And what the other person was saying, put a snake on a plane and it can indeed fly
#help-0
tribal lion
moving or able to move through the air with wings.
"a flying ant"
Similar:
airborne
in the air
in flight
fluttering
flitting
flapping
hovering
floating
gliding
windborne
soaring
winging
wheeling
winged
volitant
noun
flight, especially in an aircraft.
"she hates flying"
So true. But they are still flying
strange schooner
The question is exactly the same, is the claim:“all real numbers N such that N>7.349 round up to 7.34“ right?, Or, alternatively, a more evidently false claim:“all real numbers N such that N>7.349 are greater than or equal to 7.35“ true?
tribal lion
All snakes aren't cable of flying themselves but they can fly
It is the same with numbers, by them selves they can't do much but when matched with another one they can rise high
Its same in human physiology, we tend to be better when we have someone we can lean on
In conclusion Leila is on something
honest cairn
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coral stone
hello sorry it's me again
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hello sorry it's me again
wary fable
whats that notation?
coral stone
wary fable
huh?
coral stone
and m* is the outer measure
what?
sooo
@mortal trellis @paper mango can you help me pls
hiii
paper mango
<@132304137583984641> <@1000186270078750740> can you help me pls
sry will be absent in a sec
but state where you are stuck for passengers
coral stone
but state where you are stuck for passengers
im stuck from the beginning
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coral stone
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strange schooner
<@&286206848099549185>
Most people here(me included) probably don't know enough about measure theory to help you,so, worst case scenario
Someone in #real-complex-analysis or #advanced-analysis (since there's no channel for measure theory per se) might be able to
coral stone
ok thank you
quick karma
so, this is a measure on some space $X$ and youre defining $m_(S) = m^(X) -m^*(S^c)$, yeah
ocean sealBOT
kugelblitz
quick karma
you should have <= easily
coral stone
hooww
this is my definition
so m*(I\S)
instead of m(U) it's l(U) because we assume I is an interval
quick karma
wait i typed that wrong
although you need I to have finite measure
oh hold up i think i did it wrong again
i think you can just show that
quick karma
this expression is just the lebesgue outer measure
coral stone
u mean this one?
mighty kelp
think of it as just an abbreviation, but either way they both mean the same thing
quick karma
ie, $m^(S) = \sup {m^(K) \colon K \subseteq S, K \text{ compact}}$
ocean sealBOT
kugelblitz
coral stone
think of it as just an abbreviation, but either way they both mean the same thin...
what?
mighty kelp
the inner measure is the outer measure?
wait wdym
quick karma
the inner measure is the outer measure?
if S is lebesgue measurable they are equal
which is what you have to show, basically
do you know that $m^(S) = \inf {m^(U) \colon S \subseteq U, U \text{ open}}$?
ocean sealBOT
kugelblitz
quick karma
if S is measurable
coral stone
do you know that $m^*(S) = \inf \{m^*(U) \colon S \subseteq U, U \text{ open}\}$...
yes i ve seen this definition
quick karma
now, the monotonicity of $m$ means that $m(S) \ge \sup {m(K)}$, yeah
ocean sealBOT
kugelblitz
quick karma
so you have to prove the reverse
coral stone
now, the monotonicity of $m$ means that $m(S) \ge \sup \{m(K)\}$, yeah
what is K?
quick karma
so we'll assume S is bounded, and then take some closed set $C$ around it, then use the above to find some open $U$ so $C\backslash S \subseteq U$ and $m(U) \le m(C\backslash S) + \varepsilon$
ocean sealBOT
kugelblitz
quick karma
what is K?
compact subset
coral stone
wait, i also know that if K compact subset of I, then m*(K) + m*(I\K) = l(I). Can we use that?
wait wait im going to rewrite it
so basically
quick karma
**kugelblitz**
then take $K = C\backslash U$, and note that $C = K \cup U$, and then do some rearranging to get $m(S) - \varepsilon < m(K)$
ocean sealBOT
kugelblitz
quick karma
wait, i also know that if K compact subset of I, then m*(K) + m*(I\K) = l(I). Ca...
$K \subseteq S$ here
ocean sealBOT
kugelblitz
quick karma
you might want to draw a picture
basically were trying to find compact K so m(K) >= m(S) - eps
to get the reverse ineq
we want to show that $m(S) \le \sup {m(K), K \subseteq S, K \text{ compact}}$, by monotonicity the other inequality is trivial
ocean sealBOT
kugelblitz
coral stone
coral stone
then take $K = C\backslash U$, and note that $C = K \cup U$, and then do some re...
ok
quick karma
you probably want to draw a picture
take S, draw a closed box around it (C), take some open set U which contains C\S, and is barely larger than C\S, and then take K = C\U
thats compact, since its closed and bounded, and K is included in S
and you end up w/ $m(C) = m(K) + m(U) \le m(K) + m(C\backslash S) + \epsilon = m(K) + m(C) - m(S) + \epsilon$, so $m(S) - \epsilon \le m(K)$
ocean sealBOT
kugelblitz
quick karma
then you have shown that this inner measure agrees with the outer measure so if S is measurable then m(I) = m(S) + m(S^c), of course
coral stone
yes i think i kinda see it but just thought maybe we coule immediately take the equality and rewite inf{m*(U) ....} as -sup{-m*(U)...} and then we're gonna have sup{l(I) - m*(U)... } and l(I) - m*(U) is like m(I\U) which xould be m(K) since U is open... but yeah i understand thank you 👍
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coral zephyr
this is a multiplication problem so the inverse is division but im not understanding what to divid to get 0
lone heartBOT
this is a multiplication problem so the inverse is division but im not understan...
coral zephyr
its just 0 right?
reef wren
yep
coral zephyr
Thanks sorry I needed to know if my thought process is correct
I dont want to just guess I wanna know why I got the answer
reef wren
$\frac{0}{n}=0$
ocean sealBOT
yoboiqimmah
reef wren
where n is any number
coral zephyr
Sorry can you dumb that down
are you saying when something = 0 in a division problem its always 0
reef wren
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crystal zinc
I’m trying to better word why the theta would be -pi/2 but I’m having difficulty any advice?
crystal zinc
reef wren
I’m trying to better word why the theta would be -pi/2 but I’m having difficulty...
because cos(-pi/2)+isin(-pi/2)=0+i(-1)=-i
if that's what you are looking for
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coarse elm
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coarse elm
Can someone check my work
my teacher doesnt have an answer key for this specific question sooo
i just wanna make sure its right
zinc haven
looks good
crude sage
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tardy stag
hi this isn't really something that anyone's going to be willing to do
it takes quite a bit of time. are you fairly sure you got them and just want a check, or were you largely guessing?
crude sage
it takes quite a bit of time. are you fairly sure you got them and just want a c...
im sure I got them
lone heartBOT
im sure I got them
crude sage
i just want a check for the district 1 if i did it correctly
the weight is kg (at death) right?
the instructions are clear, they were looking for the mean, median, and mode for the age and weight
i just want to know if i did it correctly
i calculated it the age and kg (at death)
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trim garnet
I need help to make like graph for this question: A plane flies southeast at a constant speed of 900 km/h. The wind is blowing north at 100 km/h. Determine the resulting velocity vector of the plane relative to the ground. To be able to draw it
trim garnet
this is what I have so far
broken pivot
this is what I have so far
use tip-to-tail to draw another velocity vector that points 100 km/h north
trim garnet
after that would I make it into like a triangle?
broken pivot
after that would I make it into like a triangle?
i actually recommend drawing the triangle for just the plane before you start with the wind
trim garnet
like this?
broken pivot
like this?
yes, i also recommend erasing the the hypotenuse of your plane's velocity vector (and keep only the resultant velocity)
if you dont want to, thats fine
calculate the legs of the right triangle
then modify one of the legs based on the 100km/h
calculate the new hypotenuse
trim garnet
okay I’m going to try that
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trim garnet
I got it right tysmmmm @broken pivot
runic ibex
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woven moon
What have you tried so far?
woven moon
This is quite a tough one
What I would say is let the angle EAF be x
Then try and calculate that
silk zealot
Could someone explain how to do these?
lone heartBOT
Could someone explain how to do these?
crimson dawn
Could someone explain how to do these?
Have you learnt about the four quadrants in class
twin comet
Oooo
crimson dawn
Hallo
twin comet
I would like to help
silk zealot
Not yet, this is like a preview worksheet
silk zealot
yeah
crimson dawn
So for acute angles, is sine positive or negative
twin comet
eww don't learn the unit circle, that's cringe, there's like 16 things to memorize
crimson dawn
I don't mean the one with all the special angles
I just mean the bare unit circle
So we have our unit circle
For angles in the first two quadrants sine is positive
For angles in the last two quadrants sine is negative
Now we have to talk about reference angles
Have you heard of reference angles
silk zealot
nope 😭
silk zealot
i dont think so
we js started the unit yesterday so theres a bunch of stuff i probably dont know
twin comet
I would approach it like this
for the first problem
I just remember the 30,60,90 triangle and its sides
twin comet
memorize the shape like how u know the shape of a square
remember that sine = opposite / hypotenuse
and remember that (hypotenuse is always positive)
(why, idk just go with it, its just how i do it)
so that means that the opposite side is negative sqrt(3)
then draw the literal triangle in ur xy grid
label all the angles that u can see, since u already know all the angles of the 30,60,90 triangle and u know that a straight line is 180 deg
crimson dawn
You also have one more solution
twin comet
i know
twin comet
i know, i didnt draw it yet
ye
like he said u could also draw another triangle that has an opposite side of negative sqrt(3)
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kind notch
Hello, I have a combinatorics related question. Given are m marbles of which r are red and b are blue, with r > b and r + b = m. The experiment states that we draw a single marble at a time without putting it back into the urn. I would like to verify the following results I got for the following questions:
a) How many possible draws are there, when m marbles are drawn?
b) How many of those draws start with a blue marble?
c) How many draws starting with a red marble are there, such that there is a temporary equality in the colors of the drawn marbles?
For a) I got m! because I am drawing in a sorted manner without putting back a marble once drawn. I am not sure if this is correct because the red and blue marbles themselves are not distinguishable, so (r_1,r_2,r_3,b_1,b_2) and (r_1,r_3,r_2,b_1,b_2) would be the same permutation for example.
For b) my answer was (m-1)!, simply because I have one less marble to choose from. I also didn't think of the non-distinguishable marbles here.
For c) My answer was the sum of (m-2i)! over i = 1 to b. My reasoning here was, that if I start with a red marble, I just choose a blue marble, so I have 2 marbles less than before. If I start with two red marbles, I need to choose two blue marbles and have 4 marbles less and so on and so on.
lone heartBOT
Hello, I have a combinatorics related question. Given are `m` marbles of which `...
@kind notch Has your question been resolved?
kind notch
<@&286206848099549185>
somber crest
Hello, I have a combinatorics related question. Given are `m` marbles of which `...
you are right to be suspicious, (a) is incorrect, as it overcounts
by exactly what you had already said
kind notch
Perhaps I should interpret the permutations as a tuple of ones and zeros then I guess that would make it easier to think about it
somber crest
sounds fine, sure
it is salvageable, though
say you pick a permutation of the m (pretend-distinct) marbles
how many permutations are equivalent (under the all-reds-are-same, all-blues-are-same relation) to the one you picked?
kind notch
The permutations of red are r! and the permutations of blue are b! so r! + b! I think?
somber crest
you're close; the permuting of red and blue marbles are independent of each other, so these counts multiply
it's r!b! therefore
kind notch
Oh and if I divide m! by r! * b! I get the right number?
somber crest
yes; you divide out all the extra permutations that are the same
kind notch
because that would take out all the unwanted permutations if I am not wrong
somber crest
it specifically works because the number of equivalent permutations is the same for each permutation you stumble upon
kind notch
Ok then b) is also wrong and should be (m-1)!/((r-1)!b!)
somber crest
another way to find the same answer, if you like binomial coefficients / the choose function: of the m slots, you pick r of them to be red, in which case the placement of the blues is forced
this yields (m choose r)
kind notch
because i am applying the same logic but only for one less red marble
somber crest
which is equivalently m! / r!(m-r)! = m! / r!b!
kind notch
which is equivalently m! / r!(m-r)! = m! / r!b!
Oh thats nice
somber crest
Ok then b) is also wrong and should be `(m-1)!/((r-1)!b!)`
I agree, nice
kind notch
I also think my logic in c) is correct but the math is wrong so here it should be (m-2i)!/(r-i)!(b-i)! for i = 1 to b
but its not quite correct
no that doesn't imply that the sequence I drew my marbles in starts with a red marble
somber crest
yeah, it feels tricky
you also want to avoid overcounting
I think I got it, by considering the number of extra reds
no, nevermind
maybe it's easier to count all of the drawing sequences in which the number of reds is greater than the number of blues drawn at any point?
i.e. the things that aren't satisfactory
it almost feels Catalan-y
kind notch
Perhaps ((m-1)-(2i-1))!/(r-(i+1))!(b-i)!) does it
somber crest
what's the idea?
kind notch
In the beginning I have (m-1) marbles to choose from
Then if I want to equalize I only need to choose a blue marble, or draw another red and then two blue marbles and so one
So I have to draw 1, 3, 7 etc. marbles correctly in order to equalize which is what the (2i-1) is for
Then because I already drew a red marble in the beginning, I start with r-1 marbles. With each iteration giving me i red marbles less, I figured r-1-i = r-(i+1)
The blue term stays the same as I have not yet chosen any blue marbles
somber crest
I don't think I'm convinced, because I'm wondering where the drawings starting with (r, r, b, r, b, b, ...) are counted
somber crest
ah I see what you're saying, so really the problem is that some combinations are counted multiple times
e.g. (r, b, r, b, ...)
counted by i=1 and i=2
kind notch
ah yes and thats unnecessary because it already is temporarily equal for i=1
but going back to the binomial coefficient idea
i think i can work something out with that
somber crest
one thought I had was to define a sequence (p_i) in which p_i is the number of drawings in which the first occurrence of a red-blue tie occurs after 2i draws
maybe there's a manageable recurrence relation in there
although really you only need the sum of all the p_i's
it could also just be principle of inclusion-exclusion
kind notch
it could also just be principle of inclusion-exclusion
yeah that would be what I would guess too
then again they didn't include it in the lecture (it was in the lecture on discrete mathematics interestingly)
I have some notes on that let me take a look
Ye I know the size of each set so to speak
but I would need to expand this for ordered sets i think
or do i
no I don't
yeah it should be inclusion exclusion
I will think about it more after work now I will do some chilling
tyvm @somber crest for your extensive help
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somber crest
tyvm <@191038258728140801> for your extensive help
no problem, have a good chill
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bitter jasper
squares abxy and acpq are draw outwardly on the sides ab and ac respectively of triangle abc right angled at a. perpendiculars to bc at b and c meet xy and pq, produced if necessary, at m and n respectively.
a) prove triangle abc, bxm and cpn are congruent
b) prove bcnm is a square
lone heartBOT
squares abxy and acpq are draw outwardly on the sides ab and ac respectively of ...
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bitter jasper
<@&286206848099549185>
uneven ivy
maybe you have sketch?
bitter jasper
maybe you have sketch?
idrk how to draw it
but
this is what i assume it looks like
bitter jasper
<@&286206848099549185>
uneven ivy
squares abxy and acpq are draw outwardly on the sides ab and ac respectively of ...
you sure that they have to be congruent and not similar?
bitter jasper
its what the question says yea
not sure if the graph is right hto
can anyone help
lone heartBOT
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urban heron
Hi, basically idk if the first or the second one is correct. Do I have to multiply by 0 or is like everything wrong? thank you in advance
lament wyvern
I'm not sure what the first line is meant to be
jade night
Hi, basically idk if the first or the second one is correct. Do I have to multip...
could you show the question please?
urban heron
the question is to find x and the first line is the equation I was given
urban heron
-1/4 + x = 1/3 x (-1/4)
thats the line. the rest is the way Im supposed to write it down when i take an action on both sides of the = sign
urban heron
yes
urban heron
thank you that helped me a lot
jade night
you sure?
urban heron
yes I missed the step with -1/4 + x = -1/12 in my head
it makes more sense now so thank you
jade night
yes I missed the step with -1/4 + x = -1/12 in my head
ahh
jade night
it makes more sense now so thank you
nppp
urban heron
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prime nebula
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prime nebula
I did the calculus with both inequalities and it gave me this
And idk if it s ok, please help me
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alpine sable
This is confusing
lone heartBOT
This is confusing
alpine sable
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shell forge
Stop spaming yall
solemn seal
!noping
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lavish cave
This is confusing
you just need to apply this formula over and over again
lavish cave
Please do not ping individual helpers unprompted.
that's actually not relevant
x-bar is the sample mean
n is the number of observations
you just calculate the test-statistic z, then use a table or something to find the probability
and check if it is over or under 0.05
alpine sable
X is standard deviation upside down n is mean uhhh n is... o???
lavish cave
n is the number of observations
n is this
lavish cave
X is standard deviation upside down n is mean uhhh n is... o???
you really need to make a Quizlet so that you know what those symbols mean
$\sigma$ is the standard deviation
ocean sealBOT
south
lavish cave
$\mu$ is the mean, so $\mu_0$ is the mean under the null hypothesis $(H_0)$
ocean sealBOT
south
lavish cave
so mu_0 = 50 for the 1st q
lavish cave
I can't find mu
mu is unknowable
alpine sable
mu is unknowable
oh
lavish cave
you can only choose people from a group and find the mean of that group, the sample mean
like if I wanted to know the average weight of everyone on Earth
I could choose 100 random people, and I could choose another group of 100 random people, and those sample means would be somewhere near the true mean
but then finding the true mean by weighing all 8 billion people on Earth would be totally unnecessary
we don't really care about the true mean
we just want to know if we are 95% confident (0.05 significance) that our sample mean is close enough to the true mean
alpine sable
so we leave it blank
lavish cave
you just need to apply this formula over and over again
yep, so the strategy is to find z, the z-score
the z-score can be converted into a probability using a z-score table or similar
alpine sable
so I have to answer the remaining first and find mean?
lavish cave
that probability you get is how likely it would be that our sample is biased
alpine sable
like just X / o (sqrt)n?
lavish cave
so 0.05 is pretty unlikely
lavish cave
so I have to answer the remaining first and find mean?
no, you're not finding the mean at all
you're trying to find a probability, a probability of how confident you are
alpine sable
so 0.05 is pretty unlikely
wait mean is the significance level I have to find in a z table?
lavish cave
wait mean is the significance level I have to find in a z table?
no, the significance level is a probability
it's 1 minus the probability of confidence
alpine sable
So.. 1 - 0.05?
lavish cave
So.. 1 - 0.05?
yeah, so 95% confidence
that our selection of people fairly represents the entire population
alpine sable
wait 95% to a whole number is 0.95
lavish cave
mhm, 0.95 probability of confidence
lavish cave
that our selection of people fairly represents the entire population
so we can just trust the sample mean we get with 95% confidence
we can trust the mean with say 50 people is the same as with 8 billion people, or that we wouldn't be able to spot the difference
lavish cave
,calc (49 - 50)/(5/sqrt(36))
ocean sealBOT
Result:
-1.2
okay so that's -1.2 standard deviations away from the mean
ocean sealBOT
The following error occured while calculating:
Error: Unexpected type of argument in function multiplyScalar (expected: number or Unit or bigint or string or boolean or BigNumber or Complex or Fraction, actual: function, index: 1)
alpine sable
So weird
alpine sable
WAIT MAYBE I SHOULD BE SPECIFC
I'm looking for the null hyp. and alternative hyp.
how did they get 50?
lavish cave
,calc 12 - (1 - 0.05) / 3 (sqrt) 10
x-bar = sample mean = 49
mu0 = hypothesised mean = 50
sigma = standard deviation = 5
n = number of observations = 36
lavish cave
how did they get 50?
well they didn't get it
they chose 50
they're testing if 50 is the real mean of the entire population
alpine sable
Ohh
alpine sable
Is there any advice you could give me when finding those hyp.?
lavish cave
Is there any advice you could give me when finding those hyp.?
your textbook and YT videos
you really just have to write down the procedure for normal distribution hypothesis testing, which is:
- identify the variables in the z-score formula I gave you
- sub those in to find the z-score
- use a table to find the probability
- great, probability < 0.05 means alternative hypothesis (reject the null), and probability >= 0.05 means null hypothesis
and in fact hypothesis testing is like this in general
you just use a different table, so there's a t-table for example
the formula is basically the same, at this level
alpine sable
Okay thank you
lavish cave
Result:
```
-1.2
```
actually you can just compare 1.2 < 1.96, so that means you accept the null hypothesis
the higher the z-score number (including negatives), the more extreme / unlikely the result is
the closer to 0, the more normal or expected the result is
some teachers don't like you doing it this way but it works fine
lavish cave
and then we'll need this number, 1.96
1.96 is the z-score that gives 0.95 probability
lavish cave
Okay thank you
no worries!
lavish cave
some teachers don't like you doing it this way but it works fine
(some teachers want you to find the probability that your result comes from biased observations, so that you can do 1 - that and find the confidence probability you have)
(the method I gave is just, is this result wacky enough to reject the null or not, so it only tells you yes or no)
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alpine sable
p
lavish cave
ah, ln a - ln b = ln(a/b)
alpine sable
ah, ln a - ln b = ln(a/b)
oh
mental python
,tex .log rules
alpine sable
damn
ocean sealBOT
Bonk
lavish cave
nw!
alpine sable
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rotund rock
Hello
rotund rock
May someone teach me how to find the center of rotation in transformation mathematically?
strong flame
quick question if i constructed an linear order of partial order using the toplogical sorting over P(D) = { phai, {1},{2},{1,2} } by and then i wanna prove the <= satsify the totality so how ? the question is below
Let (D,⊑) be a partial order, for some finite domain D. Construct a total order ≤ on D such that
⊑ ⊆ ≤. Prove that ≤ fulfills all required properties.
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quick question if i constructed an linear order of partial order using the toplo...
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rose scroll
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proven depot
trial and error
knotty garnet
!status
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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
strange heath
try different values of a and b
proven depot
possible values for 11b = 11, 22, 33, 44
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rose scroll
trial and error
ohhh
sorry for long reply omg i forgot i sent it here
wait
thank you
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violet burrow
pls someone help me solve this
violet burrow
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lone heartBOT
lone heartBOT
Available help channel!
strange dirge
I need hellp on some general knowledge on vektors. Ive already done 1-10
strange dirge
i just have to say if they are correct or incorrect
i dont understand 11- 15
they arent vektors so do i jsut "create" them? and then deem if they are correct or incorrect?
also im unsure about this, i answered that 3)vektor AB= vektor B was incorrect since the direktion of the vektors differ. Is this correct?
lone heartBOT
@strange dirge Has your question been resolved?
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@strange dirge Has your question been resolved?
ancient saddle
they arent vektors so do i jsut "create" them? and then deem if they are correct...
Hello, yes you can just create them given the points I and H
- is incorrect
because of what you said
strange dirge
alrighty ty
so the 11th statement would look like this
and be correct
right?
strange dirge
oki ty
i have one mroe question
in this task i have to do vektor a + vektor b and vektor a- vektor b
im not sure i understand how
let me try n do it rq
on pc
i dont understand how to do this
am i allowed to move the vektors around?
brittle ember
am i allowed to move the vektors around?
As long as length and direction is preserved, yes
strange dirge
how can i solve the middle on tho since im not allowed to change a direction
im a bit confused sorry
brittle ember
vector a - vector b, the one you need to calculate, is the vector that if you add to vector b the result should be vector a
I dont know this makes sense to you
So vector b + (the answer) should be vector a
I personally think this is easy way to do vector substraction
strange dirge
ohh right i think it makes sense
so this would be drawn correct?
and to show how to draw vektor a + vektor b
i would have to do this
and like not draw vektor b down there
brittle ember
beside that I think all good
strange dirge
ty C: can i ask a last question
im a bit confused bout the bottoms ones too
would it be correct just to add them like this
strange dirge
oh but that would just elongate vektor a then?
brittle ember
for bottom left, yes!
strange dirge
ooooh
vektors finally make sense XD
wait but then if i wanna add this one
is that even possible?
cuz im guessing
if im gonna - in this i do it like this
brittle ember
I'd say for addition(a+b), you add one after another
For substraction, put their tail(opposite of arrow) together
if then you can do same method you used above
brittle ember
So if you want to calculate a+b, moving like this won't be that meaningful
strange dirge
oh so is it even possible to add vektor b in this one?
since the arrows are going towards one another
brittle ember
since the arrows are going towards one another
they just lies together
it's no problem to put together in line
strange dirge
ooh alr so it doesnt matter if they like "collide" in a a straight line
brittle ember
nice
Also, just a small tip:
-b is just flipped(rotated 180) b, so a-b is a+(-b),
therefore a-b is same as a + flipped(rotated 180) b
if you're unsure of your work, compare with this idea too
lone heartBOT
@strange dirge Has your question been resolved?
rancid tartan
dis regard thus please
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Available help channel!
ionic fossil
So basically long story short i was doing it and delta math reset all my work and i forgot what i did so i need help
patent vale
So basically long story short i was doing it and delta math reset all my work an...
Is that all of the question?
patent vale
Ye it is 2 pairs of parralel sides
Yes but do you know anything special about their angles?
ionic fossil
Nope
ionic fossil
To prove its a rectangle tho dont you need to prove all sides are right angles though?
patent vale
To prove its a rectangle tho dont you need to prove all sides are right angles t...
yes this alone should let you prove all sides are 90 degrees
ionic fossil
What alone?
patent vale
the fact that angles opposite to each other are equal
<A=~<D
if you know these are equal
you also need to know how much the angles in a quadrilateral adds up to actually
ionic fossil
I dont get it tho how does that prove its 90 degrees
patent vale
I dont get it tho how does that prove its 90 degrees
Ok what do the sides of any 4 sided shape add up to
ionic fossil
360?
patent vale
Yes correct i shouldve specified interior angles
ok you can label the angles on the triangle <A and <D as x
because they are the same
ionic fossil
So your saying if its a quadralateral its 4 sides and if you can prove the 4 sodes are the same it must be 90 degrees?
patent vale
So your saying if its a quadralateral its 4 sides and if you can prove the 4 sod...
well yes but i dont think you can prove that in this case
the 4 sides being the same thing
since you know these two angles are the same what angle is also the same as the angle A
ionic fossil
C
patent vale
Yes so what is the same as D?
ionic fossil
B
ionic fossil
Then you can use substitution for the angles next to eachother?
patent vale
Then you can use substitution for the angles next to eachother?
what do you mean by substitution?
ionic fossil
So if a=b and a=c then b=c
ionic fossil
So i have to write that all angles are equal to all angles?
patent vale
can you show me the options
patent vale
well I would assume stating perpendicularity of sides means stating there is a 90 degree angle between the sides
the uhh ⟂ one
ionic fossil
I thought you can only say they are perpindicular if you know its a 90 degree angle
patent vale
I thought you can only say they are perpindicular if you know its a 90 degree an...
well yeah you do know its perpendicular
ionic fossil
Not until you know its 90 degrees which is what i need to state correct?
patent vale
hmm but i dont see a way to state that it is 90 degrees so I kinda assume you are supposed to say that it is perpendicular
ionic fossil
It says angle x right angle
patent vale
Huh
ionic fossil
Idk dude i thought you would know
patent vale
Idk dude i thought you would know
oh maybe the option you chose was wrong
are there any other ones
lone heartBOT
@ionic fossil Has your question been resolved?
ionic fossil
are there any other ones
I finished it for some reason it would take 4 congruent angles as a reason its a rectangle
rustic gulch
I need hel pwith matrix
lone heartBOT
I need hel pwith matrix
sour verge
Do you have any particular question about matrices?
rustic gulch
yeah yeah wait let me pull it up
so what would be the exact scenario for this to happen
solve for x such that c=0
does it fall under solving AX=B? or a completely diff equation
tribal geyser
so what would be the exact scenario for this to happen
solve for x such that c=...
What are you solving for x ?
rustic gulch
What are you solving for x ?
it says here to complete the given given ? where x is voided out idk if that means I should find a number where the matrix determinat will equate to 0
tribal geyser
Can you send the original problem, I’m having trouble understanding what you mean
rustic gulch
nvm that lets just move on to the one I am confuse the most
this will come up in our incoming exam
I am just confuse how I'll use pivotal method to reduce
tribal geyser
You need to pivot this until you get only one coefficient in a lined column
rustic gulch
but in pivoting I have to locate the 1?
how on earth would it exactly look like
I am planning to R4 - R1 = R1
tribal geyser
Your determinant needs to look like this
rustic gulch
2 0 -1 1 would be the new r1?
rustic gulch
Your determinant needs to look like this
so what comes out of that will be the 3x3?
tribal geyser
see the smaller matrix on the bottom right side ?
rustic gulch
ye']
rustic gulch
wait so thats it?
tribal geyser
I just made sure that there are 0s everywhere in the first line/column.
That allows me to turn a 4x4 determinant into a 3x3
tribal geyser
I'm curious about your first question,
can you send it ?
like the original problem ?
clear hull
can someone check my logic here? I want to negate the following statement: for all but finitely many n, a_n > 0 (i.e. there exists an N s.t. for n >= N, a_n > 0)
my negation is as follows: there are finitely many n such that a_n > 0, or equivalently for all but finitely many n, a_n <= 0 (i.e. there exists an N s.t. for n >= N, a_n <= 0)
dire gazelle
"there are finitely many n such that a_n > 0" can't be the negation
consider a_n = (-1)^n
"for all but finitely many n, a_n > 0" and "there are finitely many n such that a_n > 0" are both false
a statement and its negation can't both be false
clear hull
"there are finitely many n such that a_n > 0" can't be the negation
what would the negation be then?
dire gazelle
well i think it should be "for infinitely many n, a_n <= 0"
clear hull
well i think it should be "for infinitely many n, a_n <= 0"
is there a way to rationalize that
like how for all and there exists are like negations of ecah other
is there an analagous thing for "for all but finitely many"
dire gazelle
"for all but finitely many n, a_n > 0" seems to be equivalent to "for finitely many n, a_n <= 0"
uh
typo
fixed it
dire gazelle
a cardinality is either finite or infinite
there is no other option
so yeah, i guess
clear hull
gotcha
clear hull
i saw this on mse so i just assumed it was okay 😭
do you know what this person meant by this then?
dire gazelle
idk, if it's a comment with no upvotes i wouldn't put too much faith in it
lone heartBOT
clear hull
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clear hull
wait sorry @dire gazelle , would the negation make sense if we tag on the assumption that a_n is Cauchy?
dire gazelle
oh idk the definition of cauchy
mossy lodge
I'm getting the hang of completing the square! But I'm stuck on getting 1.75 to equal 4, especially since the answer can't have the equal sign in it. What should I do to solve these kinds of problems?
buoyant saddle
I'm getting the hang of completing the square! But I'm stuck on getting 1.75 to ...
hello
well you were supposed to factor out the 4
mossy lodge
Oh wait, I keep the 4?
mossy lodge
Oh yeah, I'll add the 4 again (I divided both sides by four).
buoyant saddle
right but then youd have g(x) /4
you can only ignore it when the other side is zero
$g(x) = 4\left(x^2 - 4x + \frac{7}{4}\right)$
ocean sealBOT
knief
buoyant saddle
now
we need the constant term to be a 4
to complete the square
so what do you need to add to 7/4 to get to 4
mossy lodge
We need to add 9/4 to get 16/4.
mossy lodge
We should express it as -9/4 + 9/4.
buoyant saddle
exactly
$g(x) = 4\left(x^2 - 4x + \frac{7}{4} + \frac{9}{4} - \frac{9}{4}\right)$
ocean sealBOT
knief
buoyant saddle
now what
mossy lodge
So that means that we can group the 7/4 and the 9/4 together.
That creates 16/4, so we can factor it.
That means that the answer is 4(x^2-2x)^2-9/4, right?
Wait...
buoyant saddle
nope
mossy lodge
Sorry, I meant 4(x-2)^2-9/4.
buoyant saddle
still wrong
let’s do it one step at a time
$4\left((x-2)^2 - \frac{9}{4}\right)$
ocean sealBOT
knief
buoyant saddle
where was your mistake?
mossy lodge
Oh, that it's all in parenthesis.
But that means that we need to multiply everything by four to fit the answer.
So we get 4(x-2)^2 - 36/4.
buoyant saddle
So we get 4(x-2)^2 - 36/4.
mhm what’s 36/4
buoyant saddle
also $\cancel{4} \cdot \frac{9}{\cancel{4}}$
ocean sealBOT
knief
buoyant saddle
Or -9 in this case.
yep
mossy lodge
So that means that the answer is 4(x-2)^2-9!
buoyant saddle
yes
mossy lodge
I finally got it!
buoyant saddle
nice
mossy lodge
Sorry it took a while to learn. This was surprisingly confusing to learn.
buoyant saddle
no worries
mossy lodge
And I got it right.
Think I'm ready for vertex form now. Thank you so much for helping me over the course of two days.
mossy lodge
Yep, it's vertex form.
buoyant saddle
a(x - h)^2 + k, the vertex of the parabola is (h,k)
what’s the vertex of the parabola you’ve just solved?
buoyant saddle
Think I'm ready for vertex form now. Thank you so much for helping me over the c...
you’re welcome
mossy lodge
The vertex is (2,-9).
Wow, now that I'm past the nightmare of learning to complete the square again, I now have a new tool under my belt.
Thank you so much! I'll close this.
.close
stable jacinth
Hey I am on a problem now and I dont think its possible. I am using R studio btw. Anyone have any input?
Generate a random sample of 1000 values from the Normal distribution with the mean and variance equal to 1 and store it as the variable "sample_data2".
Using 'fitdistr' function in the MASS package. Fit the random sample data to the Exponential distribution. What are the estimated parameter values?
I know I can go exponential to normal, but I cant go normal to exponential because exponential has to be non negative right?
stable jacinth
My code:
# Generate random sample from Normal distribution
set.seed(42) # Setting a seed for reproducibility
sample_data2 = rnorm(1000, mean = 1, sd = 1) # Variance = 1 implies SD = sqrt(1) = 1
fit_exponential = fitdistr(sample_data2, densfun = "exponential")
cat("Exponential Distribution Fit:\n")
print(fit_exponential$estimate)```
The error:
Error in fitdistr(sample_data2, densfun = "exponential") :
Exponential values must be >= 0
2.
stop("Exponential values must be >= 0")
1.
fitdistr(sample_data2, densfun = "exponential")@stable jacinth Has your question been resolved?
stable jacinth
<@&286206848099549185>
lone heartBOT
@stable jacinth Has your question been resolved?
lone heartBOT
@stable jacinth Has your question been resolved?
lone heartBOT
@stable jacinth Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
frosty dune
lone heartBOT
frosty dune
heeelp pls
fierce cipher
its intersecting lines
frosty dune
what
fierce cipher
?
fierce cipher
you just did the problem that use the same concept
frosty dune
wdym
fierce cipher
INTERSECTING LINES
maiden crow
hei can somebody help me with a basic math concept , its easy but idk why am I confused , May be i am applying programming stuff to it
frosty dune
stfu and get ur own help channel
targetvn u dumb bastard
i joined this server to get fucking help
not for someone to tell me that the lines are intersecting
no fucking shit they are
give me the fuckin answer or atleast help me out
dickhead
fierce cipher
frosty dune
shag ur dad black bitch
fierce cipher
i was about to send this but it seems like you dont need my help
frosty dune
???
fierce cipher
ok
fierce cipher
for intersecting lines, opposite angles are equal
fierce cipher
does that satisfy you?
frosty dune
no
fierce cipher
ok
frosty dune
me fucking ur mum in ur bed satisfies me
maiden crow
WTF OS TJAT HELPING ME WITH
are you mad or wot , brother vertically opposite angles , so they will be same , x+2x+16 = 172 => x = 78
maiden crow
i wrote 78 its wrong
then get the fck out of there , mfcker
fierce cipher
<@&268886789983436800> we got a troll
maiden crow
<@&268886789983436800> we got a troll
hei btw can u help me with something?
fierce cipher
!occupied
lone heartBOT
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).
fierce cipher
are you mad or wot , brother vertically opposite angles , so they will be same ,...
3x = 156
maiden crow
<:cat_thonk:586238610957926430>
3x = 156
um my bad it will be 52
maiden crow
<:cat_thonk:586238610957926430>
3x = 156
can you help me with a basic math concept , Idk why am I confused with a simple thing
fierce cipher
Someone else is already using this help channel. If you need help with a questio...
!!!
i am not repeating again
lone heartBOT
@frosty dune Has your question been resolved?
fiery sundial
There is some secrate message behide this sequenz of codes, does someone know how to solve this mess?
mental python
there are columns with only 1's
hollow veldt
There is some secrate message behide this sequenz of codes, does someone know ho...
what's the context for this? Is it some kind of contest?
fiery sundial
Yeah, so my teacher gave us some kind of challenge and this is one of the tasks.
mental python
Yeah, so my teacher gave us some kind of challenge and this is one of the tasks.
can you give more context?
what class, topic, etc
fiery sundial
its about computerscience but it has also to do with math, I already tried converting the nummbers in text, but it didn't work
hollow veldt
If it's from a class presumably it uses some coding scheme that you might have studied in class, or atleast one out of some family.
So one would need the context to see what to try...
fiery sundial
thats the point, we didnt study those problems
fiery sundial
it just should be hard to solve, but the person who solves this gets like an reward or something and a better grade at the next test
fiery sundial
whats the name of the course?
I dont know what u mean
hollow veldt
name of the class...
anyway I'm not sure it's appropriate to get someone else to solve this for you to get a better grade...
it's like solving an exam question for you.
mental python
it just should be hard to solve, but the person who solves this gets like an rew...
<@&268886789983436800> cheating?
fiery sundial
My teacher thinks, that no one can solve this and just made it like a joke btw.
so its just like a funproblem to do but it isn't some sirious thing
fiery sundial
name of the class...
I'm just in highschool in an non english country, so we dont have names for classes
lone heartBOT
@fiery sundial Has your question been resolved?
boreal verge
Q is 55
B is 90
F is 80
lone heartBOT
Q is 55
B is 90
F is 80
mental python
,rccw
ocean sealBOT
boreal verge
Ok professor corrected, turns out it was hers the right one
But i cant make this equal to 162
Found it
Yeah i can be this stupid
acoustic meteor
lone heartBOT
acoustic meteor
please help me solve it but i cannot figure out the logic
modest silo
do you know 12 digit same with how much money ?
modest silo
ahh nvm wrong idea
swift grail
Product of 6 consecutive numbers is divisible by 10
acoustic meteor
Product of 6 consecutive numbers is divisible by 10
yes, but it is also divisible by 15
swift grail
Sure. But what does it divisible by 10 mean to you
acoustic meteor
well it has 2 and 5 as its factors
swift grail
Whats the last digit of a number divisible by 10
swift grail
So you have b = 0
acoustic meteor
that was great thinking
swift grail
Now 15 isnt that usefull. Notice that the number is divisible by 9.
acoustic meteor
yes so now
swift grail
Wait a , b , c , d are consecutive numbers means they are in {0 , 1 , 2 , 3} now?
If it were consecutive digits idk if you could argue that it could be {9 , 0 , 1 , 2} or something similar
lone heartBOT
@acoustic meteor Has your question been resolved?
acoustic meteor
If it were consecutive digits idk if you could argue that it could be {9 , 0 , 1...
yes i also worked that out but still the arrangement matters
autumn rampart
Ye
acoustic meteor
like a+c+d=0 (mod 9)
swift grail
More like 2a + 2c + 4b + 4d = 0 (mod 9)
acoustic meteor
okay but how do we know which are which
swift grail
You know b = 0
Now you have 2a + 2c + 4d = 0 (mod 9)
You can plug d = 1 , 2 ,3. See if there us any that has a sol.
acoustic meteor
okay
swift grail
Because a and c have the same coefficient you can put the rest in any order
Like you only need to see 3 cases
(a , c , d) in {
(1 , 2 , 3)
(1 , 3 , 2)
(2 , 3 , 1)
}
marsh wedge
yes
swift grail
so we can also deduce that a is even
How exactly?
lone heartBOT
@acoustic meteor Has your question been resolved?
lucid cargo
help
lucid cargo
These points form a four sided polygon thingy i forgot its name but anyways
Im supposed to find the area of it
Now i drew it by myself on paper
But heres an accurate desmos depiction
Now
My first thought was that this is a triangle in disguise ok
So
Height = 6
Breadth = 13
1/2(6)(13) = 39
Okay now I tried to find the area of the triangle thats like
Origin, A, D
mental python
thats not the triangle
lucid cargo
wym
mental python
the width is not 13
mental python
sharp juniper
i think
mental python
its 12.5
sharp juniper
whats the red line supposed to be
lucid cargo
ok wait how do i proceed from there then
mental python
whats the red line supposed to be
thats continuing the side of the triangle
sharp juniper
thats continuing the side of the triangle
ohh
mental python
ok wait how do i proceed from there then
keep going where you were going
lucid cargo
Wait wait i see
mental python
its just that the width is not 13