Which problem are you working on?
#help-10
bold bane
tough hull
The second pic 3 first question
bold bane
Are you familiar with the Inscribed Angle Theorem?
tough hull
Yea I know circle theorems
bold bane
Ok, I'm going to name the vertices of the triangle for c) and d) as A, B, and C from left-to-right.
What would the measure of the arc be for arc AB?
My pen died on me otherwise I would write it out on a graph.
tough hull
Im looking for a and b not c and d
bold bane
So you are looking for angle c.
If you know the arc measure of BC, you could find angle c.
To find the arc measure of BC, find the arc measure of AB.
Because AC is a diameter line, you can find arc BC that way.
tough hull
Ok but I'm talking about my equation and how far we get in theroems in the book
bold bane
bold bane
For a and b.
tough hull
Yeah
tough hull
Yes it's 50 but how do thy get there
bold bane
Find the measure of the corresponding arc for angle b.
spring trail
oh i didnt even zoom enough its just a
spring trail
Find the measure of the corresponding arc for angle **b**.
u mean then double it and THEN use sum=180?
tough hull
A is already given b is the one I found and c is the one I have to find idk how to measure arc @bold bane
bold bane
That will give you the angle from the center of the circle.
spring trail
yeah he probly doesnt
either way
its either through teh isosceles triangle i told u earlier about
and the answer in your book is sadly wrong
a=42
check out a video on isosoles triangle if u really dont get iit
bold bane
Do you know what arc measure is?
tough hull
Nope
Nvm I saw the answers and a and b are 42 and 48
The angle I was talking abt doesn't have a letter
bold bane
Arc measure is the angle of an arc from two points on the circumference of a circle with the apex at the origin.
tough hull
Ok
bold bane
The Inscribed Angle Theorem states that if you have a third point outside of that arc on the circumference of the same circle, the angle is equal to half of the measure of that arc.
Reload the link for the Geogebra file.
quasi rapids
Hi, pretty easy question I just want to double check
obtuse pebbleBOT
Hi, pretty easy question I just want to double check
tawny pulsar
Question and my working so far not sure what to do from here
obtuse pebbleBOT
Question and my working so far not sure what to do from here
tawny pulsar
got x=2y and not sure how to show it has one stationary point
obtuse pebbleBOT
@tawny pulsar Has your question been resolved?
obtuse pebbleBOT
@tawny pulsar Has your question been resolved?
obtuse pebbleBOT
@tawny pulsar Has your question been resolved?
obtuse pebbleBOT
@tawny pulsar Has your question been resolved?
mint tendon
got x=2y and not sure how to show it has one stationary point
use the original equation as well
you have two systems of equations
two variables
raven spire
Question and my working so far not sure what to do from here
x - 2y - 2xy' + 12y²y' = 0
y' = (x - 2y)/(12y² - 2x) = 0 => x = 2y;
Use with initial Equation, y^3 - 1 = 0...
tawny pulsar
use the original equation as well
so just sub x=2y into original?
mint tendon
so just sub x=2y into original?
yep
tawny pulsar
and how would that show there is only 1 stationary point? sorry im new to differentiation
mint tendon
a stationary point is defined as the point where the derivative is 0
in this case its a function of two variables
warm shaleBOT
tawny pulsar
a stationary point is defined as the point where the derivative is 0
I got y= 1 x=2 as the stationary point but how does that prove there is no others
mint tendon
x - 2y - 2xy' + 12y²y' = 0
y' = (x - 2y)/(12y² - 2x) = 0 => x = 2y;
Use with in...
assuming what this guy wrote is correct
the only real solution for y is 1
so theres only one pair (x,y)
that works
restive pilot
How would I solve this?
obtuse pebbleBOT
How would I solve this?
restive pilot
finding both an upper and lower limit to x?
cedar lichen
What have you tried
restive pilot
well I mutiplied it out
cedar lichen
You don't have to do that
restive pilot
and factorised the x^3 out
restive pilot
I can just take the square root...
cedar lichen
Be careful when you do
restive pilot
yeah inequalitites are wild
would be my next question what do I have to watch our for?
cedar lichen
Well, what do you get when you solve t² ≤ 4?
cedar lichen
You sure?
restive pilot
not really
cedar lichen
Explain your answer
restive pilot
well the first seems fine to me just taking the positive answer
and for the negative answer I would swap the sign, cause of the negative
cedar lichen
So -t > 2 --> t < -2?
The union of t < 2 and t < -2 is just t < -2
(-3)² is not ≤ 4 though
You flip the sign when you multiply or divide by a negative
You don't flip the sign when a negative just appears
restive pilot
yeah would have been my idea xD
cedar lichen
Now, t = x³ - 3
You can treat each inequality seperately
Or, if you know what you're doing, you can do them both at once
warm shaleBOT
Eichhorst
restive pilot
.close
supple epoch
Let $c > 0$ be chosen arbitrarily and $b_0 \in ]0,\frac{1}{c}[$ given. For $n \in \mathbb{N}$ we set $b_{n+1} := 2b_n - c(b_n)^2$. Find out whether it's convergent or not, and if so, find its limit.
obtuse pebbleBOT
Let $c > 0$ be chosen arbitrarily and $b_0 \in ]0,\frac{1}{c}[$ given. For $n \i...
warm shaleBOT
Levens
supple epoch
I dont understand the notation for $b_0$... isnt that an open interval?
supple epoch
this is how it was given:
mint tendon
lmao it looks like a misatke
the universally accepted symbol for open interval is ()
oh wait nvm
apparently it is open interval
wtf
supple epoch
ya i think my professor is extra
mint tendon
thats horrible notation lol
warm shaleBOT
supple epoch
i mean like in context to the question
mint tendon
well i'll just give a little intuition to what this could converge to
warm shaleBOT
mint tendon
and decreasing everywhere else
warm shaleBOT
obtuse pebbleBOT
@supple epoch Has your question been resolved?
drifting prairie
What does this mean
obtuse pebbleBOT
What does this mean
raven spire
means you put "y" in place of all the "x"s in the function...
You're given M(x, y) and you need to figure M(y, y)
raven spire
partial derivatives with respect to the respective variable
drifting prairie
partial derivatives with respect to the respective variable
I am a lil confused on what this means
obtuse pebbleBOT
Available help channel!
stable rain
given H <= G, for any coset gH=C, where g in G, is it true that for any c in C, cH = C?
obtuse pebbleBOT
given H <= G, for any coset gH=C, where g in G, is it true that for any c in C, ...
gilded needle
given H <= G, for any coset gH=C, where g in G, is it true that for any c in C, ...
yes
gilded needle
you can characterize gH as "the coset of H that contains g"
so if c is any element in gH, then cH = gH
the last equality could simply be read as "the coset containing c is the same as the coset containing g", i.e. c and g are in the same coset
stable rain
the last equality could simply be read as "the coset containing c is the same as...
hm ic
thanks
.close
green field
obtuse pebbleBOT
gilded needle
where are you stuck?
stable rain
the left u can find some value
the right ull get some value in terms of y
equate n solve for y
frozen aurora
Could anyone please help me top solve this?
obtuse pebbleBOT
Could anyone please help me top solve this?
stable rain
try guessing some groupings
frozen aurora
I've tried to solve this using all the techniques I know, and I can't get it right.
stable rain
so weve
8x^2+10x+3=
(ax+b)(cx+d)
ac=8
bd=3
so over ints
bd can be (1,3)
ignoring order
ac can b
(1,8)
(2,4)
just guess around
obtuse pebbleBOT
stable rain
i closed it alr
obtuse pebbleBOT
Available help channel!
weary quarry
how would you write this in predicate logic, if two numbers multiplied by 3 are equal then they are the same number?
obtuse pebbleBOT
how would you write this in predicate logic, if two numbers multiplied by 3 are ...
trail musk
3x = 3y <=> x=y
twin sapphire
$\forall (x,y) \in \mathbb{R}^2 , 3x=3y \implies x=y$
warm shaleBOT
Benjamin
weary quarry
thanks
broken jay
obtuse pebbleBOT
raven spire
y = 3x - 12; x + 6x - 24 = 7 => 7x = 31 => x = 12; y = 24
ocean nexus
what does mod mean
zenith raft
and in the way it's used in the problem, a ≡ b mod n means a and b leave the same remainder when divided by n
broken jay
yeah this problems got me stumped tho
ocean nexus
i only know how to solve the system of equation lol
obtuse pebbleBOT
@broken jay Has your question been resolved?
cunning berry
zenith raft
<@&268886789983436800>
obtuse pebbleBOT
fierce lagoon
<@&268886789983436800>
What happened this time
zenith raft
just ignore it
obtuse pebbleBOT
Available help channel!
dim copper
obtuse pebbleBOT
solar hornet
hold on
dim copper
the only info I have to go on is the height (144) and the length (252) of the mountain
I figure it has something to do with that
solar hornet
yeah it's a function where y = 144 and x=252
they even drew the mountain on the graph, which is pretty funny
what you can do is put these numbers into the equation to solve for A
I tried doing that but the answer isn't as pretty as I expected
gaunt iris
obtuse pebbleBOT
gaunt iris
A cone and a sphere have the same volume.
The radius of the cone,
r
, is
1/4
that of the sphere.
Find an expression for the height of the cone,
h
, in terms of
r
.
timid silo
has same volume??
gaunt iris
yup
gaunt iris
thanks
timid silo
no
gaunt iris
yea its not
gaunt iris
Alright thanks
timid silo
oh
gaunt iris
??
timid silo
the volume of cone is (pi * r^2)/3
gaunt iris
solar hornet
find the volume of the sphere first
timid silo
guys help me
solar hornet
you know the height of that blue cylinder inside
@timid silo find your own channel this one is occupied
solar hornet
ok I think best approach is to turn the volume of the sphere, into a cylinder with diameter 12cm
find it's height
once you do, add it to the height of that blue cylinder
gaunt iris
its water and you have to work out how high up the water will reach after its submerged
solar hornet
i know
the volume will increase exactly by the volume of the sphere, so you can just fit the sphere into that cylinder
and check the overall height
another way to explain, if you find a cylinder of diameter/width 12 cm that has the same volume as that sphere
you can check it's height, add it to the height of the blue one, and that's the total height the water will reach
gaunt iris
alr thx
solemn ravine
Any tips on how to solve this? Tau is the number of divisors of d
obtuse pebbleBOT
Any tips on how to solve this? Tau is the number of divisors of d
solemn ravine
(Solve, as in, find one natural number n)
royal basin
let n = prod p_i^a_i
how can this sum be expressed in terms of the a_i?
solemn ravine
do you mean d = prod p_i^a_i? because then we can use tau(d) = prod (a_i + 1)
which would give a sum in terms of a_i
royal basin
no, i mean n.
all of its divisors are then prod p_i^b_i with 0<=b_i<=a_i
i think this sum may have a nice expression
solemn ravine
gimme a sec to play around with this
solemn ravine
all of its divisors are then prod p_i^b_i with 0<=b_i<=a_i
Not sure I’m getting anywhere with this… am I missing something crucial?
royal basin
i have a feeling that this sum of products is actually the product of triangular-number sums
obtuse pebbleBOT
@solemn ravine Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
snow olive
Hello .. i was doing research on how to do math properly ... could you help with giving analogies to what the process is like? ... my closest guess is it is like passing axiom "objects" through logic circuits to explain theorems in the form of empirical mathematical observation ... somewhat like how a circuit is built in a computer ... What is your own personal experience with this?
obtuse pebbleBOT
Hello .. i was doing research on how to do math properly ... could you help wit...
@snow olive Has your question been resolved?
snow olive
<@&286206848099549185>
solar hornet
well math is fundamentally based on logic, yes
but this part.. "empirical mathematical observation", why call it empirical? it's like the opposite of what math is
sure, you can notice something and reverse-engineer it but that's not what math truly is, imo
and rarely this observation is empirical.. it's just observation and pattern recognition
sage dagger
if im trying to calculate <ABN what am i looking for i dont understand
obtuse pebbleBOT
if im trying to calculate <ABN what am i looking for i dont understand
royal basin
microsoft paint has straight line and text tools, for future reference.
royal basin
angle ABN?
royal basin
$\angle ABN$
warm shaleBOT
Ann
sage dagger
yes
royal basin
are you saying you don't know what "angle ABN" refers to?
sage dagger
i know what its talking about but what am i trying to find here
royal basin
you are trying to find this angle
the measure of this angle, if you want to go technical.
i've recreated your diagram, by the way.
royal basin
yes.
sage dagger
royal basin
angle ABN means the angle whose vertex is B and whose sides are BA and BN
no, this angle would be called BAN.
sage dagger
oh okay
royal basin
the middle letter in the name of an angle is always its vertex.
sage dagger
the middle letter in the name of an angle is always its vertex.
do i use inverse sin or tan
royal basin
first off, if you just want to ping me, then you can ping me. don't reply to a message that has nothing to do with your question!
sage dagger
ok
royal basin
and second, you can succeed with either one.
like, they'll require different inputs to produce what you actually need
sage dagger
and second, you can succeed with either one.
they dont give different results?
royal basin
but there is no prohibition against one or the other for this problem
or any problem
royal basin
they dont give different results?
they give different results on the same input, but you haven't said what you want to put into them.
sage dagger
so if im doing sin-1 i am doing sin-1(3.6/9)
royal basin
well, is sin(ABN) equal to 3.6/9?
sage dagger
i think so
royal basin
and you are right to think so.
sage dagger
alright thanks
obtuse pebbleBOT
@sage dagger Has your question been resolved?
sage dagger
@royal basin the question says; in the triangle ABC, find cosx in terms of a and b
how would i do this?
cosx = cos(b/a) ?
royal basin
no
"cos(b/a)" is something you should not be considering in all honesty
with VERY VERY RARE EXCEPTIONS, it does not make geometric sense to take the cosine (or any other trig function) of a ratio of side lengths
anyway, identify the sides whose ratio is cos(x).
one of them will be the hypotenuse.
find a way to express the hypotenuse in terms of a and b, and you will be done
sage dagger
i think the cosx is throwing me
royal basin
throwing you how?
if you remember your SOH-CAH-TOA you should have no trouble writing down which sides' ratio equals cos(x).
sage dagger
confusing me like am i still considering the adjacent/hypotenuse
royal basin
sure you are. you just haven't written that down yet...
royal basin
no, bad!!!
the stuff that goes inside the cos function is an ANGLE!
ANGLES are INPUTS to trig functions!
cos(x) = AB/AC.
sage dagger
ohh
yeah i forgot about the AB and only looked at the b part
im not sure what the 57 is referring to
the outside angle of the inside angle
or like the inside inside angle
i need to find the distance of OA
so when i add up 59 + 57
i get 116 so then
180-116 = 64
wait
no
the 59 degrees is the whole <S
@royal basin i require your assistance once again
royal basin
im not sure what the 57 is referring to
it's referring to angle ASO, whose arc-mark it is right next to.
"angle S" is ambiguous in this picture. so you should not be saying that at all.
sage dagger
what does the double angle mean though
sage dagger
this
high lily
wdym by double angle
royal basin
no, there are simply two arc-marks,
sage dagger
im strictly looking at the bottom
royal basin
one of which refers to angle BSO and the other to angle ASO
obtuse pebbleBOT
@sage dagger Has your question been resolved?
distant musk
what is linear combination in matrix or determinant? can anyone pls explain?
alpine raven
what is linear combination in matrix or determinant? can anyone pls explain?
linear combination is a property such that you can write a vector as a sum of vectors, for example :
x = au + bv
x a vector and a,b some scalars
I wrote x as the linear combination of two vectors u and v
now for matrix, its basically the same thing, I can write a matrix as a linear combination of any vectors (if those vectors respect some property)
determinant is more of a multilinear map
distant musk
linear combination is a property such that you can write a vector as a sum of ve...
thanks a lot
.close
merry stratus
Is there any difference in solving a differential equation in f: I -> R or in f: I -> C?
obtuse pebbleBOT
Is there any difference in solving a differential equation in f: I -> R or in f:...
@merry stratus Has your question been resolved?
wraith remnant
i need help for divisions
narrow vault
wraith remnant
@proven zephyr
merry stratus
.close
timid silo
The winning numbers for the Lotto 6/49 are drawn from a clear plastic drum that contains 49 ping-pong balls numbered from 1 to 49. The order of selection does not matter. Once a ball is drawn from the drum, it is put on display. The process is repeated a total of six times. Leave your answers as fractions.
a. What is the probability of you winning the jackpot (matching all six numbers)?
b. What is the probability of matching only 3 numbers?
c. What is the probability of matching at least one number?
obtuse pebbleBOT
The winning numbers for the Lotto 6/49 are drawn from a clear plastic drum that ...
brisk oracle
ok.. how do you start
timid silo
ok.. how do you start
I'm not sure about the probability percentage
brisk oracle
what aren't you sure about
timid silo
is the probability 2% * six times
brisk oracle
no, but where did 2% come from?
timid silo
1/49
brisk oracle
ah yea. no what you're saying is wrong. it would be correct if order mattered, and if a number could come up more than once
here order doesn't matter, and a number is only picked up once
timid silo
okay but how do I get the probability?
brisk oracle
you have to find out the total number of combinations of 6 elements from a set that has 49 elements
timid silo
do I need to use logic or is there a mathematical way of getting it
brisk oracle
both. but more importantly this should be in your book
there's a formula that tells us in how many ways we can choose k objects from a set that has n elements
timid silo
Okay I assume you're referring to combinations
brisk oracle
yep
latent mesa
obtuse pebbleBOT
https://prnt.sc/L4_Mz1_RO20P
latent mesa
How did they get 1/3
the rest i understand but where did they get that number from
timid silo
obtuse pebbleBOT
https://cdn.discordapp.com/attachments/903486479064522752/1045446464584831087/im...
timid silo
what is the general solution for this equation?
is "1,54" the "b" constant??
is T the b/a constant ??
sage geode
Depends on what you mean by those
Nonetheless this is a separable differential equation
Divide both sides by what you have on the right hand side and integrate
timid silo
is this not newtons cooling law?
sage geode
Yes, and you're solving for T, right?
timid silo
ye, but i just cant see how that can turn into " y = b/a + e^(-ax)"
it dosent look like the "y' = b - ay " type diff equation
sage geode
$\frac{1.54 - 0.259(T - 22)}dT = dx$, integrate
wild swallow
rip bot lol
sage geode
it dosent look like the "y' = b - ay " type diff equation
It is, just expand the brackets
fierce lagoon
rip bot lol
sage geode
Not always
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
could someone explain why we have 2 base cases here
obtuse pebbleBOT
could someone explain why we have 2 base cases here
alpine raven
there is only 1
dark stirrup
What do you mean
alpine raven
hes talking about induction
alpine raven
well they just answered your question
timid silo
yea i dont really get it
alpine raven
n=1 is obvious so it shows nothing
timid silo
there is only 1
so did u mean here that the only base case is where n = 2 since n = 1 doesnt signify anything
alpine raven
so did u mean here that the only base case is where n = 2 since n = 1 doesnt sig...
There are two cases, the solution said it
n=1 isnt enough tho
timid silo
There are two cases, the solution said it
yea i mean about what you said cuz u said theres only 1
alpine raven
I was wrong
timid silo
o ok
dark stirrup
Not to derail, but I find the solution approach kind of inelegant because you don't really need to prove n=2 as a base case. You could just go straight to n=k>1 induction case.
(Once you show true for n=1 still)
timid silo
i guess they showed n = 2 cuz they used it as their basis for the inductive step ig
alpine raven
i guess they showed n = 2 cuz they used it as their basis for the inductive step...
because thats what you need to use to prove this
timid silo
yea i meant about what swr said
timid silo
Not to derail, but I find the solution approach kind of inelegant because you do...
would you end up with the same thing in the inductive step ?
dark stirrup
You should. But I haven't written anything down yet so unsure if I'm missing anything subtle
obtuse pebbleBOT
@timid silo Has your question been resolved?
timid silo
.close
timid silo
am i dumb or
obtuse pebbleBOT
am i dumb or
timid silo
is the powerset of P(a x b) gonna be super huge if a = {1, 2} and b = {1,3}
teal prawn
2^4
sage geode
Power set of a powerset?
teal prawn
power set of a cartesian product
sage geode
They said "Powerset of P(a x b)"
teal prawn
ah
sage geode
Should be 2^16 then
teal prawn
yea it'll be big
sage geode
Well, if they didn't make typos
solar trellis
They most likely mean just P(A×B)
timid silo
They most likely mean just P(A×B)
do you know ^
civic zealot
That's just the powerset of AxB
civic zealot
yes
timid silo
is that not really big tho
civic zealot
its 16 elements. so not really big, probably tedious to write out
timid silo
uh im not sure if im doing it right
{empty set, {(1, 1)}, {(1, 3)}, {(2, 1)}, {(2, 3)}}
{empty set, {(1, 1)}, {(1, 3)}, {(2, 1)}, {(2, 3)}, {(1, 1),(1, 3)}, {(1, 1), (2, 1)}, {(1, 1), (2, 3)}, {(1, 3), (2, 1) }, {(1, 3), (2, 3)} , {(2, 1), (2, 3)}}
civic zealot
looks good so far
remote vine
Can someone help me with a task i dont come further
obtuse pebbleBOT
Can someone help me with a task i dont come further
ruby tapir
Can someone help me with a task i dont come further
What is the problem?
remote vine
Translation: 15 The graphs of f, with f,(x) - a -sin (x) and 8. with 8. (x) - - 1. sin (x) limit an area for x€ [0; mi). For which values of a is this area minimum? Specify the minimum content.
I understand what i should do, but the calculation is bullshit
Sorry for my bad writing
I write like shit
I have the solution but it doesn’t help me as i have some parts which i don’t understand and its not explained
@ruby tapir
obtuse pebbleBOT
@remote vine Has your question been resolved?
obtuse pebbleBOT
@remote vine Has your question been resolved?
uncut robin
how can I show that f(x)=f(x+kT) if f is a periodic function of period T. I just know that f(x)=f(x+T)
obtuse pebbleBOT
how can I show that f(x)=f(x+kT) if f is a periodic function of period T. I just...
uncut robin
I think my professor said to use induction but have no idea how to
drifting badger
Hmm, I've never tried to use Induction on Integers before (I assume k is an integer). I guess the Induction Principle easily could be extended for this purpose.
Under induction for all natural numbers, you want to show for some predicate p(n) that p(1) is true and that if p(n) is true then p(n + 1) is true.
Extending this to integers for a predicate p(k), we could instead show that p(0) is true and from p(k) we can show that both p(k + 1) and p(k - 1) is true.
remote vine
<@712720257810300979> Has your question been resolved?
The fuck
uncut robin
so for my case I would need to check if p(0) is true so f(x)=f(x+(0)T) which is obviously true
and then for k+1 so f(x)=f(x+T+kT) and for k-1 f(x)=f(x-T+kT)
but I have to prove those two equations to be true
right @drifting badger?
drifting badger
I think so
To show p(k) => p(k + 1), first we can assume f(x) = f(x + kT). From this we want to show that f(x) = f(x + (k + 1)T) will also hold
uncut robin
yup
drifting badger
We know from f(x) = f(x + T) that
f(x + kT) = f(x + kT + T).
From distributive axiom we then have that
f(x + kT) = f(x + kT + T) = f(x + (k + 1)T).
From our assumption p(k) is true, it holds f(x) = f(x + kT) and therefore from the equality above that
f(x) = f(x + (k + 1)T)
Therefore p(k + 1) holds to be true from p(k)
uncut robin
ohh we say k+1=n then p(n) holds because it's in the form of p(k)?
drifting badger
What do you mean k + 1 = n?
uncut robin
so like p(k) is true so f(x)=f(x+kT)
now to show that it holds for p(k+1) we do f(x)=f(x+(k+1)T)
but how do I show it holds
I have T multiplied by k+1 not just k
drifting badger
You stated in the beginning that we know f(x) = f(x + T). This means if we put x + kT into f we get f(x + kT) = f(x + kT + T)
obtuse pebbleBOT
drifting badger
Just a side note, you also need to show that p(k - 1) holds from p(k)
obtuse pebbleBOT
Available help channel!
inner terrace
obtuse pebbleBOT
inner terrace
how to do this?
timid silo
use the definition of linear independence
inner terrace
I did that
but how do I derive an expliciti equation which expresses and arbritary point
@timid silo
timid silo
a point (x,y) is in the span if there are real numbers a and b such that av_1+bv_2=(x,y)
we can solve the vector equation given explicit (x,y) since we have two equations and two unknowns (a and b)
inner terrace
but the unknowns are both 0's right?
timid silo
to check for linear independence, yes
but you are asking about an arbitrary point now
timid silo
solve the two equations for a,b in terms of x,y
inner terrace
so av1 + bv2 = (x,y)
inner terrace
wait what
timid silo
$a\begin{pmatrix}4\1\end{pmatrix}+b\begin{pmatrix}8\3\end{pmatrix}=\begin{pmatrix}x\y\end{pmatrix}$
warm shaleBOT
Toby
inner terrace
i have no clue how to solve for this
timid silo
if we had x=4 and y=1, would you know how to do it?
inner terrace
yes
timid silo
(oops bad example its v1 lmao)
inner terrace
write it in augmented form?
timid silo
yeah
inner terrace
so like this
timid silo
$\begin{pmatrix}4&8&x\1&3&y\end{pmatrix}$
timid silo
so like this
yeah, you beat me to it
inner terrace
😭
warm shaleBOT
Toby
inner terrace
anyways, we can row reduce that without having numbers for x and y
ahh like that
does this work @timid silo
timid silo
,w invert [[4,8],[1,3]]
warm shaleBOT
timid silo
does this work <@456226577798135808>
yup, thats correct!
inner terrace
what does the inversion do
timid silo
now you can read off a,b in terms of x,y
timid silo
what does the inversion do
it finds the coefficients in front of the x and y here, just easier to type into wa
timid silo
but thats not a function is it
why?
inner terrace
the excercise asks for an expliciti equtaion
timid silo
its a function that takes two real numbers
inner terrace
ah I see
timid silo
given vector (x,y), we can find a and b using those two equations
eg we could substitute (4,1) and get a=1, b=0 without doing the augmented matrix thing
timid silo
use the definition of a linear map
might help to write the function in vector form first
timid silo
you need to check that F(x,y,z)+tF(a,b,c)=F(x+ta,y+tb,z+tc)
inner terrace
which is preservation of multiplication right?
timid silo
its both additivity and scalar multiplication at the same time
you can do them separately if you've defined them seperately
so F(x,y,z)+F(a,b,c)=F(x+a,y+b,z+c) and tF(x,y,z)=F(tx,ty,tz)
inner terrace
sorry but i dont understand
timid silo
what definition of a linear map are you given?
inner terrace
timid silo
lets do addition first
v=(x,y,z) and v'=(a,b,c)
substitute everything into F(v+v') and show that its the same as F(v)+F(v')
timid silo
F((x,y,z)+(a,b,c)) = F(x+a,y+b,z+c)
then substitute the rhs into the definition of F in the question
timid silo
right hand side
yeah
timid silo
no, my notation might be a bit misleading because I reuse the same variable
but it should be (x+a)-(y+b)+2(z+c)
timid silo
$F((a,b,c)+(d,e,f))=F(a+d,b+e,c+f)=((a+d)-(b+e)+2(c+f),\ldots,)$
warm shaleBOT
Toby
timid silo
ie, in the definition, use x=a+d, y=b+c, z=c+f
inner terrace
how do I go further than that tho?
((a + d) - (b+e) + 2(c + f), (3(a + d) + (b + e) - (c + f), (4(a + d) + (c + f))
is this right
@timid silo
inner terrace
now split up the a,b,c terms into one vector, and then d,e,f into the other
is it true that my first vector would be ((a - b + 2c) + (d-e+2f)
boreal vale
oh Thank you
inner terrace
((a - b + 2c) + (d - e + 2f), (3a + b - c) + (3d + e - f), (4a + c) + (4d + f))
boreal vale
but it is not polynomials?
timid silo
inner terrace
((a - b + 2c), (3a + b - c), (4a + c)) + ((d - e + 2f), (3d + e - f), (4d + f)) =
boreal vale
a ok
inner terrace
is that my next step?
timid silo
yup
inner terrace
and does that prove the preservation of addition
timid silo
wdym? its what you did except with different variable names
inner terrace
but the final step is different
on the left side you can clearly see the map given
nevermind.
I feel stupid
.close
lone vault
obtuse pebbleBOT
tardy epoch
Use
$P(X < n) = 1 - P(X \ge n)$
warm shaleBOT
riemann
lone vault
lambda is 20 here?
tardy epoch
what's the mean of a poisson distribution?
obtuse pebbleBOT
@lone vault Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
sinful eagle
- What is vectors U”=AB, v= AC, w=AD.
- What is area abc
- Equation for planet II, with dots a,b,c.
- Volym of pyramid abcd.
obtuse pebbleBOT
1. What is vectors U”=AB, v= AC, w=AD.
2. What is area abc
3. Equation for plane...
sinful eagle
Question to 1. All those are vectors.
While A, B, C D are dots.
Anyone?
A=(1,2,2), B=2,4,3, C=4,8,4 and D=3.5.5 are 4 dots in r^3
U=ab= (1,2,2)(2,4,3) = (2-1), 4-2, 3-2
=1,2,1
I think?
Hmm
🤔
V=AC just do vector end -start vector
3,6,2
W=AD= 2,3,3
Ok think i got it.
Then at question 2…
Area of triangel is height times base/ 2
Hmm
I know of height dots but is base U vector working?
<@&286206848099549185>
Hi at question 2. How do I figure out area of triangel ABC
obtuse pebbleBOT
@sinful eagle Has your question been resolved?
dull oyster
when a number is divided by 342 it gives reminder of 47 .when the same number is divided by 19 what will be its reminder
obtuse pebbleBOT
when a number is divided by 342 it gives reminder of 47 .when the same number is...
chrome mesa
just test using any number that gives a reminder of 47 when divided by 342 (or realize the significance of the value of 342/19)
obtuse pebbleBOT
@dull oyster Has your question been resolved?
old tapir
obtuse pebbleBOT
rose parcel
oh sorry xd
old tapir
oh sorry xd
u good gang
obtuse pebbleBOT
@old tapir Has your question been resolved?
summer rain
obtuse pebbleBOT
fierce lagoon
wy would you fail
summer rain
I just failed the first quarter
I need to do better this time
<@&286206848099549185>
uneven kayak
$\angle{DCB} = \angle{5} = 124$ as a cross angle
warm shaleBOT
! Promi !
uneven kayak
$\angle{4} + \angle{5} = 180$ so $\angle{4} = 180 - 124 = 56$
$\angle{2} + \angle{1} = 90$
summer rain
how about angle 3 and 4?
uneven kayak
how about angle 3 and 4?
I just realized in your image there is no angle 4
XD
Or im wrong
uneven kayak
ok i confused it with 1
summer rain
ok i confused it with 1
ikr I got confuse too
warm shaleBOT
! Promi !
summer rain
sooo because angle 4 is a central angle that means the arc has the same measurement or degree
summer rain
ohhhh ok ok I get it
uneven kayak
$\angle{2} = \angle{3}$
warm shaleBOT
! Promi !
uneven kayak
as $CD = CA = R$
warm shaleBOT
! Promi !
summer rain
so angle 3 is equal to 34 degrees?
uneven kayak
so angle 3 is equal to 34 degrees?
No i made a mistake above
i confused angle 1 with 4
so we have to still find 2
summer rain
ohh okay
uneven kayak
$180 = \angle{2} + {\angle{4} + \angle{3}$
warm shaleBOT
! Promi !
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
warm shaleBOT
! Promi !
warm shaleBOT
! Promi !
uneven kayak
but then angles 2 and 1 makes a right angle so does that means 28
Happy to help
summer rain
THANK YOU SO MUCHH
willow briar
Could I get help with this
obtuse pebbleBOT
Could I get help with this
willow briar
willow briar
Ok
arctic ravine
or you can type it into desmos
but itll be easier for the limit
for example 1) f(x) goes to infinity as x goes to infinity
willow briar
Ok
arctic ravine
but might be worth checking what happens at negative infinity too
solar hornet
if you find the zero points, that's where it touches the x axis
if highest power coefficient is positive, it goes to positive infinity
otherwise it's negative infinity
willow briar
True but how would I go about make the shape
solar hornet
when you have x^2 it's a parabola, x^3 it's like the wave thing, x^4 it has another "groove"
it's best when you have the zero points, then you can just draw a "wave" over them
willow briar
Ok would the wave be the answer?
solar hornet
you just describe the end behavior
no need for specifics, so you can say, it starts at negative infinity, one goes up, goes down, then goes up to positive infinity
like in the first example, x^3 has positive coefficient, so on the left side it starts from the negative infinity, and on the right side it goes to positive infinity
willow briar
I think I get it
arctic ravine
if youre claiming that the end behavior adheres to the parent graph of the highest degree a proof may be required but i would agree
solar hornet
by domination highest power decides where the limit goes
you can show it by taking the limit but I don't think it's necessary here
arctic ravine
fair enough
solar hornet
but when the power is even and coefficient is positive, it also start at positive infinity from the left side
arctic ravine
Might be worth mentioning that if he takes the derivative he can find the inflection points
so hes not guessing where the line curves
for part 2
solar hornet
i mean, we did stuff like this in school before we learned limits
arctic ravine
yeah but depending on teacher
might need proof for that
especially in higher level math
solar hornet
you don't need to take the derivative, you can just use equations for parabolas
doesn't look like higher math to me tbh
arctic ravine
for question 7 and 8 its essential he takes the derivative
to find the points of inflection
zenith raft
no it's not lol?
arctic ravine
i mean he could guess
but that would be kind of ruining the point of doing the math
because he wouldnt be doing it lol
zenith raft
people usually learn how to plot things like f(x) = 2x^2 - 3 long before they learn derivatives lol
solar hornet
it's something like an introduction to graphs/functions*, learning the intuition and doing it manually
arctic ravine
oh i see he may not know derivatives yet
my bad
then he plugs in a lot of values i guess
zenith raft
a parabola is uniquely determined by 3 points...
willow briar
Y’all so smart omg😭
zenith raft
that is not always true layla
how not?
solar hornet
how is a parabola defined by more than 3 points, isn't that by it's definition
zenith raft
certainly not by definition but what i said is true?
arctic ravine
take complex numbers into consideration
zenith raft
???
solar hornet
@willow briar have you seen those?
if it's something you guys were doing, I think it's easier to do it that way
but you can sketch a parabola without those
(don't look at the rightmost column)
willow briar
Ok thanks man
obtuse pebbleBOT
@willow briar Has your question been resolved?
timid silo
I’m not sure as to how I’d covert this non monic quadratic into the form they have asked there. My understanding so far is that you’d need to take out a linear factor from the quadratic, but I’m not sure how to totally rearrange it into that form.
obtuse pebbleBOT
I’m not sure as to how I’d covert this non monic quadratic into the form they ha...
timid silo
Not sure how acceptable this is
timid silo
3x
oh wait i think I might've got it
if I take 3x out of the brackets and keep it as 3x(x+1), I have to have another term which ends up simplifying the equation to -7x as it is originally
so it would become 3x(x+1)-10x+5
👍
.close
icy cape
ax/b - cx/2 = d
obtuse pebbleBOT
ax/b - cx/2 = d
icy cape
How do I solve for x in terms of other pronumerals
copper spade
@icy cape take x common
royal basin
notice that your equation is $\frac{a}{b} x - \frac{c}{2} x = d$
warm shaleBOT
Ann
copper spade
nvm latex pro here u take over
copper spade
Take x common
icy cape
X common?
copper spade
Yes
icy cape
Common HDF?
copper spade
Like ax+bx = x(a+b)
icy cape
Like ax+bx = x(a+b)
oh
how abt the denominators
tho
one is b and other is 2
do we cross them
to the other numerators
copper spade
No need to worry coz the question says to express x in terms of other poly
icy cape
No need to worry coz the question says to express x in terms of other poly
ok
then how shall i write it
do I just leave the denominators as is
but connected
copper spade
Your wish, you can take lcm Or you can leave it as it is
icy cape
Your wish, you can take lcm Or you can leave it as it is
ok
so ax - cx/b - 2 = d
right
x (a - c)/b - 2 = d
royal basin
no
copper spade
x (a - c)/b - 2 = d
No
icy cape
why
royal basin
subtracting two fractions doesnt mean just subtracting their tops and bottoms
copper spade
Ye
royal basin
it's $\paren{\frac{a}{b} - \frac{c}{2}}x = d$
warm shaleBOT
Ann
royal basin
also do not try to do everything at once
icy cape
what the sus
royal basin
it is okay to do one thing at a time, i.e. first factor out x, then worry about subtracting the fractions.
and it is now that we can actually focus on simplifying $\frac{a}{b} - \frac{c}{2}$
warm shaleBOT
Ann
icy cape
ok
timid silo
How do i pronounce ur username, is it evbama almkhls?
copper spade
@icy cape focus on ur meth problem first lol
icy cape
who is op
icy cape
ok
copper spade
i'm not sure OP has a methamphetamine problem.
Damn what the hell is that word
timid silo
Over powered
royal basin
OP can stand for a bunch of things, but the way i used it, it means what i said it means.
anyway! let's stay on topic.
timid silo
Damn what the hell is that word
Droog
royal basin
ok guys how do I do this
do you know how to subtract fractions in general?
icy cape
do you know how to subtract fractions in general?
yes
but the problem is the denominator
royal basin
what's the problem with it?
icy cape
the denominators are not equal