Available help channel!
#help-0
lone heartBOT
Available help channel!
native gull
Please help me
lone heartBOT
Please help me
hallow vessel
native gull
Last
lone heartBOT
@native gull Has your question been resolved?
tacit arch
<@1009768715849580555> Has your question been resolved?
have you done anything?
lone heartBOT
@native gull Has your question been resolved?
leaden crescent
lone heartBOT
leaden crescent
Can someone explain how they get the basis here
I dont understand hwo they go from the rref to the bases
worn fox
using the rref, we have that x1 = x2-x3
so that a general vector in the nullspace looks like (x2-x3,x2,x3)
if you split this vector up into x2*(something) + x3*(something) you get what they have
wraith marlin
lone heartBOT
abstract fractal
What have you tried
wraith marlin
can someone please explain why the answer is b and not d??
abstract fractal
Why do you think it's d
wraith marlin
I’ve tried adding the exponents together
cause that’s what your supposed to do right?
and I got 6^4/2
abstract fractal
a^b * a^c = a^(b + c), but a^b + a^c ≠ a^(b + c)
wraith marlin
abstract fractal
Unless you think 1^1 + 1^1 = 1^2 = 1
Exponents add when you're multiplying, not when you're adding
wraith marlin
so
when you are multiplying exponents
you add them
but when you are adding
you multiply the exponents?
abstract fractal
No
wraith marlin
?
abstract fractal
When you're multiplying a^b and a^c, you add the exponents
For example, x² times x³ = x⁵
wraith marlin
but when you are adding
abstract fractal
If you're adding a^b and a^c though, you can't necessarily combine them
abstract fractal
x² + x³ can't be simplified
abstract fractal
Try writing the numbers as radicals
abstract fractal
Remembering x^(1/2) = √x
weary wyvern
Factor out 6^(1/2)
abstract fractal
what are radicals
As square roots
abstract fractal
Factor out 6^(1/2)
This works too
wraith marlin
how do you factor out?
abstract fractal
ab + ac = a(b + c)
wraith marlin
ohhh
wait
x^1/2 = square root of x
so
6^1/2 = square root of 6
but what about 6^3/2?
abstract fractal
Have you never worked with fractional exponents before?
weary wyvern
3/2 = 1 + 1/2
weary wyvern
When you're multiplying a^b and a^c, you add the exponents
Then use this
abstract fractal
no
Understanding fractional exponents is a prerequisite for this question
I find it hard to believe you'd be asked this question without ever working with them
weary wyvern
but I’m adding them not multiplying
Ok what's 6^1 × 6^(1/2)
abstract fractal
but I’m adding them not multiplying
The idea is you right 6^(3/2) as 6^(1 + 1/2)
weary wyvern
I find it hard to believe you'd be asked this question without ever working with...
Seems like it's like for the sat
wraith marlin
Seems like it's like for the sat
yes
weary wyvern
but I’m adding them not multiplying
Yea but we're just focusing on the 2nd term
abstract fractal
Taking the SAT without working with fractional exponents? When is that normally taught?
wraith marlin
currently learning everything from scratch
weary wyvern
Taking the SAT without working with fractional exponents? When is that normally ...
Idk. Middle school?
abstract fractal
The SAT is a high school test though
wraith marlin
welp I’ve moved schools like every year
weary wyvern
The SAT is a high school test though
Ik
wraith marlin
so I’ve had to learn diff things for each school so i gave up on that
especially when the pandemic hit
so I’m kinda behind
I’m in high school btw
weary wyvern
Ok what's 6^1 × 6^(1/2)
Ok this is 6^(1 + 1/2)
weary wyvern
No
alpine sable
Yes
wraith marlin
can anyone vc?
i feel like I’d understand it better if you explained it in a call and screenshared the working out steps
.close
lone heartBOT
frank plover
Is the following statement true? for A = {(x,y,z) : x = y = z $$\in$$ R} and B = {(x,0,0} : x $$\in$$ r} : A $$\oplus$$ B = R?
frank plover
In words since idk LaTeX: is R a direct sum of vectors A and B
ocean sealBOT
نعمان
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
alpine sable
Is the following statement true? for A = {(x,y,z) : x = y = z $$\in$$ R} and B =...
$A = {(x,y,z) : x = y = z \in R}$ and $B = {(x,0,0) : x\in r}$ then is $A \oplus B = R$
ocean sealBOT
Toby
marsh rapids
You mean R^3 ?
frank plover
yes R^3
marsh rapids
To check whether the sum is R^3, it would be useful to think in terms of dimensions
Or you can actually compute A+B and see by hand whether that is R^3 or not
Then for whether the sum is direct I think just applying the definition doesn't work badly
frank plover
Well i cant seem to compute (0,1,0) with it so its not R^3
How would i find an example of R^3 being a direct sum of vectors A and B
marsh rapids
Exact
marsh rapids
How would i find an example of R^3 being a direct sum of vectors A and B
Not vectors, vector spaces
marsh rapids
Well i cant seem to compute (0,1,0) with it so its not R^3
Precisely because A + B = {(x, y, y) \ x, y in R}
marsh rapids
How would i find an example of R^3 being a direct sum of vectors A and B
R^3 = ((1, 0, 0)R + (0, 1, 0)R) + (0, 0, 1)R
Is a direct sum of two vector spaces lol
marsh rapids
Definitely
marsh rapids
R^3 = ((1, 0, 0)R + (0, 1, 0)R) + (0, 0, 1)R
As long as these 3 vectors are linearly independent, it should work
frank plover
Okey awesome, makes sense
does a direct sum resulting in R^3 always have 3 components?
Or is a direct sum of two subspaces A + B = R^3 possible
marsh rapids
Think in terms of dimensions
frank plover
Im not sure how to do that 
im familiar with it but i havent revised the topic yet
but the XY plane + the Z axis is a direct sum, so yes it is possible
marsh rapids
Dim(sum) <= sum of dims, with equality iff the sum is direct
i.e. dim(A+B) <= dim(A) + dim(B)
frank plover
aha okey
so for r^3 that means dim(a) or dim(b) has to be 2 if the other is 1, right?
marsh rapids
Yes
frank plover
cool
marsh rapids
Assuming the sum is direct
marsh rapids
Entering second (and last) year of undergrad in France. Math major. See prépa MP if curious
brb 15 min
frank plover
Okey, goodluck with that! Excuser mon francais parce que ce n'est pas ma premiere language mais moi j'etude la physique en belgique
bref, merci pour l'aide
marsh rapids
Okey, goodluck with that! Excuser mon francais parce que ce n'est pas ma premier...
Auf deustch ich glaube ?
frank plover
non en neerlandais
La pluspart de belgiens parle neerlandais
une seconde proche est la population francophone
je pense que le ratio en environnement 51/49
minor night
Haha
frank plover
avec un minorite de uhhh anglophone? i forgot how to say german in french lol, anyway minorty of german speakers
prolly like <1% of the population
marsh rapids
Anglophone -> English
Germanophone -> German
Mais les germanophones parlent allemand lol
frank plover
oh wth, i thought it'd be like allemandophone or sum
yeah haha
according to wiki the ratio is 60%dutch to 40%french speaking
with 0,7 german speaking
marsh rapids
Rip German
frank plover
.close
lucid fable
$\text{True or False:}: \text{If} \sum_{n=0}^{\infty} a_{n} : \text{is divergent}, then \sum_{n=0}^{\infty} |a_{n}| : \text{is divergent}$
$$\$$
I think it’s false since $a_{n}$ can be absolutely convergent but I feel like i’m missing something/ not too confident.
ocean sealBOT
kidnamedfinger
sour dove
can you think of a counterexample that would make that false?
that's always a good first step if you intuitively think it's false
lucid fable
I tried out a few series, but I couldn’t find one that fit the bill.
sour dove
what have you tried? maybe we can see if we were on the right track
sour dove
yep that's the right track!
now think about the harmonic series, what do we know about that, if we, say have 1/n^a, where a > 1?
lucid fable
it converges
sour dove
bingo!
so taking (-1)^n / n, how can we combine these two ideas together?
oh wait crap
nvm
that won't work
I was going to say (-1)^n / n^2 diverges but the absolute value converges, but they both converge
my bay
*my abd
*bad
sour dove
yeah, that's teh rub with these problems lol
Im going to ponder it for a second
man I can't think of an example
maybe helpers can help if you @ them
lucid fable
I thought about the problem a lot, and I think the answer is true.
lucid fable
I think it’s true because the alternating series test has two conditions for $\sum_{n=0}^{\infty} a_{n} = \sum_{n=0}^{\infty} (-1)^n b_{n}$
$$\$$
$1. \lim_{n\to\infty} b_{n} = 0$
$\$
$2. b_{n} : \text{is a decreasing series}$
$$\$$
The limit must approach zero for $b_{n}$ if it’s going to be convergent by the Test For Divergence and if $b_{n}$ is increasing (or remaining constant), there’s no way that the absolute value would converge. If it meets these conditions, then the original summation must also be convergent. So I think the answer is true
ocean sealBOT
kidnamedfinger
lucid fable
also, if the series isn’t in the form a_n = (-1)^n b_n, then the absolute value would just be the original summation, which would also be divergent
sour dove
hmmm. Unfortunately I may not be the best person to ask at this point (I'm super rusty at real analysis stuff). Maybe transition over to #real-complex-analysis
lucid fable
I can’t type in that server for some reason
it just says Done Reading? check out ‘some other server’
sour dove
oooh you have to request access I think in #get-advanced-access
sour dove
yeah go ahead. Sorry I couldn't help at the end :/
feel free to re-ask down the road though!
crimson solstice
hey was wondering if anyone could help
lone heartBOT
hey was wondering if anyone could help
crimson solstice
with which one i might have missed here
note it says without algebraic manipulation
fallen verge
did you try d-subbing first?
crimson solstice
d-subbing?
lone heartBOT
@crimson solstice Has your question been resolved?
alpine sable
hey was wondering if anyone could help
Think of it this way, when you sub in the limit, which ones would you have to simplify in order to not get undefined as an answer
For example, the first example would be:
sin(0) - 0 / 0^3, which would = undefined
Thus, would need simplification through algebraic manipulation, aka L'Hopitals rule
Now do the same thing for the remaining limits
formal rampart
lone heartBOT
crude rose
worn fox
make a common denominator too
lone heartBOT
Available help channel!
high mural
lone heartBOT
high mural
12 *a)
tacit arch
Have you tried anything
lone heartBOT
@high mural Has your question been resolved?
high mural
I dont know how to start
But i do know what the graph y=e^x looks like
<@&286206848099549185>
naive valley
can you paste a screenshot that shows the whole question? yours is cut off
lone heartBOT
@high mural Has your question been resolved?
tacit arch
,w plot arcsinh(x)
ocean sealBOT
high mural
can you paste a screenshot that shows the whole question? yours is cut off
It looks like it but the sentence in question (a) stops at the word inverse
naive valley
It looks like it but the sentence in question (a) stops at the word inverse
ah i see
look at the behavior for large x and for large -x
ocean sealBOT
naive valley
or, even easier, just try plugging some specific value of x and then plug in -x
and see what you get
ocean sealBOT
naive valley
basically a parabola on steroids
tacit arch
If you understand why x^2 is not invertible on R, then this is the same logic
naive valley
with very little effort, you can prove something more general: (1) show that this is an even function (meaning f(x) = f(-x) for all x), and (2) show that an even function cannot have an inverse
limpid scroll
lone heartBOT
wary stream
,rotate
ocean sealBOT
lone heartBOT
@limpid scroll Has your question been resolved?
spiral gull
don't you just move everything to one side of the equation for k?
or something like that
wary stream
Don't do the work for people
That's not the purpose of the server
lone heartBOT
spiral gull
Don't do the work for people
That's not the purpose of the server
uhhh how to help them
ok let me just get rid of those ten
then*
lone heartBOT
Available help channel!
ocean pelican
hi how can i find the gcm of this if my inverse function is
lone heartBOT
hi how can i find the gcm of this if my inverse function is
quiet kestrel
inverse function of y=sqrt(x+2)+2 is
=> x=sqrt(y+2)+2
=> y=x^2-4x+2
alpha=4
beta=2
GCD(4, 2) => GCD(2*2, 2) = 2
too lazy to latex
ocean pelican
omayyygod im wrong
brruuh
i didnt notice that +2 is in the outsideeeeeeeeeeee
thank you soo muccchhh broooo i appreaciate it
.close
gritty adder
lone heartBOT
gritty adder
need help checking 35, 36, 37, 39 if i did them right
and got the right answers
if possible also help with 38
paper ridge
Are you only looking for solutions between 0 and 2pi?
paper ridge
In that case 35, 36, and 39 look fine. Be careful in 37, when cancelling cos(theta) one implicitly assumes cos(theta) =/= 0, there's a second case which is then missing (and thus a couple of solutions).
gritty adder
for 38 though
i simplified it to cos(2x) = -1/2
im stuck at this part no clue which identity to use
tried all 3 and hit a roadblock in all 3
figured it out, thanks
.close
dark nimbus
lone heartBOT
dark nimbus
So I just needed help figuring out how they distributed to this
I find LCD and multiply to every part but idk how the key got 12x and stuff like that and I wanted to be explained how
gray isle
10 * 6/5 * x = ?
dark nimbus
10 times 6/5 equals 12?
gray isle
yes
dark nimbus
How do I multiply it
lilac nest
How do I multiply it
Multiply by the numerator and divide by the denominator
dark nimbus
That one sentence has helped more than any of my teachers
gray isle
$\frac{10\cdot 5}{6}$
ocean sealBOT
ℝamonov
gray isle
$a \times \frac bc = \frac{ab}{c}$
ocean sealBOT
ℝamonov
lilac nest
You divide both the numerator and the denominator by their GCF, which is 5 in this case
gray isle
identify common factors in the numerator and denominator to simplify
dark nimbus
So since they both use 5 to multiply to eachother you use that?
So I get 5 but how does that get to -7/2
dark nimbus
Ohh ok ok I got it
lilac nest
So since they both use 5 to multiply to eachother you use that?
The greatest common factor is the greatest factor that divides both numbers.
dark nimbus
I’m a senior in hs and I feel slow
lilac nest
The greatest common factor is the greatest factor that divides both numbers.
5 in this case, but if you had 100 and 30 it would have been 2×5=10
dark nimbus
Yea I understand now
lilac nest
.close
wise jewel
lone heartBOT
wise jewel
how would i solve something like this?
i know how to find a certain number term but not something that doesnt contain x
or maybe im not understanding this correctly im not sure
jagged raptor
do you know the binomial formula
wise jewel
do you know the binomial formula
yes
jagged raptor
have you written it out
wise jewel
so apply it to (4x + 1/(2x))^12
so go to the 11th row of pascals?
oh wiat
wait*
so r is 12
jagged raptor
$\sum_{r=0}^{12}\left(12Cr\right)\left(4x\right)^{r}\left(\frac{1}{2x}\right)^{12-r}$
ocean sealBOT
michαel
jagged raptor
you should have something like this
now (4x)^r = (4^r)(x^r) and (1/(2x))^(12-r) = (1/2)^(12-r) *(1/x)^(12-r)
the 4^r and (1/2)^(12-r) doesnt really matter anymore because they dont affect whether or not x appears in the term
so all we care about is x^r and (1/x)^(12-r)
What does r have to be for there for the x's to cancel?
jagged raptor
that wouldnt really help because then we get 1^r = 1^(12-r)
jagged raptor
if the exponents were equal, let's say to a, then we'd be able to combine (x^r) and (1/x)^(12-r) as (x/x)^a = 1 and there would be no x
wise jewel
$x^r$ and $x^{-12+r}$ is what i have essentially
ocean sealBOT
Kold
wise jewel
i have
wait so
the term where there is no x
that means the term where x = 0
WAIT I THINK I GOT IT
R = 6????
cuz i had
$12Cr:x^{-12+2r}$
ocean sealBOT
Kold
jagged raptor
yep
jagged raptor
but dont forget about the 4^r and (1/(2x))^(12-r) terms
jagged raptor
that works
wise jewel
a.k.a.
59136
oh thank god
it was right
tysm for ur help!!!!!!!!!!!!!!!!! @jagged raptor
jagged raptor
np!!
lone heartBOT
@wise jewel Has your question been resolved?
slender marten
Well you can immediately factor out a 2x since all three terms contains this.
opal merlin
oh right
dusk umbra
(and an x)
opal merlin
so we just forget about the 2?
dusk umbra
rewrite it in terms where the 2 is pulled out
alpine sable
so we just forget about the 2?
Assuming you equate it to zero, yes
opal merlin
ok
slender marten
so we just forget about the 2?
Absolutely not. In it's current form, unless you've chopped off "a = 0" on the right hand side, we have a "expression" so you must just make something exactly equal to it.
glossy current
Should he be learnt the more general way
This problem specifically can factorize easily
The Horner's method
opal merlin
hm
dusk umbra
brandon, is there a right side to this equation by the way?
oh you just need to factor the thing?
dusk umbra
firstly what common terms do you see within the equatoin
equation*
what might all terms be divisible by
and dont say 1
opal merlin
2
opal merlin
oh I’m supposed to leave it in it’s factored form
dusk umbra
that doesn't really look factored
it's possible im misunderstanding what's being asked
slender marten
Well you can immediately factor out a 2x since all three terms contains this.
I'll repost this:
dusk umbra
oh I’m supposed to leave it in it’s factored form
maybe we should define factored form
slender marten
It probably means we have a product of linear factors in this case.
Did you factor out the 2x and get a result?
opal merlin
not really sure what to do next
slender marten
What did you get to make sure everything has gone right.
opal merlin
2x(3x-4)
dusk umbra
i see a missing term
slender marten
2x(3x - 4) = 2x^3 - 6x^2 - 8x?
dusk umbra
brandon idc what you do
but it will take us
5 minutes
if you let us do it now
but if youre tired youre tired
opal merlin
yeah let’s do it now
dusk umbra
ok so i see a missing term in what you wrote
what happened to x^3? did it just disappear?
opal merlin
yeah
dusk umbra
certainly 2x^3 / 2x isn't 0, right?
opal merlin
no
opal merlin
isn’t it ^3?
dusk umbra
We're pulling out an x here when we divide all our terms by 2x
So you end up with ^2, not ^3
opal merlin
2x^2(3x-4)
glossy current
Nah
dusk umbra
not quite
glossy current
Just multiply back
dusk umbra
ok so let me try this
opal merlin
multiply?
dusk umbra
so when you're factoring out something liek this, you're dividing each term by what you're pulling out
So you notice that a common factor is 2x, which is good
So now what's left is to divide each term by 2x, that's what's gonna be in your parenthesis later on
What darkness is saying is a suggestion for checking your work
opal merlin
alright
dusk umbra
When you arrive at an answer, you can plug your answer in to see if you arrive back a the original result
It's a good habit to get into
bringing this back down so i dont have to scroll so far
dusk umbra
dividing each by 2x, yeah
opal merlin
when dividing ?
dusk umbra
Ok, so the issue with that is it looks like you're picking and choosing what to divide
For the first one you took out the x, but not the 2. For the second term you took out that 2, but not the x. And for the last term, you took out 2 but not x
glossy current
I guess this is why we are made to study LCM and GCF in middle school
dusk umbra
Let's just do this one step at a time, what's 2x^3/2x?
It's not 2x^2
Close, but not quite
If you don't know how to do it, you can say that too
opal merlin
not sure
glossy current
@opal merlin supposed you have 5+10+15
.
5= 5×1
10= 5×2
15=5×3
So 5+10+15=5(1+2+3)
This is what factorizing is
opal merlin
alright
dusk umbra
not sure
Ok. So what you need to do is take care of both the x and the actual number in the denominator (bottom half of fraction) and numerator (top half of fraction). You need to divide the number AND the variable x
Note you can write the fraction as (2/2) * (x^3/x)
that might make it a little clearer
glossy current
alright
Now we apply to your question
2x³-6x²-8x
2x³= (2)(x)(x)(x)
-6x²= (-1)(6)(x)(x)
-8x= (-1)(8)(x)
What's the common factor you can see right away
opal merlin
2x
glossy current
2x
Then you take 2x out
So
2x³=(2x)(x)(x)
-6x²=(2x)(-1)(3)(x)
-8x=(2x)(-1)(4)
Right?
opal merlin
yup
glossy current
Write down in polynomial
2x(...)
You do it
Remember to use all. You have
(x)(x)
(-1)(3)(x)
(-1)(4)
Left
opal merlin
alright
glossy current
How is it
opal merlin
sorta gave up
opal merlin
x^2
opal merlin
-3x
opal merlin
haha not anymore
glossy current
Then write down here
opal merlin
2x (x^2)(-3x)(-4)
glossy current
That's why i split them in different line
opal merlin
what’s the next step?
glossy current
You know quadratic formula?
opal merlin
yeah
opal merlin
oh that formula
glossy current
x²-3x-4=0
glossy current
Yes
opal merlin
I’m assuming I’d leave the variables out
opal merlin
hm
glossy current
Basically ax²=x², then a=?
opal merlin
2x^2
glossy current
Nah
opal merlin
I’m sorry
glossy current
It's 1
opal merlin
I appreciate your patience though
opal merlin
2(1)
glossy current
Check square root
opal merlin
can you do the calculation
I’ll do it as well just want to make sure I get the right answer
glossy current
I got result already
glossy current
Nope
opal merlin
what’ did u get
glossy current
Check your square root again
glossy current
b²-4ac is (-3)²-4(1)(-4)
glossy current
-3.5
how awk
I think you type in the calculator wrong
Remember the bracket
There's reason why I place all brackets there
Don't omit any of them
type exactly in calculator
opal merlin
after finding this is the equation almost done?
glossy current
Just find what is b²-4ac first
opal merlin
5
opal merlin
1
glossy current
oops my bad, find it again
opal merlin
4
glossy current
Be careful with sign
Yes now you found x=4, but that's not enough
For the minus case
(-(-3)-5)/(2×1) what do you get
opal merlin
-1
glossy current
Now you have x=-1
glossy current
thanks I appreciate your help
Not done yet
opal merlin
oh alright
glossy current
x=4 means x-4=0
x=-1 meand x+1=0
There now substitute them in the quadratic one
2x(x²-3x-4)
2x(x-4)(x+1)
^ this is the answer
opal merlin
that’s it?
opal merlin
ok
glossy current
Right
opal merlin
Thank you so much
glossy current
Thank you so much
You are allowed to use calculator right
opal merlin
yeah
glossy current
Can your calculator solve cubic equation
Because calculators has the mode to solve them
lone heartBOT
lone heartBOT
Available help channel!
cunning trout
How do I solve this graphically ?
lone heartBOT
How do I solve this graphically ?
gray isle
have you drawn the graph?
cunning trout
Yeah
gray isle
identify where the y-value of the graph is less than or equal to
gray isle
no
cunning trout
Wait so let’s get this for easiness
gray isle
at what values of x is the y-value less than 0
cunning trout
-3
coral vector
Look at the x-intercepts
slender gull
Sure but that isn't the only value.
cunning trout
0
coral vector
Not just =0 but below too
cunning trout
Ya
slender gull
You're missing non integral values.
There are infinite values of x.
In an interval. That interval is where you should be focusing.
cunning trout
I see
slender gull
Like it could be -2.9, -2.8, -2.988888 or whatever.
cunning trout
Yeah
slender gull
So basically it's all the values between x = -3, and 1.
slender gull
Yes.
cunning trout
Ah I see
gray isle
note that the original question also wants where its equal to 0
lone heartBOT
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blissful rampart
Guys, hello there. Now I am learning collections, but when I learned the point set, I couldn’t find the entry point to solve the problem (I haven’t learned before), what should I do?
lone heartBOT
Guys, hello there. Now I am learning collections, but when I learned the point s...
@blissful rampart Has your question been resolved?
blissful rampart
what do you mean collections
It could be a translation error.
blissful rampart
like in set theory?
Yes.
small helm
if you're entirely new to set theory ig khan academy is a good place to start
if you're oing more advanced things, I would say either just find a textbook on it or take a uni/college class on it if you can
blissful rampart
if you're entirely new to set theory ig khan academy is a good place to start
Are you referring to this?
small helm
ye
dark trail
Hi there
dark trail
Im in need of some help for this question
so
lemme send it actually
Q5ii
Is my issue
Here’s what I’ve done so far
I’ve shown how to represent the x but I don’t know what to do from here
dark trail
oh
wait
thats kinda right that it should be 2x+1^1/3
is that because it wants a positive square root?
wait
NAHHH
i see why
by moving the -2x1 to lhs
i have to make them positive
ive corrected that but i dont understand what to do forward from here @rose sigil
thanks for correcting mr
rose sigil
does iterative process mean newton rhapson here?
dark trail
someone said use the iteration formila but i dont know it
knowing my syllabus
it could be
does everything check out in ym answer to use the newton raphson method?
@rose sigil
do i have all the pre requisites
rose sigil
after reading it again that's probably not what it wants
dark trail
wait it says use this arrangement AS an iterative formula
should i make x equal -2 or 2 from the part 3i
?
jagged raptor
maybe just pick a seed value for the sequence between 1 and 2 and then show convergence (hopefully to a value between 1 and 2)
dark trail
convergence?
jagged raptor
And then do the 3 decimal point accuracy thing
dark trail
so maybe 1 since its equal distance between them
ohhh
no beywee 1 and 2
why specifically those numbers
and how do i do convergence
from the examples im seeing
theyre implementing x = -2 and then replacing the result of -2 and redoing that over and over
so -2 in the formula found gives 1.91 for example
then 1.91 is placed and they do that over and over
@jagged raptor
I think they stop when you get values that appear more than once
jagged raptor
Oh okay so they just want you to apply the recursion until you geta decent decimal approximation
dark trail
Mate i got no idea what your saying but I’ll go with whatever you recommend at this point 😂
But yes knowing my exam board they’d do something like what I mentioned
jagged raptor
x=-2 as a starting point isnt that important probably
dark trail
Since it’s 4 marks and I’ve got 2 of them the process had to be simple
I forgot that the range is 1-2
So I’ll start with +2
Im confused lioool
jagged raptor
if you dothe same process with numbers decently close to it you'll probably converge to the same value of about 1.9
Yeah try with 2
jagged raptor
I dont follow
dark trail
So x1= 2 x2= value x3= diff value and perhaps x4 = repeats diff value for the gormula (2x+1)^1/3
And therefore x4 is solution? Showing the convergence?
That’s what I mean @jagged raptor
But the question does say given the solution is near 2 find root
I think I have to do iteration but bisection
That seems the most similar
jagged raptor
And therefore x4 is solution? Showing the convergence?
Well we cant show convergence by just applying this process a bunch of times. What course is this for? (So i can get a sense of what sort of rigor they may want)
dark trail
A level year 2 maths
This is the maths I do one year before university
So I’m 17 if that helps and in the uk
jagged raptor
Okay
jagged raptor
So this is probably what they want
dark trail
Ight I’ll go with that
jagged raptor
The starting value of -2 doesnt realy matter as long as the x_n's steady around something between 1 and 2
dark trail
So I should start with 2 like we said before
jagged raptor
Its possible that you get the same answer with that yeah
dark trail
Okay imma try that now thank you
I got 1.618
For q6
I do the same thing but x 0 is -5
Here’s how I did my answer for q5ii
@jagged raptor
Imma skip q6 and do q7
brisk panther
15x+41y = 1.
(b) 1234x + 4321y = 5.
dark trail
15x+41y = 1.
(b) 1234x + 4321y = 5.
?
brisk panther
euclidians algorhithim
dark trail
Nah I can’t skip 6 I’ll do it first but I don’t know how @jagged raptor
brisk panther
could i pls ask a question
dark trail
But I’m not a helper
brisk panther
wait who r u then
dark trail
You can go to the gree servers for help
Im the dude occupying this server and asking for help
You’ve joined an occupied server is what I mean
Do you have to get a server from math help available servers @brisk panther
brisk panther
oh sorry]
lone heartBOT
@dark trail Has your question been resolved?
silver marsh
however ive not been given x0
Make an initial estimate yourself
silver marsh
im gonna rearrange for x
What do you mean by this? You just need something in the form f(x)=0
dark trail
Make an initial estimate yourself
i made the initial estimate of 0
OHHH
so any value that makes f(x)= 0
and f(x) is x^3+ x -18 @silver marsh ?
how would i find that value tho?
silver marsh
how would i find that value tho?
By using Newton’s method
You start with your initial guess and continue estimating use f(x)
lone heartBOT
@dark trail Has your question been resolved?
dark trail
By using Newton’s method
The closest guess to 0 I’ve got is 1.5
silver marsh
Wdym you’re not trying to get close to 0, you’re trying to get so that two subsequent estimates have a difference <= 0.01
dark trail
Hmmm
I’ll do this at 6pm but generally speaking I need to find 2 values that have a difference that is less than or equal to 0.01
Like 1.819 and 1.818
As x that needs to be out in f(x)
@silver marsh
silver marsh
Idk what you mean but I’ll assume you understand what you’re saying.
If you continue struggling, watch a few YouTube videos on it
dark trail
Can u give me some videos that are good?
silver marsh
I don’t know of any, just look a few up
lone heartBOT
@dark trail Has your question been resolved?
lone heartBOT
@dark trail Has your question been resolved?
lone heartBOT
@dark trail Has your question been resolved?
mighty zenith
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mighty zenith
What step did I mess up on?
trim wagon
What step did I mess up on?
The 0 after the decimal
trim wagon
Np 
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@mighty zenith Has your question been resolved?
next marsh
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gray isle
what have you tried
lone heartBOT
@next marsh Has your question been resolved?
next marsh
what have you tried
tbh im lost
gray isle
start by introducing a variable to represent what you want to find
next marsh
ok
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Available help channel!
tidal lava
Six cards numbered 1,2,3,4,5,6 were placed in a box. Matt selected three cards, one after the other, from the box and placed them side-by-side on a table forming 3 digit numbers. How many numbers :
d) began and ended with an even digit?
tidal lava
im rlly bad at perms
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@tidal lava Has your question been resolved?
tidal lava
.close
cunning trout
Not sure where to start
lone heartBOT
Not sure where to start
cunning trout
I was considering the equation of the parabola ax^2+bx+c but I’m not sure where I should go from there
cunning raven
they literally already tell you all the info you need in the sentence
scratch what I said earlier you don't really "need" to graph this one
first let's think about the vertex
what info within the sentence tells you what the vertex is
cunning raven
^ this is x intercept
cunning trout
Hmm..
cunning raven
"from a height of 1m"
which means at this point of time, you haven't started throwing yet
so y intercept at y = 1
btw y = h = vertical axis
x = t = horizontal axis
wait what am I typing
srry give me a sec
Oh frick srry scratch everything I said earlier
cunning trout
Ok
cunning raven
Ok let's first look at what the vertex is
cunning trout
Ok
cunning raven
the sentence tells you what the vertex is already
the keyword is "maximum" or "minimum" for vertex
cunning trout
Wait so maximum height would be 4
cunning raven
no it just means you start at height 1m
cunning trout
Hmm I see
cunning raven
$y = a(x-h)^2 + k$
ocean sealBOT
Salt
cunning raven
^ this is the vertex form
so what we need to find in order to write down this equation are
a
h
k
vertex is (h,k)
cunning trout
Yep
cunning raven
so can you now tell me what the vertex is?
cunning trout
(1,3)
ocean sealBOT
Salt
cunning raven
now you just need to find 'a'
cunning trout
Yes
cunning raven
do you know how to do that?
cunning trout
No
cunning raven
you see how other than 'a' the rest of the variables are 'x' and 'y'?
cunning trout
Yes
cunning raven
you can just plug a point into the equation to find 'a'
cunning trout
Ok I see
cunning raven
and you're done
alpine sable
How can I add cases in permutations??
lone heartBOT
How can I add cases in permutations??
@alpine sable Has your question been resolved?
gentle oyster
.close
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lucid hollow
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lucid hollow
Hi guys
Part d
(By the way, you see the small 2 I put here and there in those boxes? They’re the second differences between the numbers above them. Example:
2,6,12. They have a difference of 4 and 6 respectively. 4 and 6 have a diff of 2)
lucid hollow
My question is, what do you do if you have an unfixed difference?
neat frost
so in this specific case we see that the difference increases each time, correct? from 2 to 3 to 4 etc
lucid hollow
Yep
neat frost
Now that may seem confusing at first, but to our relief, we see that the difference between each of these differences are 1 every time?
you see that
neat frost
ye so we can write a summation based on these differences and find the formula for the whoel thing
lucid hollow
Damn
neat frost
well, the orirginal thing we wanted to find
lucid hollow
I—
neat frost
yeah
lucid hollow
My mind just excluded the fact that the second difference could be 1 too
So now we use the huge second diff formula
neat frost
i only remember this bc we wrote a proof in my discrete math class a year ago
lucid hollow
Oh lol
@neat frost is this the ans?
Sending
Sending
Sent
Yup it’s correct ty
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@lucid hollow Has your question been resolved?
alpine sable
hello
alpine sable
An airplane is flying horizontally, directly towards the city of Melbourne at an altitude of 400 meters. At a given time the pilot views the city light of Melbourne at an angle of depression of 1.5 degrees. Two minutes later the angle of depression of the city lights is 5 degrees. Find the speed of the airplane
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
***Cosine Rule ***
lone heartBOT
***Cosine Rule ***
alpine sable
<@&286206848099549185> It would be delightful if I could obtain some support in resolving this problem. 8
gilded citrus
