well x^-3 = 1/x^3, so I'd say just multiply it out
#help-27
vital sedge
elder pelican
And what about x^15 that’s at the bottom, do you leave it alone?
vital sedge
If the question says that you have to use the quotient rule, yeah just leave it alone
elder pelican
Okay! That makes sense.
If it were to say simply the expression and everything in that problem held a negative exponent, you’d do what?
vital sedge
Personally, I'd try to rewrite it to use the power rule. But you can just use the quotient rule with negative exponents.
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dull belfry
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wind mason
Hm?
wind mason
You wanna use the hints I gave you?
dull belfry
I tried but still got stuck
tribal cairn
the square and the uppermost triangle share a side, so if you were able to find the side length of one of the triangles, you would be able to find the area of the square
what type of triangle do you think the uppermost triangle is?
dull belfry
what type of triangle do you think the uppermost triangle is?
equilaterial
tribal cairn
why is that
wind mason
I tried but still got stuck
Ok. Do you know the relationships between the 30-60-90 right triangles?
dull belfry
Yes 30 = x, 60 = xsqrt(3) and 90 = 2x
wind mason
Yeah, with the angle correspondence.
Now make 60 be x; i.e., divide everything by sqrt(3). What results?
dull belfry
I am not understanding, you want me to make 60 = x and then divide just that by sprt(3)?
wind mason
I am not understanding, you want me to make 60 = x and then divide just that by ...
Hmm...eh, you know what, for this purpose, you don't have to.
We just need to shift the necessities a bit.
So if 30=x and 60=x*sqrt(3), then what is side length AB in terms of x?
dull belfry
How would I use variables in angles to find the length, I am so sorry for my confusion
Oh sorry I think I understand what you are saying now
dull belfry
So if 30=x and 60=x*sqrt(3), then what is side length AB in terms of x?
Just please give me some time to solve that
wind mason
Oh sorry I think I understand what you are saying now
Okay.
dull belfry
Is it 2x + x*sqrt(3)?
wind mason
Is it 2x + x*sqrt(3)?
Good.
Now what do we know AB is equal to, given in the problem?
dull belfry
3 + 2sqrt(3)
dull belfry
Set them equal, square it, and you're all set.
Set what equal?
wind mason
Oh, and don't forget to get a 3x^2 term.
wind mason
Set what equal?
The given definition of AB, with the other that you just derived.
wind mason
Oh, and don't forget to get a 3x^2 term.
Since we set DE=x*sqrt(3), and we want [DEFG].
dull belfry
So how would would we remove 2x from "2x + x*sqrt(3) to make it equal 2sqrt(3) from "3 + 2sqrt(3)"?
wind mason
So how would would we remove 2x from "2x + x*sqrt(3) to make it equal 2sqrt(3) f...
Factor out the x.
dull belfry
So DE=2sqrt(3)?
wind mason
how’d you do on the test
Not good, but not bad either.
I did better on the calculator than non-calculator.
misty crest
typical
wind mason
So DE=2sqrt(3)?
How did you reach that conclusion?
misty crest
i always found non calculator easier since i couldn’t make some trivial mistake
wind mason
#「helpers-lounge」 , if you want.
dull belfry
How did you reach that conclusion?
I took away the 2x and the 3
wind mason
I don't mind having a chill conversation, it's been a long day.
misty crest
nah lol i’m just procrastinating
wind mason
I took away the 2x and the 3
misty crest
that’s my reminder to get back to homework
wind mason
Do you know what I mean by "factor out"?
dull belfry
Do you know what I mean by "factor out"?
No.
wind mason
Ok.
dull belfry
Could you give a brief description
wind mason
What I mean is to "take out" the x, such that the expression 2x+x*sqrt(3)=x*c where c is some constant.
Obviously, you have to determine that constant. I'm not giving handouts.
dull belfry
Alright.
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dull belfry
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amber hull
How would you intepret a diagram for this question?
devout snowBOT
How would you intepret a diagram for this question?
dry oxide
yea seems fine to me
u forgot to show the string tho
wait no actually, initially the string will have no length since the package is kept at A and the other end is also attached to that point
devout snowBOT
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toxic herald
For a positive integer n >= 2, does there exist positive integer solutions to the following system of equations
a^n - 2b^n = 1
b^n - 2c^n = 1
devout snowBOT
For a positive integer n >= 2, does there exist positive integer solutions to th...
slender mirage
uhh that's MODS potd 2140, you can check the hint there
toxic herald
.close
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topaz umbra
Hello
wheat pawn
!status
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 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
also, that translation seems awful, ngl
topaz umbra
Um
I didn't know how to solve 3
I kept trying
No result
Don't really know what to start with
Bro
wheat pawn
what is R(O) supposed to be?
topaz umbra
what is R(O) supposed to be?
Rotation of O
With respect to center I
With rotation pie/4
wheat pawn
okay
wheat pawn
im thinking, i'm having a lot of trouble understanding the problem as stated tbh
topaz umbra
Do you know transformations?
toxic herald
im thinking, i'm having a lot of trouble understanding the problem as stated tbh
same
wheat pawn
Do you know transformations?
yes, but the problem is very weirdly worded
topaz umbra
Hmm
I can make you understand the given
Will you be able to help
Wait
I think I got the answer
It is pretty easy
Oh no I didn't
quiet obsidian
The only rotation by π/4 radians that transforms C into A is the one with center of rotation I. You can see this by noticing that the angle CIA is equal to π/4 and the line segments IA and IC are equal.
quiet obsidian
Of course you could argue that the point symmetric to I with respect to CA would also transform C to A but then that rotation would have oposite orientation by the one given to you
quiet obsidian
Consider a circle with radius equal to IO and center I
The point O, R(O) and Q have to be point of intersection of the circles (I,IO) and (A,AQ)
Since two circles can have at most 2 common point and O is not the same point as R(O) (a rotation can have only one fixed point, unless it is the identity which in our case it is not) we have to conclude that either Q is O or R(O)
Since O does not lie on the sqgment AB we conclude that Q = R(O)
quiet obsidian
AO = CO = AQ
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ebon widget
Guys help w/ this question pls
"Find matrices A and B such that, A + B = [5 4] and A - B = [11 2]"
7 3 -1 7
regal moat
ebon widget
how tho
ebon widget
hmm and then how do I find A?
faint gorge
forget what i just said
olive snow
Just sub B that you found
faint gorge
if you add both equations you will have to solve for A
devout snowBOT
ebon widget
if you add both equations you will have to solve for A
wait no.
if u add both equations
u can get 2a
which u divide
and then u get a
then u sub for b
ohhh
im stupid :/
faint gorge
you was just too fast 😂
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Available help channel!
arctic delta
i'm stuck in this question
devout snowBOT
i'm stuck in this question
arctic delta
(this is what I did so far)
arctic delta
so I do 36-18 to get n(A) ?
also what calculation errors did I make? ;-;
I just learnt this topic today so I'm not great at it yet
arctic delta
the pink part?
woven radishBOT
🫎 Moose Michael 🫎
thin inlet
you know n(B) is 21, and n(A n B) is 8, so you can figure out the total of the stuff in B that's not in A
thin inlet
n(A')+n(A)= n(e)
and note this $n(A)+n(A^{\prime})=n(\xi)$
woven radishBOT
🫎 Moose Michael 🫎
arctic delta
would the '21' be in set B only or the middle of both sets or in both?
thin inlet
would the '21' be in set B only or the middle of both sets or in both?
n(B) includes n(A n B) yes
sand quarry
21 is the entire B circle
thin inlet
yes
arctic delta
you know n(B) is 21, and n(A n B) is 8, so you can figure out the total of the s...
is the answer 13 here?
for in set B but not A
thin inlet
then this allows you to figure out all the stuff thats outside A u B
i.e. n( (A u B)')
thin inlet
**🫎 Moose Michael 🫎**
or you can use this to find n(A) then use n(A u B)=n(A)+n(B)-2n(A n B)
arctic delta
i.e. n( (A u B)')
would this be 15?
i'm too confused
how do u find n(A)?
<@&286206848099549185> can someone help me with this plz? ;-;
mossy token
<@&286206848099549185> can someone help me with this plz? ;-;
Wait let me write it for you on a paper
Sorry for the handwriting
mossy token
<@&286206848099549185> can someone help me with this plz? ;-;
You can do it from here 😁
arctic delta
so I do 36-18 to get n(A) ?
I said n(A) = 18 here but the other helper said it was wrong 😅
wait is the answer 39
or 31
oh nvm it's 31
thx
.close
ancient sluice
If the values of the iterated limits are different when the order is changed, then can we conclude the double limit doesn't exist too?
devout snowBOT
If the values of the iterated limits are different when the order is changed, th...
supple knot
Yea
ancient sluice
Is there any proof regarding this ?
stone stump
write down the def of double limit
devout snowBOT
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fervent breach
Can you think of any problems that aren't easily solved?
jagged thorn
i dont really understand how to solve b, do i find all the possible outcomes that M could be first?
devout snowBOT
i dont really understand how to solve b, do i find all the possible outcomes tha...
polar chasm
i dont really understand how to solve b, do i find all the possible outcomes tha...
Yeah, that works
jagged thorn
hmm okay so is the max number 3?
jagged thorn
okay is it 3 for x and y?
polar chasm
okay is it 3 for x and y?
M is 3 iff either X or Y is 3, is that what you mean?
or are you talking about the pmf now?
jagged thorn
yeah exactly, so if x for example is 3 max is y 2 then?
polar chasm
if X = 3, then Y = 0 and so max(X, Y) = max(3, 0) = 3
polar chasm
yeah exactly, so if x for example is 3 max is y 2 then?
i dont quite get what you mean by this
jagged thorn
ohh okay so is 3 the only possible outcome that i need to calculate the pmf for?
polar chasm
ohh okay so is 3 the only possible outcome that i need to calculate the pmf for?
there is one more possible outcome for M
not just 3
jagged thorn
hmm okay
jagged thorn
then M would be 2?
polar chasm
you can calculate the probability of 3 happening, since that's really simple
and then P(M=2) is just 1 - P(M = 3)
jagged thorn
ahh i see okay
do i think the same for question c? find the possible outcomes first?
polar chasm
do i think the same for question c? find the possible outcomes first?
I think that there is a simpler approach
note that X + Y = 3
can you use this to simplify the expression X - Y
polar chasm
exactly
jagged thorn
so we get 2x - 3?
polar chasm
yeah, so now we know exactly how the distribution of D depends on the one of X
jagged thorn
ahh so x can be 1, 2 or 3 and we get D = (-3, -1, 1, 3)?
polar chasm
ahh so x can be 1, 2 or 3 and we get D = (-3, -1, 1, 3)?
*0, 1, 2 or 3
but yep, the range of D is correct
jagged thorn
right
polar chasm
and you also know the probabilities of each
because they're the same as the corresponding X - probabilities
e.g. P(D = 1) = P(2x-3 = 1) = P(2x = 4) = P(x = 2)
polar chasm
Alright, if you have no other questions you can close this channel with .close
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south walrus
pls help
south walrus
idky the greatest value to part b isnt correct
vital dagger
idky the greatest value to part b isnt correct
yes but how did you get 1/2
restive river
im confused on this question
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restive river
.close
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mild fog
in a round robin tournament, a cyclic 3-set occurs occasionally; that is, a set {a, b, c} of three teams where a beats b, b beats c, and c beats a. If 23 teams play a round robin tournament without ties, what is teh largest number of cyclic 3-sets that can occur?
devout snowBOT
in a round robin tournament, a cyclic 3-set occurs occasionally; that is, a set ...
devout snowBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
wheat pawn
there's millions of servers for memes and jokes, this aint one of them
supple knot
It was for the joke
Uhh don't troll help channels then
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tulip pendant
Which method is correct
devout snowBOT
Which method is correct
tulip pendant
The questions was something about a marble rotating around an ice cream cone with radius 0.2 and with velocity of 0.2
What is the angle with respect to the horizontal
!close
I got it idk how to close this though
?close
.close
zenith whale
devout snowBOT
zenith whale
why isnt this right
tropic skiff
The graph intersects the point (4, 2)
y = (x - 2)^3 - 2 intersects the point (4, 6)
woven radishBOT
King Leo
tropic skiff
(im omitting one transformation here, but it doesnt matter in the context of y = x^n)
zenith whale
how do i know what number its stretched by
young spade
replace x by 4 here, and make it equal to two
zenith whale
is it a vertical tranformation?
young spade
i fucked up big time
tropic skiff
is it a vertical tranformation?
*stretch, but yes
tropic skiff
replace x by 4 here, and make it equal to two
You shouldnt have a inside the (...)
young spade
You shouldnt have `a` inside the `(...)`
its easier that way, dont have to deal with the fact that the h displacement will be affected.
it also matches up
tropic skiff
it also matches up
How does it match
zenith whale
isnt it the difference from 4,6 and 4,2?
tropic skiff
its easier that way, dont have to deal with the fact that the h displacement wil...
No, the h displacement is affected by a with your expression
young spade
you "stretch" it by, in really dumb words, making x increase slower.
tropic skiff
Because now youre basically going to the left by h/a units
tropic skiff
When a = 1 there is no effect
zenith whale
im so confused i already tried 1/2 and it didnt work but it just did
young spade
im so confused i already tried 1/2 and it didnt work but it just did
try this answer for the problem $\ \left( \left( \sqrt[3]{\frac{1}{16}}+\frac{1}{2} \right)x-2 \right)^3-2$
woven radishBOT
zzz0nnn
zenith whale
huh?!
young spade
looks awful, unless im not seeing something, this is the same as the one from the question > well, at least matches to every point that is made obvious
woven radishBOT
toast
young spade
we base ourselves on (x-2)^3 - 2, which is somewhat similar to this
the problem is that (x-2)^3 - 2, doesnt cross 4;2, so, just find a coefficient for x that does make it pass through it
cerulean ruin
oh it doesnt cross 4;2?
cerulean ruin
if you think about it
from the inflection point
we should expect
if we go right by 2
we go up by 8
in this case when we go right by 2 we only go up by 4
so we're effectively halving our cubic equation
young spade
both are quite similar, they cross through the origin point at different places at distinct moments
cerulean ruin
green should be right
cerulean ruin
because in that case
any rational number close to 1/2 would work
actually any number close to 1/2 woudl work
young spade
mb
cerulean ruin
all g
inner rampart
hi! i am needing help on my review for an exam. i have completed all the questions that have been taught to us, but there are a couple questions my teacher hasn't taught yet but she still expects us to finish them and i am really struggling. can anyone help?
devout snowBOT
hi! i am needing help on my review for an exam. i have completed all the questio...
plain coral
try expanding out (d+2)(d+k) and see what you get
your goal should then be to answer the following question:
what must k be in order for
(d+2)(d+k) = d^2-d-6
to be true?
inner rampart
i haven't learned this material yet so i am really confused rn
what is the purpose of the boxes?
misty crest
no clue
inner rampart
oh
crisp tapir
no need, for what value of k is 2 + k = -1
She may not have learnt vietas
plain coral
likewise for what value of k is 2k =-6
that also works
inner rampart
She may not have learnt vietas
yeah im not sure what that is
plain coral
yeah
misty crest
two numbers that add to b and multiply to ac
plain coral
wait so how do i solve problems like this?
i whipped up a sketch of the basic principle
inner rampart
ohh i kind of get it now
that's really helpful thanks
let me try to apply this to my problem
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toxic spire
Letters AAABBCCC
devout snowBOT
Letters AAABBCCC
toxic spire
We want to arrange those
So what we do here is AAA can be arranged in 3! Ways so to make sure we dont overcount we divide by 3!, right?
But doesnt this assume that AAA is one singular set
Would it count if the As are seperate like ABBACCA
cinder bobcat
strategy for these types of problems:
-
choose where the A's go in (8 choose 3 ways) since there are 8 possible positions and 3 A's
-
choose where the B's go in (5 choose 2) ways
etc
toxic spire
As can go in 8x7x6 ways but there is the issue of overcounting
strange nimbus
You can use a multinomial.
toxic spire
Dunno what that is
cinder bobcat
As can go in 8x7x6 ways but there is the issue of overcounting
if you wanna look at it that way sure, just divide by 3! to account for that
strange nimbus
Do you know what a binomial coefficient is?
toxic spire
So what we do here is AAA can be arranged in 3! Ways so to make sure we dont ove...
Just tryna understand the theory behind this
strange nimbus
Like this: (\binom{5}{1})
woven radishBOT
Chai T. Rex
toxic spire
Ye
strange nimbus
OK, that's the same as the multinomial coefficient (\binom{5}{1, 4}) where you do (\frac{5!}{1! 4!}) and where the bottom numbers add to the top number.
woven radishBOT
Chai T. Rex
strange nimbus
Does that make sense?
toxic spire
Oh
strange nimbus
Here it would be (\binom{8}{3, 2, 3}).
woven radishBOT
Chai T. Rex
strange nimbus
Or (\frac{8!}{3!2!3!}).
woven radishBOT
Chai T. Rex
strange nimbus
You basically permute all the letters.
Then, you stop the double counting of As.
Then, you stop the double counting of Bs.
Etc.
strange nimbus
Because let's say you have ABAABCCC.
toxic spire
But we are placing 3 As into 8 possible possitions
strange nimbus
If you ignore the other letters, you have three As in a row.
toxic spire
That can be done in 8x7x6 ways, then we have to stop doublecounting
Since there are 3 As, one position can be repeated 3 times, so we divide by 3
strange nimbus
Like you have (A_1BA_2A_3BCCC) or (A_2BA_1A_3BCCC) or so forth.
woven radishBOT
Chai T. Rex
toxic spire
Ye
strange nimbus
There are 3! ways of rearranging the subscripts there.
So, dividing by 3! means that it doesn't matter what order they're in.
toxic spire
Yes but thats just one way
strange nimbus
What's just one way?
strange nimbus
Right.
toxic spire
But wouldnt A1BA2BA3 be a different way
strange nimbus
Not of that.
strange nimbus
It's like the distributive property.
You multiply each order-ignoring combination by 3! to get the positions of the distinct As.
Like ABAABCCC has 3! arrangements of As.
toxic spire
Yes
strange nimbus
ABBAACCC has 3! ways.
toxic spire
Oh wait so thats why we divide
strange nimbus
CABACBCA has 3! ways.
toxic spire
Divison is repeated substraction
strange nimbus
Well, it's like factoring out the 3!.
toxic spire
And we are removing the 3! Combinations again aad again?
Ahhh
Now i get it
The divison accounts for each 3! Ways?
strange nimbus
Right.
toxic spire
ABBAACCC has 3! ways.
I assume that we add this case
strange nimbus
To see more clearly, it's about factoring out the 3!.
One moment.
You have something like this:
Each of those has 3! arrangements of As.
toxic spire
Yes
And i assume at the we add those 3! Arrangments to get the total
And thus when we divide once by 3!
It strips all those 3!s?
Or well factors them out
strange nimbus
Right, it's like:
So, instead of having 3! copies of each thing in the brackets, you now only have 1 of each, and the 3! is factored out.
toxic spire
Ahhh
Ahh
You see the problem was i thought each of the cases were multipled with each other
To get the final combinations
If they are added it makes more sense
strange nimbus
Sorry, my example wasn't the best. It's more like [AAABBCCC, AAABBCCC, AAABBCCC, AAABBCCC, AAABBCCC, AAABBCCC, AAABCBCC, AAABCBCC, AAABCBCC, AAABCBCC, AAABCBCC, AAABCBCC, ...] -> 3! [AAABBCCC, AAABCBCC, ...]
toxic spire
Yea got that
strange nimbus
OK.
toxic spire
That 3! Applies to each possible case right?
Like. ABBAACC
Is 3! Ways
And the division applies to that as well?
strange nimbus
Right.
devout snowBOT
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Available help channel!
languid mango
In this problem:
devout snowBOT
In this problem:
languid mango
Why is the horizontal compression first?
Before translation
(the window on the right is the answer)
for the transformations
for horizontal transformations isn't it translations then dilations?
i found this online:
but i don't quite get it
cause in the original problem of -3 sin (4x-pi) -1
its not in the b(x-h) form is it?
devout snowBOT
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languid mango
<@&286206848099549185>
queen veldt
<@&286206848099549185>
I don’t really think it matters
languid mango
I don’t really think it matters
huh?
queen veldt
Like it doesn’t matter the order you do it in
languid mango
wait but it does with quadratics and absolute values
queen veldt
The way I was taught was to go off this formula and plot the points down
languid mango
hmm
queen veldt
Yeah I don’t really know. We used a table back in hs now in uni they don’t even touch graphing so that’s cool
devout snowBOT
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wispy geyser
so this is my question
devout snowBOT
so this is my question
wispy geyser
and this is what i have so far
i just need help on what to do next
is my work right so far
there aren't any triangle so what does that mean
<@&286206848099549185>
rotund umbra
part A - use the cosine rule
vital dagger
what is A,B,C and a,b,h
rotund umbra
part B - use "area = 1/2 base * height" with "base = 14" and you need to calculate the height
wispy geyser
Why are you using sine rule
man im so confused i was just following a vid my teacher sent. she was using it
so do i have to use cosine
do i have a Side side angle triangle?
wispy geyser
part B - use "area = 1/2 base * height" with "base = 14" and you need to calcula...
but they say the height is 14 inches
vital dagger
do i have a Side side angle triangle?
Yes but you don't need to find an angle
You need to find the length of the upper line
wispy geyser
this is a similar question my teacher was doing
rotund umbra
but they say the height is 14 inches
the length allong the flag pole is 14 inches. they're calling this the height
wispy geyser
i guess this is different
wispy geyser
the length allong the flag pole is 14 inches. they're calling this the height
ohh okay so i have to calculate the height?
wispy geyser
part B - use "area = 1/2 base * height" with "base = 14" and you need to calcula...
so the height is 7?
rotund umbra
flip it on it's side and calculate the height that way
wispy geyser
part B - use "area = 1/2 base * height" with "base = 14" and you need to calcula...
can you do this with me
please
fresh agate
nice
rotund umbra
Part A - use the cosine rule.
fresh agate
Hit the rolly store wit a rolly On
wispy geyser
Part A - use the cosine rule.
how would i do this sorry for asking so many questions 😭
wispy geyser
isn't it c2 = a2 + b2 − 2ab cos(C)
rotund umbra
yep
wispy geyser
okay
rotund umbra
let's label the angles and side lengths of the triangle
The coside has only 1 angle, so let's label angle C and side c first
wispy geyser
let's label the angles and side lengths of the triangle
The coside has only 1 an...
like do i draw it on the triangle?
where would side C be
rotund umbra
like do i draw it on the triangle?
yes
rotund umbra
where would side C be
first, what is angle C?
wispy geyser
30 right?
wispy geyser
14?
rotund umbra
that's the side, not the angle
wispy geyser
almost right, but the angle needs to be inside the triangle
wdym inside the triangle
wispy geyser
would it be 60?
wispy geyser
and side c is opposite to angle C, which is?
would that be 30?
rotund umbra
nope, we want side c
wispy geyser
nope, we want **side** c
is it 28?
wispy geyser
isn't it top like this
rotund umbra
that's a point, not a side
wispy geyser
oh okay hold on
rotund umbra
we want to label one of the sides c.
rotund umbra
yes
because it's opposite to the angle we've worked out
now, does it matter which of the other two sides we label a or b?
wispy geyser
okay yeah
wispy geyser
now, does it matter which of the other two sides we label `a` or `b`?
yeah since a = 36 and b = 14
wispy geyser
*(I've underlined the angle `C` so it looks different from the side `c`)*
okay let me save this
rotund umbra
don't look at numbers yet. we're just labeling things
I can label the other two sides like one of the images. does it matter which?
remember, we're just labeling things for now
wispy geyser
I can label the other two sides like one of the images. does it matter which?
okay no it doesn't matter
rotund umbra
yep
wispy geyser
remember, we're just labeling things for now
got it ok
rotund umbra
let's use this one
So, we have a formula, and labels for everything. Let's now plug the numbers into the formula.
woven radishBOT
Shuba
rotund umbra
nope
wispy geyser
wait whats wrong here
rotund umbra
wait so dont i use b^2 = c^2 + a^2 - 2ac cos(B) to get b
nope, because we don't have angle B.
you should have the following
$$36^2 = 14^2 + b^2 - 2 \times 14 \times b \times \cos{60}$$
woven radishBOT
Shuba
wispy geyser
oh okay so just leave it b
rotund umbra
yep
now it's algebra time
Let me rewrite the formula. I'm going to group multiples of b.
$$b^2 - (2 \times 14 \times \cos{60}) b + (14^2 - 36^2) = 0$$
woven radishBOT
Shuba
rotund umbra
see what I've done there?
rotund umbra
first, we can simplify the number terms for example (14^2 - 36^2) is what?
wispy geyser
thats -1100
wispy geyser
i dont think so
wispy geyser
ok yeah we do actually so 2 x 14 x cos(60) is 14x^2 when simplified
rotund umbra
not quite. the xs are me writing multiply signs
rotund umbra
yep
woven radishBOT
Shuba
rotund umbra
We now have a quadratic in terms of b, which we can solve for b.
wispy geyser
yes okay so i would use the quadratic formula here right
rotund umbra
yep, I'd do the same
wispy geyser
let me work it out real quick and send you an image to check
rotund umbra
If you're wondering why there's two solutions, it's because there's another line of length 36 we can draw
How are you getting on?
wispy geyser
If you're wondering why there's two solutions, it's because there's another line...
okay got it
rotund umbra
no problem
rotund umbra
Let's change b to x first, and say we're trying to now work out x
$$x^2 - 14 x - 1100 = 0$$
woven radishBOT
Shuba
rotund umbra
Plugging that into the quadratic formula, we get the following
$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{- (-14) \pm \sqrt{(-14)^2 - 4 \cdot 1 \cdot (-1100)}}{2 \cdot 1}$$
woven radishBOT
Shuba
rotund umbra
keep going
wispy geyser
okay
devout snowBOT
@wispy geyser Has your question been resolved?
rotund umbra
<@211475256689426432> sorry it took so long 😭
looks good
and, clearly a length must be positive, so it's the 40.8969 answer 🙂
wispy geyser
and, clearly a length must be positive, so it's the 40.8969 answer 🙂
THANK YOU SO MUCHHH i'll write down 40.8969 inches as my answer
i have to write everything i just did on notepad
wispy geyser
looks good
i dont want to bother i know ur busy i just wanted to ask if you can also help with part B
it doesnt look like it takes long
devout snowBOT
@wispy geyser Has your question been resolved?
wispy geyser
@rotund umbra are you still here
neat coral
wispy geyser
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wispy geyser
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tropic skiff
am i right with C here?
That doesnt look right
wispy geyser
That doesnt look right
oh so then it has to be D
this is what i get when i grpah on desmos
@tropic skiff is that right
tropic skiff
One sec
tropic skiff
am i right with C here?
D isnt right either
wispy geyser
D isnt right either
im genuinely confused then i guess its A
<@&286206848099549185>
tropic skiff
im genuinely confused then i guess its A
Lol thats also wrong
wispy geyser
Lol thats also wrong
😭 😭
u cant be serious no way
wow it was B
idk how i messed this up
mighty galleon
Your scaling, if that is worded correctly, if you zoom in on desmos you can also see where A and B come from
devout snowBOT
@wispy geyser Has your question been resolved?
crimson silo
devout snowBOT
crimson silo
(2x+2)+(2x+2)+(2x+2)+(2x+2)
crimson silo
8x+x
crimson silo
8x+8 = perimeter of rectangle
How?
restive river
solve it
restive river
How?
no i meant the equation
i didnt mean it like perimeter of rectangle is that
i meant u equal it to that
crimson silo
Huh
restive river
perimeter of square = perimeter of rectangle
substitute perimeter of square
u get
crimson silo
Oh yea
restive river
8x+8 = perimter of rectangle
substitute perimeter of rectangle
u get
8x+8=2(l+w)
crimson silo
2 short sides= (2x+6)
restive river
yes
crimson silo
LONG SIDES= (6x+2)
restive river
yes
devout snowBOT
restive river
np
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marsh bane
Yoyoyoyoyoyoyooyooo
devout snowBOT
Yoyoyoyoyoyoyooyooo
marsh bane
Help
grand warren
for ?
devout snowBOT
@marsh bane Has your question been resolved?
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muted lintel
I need help understanding one specific symbol used for logic, the implication symbol
devout snowBOT
I need help understanding one specific symbol used for logic, the implication sy...
night lance
kinda tricky to explain but basically if p is false then it implies nothing about q
and since theres no implication made then the statement basically hasn't been falsified or proven false
muted lintel
that makes sense but then how would i use implication
because P can just be whatever, its just Q that matters
night lance
that makes sense but then how would i use implication
what exactly do you mean by 'use implication'..?
muted lintel
like the symbol
how would i use it properly
because if I do
1 -> 2+2
and
4 -> 2+2
then it would basically be the same
storm storm
because if I do
1 -> 2+2
and
4 -> 2+2
then it would basically be the same
are you using it like equality symbol here?
p and q must be statements that are true or false
muted lintel
ohhh that makes more sense now
night lance
p and q should be statements not just numbers right..?
also when the statement p is false and q is correct then you could logically imply it
doesn't really help with proofs though
storm storm
2+2 is not a statement, but 2+2=5 is a statement
because 2+2 doesn't claim anything. while 2+2=5 is a false claim
storm storm
in programming?
muted lintel
yeah
storm storm
yes
devout snowBOT
wise bronze
dead server
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dark finch
I discovered that for even values of x, x!! Is equal to (x/2)! * 2^(x/2)
How can I make this work for odd numbers?
devout snowBOT
I discovered that for even values of x, x!! Is equal to (x/2)! * 2^(x/2)
How can...
cinder bobcat
doesn't really work for odd numbers since they don't all share a common factor
acoustic leaf
cinder bobcat
oh my bad, i didn't realize it said double factorial. ^
acoustic leaf
under "relation to the factorial" you can find your identity as well as another identity relating double factorials of odd numbers to powers of 2 and factorials
arctic field
I discovered that for even values of x, x!! Is equal to (x/2)! * 2^(x/2)
How can...
use the gamma function
dark finch
use the gamma function
The intent is to calculate double factorials on calculators that lack such luxuries.
dark finch
Yeah, looking at that page, I should've seen that I can just divide a factorial by my even double factorial to create an odd facttorial.
Thanks!
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digital whale
i think its impossible right
lyric hornet
well when I see an x multiplied by an exponent right off the bat I'm thinking something with Lambert W
(x-1)e^x=1
digital whale
this is the 1st derivative of a function
and i have to find when it equals zero
to plot the graph
wtf am i supposed to do
lyric hornet
xe^x-e^x-1 is f'(x)?
digital whale
should i just manipolate it until i find a nice way to approximate it
lyric hornet
what is f(x)?
digital whale
this question was on the previous exam
we had to plot the graph
no calcs were allowed
calc is short for calculator btw
its slang
smoky nimbus
calc is short for calculator btw
3 is short for pi. It's engineering slang
digital whale
relatable
lyric hornet
yeah no but I really don't get that, the only way I see it without using Lambert W is approximation lmao
but maybe I'm overlooking something
digital whale
but maybe I'm overlooking something
i dont think u r
thats also why W exists
i mean i also hoped i overlooked something somehow thats why i asked
but i dont think so
i guess we just have to approximate the value
those r the grapsh
i didnt ask chatgpt but he will probably just brute force it
so ye i guess our professor wanted us to guess
which is lame
lyric hornet
yeah idk that's a pretty odd question especially for a non-algebraic equation or one that doesn't have an algebraic solution, I forget the exact terminology but yknow what i mean
visual hazel
i dont suppose numerical methods is something you know
digital whale
ye
visual hazel
a way to approximate zeros of a function
newton's method, bisection method etc
but since you dont know them then it doesnt matter
digital whale
oh ye i know em
still thats jsut smart guessing
but ye alr might speed up the process
visual hazel
¯_(ツ)_/¯
digital whale
actually its the only way
alr
whatever ill figure it out
thanks people
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peak coyote
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restive river
I want to calculate the chance of 3 times tails when flipping 5 coins
K K K M M
K K M K M
K K M M K
K M K K M
K M K M K
K M M K K
M K K K M
M K K M K
M K M K K
M M K K K
these are the outcomes of 3 times tails
To calculate this I need to use the binominal coefficient 5C3 = 10
But from what I understand binominal coefficient doesnt care about the order of the elements, here there are 10 outcomes but they only differ in order so shouldnt it be counted as 1. I know this is wrong, but I can't figure out what is wrong
crisp tapir
I want to calculate the chance of 3 times tails when flipping 5 coins
K K K...
these are the ways you can get 3 tails when flipping 5 coins
vital dagger
I want to calculate the chance of 3 times tails when flipping 5 coins
K K K...
but they only differ in order
In this case nCr doesn't count the order between Ks and Ms
as in $K_1 K_2 K_3 M_1 M_2$ is not different to $K_2 K_3 K_1 M_2 M_1$
woven radishBOT
AkitoLite
devout snowBOT
@restive river Has your question been resolved?
jagged flax
guys take a look at this
devout snowBOT
guys take a look at this
jagged flax
is there a problem witht he question or like
from like what i know
P(X=x) part
all of those fractions are suppos eto ad dup to one
but they go beyond one
is this
suppose to happen
can i fix it
devout snowBOT
@jagged flax Has your question been resolved?
tropic skiff
can i fix it
Probabliity distributions like the one shown are supposed to add up to 1
As you said, they dont in this case
feral agate
Are these supposed to have some pattern?
devout snowBOT
Are these supposed to have some pattern?
feral agate
the RREF of A is $$R=\begin{bmatrix}1&2& \ & &1\ & &\end{bmatrix}$$
acoustic leaf
that's not rref
woven radishBOT
kheerii
feral agate
that's not rref
my bad
is the RREF of [A A] just [R R]?
seems like it should be because we're just doing the same operations
acoustic leaf
so it would seem
feral agate
hmm
for C we should have {R, R; 0, 0}
because once we reduce the first three rows the bottom three go to 0
hmm, actually
the intermediate step will be {R, R; A, 0}
we can't get the A to a 0 without changing the 0
we can get it to {R, R; 0, -A}
oh no wait we will have to do row permutation as well
so it won't be in terms of A and R i guess
acoustic leaf
well you can put it in terms of the nonzero rows of R at least
woven radishBOT
kheerii
feral agate
should be this
acoustic leaf
yes
feral agate
neat
$$\begin{bmatrix} I_r & 0_{r\times (n-r)}\ 0_{(m-r)\times r} & 0_{(m-r)\times (n-r)}\end{bmatrix}$$
woven radishBOT
kheerii
feral agate
should just be this
faint hearth
yeah
you can also do this by picking good bases
which is the same as performing row and column operations
feral agate
isn't this basically just diagonalisation
faint hearth
feral agate
like if m=n=r this process is just diagonalisation
faint hearth
a map is diagonalisable if there is a basis of eigenvectors
feral agate
right
feral agate
right okay
faint hearth
you are just picking nice bases for your source and target (possibly different) and getting a diagonal matrix. that is different from diagonalisation, which is picking the same basis for the source and target, plus the basis must consist of eignevectors
feral agate
but doing column operations does what for us?
we're basically permuting and doing stuff to the input variables
faint hearth
row and column operators are just changing bases. infact any invertible matrix can serve as a change of basis matrix
feral agate
hmm
faint hearth
**kheerii**
i mean you can view it the way you did but idk how to make much sense of it. anyways what you wrote here is correct
feral agate
I think it might be more insightful if m=n
under certain bases of the domain and range we have r vectors which are invariant under the transformation and n-r vectors which go to 0
faint hearth
thats not true tho
feral agate
uh wait
faint hearth
just take a rotation in R^2 (not multiple of pi)
feral agate
the first r components of those vectors are invariant
faint hearth
just take a rotation in R^2 (not multiple of pi)
there is no vector that is invariant under this
faint hearth
**kheerii**
this is actually just saying a pretty boring fact
feral agate
right okay I think I'm just trying to find some explanation where there is none
faint hearth
its saying, take a basis of the kernel, extend to basis of whole space. then a basis for the image is the image of the basis vectors not in the kernel
feral agate
lol when you say it like that
faint hearth
its saying, take a basis of the kernel, extend to basis of whole space. then a b...
because that is the matrix of the map under this basis
vivid hearth
i cannot understand why cross product of two vectors will result in vector that is perpendicular to the plane that two vectors make? like if dot product is how one vector "projects" to another then what is cross product?
devout snowBOT
i cannot understand why cross product of two vectors will result in vector that ...
sand dove
i cannot understand why cross product of two vectors will result in vector that ...
as you said, cross product is for finding a normal vector to the plane created by the two vectors
vivid hearth
normals have like their own like lengthes?
sand dove
and its magnitude is proportional to "how perpendicular are they"
vivid hearth
and its magnitude is proportional to "how perpendicular are they"
oooh i see now
why we need to find normal for it? my teacher tried to explain it mechanically like with physics but i didnt really understand
she said something about rotation
sand dove
there are several applications
for example finding the equation of a plane
a plane in 3d can be given by its cartesian equation ax + by + cz = d
and (a,b,c) is actually a normal vector
so to compute the cartesian equation of a plane containing 3 points, say A,B,C
compute vectors AB, AC (for example)
compute their cross product (a,b,c)
then find d by injecting point A into the equation (or B or C)
vivid hearth
i put them into x y z yes?
sand dove
A = (x,y,z)
vivid hearth
thank you bro you are very helpful
how do i close the question now? will it automotically close?
iron kindle
how do i close the question now? will it automotically close?
!done
devout snowBOT
how do i close the question now? will it automotically close?
If you are done with this channel, please mark your problem as solved by typing .close
vivid hearth
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acoustic plank
Anyone can help me find O
devout snowBOT
Anyone can help me find O
acoustic plank
I can't draw
gray axle
Anyone can help me find O
Redraw it
devout snowBOT
@acoustic plank Has your question been resolved?
acoustic plank
No
gray axle
<@&286206848099549185>
BDC = 40⁰
Angles DBO and DCO
Are similar
The shape has 4 sides.
acoustic plank
Only difference is there is a y in the bottom right on the left and that's what I need for part 2
gray axle
Only difference is there is a y in the bottom right on the left and that's what ...
U need angle P, Right?
Angle P = 360⁰ - Angle D + angle B + angle C
Angle B = ( 180⁰ - angle D ) ÷ 2
Angle C = ( 180⁰ - angle D ) ÷ 2