bc it could be i think im not sure
#help-10
timid silo
oblique sage
How do I sketch this
obtuse pebbleBOT
How do I sketch this
short spruce
it seems you already know, seeing your notes to the side
just follow what you've written
oblique sage
how do i draw from -inf,-1 something that is increasing Concave down
short spruce
i'd suggest writing at the top of the graph where it's increasing, decreasing, concave up, and concave down
there are four possibilities: increasing CU, increasing CD, decreasing CU, and decreasing CD
try drawing graphs off to the side, see if you can get the general shapes for those types of graphs
oblique sage
This?
short spruce
looks alright to me
oblique sage
aighjt
wispy parrot
thanks for all the help earlier @tired shell i solved all of it 👍
dire pollen
Divide top and bottom by x^3
when you're working out limits, divide by x to the highest degree of the denominator
@eager bobcat
eager bobcat
dire pollen
can you post your result after dividing top and bottom by x^3?
karmic grove
we can also apply l hospitals's rule 2 time
worldly quartz
hello
karmic grove
which one?
worldly quartz
number 40.
karmic grove
diameter=32+7*year
worldly quartz
is that
3cm=32+7
karmic grove
no 88=32+7y
worldly quartz
oh i forgot the pi
should i multiply the diameter
by 3.14
or something
32x3.14=100.48
im confused
.close
visual hornet
Could someone please help @cold brook and me in question #11
(A level probability and statistics)
obtuse pebbleBOT
Could someone please help <@793385686354755615> and me in question #11
(A level ...
@visual hornet Has your question been resolved?
swift wing
Hi
How can I solve
$arccos(y - x)$
?
obtuse pebbleBOT
Hi
How can I solve
$arccos(y - x)$
?
warm shaleBOT
Fegres
obtuse pebbleBOT
@swift wing Has your question been resolved?
carmine gorge
obtuse pebbleBOT
carmine gorge
So here, I am given this, and is asked to demonstrate whether it is a subspace
Here, I am seeing if it is closed under addition, which I've shown that it is not with the work above
Is the way I approached this proper and sufficient to say that it is not closed?
severe marsh
subspace of what?
carmine gorge
I don't know how to answer that question, can you clarify?
This is all I was given
severe marsh
subspaces of R, then?
carmine gorge
That sounds right
severe marsh
welll, if it fails to be closed under addition, it's not a subspace
carmine gorge
Right
carmine gorge
So what I've written up there is correct and sufficient to conclude that it is not a subspace?
severe marsh
and the condition being that the second entry = 1st entry + 3rd entry + 1
sure
you'd probably have to say that the sum is not equivalent to the one in the initial condition, though
carmine gorge
Yeah, you're right. It would be better to refer back to "and the condition being that the second entry = 1st entry + 3rd entry + 1"
severe marsh
say that explicitly, then you're good
carmine gorge
Thinking about it, that last statement is probably pretty important because what I've written up there doesn't tie to it not being a subspace if I don't state that
severe marsh
it also fails to be closed under multiplication by scalars
which might be more brief for you
carmine gorge
Oh I didn't consider that, thank you
Alright, this was very helpful, I thank you for your time and response
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
worldly violet
Hi!
so, i defined u=(1,1) v=(1,-1) and u* = (t,-t) as the projection of u on the span
and i plugged those into the following: ║ u - v ║² =║ u - u* ║² + ║ u* - v ║²
i was expecting it to simplify to a t value of u* as the projection (specifically expecting t=0), but i can't get there
to be clear
all norms are p-norms,
i plugged the norm in and expanded it like so:
(|u1-v1|^ᵖ+|u2-v2|^ᵖ)^(²/ᵖ)
where u=(u1,u2), ( ie the elements of the vectors) and so on for RHS
obtuse pebbleBOT
Hi!
so, i defined u=(1,1) v=(1,-1) and u* = (t,-t) as the projection of u on the...
@worldly violet Has your question been resolved?
worldly violet
<@&286206848099549185>
worldly violet
<@&286206848099549185>
worldly violet
<@&286206848099549185>
worldly violet
<@&286206848099549185>
obtuse pebbleBOT
@worldly violet Has your question been resolved?
worldly violet
<@&286206848099549185>
worldly violet
<@&286206848099549185> 😦
worldly violet
<@&286206848099549185> 😦😦
worldly violet
<@&286206848099549185> 😦😦😦
worldly violet
<@&286206848099549185> 😢
worldly violet
.close
verbal crown
Simple question
obtuse pebbleBOT
Simple question
verbal crown
In direct variation how many points have to pass through the origin to be called a direct variation
only one points
point*
passes through the origin
where people at
<@&286206848099549185>
obtuse pebbleBOT
mild ocean
you just do it until j = n
which you can’t really because the upper bound isn’t an actual number
maybe from a partial sum formula
but right now it has no value because the upper bound isn’t defined
i honestly don’t know
no problem
hardy dust
what is the meaning of this alpha symbol over P ?
obtuse pebbleBOT
what is the meaning of this alpha symbol over P ?
@hardy dust Has your question been resolved?
obtuse pebbleBOT
@hardy dust Has your question been resolved?
hardy dust
.close
stone crypt
will a graph will contain an Euler path only if all edges have even degree.
obtuse pebbleBOT
will a graph will contain an Euler path only if all edges have even degree.
@stone crypt Has your question been resolved?
obtuse pebbleBOT
@stone crypt Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
bitter frost
just not sure how to integrate a and b into the answer/what the question is looking for. I know that numerically the maximum value is infinitely close to 1
obtuse pebbleBOT
just not sure how to integrate a and b into the answer/what the question is look...
@bitter frost Has your question been resolved?
warm siren
obtuse pebbleBOT
warm siren
i got 12.5 for width and length does that sound right?
bitter frost
yeah, a square maximizes surface area with respect to perimeter
spiral maple
spread out is vague
you'd see an x^2
or x*x
yeah, the definition of exponents help with exponents
obtuse pebbleBOT
cunning quail
Could someone explain what this question means?
obtuse pebbleBOT
Could someone explain what this question means?
cunning quail
I don't understand "the restriction, f|{1,2,3}, of f"
Does that mean only the values in the subset {1,2,3} are being mapped from?
tired shell
yeah, ignore 4 (because it messes up the injection)
cunning quail
alright ty
so I could just give examples of mappings?
like f(1) = 2, f(2) = 3, f(3) = 4, f(4) = 2
cunning quail
get it to 2|z-(2+i)| = |z-(-i)| and you can see it's a line bisecting the two points
but please read #❓how-to-get-help lol
waxen plume
no worries
obtuse pebbleBOT
@cunning quail Has your question been resolved?
cunning quail
would a correct answer be f(1) = 2, f(2) = 3, f(3) = 4, f(4) = 2
wary scarab
would a correct answer be f(1) = 2, f(2) = 3, f(3) = 4, f(4) = 2
Nope, the restriction is not surjective to the subset they’re mentioning
obtuse pebbleBOT
@cunning quail Has your question been resolved?
wary scarab
Haha apparently so do I, they didn’t require surjectiveness. But yup, that works
warm shaleBOT
papaustin
obtuse pebbleBOT
tidal ingot
sharp talon
tired shell
@tidal ingot it'd be an empty set
obtuse pebbleBOT
Available help channel!
opaque wren
obtuse pebbleBOT
opaque wren
Help
tired shell
where are you at on this?
opaque wren
where are you at on this?
Have doubts in other 2 as well
tired shell
well here's all the permutaitons
1234 1243 1324 1342 1423 1432 2134 2143 2314 2341 2413 2431 3124 3142 3214 3241 3412 3421 4123 4132 4213 4231 4312 4321
see which ones don't have i in the ith position ever
tired shell
do you know about the principle of inclusion exclusion?
where you add both cases then subtract the intersection
opaque wren
Yeah
tired shell
oh wait I misread, that's an AND
so 3 and 9 are fixed in place, and the other 8 can be in any order
so just 8!
opaque wren
Yeah
opaque wren
well here's all the permutaitons
1234 1243 1324 1342 1423 1432 2134 2143 2314 23...
Just a second
in this you mean 1 can't be in 1st place, 2 in 2nd 3 in 3rd 4 in 4th right?
opaque wren
Ok
opaque wren
so 3 and 9 are fixed in place, and the other 8 can be in any order
Can you give me the idea about how to do 3rd part with inclusion exclusion principal
tired shell
it's a giant formula of
(all permutaitons) - #*(1 fixed point) + #*(2 fixed points) - ... #*(10 fixed points)
opaque wren
Ahh I see
Will try
So in 2nd part A3 intersection A9 is 8!?
I still don't understand how though?
tired shell
you have {1,2,4,5,6,7,8,10} left over to place in the permutation
and there are 8 slots with no restrictions
opaque wren
Ok got it 👍🏻
opaque wren
it's a giant formula of
(all permutaitons) - #*(1 fixed point) + #\*(2 fixed po...
Hey here though the question said no fixed point
tired shell
right
and you'd think that'd be (all permutations) - #*(1 fixed point)
but turns out there's a bunch of overlap
so you need to add back some
and it just keeps going
opaque wren
Like how?
tired shell
what are you asking?
opaque wren
U mean just permutate them all and remove the extra stuff?
tired shell
yeah, naively you say it's 10! minus 10*9! because when you fix a point there are 9 other places
but 10!-9!=0, clearly too low
opaque wren
Count the number of ways to partition {a, b, c, ..., s, t} into 5 disjoint sets such that the sizes of the sets are 0,4,4,4,8 respectively.
Any idea?
tired shell
well start with 20!, and divide by things that are rearrangeable
opaque wren
Is it ok if I use combination and do 20C4 + 16C4+12C4...?
Or it won't work?
@tired shell ?
tired shell
you'll have to multiply them, and that method seems harder
opaque wren
there'll be no +'s but yeah
Multiplication?
tired shell
the answer will look like 20!/x!/y!/z!/...
tired shell
yeah just a bunch of factorials in the denominator
opaque wren
What factorials?
tired shell
the things you can rearrange, where order doesn't matter
like in the set of four you can rearrange them, so /4!
tired shell
yeah so 20!/4!/4!/4!/8! is close
opaque wren
And 1 8!
opaque wren
yeah so 20!/4!/4!/4!/8! is close
Yeah that's what I was saying
tired shell
there's also the three sets of 4 that can go in any order
so 20!/4!/4!/4!/8!/3! would be the answer
obtuse pebbleBOT
@opaque wren Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
atomic quest
tardy marten
critical points meaning vertex, x and y intercepts?
you can find the vertex/turning point/maximum by using the formula
-b/2a
in ax^2+bx+c
atomic quest
y=x²+1
The derivative is
y'=2x
Setting the derivative = 0
2x = 0
x = 0
This means there's either a min or max at x = 0
The y point is found using
y = (0)²+1
y = 1
So there's either a min/max at (0,1)
You can then see if it's a min or max by looking at the points around it which in this case will be a minimum
@tardy marten
tardy marten
yes
you are rtying to find the stationary points?
y=x^2(x-2)^2
just expand
then derive
atomic quest
How
atomic quest
tardy marten
not sure sorry
atomic quest
So how haha?
atomic quest
I don't get it
tardy marten
maybe try 7,x
tardy marten
wydm
atomic quest
It's blackoutnl here I'm using data
atomic quest
You sure because I'm not sure hahaha
tardy marten
i mean
atomic quest
We need someone to recheck
atomic quest
Okay
obtuse pebbleBOT
@atomic quest Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
spice totem
can someone help please
obtuse pebbleBOT
can someone help please
obtuse pebbleBOT
@spice totem Has your question been resolved?
timid silo
obtuse pebbleBOT
timid silo
i presently have proved that if gcd(k,n) is not 1, then its not true and that is all i could do, an intuitive explanation is achievable by me, but not a rigorous one.
<@&286206848099549185>
royal basin
'the counterpart'?
timid silo
yeah i mean that if gcd(k,n) sis not 1
obtuse pebbleBOT
@timid silo Has your question been resolved?
lament vapor
9x^2 - 9y^2 +6xy, has a gcf of 3, so if i factor it out would the answer be this:
obtuse pebbleBOT
9x^2 - 9y^2 +6xy, has a gcf of 3, so if i factor it out would the answer be this...
obtuse pebbleBOT
@lament vapor Has your question been resolved?
frigid jasper
3(3x^2 -3y^2 + 2xy)
yeah
obtuse pebbleBOT
@lament vapor Has your question been resolved?
cobalt locust
hello
ancient jetty
hi
cobalt locust
I need help with an integral problem
using substitution
one sec
not sure how the solution was reached
lethal crest
by parts
cobalt locust
show me the steps
ancient jetty
that's very specific
lethal crest
try it yourself
cobalt locust
i did
obtuse pebbleBOT
@cobalt locust Has your question been resolved?
cobalt locust
no
molten mason
what did you use as your substitution?
molten mason
hmm, try u = sqrt t^2 +3?
nocturne minnow
I used t^2+3 but it could be a bad choice
Pretty sure that's the right choice
cobalt locust
well I wasn't able to solve it
molten mason
what expression did you write once you substituted for that?
molten mason
yup so I think the issue is once you substituted you were still left with both u and t in your expression
the goal of substitution is to simplify it by replacing all of t with expressions in terms of u
you have to figure out how to get rid of those extra t's by continuing to substitute
I think letting u = sqrt t^2+3 might make it easier
(unsure though)
cobalt locust
how would you even differentiate that
cobalt locust
yeah i think i may have figured it out let me work it out
nvm
dead end
I got t out of the equation but that's it
nocturne minnow
I got t out of the equation but that's it
Use an integral calculator, I think the substitution is much more complex than expected
molten mason
ok so I cheated and used the answer and the substitution that worked is u = t + sqrt(t^2 +3)
allows for int (1/u) du
if you differentiate the answer, you'll see why it works
nocturne minnow
ok so I cheated and used the answer and the substitution that worked is u = t + ...
The other one that works too is $u=\frac{t}{\sqrt{3}}$
warm shaleBOT
dldh06
odd bluff
just wanna check my answer
odd bluff
i just drew some constructions at OB, OC, OA, OD and bisected AD and called it OE
i then said since OBC and OAD are isosceles that AE=ED and BE=EC
then i just went AE-BE=AB and ED-CE=CD
then i said therefore AB is congruent to CD
is that correct?
latent nova
you have to prove that OE is perpendicular to BC
or maybe you are allowed to accept it as true?
odd bluff
how 2 do?
latent nova
So E is the midpoint of AD and OAD is an isosceles
That means OE is a perpendicular bisector of AD
Thus it is perpendicular to BC
odd bluff
how tf is OAB isosceles
obtuse pebbleBOT
odd bluff
.reopen
obtuse pebbleBOT
✅
odd bluff
@latent nova
latent nova
OAD sorry
onyx dust
from what I read on https://en.wikipedia.org/wiki/Cube_root
one complex cube root for 1 is -0.5 + sqrt(3)/2 * i
now if I cube that again, I get (question: what have I done wrong or understood wrong?):
obtuse pebbleBOT
from what I read on https://en.wikipedia.org/wiki/Cube_root
one complex cube ro...
onyx dust
(it seems, I need to understand cube roots in the context of complex numbers to be able to derive the cubic formula; dunno if it helps that the topic is related)
obtuse pebbleBOT
@onyx dust Has your question been resolved?
onyx dust
made some calculation mistakes, currently fixing brb
nvm got it, just here if anyone interested 
.close
sinful kraken
Hello everyone how do i find a perpendicular vector to this one: (2,-3,1)
latent nova
It’s a 3D vector right?
sinful kraken
yes
latent nova
Then there’s an infinite number of possible vector that is perpendicular to that
latent nova
Oh
sinful kraken
doesnt matter which one it is
sinful kraken
(-b,a,0) ?
so a perpendicular vector to (2,-3,1) would be (3,2,0) ?
works thank you so much
@latent nova
.close
fair bay
i am stuck on this question: prove that a^3 + b^3 + 4 is not a perfect cube for any positive integers a and b
obtuse pebbleBOT
i am stuck on this question: prove that a^3 + b^3 + 4 is not a perfect cube for ...
obtuse pebbleBOT
@fair bay Has your question been resolved?
obtuse pebbleBOT
@fair bay Has your question been resolved?
coarse laurel
How can I use matrix multiplication to solve this problem?
obtuse pebbleBOT
How can I use matrix multiplication to solve this problem?
@coarse laurel Has your question been resolved?
obtuse pebbleBOT
@coarse laurel Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
hushed escarp
Super basic Question. If I have events A , B what does a boolean combination of those two events mean
obtuse pebbleBOT
Super basic Question. If I have events A , B what does a boolean combination of ...
hushed escarp
So if I want to say event C is independent of any boolean combination of the events A,B, Does that mean the probabity p(C| A \cap B) = p(C)
unique solstice
Uhh
That seems like it would make sense
But that's a really weird way to say that
"Any boolean combination" would imply like anything
Not just intersection
empty falcon
How do i get the magnitude (length) of r ?
obtuse pebbleBOT
How do i get the magnitude (length) of r ?
empty falcon
Do I need to know the vector a and b?
If so I don't know how to get them from what i was given
The closest to vectors a and b that i can get is: a * b = -5
spiral maple
$\norm{\vec{r}}^2=\vec{r}\cdot\vec{r}$
warm shaleBOT
Mosh
empty falcon
$\norm{\vec{r}}^2=\vec{r}\cdot\vec{r}$
I used that formula on a vector r and i got 91, but I need to get 91*sqrt(19).
Sry but I've hit a wall with this one.
I got it know, I made a mistake in a calculation. Thank you.
forgot about that formula you wrote and it did help me solve the problem. Thank you.
.close
austere grove
hey i need help understanding how to do this question
obtuse pebbleBOT
hey i need help understanding how to do this question
austere grove
to my understanding it should be -iarctan(b/a) but i dont see the option
does that transfer into the other options?
obtuse pebbleBOT
@austere grove Has your question been resolved?
obtuse pebbleBOT
@austere grove Has your question been resolved?
echo heron
obtuse pebbleBOT
@austere grove Has your question been resolved?
timid silo
obtuse pebbleBOT
timid silo
im so confused
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
Help, i know i have to factorize this. But idk how to solve it https://media.discordapp.net/attachments/903463353417072641/908180600865837076/unknown.png
obtuse pebbleBOT
Help, i know i have to factorize this. But idk how to solve it https://media.dis...
elder helm
Bring 20 over to the left hand side
Then think about what 2 numbers multiply to -20 and sum to -8
timid silo
-2 and 10
elder helm
Yup thats the solutions to the equation
timid silo
I see
elder helm
and the solutions for x are -2 and 10
timid silo
Aight ty
obtuse pebbleBOT
Available help channel!
shy inlet
Hi! This is a practice problem, I can share the provided solution
obtuse pebbleBOT
Hi! This is a practice problem, I can share the provided solution
shy inlet
I believe it wants the answer to contain the A and B in place of the so called undetermined coefficients, but all I know from class is that I am just supposed to "guess" as to what it is. So far in this homework, I've been able to guess effectively but not on this one.
This is what I have tried so far, I have also tried Ax^2+Bx+C+De^(4x)
here is the provided solution if that helps, i dont think it is correct, as it seems pretty messy and there are other such practice solutions that are incorrect in this homework
<@&286206848099549185>
obtuse pebbleBOT
@shy inlet Has your question been resolved?
obtuse pebbleBOT
@shy inlet Has your question been resolved?
radiant cobalt
does anyone know how to solve this?
obtuse pebbleBOT
does anyone know how to solve this?
@radiant cobalt Has your question been resolved?
radiant cobalt
tangent =1
radiant cobalt
tangent = 1 when it is parellel to the line y=x
radiant cobalt
Ohh
celest sun
Okay, so the tangent is of the form y = x + c
We need a point to plug in to find c
Find the point where this is the tangent line
Then plug in that point
radiant cobalt
ok
celest sun
Try and show what you got if you want to
radiant cobalt
ok
radiant cobalt
Try and show what you got if you want to
is it like this
celest sun
Everything except the last line is good
radiant cobalt
but the answer is y=x+3/4
radiant cobalt
ohh
obtuse pebbleBOT
@radiant cobalt Has your question been resolved?
hot compass
obtuse pebbleBOT
https://cdn.discordapp.com/attachments/903486480075354182/908104728511123496/3bc...
hot compass
where did these two terms come from?
rocky zephyr
Hello does anyone know how to do state machine diagrams
hot compass
obtuse pebbleBOT
@hot compass Has your question been resolved?
hot compass
<@&286206848099549185>
obtuse pebbleBOT
@hot compass Has your question been resolved?
warm shaleBOT
liks
warm shaleBOT
liks
meager raptor
obtuse pebbleBOT
high lily
what have you tried?
high lily
show your work
meager raptor
Ok but do u know the answer ?
high lily
I know how to get it if needed
meager raptor
I know how to get it if needed
It is needed
I'm crying dude bc of that question
I tried sine law... z/50 = 36/the opposite side
frank quartz
meager raptor
U r a genius
high lily
I tried sine law... z/50 = 36/the opposite side
is not a valid application of the sine law
meager raptor
Thanks @frank quartz
frank quartz
Kk
timid silo
Let D be the symmetric difference between two sets A and B. I need to show that D = (A $\setminus$ B) U (B $\setminus$ A). I first started showing that D $\subseteq$ (A $\setminus$ B) U (B $\setminus$ A). In my proof I determined that x $\in$ A and x $\notin$ A $\cap$ B or x $\in$ B and x $\notin$ A $\cap$ B.
obtuse pebbleBOT
Let D be the symmetric difference between two sets A and B. I need to show that ...
warm shaleBOT
Outlander
timid silo
The problems is I don't know how to go forward from there.
jagged solstice
Hi, how would I go about solving limits with 2 k values?
obtuse pebbleBOT
Hi, how would I go about solving limits with 2 k values?
spiral maple
- not a limit
2 there's only 1 k
But you can partial fraction and hope it's telescoping
obtuse pebbleBOT
@jagged solstice Has your question been resolved?
jagged solstice
Apologies, series with 2 k
How would I go about doing that? Can’t seem to find anything on it
I’d know how to solve it if the first k was swapped with an infinite sign for example
solemn sleet
obtuse pebbleBOT
solemn sleet
Im having problems adding and subtracting fractions
timid silo
Make the base same using lcm
solemn sleet
8 : 8 ,16 , 24 ,32 ,40
4 : 4 , 8 ,12 ,16 ,20
They both have 16 in common
But I dont know what to do from there
timid silo
Both also have 8 common which is easier to do. So now 3/8 already has 8 in denominator, in 1/4 you multiply 2 to both numerator and denominator
Tell me what you have now
timid silo
Which can be written as (3+2)/8 now
solemn sleet
Oh so I add both numerators?
timid silo
Solve this and congrats, there's your answer
timid silo
Oh so I add both numerators?
Yep
obtuse pebbleBOT
gusty crow
im confused. how do you solve for final velocity in this problem? i honestly think there is missing information
timid silo
Isn't this a physics question
obtuse pebbleBOT
Available help channel!
trim field
prove that for any x, y, z, a, b, c € R, we have:
obtuse pebbleBOT
prove that for any x, y, z, a, b, c € R, we have:
trim field
I need help with d)
glossy yacht
@trim field algebraically?
trim field
<@477823425893629952> algebraically?
Yes
glossy yacht
how did you do c?
glossy yacht
try what you did there for d
glossy yacht
hm ok hold on
let me think about this
@trim field what did you do in a?
notice how
$(x+y+z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2xz$
warm shaleBOT
Xetrov
trim field
<@477823425893629952> what did you do in a?
I'm doing it now
trim field
$(x+y+z)^2 = x^2 + y^2 + z^2 + 2xy + 2yz + 2xz$
So will be $frac{x²+y²+z²+2xy+2yz+2xz}{3}
glossy yacht
$
glossy yacht
$\frac{x²+y²+z²+2xy+2yz+2xz}{3}$
warm shaleBOT
Xetrov
glossy yacht
no its fine
trim field
**Xetrov**
At a), can I write this orh
today I had 4 hours of math at school
Also, I did b)
$x²+y²+z²≥xy+xz+yz
x²+y²+z²-2xy-2xz-2yz+xy+xz+yz≥0
(x-y-z)²+xy+xz+yz≥0
(x-y-z)²≥0
xy+xz+yz≥0$
@glossy yacht is it okay how I did?
<@&286206848099549185>
glossy yacht
Please don't ping helpers
Because you're already receiving help
do it on paper and send pictures
Texit can be an arsehole
trim field
yuh, ok
flat rune
(don't write x² in texit -- write x^2)
flat rune
and.. well.. there are more errors
obtuse pebbleBOT
@trim field Has your question been resolved?
obtuse pebbleBOT
@trim field Has your question been resolved?
flat rune
how did you solve a) again...? i don't get it
trim field
1s
flat rune
$$\frac{x^2 + y^2+ z^2}{3} \geq \left( \frac{x+y+z}{3} \right)^2$$
$$\frac{x^2 + y^2 + z^2 - \frac{1}{3}\left( x^2+y^2+z^2+2xy+2yz+2xz \right)}{3} \geq 0$$
$$2 \frac{x^2+y^2+z^2 - xy - yz - xz}{9} \geq 0$$
Then what?
trim field
warm shaleBOT
reking
trim field
Off
timid silo
obtuse pebbleBOT
timid silo
How did we get from the top line to the bottom line
flat rune
through the middle line? 😄
flat rune
yes
timid silo
oh ok
flat rune
i just dont know what the question is, there is a line between top and bottom that you asked about? where exactly are you unclear
timid silo
I meant
trim field
....
flat rune
well for example, the first part becomes
$$\frac{81}{n^4}\left( \frac{n(n+1)}{2} \right)^2 = \frac{81}{4n^4} n^2(n+1)^2$$
$$ = \frac{81}{4n^2} (n+1)^2 = \frac{81}{4} \left( \frac{n+1}{n} \right)^2 $$
$$ = \frac{81}{4} \left( 1 + \frac{1}{n} \right)^2 $$
mild ocean
for the first term, they changed 1/n^4 into 1/(n^2)^2
warm shaleBOT
reking
flat rune
you mean the n^4 and the n^2 is cancelling out?
timid silo
I meant that a 4 appears in the denominator of 81
mild ocean
they just switched the denominators
flat rune
it comes from the 2 in the denominator at the beginning
it is squared, so i can take it outside and it becomes 4
$\left( \frac{1}{2} \right)^2 = \frac{1}{4}$
warm shaleBOT
reking
timid silo
lol
im lost
I understand the denominator in the expression is squared. That its denominator will equal 4
ok
so
the denominators are multiplied giving 81/4n^4
n^2 is cancelled out
leaving 81/4n^2
(n+1)^2 = (n+1)(n+1) = n^2 +2n +1
81/4n^2 = 81/4 because n^2 is now canceled
flat rune
(n+1)^2 = (n+1)(n+1) = n^2 +2n +1
there is no need to multiply that out
you can just move the n^2 inside
$\frac{1}{n^2} \left( n+1 \right)^2 = \left( \frac{n+1}{n} \right) ^2$
warm shaleBOT
reking
flat rune
because.. well
$\left(\frac{A}{B} \right)^2 = \frac{A^2}{B^2}$
warm shaleBOT
reking
flat rune
you see??
timid silo
yes
(n+1)^2 / n^2 = (n+1 / n )^2
I'm sorry, I forgot a lot of basic math skills
going from step 2 to step 3
flat rune
yes? or ?
flat rune
$\frac{n^2}{n^4} = \frac{1}{n^2}$
warm shaleBOT
reking
flat rune
$\frac{n \cdot n}{n \cdot n \cdot n \cdot n}$
warm shaleBOT
reking
flat rune
they cancel out, right?
flat rune
i guess i dont know what you mean by step 2 and step 3
timid silo
I understand now how we go from step 1 to step 2
thanks for that
but now I am asking
how do we go from step 2, the middle line, to step 3
where n is no longer present and the solution is given as -6.75
flat rune
because when n goes to infinity, you can simply remove all 1/n
it goes to zero
so you have
$\frac{81}{4}(1+0)^2 - 27(1+0)^2$
warm shaleBOT
reking
timid silo
is that true for all variables when their limit is infinity?
flat rune
yeah, well, theres nothing special about the l etter 'n'
if x goes to infinity, 1/x goes to zero
timid silo
what about just x
flat rune
thats why they did the stuff from top line to middle line. to get rid of n in the numerator
timid silo
I see
well thanks for the help
that has helped a lot
is there a place where I can find the limit laws?
so I know that as n approaches infinity that 1/n = 0
flat rune
it can be shown like this. for any small $\epsilon > 0$, we can find a large $N$ such that the distance between 1/n and 0
$$|1/n - 0| = |1/n| $$
is less than $\epsilon$, whenever $n \geq N$
warm shaleBOT
reking
flat rune
but if that doesn't make sense to you yet, i don't know how else to show it :v
sly olive
heewo. I need to find the ordinate to the origin 4x + 2y = 103, I can't really solve it, I saw several videos and I don't know if you could help me please 🥺
obtuse pebbleBOT
heewo. I need to find the ordinate to the origin 4x + 2y = 103, I can't really s...
tired shell
is that the y-intercept?
sly olive
is that the y-intercept?
ye
i need to find
That equation in origin-ordered slope form and determine the origin-ordered slope
tired shell
oh I don't know what that is
tepid mantle
Moments question: it says its on the point of tilting about C, so what I did is at A the force is 0, however the markscheme takes A into account
obtuse pebbleBOT
Moments question: it says its on the point of tilting about C, so what I did is ...
tepid mantle
this is what i did so far but its wrong
tired shell
tilting about C just means C is the fulcrum
and since it's barely tipping, the platform can only push up at that point
tepid mantle
tilting about C just means C is the fulcrum
but for example in this question
it also says its on the point of tilting about C and D is considered 0
tired shell
that question is pretty different because it has 2 fulcrums that might push up
there if it tilts on C then it's barely not touching D so it can't apply a force
tepid mantle
that question is pretty different because it has 2 fulcrums that might push up
so is it because there force at D is a reaction force upwards whereas in the first questsion there is a weight applied to A so it's downwards and it still is considered even though its about to tilt?
obtuse pebbleBOT
@tepid mantle Has your question been resolved?
tired shell
yeah all the downward forces will still be there
when things are tilting sometimes some upward forces become 0
because they lose contact
desert pagoda
does anyone know if i did this right
obtuse pebbleBOT
does anyone know if i did this right
warm shaleBOT
The following error occured while calculating:
Error: Invalid left hand side of assignment operator = (char 20)
tired shell
,w (1+sin(x))/(1+csc(x))
warm shaleBOT
tired shell
yup that's right
desert pagoda
that 1 side = the other
i know its right but i just want to know did i do it right
like my work
steady marsh
yeah
desert pagoda
i cant divide 1 by1?
steady marsh
what is 1/1
desert pagoda
oh yea i fogot
steady marsh
or 2/2
desert pagoda
i didnt do anything to the rhs
steady marsh
how did you get 1+sin(x)/(sin(x)/sin(x))
steady marsh
sin(x) + 1 is not equal to sin(x)
desert pagoda
so how do u do it then
steady marsh
multiply your denominator and numerator by sin(x)
then you should be able to cancel out a 1 + sin(x)
leaving you with just sin(x)
desert pagoda
how can i cancel out the 1+sinx?
steady marsh
steady marsh
Not quite...
You can't just cancel out numerator terms like that
I suggest you to practice simplifying rational functions
desert pagoda
we did those last year
i am really confused
on what u did
how did u get sin(x) (1+sinx)
on the numerator
steady marsh
do the same process, but this time you're going to have to factor out a negative
steady marsh
notice that 1 - tan(x) = -(tan(x) - 1)
steady marsh
do the same process, but this time you're going to have to factor out a negative
so apply what we did with sin(x) but multiply by tan(x)
desert pagoda
so apply what we did with sin(x) but multiply by tan(x)
and do we turn them into sin/cos and cos/sin?
obtuse pebbleBOT
@desert pagoda Has your question been resolved?
slim relic
Hey, I'm struggling to understand how this tree diagram works (it's basic probability) but I'm not very good at it! Thanks :)
obtuse pebbleBOT
Hey, I'm struggling to understand how this tree diagram works (it's basic probab...
slim relic
Here's the question
I have the answers but I don't really understand how to get them.
I'd like if someone could walk me through the process to finding out what the chances are for each part.
<@&286206848099549185> Sorry for the ping! I have been trying to understand and guess how to go about it but I'm not getting anywhere :(
timid silo
whats the answer for a
slim relic
It is 4/9
zinc stump
Start with c and d, it's easier. There is a 1/3 chance in getting every question right, and all questions are independant
slim relic
I just don't know at all how to go about solving it :/
slim relic
give me a few minutes
timid silo
i’m not sure if that’ll work but that’s the first thing that comes to mind for this question
this is messy but something like this
timid silo
no because each question does not effect the next
the events are independent of one another
timid silo
hmm u could do it like that but think what are the two outcomes of the questions?
either correct or incorrect right
slim relic
yea i was about to say that
ok right and then it should be a 1/3 chance to get it right
what do i do next?
timid silo
u wanna answer (a) yeah?
slim relic
yep :)
timid silo
so 3 questions and what is the probability of the person getting 1 correct answer, so now think what are the ways that the person could get 1 correct answer
slim relic
i dont know, what do you mean by 'ways that the person could get 1 correct answer'?
timid silo
okay think of it like this there’s 5 blue pens around a room and if a question asked what is the probability of getting 1 blue pen, then for this the different ways would be the person getting the blue pen to their right, OR they could get the blue pen infront of them , OR any of the other 3