- Write a Matlab function that gives the value of S100 where limn→+∞ Sn = S
#help-13
maiden garnet
- Create a Matlab function that uses Newton's method to evaluate S, taking
|S100 − Sn| as test stop
anyone good at numeric analyse can help me in the second Q
cedar kilnBOT
@maiden garnet Has your question been resolved?
maiden garnet
- Write a Matlab function that gives the value of S100 where limn→+∞ Sn = S
- Create a Matlab function that uses Newton's method to evaluate S, taking
|S100 − Sn| as test stop
anyone good at numeric analyse can help me in the second Q
cedar kilnBOT
@maiden garnet Has your question been resolved?
maiden garnet
ccc
cedar kilnBOT
@maiden garnet Has your question been resolved?
cedar kilnBOT
@maiden garnet Has your question been resolved?
crimson sedge
cedar kilnBOT
crimson sedge
So my proposed solution to b) is that the coefficient matrix defines a linear map that takes the solution vector to the 0 vector
and there is a property of linear transformations s.t. if there is a linear transformation T, a solution vector v and a scalar multiple c then T(cv) = cT(v) = c * 0 = 0
is this correct?
<@&286206848099549185>
cedar kilnBOT
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cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
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old salmon
still tartan
limpid brook
cedar kilnBOT
limpid brook
Im doing this rn but i dont understand how google got 36 for one of it
where did they get -36x
i got 3(36x^2 - 18x + 2x)
= 108x^2 -54 + 6x
(not including the other side)
cedar kilnBOT
@limpid brook Has your question been resolved?
rain drift
lol
cedar kilnBOT
cedar kilnBOT
Available help channel!
slender warren
At where the arrow pointed, I'm wondering can I perform integration at this state cuz I still see e^2x? Or I can just do integration like what I've written
slender warren
aww
solid juniper
but e^(2x) = 1 - u
solid juniper
never mind haha
solid juniper
how not $-\frac{1}{2}\int\frac{u^{-1/2}}{1-u}du$?
wraith daggerBOT
💜𝓁𝒶𝓎𝓁𝒶💜
slender warren
what's this?
solid juniper
solid juniper
nooo 😭
slender warren
yea I swapped the numerator instead of the denominator after u hinted HAHA
solid juniper
the integral is still ☠️
slender warren
I think this time I got it right?
solid juniper
idt that's right 
slender warren
nani
slender warren
cedar kilnBOT
@slender warren Has your question been resolved?
solid juniper
i think still wrong and i can't follow the algebra 
slender warren
i think still wrong and i can't follow the algebra <:sadcat:547124024585486359>
oh, which part is confusing
I just press calculator
solid juniper
idt this is right?
slender warren
oh ya now u remind me, I couldn't just separate
man idk how to continue with this
cedar kilnBOT
@slender warren Has your question been resolved?
cedar kilnBOT
@slender warren Has your question been resolved?
pulsar pulsar
At where the arrow pointed, I'm wondering can I perform integration at this stat...
This could be a possible solution (using some trig substitution)
pulsar pulsar
if you're unsure whether your solution is correct, a way to verify it is by just differentiating your solution and checking whether it matches the given integrand
pulsar pulsar
let me get more paper
pulsar pulsar
im kinda a slow learner, can u explain a bit on the denominator part?
when e^(-x) goes into the square root, it should be squared
Technically
√(a²) = |a|
but the exponential function has the range (0, +∞) so I can just say
√(exp(-x)²) = exp(-x)
and
(exp(-x)²) = exp(-2x)
just some exponent laws
slender warren
wowww understood the denominator part
pulsar pulsar
👍
slender warren
This could be a possible solution (using some trig substitution)
why are we adding this?
pulsar pulsar
because we want to bring it into a form such that the denominator's derivative is in the numerator
because ∫ f'(x)dx/f(x) is something we can integrate to log| f(x) | + C.
slender warren
U mean like this formula?
pulsar pulsar
mhm
slender warren
They are same right?
pulsar pulsar
yep, just θ as the variable instead of x
slender warren
ok I understood the rest, but this part is so hard, I dont think I can think of it when it comes to exam 🗿
thanks for teaching me patiently btw
pulsar pulsar
ok I understood the rest, but this part is so hard, I dont think I can think of ...
lol you don't have to do this explicitly usually you can just say ∫ secx dx = log|secx + tanx| + C
it's a standard form
I did it just to show you
slender warren
ohhhh
pulsar pulsar
ok I understood the rest, but this part is so hard, I dont think I can think of ...
you just need to know that the derivative of secx is secx • tanx and the derivative of tanx is sec²x in that part btw
slender warren
yeah
slender warren
lol you don't have to do this explicitly usually you can just say ∫ secx dx = lo...
I dont have fomula showing integration of secx, so ur method helps better
pulsar pulsar
I see
slender warren
pulsar pulsar
There are more 'standard form' integrals which you might learn later on
bold hazel
cedar kilnBOT
bold hazel
is this the right approach?
cedar kilnBOT
@bold hazel Has your question been resolved?
supple mortar
Anyone know what tally means
cedar kilnBOT
Anyone know what tally means
supple mortar
for example, if 4, tally is llll
What do you mean
So just tally like
So the first one would have no tally
tame zodiac
yes but over 5 is different
supple mortar
But the third one will have I
tame zodiac
yes
tame zodiac
yrs
cedar kilnBOT
Available help channel!
fickle ermine
cedar kilnBOT
crimson sedge
100=2^2*5^2, so you could use crt
crimson sedge
no, the right is still 21 in both lines
fickle ermine
and what is crt?
dry heart
chinese remainder theorem
fickle ermine
oh got it
then
y^3 =21 (mod 4), y^3= 21 (mod 25)
=> y^3= 1 (mod4) , y^3 = 21 (mod 25) right?
crimson sedge
yea
crimson sedge
we know y^3=1 mod 5, so we only have to check 5 things
fickle ermine
wait where it is come from y^3=1 mod 5
crimson sedge
well if y^3=21 mod 25, then we definitely have y^3=1mod5
fickle ermine
how does it work?
crimson sedge
25=5^2
fickle ermine
yep
crimson sedge
so anything that holds mod 25 must hold mod 5
crimson sedge
its 1 mod 5, but we need to check 1,6,11,16,21 mod 25 (because crt only works if its coprime)
fickle ermine
.close
cedar kilnBOT
cedar kilnBOT
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patent bone
does anybody know the answer to this?
cedar kilnBOT
does anybody know the answer to this?
patent bone
I’ve already solved it but it doesn’t give me the correct answer
opal basin
what answers did you get?
patent bone
2(x-2)(x-1/2)
opal basin
one of them is correct, but it's written in another way
patent bone
which one?
opal basin
notice how you can distribute the 2 to get (x - 2)(2x - 1), which is closer to the answer
opal basin
how do you mean, x can be any real number
patent bone
2(x-2)(x-1/2)
Yeah but even if I distribute it x comes out positive
opal basin
that's the same as (x - 2)(2x - 1)
but (x - 2) = -(2 - x) and (2x - 1) = -(1 - 2x)
so (x - 2)(2x - 1) = -1 * (2 - x) * -1 * (1 - 2x)
wintry wasp
How do i write the following sum in closed form: $$\sum_{i=1}^{100} i*x^{i-1} $$
south tundra
100 instead of \100
wraith daggerBOT
نعمان
wintry wasp
100 instead of \100
Thanks!
crystal raptor
The inside looks suspiciously like a derivative..
wintry wasp
yeah you're right
Weve never really been thought about evaluating sums, this was a problem from the chapter on integration so idk how to go about this.
crystal raptor
The inside looks suspiciously like a derivative..
This is how, the whole sum is the derivative of some other sum you know a closed form for, figure out the details
crimson sedge
cedar kilnBOT
crimson sedge
I had those questions and a document attached, those are just my answers
I have no way to know if that's how to do it and was lost on q4 especially
Skipped a for q4 for now
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
<@&286206848099549185>
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
<@&286206848099549185>
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
short blade
@crimson sedge what do you need help with exactly
short blade
part a should be fairly clear. the function is even and they provide you what it looks like from x=0 to x=2pi, so for x=-2pi to x=0 it's just the mirror image of that
then the function repeats since it is periodic with period 4pi
for b, recall that the fourier series for $f(x)$ with period $2p$ is expressed as $$f(x)=\frac{a_0}{2}+ \sum_{n=1}^\infty a_n\cos(\frac{n\pi x}{p}) + b_n\sin(\frac{n\pi x}{p})$$ where $$a_n=\frac{1}{p}\int_{-\infty}^\infty f(x)\cos(\frac{n\pi x}{p}), dx$$ and $$b_n=\frac{1}{p}\int_{-\infty}^\infty f(x)\sin(\frac{n\pi x}{p}), dx$$
since f(x) is even, it should be clear that b_n is 0 for all n
so your task is to find the first 5 a_n such that a_n=/=0
wraith daggerBOT
maximo
crimson sedge
Thx for the reply mate
I'm prolly in a different timezone to u
The a_n I found includes like a sin(npi/2) and I don't know how to simplify that
@short blade
granite peak
a level math right there
open plover
short blade
**maximo**
just noticed my integral bounds should have been from -p to p, but i’m sure you caught that
short blade
The a_n I found includes like a sin(npi/2) and I don't know how to simplify that
anyhow, sin(npi/2) = (-1)^(n+1) for n>=1
crimson sedge
a level math right there
Fr? 😂
short blade
and also, i didn’t mention this but your $a_0$ can be found with $$\frac{1}{p}\int_{-p}^p f(x), dx$$
wraith daggerBOT
maximo
crimson sedge
a level math right there
Actually ngl I see it. Tbh I just wanted to find someone to go through my work. I make dumbass mistakes smh🤦🏽♂️
crimson sedge
and also, i didn’t mention this but your $a_0$ can be found with $$\frac{1}{p}\i...
Thankss,
I actually did aready find that
crimson sedge
anyhow, sin(npi/2) = (-1)^(n+1) for n>=1
What about cos(npi/2)
short blade
What about cos(npi/2)
0
oh
so
sin(npi/2) can be 0 as well
and cos(npi/2) can be nonzero
it’s a little more nuanced than that i guess 😂
i think it should be fine to leave them as they are
crimson sedge
Lol😂
Aight g 🙌
I looked through it earlier and picked out my miscalculations too
Thanks
.close
cedar kilnBOT
crimson sedge
sin(npi/2) can be 0 as well
Was actually my dilemma but yeh
cedar kilnBOT
Available help channel!
crimson sedge
Anyone know how to find θ?
crimson sedge
.close
slim crown
I end up getting an awful looking cubic, how am I meant to do this?
slim crown
I have (2(n+1)(n+2)(2n+1))/6 + (n(n+1))/2 - n = 454n
cedar kilnBOT
@slim crown Has your question been resolved?
dire geode
I have (2(n+1)(n+2)(2n+1))/6 + (n(n+1))/2 - n = 454n
Did you try moving all terms to one side and factoring/simplifying?
fair geyser
i was going to explain how you have (2(n+1)(n+2)(2n+1))/6 + (n(n+1))/2 - n = 454n
then i read that you already do
slim crown
Did you try moving all terms to one side and factoring/simplifying?
I've tried that however my n coefficient ends up being -2713
and I dont feel I can factorise something with that
dire geode
I have (2(n+1)(n+2)(2n+1))/6 + (n(n+1))/2 - n = 454n
Your first equation looks wrong. Factor out the 2 and split the 1 before using the sum formula
Something like 2 * sum r^2 + sum r - sum 1
dire geode
the sum of r^2 is (n+1)(n+2)(2n+1)/6 right?
crimson sedge
Finding z1 and z2?
cedar kilnBOT
Finding z1 and z2?
crimson sedge
Let $z_1 = x + iy$ and $z_2 = u + iw$
wraith daggerBOT
Maxim
wraith daggerBOT
Maxim
crimson sedge
$(x + u) + i(y + w) = 4 + 4i \implies x + u = 4, y + w = 4$
wraith daggerBOT
Maxim
crimson sedge
now do the same for the second equation
keeping in mind that $\overline{z_2}$ is the conjugate of $z_2$, i.e. the complex number whose imaginary component is $-iw$
wraith daggerBOT
Maxim
cedar kilnBOT
@formal geyser Has your question been resolved?
formal geyser
.close
ivory finch
$ Compute\ \frac{dy}{dx}\ if\ xe^{y}\ =\ 2xy$
cedar kilnBOT
$ Compute\ \frac{dy}{dx}\ if\ xe^{y}\ =\ 2xy$
wraith daggerBOT
cookie2
ivory finch
Can anyone tell me step by step what I do?
runic garnet
Product rule on both sides
cedar kilnBOT
@ivory finch Has your question been resolved?
cedar kilnBOT
@ivory finch Has your question been resolved?
dire geode
Can anyone tell me step by step what I do?
Implicit differentiation
mossy spruce
are these the same
cedar kilnBOT
are these the same
zenith sail
No, $\sqrt{a+b}$ is not the same as $\sqrt{a}+\sqrt{b}$ in general
wraith daggerBOT
tatpoj
plush solstice
Hi :)) Small question, how do I develop a power series (?) of a given function like this one? I know already the formula of the power series but cant seem to be able to apply it efficiently. I need to develop this power series given a development point "a" and further give its convergence radius
plush solstice
so 1/c-x for c != "a" and with "a" part of R
As a help tip we know that the geometric series is of help in this case
cedar kilnBOT
@plush solstice Has your question been resolved?
plush solstice
<@&286206848099549185> Do you have any idea? If not I can just leave it, no problem
dire geode
Hi :)) Small question, how do I develop a power series (?) of a given function l...
Is this just a geometric series?
c-x = c(1-(x/c))
plush solstice
this is supposed to be a function f(x) and we are supposed to look for the correspondent power series
ok no worries
ill figure it out somehow
.close
ivory finch
ivory finch
How do I simplify if it's 0/0?
dire geode
How do I simplify if it's 0/0?
L'hopital usually
cedar kilnBOT
cedar kilnBOT
Available help channel!
bold hazel
trying to understand what this problem is asking
cedar kilnBOT
trying to understand what this problem is asking
bold hazel
"For the following exercises, draw an outline of the solid and find the volume using the slicing method."
this is the example it gives
cedar kilnBOT
@bold hazel Has your question been resolved?
hardy island
How could I find the Minimum distance between two functions, for optimization
tough aurora
wraith daggerBOT
donut
hardy island
Yea I got the distance formula
Also I’m specifically trying to find the minimum vertical distance
cedar kilnBOT
@uncut crow Has your question been resolved?
cedar kilnBOT
@uncut crow Has your question been resolved?
vestal bear
cedar kilnBOT
vestal bear
I put it into photomaths and i got some bizzare answer
gaunt hamlet
I can see why
vestal bear
I have no clue how to do this and I think its kind of embarrassing for me
vestal bear
I did
gaunt hamlet
What did you get
crimson sedge
You can take u = x+2 and then x^2 = (u-2)^2 lol
vestal bear
Wait shit
I thought of that but rejected it because it didnt work another time
Because it was on the bottom of the fraction
I'm stupid
Ty
.close
keen furnace
calm sierra
@keen furnace pls use only 1 channel
cedar kilnBOT
@keen furnace Has your question been resolved?
obsidian tinsel
The formula for distance between two points is sqrt((x1-x2)^2 + (y1-y2)^2)), and we are comparing the points on a line and the point at the origin, so we plug in 0 and 0 for x2 and y2, and we plug in x and y(which is 3x-10) into x1 and y1.
We get Distance = sqrt(x^2 + (3x-10)^2)
But we want to find the least distance, an x that makes the distance the smallest, a minimum. Thus we want the derivative. Take the derivative of Distance. Find it’s critical point where derivative is zero. Find the minimum. BOOM, u found the x that makes a minimum
We know the x that gives the shortest distance between one of the points on a line and the origin. In order to find the value of that distance, we plug in this x back into our equation for the distance between points on a line and the origin.
@keen furnace
cedar kilnBOT
@keen furnace Has your question been resolved?
cloud lily
turbid portal
Does anyone know how to do the Empirical Rule part? I am confused since we hardly covered this part in class
cedar kilnBOT
Does anyone know how to do the Empirical Rule part? I am confused since we hardl...
@turbid portal Has your question been resolved?
rain drift
The empirical rule, also known as the three-sigma rule or the 68-95-99.7 rule, is a statistical rule that states that almost all observed data for a normal distribution will fall within three standard deviations (denoted by σ) of the mean or average (denoted by µ).
so it looks like 68%
turbid portal
Oh I see. I knew it had those three numbers but didn't know if I could use it in my answer
lyric nymph
Yall could anyone help with this problem: A street light is at the top of a 18 ft pole. A 5 ft tall girl walks along a straight path away from the pole with a speed of 7 ft/sec.
At what rate is the tip of her shadow moving away from the light (away from the top of the pole) when the girl is 28 ft away from the pole?
I got 126/13 but it's not the right answer.
turbid portal
It's not 68
rain drift
Yall could anyone help with this problem: A street light is at the top of a 18 f...
Hi there this cannel is occupied, could you head to #❓how-to-get-help and use a free channel to ask your question?
lyric nymph
Hi there this cannel is occupied, could you head to <#488120190538743810> and us...
Yes I just realized oops sorry
(Don’t mind the questions everyone)
cedar kilnBOT
turbid portal
.reopen
cedar kilnBOT
✅
wraith daggerBOT
MellowDramaLlama
rain drift
so you've already figured out that $\mu - \sigma = -28$
wraith daggerBOT
MellowDramaLlama
turbid portal
yes
rain drift
uhhhhh. Okay so like just a stretch but like if you did 100 - 68, you get 32%. So then we have for anything past 68% (aka 1 std deviation), then at least 1 would exclude the middle section
so then we get 32%
however since we're only dealing with 1 std deviation away, then we only need to worry about 1 side of the bell curve
so uhh
I'm gonna say 16%?
I have no idea if that's right or not lol but try it out
so like this is the idea
the dark yellow box is what we care about here
rain drift
well I'm currently in probability
actually yeah now that I"m looking at it I think that answer makes sense
turbid portal
16%?
Yes it was correct
i was literally in between
i was either putting 15.5 or 16.5 lol
crimson sedge
what does 5 units and ten square means on a graph
cedar kilnBOT
what does 5 units and ten square means on a graph
echo veldt
I guess the graph's "boxes" just represent 1/2 or 0.5. So 2 "boxes" means 1 unit. Just how the graph was designed
crimson sedge
right - ty
cedar kilnBOT
@crimson sedge Has your question been resolved?
winged pewter
I don’t get the 1/2
cedar kilnBOT
I don’t get the 1/2
winged pewter
How is it 1/2
dire geode
How is it 1/2
It's absolutely confusing
What they mean is each term in parentheses is greater than 1/2
n/n > 1/2, (n-1)/n > 1/2, etc
dire geode
Should have > next to each of the 1/2
cedar kilnBOT
@winged pewter Has your question been resolved?
winged pewter
What they mean is each term in parentheses is greater than 1/2
Oh ok
Thanks
.close
rocky wave
$x^\log(x) = \log_x(\frac{x^3}{100})$
cedar kilnBOT
$x^\log(x) = \log_x(\frac{x^3}{100})$
wraith daggerBOT
WhyWouldYouKap
$x^\log(x) = \log_x(\frac{x^3}{100})$
```Compilation error:```! Missing { inserted.
<to be read again>
\tex_let:D
l.57 $x^\log
(x) = \log_x(\frac{x^3}{100})$
A left brace was mandatory here, so I've put one in.
You might want to delete and/or insert some corrections
so that I will find a matching right brace soon.
(If you're confused by all this, try typing `I}' now.)```
rocky wave
$x^{\log(x)} = \log_x(\frac{x^3}{100})$
wraith daggerBOT
WhyWouldYouKap
rain drift
so just to double check, the LHS is $x^{log_{10}(x)}$?
wraith daggerBOT
MellowDramaLlama
rocky wave
yes
rocky wave
i assumed i didnt need the base
rain drift
hmm
rocky wave
with base 10
rocky wave
ok chill
rain drift
but it's good to double check
okay so the first thing I can see that we can do is simplify the RHS
$log_x\left(\frac{x^3}{100}\right) = log_x(x^3) - log_x(100) = 3 - log_x(100)$
wraith daggerBOT
MellowDramaLlama
rocky wave
ok fair
rain drift
not sure if that will help
just trying stuff out lol
dang
I know I'm just barely missing something lol
so there's a log rule that states $log_a(b) = \frac{1}{log_b(a)}$. So we could transform $x^{log(x)}$ into $x^{\frac{1}{log_x(10)}$
rocky wave
u need the slash before the logs
wraith daggerBOT
MellowDramaLlama
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
rain drift
So then $\frac{1}{log_x(10)} = log_x(10)^{-1}$, so $x^{(log_x(10)^{-1}}$
wraith daggerBOT
MellowDramaLlama
rain drift
I dont think that'll help though
rocky wave
nah i dont think that will help
rocky wave
idk
rain drift
and you're not allowed to just graph it and look? lol
it looks like the answer is x = 0.14
I think
aaaand just to confirm the goal is to find x right? Lmao
rocky wave
this was in my maths test earlier
is there any way to remove the power
bc that would help to isolate the x
wraith daggerBOT
MellowDramaLlama
rocky wave
yeah was about to say
rain drift
and we're sure that the RHS has log_x? and it's not just x^3/100?
rain drift
yeah no problem
I'm just looking for holes lmao
see it's such a weird problem because like if it was x^3/1000, then we could do (x/10)^3 and pull out that 3
all of my normal tools are not working! D:
rocky wave
sorry
rain drift
no worries
honestly I gotta go to bed, I was trying to solve this before bed. If I come up with a solution I'll DM yeah
rain drift
in the meantime it might be good to see if @Helpers can help or just .close the thread and reopen to get pushed on the stack
lol thank you
g'night!
rich sandal
If you tried to evaluate this from left to right, would it be the same as taking two double integrals? One for the region above the x axis and the one below.
rich sandal
So it's easier to just go from -x to sqrt of x
and 0 to 3
More like I'm wondering if these are both the same
cedar kilnBOT
@rich sandal Has your question been resolved?
cedar kilnBOT
@rich sandal Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
void marsh
x
void marsh
please hel
upbeat lotus
cedar kilnBOT
@void marsh Has your question been resolved?
zenith sail
x
You're provided a diagram, it just isn't completely labeled.
Which segments can you label from the given information?
crimson sedge
I Need help with a question about probability
cedar kilnBOT
I Need help with a question about probability
celest maple
Like what’s X
I think that X is a number after 6 on the table
Try using that
Like a random number other and greater than 6
celest maple
Start a new one
crimson sedge
A new what
celest maple
Nvm
I just reread it
X is like the number that appears the most when you roll the dice
celest maple
I think they are asking on what’s the number after 1 roll
celest maple
Since they have .25
25% of landing it
crimson sedge
Yeah so I’d write down 25%
crimson sedge
This question is bugging me greatly it’s so weird the way they structured it
celest maple
This question is bugging me greatly it’s so weird the way they structured it
Yeah i know
It’s hard to understand
But I hope you get an point
crimson sedge
Exactly yeah I get a point but it has to be right it’s worth like 10% of the test
That were doing tomorrow
crimson sedge
Exactly
Why does this happen to people man
10% for a question that doesn’t make sense
crimson sedge
I think so
crimson sedge
Yes please I reread the question
crimson sedge
Yes
celest maple
There are different chances of getting that number
The highest one is 1 and 2 and mostly the chances of landing that are 1 in 3
The variable X
Asks you to find the number that has the highest chance of pulling it
Then to the lowest number
Alright?
crimson sedge
How would it be 1 in 3 wouldn’t it be in one in six or two in six since that’s how many chances you have
No it’s how many options they’re are
celest maple
How would it be 1 in 3 wouldn’t it be in one in six or two in six since that’s h...
It’s 1 and 3 for both the number 1 and 2 on the dice
So there’s a chance on landing it and not
celest maple
Yes so it would be 2 chances instead of 3 wouldn’t it
If you want to say that
That’s optional
crimson sedge
Your 13?
celest maple
Yes going to school
crimson sedge
And your good at math?
celest maple
celest maple
And your good at math?
Yea
crimson sedge
How?
celest maple
Don’t ask
crimson sedge
Alright thanks for your help
celest maple
Np
crimson sedge
Appreciate your time
crimson sedge
.close
halcyon jacinth
cedar kilnBOT
halcyon jacinth
Can anyone help me to solve 4 and 5?
crimson sedge
just think of it as f(g(h(x)))
for the first one
and work from inside out
the h(x) will be considered as the input to function g
so you would substitute the h(x) into g(h(x)) as you would for say, g(2), g(x+1), g(z)
For your second question, a one to one function basically denotes the mapping of two sets. A function g is one-to-one if every element of the range of g corresponds to exactly one
halcyon jacinth
For your second question, a one to one function basically denotes the mapping of...
How will I show that?
crimson sedge
Well, there is a lot of methods
halcyon jacinth
Can u show one pls?
crimson sedge
most commonly is the horizontal line test. But that isn't available right now
So instead, if you can show that $f(x) = f(y) \to x = y$ then a function is one-to one
wraith daggerBOT
♡LexQa♡
halcyon jacinth
Can I solve it and show it to you in your dms?
crimson sedge
the converse is also true, if you can show that $x \neq y \to f(x) \neq f(y)$ then the function is one-to-one
wraith daggerBOT
♡LexQa♡
crimson sedge
Can I solve it and show it to you in your dms?
sure..
halcyon jacinth
Dming u
cedar kilnBOT
@halcyon jacinth Has your question been resolved?
autumn oxide
Have you been given a formula for the volume of a sphere?
If you're given a reference/formula sheet of any kind it's typically on there
cedar kilnBOT
@slow mirage Has your question been resolved?
autumn oxide
sorry I was called away
@slow mirage in the formula r stands for radius
and V for volume
$pi$ is a number on your calculator
wraith daggerBOT
neptune-a-fish
smoky terrace
Hannah finds two dice in the attic with a rather peculiar feature: they are not standard dice (which have every natural number between 1 and 6 exactly once), but both have six
certain (not necessarily different) non-zero natural numbers. Hannah notes that the probability distribution
the sum of the eyes of both dice is exactly the same as that of two standard dice.
For example, the probability of rolling a sum of 12 pips is equal to 1 . in both cases
36 .
What are all the possible pairs of dice that match the above
fallow steppe
Hannah finds two dice in the attic with a rather peculiar feature: they are not ...
what have you tried?
fallow steppe
well, maybe start by writing down the probabilities of standard dice then
smoky terrace
i dont have time
and thats not the solution at all
so you wont help me with that
fallow steppe
its part of the (or at least a) solution
but if you dont have time to put in work, this server cannot help you
cedar kilnBOT
@smoky terrace Has your question been resolved?
cedar kilnBOT
@smoky terrace Has your question been resolved?
cedar kilnBOT
@smoky terrace Has your question been resolved?
cedar kilnBOT
@smoky terrace Has your question been resolved?
fresh summit
How do I find out the exponential function just by using these graphs?
wraith daggerBOT
humble sleet
idk if u have a point cant you substitute it to get the answer?
for a
the y intercept is (0,4)
so
f(x) = a b^x + 4
then
actually idk
i dont do exponentials
late vector
This might be a different question. But is there an online calculator or anything that can find the equation for a polynomial from a graph?
late vector
Possibly data points or image?
patent belfry
i mean with data points
crimson delta
plenty of interpolation calcs on the internet I would assume
patent belfry
there can be an infinite amount of polynomials that pass through a set of points
dire geode
sonic bramble
hi
cedar kilnBOT
@sonic bramble Has your question been resolved?
sonic bramble
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
tacit crescent
Help
tacit crescent
tacit crescent
Can I get help on this
tacit crescent
?
tacit crescent
What’s the range
toxic moat
ok
so thats ur q
um
well
a function f takes in some inputs and maps it to some outputs
inputs it can take in is the domain
outputs it spits is called range
tacit crescent
I think the range is [-5, 5]
tacit crescent
You sure
tacit crescent
You know what range means what’s the lowest and what’s the highest
tacit crescent
So what do you think the range is and why
toxic moat
ye
tacit crescent
Can you write it in [
*[,]
[-5,5]
Am I correct because if I get it wrong I can’t go back
@toxic moat you there?
toxic moat
sounds like a test
tacit crescent
No it’s an assignment
Delta math
So what do you think the range is?
Hello? @toxic moat
.close
desert zinc
I forgot what to do when 3b...
cedar kilnBOT
I forgot what to do when 3b...
desert zinc
<@&286206848099549185>
eager sparrow
I forgot what to do when 3b...
,rotate
wraith daggerBOT
desert zinc
How do I also do B, C and D
weak lake
can you find the center of the circle?
desert zinc
How do I also do B, C and D
desert zinc
can you find the center of the circle?
Is it a point on a perpendicular line with the point (-7,-6)
Idk
eager sparrow
,rotate
wraith daggerBOT
desert zinc
Isn't it the values in the circle equation
weak lake
the equation of circle is (x – h)^2 + (y – k)^2 = r^2
eager sparrow
Have you find the equation of the line?
desert zinc
18 and 2
weak lake
which question are you on?
desert zinc
5b
eager sparrow
Find the slope first
And sub either values between two points
Either way they both work
desert zinc
Do I do -6+2=m(-7-18)
eager sparrow
Nooo
Find the slope first using the two points
Do you also know how to find the slope of a line?
desert zinc
No
eager sparrow
Bruh
desert zinc
Isn't it the gradient
desert zinc
Do I do -6+2=m(-7-18)
I get the gradient and then swap the y and x to get perpendicular line gradient?
I then found an equation to the line by applying the gradient to the coordinates I already have?
desert zinc
Yes
eager sparrow
Ok, so find the gradient
eager sparrow
Then sub the gradient here at m
Then use either the two set of points for y_1 and x_1
Either way, both points will work
Then find the perpendicular
Then you will have the equation of the perpendicular line for the equation
I got something like this @desert zinc
If you want to do checking or to show that this perpendicular line is correct, sub something for your equation of a circle
you will get a point there
desert zinc
Ugh
I got the gradient of the center of the circle and the tangent
But its all coming out wrong
eager sparrow
I got the gradient of the center of the circle and the tangent
Tangent, is this a different number now?
eager sparrow
If you want to do checking or to show that this perpendicular line is correct, s...
I messed up here, you should probably use the the equation for the perpendicular line and substitute the point of the circle to see if it is correct
lapis sleet
could somebody please help with part B
cedar kilnBOT
could somebody please help with part B
@lapis sleet Has your question been resolved?
cedar kilnBOT
@lapis sleet Has your question been resolved?
Available help channel!
Available help channel!
crimson sedge
could someone explain why I get 675.88
cedar kilnBOT
could someone explain why I get 675.88
@crimson sedge Has your question been resolved?
crimson sedge
<@&286206848099549185>
cedar kilnBOT
@crimson sedge Has your question been resolved?
eager sparrow
could someone explain why I get 675.88
Did you use a calculator?
crimson sedge
Yes
eager sparrow
If the calculator isn't set correctly, then it might be that you used degrees instead of radians.
You need to set your calculator first from degrees to radians
eager sparrow
could someone explain why I get 675.88
I see you actually did not set your calculator correctly
I tried to answer the question but I set it to degrees. I also got 675.86
Just set it to radians and you're good to go
Can you take a picture of your calculator @crimson sedge ?
cedar kilnBOT
@crimson sedge Has your question been resolved?
dull stratus
Hello everyone, if a sequence of simple functions converges point wise to a function f, does f have to necessarily be a simple function?
dull stratus
I know the answer is no but not why
cedar kilnBOT
@dull stratus Has your question been resolved?
solid juniper
Hello everyone, if a sequence of simple functions converges point wise to a func...
i think you could try to think of a sequence of simple functions that converges to something like the identity function on [0,1] if you wanted an example
there are also some more overkill theorems that would tell you this
like every measurable function is the limit of a sequence of simple functions
provided you believe not every measurable function is simple
solid juniper
i think you could try to think of a sequence of simple functions that converges ...
think riemman sums if you need a hint
alternatively, you don’t need to start with a function and try to build a sequence of simple functions that converges to it
but instead just try to think of a sequence of simple functions, where each has an image larger than the previous, that converges to something
cedar kilnBOT
@dull stratus Has your question been resolved?
grim fulcrum
hey what does this mean?
cedar kilnBOT
hey what does this mean?
grim fulcrum
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
celest ibex
Hi, I have this exercice :
cedar kilnBOT
Hi, I have this exercice :
celest ibex
With this definition for the lim sup and inf :
I don't know how to solve that... Please help
I think is ? b) lim inf = N
c) lim inf A_2p = [-1,2] = lim sup A_2p and
lim inf A_2p+1 = ]-2, 1] = lim sup A_2p+1 ?
cedar kilnBOT
@celest ibex Has your question been resolved?
olive heart
{xt=2t
olive heart
{xt=2t
{y(t)=t-1
write each pair of parethmetic equation as a single equation in x and y
crimson sedge
I assume u mean x(t) with that
crimson sedge
But anyways, solve for t for one of them and sub it in in the other
crimson sedge
Well uh it is
crimson sedge
t= x(t)/2
olive heart
ye
olive heart
ye
crimson sedge
I think you should look that up
Pretty dangerous to not know how to add with fractions while taking a pre calculus topic
olive heart
bro