or like this
#help-0
rotund crater
the computatiton , graph i dont understand
heady pollen
if you dont understand the graph, i dont recommend doing the computation
i would suggest first getting some intuition.
you can do that by watching some youtube videos about this
they tend to have nicer graphics than what i can do in ms paint
rotund crater
how u get sqrt y/2
heady pollen
this here
rotund crater
what is f(x) and g(x0
heady pollen
what f and g?
brazen rover
hi
lone heartBOT
@brazen rover Has your question been resolved?
brazen rover
<@&286206848099549185>
lone heartBOT
@brazen rover Has your question been resolved?
brazen rover
.close
broken stream
lone heartBOT
limpid spade
?
lone heartBOT
@broken stream Has your question been resolved?
tight thunder
lone heartBOT
tight thunder
Guys
what is general rule here?
I always get mental blockade
I need to resolve this
Who gets deleted who stays where how?
low sparrow
if you're trying to throw everything to the numerator it'd be x^(b-1) i believe
remember 1/x=x^-1
so basically x^b*x^-1=x^(b-1)
low sparrow
well it's not that you remove it
it's just that x^b/x is equivalent to x^b * 1/x
and since we know that 1/x=x^-1, then it's equivalent to x^b*x^-1
low sparrow
what are you confused about specifically?
tight thunder
I am trying to understand and remember what you said
low sparrow
do you understand that 1/x=x^-1?
tight thunder
oh
I have much complexer example
(w* y^^1/2 * (w/r)^1/2 + ry(w/r) 3/2) / y
dramatique
So I just remove the second y
and first 1 will then be y^-1/2 ?
and it can be written as
low sparrow
do u have that first form written out? ur right that it's hard to read in text lol
tight thunder
I go ask chatgpt to make it
\frac{w \sqrt{y} \sqrt{\frac{w}{r}} + r y \left(\frac{w}{r}\right)^{\frac{3}{2}}}{y}
how to call that math bot
@low sparrow yo i send
LAC sucess?
low sparrow
oh you're trying to simplify this as well?
low sparrow
i mean like, you're trying to simplify the fraction right?
like cancel out the y's to get a simpler result
tight thunder
Yes isnt that the process
You propose i leave it as it is?
oh wait
i just realised that I did a mistake
or did I?
low sparrow
not sure, but i can help you simplify it
you not sure
low sparrow
\frac{w \sqrt{y} \sqrt{\frac{w}{r}} + r y \left(\frac{w}{r}\right)^{\frac{3}{2}}...
well, i don't know how you got to that result, but i can help you simplify this
low sparrow
yepyep
low sparrow
i don't think so, look at this instead,
technically you're right on cancelling out for the right side, but you don't quite get sqrt(y^2) (which is equivalent to y), but y^(-1/2) instead
tight thunder
with great struggle I try to understand what you did
Its insanely hard
this that nefarious thing that shot 2pac
low sparrow
oh so you basically just factorize sqrt(y) out of your numerator
low sparrow
and since you end up with y^(1/2)/y, it's the same thing as we did,
y^(1/2)/y^1 = y^(1/2-1) = y^(-1/2), which is equivalent to 1/sqrt(y) or 1/y^(1/2), both of which are the same
same thing as we did for x^b/x^1, where we get x^(b-1)
just this time, we just subtract 1/2-1 and get -1/2
tight thunder
I cant read this man like
I was designed to hunt antilopes in africa
but I dont exist
Its just subject object invention by language
low sparrow
let me see if this works, $y^{(1/2)}/y^1 = y^{(1/2-1)} = y^{(-1/2)}$
ocean sealBOT
end
low sparrow
same thing as we did for $x^b/x^1$, where we get $x^{(b-1)}$
ocean sealBOT
end
tight thunder
Yes
low sparrow
and there u go
low sparrow
oh i'm just factoring out sqrt(y)
you see, if you multiply it times whatever's on the inside, you'll still get the same numerator as above
lone heartBOT
@tight thunder Has your question been resolved?
untold dove
summer hull
I have been struggling with this integration for a while.
I don’t know why we multiplied the denominator by sqrt(2)
rough grove
How do I make an exponential function?
lone heartBOT
How do I make an exponential function?
quick peak
@mossy olive #❓how-to-get-help
lone heartBOT
Available help channel!
radiant dirge
can a bipartite graph be disconnected i.e. can there be a vertex that doesn't connect to any other vertex for example this pic
dapper horizon
sorry i didn't realize im new
worn fox
they can be disconnected yeah
lone heartBOT
radiant dirge
Bone soup now you can ask
radiant dirge
wait for the bot to free this channel first
lone heartBOT
Available help channel!
alpine sable
Basic question. Given the AB midpoint C, I need to find a way to calculate D or E according to an X offset value. I don't understand what to look up on internet for this.
vapid steppe
do arithmetic infinite sums ever converge
lone heartBOT
do arithmetic infinite sums ever converge
limpid turret
didn't you just do one that converged?
placid zinc
Like, sums of the form mx + b?
vapid steppe
that was geometric
limpid turret
oh
placid zinc
No they never can
limpid turret
vapid steppe
Like, sums of the form mx + b?
ye i have sum from 1 to inf of (4+(1/2)n)
placid zinc
Other than Σ 0 ig
vapid steppe
is it because arithmetic dont have horizontal asymptote
For an arithmetic sequence with $a_1=-6$ and $S_{50}=-5150$, find $a_{50}$
pseudo ice
more that e.g. when you take the partial sums, you get $\sum_{k=1}^{n} a + (k-1)d = \frac{n}{2}(2a + (n-1)d)$ and that diverges as $n\to\infty$ (unless of course your first term $a$ and common difference $d$ are both zero
ocean sealBOT
@pseudo ice
pseudo ice
For an arithmetic sequence with $a_1=-6$ and $S_{50}=-5150$, find $a_{50}$
a_{50}
ocean sealBOT
Jash
placid zinc
Well, you don't need it to converge, in order to find a50
vapid steppe
ye ik this is different problem
i have the equation 25(-6+a_50)=-5150
is is this correct
vapid steppe
i used the formula $\frac{n}{2}(a_1+a_n)$
ocean sealBOT
Jash
vapid steppe
Why -25 tho?
i meant to type 25 srry
pseudo ice
In that case you're fine then 
vapid steppe
i got a_50=-200
vapid steppe
more that e.g. when you take the partial sums, you get $\sum_{k=1}^{n} a + (k-1)...
if its in mx+b can i just look at the constant since ur adding a constant infinite times so it becomes infinity
pseudo ice
that's kind of the idea, you have something that blows up (though of course be careful with the "x" too, in any case it'll be ±♾️ you get if the first term and common ratio aren't both zero)
nocturne spear
When I select second function on a calculator what X do i have to select 1, 2, or 3, when I am doing A2+B2=C2
opal yacht
WHY is this wrong
lone heartBOT
WHY is this wrong
heady pollen
not sure, but maybe your input implies taht you have two vertical asymptotes
one at x=4, one at x=0
hmm
opal yacht
I put just 4 and 0 in the ans and doesn't work still
outer lark
'enter your values as a list of equations'
heady pollen
oh
outer lark
0,0 is most definitely not an equation
outer lark
I would agree hopefully the software also does
opal yacht
RIp used my last attempt
outer lark
did it not work?
opal yacht
no
outer lark
urgh
well
the vertical asym is defo x=4 and the horizontal is 100% y=0
so don't worry about it
alpine sable
would these angles be right
lone heartBOT
would these angles be right
alpine sable
or would the angle of the bottom triangle be at the bottom of its triangle
lone heartBOT
@alpine sable Has your question been resolved?
gray heart
What do you mean by this
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
What do you mean by this
interior angles
gray heart
interior angles
Can i see your exact problem?
heady cave
gray heart
Nvm idk sry
lone heartBOT
@alpine sable Has your question been resolved?
rustic drum
Hello?
lone heartBOT
@alpine sable Has your question been resolved?
odd nest
does this look right
lone heartBOT
does this look right
odd nest
also changed it to sin
odd nest
so the only thing off is the period
cause in the graph the wave repeats 7 times
starting from the left to right
vapid shuttle
the graph is going to keep repeating forever
the amount of times you can see it repeat isn't what matters
what matters is the distance in between each repetition
odd nest
so would the period be 2
odd nest
then i need help understanding because it’s the only thing i’m stuck on
i know the amp is 2
i know the wave is shifted down -1
but the period is the only thing i’m not sure how to get
vapid shuttle
but the period is the only thing i’m not sure how to get
the period is how often the function repeats itself
,w plot sin(x)
ocean sealBOT
vapid shuttle
look at this
the reason we say the period is 2pi
is because that is how often the function does the same exact thing
see how the first peak, is at -3pi/2?
when is the next peak
it's at pi/2
what is the distance in between -3pi/2 and pi/2?
it's 2pi
so the period is 2pi
because that is how often it repeats
for your function, the distance is different
vapid shuttle
you'd put 1/2 inside the function like this
sin(x/2)
but that is because the period is 4pi
the period isn't 1/2
you understand that right?
vapid shuttle
So
here is how
sin(x) has a period of 2pi
for a sine function to have a period of 4pi
this means we want it to repeat itself, 2x slower
right?
we want x to travel 2x slower
so instead of sin(x)
we get sin(x/2)
If we wanted ours to have a period of 6pi
this would be 3 times slower
so we would put sin(x/3)
odd nest
and let’s say it was 8pi it would be sin(x/4) right
vapid shuttle
yes
vapid shuttle
looks good to me
odd nest
okay thank you i understood how to get the amp and C to shift up and down but learning the period is still something i need to work on but i’m going to ask my teacher to help me but i do really appreciate you helping me
odd nest
okay i appreciate that a lot have a good rest of your night
vapid shuttle
you too!
lone heartBOT
@odd nest Has your question been resolved?
vapid shuttle
.close
alpine sable
lone heartBOT
alpine sable
<@&286206848099549185>
tacit arch
<@&286206848099549185>
!15m
lone heartBOT
<@&286206848099549185>
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.
mortal trellis
what about x=0
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
@crisp iron
mortal trellis
maybe helpers would be more likely to help if you showed that you didnt ignore hints given to you
ocean sealBOT
[code{RED}]
copper delta
,,p(0) = c_{0}
ocean sealBOT
[code{RED}]
mortal trellis
well first dont give out solutions. wait for them to do stuff before giving more. second you can get more than that from the information given.
copper delta
ok
open perch
copper delta
thanks?
lone heartBOT
@alpine sable Has your question been resolved?
mortal trellis
well exactly how they said
they add the diagonal to the relation
which gives a new relation which is now reflexive and not irreflexive anymore
slim moat
i understand the answer and the question but idk how to simply the arccot to 67.5
earnest saddle
,w arcsin(cos(2arccot(sqrt(2)-1)))
ocean sealBOT
lone heartBOT
@slim moat Has your question been resolved?
broken falcon
lone heartBOT
broken falcon
Help with this limit pla
Plus*
Pls*
i would start with taylor
because 1/x is tendent to 0
median oar
use a .
broken falcon
.close
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
Need help with stats
lone heartBOT
Need help with stats
alpine sable
Determine the most conservative sample size for the estimation of the population proportion for the following.
E= 0.026, confidence level = 95%
n = ?
Can anyone help me solve this lol
E = 0.09, confidence level = 90%
lone heartBOT
@alpine sable Has your question been resolved?
formal tide
I need a lot of help please, i don't get it but how can i rearrange to solve for v in this?
formal tide
70 = (V divided by 3.6)^ 2 over 14 + 0.75 x (V divided by 3.6)
Not sure if this helps but the question is: A test is run and measure the total stopping distance of a car to be 70 metres. Investigate what the initial velocity of the car could be.
I'm assuming "could" is a big part in this question
nimble latch
70 = a^2 / (14+0.75a)
formal tide
right
nimble latch
70*14 = a^2 + 0.75*14a
rocky atlas
Multiply both sides
nimble latch
but why 0.75 x 14a
to remove the fraction
formal tide
Multiply both sides
hmm but i thought multiplying both sides would only just be 70 x 14
but uhhh alright
nimble latch
so rearranging everything, we would have a^2 + 10.5a - 980 = 0
and if we use quadratic formula, we'll get the value of a
formal tide
sorry but could you remind me, what's the quadratic formula again?
could you find the answer by going 980 = 10.5a + a^2
nimble latch
rocky atlas
a^2 + 10.5a - 980 = 0 can also be written 2a^2 + 21a -1960=0
nimble latch
factoring doesnt work
rocky atlas
factoring doesnt work
Discriminant is positive though?
Factors exists if b^2-4ac is greater than or equal to 0
nimble latch
,w (V/3.6)^2 + 10.5*(V/3.6) - 980 = 0
formal tide
can i ask what does x represent
nimble latch
a
ocean sealBOT
rocky atlas
Btw can Initial velocity can be negative though?
formal tide
Btw can Initial velocity can be negative though?
... It's a car
it cant go -40km/h 😭
rocky atlas
But velocity can be negative
nimble latch
it could be moving backwards
formal tide
can i ask why there are two different answers
rocky atlas
can i ask why there are two different answers
Because mathematically formula is quadratic so it will have 2 answers
formal tide
i see
formal tide
you'll get the ans in surd form
i know this sounds super stupid
but how do you use the quadratic formula again
as in what situation would you use it
nimble latch
you use it in situations where you have the equation in the form ax^2 + bx + c = 0
formal tide
ah i see
rocky atlas
but how do you use the quadratic formula again
- It is used for quadratic equation of format ax^2 + bx + c=0 only
formal tide
thank you very much man
i was on the verge of tears
trying to solve it
wait a minute
so do you
x by 3.6
to find the velocity
cause a = v/3.6
nimble latch
70 = ((V/3.6)^2 /14) + 0.75(V/3.6)
wait, but where did you get these numbers
formal tide
wait, but where did you get these numbers
well you see
formal tide
i have an investigation/test
and the teachers were like
there is no definitive asnwer
you must do research
to find some of your variables
so i used the average time reaction from reaction to putting down the brakes
and the average deceleration rate of a vehicle
which are 0.75s and 7m/s^2
nimble latch
i see
formal tide
yep
thats why i wanted to die
its weird that there are no definitive answers
thats why i figured in the validation
you must use the formulas you found
and input it
rocky atlas
its weird that there are no definitive answers
What does definitive answer means, not irrational?
formal tide
What does definitive answer means, not irrational?
it can be anything
because some of the variables
depend on the person
how they did it
rocky atlas
I see
nimble latch
then just take two decimal places from these answers and multiply by 3.6
formal tide
wait
but can i ask
how can i solve it like
without the thingy
like assume it's the same
how can i find the answer
like without a calculator
nimble latch
the quadratic formula?
rocky atlas
a^2 + 10.5a - 980 = a
Wait why is there a in rhs
nimble latch
a^2 + 10.5a - 980 = a
= 0
in some cases, you will have a nicer polynomial where you can easily factorize and not have to use the formula
but this is not the case
formal tide
0
sorry misclick
what's a polynomial
oh wait a second
yeah how would i solve it
from the quadratic equation
say i have all the variables input
how do i solve it form there
from
nimble latch
what's a polynomial
basically any equation consisting of a variable and a coefficient
rocky atlas
But there are restriction like power can't be fractional or negative
nimble latch
say i have all the variables input
we have this 1a^2 + 10.5a - 980 = 0
a = 1, b = 10.5 and c = -980
we then plug these values into the quadratic formula
formal tide
so 11.5 a = -980???
wait
oh i see
gimme a sec
ima writ ethis down
thank you very much btw
nimble latch
think back to this form, ax^2 + bx + c = 0
formal tide
gimem asec
okay i just got info
apparently from a teacher
we shouldn't use the quadratic formula???
this makes no sense
is there any other way shik
nimble latch
can you send the full question here
formal tide
cause in the test
formal tide
can you send the full question here
what
nimble latch
your investigation
formal tide
ok the guy said something about
the difference of squares thing
but that makes 0 sense
we are coincidentally learning that right now
which would make sense
but i fail to see how it could possibly be used as a solution
nimble latch
i dont see how that's applicable with the equation we have
formal tide
hmmm
i think it's a bit stupid
considering how we can have different values
but only one solution
there must be multiple solutions
would there not
nimble latch
,w (V/3.6)^2 + 10.5*(V/3.6) - 980 = 0
ocean sealBOT
formal tide
to have undefinitive variables and to have. a definitive answer would be stupid
rocky atlas
The answer seems different
formal tide
unless it just multiplied it
nimble latch
considering how we can have different values
I can't say much without further context
formal tide
I can't say much without further context
ok
do you mind if i uh
send the questio
as in what they say
nimble latch
yea sure
formal tide
Part A reaction distance
Research some factors which may affect a driver's reaction time and determine some approximate reaction times in each situation
How does age appear to affect average reaction times? (there was a table above but irrelevant)
rocky atlas
Part A reaction distance
Research some factors which may affect a driver's react...
This seems like a research for social science experiment
formal tide
why and how might the average reaction times achieved in these trials differ to the breaking reaction times in an actual driving situation
suppose that a car was travelling with a constant speed v km/h. for a reaction time of t seconds, determine a formula to calculte the reaction distance ( d in metres)
Part B
Research some factors which may affect the braking distance of a car.
some stuff about final velocity and initial velocity
(Vf)^2 = (Vi)^2 = -2ad
i rearranged it to get D = (Vi +3.6)^2 /2a
Determine a formula for the stopping distance of a car.
rocky atlas
(Vf)^2 = (Vi)^2 = -2ad
Do you mean (Vi)^2-2ad?
formal tide
and it said that total stopping distance = reaction distance + braking distance
nimble latch
(Vf)^2 = (Vi)^2 = -2ad
v^2 = u^2 - 2as?
formal tide
v^2 = u^2 - 2as?
yep
a table investigating effect of speed reaction time and deceleration rate on tsd
Investigate the effect of each of the following on the total stopping distance:
Speed by 5km/h in a school zone
Doubling the speed in a residential area.
ocean sealBOT
Calamity
formal tide
and the last question
nimble latch
Determine a formula for the stopping distance of a car.
so, we were doing this?
formal tide
so, we were doing this?
nope
the one we were doing
A test is run and measures the total stopping distance of a car to be 70 metres.
Investigate what the initial velocity of the car could be.
formal tide
70 = Vi*t + breaking distance
what
nimble latch
and the reaction time you used was 0.75 right?
formal tide
mmhmm
nimble latch
breaking distance = (u^2 - v^2) / 2a
70 = 0.75u + u^2/14
oh wait
we get the same exact thing
formal tide
ok
nimble latch
so, uhh
formal tide
i think it doesn't matter
because right now
we already are capable of doing quadratic
i think this guy just
really sucks at quadratics
sorry to ask again but what would the solution be
wait no
like the quadratic formula
nimble latch
i dont see how differences in squares makes sense here
nimble latch
nimble latch
we have this 1a^2 + 10.5a - 980 = 0
wait it a little easier by multiplying both sides with two to get integer inputs
so we'd have a = 2, b = 21, c = -1960
it looks ugly, but it is what it is i suppose
formal tide
okay continue
nimble latch
no, it looks confusing here, but we're talking about the number beside the term that is squared when we look for inputs
so the term beside 2(a^2) is 2
and a = 2
it's clear if you replace the term being squared with an x
formal tide
i'm sorry but my brain is melting to sludge but keep going
nimble latch
for the sake of simplicity, we'll use x instead of a
rocky atlas
Number beside variable known by the name coefficients
nimble latch
@rocky atlas , can you type in latex of what x would be when a, b, c is plugged in
im cluless abt latex
rocky atlas
<@561270415008333847> , can you type in latex of what x would be when a, b, c is...
Plug where btw
nimble latch
the quadratic formula
nimble latch
pm i think
rocky atlas
What's pm?
nimble latch
\pm
rocky atlas
Oh
formal tide
i'm sorry to bother you guys
rocky atlas
Plugging a=2, b=21 and c=-980 into quadratic formula $$(-(21) \pm √((-21)^{2}-4(2)(-980)))/2(2)$$
ocean sealBOT
Calamity
rocky atlas
Lol I'm also less knowledgable
nimble latch
a = 2, b= 21, c = -980
do you understand where a, b, c came from?
formal tide
yes
the 3 different coefficients
right
well 2 coefficients
and that one number
rocky atlas
No
nimble latch
then, using those values, u plug those values into the formula
rocky atlas
That number is coefficient of x^0
nimble latch
i hope it clears it up
let's try a simple problem now if you dont mind, x^2 + 4x + 4 = 0
formal tide
ok
rocky atlas
Oh its the question of completing the square
nimble latch
yes, but let's use quadratic formula
nimble latch
ye
formal tide
nice
nimble latch
and try plugging those in into the formula
formal tide
the people told me
that quadratic seems a bit hard
and there might be an easier formula
but i said that
with no definitive variables and answers
how can there be 1 single solution?
There can't
rocky atlas
You did a good dialogue 👍
formal tide
although it is a bit suspicious the teacher said you shouldn't use the quadratic formula
that is suspicious indeed
rocky atlas
that is suspicious indeed
Suspicious in a way that teacher found answer through quadratic formula and wants to know if there is a genius student who can think of a outside the box method.
Maybe
formal tide
Suspicious in a way that teacher found answer through quadratic formula and want...
perhaps
formal tide
do you understand where a, b, c came from?
wait
@nimble latch
sorry but
c = -1960 right
because
everything else
is multiplied by 2
rocky atlas
c = -1960 right
Yes
formal tide
ok
rocky atlas
for $$2x^2 + 21x - 1960=0$$ a is 2, b is 21 and c is -1960
formal tide
oh uh wait
for the thing
do i leave it as plus minus
or can i just find it
somehow
ocean sealBOT
Calamity
rocky atlas
do i leave it as plus minus
Find once for plus and then minus
nimble latch
do i leave it as plus minus
if x = 1 + or - 2, it becomes something like x = 1 + 2 or x = 1 - 2
rocky atlas
+- indicates there will be 2 answers
nimble latch
x = 1 ± 2
formal tide
Is this the answer? Or is the first one the answer
nimble latch
then you will have x = 1 + 2 or x = 1 - 2
rocky atlas
1 /pm 2
nimble latch
Is this the answer? Or is the first one the answer
this is the final answer
formal tide
this is the final answer
ok
oh wait
is it because earlier
we didnt multiply it
so that is the answer after multiplying
thank you due
i mean it sounds right
because stopping distance = 70
nimble latch
yea
formal tide
that's a lot
lol
Okay
thank you very much man
you just saved me
from buckets of tears
WAIT
@nimble latch
i'm super duper sorry
for asking you again
but on a calculator
how do i find both answers?
so i have the finalised
quadratics
but how do i solve it
nimble latch
so u have x = something with ± in it right?
formal tide
yes
nimble latch
type in once for +
and write that ans down as one of the answers
and type in another time for -
formal tide
i have (x = -21 +- sqr 441-15680) / 4
OHHHHHH
wait
how do i solve it though
in the calculator
oh wait
im a fucking idiot
i get it
oh my god
thanks a lot man
saviour
my lord and saviour dude
fair elk
For this question a and b seem rather straightforward however are my workings for c and d accurate or have I erred in some way. Is this the correct approach for solving such questions and are my answers accurate?
chrome salmon
For this question a and b seem rather straightforward however are my workings fo...
How did you find T(p)
fair elk
How did you find T(p)
Like so?
chrome salmon
Okay
fair elk
oh sorry wrong image
chrome salmon
I thought you had to get form like this
You want transformation for that specific p
fair elk
Like this?
chrome salmon
It's okay I've seen this
chrome salmon
So is this working accurate?
Well d was to be done using c
With what you wrote, you will be multiplying the matrix by (a,b,c,d) cuz you used the basis in {1,x,x²,x³} arrangement to find the matrix
fair elk
a,b,c,d or d,c,b,a?
chrome salmon
And btw the transformation matrix will be the transpose of whatever you wrote
fair elk
Also, sorry but I have just got a clarification but for the matrix, I've written T(1), T(x), etc. with the resulting matrices horizontally, should this be vertical, e.g. T(x) = 0,3,2,0 downwards instead of horizontally.
chrome salmon
a,b,c,d or d,c,b,a?
a b,c,d
chrome salmon
Also, sorry but I have just got a clarification but for the matrix, I've written...
Yeah that's what I said, it's transpose will be the transformation matrix
Your notations are pretty bad for d
And wrong too
fair elk
So c with the transpose is right, but I stuffed up d?
chrome salmon
You must write c full
From start
Discard this
T(p) = p(y(x)) = 4 + (2x+3) - (2x+3)³
Just write T(1) = 1
T(x) = y(x)
T(x²) = y(x)²
Writing (xoy)(x) makes it too much confusing and isn't right either
fair elk
ok, but other than that it is ok. For d, if it is right is this accurate for checking it?
chrome salmon
ok, but other than that it is ok. For d, if it is right is this accurate for che...
I told you d has to be done using c
e isn't hard and you did it right
fair elk
Well if I did e right then my d must be right?
chrome salmon
Well if I did e right then my d must be right?
The method is what makes it right
You have to solve d using c brain
fair elk
But the values are wrong?
chrome salmon
But the values are wrong?
In c you have solved whole thing wrong
fair elk
In c you have solved whole thing wrong
How do I begin to solve it?
So even when the x o y is removed it is still incorrect?
chrome salmon
T(p) = p(y(x)) = 4 + (2x+3) - (2x+3)³
Just write T(1) = 1
T(x) = y(x)
T(x²) = y(...
.
chrome salmon
So even when the x o y is removed it is still incorrect?
Yes
fair elk
(c) To find the standard matrix representation [T]S of T, we need to find the images of the basis vectors under T and write them as column vectors. We have:
T(1) = 1 ◦ y = 2x + 3 = 0(1) + 2(x) + 0(x^2) + 3(x^3)
T(x) = x ◦ y = 2( x ) + 3 = 0(1) + 0(x) + 2(x^2) + 3(x^3)
T(x^2) = x^2 ◦ y = 2( x^2 ) + 3 = 0(1) + 0(x) + 0(x^2) + 2(x^3)
T(x^3) = x^3 ◦ y = 2( x^3 ) + 3 = 0(1) + 0(x) + 0(x^2) + 0(x^3)
Would something like this be on the right track?
And then a resulting matrix
chrome salmon
T(1)=1
T(x)=y(x)=2x+3
T(x²)=y(x)² = (2x+3)²
T(x³)=y(x)³ = (2x+3)³
That's how easily it is to be done
What's with all the notations you are using and wrong substitutions
chrome salmon
Yeah that's it just expand all expressions
fair elk
Ngl that smiley face is creepy
chrome salmon
It is supposed to be
fair elk
It is supposed to be
Resulting matrix?
Because when expanded, e.g. T(x^2) = 4x^2+12x+9, so [9,12,4,0]
chrome salmon
Resulting matrix?
Alright
fair elk
What? So it is just the transpose of the above matrix?
What is the reason for transposing the matrix?
chrome salmon
What is the reason for transposing the matrix?
We already discussed this
lone heartBOT
@fair elk Has your question been resolved?
fair elk
We already discussed this
So once we find the polynomials and then the coefficients of the polynomials, we then transpose them to get the standard matrix representation, is that right
chrome salmon
Ok
fair elk
Please, ok is rather vague, this gives me the impression that I am still not following and am travelling down the wrong track.
chrome salmon
Please, ok is rather vague, this gives me the impression that I am still not fol...
Don't worry honey
fair elk
Ok
I am so very sorry kind sir but I am quite obviously struggling, I have expanded the expressions as you have instructed and then put the coefficients into a matrix and then transposed that particular matrix to then find the standard matrix representation. I have done as you you said.
chrome salmon
[1 0 0 0; 3 2 0 0; 9 12 4 0; 27 54 36 8] multiplied by [a;b;c;d]
Ok good
chrome salmon
Nothing
fair elk
Nothing
Normally, isn't the matrix representation just normal values without variables?
What was the need for to multiply by a,b,c,d again and now with c, how do we do question d).?
chrome salmon
What was the need for to multiply by a,b,c,d again and now with c, how do we do ...
For d
chrome salmon
So T(p) = matrix in image?
They are coefficient of (1,x,x²,x³) in T(p)
fair elk
They are coefficient of (1,x,x²,x³) in T(p)
What does it mean by compute directly from the definition of T? Would it be something like T(p) = a + (3a+2b)*x+(9a+12b+4c)*x^2+(27a+54b+36c+8d)*x^3?
chrome salmon
What does it mean by compute directly from the definition of T? Would it be some...
A bit unclear but I would say be c) part
fair elk
A bit unclear but I would say be c) part
Since they are the coefficients in T(p), how would T(p) look like?
<@&286206848099549185>
damn, guess I just gotta suffer then
chrome salmon
damn, guess I just gotta suffer then
Or just at least figure it out since there is nothing much that is to be done anyway
lone heartBOT
@fair elk Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
noble frost
how do i get the roots for tanx = -2x without a calculator
lone heartBOT
how do i get the roots for tanx = -2x without a calculator
noble frost
0<x<2pi
last spire
only numerical solutions i believe
subtle birch
thick lynx
Here are two very similar questions asked on Math StackExchange:
https://math.stackexchange.com/questions/3328473/how-to-solve-for-2x-tanx-0?noredirect=1
https://math.stackexchange.com/questions/2566965/is-there-an-algebraic-way-to-solve-an-equation-with-linear-and-trigonometric-ter?noredirect=1
tacit arch
so i gave you the range
what range
tacit arch
idk maybe i dont need the exact values
depends on the class and wording of the quesiton
tacit arch
,w diff 2x sin(x) + cos(x)
ocean sealBOT
tacit arch
,w solve sin(x) + 2x cos(x) = 0, 0 < x < 2pi
ocean sealBOT
noble frost
yeah but im not supposed to use a calculator
tacit arch
you know beta and alpha satisfy $\tan(x) = - 2x$, try finding $\sec^2(\alpha)$ from that equation
ocean sealBOT
riemann
noble frost
ok
uh
sin(a)/cos(a) = -2a
sin²a/cos²a = 4a²
1-cos²a/cos²a = 4a²
sec²a = 4a²+1
i did it
or use 1 + tan²a??
nvm its the same
@tacit arch i found it
tacit arch
oh i thought you meant you were done with the problem
noble frost
not yet
tacit arch
sec²a = 4a²+1
plug this in to your inequality
noble frost
(2b-2a)/(a+b+pi)<4a²+1
tacit arch
looks like a lot of algebra
noble frost
how do i express b with a
lone heartBOT
@noble frost Has your question been resolved?
rotund crater
help
tough sedge
what
quasi vector
the order dont matter
echo socket
If you want to simplify: Note that the expression under the sqrt can be rewritten as (x^3/2)^2 + 2 * (x^3/2) * (1/2x^3) + (1/2x^3)^2
If you want to know about the order: Order of addition (in finite cases) does not matter, it just looks better when you have powers in a descending order
quasi vector
oh
echo socket
Does it remind you of anything?
quasi vector
wait
tough sedge
addition is associative
tough sedge
If you want to simplify: Note that the expression under the sqrt can be rewritte...
i mean its a perfect square but thats obvious
tacit arch
i mean its a perfect square but thats obvious
Not your channel. Let OP respond
echo socket
(The question was directed to them)
rotund crater
who is op
tough sedge
Not your channel. Let OP respond
how do you open a help channel
echo socket
Original poster
lone heartBOT
how do you open a help channel
Please read #❓how-to-get-help
echo socket
how do you open a help channel
Go to an available help channel, below #❓how-to-get-help
rotund crater
a okay and then why you need the reorder term
echo socket
It just looks better when you have powers in a descending order
But there is no need to reorder the terms
echo socket
Right, does $(\frac{x^3}2)^2 + 2\cdot(\frac{x^3}2)\cdot(\frac1{2x^3}) + (\frac1{2x^3})^2$ remind you of anything more familiar?
ocean sealBOT
A Lonely Bean
rotund crater
Right, does $(\frac{x^3}2)^2 + 2\cdot(\frac{x^3}2)\cdot(\frac1{2x^3}) + (\frac1{...
.
echo socket
What topic?
rotund crater
this , explain em this
echo socket
Which bit is confusing?
rotund crater
f=kx what is k and what is x
echo socket
Here we are dealing with gravitational work
Which is the product of mass and the gravitational acceleration
Here the former is 150 - x I believe
And g is approximated as 10
rotund crater
why is 150-x
river swan
lone heartBOT
river swan
Not sure where to start for ii.)
do i do it in terms of:
change in kinetic energy=change in GPE-energy lost from friction
I put change in gpe to be (88.2J) and Energy lost to firction as 57.538. But these numbers don't really match
deep moon
Physics server would be more appropriate I think
lone heartBOT
@river swan Has your question been resolved?
limpid lotus
How was Additivity proven here?
lone heartBOT
How was Additivity proven here?
alpine sable
you can write it out like the red scalar multiplication argument
it should look fairly similar
limpid lotus
Oh so he just skipped it cuz it's similar?