#help-39
pearl pondBOT
somber schooner
Help please
steel dagger
!status
pearl pondBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
somber schooner
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
1
steel dagger
Assign variables to sides of both rectangles
somber schooner
can you just say AB and GH
pearl pondBOT
somber schooner
I closed it
pearl pondBOT
✅
pearl pondBOT
steel dagger
Alright
pearl pondBOT
Available help channel!
dark ingot
Suppose a man of mass m stands on a disc with moi I and radius r and starts moving witha velocity v relative to the disc. Then is this a correct way to write the angular momentum of system
L system,ground = L system, disc+ L disc,ground
L= mvr -(I+mr²)ω
dark ingot
Tag when replying
pearl pondBOT
@dark ingot Has your question been resolved?
pearl pondBOT
@dark ingot Has your question been resolved?
winter valley
could someone do these questions so i could check my answers please?
unborn abyss
how about you post your answers
winter valley
how about you post your answers
ok i shall could you gimme a few minutes to do them please?
winter valley
how about you post your answers
should i post my final answer?
unborn abyss
well ideally with your work so someone can check it
unborn abyss
okay, sure
you know, when you initially asked the question, I kind of assumed you'd already done the problem
winter valley
you know, when you initially asked the question, I kind of assumed you'd already...
o sorry
im alomost done
winter valley
okay, sure
thanks sm for checking through it
hola?
<@&286206848099549185>
<@&286206848099549185> could someone check my answers pls
pearl pondBOT
@winter valley Has your question been resolved?
visual canyon
is a correct?
pearl pondBOT
is a correct?
jolly parrotBOT
Adam
tawny drift
so pi/6 radians is one of the solutions
but recall the sine curve
there are two points where theta/x satisfies the equation
since there are two points within the interval which are where sin(x) = 1/2
so one is pi/6
and the other
is (pi - pi/6)
due to the symmetry
pearl pondBOT
@visual canyon Has your question been resolved?
pearl pondBOT
pearl pondBOT
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fast lion
pearl pondBOT
frank goblet
n-th term of sequence
fickle schooner
(Guessing the nth term of the sequence)
fickle schooner
The question is incomplete atm
fickle schooner
!status
pearl pondBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
Yes this
remote falcon
here we are supposed to find n th term and take a = first term right?
fast lion
here we are supposed to find n th term and take a = first term right?
I think so
Im really confused right now
frank goblet
isn't the question what the student wrote there?
i took it like op is grading someone and doesn't understand the writing of the student
fast lion
Oh okay, I also want to double check if Im doing something right
fast lion
isn't the question what the student wrote there?
i took it like op is grading so...
no no, Im studying the work
frank goblet
ah kk
fast lion
I just got stuck mid way
remote falcon
alrighty
fickle schooner
could you please post the entire question instead of tidbits
fast lion
Yeah
fickle schooner
thanks
fickle schooner
It's fine. Just want to have all the information
remote falcon
a1 = 33
fickle schooner
Do you know the general formula for an arithmetic sequence?
fast lion
Do you know the general formula for an arithmetic sequence?
Yes
fickle schooner
$$ a_n = a_1 + d(n - 1) $$
good
jolly parrotBOT
StrangeQuarkAL
fast lion
yup
fickle schooner
If you let n = 6, what does that simplify to
fickle schooner
$$ a_6 = a_1 + 5d $$ I
jolly parrotBOT
StrangeQuarkAL
fickle schooner
$$ a_6 = a_1 - 25 $$
Right
jolly parrotBOT
StrangeQuarkAL
fast lion
okk
fickle schooner
**StrangeQuarkAL**
Your expression for $a_n$ is basically this but you sub 33 for $a_1$ and -5 for d
jolly parrotBOT
StrangeQuarkAL
fast lion
and I should get
38 -5n
I subbed it in
wait okay, I think I figured it out
I got -37 for a_15
Thank you for your assitance!
.close
pearl pondBOT
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visual moon
can someone explain how to even start this question, bit stuck on how im supposed to solve it
visual moon
5=b
a=-2
yea would love some tips on what this means
i asked my prof but i still dont understand, they said "It might be easier to think about this in terms of the areas these integrals represent.
"If the area under f from -2 to 5 is 3, and the area under f from 1 to 5 is -2, what is the area under f from -2 to 1"?
Once it clicks, you'll see that (beneath all the terminology) the underlying question is arithmetic. "If (a+b) = 3 and b=-2, what is a?""
warm current
fundamental theorem of calculus
you need some properties of integrals
$\int_a^b f(x)dx=-\int_b^a f(x)dx$
jolly parrotBOT
SWR
warm current
$\int_a^b f(x)dx=\int_a^c f(x)dx+\int_c^b f(x)dx$
jolly parrotBOT
SWR
warm current
These are fundamental, and you would be wise to understand, on a visual level, why they are true
visual moon
so can i let b = 5, a = -2, c = 1, use that FTC equation and solve for the integral
$\int_a^b f(x)dx - \int_c^b f(x)d =\int_a^c f(x)dx$
jolly parrotBOT
Thyroxine
warm current
so can i let b = 5, a = -2, c = 1, use that FTC equation and solve for the integ...
should work. yea
visual moon
thank you!
atomic oracle
pearl pondBOT
lime river
Is it a typo?
It should be as per me only x=o satisfies
atomic oracle
X = 0 doesnt satisfy it -1 = 1?
raven girder
If you are on the affine plane, it definitely has only one solution but it is not x=0
atomic oracle
By affine do you mean real?
atomic oracle
I am confused
atomic oracle
So one solution and they made a typo?
raven girder
Yes
atomic oracle
Without a graphing calculator, am i supposed to solve questions like this by like plotting the general shape of the curve?
raven girder
I think so. These equations are not solvable with simple calculations by hand
lime river
X = 0 doesnt satisfy it -1 = 1?
Oh my bad sorry
raven girder
I would graph or use a numerical method
lime river
I would graph or use a numerical method
Use the Taylor series expansion of e^x and simplify
raven girder
Bisection, Newton-Raphson...
atomic oracle
Taylor series till x2?
atomic oracle
Use the Taylor series expansion of e^x and simplify
Not sure how I would get number of roots with this
lime river
Not sure how I would get number of roots with this
Hmm well one way can be to plot the graph
I mean it's not diff to plot the graph of x²-1 and e^x
pearl pondBOT
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pastel remnant
hello im a little confused on part b of this question . i dont understand how to find lines BD and AD
warm current
perimeter of DAB is just the length of BD+DA+arc length of BA
oh. You don't know how to find BD and AD
pastel remnant
yes
warm current
yeah you want to use similar triangle theorems here
pastel remnant
arc length of BA is 14.4cm if thats useful ?
warm current
arc length of BA is 14.4cm if thats useful ?
you will need it to find the perimeter, yes
pastel remnant
im not sure how i would use the similar triangles tho
i have no value for a side of the triangle OBD
warm current
you have OB
you can do this with trig too. It's just similar triangle laws with less steps
pastel remnant
how do i get OB ?
warm current
Think of O being the center of the circle and what that means
pearl pondBOT
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minor eagle
can someone help me with this
pearl pondBOT
can someone help me with this
tall flint
minor eagle
first i converted the annual interest rate to a monthly interest rate
then i converted the annual interest rate to a monthly interest rate, then I determined the total number of payments, then I used the formula for the future value of an ordinary annuity, then I calculated the amount and got $92.91
but idk if thats right
@tall flint
pearl pondBOT
@minor eagle Has your question been resolved?
pearl pondBOT
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flint oracle
pearl pondBOT
flint oracle
Hints?
next dove
Telescoping series
pearl pondBOT
@flint oracle Has your question been resolved?
flint oracle
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short orchid
pearl pondBOT
rare scaffold
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pearl pondBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
short orchid
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
3
cursive wraith
range of f on [a,b] isn't just f(a) <= f(x) <= f(b)
imagine your function starts by decreasing and then increases
like x^2+3
obviously the lowest you're gonna be able to go isn't (-2)^2 + 3
short orchid
oooh
cursive wraith
have you seen limits/derivatives yet or?
cursive wraith
ok nvm
basically
you kinda have to visualize the function
like x^2 decreases until it reaches 0, and then it increases again
and it's the opposite for -x^2
so when you study functions with constant+...x^2, if 0 is in your domain then f(0) is probably the min
and when you study functions with constant-...x^2, f(0) is probably the max
short orchid
ooohhh
short orchid
you kinda have to visualize the function
i think i have a problem visualizing functions
cursive wraith
ok
short orchid
i can visualize quadratic and linear, but what is “x^2 -2”??
cursive wraith
you've seen the curve for x^2 right?
short orchid
yess
short orchid
ohhhhh
cursive wraith
like so
so the minimum is still at the same X coordinate
(but at a different y coordinate)
short orchid
ooooo
cursive wraith
(and vice versa)
cursive wraith
that's the next part
the curve actually runs "faster" through the values
x^2 = 1x^2, so 1 is "normal speed"
2x^2, 2 is "faster speed"
short orchid
ohhhh wow
cursive wraith
and 0.5x^2 for example
0.5 is "slower speed"
so as long as the coefficient is POSITIVE, it doesn't change the increasing/decreasing behaviour
it just accelerates/decelerates it
cursive wraith
the curve is flipped
and when the coefficient is negative, well... we saw what happens
cursive wraith
so now, all functions that look like ax^2 + b have no secrets for you
since the constant 'b' only moves the curve up or down
and 'a' tells you how fast we're running through the values, and if the curve is flipped or not
cursive wraith
👍
short orchid
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pearl pondBOT
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frank goblet
hello^^
frank goblet
i have this graph as an example
i want to calculate the green area by numeric integration
in the real context, i have discrete data
thin sigil
That graph is lowkey a sh*tpost
frank goblet
now to calculate the area, i could calculate rectangles as shown
or i could calculate trapezoids
i have heard to never use rectangles for this
however with trapezoids, the calculated area will always be too small
are trapezoids still the way to go?
thin sigil
This really depends on the situation, what kind of precision are you looking for?
frank goblet
i also heard of simpsons way, but that apperently requires an even number of areas to calculate
frank goblet
This really depends on the situation, what kind of precision are you looking for...
the higher the better
thin sigil
I don't fully remember all the details of numeric integration, do you have the function in analytic form given as well?
thin sigil
Well trapezoidal will always give you smaller result with the error tending to 0 as the discretion become smaller and smaller
thin sigil
Mind sending a snipit of the data here?
frank goblet
yeah, one second
one sec, im gonna search for the peak data
that makes it easier
thin sigil
In theory, trapezoidal should be more accurate for lower discretion than rectangles, but I don't think it's guaranteed
frank goblet
ok i just found out there are even peaks with only one data point
because sometimes, the frequency of measurement is that bad 😦
thin sigil
yea in those cases the error will be more significant because the trapezoids will make like a sharp triangle
if that makes sense
frank goblet
hmm
thin sigil
Funnily enough I don't have excel and can't open that file, lol
hold on, let me figure something out
Nvm got it to work
So I assume you're integrating acceleration with respect to time
there are 2 time bars?
frank goblet
yeah i think they are equal
example values:
(8.2168, -10,29)
(8.2174, -4.77)
(8.2180, -2.39)
(8.2186, -2.27)
(8.2193, -7.87)
(8.2199, -19.92)
meaning: (time/s, acceleration/ m/s^2)
here the first and last pair would be ignored due to them being lower than the baseline acceleration g
so we would have 4 points
i think here the trapezoids would be better
thin sigil
I mean this data is kinda funky tbh
frank goblet
yeah it is haha
thin sigil
thin sigil
Unless I messed up with graphing this
frank goblet
column H works better
thin sigil
but that lonely point down there be really weird
frank goblet
context is a ball bouncing on a table
we have a smartphone on the table
smartphone measures x y and z acceleration
so its pretty much only noise
but when ball bounces -> acceleration
therefore it is most notable in z direction (column H)
thin sigil
I'm actually an engineer, so this looks interesting to me
There's a lot of noise here
frank goblet
the idea here is that the change in velocity can under certain circumstances depend on the change in velocity of the table and in turn on the change of velocity of the ball
the noise is sadly not really reducable without ai or something else because people run around
that's why we also took data with a machine instead of humasns
thin sigil
Well, the thing is, if we assume the surface is nice and flat (which I guess you made sure using a leveler) then the z acceleration should be constant for the most part, the slight change in altititude from the bounce shouldn't affect the graitational acceleration by a significant ammount right?
frank goblet
it should
thin sigil
Nice and flat and horizontal**
frank goblet
ah you mean the horizontal acceleration shouldn't change?
it does change because of the ball's spin
thin sigil
No I mean the vertical acceleration shouldn't change
assuming you're only meassuring positional acceleration
Collumn H
frank goblet
ball bounce on table -> table oscillates -> phone oscillates -> oscillation requires acceleration other than g
thin sigil
ah so the phone isn't seperated from the table
I assumed it would have it's own stand or something
frank goblet
it is on the table, at best fixed to it
thin sigil
Well, anyway, since you have a lot of data points and the discretion step of time is small I'd argue that using trapezoid aproximation is fine here, thought you look into applying simpsons rule somehow
Generally, the higher order the function you use the more accurate the method should be (this is not a guarantee though, since some functions are just wacky like that)
frank goblet
thx for the info^^
thin sigil
But remember, the method will only give you as good an answer as the data set itself is good even in the best case scenario, so in your analysis take into account both the error of the method and the error of the meassuring method with all the noise present (possibly creating an analytical model, solving it and comparing)
frank goblet
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pearl pondBOT
pearl pondBOT
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tawny harness
(C) and (C') are two circles with respective centers O and O', they intercept in both points A and B. M is a point (C) distinct from A and B and MB intercepts (C') in a different point M'
How do i prove that angle OAO' = MAM'
pearl pondBOT
(C) and (C') are two circles with respective centers O and O', they intercept in...
@tawny harness Has your question been resolved?
brisk steeple
,w rotate
tawny harness
tawny harness
green dew
u can prove that triangles AOO' and BOO' are congruent
so then angles AOO' and BOO' are equal
tawny harness
ok
green dew
and that also AO'O and BO'O are also equal angles
angle M'MA = 1/2 BOA
its the inscribed angle theorem and the angle located at center in circle C
tawny harness
alr and?
green dew
since angle AOB = AOO' + BOO' which are equal so AOB = 2AOO'
then M'MA = AOO'
same justification for the equal angles MM'A = OO'A
thus the two triangles AOO' and AMM' are similar and the angle OAO' = MAM'
tawny harness
yeah i got it now ty
green dew
npp
tawny harness
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pearl pondBOT
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gusty sail
pearl pondBOT
gusty sail
The answers B right???
long coral
b is not right, you essentially have to find how many combinations of the genders in the 3 children they can have like what atif sent
long coral
When would it be 1/8
if the questions asked, if theres a family of 3 children, what is the probability they are all boys
that can only be 1/8 because there is no way for there to be another combination in which all 3 are boys
gusty sail
Yeh yeh
long coral
or it can ask for the probability that they are all girls which would be 1/8
gusty sail
That’s what I did
long coral
i see
long coral
^
gusty sail
Like first is boy second is girl third is boy
gusty sail
Oh
red falcon
you can take head tails example its the same as boy girl
gusty sail
Ahhh
red falcon
because it says they have equally likely outcomes
just like h/t
i remembered this with the basketball analogy
if a player hits a point with the probability of 0.9
then he has 0.9*0.9=0.81 probability scoring
on the second throw
red falcon
so if he had 1/2 it would be 1/8
on the third throw
wait i need to look this up im rusty
gusty sail
I think ur right
red falcon
yeah but i can’t remember the intuition for why
distant plinth
what are you guys talking about?
red falcon
intuition when u should multiply probabilities
gusty sail
I rlly hate probability because of this
I don’t know when to add or multiply
Or like do something with the numbers
The last chapter I need for my uni test as well
red falcon
basketball plyr shoots 3 times in a row w prob 0.8 of making a shot. whats the prob that he makes all 3
@distant plinth
distant plinth
Desired cases/Total cases
distant plinth
basketball plyr shoots 3 times in a row w prob 0.8 of making a shot. whats the p...
the probability of making all 3 is making the first 1: 80%, making the second one: 80%, and making the third one: 80%
Thus, the probability is 80%^3
long coral
i believe that knowing whether the events are mutually exclusive or not can help
red falcon
the probability of making all 3 is making the first 1: 80%, making the second on...
yes we know, explain to the guy why did u multiply and not add
he struggles w that
red falcon
@gusty sail u know any set theory, unions intersections etc?
gusty sail
Yeh I do
gusty sail
<@831414327180787732> if u have or in wording u add if u have and u multiply
I do get this
But like
The example I gave u
There’s no or but it’s still add
red falcon
yeah i get you, you want to get good at identifying when is and and when is or
thats the issue
distant plinth
wdym when is or?
distant plinth
yeah i get you, you want to get good at identifying when is and and when is or
can you give an example
red falcon
distant plinth
There’s no or but it’s still add
wait this example
red falcon
unions are or intersections are and
gusty sail
red falcon
so lets try help him
identify the events
in probability sense
so he can frame it as p(A u B) or p(A \cap B)
distant plinth
What's A/B
gusty sail
Yeh
red falcon
ok those are then A B C
red falcon
in this context
red falcon
yes
red falcon
but im trying to think of a wording where we would need to use intersection
red falcon
whats a work book?
gusty sail
Including everything
red falcon
textbook?
red falcon
we used sheldon probability textbook but i have the exam in september
sheldon ross. its good
it goes slowly and thoroughly. but for this level khan academy helped me
but it’s been a year so i forgot
gusty sail
Maybe I should try
red falcon
you can speed run
gusty sail
I’m gonna be cooked if the test has too many probability questions
red falcon
just believe in urself
and u can go fast
x2 speed
videos
or 1.5
if u dont have time
if u do, go 1.25
gusty sail
Khan academy?
gusty sail
Is organic chem tutor good?
red falcon
you will be master of these things
red falcon
Is organic chem tutor good?
i think so, but for this id prefer khan
red falcon
because he explains to u like ur first time seeing it
gusty sail
Yeh
red falcon
whats the probability that u ll roll 3 times in a row a two?
i just thought of this
its the basic example
red falcon
glgl
gusty sail
Thanks for recommendations friend
red falcon
khan the best bet honestly
gusty sail
.close
pearl pondBOT
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drifting dawn
what is the function that gives the curved part of the relation, the problem with looking this up is that most of the talk around this is how it can be parametrized, which isn't what I'm looking for
drifting dawn
I also don't want to conditionally define it like in the second image with the cutoff at x=e
pearl pondBOT
@drifting dawn Has your question been resolved?
drifting dawn
<@&286206848099549185>
I got the bottom half with lambert w but I want the top left part instead of the straight part
distant plinth
I got the bottom half with lambert w but I want the top left part instead of the...
what's the top left part
drifting dawn
what's the top left part
the rest of the curved part
drifting dawn
yes
I don't know of a method that would combine the functions even if we had the top part too
distant plinth
idk how to do that either I'll think for a bit
drifting dawn
I thought of trying to eliminate the part where x = y using math logic gates like
f(x) \ c = f(x) * (x-c)/(x-c)
but you need both x and f(x) as a combined condition
distant plinth
I thought of trying to eliminate the part where x = y using math logic gates lik...
hm
distant plinth
but you need both x and f(x) as a combined condition
wdym by this
drifting dawn
wdym by this
if you had the condition so that x = e then both the straight part and the curved part are lost
distant plinth
how?
drifting dawn
at x = e f(x) = e
it's just a point
I randomly tried this and it worked so now I just gotta solve for y
..
.close
pearl pondBOT
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sterile turtle
hi can i have help with part b
pearl pondBOT
hi can i have help with part b
pearl pondBOT
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sterile turtle
can I have help with d
pearl pondBOT
can I have help with d
tulip ore
my eqs
- write another copy of equation 1 then square both sides
- use this to solve for alpha * beta
- use alpha + beta and alpha * beta to solve for alpha and beta
- with that, find m and b
sterile turtle
1. write another copy of equation 1 then square both sides
2. use this to solve ...
wdym write another copy?
tulip ore
🤔 write down alpha + beta = 2
another time
preferably somewhere else
so that you can square both sides of it
tulip ore
@sterile turtle no
sterile turtle
does this not work?
tulip ore
oh wait nvm I misread what you wrote, yea thats correct
pearl pondBOT
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pulsar stump
how to find sp_R(S) = W_1
pearl pondBOT
how to find sp_R(S) = W_1
pulsar stump
as in, how to find the set S
p=polynomial function
i cant find a linear combination
pulsar stump
finding a set that spans W_1?
need to find set S such that
span_R(S) = W_1
R is for under reals
W_1 is a vspace
grizzled dust
what is this notation R_3[x], does that mean VS of polynomials of degree 3 or less?
pulsar stump
what is this notation R_3[x], does that mean VS of polynomials of degree 3 or le...
latter
grizzled dust
huh?
pearl pondBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
jolly parrotBOT
∫oosh (lemonsaurus appreciator)
grizzled dust
so P_3 would mean polynomials of degree 3 or less. i.e. VS that contains polynomials of degree 3, 2, 1 and 0
so you mean P_2 or P_3 with your notation?
pulsar stump
so P_3 would mean polynomials of degree 3 or less. i.e. VS that contains polynom...
here is most likely 3 exactly and not 3 or less
they use the <=3 for three or less
grizzled dust
here is most likely 3 exactly and not 3 or less
but thats not a vector space. i.e. (x^3 + x^2) + (-x^3) = x^2, that wouldn't be closed under vector addition
pulsar stump
but thats not a vector space. i.e. (x^3 + x^2) + (-x^3) = x^2, that wouldn't be...
it's a sub vspace
pulsar stump
<:this:489575168314966026>
well then it has to be <= 3
grizzled dust
ok
pulsar stump
how do we go from here?
grizzled dust
well an element of that set would be $a_0+a_1x+a_2x^2+a_3x^3$
jolly parrotBOT
∫oosh (lemonsaurus appreciator)
grizzled dust
plug in 1 and 2 for x and you get some equations i guess that restrict the coefficients
pulsar stump
plug in 1 and 2 for x and you get some equations i guess that restrict the coeff...
yeah
i already can represent a0 and a1 both by a3 and a4
a0*x^3...
now what
grizzled dust
you should have 2 degrees of freedom with what coefficients you pick yeah, then you can get the other 2 coefficients based on that
and you should be able to get 2 linearly independent vectors from that which form a basis for what you need
pulsar stump
and you should be able to get 2 linearly independent vectors from that which for...
basis to what i need? wdyn
sure i can get s(...
...
...
0)
+
t(...
0
...
...)
s and t are reals
u mean spam s=t=1?
grizzled dust
well W is a subspace of P3 (it's trivial to verify the properties) so if you find a basis for W then by definition that basis spans W
so it's a set that spans W as you need
pulsar stump
so it's a set that spans W as you need
so you're baiscally saying what i think right? represnet like i did above the solution vspace and set s and t to be 1
and then the basis solution (we set s=t=1) and with the x and x^2... in the right formula will form the set
there will be 2 elements in the set S
grizzled dust
i'm not sure exactly what you mean, maybe i'm also not expressing it the best way, but yeah the whole solution set should be expressible as a LC of 2 vectors (i.e. polynomials) (since you have 2 independent coefficients and 2 dependent ones)
so what are the equations with the coefficients you ended up with?
pulsar stump
so what are the equations with the coefficients you ended up with?
1s ill calc
grizzled dust
like to give an example with a plane in R3: say you have some random general plane equation like $ax+by+cz = d, you can pick any values for up to 2 of the variables x, y, or z and then solve for the 3rd in terms of the other 2. so we can think of that as 2 variables being independent and 3rd one being dependent, so this ends up being a 2 dimensional vector space (a plane) b.c. 2 independent variables
if you are expressing equation of a line, for any given x, y, or z there will be unique values of the other 2 (ok excepting lines parallel to one of the axes), so single independent variable => 1 dim vector space
pulsar stump
so what are the equations with the coefficients you ended up with?
i got
p1 = (3/4)x^3 -(7/4)x^2 + 1
p2 = (1/2)x^3 -(3/2)x^2 + x
grizzled dust
ok so that should be a basis since theyre linearly independent
pulsar stump
ok so that should be a basis since theyre linearly independent
yes so those are the 2 elements of the set right?
well i think so
ty for your help mate
.close
pearl pondBOT
pearl pondBOT
Available help channel!
vernal grove
this will just be
101.82 pm (1.96)(1.2/(sqrt(6)) right?
pearl pondBOT
this will just be
101.82 pm (1.96)(1.2/(sqrt(6)) right?
cosmic charm
yeah
pearl pondBOT
pearl pondBOT
Available help channel!
iron basin
How would I go on about proving that $\lim_{x \to 0} \left( \frac{x-sin(x)}{x} \right) sin \left(\frac{1}{x}\right) = 0$?
jolly parrotBOT
iron basin
I tried graphing it and it indeed approached zero.
Although the latter function didn't seem like it approached zero.
gloomy scroll
I‘d split the fraction in the brackets
iron basin
I‘d split the fraction in the brackets
Would just give $1 - \frac{sin(x)}{x}$. How would I proceed after that?
jolly parrotBOT
iron basin
Distributing the brackets seems to complicate it further.
random yacht
Would just give $1 - \frac{sin(x)}{x}$. How would I proceed after that?
As x tends to zero, sinx/x approaches zero
I mean one
iron basin
As x tends to zero, sinx/x approaches zero
I don't think that's correct; it approaches one
Yes.
gloomy scroll
I didn‘t want to distribute, it was just to prove that the part in the brackets goes to zero
Now for the other bit, notice that the sin function is bounded
!nosols
pearl pondBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
iron basin
Oh, that's a fair point; seems like that was the only part where I was lacking enough thought. That solves the problem then, I guess. Thanks.
.close
brisk steeple
pearl pondBOT
brisk steeple
How do I find the value of k such that the intersection of x^2 - 6x +k and the black line meet the at intersection of the black line and the red line?
everything is right in front of you
the black line represnts x = 4
tender gate
since they intersect that means that their y values are the same
so you can equate both equations
brisk steeple
how to find where line ax+b and cx+d interesect?
tender gate
wait hold on i think i read it wrong
thorny zenith
solve
$24+7 = 4^2-64+k$
jolly parrotBOT
psychoFungus
jolly parrotBOT
brisk steeple
where would lines ax+by + c and dx+ey+f interesect?
2x+7-y
x-4+y^0
,w 2x+7-1 = x-4+1
jolly parrotBOT
jolly parrotBOT
brisk steeple
,w 2x+7 = x/4
jolly parrotBOT
jolly parrotBOT
jolly parrotBOT
jolly parrotBOT
brisk steeple
,w substitute x=4 in x^2 -6x+k = 1+k
jolly parrotBOT
brisk steeple
,w substitute x=4 in x^2 -6x+k = 15
jolly parrotBOT
pearl pondBOT
brisk steeple
I have found that at k = 23, curve x^2-6x+k is tangent to 2x+7
pearl pondBOT
Available help channel!
visual canyon
is 1/sin x cos x correct?
pearl pondBOT
is 1/sin x cos x correct?
inland ivy
Yes
pearl pondBOT
pearl pondBOT
Available help channel!
restive wedge
guys help
restive wedge
for like
d and after
i am very confused
idk what is hould do about that denominator on d
wet swallow
L'hopital
cloud zephyr
the method for d is usually called "multiplying the conjugate"
restive wedge
the method for d is usually called "multiplying the conjugate"
is that the one wher ei multiply it by 1 in the form of denominator/denominator?
cloud zephyr
is that the one wher ei multiply it by 1 in the form of denominator/denominator?
like you can multiply the expression in by
(3+√(2x+9))/(3+√(2x+9))
vital anchor
yes
upper drum
is that the one wher ei multiply it by 1 in the form of denominator/denominator?
yea rationalisation
restive wedge
alright
cloud zephyr
is that the one wher ei multiply it by 1 in the form of denominator/denominator?
but this time we multiply the 1 with a new expression with the middle +/- sign changed
upper drum
and then you can apply standard limits
restive wedge
ohh ic
ok so witht aht im left with
3sin6x+rt(2x+9)sin6x/(2x)
alright
now
do i substitude?
wait no that'd make
2.0
cloud zephyr
or you can keep the brackets 🙂
(3+√(2x+9))sin(6x)/(-2x)
cloud zephyr
3sin6x+rt(2x+9)sin6x/(2x)
oh, yea, the negative
restive wedge
oh alr ill keep the brackets
cloud zephyr
yea, then you can sin(x)/x identity when limit tends to 0
cloud zephyr
yea, then you can sin(x)/x identity when limit tends to 0
(3+√(2x+9)) times sin(6x)/(-2x)
and try to do something on the second expression to make it work with this
cloud zephyr
yep
cloud zephyr
sub the 0 in the last step
restive wedge
substitude first?
cloud zephyr
that'll do!
restive wedge
alright yay
cloud zephyr
so it will become
(3+3)(-3)
restive wedge
wait
oh wait yeah
yeah i got -18
got scared bc iw rote it diff
uhh do you have the time to help me do the entire thing?
like e til j?
cloud zephyr
uhh do you have the time to help me do the entire thing?
ok~
restive wedge
thank you so much
cloud zephyr
let's do those until I'm busy
restive wedge
cloud zephyr
so, (e) do you have any clue so far?
restive wedge
im trying to find a rule that transforms the tan
ive been told to like
maybe remove the numbers on the x
to be
oh ig i cant do it here
cloud zephyr
my approach would be tranform cos(2x) something in sin²(x)
cloud zephyr
my approach would be tranform cos(2x) something in sin²(x)
do you know how to do that?
restive wedge
yeah
using the rule
i dont remmeber it so im kinda looking at it
while doing this
cloud zephyr
sure, no worries, i also googled it lol
restive wedge
what does that do?
restive wedge
oh alr
cloud zephyr
$\frac12\cdot\frac{\tan^23x}{x^2}\cdot\frac{x^2}{\sin^2x}$
jolly parrotBOT
Biscuity
cloud zephyr
woah wait i get the 1/2
yea?
restive wedge
oh yeah ig
i c
since
multiplying fractions
the denominator getsmultiplied
you can just switch their places
cloud zephyr
**Biscuity**
so, any clues do you recall for after this?
cloud zephyr
nice
cloud zephyr
recall tan²3x=(tan3x)²=(tan3x)(tan3x)
cloud zephyr
so, we can further break it into
restive wedge
since there's now 2 of them
cloud zephyr
$\frac{\tan 3x}{x}\cdot\frac{\tan 3x}{x}$
jolly parrotBOT
Biscuity
restive wedge
3/1*3/1
jolly parrotBOT
veryhuman
cloud zephyr
XD
restive wedge
wrong x
restive wedge
4.5?
cloud zephyr
yep
cloud zephyr
ahhh
cloud zephyr
i love that jellyfish dude if i had nitro those would be stickers
coooool
cloud zephyr
into sin²(3x) with things
cloud zephyr
oh nvm cant change the cos
nah, you can
cloud zephyr
yay
restive wedge
and just makin sure thats 2/3?
cloud zephyr
lemme double check
cloud zephyr
yea that
restive wedge
1/3
cloud zephyr
yep
restive wedge
ok this one is kinda
ok wait no
i can take the tans out
to be
tan3x(1-cos2x)/4x^3
restive wedge
ok so
now im at
ive decided to do this actually
$\frac{2sin^2(a)}{4x^2}\cdot\frac{tan(3x)}{x}$
(lol idk how to do the multiply sign)
cloud zephyr
you can use \times or \cdot for multiplication
restive wedge
oh ok
jolly parrotBOT
veryhuman
restive wedge
oh yeah that a is supposed to be an x
cloud zephyr
and then final step, easy
restive wedge
3/2?
cloud zephyr
yep
cloud zephyr
this is interesting
restive wedge
this rule?
restive wedge
oh wait same trick
cloud zephyr
make the denominator looks like (x+2) too
cloud zephyr
i thought there would be 2 possible answers
nah
restive wedge
(x+2)^2
cloud zephyr
that's what happens when we solve quadratic equations