I wrote a script to check it real fast and got 1381.
#help-10
wheat vapor
daring cairn
bro wrote a script?
wheat vapor
>>> n = 1
>>> while n < 5000:
... if n%2 == 0 and checkUnique(n):
... count += 1
... n += 1
...
>>> count
1381
>>> ```Yeah.
daring cairn
damn how could i be off by 8 though
warm shaleBOT
obtuse pebbleBOT
daring cairn
.reopen
obtuse pebbleBOT
β
daring cairn
.close
obtuse pebbleBOT
daring cairn
.reopen
obtuse pebbleBOT
β
daring cairn
u mind helping me with another?
wheat vapor
What's up?
daring cairn
its a flag where you can use ten colours but none can be the same in adjacent squares
wheat vapor
Do you know the answer?
daring cairn
no clue. done some with 2 cases only being distinct vs 2 boxes the same but this one has mulitple
this test q was from like 2019 so idk teach only said a max of 2 cases for flag questions
wheat vapor
I've got a best guess that might be right. I just figure pick one of the spots to have 10, then pick 9 or less based on how many possibilities it can be considering the ones next to it that are already picked.
Like, A:10, B: 9, C:8 (since it's next to A and B), D: 9, F: 9, E: 8 (since next to D and F), G: 9, H: 8. Then multiply.
daring cairn
that is one case however, since you can pick a colour twice, if d and f are the same coluor that adds a colour to choose from for c and e
and so one and so forth for gh ab
wheat vapor
Oh yeah, I was just listing number of possible choices given how many adjacent things are next to it that I've already picked a color for. My method accounts for A and D both being green.
Otherwise it'd just be 10x9x8x7x6x5x4x3
I may be off in my thinking. That's just how I'd try to do it.
daring cairn
.close
patent marten
obtuse pebbleBOT
patent marten
Hi, I wanted to check if the domain for this would be (-infinity, infinity) and the range (2, infinity)?
empty cypress
it really depends what you think is happening off this page
do you care about inclusive/exclusive difference?
because it is wrong if you do
patent marten
In that case it would be (-infinity, -1)U(-1,1)U(1, infinity)?
empty cypress
no
i mean that range: (2, infinity) inplies y = 2 is not possible (which is clearly is)
so it should be [2, infinity), notice the inclusive parens
patent marten
I thought would be excluded because of the open circle also being present or having the chose of using ()/[].
empty cypress
I thought would be excluded because of the open circle also being present or hav...
whats f(1)?
or g(1) in this case
patent marten
2
This is a different problem but it was what I was going by when dealing with the current one.
So, if I understand correctly, if the function exists even if an open circle is present, that value is still inclusive?
?
.close
wind sierra
obtuse pebbleBOT
wind sierra
Can anyone even briefly give a hint
(for the first one)
Im trying to analyse the terms
perhaps something that differentiaties to x sec^2(x)*tan(x)
this is A level (17 year old maths) btw
weary delta
Derivative of tanx is sec^2(x) maybe that can work somehow
weary delta
it cleanly differentiates
Now that was unexpected π
hearty snow
Simple math, but for the life of me I cant figure out how to show the answer
Pete bought a car for 3000β¬, how much does he need to sell the car for, when heβs giving a 20% sale, but wants 25% profit from the original price ( answer is given on the equation 4687,50β¬, but I deadass js cant figure out how to get to that point π€¦π»ββοΈπ)
obtuse pebbleBOT
Simple math, but for the life of me I cant figure out how to show the answer
Pe...
weary delta
First figure out how much he needs to sell it for to make his desired profit
hearty snow
Like without the 20% sale?
orchid wind
neon eagle
How much just to make 25% profit basically
weary delta
Hm, are you sure about the answer given?
hearty snow
Like the answer given at the start?
weary delta
Oh, oh, nvm. I misread, yeah itβs fine
hearty snow
Alr
weary delta
3750 is the price on sale then, yes?
hearty snow
Yh answer is βabout 4687,50β¬β
Thats the price needed to make 25% profit w/o the 20% sale
weary delta
Letβs say X is the price before sale, so we have that x - 0.2x = 3750
hearty snow
Wait
dont send it e
mightve js figured it out hold up π
wait no keep going
π
@weary delta Able to help me finish this? Tryna go sleep
weary delta
Or equivalently you can say that, 80% of the price before discount is 3750, either way, simple to solve
weary delta
<@216912122083409925> Able to help me finish this? Tryna go sleep
You could just solve what I sent for x and you are done π
hearty snow
OHHHHH
hearty snow
You could just solve what I sent for x and you are done π
preciate it brodie π
.close
wise panther
obtuse pebbleBOT
wise panther
I thought there would be no more disconitniues other than 6
I put dne earlier but didnt work
haughty coyote
-4 is the root, not 4
neon eagle
rip
daring rock
I thought there would be no more disconitniues other than 6
a factor that cancels with the numerator still gives a removable discontinuity
daring rock
it happens lol
wise panther
but
arentn the roots
(x+4)(x-6)
bruh
I just proved my self wrong
by being a geniuus
daring rock
that is the factored form of the denominator
wise panther
ik
daring rock
x=-4 and x=6 are the roots
wise panther
Ik i REALIZed as I typed it ol
daring rock
lmao
daring rock
because the numerator also has a factor of x+4
daring rock
np π
wise panther
I swear whenever you dont understand smth in math and someone explains it its always
"Oooohh"
thats what I think everytime I hear an explenation lmao
daring rock
i know what you mean lol
elfin sequoia
obtuse pebbleBOT
golden sand
!show
obtuse pebbleBOT
Show your work, and if possible, explain where you are stuck.
golden sand
draw a diagram
golden sand
you can find the angles and the radius
golden sand
and after you find the angles there is a formula relating two sides and angle between them to opposite side
golden sand
you've got arcs
elfin sequoia
ok
golden sand
how much is 5/(3+4+5) of a circle
elfin sequoia
5/12
golden sand
what angle with the vertex at the circle center does the arc of length 5 subtend?
golden sand
yes
You should know the formula involving two sides of a triangle and an angle between them
elfin sequoia
let me look for it, i think i have it written down
is it 1/2 ab sin C?
wait the sides are radii
golden sand
or yeah, you could use some properties of those triangles to just use sin
elfin sequoia
ok
golden sand
not 1/2absinC though
elfin sequoia
$(27+9sqrt(3))/pi^2$
warm shaleBOT
fokeww
golden sand
what is this
elfin sequoia
golden sand
that's the area?
elfin sequoia
yep
golden sand
ok, and?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
rotund vector
Can someone help me solve this differential equation?
obtuse pebbleBOT
Can someone help me solve this differential equation?
visual gulch
Can someone help me solve this differential equation?
... what's the equation?
obtuse pebbleBOT
@rotund vector Has your question been resolved?
torn knoll
need discrete math folks to tell me if i made a mistake or this is valid
obtuse pebbleBOT
@torn knoll Has your question been resolved?
fallow tusk
obtuse pebbleBOT
fallow tusk
Do I do the cross product between 4, 10, -13 and 3, -1, 1 here?
doesnt really sound right...
latent walrus
(4,10,-13) is normal to the plane already
so you can take that as your direction vector for the line
fallow tusk
so do I subtract 3,-1,1 from 4,10,-13?
latent walrus
so, do you know this form of equation for a line? (a)+t(d) where a is a point on the line and d is the direction vector and t is some scalar
fallow tusk
so then x = 3+4t, y = -1+10t, z = 1-13t
latent walrus
exactly
fallow tusk
do I have to solve for t?
latent walrus
so then x = 3+4t, y = -1+10t, z = 1-13t
which you have here
real gorge
for A3
I got x_1 = 1
x_2 = 1
x_3 = 0
the answer to the homogenous system defining the subspace was x_3 = 0
I see the method of getting it, but I don't understand why/how. Can someone explain what this means actually
real gorge
please use reply
obtuse pebbleBOT
@real gorge Has your question been resolved?
brave bramble
We have a system that can take an (x1, x2, x3) and returns "yes" or "no"
For A3, the system returns "yes" if x3 = 0
That means a few vectors like (1, 1, 0), (5, -4, 0) satisfy the system
real gorge
ok let me try understanding 1 sec
brave bramble
But that's exactly the same as the span definition they gave. That is, vectors that satisfy the system are in that span, and vice versa
real gorge
alright so im a bit bad with technical deifitinitons in linear algebra
so a homogenous system of linear equations means they = 0
i got x_3 = 0
and x_1 = 1 and x_2 =1
in the augmented matrix
real gorge
But that's exactly the same as the span definition they gave. That is, vectors t...
yeah no row reducing had to be done
not sure if you can simply this for me
but what does the question even mean
brave bramble
Forget matricies for a sec. You're concerned with Span{(1,0,0) , (0,1,0)}
real gorge
yes
brave bramble
That is, this is the set of vectors you can make by freely adding and scalar multiplying, but only using the vectors (1,0,0) and (0,1,0)
real gorge
yes
brave bramble
It should be clear that, no matter what you do, the third component will always be 0
That's another way to define this set
brave bramble
That's it. If you get that, then you get everything.
real gorge
well yeah i guess it wasnt that difficult
but then for A4
how would you do that
i mean i can just equate each to a value of x_n
brave bramble
So note the first component will always be double the second component
real gorge
yep
brave bramble
Arrange those into the form you want, you're done
real gorge
so i'd like to ask something
i dont always have to
row reduce
and get something like this
brave bramble
You could row reduce
[1| x1]
[2| x2]
[0| x3]
And you'd get the same answer
real gorge
yeah so i did that
well there isnt really row reducing
but isnt it 3 separate answers
unless i make the first one 2 = 2x_1
real gorge
You could row reduce
[1| x1]
[2| x2]
[0| x3]
And you'd get the same answer
OH R2 - 2R1
amazing
one last thing
i did a problem
row reduced twice
got 2 different sets of answers
like the first time was answers A and B
second time was answers C and D
and the textbook onoly had answers A & C
brave bramble
But it's a good idea do to some of this stuff without the matrix tech.
real gorge
like the first time was answers A and B
second time was answers C and D
Is it possible that you can get different answers depending on how u row reduce
all correct?
brave bramble
Depends on the question haha
brave bramble
No an rref is unique
real gorge
no for these problems i just get the REF
because that's as far as the textbook went
i guess i should recheck problems with the RREF?
brave bramble
Without seeing the problem, I can't be sure haha
brave bramble
Okay! Feel free to ask if you have anything else.
latent walrus
who has this half chicken
wooden cipher
I would argue half a chicken doesnt count but yes, 1.5
What do you think the answer is?
tepid sedge
its 1.5
surreal jetty
yeah 1.5
wooden cipher
The amount of eggs laid is proportional to the amount of chickens or amount of days
tawdry arrow
1.5
wooden cipher
The amount of eggs laid is proportional to the amount of chickens or amount of d...
This can be written as chickens*days is proportional to eggs
Since both days and eggs are multiplied by 4, chickens stays constant
tawdry arrow
Eggs = 2/3 (Chickens x Days)
wooden cipher
The fact is you have like 5 people telling you 1.5 is correct
daring rock
You give the chickens 4 times more time, they'll give you 4 times more eggs. Why wouldn't you multiply by 4?
with the same number of chickens
latent walrus
wooden cipher
Tell us whats right then please
Explain
The burden of proof is on you to prove it now
tawdry arrow
Chickens and Days are independent of eachother. Eggs are dependent on both Chickens and Days. So, if the value of Days changes, Chickens' value doesn't, but Eggs' does.
daring rock
your teacher is mistaken, or you are mistaken. The answer is 1.5
autumn adder
...
daring rock
then you have misrepresented the question
daring rock
it's not a matter of opinion dude lol
tawdry arrow
autumn adder
What's up here.
surreal jetty
1.5 chickens = 1.5 eggs/1.5 days
6/1.5 = 4
1.5 x 4 = 6 eggs/6 days
tawdry arrow
this conversation is a mobius loop man
autumn adder
Check if you wrote your question correctly @timid silo
tepid sedge
its 1.5 chickens bro
tawdry arrow
tony over here with the facts
surreal jetty
1.5 chickens = 1.5 eggs/1.5 days
6/1.5 = 4
1.5 x 4 = 6 eggs/6 days
^
daring rock
Genuinely cannot wait
tawdry arrow
latent walrus
what time shall this event be
tawdry arrow
its been a min@autumn adder
autumn adder
Figure of speech.
tawdry arrow
i know
autumn adder
Do you understand your question first
I don't want your friend or professor to influence you.
What do YOU say
minus your friend and professor.
Look.
There's 1.5 chickens
(I dont know how but its akin to carrying 600 watermelons in elementary school)
So there's 1.5 chickens
They lay 1.5 eggs in 1.5 days
Can you listen?
Have a plate for listening (thats what we say in our language).
There's no need to overthink
Use common sense
If you let the 1.5 chickens sit for more 1.5 days
They gonna give more 1.5 eggs
Can you stop overthinking?
University has asked 1+1
Doesnt mean you need to do a whole riemann zeta on it.
daring rock
Using a more complicated method isn't going to magically change the answer
autumn adder
You're unnecessarily complicating an easy question
You want a complicated method?
I'll tell you what
tawdry arrow
Have a plate for listening (thats what we say in our language).
what language
autumn adder
1.5 chickens lay 1.5 eggs in 1.5 days
autumn adder
what language
I won't say
tawdry arrow
respect that
autumn adder
Leave that question
Come to a real question
1 CHICKEN lays 1 EGG in 1 DAY
This is nonsense to me.
tawdry arrow
thats literally the thing i sent earlier
autumn adder
And trust me I do more math than you everyday
tawdry arrow
Eggs = 2/3 (Chickens x Days)
literally just this
autumn adder
If you had to assume a calendar with leap years in the simplest form, you could just use 365.25 which was as simple.
That's a kids topic.
Sorry but that isn't some hyped uni topic
We solve better questions than this in high school
I remember solving <<insert dramatic music>> inverse proportionality questions
It was the worker problems if you know
You aren't required to overthink stuff, go by logic wherever you can.
I bet if the professor says the answer is four, you have written your question wrong
I bet, I bet you're either gonna change your question or do whatever nonsense you can to keep yourself right
autumn adder
Did you just mistake his "1" for a "4"
daring rock
Either you are misremembering what she said, or you misunderstood her, or you did not write the question down correctly
autumn adder
astaghfirullah
I am
tawdry arrow
I bet if the professor says the answer is four, you have written your question w...
you said 4 here so he got confused where YOU got the 4 from
autumn adder
you said 4 here so he got confused where YOU got the 4 from
Aight I see
tawdry arrow
man im going crazy
tawdry arrow
some profs really got the worst handwriting
autumn adder
I hate the fact how people put their professors as the absolute truth
I respected my teachers, gave their solutions the first preference but always voiced my concerns if I found something wasn't right
tawdry arrow
theyre glorified a lot
autumn adder
I didn't agree to the fact that if a professor proved a flawed logic it should be right
They're like you, glory to the professor kids
tawdry arrow
now im thinking if she was explaining a wrong example of something
autumn adder
Or just didn't wanna work their brain a little
tawdry arrow
and he thought it was right
autumn adder
...
If you can't take logic and arguments you're the one who should shush. But anyway, I won't be remotely interested in knowing
I have better things to do in Desmos, and life.
tawdry arrow
desmos is life
autumn adder
Rather than run after a person who has a wall instead of an ear
There's never two answers to a linear question unless it's quadratic.
No, I don't take wrong things.
I'll leave you be, though
thin star
can someone give a tldr of this thread lmao
tawdry arrow
1.5 chickens
autumn adder
can someone give a tldr of this thread lmao
Messes up logic, says professor said some answer, glorifies them, even if the answer is wrong according to the QUESTIOn she shared.
daring rock
Dude you're the one who can't accept that you could have possibly misunderstood the question or your teacher's answer, and you're telling someone else that their ego is too big?
fierce lagoon
Okay what's the original question
How the fuck do you have half a chicken
6 eggs in 6 days is equivalent to 1.5 eggs in 1.5 days
Since they're all 1 egg : 1 day in proportionality
So you'd still need 1.5 chickens
If you want it in fractions:
$$\frac{1.5}{\parens{\frac{1.5}{1.5}}} = \frac{x}{\parens{\frac{6}{6}}}$$
warm shaleBOT
Umbraleviathan
fierce lagoon
It's quite obvious what x is
Now why the answer is meant to be 1.5 chickens, no idea because you cannot have half a chicken and have it function
autumn adder
Okay what's the original question
||Hi Umbralevi don't engage is my advice||
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
@timid silo Has your question been resolved?
sage dagger
A cylindrical tank standing upright (with one circular base on the ground) has radius 1 meter. How fast does the water level in the tank drop when the water is being drained at 3 liters per second?
So I know dV/dt is -0.003 and dV/dt = dH/dt? I donβt know Iβm a little confused
obtuse pebbleBOT
A cylindrical tank standing upright (with one circular base on the ground) has r...
@sage dagger Has your question been resolved?
tardy epoch
A cylindrical tank standing upright (with one circular base on the ground) has r...
no dV/dt does not equal dH/dt. write the volume of the cylinder in terms of r and h, then differentiate using product rule
obtuse pebbleBOT
@sage dagger Has your question been resolved?
outer socket
can anyone help me making integrating factor from this equation?
obtuse pebbleBOT
can anyone help me making integrating factor from this equation?
@outer socket Has your question been resolved?
thin star
is I a constant?
obtuse pebbleBOT
@outer socket Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
fringe trellis
Hi are these correct?
obtuse pebbleBOT
Hi are these correct?
fathom flicker
Hi are these correct?
use a limit calculator online
fringe trellis
use a limit calculator online
I did, but I want to see if the work is correct also
The procedure
The answers match up tho
But I want to make sure that I'm doing it correctly
obtuse pebbleBOT
@fringe trellis Has your question been resolved?
fringe trellis
But I want to make sure that I'm doing it correctly
<@&286206848099549185> can someone check through the work procedures to see if they're correct, thx
fringe trellis
Hi are these correct?
^
flat sparrow
obtuse pebbleBOT
@fringe trellis Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
lunar rover
Hey, bit unsure how to do this, the question states to write the following as one fraction.
obtuse pebbleBOT
Hey, bit unsure how to do this, the question states to write the following as on...
lunar rover
$$\lg(\sqrt[x]{10y})$$
warm shaleBOT
Totalani
errant lark
What have you tried?
lunar rover
Im trying to remember what happaned to the \sqrt[x] when you move it down
other than that nothing
I tried $$\frac{\lg(10y)}{x}$$
warm shaleBOT
Totalani
errant lark
That is correct. However, that's not sqrt{x}. It's a power of (1/x).
royal basin
I tried $$\frac{\lg(10y)}{x}$$
was this rejected?
royal basin
can you show the entire problem
yes even if it is in one of swedish, danish and norwegian
royal basin
oh because it's $\sqrt[x]{10^y}$ and not $\sqrt[x]{10y}$
warm shaleBOT
Ann
lunar rover
aaah
royal basin
you are misreading the problem
lunar rover
it was hard to see π
wait so my inital thing was correct, just change the y?
still says wrong
lunar rover
y
royal basin
yeah so
lunar rover
oh ok
royal basin
you should be getting y/x
lunar rover
y/x
yea
so when you have \sqrt[x] you can move it to fraction and whatever x is becomes the numerator?
frail depot
$f(x)=x^3-2x^2+31x+7$
Extremal and critical points?
obtuse pebbleBOT
$f(x)=x^3-2x^2+31x+7$
Extremal and critical points?
warm shaleBOT
SimonWin
frail depot
Is the answer just that there is none, since after calculating the discriminant to $d=-356$ there are no solution for $f'(x)=0$
warm shaleBOT
SimonWin
frail depot
So, there are zero critical points and extremal?
lone echo
what are you calling critical points? derivative 0?
if so, correct, since derivative cant be 0 as you explained
warm shaleBOT
SimonWin
obtuse pebbleBOT
@frail depot Has your question been resolved?
opaque galleon
A six-sided die is loaded in a way that each even face is twice as likely as each odd face. Construct
a probabilistic model for a single roll of this die, and find the probability that a 1, 2, or 3 will come
up.
My solution: P(E) = 2 P(O)
P(E) + P(O) = 1
2P(O) + P(O) = 1
P(O) = 1/3
so P(E) = 2/3
but my answer is wrong and the correct answers are P(E) = 2/9, P(O) = 1/9
obtuse pebbleBOT
A six-sided die is loaded in a way that each even face is twice as likely as eac...
opaque galleon
what did I do wrong?
obtuse pebbleBOT
@opaque galleon Has your question been resolved?
opaque galleon
nope
abstract beacon
what did I do wrong?
You forgot that there are 3 even faces, and 3 odd faces
opaque galleon
You forgot that there are 3 even faces, and 3 odd faces
oh yeah
opaque galleon
You forgot that there are 3 even faces, and 3 odd faces
thank you so much
obtuse pebbleBOT
@opaque galleon Has your question been resolved?
silver ore
Assume the exponent of a number is β127 and the sign bit is 0. Find the decimal number represented by a mantissa of: 00000000000000000000000 and find the decimal number represented by the mantissa 00000000000000000000001 Finally, find the difference between these two numbers, giving the resolution of decimal representation for small numbers (since we incremented the mantissa by 1, the smallest resolution in binary representation).
can i have help?
obtuse pebbleBOT
Assume the exponent of a number is β127 and the sign bit is 0. Find the decimal ...
@silver ore Has your question been resolved?
silver ore
<@&286206848099549185> would the decimal number for the mantissa 00000000000000000000000 be 0?
.close
swift moat
The number 11 is a prime number. Are there any more prime numbers among palindromes of the form 111...111?
obtuse pebbleBOT
The number 11 is a prime number. Are there any more prime numbers among palindro...
swift moat
Are there?
swift moat
1111..1111 with 19 ones???
kind hawk
yes
obtuse pebbleBOT
kind hawk
can't even cheat yourself with the internet?
reef cobalt
Yes
obtuse pebbleBOT
Available help channel!
thin oxide
Can anyone provide me with resources in Statistics?
(Could be cool if it contains the last three)
obtuse pebbleBOT
Can anyone provide me with resources in Statistics?
(Could be cool if it contain...
@thin oxide Has your question been resolved?
empty cypress
not English + not math question, should probably ask elsewhere
tender meteor
obtuse pebbleBOT
tender meteor
can anyone do 3 c and d
this is example 23
<@&286206848099549185>
@regal jewel surely still help ππ
obtuse pebbleBOT
@tender meteor Has your question been resolved?
tender meteor
.close
timid silo
<@&286206848099549185> would the decimal number for the mantissa 000000000000000...
check out this circuit i made for comparing floating point values in binary!
obtuse pebbleBOT
@timid silo Has your question been resolved?
lusty shore
Open
lusty shore
obtuse pebbleBOT
lusty shore
Part b havenβt been specifically taught but Iβm just curious how to do it
obtuse pebbleBOT
Available help channel!
jovial lynx
obtuse pebbleBOT
jovial lynx
<@&286206848099549185>
obtuse pebbleBOT
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
1
obtuse pebbleBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
jovial lynx
?
fathom flicker
if your question has not been answered for 15 mins..
jovial lynx
**if your question has not been answered for 15 mins**..
sorry
fathom flicker
Anyways youβre much more likely to get help if you put any effort into describing why youβre confused and what you need help with
jovial lynx
I need to find the subspace
the notation is a bit confusing, but we need to do direct sum
<@&286206848099549185>
obtuse pebbleBOT
@jovial lynx Has your question been resolved?
jovial lynx
<@&286206848099549185>
jovial lynx
<@&286206848099549185>
the orthogonal complement consists of all vectors x in R4 such that x * <1,1,1,1> = 0, since T^β₯
from there we get x1 + x2 + x3 + x4 = 0
the vector <1, a, 1, 1 ,1> is in T^β₯ if 1 + a + 1 + 1 = 0, no? => a = -3
jovial lynx
||<@&286206848099549185> ||
jovial lynx
||<@&286206848099549185> ||
jovial lynx
|| <@&286206848099549185> ||
jovial lynx
|| <@&286206848099549185> ||
dreamy ridge
the orthogonal complement consists of all vectors x in R4 such that x * <1,1,1,1...
i would try to work out the orthogonal space first
you know its a subset of $\mathbb{R}^4$ so its basis vectors will be of the form $(x_1,x_2,x_3,x_4)$
warm shaleBOT
kitty queen
dreamy ridge
from what you worked out, $x_4=-x_1-x_2-x_3$
letting $x_1=1$ and $x_2=x_3=0$ we get $(1,0,0,-1)$
similarly, we can obtain $(0,1,0,-1)$ and $(0,0,1,-1)$
jovial lynx
yes but x3 is free, x3 = c , c β R
if we see H
x3 is not present
I assume x3 is free unrestricted , while x β R
dreamy ridge
if we see H
im calculating the orthogonal subspace of T
now i should be able to find a vector in that subspace of the form $(1,a,1,1)$
warm shaleBOT
kitty queen
dreamy ridge
set $(1,a,1,1)=x(1,0,0,-1)+y(0,1,0,-1)+z(0,0,1,-1)$
warm shaleBOT
kitty queen
dreamy ridge
you obtain a system with 4 equations and 4 unknowns
but its really easy
$x=1, y=-3, z=1, a=-3$
warm shaleBOT
kitty queen
dreamy ridge
next i would calculate H
we see that the vectors are of the form $(2x_2+x_4,x_2,x_3,x_4)$
warm shaleBOT
kitty queen
dreamy ridge
actually you just need two linearly independent vectors that are both in T orthogonal and H
one of them could be (1,0,-2,1), because $(1,0,-2,1)\cdot (1,1,1,1)=0$ and it is obtained by letting $x_2=0,x_3=-2$ and $x_4=1$
warm shaleBOT
kitty queen
dreamy ridge
same argument applies to (2,1,-3,0)
so we can let $S=\langle (1,0,-2,1),(2,1,-3,0)\rangle$
warm shaleBOT
kitty queen
dreamy ridge
@jovial lynx
obtuse pebbleBOT
@jovial lynx Has your question been resolved?
silver cove
Helpp is this correct
obtuse pebbleBOT
Helpp is this correct
minor vortex
express this in scientific notation
0.0025=
silver cove
Helpp is this correct
Problem is , find the four arithmetic means between the numbers -17 and 53
<@&286206848099549185>
keen garnet
Helpp is this correct
,rotate
warm shaleBOT
silver cove
Yes
keen garnet
Problem is , find the four arithmetic means between the numbers -17 and 53
What do mean by that ?
silver cove
Ehh
Find the four arithmetic means
But firs i have to find common difference which is d
Omg nvm
I realized i was wring
.close
timid silo
bro
timid silo
I keep making mistakes 
How do i determine what's the remainder and what's the quotient when doing synthetic division
Is the remainder any values that aren't under the bottom line after the last multiplication is done?
so this
hasty viper
timid silo
How do i determine what's the remainder and what's the quotient when doing synthetic division
$$\frac{x^3}{x^2 + 0x+8}$$
warm shaleBOT
What should I do
obtuse pebbleBOT
@timid silo Has your question been resolved?
wet storm
could someone explain what this notation means?
obtuse pebbleBOT
could someone explain what this notation means?
gilded needle
do you know what sup A and sup B mean?
gilded needle
so those are two numbers
sup(sup A, sup B) is just the bigger of those two numbers
could equally well have written
max(sup A, sup B)
obtuse pebbleBOT
brisk grove
That's correct
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
tame relic
obtuse pebbleBOT
high lily
- g(a)
sharp pecan
does anyone know how to differentiate this?
obtuse pebbleBOT
does anyone know how to differentiate this?
gilded needle
doesn't the usual quotient rule work?
sharp pecan
its too complicated and i need to find the horizontal points
gilded needle
what leads you to suspect that there's a simpler method?
and what do you mean by horizontal points?
obtuse pebbleBOT
@sharp pecan Has your question been resolved?
static furnace
you could make turn sqrt(x) into x^(1/2) and then separate the fractions into two parts
then simplify the exponents of x in each fraction
and then differentiate
pure sun
anyone know of a site i can use to graph ordered pairs?
obtuse pebbleBOT
anyone know of a site i can use to graph ordered pairs?
pure sun
stuff like this:
5.37,0.2
6.3,0.28
7.33,0.32
7.93,0.34
7.42,0.32
nvm turns out desmos works very nicely for this
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obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
hexed cape
obtuse pebbleBOT
obtuse pebbleBOT
@hexed cape Has your question been resolved?
obtuse pebbleBOT
@hexed cape Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
indigo cypress
Hello guys, I am having trouble solving this matrix
obtuse pebbleBOT
Hello guys, I am having trouble solving this matrix
indigo cypress
what should my next step be?
I would be really thankful for your help
I must use the Gaus method
Is subtracting line 2 from line 3 the right choice?
obtuse pebbleBOT
@indigo cypress Has your question been resolved?
obtuse pebbleBOT
@indigo cypress Has your question been resolved?
obtuse pebbleBOT
@indigo cypress Has your question been resolved?
drowsy burrow
You know you can immediately multiply a row with a scalar and add it to a different
And do the calculating in your head
Actually i dont get what youre trying to do, you subtracted 4th from 3rd and then you just undid it?
obtuse pebbleBOT
@indigo cypress Has your question been resolved?
jagged wyvern
Hello guys, I am having trouble solving this matrix
Ngl I have 0 clue whatβs going on here
burnt urchin
what is patellorgorms theorm i forgot
indigo cypress
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obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
deep cairn
What happened between the highlighted parts?
obtuse pebbleBOT
What happened between the highlighted parts?
deep cairn
How did a n magically pop in with an inequality?
glacial obsidian
How did a `n` magically pop in with an inequality?
It says it's because n >= 1
So n+3 >= n+3n
glacial obsidian
Yes, I wrote the inequality in the wrong way
deep cairn
also in the solved example, it says <= 1/2 [ ... ]
less than equal to what?
1/n ?
also why magically n+3 suddenly n+3n, no change to the rest of the quantities?
I think the book is either flawed or they skipped a lot of steps
glacial obsidian
also in the solved example, it says <= 1/2 [ ... ]
less than equal to what?
Where does it say that?
glacial obsidian
I think the book is either flawed or they skipped a lot of steps
Yes, a lot of steps were skipped, but it is not flawed
deep cairn
Yes, a lot of steps were skipped, but it is not flawed
I see
golden sand
3 < 3n if n>1
deep cairn
yep
golden sand
all good there
glacial obsidian
If 1 <= n then 3 <= 3n, then n+3 <= n+3n, then |n+3| <= |n+3n| (because both are positive numbers), then k|n+3| = k|n+3n| for all positive k. Then let k = 1/2 times 1/|2n^2+5n+7|
deep cairn
I think my understanding of inequalities is not proper
deep cairn
If 1 <= n then 3 <= 3n, then n+3 <= n+3n, then |n+3| <= |n+3n| (because both are...
I see
golden sand
n>1 in the text though
deep cairn
n>1 in the text though
yeah, my inferring skills are not that sharp
More practise will probably lead to better understanding
golden sand
- n>=1
golden sand
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deep cairn
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obtuse pebbleBOT
deep cairn
@golden sand @glacial obsidian Thank you both, esp. D for spoon feeding me the inference
obtuse pebbleBOT
Available help channel!
sharp isle
Hi, I'm new haha. So I don't really know how this works. Can someone help with this? I tried using QR
obtuse pebbleBOT
Hi, I'm new haha. So I don't really know how this works. Can someone help with t...
sharp isle
Q needs to be orthogonal, but as QM is full rank, m22 can't be nonzero for a upper triangular M. I don't know how this can be decomposed easily
*can't be zero
:((
<@&286206848099549185>
obtuse pebbleBOT
@sharp isle Has your question been resolved?
sharp isle
no
warm shaleBOT
royal basin
and $M = \bmqty{&0&0 \ &0& \ &&}$
warm shaleBOT
Ann
royal basin
right?
which means that M is lower triangular up to a column permutation @sharp isle
sharp isle
Hi, ok, so up to a column permutation is bc U can switch column 2 and 3 and get a lower triangular matrix right?
But how go about it? Haha
*to
obtuse pebbleBOT
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sharp isle
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frail depot
obtuse pebbleBOT
frail depot
We have found the x-axis for the critical point $x=e^{-1/e^n}$
warm shaleBOT
SimonWin
frail depot
And we just want to show whether it's a minimum or maximum by calculating f(x+ 0.1) and f(x - 0.1)
But that is pretty hard given the function 
kind hawk
this isn't how you determine whether something is a max or min anyway. instead you can for example consider the second derivative
frail depot
this isn't how you determine whether something is a max or min anyway. instead y...
I thoguth that was for showing
frail depot
this isn't how you determine whether something is a max or min anyway. instead y...
showing concave up and downwards?
i guess it makes sense if we can show it's concave up then it must be a minimum right?
I guess that's the though process?
kind hawk
yes
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
lean tendon
Given the 16-element set consisting of the ten digits ${0,1,2,...,9}$ and the six capital letters ${A,B,C,D,E,F}$.
obtuse pebbleBOT
Given the 16-element set consisting of the ten digits $\{0,1,2,...,9\}$ and the ...
warm shaleBOT
Ziggy
lean tendon
How many strings of length 9 can be formed using exactly two 6's, three B's and four D's if the four D's are required to occur consecutively in the string?
obtuse pebbleBOT
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
coarse path
x^2 +7x-8
Factor the expression
obtuse pebbleBOT
x^2 +7x-8
Factor the expression
timid silo
x^2 +7x-8
Factor the expression
x^?
wide rose
x^2 +7x-8
Factor the expression
what method of factorising you know?
jovial moss
x^2 +7x-8
Factor the expression
use your calculator
coarse path
? + ? = 7
? * ? = -8
wide rose
? + ? = 7
? * ? = -8
right, but -7
coarse path
I canβt donβt have one
coarse path
right, but -7
It +7 in question
wide rose
$(x-x_1)(x-x_2) = x^2-(x_1+x_2)x+x_1 x_2$
warm shaleBOT
TimK
timid silo
Right, I was gonna ask if you had that in mind
wide rose
it's minus
coarse path
Thatβs not how you do it
wide rose
Thatβs not how you do it
-_-
timid silo
It's another way of doing it
wide rose
what is $(x-1)^2$?
warm shaleBOT
TimK
coarse path
Let me give you a example
wide rose
you know Viet?
timid silo
It's another way to do it
It's just the way your school taught you
Which is totally fair because this works just fine
wide rose
x^2 +10 + 24
4+6= 10
4*6= 24
(X+4)(X+6)
i mean, roots are not +4 and +6
coarse path
i mean, roots are not +4 and +6
4+6= 10
wide rose
coarse path
4x6 = 24
coarse path
so are 4 and 6 roots?
Wdym roots
wide rose
Wdym roots
$x_1, x_2$
warm shaleBOT
TimK
warm shaleBOT
TimK
coarse path
x^2 +7x-8
Factor the expression
Can we do this
wide rose
Can we do this
yes
coarse path
What are the 2 numbers that ?+? = 7 and ?*?= -8
wide rose
What are the 2 numbers that ?+? = 7 and ?*?= -8
-8 and 1?
coarse path
Dam you are smart
jovial moss
isnt it 8 and -1
wide rose
isnt it 8 and -1
right
coarse path
Oh yeah
wide rose
I've mistaken
coarse path
.close
obtuse pebbleBOT
coarse path
Thanks btw
timid silo
Dam you are smart
It's just a matter of considering every factor of 8, then from that finding all the ways to multiply up to 8:
\1*8
2*4
Then 4*2 and 8*1 are just these 2 backwards
Then if you look at the list for answers you find 8-1=7 which solves your problem
obtuse pebbleBOT
Available help channel!
pallid berry
is there a clever way to do this or is it just bashy
obtuse pebbleBOT
is there a clever way to do this or is it just bashy
wide rose
start from the cheapest?
pallid berry
yeah, initially thought 8 + 5 + 2 was best but given enough time realised that 8 + 3 + 3 + 1 was best
ill try that thanks
.close
timid silo
obtuse pebbleBOT
timid silo
so i know how i solved it using the top method but im unsure how the bottom method works
timid silo
where did i get "16^1/2 x 16^1/4" from
timid silo
law of indices
yeah
timid silo
they simplified 2/4 to 1/2
where did you get 2/4 from?
timid silo
ok ok starting to make sense for me
so 3/4 is simplified to 1/4 + 2/4 to make it easier for me?
jovial moss
is not to make it easier
is to find a way to solve it
unless u have learnt the last indices law
timid silo
i have that law noted down
timid silo
many methods
ah i see
jovial moss
so why can i not just do
Because u asked how to do the bottom method...
timid silo
Because u asked how to do the bottom method...
sorry ur right
mb
so the 3/4 is broken down into 1/2 x 1/4 got it
timid silo
- i mean
jovial moss
yes
timid silo
then u use both them as a power
bright sleet
Can someone explain what the symbol on the right is? The image has to do with set theory
obtuse pebbleBOT
Can someone explain what the symbol on the right is? The image has to do with se...
warm canopy
Usually denotes a partial order
bright sleet
Thank u
raven bluff
Please help with this i understand most of it just have a quick question
wide rose
sum of vectors?
wide rose
draw the plane's vector
raven bluff
The 250km/hr?
wide rose
right
warm shaleBOT
wide rose
can you add 2 vectors?
warm shaleBOT
raven bluff
Like this?
raven bluff
but both
Got it
By the way do I always add it to both when I have 2 triangles with a 45 angle
wide rose
By the way do I always add it to both when I have 2 triangles with a 45 angle
i got confused
just add the planes speed at the end of the first vector
then the vector start -> final is your planes final speed
wide rose
like this
wide rose
Do I put that value on both triangles
yes
raven bluff
but, this is not the answer
I have the answers btw I can send the answer sheet but I donβt understand how my teacher came to the conclusion
wide rose
yup
obtuse pebbleBOT
@raven bluff Has your question been resolved?
long plaza
help plz
vast willow
