Please ignore my work there for now, I started doing this using some weird formula but I couldn't really figure out what it meant, looking for some insight into it possibly?
#help-10
fickle dagger
obtuse pebbleBOT
Please ignore my work there for now, I started doing this using some weird formu...
fickle dagger
it is definitely much easier to solve for in terms of tau, which is how I did it now
but my TA told me to use this formula
which gives me this
but this does not make sense as an answer
:/
!status
obtuse pebbleBOT
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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
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
!status 5
obtuse pebbleBOT
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
5
obtuse pebbleBOT
@fickle dagger Has your question been resolved?
obtuse pebbleBOT
@fickle dagger Has your question been resolved?
obtuse pebbleBOT
@fickle dagger Has your question been resolved?
fickle dagger
No
obtuse pebbleBOT
@fickle dagger Has your question been resolved?
ebon hull
obtuse pebbleBOT
@fickle dagger Has your question been resolved?
obtuse pebbleBOT
@fickle dagger Has your question been resolved?
obtuse pebbleBOT
@fickle dagger Has your question been resolved?
brazen viper
@fickle dagger the autocorrelation function should be a convolution of a function with itself. The formula given is the convolution but in the frequency domain. Remember, convolution becomes multiplication when moving between time and frequency.
I think why it doesn't make sense is you were expecting the answer to be a series of triangle waves, which it is in the time domain.
fickle dagger
I see
but even in the case of that series, I just didn't really understand how I could try to simplify that expression
since I'd have a sum of sincs
brazen viper
You can try moving back to the time domain
fickle dagger
I mean I already figured out how to do this with a discrete expression for the time domain
I was just wondering if there was a way to make sense of it in the frequency domain
brazen viper
Well, specifically how do you want to "make sense of it?"
fickle dagger
I guess what I mean was that I wanted to be able to evaluate it in a way that made sense, but that might not necessarily be possible, i.e. using the formula we would get a sum of sin(2pi f_0 n) cos(2pi f_0 n tau)
frail coyote
hello
fickle dagger
.close
obtuse pebbleBOT
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stable wyvern
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stable wyvern
Im thinking i should first show that the 3rd and 4th cases can be proved together
any ideas?
?
?
<@&286206848099549185>
<@&286206848099549185> 🙏
obtuse pebbleBOT
@stable wyvern Has your question been resolved?
stable wyvern
nvm I'm going to sleep, anyone dm me if you wanna talk about the problem! One last <@&286206848099549185> for visibility.
.close
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earnest mural
hlow
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fresh ruin
Let’s say the distance is 100 meters we go 50 KM per hour on the way there and 40 KM per hour on the way back. I realize I need to account for the different times so it Intuitively makes sense for me to take the reciprocals of 50 and 40 But then without looking at the harmonic mean formula I am not exactly sure what to do I’m not exactly sure why I divide two by the sum of the reciprocals and not something else I guess I’m just so used to doing arithmetic mean and geometric mean this is throwing me off. I know what the formula is and when to use it but am just trying to picture why divide 2 by sum of reciprocals
obtuse pebbleBOT
Let’s say the distance is 100 meters we go 50 KM per hour on the way there and 4...
@fresh ruin Has your question been resolved?
obtuse pebbleBOT
@fresh ruin Has your question been resolved?
orchid wind
obtuse pebbleBOT
orchid wind
I don’t need help with the math but
For part c
Do I have to include the restriction for r(x)
toxic arch
so easy
orchid wind
Originally
serene fossil
Do I have to include the restriction for r(x)
The domain of the rational polynomial is determined by the roots of r(x)
Since r(x) cannot be zero
So if that’s what you’re asking then yes include where r(x) = 0
Since that should be the only points that aren’t in the domain
Apart from those spots it should be the rest of R
serene fossil
Well r(x) is undefined at 5/2 and where is it 0?
orchid wind
Oh (5/2?
serene fossil
It’s not 0 there it’s zero at -1/7 I believe
orchid wind
But it has to be greater than 2
For the numerator
Because of the square root
Doesn’t it have to positive
serene fossil
But since r(x) is limited to be greater than 2 yeah you already exclude that part
Yeah you’re right
orchid wind
So is it [2, infinity) or (5/2, infinity)
serene fossil
So your domain is [2, 5/2) U (5/2,infinity)
It’s not [2, infinity)
It’s [2, 5/2)
And then you union that with 5/2 to infinity to get the whole domain
Because values in [2,5/2) are allowed
timid silo
Let’s say I’m asked to find the inverse of f(x), and I find f^-1(x) okay.
Now let’s say I want to check my answer to make sure I calculated the inverse correctly, is there a way to do this?
obtuse pebbleBOT
Let’s say I’m asked to find the inverse of f(x), and I find f^-1(x) okay.
Now l...
worn yoke
you should be able to find that
f(f^-1(x)) = f^-1(f(x)) = x
worn yoke
yes
obtuse pebbleBOT
@timid silo Has your question been resolved?
static furnace
f(f^-1(x))=x
timid silo
timid silo
f(f^-1(x))=x
Uhh
timid silo
@worn yoke
static furnace
you did f^-1(f(x)) and f(f^-1(x))
you proved it twice so you're good lol
next time when you want to check you only need to choose one of those
worn yoke
yeah just check whichever is easier
timid silo
Oh I just have to choose one?
timid silo
next time when you want to check you only need to choose one of those
As long as one of them = x I’m good?
@worn yoke @static furnace Hey what if something = -x?
static furnace
then the inverse you found is incorrect
static furnace
As long as one of them = x I’m good?
yes
worn yoke
that or the composition. either way it's a signal to double check your work
timid silo
@static furnace @worn yoke would one of u guys have a look at this one…? I think I did everything right
This is what the answr key says… super weird
worn yoke
the last step is incorrect, when you cancel the square
timid silo
the last step is incorrect, when you cancel the square
Pls explain
worn yoke
anything inside a square root is positive, so multiplying that by -1 gives a negative
what happens when you square a negative number?
timid silo
It’s undefined
timid silo
what happens when you square a negative number?
When you square or square root?
When you square a negative it turns positive , when sqrt a negative it’s undefined
worn yoke
we can write $-\sqrt{x+5} = (-1)\sqrt{x+5}$. what happens to the $-1$ when you square it?
warm shaleBOT
cloud
timid silo
It turns positive
worn yoke
yes
worn yoke
so we can write $(-\sqrt{x+5})^2 = (-1)^2 \cdot (\sqrt{x+5})^2$. which is...?
warm shaleBOT
cloud
timid silo
Just rootx+5
But I don’t understand how we can write it as (-1)^2??? @worn yoke
So a negative sign to the left of the root is essentially non existent is that what you are saying?
worn yoke
whenever we have a - sign to the left of anything, it's the same as multiplying the whole thing by (-1). we can split up exponents, so $(xy)^2 = x^2 y^2$. so the - sign must disappear when we square it
warm shaleBOT
cloud
timid silo
But where are you even getting the exponents from in this case…?
@worn yoke
My inverse contains no exponents…
worn yoke
im the second to last step you wrote
[(-\sqrt{x+5})^2 -5 = -x + 5 - 5] which is incorrect
warm shaleBOT
cloud
timid silo
im the second to last step you wrote
\[(-\sqrt{x+5})^2 -5 = -x + 5 - 5\] which i...
It’s incorrect because I didn’t apply the square to the -1 to the left?
worn yoke
yes, the -1 should have gone away because of the squaring
timid silo
This only apply when the the whole sqrt is squared right?
Not like -root((x-2)^2)
Then the negative would stay yeah?
worn yoke
it depends on whether the - is inside or outside the square
if it's outside then it stays
worn yoke
in that case the - would stay put (although now you have ± or absolute value to deal with)
timid silo
@worn yoke does BEDMAS always apply to everything?
worn yoke
in principle you could enclose absolutely everything in parentheses everywhere, and the rules of math would still function, but that would be hard to read, so we chose BEMDAS to require as few parentheses as possible while still being clear
(you could define your own personal system with a different order of operations and the math would still work fine, but other people reading it wouldn't be able to understand what you wrote)
obtuse pebbleBOT
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balmy crater
How would I do this:
obtuse pebbleBOT
How would I do this:
balmy crater
Would i use a binomial distribution model?
placid badge
yep
$\sum_{k=0}^{98} \mathbb{P}(X = k) = 1 - \mathbb{P}(X = 100) - \mathbb{P}(X = 99)$
warm shaleBOT
AlphaNull
obtuse pebbleBOT
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narrow jackal
find the values of the parameter a for which the equation has 3 solutions on [0, 2pi] interval
obtuse pebbleBOT
find the values of the parameter *a* for which the equation has 3 solutions on [...
narrow jackal
multiplying the values doesn't really give anything sensible or usable
tacit scarab
notice that if ab=0, either a = 0 or b = 0
tacit scarab
no problem
narrow jackal
.close
obtuse pebbleBOT
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marble wyvern
help
dense imp
i guess you could rewrite it just in terms of sin x
using sin^2 x + cos^2 x = 1 right?
warm shaleBOT
Soosh
dense imp
$-2\sin^2 x - \sin x + 1 = 0$
warm shaleBOT
Soosh
marble wyvern
oh
i see
but after i find x
how do i find the other angles?
since x isn't the only angle
if im not wrong
dense imp
i guess no need to worry about subsitution if it can just be factored
just factor it as:
(-2 sin x + 1)(sin x + 1) = 0
now set each factor = 0 and solve, making sense?
marble wyvern
yeah
dense imp
you got it from there?
marble wyvern
yeah
obtuse pebbleBOT
@marble wyvern Has your question been resolved?
formal turtle
obtuse pebbleBOT
formal turtle
am i donig it right?
when i plug it into desmos i just get y=0
which isnt the correct interpolation yk
obtuse pebbleBOT
@formal turtle Has your question been resolved?
cyan forge
which isnt the correct interpolation yk
why not?
yk that the sin(x*2pi) would reach 0 at each integer or half-integer (imagine the unit circle if you have a problem w/ this), so f of each point is just 0: y=0
what you got is actually the same as y=0, cause sin(pi) is 0 so it just makes everything 0
slim sequoia
obtuse pebbleBOT
inland matrix
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obtuse pebbleBOT
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
What is the formula for area of a triangle?
cyan forge
A=bh/2
cyan forge
What is the formula for area of a triangle?
oop mb
inland matrix
A=bh/2
If any 2 of them are known, we can find the third
In this case we know A and b
h= 2A/b, to find A/b you'll need to use long division for polynomials
cyan forge
in this case you can factor tho
no need to do long division
See any way you can factor by grouping?
inland matrix
in this case you can factor tho
Hmm true
obtuse pebbleBOT
@slim sequoia Has your question been resolved?
slim sequoia
.close
obtuse pebbleBOT
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rich plume
How would I find the range of this: $\left(2+\cosθ\right)\left(2+\sinθ\right)$
warm shaleBOT
B-eard
rich plume
probably this is an easy one im just not seeing it
also I don't want to solve it using cos(θ)=sin(θ)
the function in this case is symmetric but there may be unsymmetric functions
kind hawk
you could differentiate to find min and max
rich plume
you could differentiate to find min and max
differentiating gives (cosθ-sinθ)(cosθ+sinθ+2)=0
so, cosθ=sinθ
now putting back: (2+sinθ)^2
so am I basically find the min and max of this function?
kind hawk
no
that would be 9 obviously
but at that point cos and sin arent the same
you will obviously in some way have to use how sin and cos "interact"
so why do you not want to use costheta=sintheta
kind hawk
yes
rich plume
so considering this, I get max[sinθ]=1/sqrt(2) and min[sinθ]=-1/sqrt(2)
Putting back: min = (2-1/sqrt(2))^2 and max = (2+1/sqrt(2))^2
Ah ok thanks
.close
obtuse pebbleBOT
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olive jungle
obtuse pebbleBOT
olive jungle
How on earth do I do this
tacit scarab
how do you calculate volume
static furnace
yes
static furnace
you don't need excel, just a calculator
static furnace
yeah why would you need excel
static furnace
okay well then
you need to use excel
bruh the formula is on your page
both are
static furnace
yeah just type it into a box
try experimenting with excel. you'd be surprised how intuitive it can be
olive jungle
Can u do it real quick for me it’ll take me ages
calm cloak
Not sure if my primitive of (k+3x) is right and also don’t know where I went wrong integrating k into the primitive. The answer is k=2. Question is find the value of k if k>0
obtuse pebbleBOT
Not sure if my primitive of (k+3x) is right and also don’t know where I went wro...
lost otter
0=2.5k^2-k-8
sigma alpha male
calm cloak
wait how does that even worl
where did i go wrong
wait lemme redo the question
ohhhhhhhh
i see thanks
.close
obtuse pebbleBOT
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languid harness
obtuse pebbleBOT
languid harness
hey how do i factorise this
im confused because what multiplies to something y^2 but adds to something xy
inland matrix
You can try to solve the quadratic in x
||(Note that here you can take a=6, b=-8y and c=-8y² as the coefficients)||
Are you allowed to use the quadratic formula tho?
ruby path
or you could factor out y^2 and work in a quadratic in (x/y)
then multiply the y^2 back into the factors when youre done
languid harness
Are you allowed to use the quadratic formula tho?
im not sure
languid harness
or you could factor out y^2 and work in a quadratic in (x/y)
what do you mean?
dense imp
or you could factor out y^2 and work in a quadratic in (x/y)
that's clever but probably more confusing than anything for someone new to this stuff 😄
languid harness
You can try to solve the quadratic in x
||(Note that here you can take a=6, b=-8...
its saying to factorise
not use the quadratic formula
inland matrix
Yeah that way works too
Note that the thing inside the brackets is a quadratic in (x/y)
So you can use the same method you use to factorise quadratic expressions
inland matrix
For simplicity, we can take (x/y)= t
So 3(x²/y²)-4(x/y)-4 becomes
3t²-4t-4
Which can be factorised
inland matrix
Oh right mb
inland matrix
Yes
inland matrix
For simplicity, we can take (x/y)= t
So 3(x²/y²)-4(x/y)-4 becomes
3t²-4t-4
Then try this
languid harness
Then try this
ok
obtuse pebbleBOT
@languid harness Has your question been resolved?
languid harness
sorry
im back
hey sorry about the delay
had some stuff going on
@inland matrix
is this right
obtuse pebbleBOT
inland matrix
.reopen
obtuse pebbleBOT
✅
languid harness
so then how do i simplify
the answer is without those x/y fractions
this is the answer @inland matrix
sorry im replying so slow i was also having a second question answered
inland matrix
It's ok
inland matrix
Here there's a y² outside, which is the same as y*y
Multiply each y with each term inside the brackets
inland matrix
You can take that within one of the brackets too
languid harness
ok let me do this one sec
languid harness
Which is the same as 2(x-2y)
what about the y^2 tho
inland matrix
Multiply each y with each term inside the brackets
.
languid harness
inland matrix
2(3x+2y)(x-2y) is what you get after multiplying y²
languid harness
o
inland matrix
Now this 2 can be multiplied with either of the terms in the brackets
But only within one bracket
Ye
languid harness
wait what
the y^2
dosent that make the constants
2y^2 and -2y^2
what did i do wrong
inland matrix
$$2y^2(\frac{3x}{y}+2)(\frac{x}{y}-2)$$
$$= 2y(\frac{3x}{y}+2)\cdot y(\frac{x}{y}-2)$$
$$=2(3x+2y)(x-2y)$$
warm shaleBOT
Sulphur
inland matrix
So far so good?
languid harness
**Sulphur**
oh that is what you mean
inland matrix
Ye
languid harness
let me have a good look at it one sec
inland matrix
The reason we multiplied y within both brackets is coz there was a y² which could be written as y*y
But the same isn't possible with 2, it can be multiplied within only one of the brackets
inland matrix
It's alright
languid harness
people like you are hard to come by in these servers
inland matrix
Fr?
inland matrix
Ppl do exist in different forms
languid harness
happened to me which is why i was takling long breaks between messages
inland matrix
But I'm glad you understood
languid harness
i was arguing with some person in another server
inland matrix
Damn
languid harness
absolutely terrible human being
he was being so passive aggressive
egotistical
lack of empathy
the whole lot
so thank you
inland matrix
Np
inland matrix
You too
obtuse pebbleBOT
obtuse pebbleBOT
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honest rover
A group of tourists will go on a ship cruise. Of that
group, 15% have already taken a cruise once and 528
people have been on a cruise exactly 2 times.
If 6% of people in this group have already been on a cruise
3 or more times and 2,000 people will take a cruise along the
For the first time, the number of people in this group is
understood between: (X) 4500 and 5000
obtuse pebbleBOT
A group of tourists will go on a ship cruise. Of that
group, 15% have already ta...
honest rover
Can someone explain me step by step?
obtuse pebbleBOT
@honest rover Has your question been resolved?
obtuse pebbleBOT
@honest rover Has your question been resolved?
hybrid quiver
could you reframe that question or send a photo perhaps
honest rover
A group of tourists will go on a ship cruise. Of that group:
• 15% have already taken a cruise once
• 528 people have been on a cruise exactly 2 times
• 6% of people in this group have already been on a cruise 3 or more times
• and 2,000 people will take a cruise for the first time.
The number of people in this group is understood between:
( ) 2500 and 3000
( ) 3000 and 3500
( ) 3500 and 4000
(X) 4000 and 4500
obtuse pebbleBOT
@honest rover Has your question been resolved?
obtuse pebbleBOT
@honest rover Has your question been resolved?
obtuse pebbleBOT
@honest rover Has your question been resolved?
tough vessel
I generally get how to do a partial integral but im@kinda stuck on the first one as a whole ik i have to switch the order and bounds but idk what to do with that
obtuse pebbleBOT
I generally get how to do a partial integral but im@kinda stuck on the first one...
robust raven
I generally get how to do a partial integral but im@kinda stuck on the first one...
it is enough to read the new integration bounds to define a new integral iterated with respect to the OX axis
tough vessel
Could you explain that sorry I’m dumb😭
robust raven
Could you explain that sorry I’m dumb😭
Have you ever calculated an iterated double integral?
tough vessel
yea where you like take the integral w respect to the first variable then the second
robust raven
so you shouldn't have a problem here either, you can see right away how to set the integral bounds
look, in your i ntegral
the ergion D
is of the form:
that is in respect to OY
and now
you need to do it , in respect to OX
literally it requires take names of lines and curve from the picture i gave you
tough vessel
Ohh that makes sense thank you so much 😔
robust raven
yvw)
tawny kite
If a sequence is monotonic, can I just directly say it is bounded?
obtuse pebbleBOT
If a sequence is monotonic, can I just directly say it is bounded?
tawny kite
I don't have to prove that?
There's this question... Its all just stating the definitions, Im not sure what I even have to prove
well, if a sequence is decreasing, we can say its monotone, but it doesn't necessarily mean its bounded
it could diverge to -inf
and it has an upper bound
but bounded would mean both lower and upper
this is the question
Im gonna type stuff out here actually I feel like it helps so much for clarifying my thoughts
so to prove its bounded, I can either show that there is an inf of Xn, OR proof by contradiction and assume Xn is not bounded, so diverges...
I think I have to do smth with the term 1/2^n
because the limit is 0
and I will check for this, but there is prob some rule where addition of conv sequence and divergent sequences = convergent or smth like that
i have no idea lol
oh
damn
well there goes my lead
ahhhhh so if theres inf, then there is an M>0 s.t |Xn| >= M
but HOWWW
can I find such M???
what is this madness
tame python
If a sequence is monotonic, can I just directly say it is bounded?
1/n is monotonic, it's bounded
n is monotonic, it's not bounded
tame python
change this to x(n+1) - xn ≤ 1/2^n
then consider xn - x(n-1) ≤ 1/2^(n-1)
then consider adding both equations together
obtuse pebbleBOT
@tawny kite Has your question been resolved?
crystal notch
Is it still for this ?
crystal notch
I dont really want the answer
if u want, i can give u a small hint
(i'm going offline in at most 10min)
obtuse pebbleBOT
@tawny kite Has your question been resolved?
tawny kite
ok yea no
so how can I prove that the infinite sum indeed has an upper bound of 2
because I tried the eps delta method at first, for n->0, but thats hard to work out
<@&286206848099549185>
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daring salmon
can someone help me with this please
obtuse pebbleBOT
can someone help me with this please
timid silo
can someone help me with this please
first reduce it to echelon form
daring salmon
first reduce it to echelon form
yes whats next
timid silo
show me what u got
daring salmon
timid silo
ok cool
so now
transform that to your standard equation form
what would it be
x_1 + x_2 = 5 is what i mean, for example
daring salmon
timid silo
also i think u messed up
it's asking you to find Ax = 0
so you are equating it to the 0 vector
daring salmon
so there are 4 variables?
daring salmon
and i add a column with just 0's
timid silo
yeah
daring salmon
note it in equation form
daring salmon
solve for x_1 and x_2 in both equations
timid silo
Now, you need to plug in those values into the solution vector [
\vj x = \mat[b]{x_1\x_2\x_3\x_4}
]
warm shaleBOT
daring salmon
am i putting the expression into x1 and x2
timid silo
yes
daring salmon
oh ok
timid silo
you dont know anything else about them
daring salmon
timid silo
ok great
now
you can separate this vector into two
by the additivity property of vectors
make a vector only consisting of the x_3's and the other only for thr x_4's
daring salmon
timid silo
where did the x's disappear and why is it a row shorter
daring salmon
where did the x's disappear and why is it a row shorter
thank you
sacred jetty
i need urgent help
obtuse pebbleBOT
i need urgent help
sacred jetty
don't know what to do
stoic token
Bro volume of prism is area of base * height
stoic token
don't know what to do
Calculate the area of base first
also the "p" can be calculated using trigonometry in the triangle
q also
sacred jetty
well i got p as 4.9998661358
and q as 16.000133864
do you mind checking of i got the right values
and what is the formula to find the volume for this
sacred jetty
I think p can be considered 5 at this point
are we allowed to do that?
stoic token
Um 4.99999999 is roughly 5
stoic token
No take q as 16
sacred jetty
then what do we do?
stoic token
I said area of base
sacred jetty
this is what my module says
stoic token
stoic token
this is what my module says
Wait
sacred jetty
like how do i get the values of the base
stoic token
What is 10mm
sacred jetty
ok
no that is for another example question
it would be the width
instead of 10
bro who cares how do i get the measurements of the base
stoic token
i need urgent help
Area of base can be calculated
See the 7 cm
On top
It's the same as 7cm at bottom
Here is clear example man
Vol. Comes to be 1/2 * 5* 16 * 7
stoic token
35x5 is the answer
What did u do here
sacred jetty
What did u do here
mb
i messed up
its wrong
for some reason
it says answer to the nearest whole number
and idk if we are allowed to consider it 5 and 16
stoic token
What did u wrote as an answer
sacred jetty
280
sacred jetty
can you check for me
stoic token
I mean did u put your cal. On degree
sacred jetty
i think its right
sacred jetty
I mean did u put your cal. On degree
yes
bro just plsss check for me
im bad with calcs
sacred jetty
i mean they did give h = 51.34
stoic token
Bro p is 3.9999
stoic token
Just try once more on calc
sacred jetty
then what is the other way?
stoic token
then what is the other way?
U know this method right ?
stoic token
First convert 352m into cm
sacred jetty
35200
stoic token
Ok
Now find the circumference of wheel
U have been given the diameter
Take it's half to get radius
stoic token
Now divide the whole journey by circumference
sacred jetty
ok what is the formula you used?
stoic token
The one revolution is equal to how many cm.
According to your question
sacred jetty
35200
stoic token
No
sacred jetty
88cm
stoic token
One revolution= circumference of the circle
Yes
Now simply u think of is how many revolutions can be completed in your journey
sacred jetty
ok cya
stoic token
Cya
sacred jetty
accept my request!
sacred jetty
k thanks
stoic token
Welcome
obtuse pebbleBOT
@sacred jetty Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
sudden axle
Hello.Could someone help me with this?
obtuse pebbleBOT
Hello.Could someone help me with this?
sudden axle
The second question
Only help me with the first 2 questions.I know the others
<@&286206848099549185>
versed stratus
!15m
obtuse pebbleBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
@sudden axle Has your question been resolved?
timid silo
are their more rationalnnumbers or integers
obtuse pebbleBOT
are their more rationalnnumbers or integers
grizzled shore
There are the same number of them
timid silo
from a number line perspective, i see more integers
grizzled shore
There exists a bijective function $f:\mathbb Z \to \mathbb Q$
warm shaleBOT
Frosst
timid silo
sorry i mean
i see more rationals
cause u can like fit so many
decimals in between yk
drifting wraith
there's way more rationals
timid silo
like fit infinities
drifting wraith
if you don't mean cardinality
timid silo
between two integers
drifting wraith
yeah
grizzled shore
I guess it matters how you mean “more”
timid silo
so how can they be same-
when there are more infinite decimals
in between
two integers
hollow lynx
If any rational number is p/q then there would always exist integer 2^p*3^q
grizzled shore
But if you’re given just the sets ℤ and ℚ you can’t do much but compare their cardinality
drifting wraith
you don't run out of integers faster than rationals, if you match X integers with Y rationals
there's infinite amount of both
on a given interval, it's not true as you noticed
timid silo
2^p*3^qcan u give another example
timid silo
you don't run out of integers faster than rationals, if you match X integers wit...
you mean both increment at the same time so they both are the same?
i mean amount wise
drifting wraith
i don't know what you mean
timid silo
like both spawn
at the same time
um
cause if their spawning speed differ
like if rationals were faster
wait
grizzled shore
What do you mean “spawning speed”
drifting wraith
it's called density or something
hollow lynx
speed is relative
timid silo
like for every integer, there is a rational so they must be the same amount then? like for 0, we got 0/1, for 1 we got 1/1, for 2, 1/2
drifting wraith
no
grizzled shore
**Frosst**
This
grizzled shore
It’s a mapping between 2 sets such that everything in the domain is sent to something in the target
timid silo
It’s a mapping between 2 sets such that everything in the domain is sent to some...
so for every x, there is a y which means both x and y are the same amount of infinities?
hollow lynx
Yes but actually no
grizzled shore
so for every x, there is a y which means both x and y are the same amount of inf...
Not necessarily
Yes in this case but the logic you wrote doesn’t hold
grizzled shore
We need the bijectivity part as well
So for every y there’s also an x
Not just one way it needs to go both ways
timid silo
ok bijection
hollow lynx
Are you greater than 13 ?
grizzled shore
Are you greater than 13 ?
No?
timid silo
So for every y there’s also an x
ah both ways
okay
hence both are the same amount of infinites
grizzled shore
Something like that
timid silo
wdym something like thaat
it is that right?
leaving suspense
oksy ty 😄 @grizzled shore
.close
obtuse pebbleBOT
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graceful marten
Does this mean the same thing?
timid silo
Yes sin is an odd function
sudden axle
Hello
graceful marten
Yes sin is an odd function
Im not sure what that means
But it means im correct what i said
(the red stuff)
Is the equivilent
Saying
obtuse pebbleBOT
graceful marten
.reopen
obtuse pebbleBOT
✅
plucky rivet
Only former is true@graceful marten
cosine function is a even function
And even functions satisfy the following equation $$
f(x) = f(-x) $$
warm shaleBOT
Cyrenux
plucky rivet
White part of the latter image is true though @graceful marten
It seems like you came up with red text on your own, which i cant see how
graceful marten
It seems like you came up with red text on your own, which i cant see how
I thought the red text is the same as the white text no?
graceful marten
yes
Cos(x+3) = cos -3
no?
maybe im mixing transformations
into it I think
So these are the only possible even and odd functions?
tender tusk
wdym?
plucky rivet
I thought the red text is the same as the white text no?
How did you conclude that
graceful marten
I guessed
plucky rivet
Wrong guess
graceful marten
fair enough
I just dont know what this is tbh
Like I can do graphs
but I never use this stuff
or the CAST diagram
so this stuff confuses me everytime i see something
Ok-
I understand where i went wrong
Thank you
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
fair helm
how do i get the area of a curved rectangle
obtuse pebbleBOT
how do i get the area of a curved rectangle
fair helm
fair helm
Basically you need to figure out the arc_length then multiply by height
to get the area of the curved one?
cunning burrow
I have told you how
fair helm
how do i get the arc length
fair helm
I have told you how
😅
cunning burrow
Use the theorem arc_length = r*theta where theta is in radians
fair helm
Use the theorem arc_length = r*theta where theta is in radians
what would b the value of theta
cunning burrow
So how are radians defined?
fair helm
i forgot man
cunning burrow
pi radians = 180 degrees
Now using this definition you want convert the 35.13 degrees to radians
fair helm
Now using this definition you want convert the 35.13 degrees to radians
how would u use the formula
cunning burrow
Divide by 180 degrees first
fair helm
pi radians = 180 degrees
i kinda dont get that
cunning burrow
i kinda dont get that
??
fair helm
Divide by 180 degrees first
0.20
fair helm
Divide by 180 degrees first
do u not multiply by pie first?
cunning burrow
You want to make 1 of the numbers 1. 1*anything = anything
pi radians = 180 degrees
Divide by 180 both sides
pi/180 = 1
Hi zzzzx, unfortunately, I have to go all the best
fair helm
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obtuse pebbleBOT
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onyx girder
why is h(x)>g(x) when x>0?
obtuse pebbleBOT
why is h(x)>g(x) when x>0?
onyx girder
i dont understand the logic
since g(x)>f(x) for a bit of x>0, shouldnt h(x)<f(x) for this portion?
obtuse pebbleBOT
@onyx girder Has your question been resolved?
onyx girder
<@&286206848099549185>
obtuse pebbleBOT
@onyx girder Has your question been resolved?
onyx girder
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fervent cradle
why is h(x)>g(x) when x>0?
the idea is that g(x) is always < 1
so f(x)/g(x) is always > f(x)
ie. h(x) > f(x)
well, for positive f(x)
when x is negative it's the other way around
obtuse pebbleBOT
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Available help channel!
final birch
I have to determine a parametric equation for this ellipsoide... but i dont know how to start
obtuse pebbleBOT
I have to determine a parametric equation for this ellipsoide... but i dont know...
final birch
do i use spherical coordinates and use these?
obtuse pebbleBOT
@final birch Has your question been resolved?
obtuse pebbleBOT
@final birch Has your question been resolved?
tardy epoch
do i use spherical coordinates and use these?
you don't have to. you can shift and scale your old x for new x'
e.g. you can just get new (X, Y, Z) with simple shift and scale https://math.stackexchange.com/a/205919
obtuse pebbleBOT
@final birch Has your question been resolved?
tacit wing
obtuse pebbleBOT
tacit wing
having trouble understanding this rule
do I get to choose what b is or does it have to be related to a?
brave bramble
You get to choose
tacit wing
anything?
brave bramble
anything
tacit wing
all my examples show log_4 becoming log_2 or something like that
brave bramble
There's usually a "smart" pick, but you can pick anything
The base of a logarithm ends up being pretty unimportant
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
√x - √y = 9
And x . y = 4
Find √x³ - √y ³
obtuse pebbleBOT
√x - √y = 9
And x . y = 4
Find √x³ - √y ³
dark stirrup
$\sqrt{x^3}$ right? You didn't mean $\sqrt[3]{x}$?
warm shaleBOT
SWR
dark stirrup
Ok. Thought so just wanted to be certain
timid silo
a3 - b3 = (a-b)(a2 + ab + b2)
timid silo
a3 - b3 = (a-b)(a2 + ab + b2)
3 is the power i cant do that
timid silo
Ok. Thought so just wanted to be certain
yeah well i did that but couldnt come to a conclusion
dark stirrup
3 is the power i cant do that
Hm?
timid silo
which got me confused
timid silo
Hm?
i mean i said a3 but i meant a to the third power i just dont know the key on my keyboard to do that
its not related with the question
dark stirrup
Gotcha
dark stirrup
√x - √y = 9
And x . y = 4
Find √x³ - √y ³
Hint : square your first equation here
dark stirrup
We get it a lot here
timid silo
oh its probably because im in a different country
or i just heard it but dont know the english
it looks complicated thats something i can say
so what do i square
dark stirrup
so x - y is 81?
The point is that this is incorrect
timid silo
wait lemme go to google to copy the square root emoji
ok
so its x - 2√ xy + y
?
and x . y is 4
so √ xy is √ 4
which is 2
so its x - 2 + y
is 81
so x + y is 83
i just realized
the thing that the question is asking is way different than what i did
but at least i think i get the point
so how do i relate it to Find √x³ - √y ³
from this point
i got it all messed up
dark stirrup
but at least i think i get the point
Difference of cubes like you did before. Just don't forget the square root
dark stirrup
On $\sqrt{x^3}-\sqrt{y^3}$