verbal silo
#

yeah sorry still don't have a clue

#

all i've tried so far is
Wine = x, Water = y

A=2xy

#

B=5yx

dense jungle
#

X and y are the liquid volume from each bottle

#

Not distinguishing between water and wine

#

Set up your equations to be something like this
%1 X + %2Y = %3V
X + Y = V

verbal silo
#

i'm confuse

#

d

#

am i supposed to aim for simultaneous equations

verbal silo
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verbal silo
#

.close

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sinful raven
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sinful raven
#

using ln integration

#

calc chat just teleports and idk what happened

hollow herald
#

so? what's the issue?

sinful raven
#

im not sure how they get from step 2 to 3

hollow herald
#

you don't know the integral for cosec x?

sinful raven
#

oh thats how they got there

woven snow
sinful raven
#

alr thank you forgot about those lol

hollow herald
#

the 4th one is particularly sketchy

sinful raven
#

.close

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woven snow
severe basin
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torn jolt
#

Hello i need help out the steps to solve the sqrt(a^6) * sqrt (a^6)

shrewd cargo
#

√(a÷6) × (√a÷6) right?

spice orchid
torn jolt
#

No it is sqrt of a^6

#

times sqrt of a^6

shrewd cargo
#

Idk

torn jolt
#

can you help out with the steps to follow inorder to find out the solution

shrewd cargo
#

It's just a a^6

#

Unless I'm missing something

#

When you times a square root by it's self you just get rid of the square root

torn jolt
#

i know the answer is sqrt a^6 but what idk is the steps on how we get the answer

shrewd cargo
#

What's √4?

torn jolt
#

2

shrewd cargo
#

What's 2 × 2?

torn jolt
#

4

shrewd cargo
#

The square root of something is finding out what needs to be times together to find the number

#

So √(a^6) × √(a^6) is just a**6

torn jolt
#

I understand that but how do we solv a question like this for example: sqrt (a^6) * sqrt (a^4)

shrewd cargo
#

You're not doing imaginary numbers right?

torn jolt
#

yeah, what i need is just method that is used to solve questions like these

shrewd cargo
#

The answer is a**5

#

Just halve both powers and add them together

#

Since when you times you add the powers

#

And when you square root you'll divide the power by 2

torn jolt
shrewd cargo
#

What's halve of 6?

#

√(a^6) = (a^3)

#

√(a^4) = (a^2)

#

a^3 × a^2 = a^5

torn jolt
torn jolt
shrewd cargo
#

Yeah

torn jolt
#

thanks for helping out

#

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acoustic pebble
#

Helo

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acoustic pebble
#

Does the diagonals of an isosceled trapezium bisect each other?

#

Bruh

tardy verge
#

Stop asking help in multiple channels

#

Please stick to only one channel

#

Thank you

onyx glen
#

(in fact they only do that if your trapezoid is a rectangle, or so it appears to me at first glance.

acoustic pebble
#

Ok

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mighty torrent
#

Denominator you have -(x²+y²)

#

and numerator you have (x²+y²)²

valid stump
#

it's all about being able to spot these things isn't it

#

I'll practice more, thank you

#

I won't close this just yet, I still want to solve it

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thanks

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vernal haven
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torn jolt
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torn jolt
#

we're asked to solve for theta

#

I got 31.4

#

wouldn't there be a second solution of 148.6?

#

on the ans key though they say only 31.4 degrees

#

why is 148.6 not a second solution? It's under 180 degrees

calm kite
#

Bro 148.6 + 38 is more than 180

#

Show your working, I'm not professional but probably i can help

torn jolt
#

how did you get 38

#

it's 31.4

calm kite
#

It's given in ques that one angle is 38, so if you take any other angle as 148.6 then it's not possible to make triangle

torn jolt
#

ohhh I c my mistake

#

thank you admiral 🫡

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thick phoenix
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thick phoenix
#

Hi i am unsure on how to do this question

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thick phoenix
#

<@&286206848099549185>

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gritty rose
#

wtf

#

khan has videos on almost all of these. a single help channel can't teach you a whole month's+ worth of knowledge

#

pick one topic at a time to learn and add "khan academy" to your search topic

#

past month

#

help channels are meant for specific problems, typically exercises from books

#

you either need a tutor or just be disciplined enough to watch khan academy videos of all your subjects

eternal quiver
#

depends on your skill, but yeah overnight study doesnt work for mathematics

torn jolt
#

Your time has come

#

Explain one month of study content in a day

#

I believe in you champ

gritty rose
eternal quiver
#

nevermind math students are usually broke

gritty rose
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void arch
#

I’m not really understanding the idea of continuity of the probability measure

void arch
#

In the proof they considered increasing and decreasing sets to be A?

#

But how do you know there exists these montonical sets to become A?

spice orchid
#

What's the statement of the theorem

#

Or the statement of continuity

void arch
#

My bad, I didn’t even read the theorem that we’re trying to prove

spice orchid
#

Lmao

void arch
#

I mean now it makes sense

spice orchid
#

Yeah reading everything usually helps things make sense lol

void arch
#

Why is right continuity analogous with monotonically non-increasing sets?

#

Actually I think I do see it now I think? it’s coming from the right since the nested sets are x1=>x2=>…?

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random pollen
#

More of a techy question about Maple:
I have a 4000*2 matrix, left row represents years, right row represents something else irrelevant. Important thing is that each year appears many times.

How do I extract all values in the right row that correspond with a certain year in the left row?

I'm on Maple BTW

random pollen
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limber flicker
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limber flicker
#

Not sure how I should go about proving this

#

I have a goal of |u| = |v|

hollow herald
#

first write down what it means for the two vectors to be orthogonal

#

then wonder how you can come to |u| = |v|

limber flicker
#

all of this is just nonsense

#

but the middle bit

hollow herald
#

???

#

why the cos theta?

limber flicker
#

should it not be there

hollow herald
#

You'll only have: (u + v) . (u - v) = 0

#

=> u² = v²

limber flicker
#

oh ok I see

#

lemme do full working to make sure

gritty rose
limber flicker
#

yeah

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ok

#

makes sense

#

ty

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restive hawk
#

could someone explain to me how i do these kinds of questions?

restive hawk
#

as far i as know it has to do with limits

#

but other than that im not sure

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dense edge
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dense edge
#

Is this second line I highlighted correct?

sharp vine
#

no

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untold gulch
#

Hi

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untold gulch
#

Im stuck on part (ii) of this question
I found from (i) the mean = 38.19
variance = 668.9139
sd = 25.86
how would i approach each department/the question itself?

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waxen cloud
#

For the question 3) a) i), I need to develop with the MAClaurin method but I don’t understand why the last term has the exponent 2n +1 and is at the bottom (2nd photo bottom right)

waxen cloud
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quasi dust
#

I have 2 values, Value A, and Value B, both worth the exact same.

I have 3000 of value A, and 4500 of Value B. I have to split these 2 values with a group of 8 people, with each person having different preferences as to what value they'd like to receive, as well as each person getting a different cut (as in, % of the values combined, so 7500). Value B can be turned into Value A at the same rate, but, Value A can't be turned into Value B.

How do I make a formula or equation (for repeat use with different cuts, preferences and total A/B values) to split this as fairly as possible based on each persons' preferences, while making everyone as happy as possible?

Sorry if this is a mess, I can elaborate on anything if needed.

Example;
Person 1 gets a 20% cut (1500 total value), and prefers Value B
Person 2 gets a 10% cut (750 total value), and prefers Value A
Person 3 gets a 5% cut (375 total value), and prefers Value A
Person 4 gets a 5% cut (375 total value), and prefers Value B
Person 5 gets a 10% cut (750 total value), and prefers Value B
Person 6 gets a 15% cut (1125 total value), and prefers Value A
Person 7 gets a 15% cut (1125 total value), and prefers Value B
Person 8 gets a 20% cut (1500 total value), and prefers Value B

People would still be content/satisfied if all of Value B is distributed, and the "owed" amount given in Value A, but only if the people who want Value A get their fair cut.

Important: People who prefer Value A are unable to receive Value B.

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@quasi dust Has your question been resolved?

quasi dust
#

<@&286206848099549185> melody_wave

wicked condor
#

then just distrubute the rest blindly

quasi dust
wicked condor
#

like for the rest it doesnt matter if you know its A or B

#

wait what if

#

the people want like

#

not all the A

#

what if the total preffered for A is less than 3000

#

what do you do with the extra A

wicked condor
#

if you have value B, cant you just make it value A and give it to them

quasi dust
#

I think I made a giant oversight thank you lmao

#

!close

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marsh ibex
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marsh ibex
#

My final points should be right

#

but they dont align on desmos

#

they are sligtly off

#

did i do something wrong at the start ?

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honest bane
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honest bane
#

I'm having a little trouble understanding the concept of a proper divisor of 0

#

so from Z5 if i take a = 3 and b = 1

deft zodiac
#

if there are any 0s

#

ignoring those in the row/columns of 0

vague kayak
#

So 2≠(congruent)≠ 0mod4 but 2•2=0mod4

honest bane
deft zodiac
#

💕

honest bane
#

than just trying everything in Z5 to see if there's a proper divisor

deft zodiac
#

well

#

generally for some

#

Z/nZ

#

if n is prime theres no 0 divisors

#

if n is composite there is

honest bane
#

ahhh i see i see

#

does this tie in into finding inverses

deft zodiac
#

of what

honest bane
#

oh like inverse of 11 mod 47

deft zodiac
#

er idk im lost

honest bane
#

if the two of them are relatively prim then there's an inverse ?

deft zodiac
#

sry

honest bane
#

oh i think it's unrelated

#

i've just been doing over modular arithmetic

#

but thank you i get the residue tables

deft zodiac
#

yayy

#

💕

honest bane
#

Have a good one man

#

appreciate it

#

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echo gale
#

Hey, I’m not sure where to go from this

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echo gale
#

Do I use the quadratic formula?

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vivid aurora
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vivid aurora
#

its easy

#

take x+2 and divide the cubic with it

#

cubic equation with it

#

you will get the quadratic eq

#

solve it using factorisation

#

you will get roots

#

if you wanna know solution dm me

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.reopen

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torn jolt
#

If f(x) = p(x)+q, where p and q are integers ,
f(-1) = 5, and f(3) = 3 then p and q are equal to :

torn jolt
#

is the answer -0.5 and 4.5?

vast fossil
#

I got 2 and 7

onyx glen
#

@torn jolt well -0.5 and 4.5 aren't integers, so

#

probably not

#

unless it so happens that the problem itself is fucked up

#

which it may well be

#

ok yeah like. are you sure you copied the problem correctly?

#

p = -1/2 and q = 9/2 does match up with the problem data, except that these numbers are not integers so the "p and q are integers" stipulation is violated

onyx glen
#

ok then the problem is screwed up.

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sacred sequoia
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sacred sequoia
#

how am i supposed to answer this

#

what lesson even is this

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sacred sequoia
#

pls help

torn jolt
#

<@&286206848099549185>

forest widget
#

it's just ratios i guess

how many degrees are there in a circle

and what proportion of people selected tennis

sacred sequoia
#

360..

#

1...

#

I can't solve it

#

oH

#

0.025X 660

#

360*