What angle does
#help-27
sudden wyvern
devout snowBOT
What angle does
sudden wyvern
what angle does RNB add up too
lament cradle
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devout snowBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
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spring sundial
devout snowBOT
spring sundial
Can someone please explain how the pigeonhole principle is applied here?
What is the domain and codomain sets in question here?
what are the pigeons
what the holes?
livid geyser
holes are sequences, pigeons are perpendiculars
By plane im guessing it's referring to a grid where the vertices of the grid are colored right?
devout snowBOT
@spring sundial Has your question been resolved?
spring sundial
By plane im guessing it's referring to a grid where the vertices of the grid are...
yeah probbaly
doesn't really specify
spiral harbor
Hello, can someone please check this for me? i worked it out but not sure if im correct
devout snowBOT
Hello, can someone please check this for me? i worked it out but not sure if im ...
spiral harbor
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@spiral harbor Has your question been resolved?
restive river
restive river
Ok
winter torrent
am i tripping or is that fraction the same on top and bottom
rough quail
am i tripping or is that fraction the same on top and bottom
thats what I was thinking
its always supposed to be a constant then if its same
the constant being 1
tall knoll
I imagine the num should be -6.3etc
winter torrent
yeah gotta be
sinful gust
I think they meant to have $9\cdot3^{2x} - 6\cdot3^x + 4$
woven radishBOT
nebula40
devout snowBOT
@restive river Has your question been resolved?
devout snowBOT
devout snowBOT
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sweet tide
what am i missing on exercise part a?
devout snowBOT
what am i missing on exercise part a?
@sweet tide Has your question been resolved?
devout snowBOT
@sweet tide Has your question been resolved?
charred zodiac
what am i missing on exercise part a?
Hello. Maybe they want you to write -½g there instead of +½g
sweet tide
Hello. Maybe they want you to write -½g there instead of +½g
i belive you are correct for the "express the vertical position..." one but i'm asking about exercise part a
charred zodiac
Mmm ok
charred zodiac
Ok let me see
charred zodiac
what am i missing on exercise part a?
They mention that it's thrown horizontally. So initial velocity in y is 0
They ask for the angle when it impacts
With that, you can find the time
Then, find the initial velocity (which is equal to vx)
devout snowBOT
@sweet tide Has your question been resolved?
sweet tide
(will review this in a sec and reply back, busy for a few more mins)
sweet tide
They mention that it's thrown horizontally. So initial velocity in y is 0
thanks, this was my oversight fml, seems so obvious in hindsight
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loud grove
where did i go wrong?
devout snowBOT
where did i go wrong?
long pasture
³√(2a⁶-a³) is not ³√2 a² - a
loud grove
what should it be though
long pasture
oh, it would just be
³√(2a⁶-a³), can't simplify much
you can do
a * ³√(2a³-1) if you want
loud grove
simplest way is to treat it like a quadratic
like this?
ohh its correct
thanks 👍
.close
tired delta
so again I get almost the right answer with something off
devout snowBOT
so again I get almost the right answer with something off
tired delta
simplifies to this
Which then simplifies further
and you can see how that nearly leads to the answer, I just am not sure what method you use to bring the 3 up to the top
when you get a negative exponent in the denominator does that just mean you bring it upwards? Since the 3^-1 would be 1/3 but it's already in the denominator
left pagoda
simplifies to this
You forgot to distribute the -1 to the 3 in the denominator
left pagoda
when you get a negative exponent in the denominator does that just mean you brin...
Yea
tired delta
well I was aware it'd equal to 1/3 so in that attempt I left it as-is
gotcha thanks
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hazy roost
devout snowBOT
hazy roost
I did draw a graph of how it basically looks
but do not know how to answer the questions really
silver fjord
Well it's asking for the last point D which is located at the other end of the second line
You weren't given B but you can solve for it
The fact that you're dealing with midpoints here means you're just doing averages
So your first task is to find B
silver fjord
That's the location of B, yes
Okay. Now you're told that E is the midpoint of B and D
silver fjord
So when you take the average of (-5,1) and (x,y) you get E
which is (-4,-3)
solve for (x,y)
silver fjord
yeah that's what I got too. good job
silver fjord
sure thing
hazy roost
i solved it by doing
x-7/2 =4
and then got -1 as the result
and did
y-6/2
and got 0 as the result
what do you think I did wrong?
silver fjord
good
hazy roost
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devout snowBOT
boreal island
sad
silver fjord
open a thread
boreal island
nah its alr
silver fjord
what's your question
boreal island
couldnt we just ddo Δx and Δy annd add to x_S annd yS
devout snowBOT
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silver fjord
That does the same thing, yeah
devout snowBOT
That does the same thing, yeah
silver fjord
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fallen spindle
Correct?
winter torrent
👍
devout snowBOT
@fallen spindle Has your question been resolved?
bold prism
can this be proved using epsilon delta?
devout snowBOT
can this be proved using epsilon delta?
wheat pawn
yes
sonic smelt
Although it is not suggested to do so
stone stump
well in theory you could plug in all the proofs of all the theorems you use along the way until you get back to eps-delta
stone stump
just because you could do something really doesnt mean you should
spiral gazelle
spiral gazelle
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steel halo
Is there an integer solution to the possible x-solutions to this formula? I get like sqrt(43/3) from using the quadratic formula (before -b/2a). All types of factorization I messed up too. Any advice?
devout snowBOT
Is there an integer solution to the possible x-solutions to this formula? I get ...
silver fjord
I don't think so
steel halo
the exercise is telling me to find the x-intersection points and to plot on a single-decimal based graph
sour dragon
do u know the squaring method
steel halo
to just isolate x^2 and take the square root?
silver fjord
I think she's referring to completing the square
sour dragon
wait nvm i misunderstood the question
devout snowBOT
@steel halo Has your question been resolved?
prime hollow
I think you just got to deal with a non- integer solution
modern bay
Alright so heres the problem I'm having issues with: n amount of hunters are hiding in the woods. All at once they see the closest person next to them and attack them. Ignoring distance and no 2 hunters being the same distance from eachother, what is the minimum and maximum amount of hunters that can survive? For more info n > 2 and is odd.
modern bay
I can show an example if confused.
By the way n is always odd and greater than 2.
they all kill eachother at the same time
There was a third problem which i did solve, where I had to prove that at least 1 hunter would always survive
which I proved by showing that if everyone were to die, it was represeent infinite ascent, since the distance is always different
as distance a<b<c<a which is impossible
devout snowBOT
@modern bay Has your question been resolved?
devout snowBOT
@modern bay Has your question been resolved?
lusty swift
Why would the leading coefficient of this polynomial stay positive, instead of becoming negative when multiplied by -x?
devout snowBOT
Why would the leading coefficient of this polynomial stay positive, instead of b...
lusty swift
I expected to see = -5x^4 -9x^3 .....
livid carbon
You're not multiplying P(x) by -x
P(-x) means put -x in place of x everywhere in the expression
P(-x) = -P(x) iff P(x) is odd
stone stump
-x^4 and (-x)^4 are different
livid carbon
And P(x) is not odd in this case
fringe portal
Sorry for the bad handwriting
devout snowBOT
Sorry for the bad handwriting
fringe portal
But when I use a calaculator
I get a completely different value to the original equation
What have I done wrong
To clarify, my equation that was formed using integration by substitution is not the same as the original
(sorry for the messy work)
devout snowBOT
@fringe portal Has your question been resolved?
supple knot
To clarify, my equation that was formed using integration by substitution is not...
where even is your answer
this?
you didn't substitute back in for x
or you didn't change the bounds to be in terms of u
gotta do one of those
fringe portal
There is no answer because I stopped
fringe portal
or you didn't change the bounds to be in terms of u
I did change bounds tho
supple knot
But when I use a calaculator
you use a calculator
what did you input into the calculator
supple knot
Both of these equations
what are "both"
supple knot
what number did you get for the original integral
fringe portal
My integral that I create using substitution is -340
fringe portal
what number did you get for the original integral
20?
supple knot
My integral that I create using substitution is -340
show this
fringe portal
I just put it in the calaculator
supple knot
I just put it in the calaculator
show it
supple knot
,rotate
woven radishBOT
supple knot
that's because you substituted back in terms of x into the intgrand for some reason
you realize this
does not equal this
supple knot
yea user error
supple knot
It still doesn't help me
fix your mistake
supple knot
you realize this
put this into your calculator
fringe portal
Oh
Gets me 20
Thank you
I don't know why I was so dumb
But thank you very much for your help!
.close
restive river
Hi, I just want to verify my answers, it says:
- Determine the length of the latus rectum of the ellipse:
25x^2 + 169y^2 = 4,225
- Obtain the equation of an ellipse whose center coincides with the center of the circle: x^2 + y^2 – 4x – 10y – 20 = 0 and its foci are at the ends of the horizontal diameter of said circle. The circle is an interior tangent to the ellipse.
devout snowBOT
Hi, I just want to verify my answers, it says:
1. Determine the length of the la...
woven radishBOT
ale.r
restive river
(LR)
devout snowBOT
@restive river Has your question been resolved?
restive river
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fickle ginkgo
I dont understand how we get -5/3 from the second to last step
devout snowBOT
I dont understand how we get -5/3 from the second to last step
arctic temple
where is the question?
supple knot
I dont understand how we get -5/3 from the second to last step
can you put all the relevant details in your channel
devout snowBOT
@fickle ginkgo Has your question been resolved?
fickle ginkgo
devout snowBOT
fickle ginkgo
wouldnt the 16 in the sqrt be positive?
warped relic
Well after you square it yeah
But it is intrinsically negative
Wait
My bad
It is positive
And inside the square root it should also be positive
The -16 inside the square root was probably a typo lol
fickle ginkgo
has the system goofed me
yeah okay lol
so fixing that error, how do I get "-5/3 = x" from the previous equation
warped relic
One of the solutions will give you an error in the original equation
(-16 + 4)/12 = -1
Plug that in $\frac{2}{3x+3} + \frac{x-1}{x+1}$
woven radishBOT
VulcanOne
warped relic
Will be indeterminate
fickle ginkgo
ah ok
warped relic
fickle ginkgo
many thanks
jaunty gazelle
Does anyone understand part b?
tropic fog
(1 -x) - (4 - 3x) = (3 + 2x) - (1-x)
devout snowBOT
(1 -x) - (4 - 3x) = (3 + 2x) - (1-x)
tropic fog
pls help expand
dense jay
start with the LHS, how would you go about it?
tropic fog
left hand side?
dense jay
yeah
dense jay
you could expand all the brackets first if that helped
tropic fog
thats what im asking for
dense jay
(1-x) just stays the same, but what do you think -(4-3x) becomes?
dense jay
not quite, but nearly
tropic fog
4-(-3x)
dense jay
youre forgetting about the 4
tropic fog
(-4)-(-3x)
dense jay
yup
tropic fog
So basically 4+3x
dense jay
-4+3x
dense jay
okie dokie
tropic fog
the next one is uh (3+ 2x)-(-2x)-(-1)
devout snowBOT
tropic fog
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devout snowBOT
✅
dense jay
what step have you gotten to?
tropic fog
Im lost caus for a_3 = 12 which is wrong
x that i found is 4
which is i rhink is wrong
dense jay
a_3?
dense jay
i mean what is a_3?
dense jay
(1 -x) - (4 - 3x) = (3 + 2x) - (1-x)
ah okay so from here i assume you simplified down to -3+2x=2
tropic fog
ah okay so from here i assume you simplified down to -3+2x=2
How does it become -3
dense jay
the constants on the LHS are 1-4=-3
tropic fog
the constants on the LHS are 1-4=-3
is this what you mean
dense jay
yeah, whats that + after the 2 on the RHS though
dense jay
there shouldnt be any x values on the RHS when youve simplified it
tropic fog
no?
dense jay
the RHS is 3+2x-2x-1=2
dense jay
(3+2x)-(2x)-(1)
the rhs is just this simplified, the 2x cancel out
dense jay
i see the issue
dense jay
(1 -x) - (4 - 3x) = (3 + 2x) - (1-x)
this is different from this
tropic fog
OH SHIT
dense jay
was 2x+1 supposed to be 1-x?
tropic fog
We werent on the same page
dense jay
aha, no problem, so the RHS is 3+2x-1+x=2+3x as you said
tropic fog
yes yes
dense jay
-3+2x=2+3x -> -5=x
tropic fog
its -5?
dense jay
yup
tropic fog
so x=5?
dense jay
x=-5
tropic fog
OHH
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Available help channel!
soft stump
op
soft stump
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devout snowBOT
soft stump
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devout snowBOT
✅
soft stump
like how am i meant to solve this
or not solve but
state if there is removable non removable jump/infinte
soft stump
is there an alternative way
autumn pier
or think about what happens as x approaches 2
here
what happens as x approaches 2 from the left?
soft stump
it equals 3
orchid bronze
You could plug in an x value for where you assume they meet and observe the coordinates which is produced.
autumn pier
it equals 3
what about from the right?
soft stump
You could plug in an x value for where you assume they meet and observe the coor...
assume they met?
soft stump
what about from the right?
5
autumn pier
so it approaches 3 from the left, 5 from the right, and at x = -2 the y-value is -1
try visualizing that in your head
what type is that?
soft stump
jump
autumn pier
yep
orchid bronze
Yes
soft stump
adn then uhh how to know removable
soft stump
and how would we know if there is hole, would we have to solve (factor). I assume you can only factor the ones like number 4 then find holes
autumn pier
for number 6 if f(x) approached 3 from the left and 3 from the right then that would be removable
because it approaches the same value from the left and right
soft stump
3 from the leftt?
3 from the right is uh 3^2 +1 =10?
orchid bronze
So do you know what x < 2 fundamentally means?
soft stump
yes
orchid bronze
it is smaller than 2, but not equal to. Which means it gets ever so close to 2 but never gets to it
if we have 2 different equations which approach 2
autumn pier
3 from the leftt?
3 from the right is uh 3^2 +1 =10?
i was talking about the y-values of the function
orchid bronze
but do not touch it, it is removable (i actually don't know what this means I'm assuming based on what has been said)
autumn pier
if f(x) approached y=3 as x approaches 2 from the left and f(x) approached y=3 as x approaches 2 from the right, then it would be removable
but this is a hypothetical
the actual answer to number 6 is jump
soft stump
well yess i see why it is jump
i was wondering if we can determine if removable or non removable
autumn pier
a jump is non-removable
devout snowBOT
@soft stump Has your question been resolved?
soft stump
Ah
I didn't not know that
What makes a jump nom removable, what property.
Is it because there is still a value after it jumps, it's still a function
autumn pier
removable means you can remove the discontinuity by filling in one point (i.e. by removing the hole)
with a jump discontinuity you can't remove it just by filling in one point
autumn pier
yes
devout snowBOT
devout snowBOT
Available help channel!
restive river
Using mathematical induction, prove that for all n e N is valid:
restive river
Im unable to solve this by myself
devout snowBOT
@restive river Has your question been resolved?
devout snowBOT
@restive river Has your question been resolved?
supple knot
Im unable to solve this by myself
!status
devout snowBOT
Im unable to solve this by myself
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
im not stuck bruh i just dont know how to solve it correctly
Here is the work tho
supple knot
where does the left side of this equaiton come from?
restive river
where does the left side of this equaiton come from?
when you put n+1 instead of n
supple knot
when you put n+1 instead of n
not following. does it follow from your previous equation's n?
supple knot
show those steps
restive river
nah bruh I want another helper
supple knot
https://giphy.com/gifs/best-gifs-christmas-80s-1987-yPhqlJccIOaru
i'm trying can't you see
restive river
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devout snowBOT
topaz beacon
Wassup
devout snowBOT
Available help channel!
torpid elbow
which one is slope 3 or 2?
devout snowBOT
which one is slope 3 or 2?
restive river
\dm
[
3(-1) +2 \mathrel{{\c r \ne}} 1
]
woven radishBOT
torpid elbow
what does thid mean
restive river
no
restive river
no
torpid elbow
3 is slope?
restive river
are you calculating the slope or this
torpid elbow
slope
raw knoll
devout snowBOT
@torpid elbow Has your question been resolved?
polar trout
Friend needs help on this question I have no idea, they have no idea
Can someone explain how to do this?
main gull
Friend needs help on this question I have no idea, they have no idea
Can someon...
What's the goal?
polar trout
I think it’s to solve for x
main gull
Is there anything else given for this problem?
main gull
Can you get a picture of everything on that paper?
polar trout
I’ll ask
They’re getting it now, the question doesn’t seem solvable, but I might be wrong
@main gull
main gull
Law of cosines
polar trout
Law of cosines
Could you explain how to do it please, I’ve been told the question is possibly impossible?
polar trout
Have you attempted to solve it like this?
polar trout
Hm
polar trout
That's why I suggested it
When you solve what answer do you get?
main gull
A number
I'm not giving answers
I'm suggesting what should be done, and your friend should try it
polar trout
I'm suggesting what should be done, and your friend should try it
What do you think the line on the left is?
polar trout
Yeah what do you think the question says it is
Like how the others are 2x-1 and x+1
polar trout
You still get an answer
These are the answers they get
main gull
Get them to show their work
polar trout
Get them to show their work
Alright
devout snowBOT
Available help channel!
chrome gulch
hey, i am kinda stuck on this one and i dont know how to proceed to get z
sand dove
you have to write it as a quadratic in z
livid carbon
Bit hard to read, you should cross out the z ig
chrome gulch
you have to write it as a quadratic in z
what do you mean with that??
sand dove
what do you mean with that??
write it as az^2 + bz + c = 0
chrome gulch
Bit hard to read, you should cross out the z ig
my z should be smaller than my 2's
chrome gulch
write it as az^2 + bz + c = 0
do you mean like that?
sand dove
I'm not sure those are the correct coefficients
You should get $(-2-i)z^2+(2i-1)z -6i-12 = 0$
woven radishBOT
rafilou2003
chrome gulch
You should get $(-2-i)z^2+(2i-1)z -6i-12 = 0$
this is what you are looking for, correct?
one typo, its +2i not -2i
in second one
sand dove
yep, other than that it's correct
You remember the method for solving ax^2 + bx + c = 0 where a,b,c are real coefficients?
This one will be similar, but with a few extra steps
chrome gulch
i dont know if thats also same word for english but you mean the pq formula?
sand dove
kind of, yes
Also if you've ever seen the quadratic formula
$x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}$
woven radishBOT
rafilou2003
sand dove
This formula still applies for complex a,b,c, however the "square root" part of the formula is tricky
sand dove
this is what you are looking for, correct?
So first, this is of the form az^2+bz+c = 0
We have to compute b^2 - 4ac in a first part
chrome gulch
i am looking for the formula right now but dont really know where the 4 is from
i only know the whole thing as
x = - (p/2) +- sqrt( (p/2)^(2) - q)
but since i dont have x but (...)x i need to divide it before or use the "4-method"?
sand dove
This is for x^2 + px + q = 0
sand dove
but since i dont have x but (...)x i need to divide it before or use the "4-meth...
yes both are valid
chrome gulch
yes both are valid
is this correct?
sand dove
is this correct?
there is an unnecessary ((2i-1)/2)^2 inside the square root
chrome gulch
ah true its only b^2 and not /2
sand dove
it should just be (2i-1)^2
sand dove
Now, it's about finding the square root of a complex number
try to expand what's inside it and see if you can apply a method
You should find that the thing inside the square root is -75 - 100i
we can factor it as 25(-3 - 4i)
chrome gulch
You should find that the thing inside the square root is -75 - 100i
got to that
whats the reason you go for 25(-3 -4i) and not -25(3+4i) ?
sand dove
whats the reason you go for 25(-3 -4i) and not -25(3+4i) ?
both are valid
chrome gulch
oh okay thought there might be a reason for it 😄
sqrt(25) = 5, so we can get the 5 out ?
sand dove
sqrt(25) = 5, so we can get the 5 out ?
yep
You know the method for finding a number x such that x^2 = -3-4i?
chrome gulch
yea
sand dove
so x^2 = (a^2-b^2) + 2abi = -3 -4i
So ab = -2
and a^2-b^2 = -3
maybe try with values of a and b not greater than 3
chrome gulch
so x^2 = (a^2 - b^2) + 2abi is understandable, but how do you know ab = -2?
sand dove
so x^2 = (a^2 - b^2) + 2abi is understandable, but how do you know ab = -2?
2abi = -4i
identify real part and imaginary part
chrome gulch
yea, re(z) = -3 and im(z) = -4i
chrome gulch
2abi = -4i
2abi = -4i
abi = -2i
ab = -2
?
sand dove
yes
chrome gulch
and how did you get a^2 - b^2 = 3 ?
chrome gulch
i dont understand this so far.
a^2 - b^2 = y
y is something i would not know so far, how did u get y = -3 ?
nvm i got it now
sand dove
a^2 - b^2 - ...i = -3 - ...i
chrome gulch
yea i just got it, i thought we need to calculate it somehow 💀
sand dove
So any idea what a and b would be if they were integers?
Since we have ab=-2, there's not many options...
sand dove
yes
sand dove
correct?
sorry for responding late
-3 - 4i = (1-2i)^2
and so now the toughest part is done
chrome gulch
basically i got 5(1-2i) now?
chrome gulch
sorry for responding late
no worries, i am very thankful that you are helping me for this long time
sand dove
basically i got 5(1-2i) now?
yes the whole square root thing becomes 5(1-2i)
chrome gulch
no worries, i am very thankful that you are helping me for this long time
this helps me understanding complex numbers more for the toughest exam of my university
sand dove
We're left with $\frac{1-2i \pm 5(1-2i)}{-4-2i}$
woven radishBOT
rafilou2003
chrome gulch
Yep, got to (-(2i-1) +- (5-10i)) / -4-2i
chrome gulch
(-4+2i)
sand dove
exactly
chrome gulch
is 20 as new denominator correct ?
sand dove
yes
after a lot of simplification, your two solutions will be able to be written as a complex number with integer coefficients
chrome gulch
sand dove
If you want to check your answers : ||x = 3i or x = -2i||
sand dove
you forgot to multiply the numerator by -4+2i as well
sand dove
oh I meant you forgot from line 1 to line 2 to multiply numerator by (-4+2i)
you changed the denominator to 20 without changing the numerator accordingly
sand dove
yes!
chrome gulch
Whew, Thanks a lot my friend. You helped me very much 🙂
just to let you know, this was just f) of r) lol
but the other ones before were all way way easier
unreal plover
I got x=0.1, but answer is x=11
devout snowBOT
I got x=0.1, but answer is x=11
unreal plover
and this is segment addition, geometry.
please ping me if you can help, i’m going to try and figure out some other problems :)
I got a different answer..
and when combining like terms, terms with variable x resulted to -11x, whereas in my first solvethrough, it was -9x
sick shore
winter patrol
well there's already an issue at the start
you should have
-12 + 2x
NOT -12x + 2x
unreal plover
oh shoot
winter patrol
also splitting up calculations like that isn't ideal, ironically makes it more difficult to see what's happening overall.
it seemed to also have some effect on the sign error that followed.
anyway try restarting from the beginning
winter patrol
show work
unreal plover
winter patrol
you ignored the presence of the -x
unreal plover
crud
winter patrol
also that 18 should've also been present in that line
upon subtracting both sides by 18
leaves you with
2x - x = 11
which simplifies to the answer the teacher gave
winter patrol
that works
unreal plover
also that 18 should've also been present in that line
yeah, i got a little lazy and didn’t add it because i was going to later subtract it but ended up labeling that i subtracted it
it’s hard to explain
unreal plover
noted.
i have 3 more, 2 are quadratic and one is like question eight (the one we just did)
HJ = 6x+198
GJ= x+141
GI= 7x+313
good thing they are all same variable
devout snowBOT
Available help channel!
lavish cypress
Is -5 times x = -5x?
devout snowBOT
Is -5 times x = -5x?
robust dust
yes
lavish cypress
whered i mess up on calculations
devout snowBOT
whered i mess up on calculations
quaint citrus
main gull
It said to do it with long division but I cannot be bothered
There's no remainder
25 - 25 = 0
And with synthetic division, you don't write the x
lavish cypress
oh
lavish cypress
There's no remainder
mane so my answer should be right 
main gull
whered i mess up on calculations
What you typed in here is wrong
main gull
And with synthetic division, you don't write the x
.
main gull
Try it and see
lavish cypress
epic
plucky vale
devout snowBOT
plucky vale
so my approach is taking the cross product, which iss (1,4,3)
then getting a vector perpendicular to that (4,-1,0)
and then using the point (0,0,0) to find an equation
but idk whats wrong
robust dust
where did you get (4,-1,0) from?
(1,4,3) is already perpendicular to the given lines as required
plucky vale
yea
but if i use that to make a plane
wouldnt i get a plane thats perpendicular to (1,4,3)
which would be parallel to the give planes
robust dust
ah I see
could take one of the original lines to be the normal vector, then use a dot product to form simultaneous equations to make it perpendicular to the second
plucky vale
could take one of the original lines to be the normal vector, then use a dot pro...
idk actually i just tried using 1,4,3 to form the line
and it worked
maybe its perpendicular in the right direciton or something
dire forge
are you working in 3 dimensions? if so I don't think it's possible to have a plane that's perpendicular to those two lines at the same time? since they're not parallel
oh wait those are planes, now I'm even more confused 
you can't have a plane that's perpendicular to another plane in 3D so I'm very confused by this question lol
plucky vale
you can't have a plane that's perpendicular to another plane in 3D so I'm very c...
bruh waht
u literally can
robust dust
oh wait
the coefficients give the normal vectors of the two given planes
so the planes are perpendicular to those normal vectors
so when you cross them, and use that to make a plane
plucky vale
oh wait ur right
robust dust
that resultant plane will be perpendicular to the two original planes
plucky vale
i missed that the vectors were perpendicular
dire forge
what's the definition of perpendicular here? the most usual one I know is that every vector in the one plane is perpendicular to every vector in the other plane
plucky vale
thinking in 3 dimensions is challenging
i just gotta get used to it like with 2d
thanks desync
devout snowBOT
@plucky vale Has your question been resolved?
plucky vale
.close
feral sun
can someone please help me understand this
devout snowBOT
can someone please help me understand this
feral sun
i know this wont help to say but im quite lost reading the whole thing
versed vault
So basically you start by
And then
And then finally you
(I have no idea what any of thing means)
feral sun
good try
devout snowBOT
@feral sun Has your question been resolved?
timber pebble
i know this wont help to say but im quite lost reading the whole thing
do you get the idea of the proposition?
feral sun
do you get the idea of the proposition?
i dont get whats inside of the parentheses on the left side
i understand that i belongs to the index set but i dont get what B_i is
timber pebble
i dont get whats inside of the parentheses on the left side
B_i is some set
i believe in this case B would be called a family?
i cant remember the exact language
B is a collection of sets
it can be indexed using I
so B_i is just some set that belongs to B
feral sun
so B_i would just be one set of the collection of sets B
timber pebble
correct
and I is the thing that has elements which allow you to select some B_i from B
feral sun
so we're indexing B with I so that we can specifically take out B_i?
timber pebble
you could think like elements of some B_i are the stuff in some locker, B is a wall of lockers, and I is the numbers on the locker
so if you pick a number, this corresponds with some locker
and lets you get at the stuff inside
timber pebble
so we're indexing B with I so that we can specifically take out B_i?
yea
its helpful i mean
you can think of just some bounded subset of naturals or whatever if its helpful
I could be something like I = { 1, 2, 3, 4, 5 }
and you have B_1, B_2, ...
feral sun
ah ok so we're using I to get any i we want
timber pebble
well I is what you use to index B
We use I to hold like
I holds all the addresses
or maybe its helpful to think of names?
idk what kind of analogy is really helpful
for all of the B_i, there is an element in I that corresponds to the subscript
so you can for sure grab some element idk
some element j from I
and B_j will be sitting there in B
likewise if you pull out some B_k from B, there will be that k in I
well i guess that doesnt have to be true
you could have stuff in B thats not indexed by I
feral sun
so i is a number in I?
timber pebble
its an element, yea
I mean you could have like B = {B_1, B_2, ..., B_10}
and I = {1, 2, 5}
feral sun
but in the case shown above, there is no set numbers right?
timber pebble
in this case $\cup_{i \in I} B = B_1 \cup B_2 \cup B_5$
woven radishBOT
jan Niku
timber pebble
but in the case shown above, there is no set numbers right?
its not important that theyre numbers or whatever, no
its pretty general
I is some set that is used to selects elements from B
(these elements happen to be sets, since B is a family)
timber pebble
idk if its fair to call i being defined
feral sun
B_i is an element?
timber pebble
B_i is an element of B yea
but theyre sets
like elements of a power set are sets
woven radishBOT
jan Niku
timber pebble
feral sun
thats what i was thinking
timber pebble
this is like one of those quiz questions that 50% of the class messes up
so dont take my word for it
feral sun
oh ok
timber pebble
haha
feral sun
i only started learning this stuff for like a week
its my first time with all this set stuff so im just trying to understand lol
feral sun
hmmm
timber pebble
thanks eric
feral sun
what im getting from the proposition is that we have sets I, A and B_i (where i belongs to the set I)
timber pebble
**jan Niku**
think this is right
feral sun
oh ok
timber pebble
what im getting from the proposition is that we have sets I, A and B_i (where i ...
what the proposition is saying is like this
can we use an analogy
feral sun
yes
dire forge
Yo I have come to help
feral sun
i dont mind an analogy
timber pebble
well u can take over if u want
dire forge
this is just saying that intersection distributes over union
feral sun
Yo I have come to help
hello !
timber pebble
im not certain they understand what its saying on a more basic level
dire forge
so for example
[A \cap (B_1 \cup B_2 \cup \dots \cup B_n) = (A\cap B_1) \cup (A\cap B_2) \cup \dots \cup (A\cap B_n)]
timber pebble
they have only had me to explain so u can see the position we are in
woven radishBOT
propERICly_embedded
dire forge
just like how multiplication distributes over addition
[a(b_1+b_2+\dots+b_n) = ab_1+ab_2+\dots+ab_n]
woven radishBOT
propERICly_embedded
feral sun
**propERICly\_embedded**
i get this part
but i dont get what the proposition says at first
let me show
like this part
dire forge
(I have no idea what any of thing means)
Also don't troll the help channels
dire forge
Yeah so let's consider a simple example
Let's say I = {1, 2}
In that case, it's just saying, consider any sets you want named A, B1, and B2
then
[A\cap(B_1 \cup B_2) = (A\cap B_1) \cup (A\cap B_2)]
woven radishBOT
propERICly_embedded
dire forge
does that make sense?
feral sun
yes i understand that but what does B_i and i belongs to I have to do with it
feral sun
**propERICly\_embedded**
because this makes sense to me
dire forge
yes i understand that but what does B_i and i belongs to I have to do with it
I is the index set
it tells you what indices go there
in this example, I = {1, 2}
which tells us that we have B1 and B2 (since it says Bi, i in I)
feral sun
ok so then for me it would be I = {i} and so i have B_i?
dire forge
ok so then for me it would be I = {i} and so i have B_i?
No, I is any set
B_i, i in I means that we have one set B_i for every element i in I
feral sun
oh i see
dire forge
so if I = {1, 2} then we have one set B_1 corresponding to i=1 and one set B_2 corresponding to i=2
feral sun
so wouldnt B_i be an infinite number of sets?
dire forge
so wouldnt B_i be an infinite number of sets?
If I is an infinite set, then you would have infinitely many B_i's
If I is finite (like in the example we just did) then you would have finitely many
feral sun
ok so since I is simply a set then B_i is representing all the sets for all the i's in I?
dire forge
ok so since I is simply a set then B_i is representing all the sets for all the ...
yup
there's one B_i for each i in I
so if I={1,2,...,7} has 7 elements, then there are 7 different sets B1, B2, B3, ..., B7
feral sun
i see ok i think i get it
feral sun
but whats the importance of this all to the proposition?
dire forge
but whats the importance of this all to the proposition?
What do you mean? You have to define the symbols that the proposition uses before you can state the proposition
dire forge
**propERICly\_embedded**
this is a special case of the proposition, but the claim made in the proposition is actually stronger
do you see why?
feral sun
i understand i just mean, why did they have to use B_i and i belongs to I specifically
dire forge
How would you write it without that?
feral sun
do you see why?
i dont
feral sun
**propERICly\_embedded**
like this
dire forge
I only stated it for finitely many B_is
with i ranging from 1 to n
But in fact it works with any number of B's
Which is important because a lot of things in math work for finite things but fail for infinite things
feral sun
lets flipping go