#help-17
plain minnow
is CD parallel to AB?
vocal sleetBOT
@chrome ridge Has your question been resolved?
chrome ridge
is CD parallel to AB?
that hasn't been stated
magic wasp
If you don't have more information, you can't really tell
vocal sleetBOT
magic wasp
The angle OPA for example
vocal sleetBOT
Available help channel!
rain hollow
Triangles 2 sides are 13 and 14 area is 84 need to find the third side
elfin surge
Triangles 2 sides are 13 and 14 area is 84 need to find the third side
use heron's formula
rain hollow
Thats too long tho
lusty snow
Thats too long tho
Do you want to invent a bicycle ?
rain hollow
What?
lusty snow
nvrm
tidal dock
Triangles 2 sides are 13 and 14 area is 84 need to find the third side
do $\frac{1}{2}ab\sin(\theta)=84$ and solve for $\theta$
twin meteorBOT
artemetra
rain hollow
I just think there is a ez way to do it
tidal dock
and then substitute into cosine rule
tidal dock
not necessarily
rain hollow
Ok ill just do herons then
tidal dock
actually heron's formula is better
tidal dock
**artemetra**
this won't give you a precise answer
tidal dock
How do i find p without knowing all sides tho?
$p=\frac{a+b+c}{2}$, right?
twin meteorBOT
artemetra
rain hollow
X?
tidal dock
<@&268886789983436800> love them too
rain hollow
Is there a better way?
tidal dock
but the point is $p=\frac{27+c}{2}$
twin meteorBOT
artemetra
tidal dock
yep
rain hollow
I can make the c x right
tidal dock
yes
rain hollow
Ill try and send it
tidal dock
the naming of things doesn't matter, as long as it's consistent ๐ is a perfectly valid name for a variable
wide sundial
I can think you can do a bit of trial and error
if u can think of a standard pythag triplet then you'd have that the left triangle could maybe be (5,12,13) with 12 as the height
then the right side would be (9,12,15) because it's scaled version of the primitive (3,4,5)
anyway you can try and see:
,calc (14 * 12)/2
twin meteorBOT
Result:
84
goddayum
wide sundial
so the hypothesis is right and then yeah you can trivially say the third side is 15
tidal dock
that's very neat
wide sundial
tidal dock
idk if you can assume that the triangle has height 12
but ig if it clicks then it's okay
rain hollow
Ill do it with herons too
wide sundial
i mean if 14 is the base then the height necessarily has to be 12
then it's how you split the scalene into two rights
anyway herons always works so that should definitely be the go to method
rain hollow
Yea i think this is more reliable
wide sundial
Yea i think this is more reliable
so how are you planning on solving that? lol
wide sundial
chatgpt doesn't know math
also yeah you shouldn't use heron's
that doesn't look neat at all
rain hollow
Ill square it
outer dune
Are you solving for x๐ญ
plain minnow
chatgpt doesn't know math
fr
rain hollow
I think it is
plain minnow
just use area of triangle
rain hollow
Wdym?
plain minnow
$\Delta = \frac{1}{2}absin(\theta)$
twin meteorBOT
Wither
plain minnow
solve for $\theta$
twin meteorBOT
Wither
wide sundial
i'm guessing that he doesn't have access to a calculator
,w 84 = 1/2 13 (14) sin(theta) solve for theta
twin meteorBOT
wide sundial
,w 180/pi * arcsin(12/13)
twin meteorBOT
wide sundial
I think it is
and you have access to a calculator?
rain hollow
I can think you can do a bit of trial and error
Ill just solve it this way and also write herons without solving it
Yea
wide sundial
oh
then u can do heron's
just graph it
or there's a solving feature in the calculator ofc
rain hollow
Yea ill do it thanks guys
wide sundial
,w (27+x)(1+x)(-1+x)(-x+27) = 16 * 84^2
twin meteorBOT
wide sundial
lol, okay sure gl
rain hollow
.close
vocal sleetBOT
vocal sleetBOT
@stuck maple Has your question been resolved?
vocal sleetBOT
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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
vast shale
<enumitem>*
okay i guess i will go back to this, but for subtracting two numbers in some base $r$ using the $r$-complement. Say $A-B$, we can calculate
\env{equation}{
A + (r^n - B)
}
and then sum up the values. And then we separate into cases of
\env{enumerate}{[a)]
\ii if $A > B$ you will get an extra carry on term of $r^n$ from the sum of equation (1) and we can subtract $r^n$ to get the desired result of $A-B$, but the second case of
\ii if $A < B$ then there is no $r^n$ carry on term and we instead rearrange (1) to \env{equation}{
r^n - (B-A)
}
which represents the $r$-th complement of the negative of the subtraction $A-B$, so we append a negative sign to retrieve our desired result
}
vocal sleetBOT
<enumitem>*
okay i guess i will go back to this, but for subtracting two numbers...
twin meteorBOT
vast shale
it's just the above process seems so weirdly arbitrary to me
could we have not applied b) to a) as well?
how does (2) even make sense if the r^n term is supposedly not there after the summation?
vast shale
for the sake of example to avoid unnecessary abstraction
vast shale
for the sake of example to avoid unnecessary abstraction
the process in a) makes sense, which is fine, but what's happening in b) seems very stupid
i understand i can totally avoid this by just saying Y-X = -(X-Y) and then calculating what's being done in a), but i still would like to understand i suppose
limber halo
i understand i can totally avoid this by just saying Y-X = -(X-Y) and then calcu...
is your question soley regarding binary?
limber halo
okay, well for the sake of the argument Ill use binary but the properties would still apply in other bases
when computers use binary they dont actually have negative numbers. there is no - symbol, everything is either 1 or 0
limber halo
okay
the numbers are also of a set size
say 4 bits long
when we try and so subtraction with this in mind, set length and no negatives, doing
0000
- 1000
-------
doesn't work
there is no number to carry from and we can't just say the number is negative because negative numbers don't actually exist
vast shale
sure
limber halo
could we have not applied b) to a) as well?
With that in mind what happens when you apply b to a
vocal sleetBOT
@vast shale Has your question been resolved?
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hard atlas
well u sub is to undo chain rule
if you differentiate 1/x you dont use the chain rule
paper depot
what are you going to do with that lone x that you can't get rid of?
@stuck maple
I thought I can just turn my brain off and just solve every problem with it
bad attitude
hard atlas
u-sub is a powerful tool but not that powerful
paper depot
there is not and never will be a panacea for integrals.
nor is there any algorithm for it that's easy to learn and understand for humans
hard atlas
if anything you should first look if you can just use simple integral rules
just solve lots of integrals
a lot of it comes with experience
also dont forget ibp
not really...
paper depot
you try shit, sometimes it works, sometimes it doesn't
you develop your own intuition for it
it is impossible to teach this intuition or explain it explicitly
hard atlas
roughly speaking, u-sub is good for compositions and ibp is good for products
but thats just a rule of thumb
I mean who knows how hard the integrals you will have to solve are
but integration is significantly harder than differentiation
agile arch
- Evaluate the double series
sum j = 0 to โ sum k = 0 to โ 2 ^ (- 3k - j - (k + j) ^ 2)
Please help me
vocal sleetBOT
4. Evaluate the double series
sum j = 0 to โ sum k = 0 to โ 2 ^ (- 3k - j - (k ...
half imp
how do you think this works
willow bridge
what have you tried?
agile arch
- Evaluate the double series
sum j = 0 to โ sum k = 0 to โ 2 ^ (- 3k - j - (k + j) ^ 2)
This double sum
vast shale
!status
vocal sleetBOT
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
is this your series?
agile arch
Yes
vast shale
okay i will think
vast shale
are you supposed to prove or say that this converges or diverges??
vocal sleetBOT
@agile arch Has your question been resolved?
vocal sleetBOT
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tulip sleet
Need help with this one:
vocal sleetBOT
Need help with this one:
tulip sleet
$$\lim\limits_{x \to 1} x^{\frac{1}{x^2-1}}$$
twin meteorBOT
rainy
left lichen
1^inifnity form
tulip sleet
would it be smart to take ln ?
vast shale
firstly i think you are meant to assume the right handed limit of this
but substitute x = 1/(x^2-1)
autumn stratus
would it be smart to take ln ?
not when the base is one. will give you infinity times 0
left lichen
the answer is e^0 then?
tulip sleet
thats my answer
left lichen
thats my answer
yes
left lichen
this part
tulip sleet
ohh ok
left lichen
np :)
vocal sleetBOT
@tulip sleet Has your question been resolved?
formal bronze
e * e = e ???
(*) est une L.C.I
vocal sleetBOT
e * e = e ???
(*) est une L.C.I
vocal sleetBOT
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austere dagger
What do u all think about ๐ฎ๐ณ mathematics?
vocal sleetBOT
What do u all think about ๐ฎ๐ณ mathematics?
worthy citrus
Try #discussion or #math-discussion
Not the kind of questions these channels are for sorry
vocal sleetBOT
@austere dagger Has your question been resolved?
worthy citrus
.close
vocal sleetBOT
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zinc quail
does that condition mean AND or OR
vocal sleetBOT
does that condition mean AND or OR
granite oxide
and
vocal sleetBOT
hard atlas
how dare you
thin root
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@grim hollow Has your question been resolved?
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vast shale
is x!y!=z!w! = xy=zw ?
vocal sleetBOT
is x!y!=z!w! = xy=zw ?
hard atlas
what are x,y,z,w and !
plain minnow
what are x,y,z,w and !
! is factorial ig
keen herald
Yeah
plain minnow
x!y! is definitely not equal to xy
ig they are asking
lapis marten
I think they meant x!y!=z!w! <=> xy=zw
plain minnow
yea
lapis marten
but that's not true
vast shale
ok thank u
plain minnow
frfr
keen herald
If you plug in random values like 2,3, 4,5 then it shouldn't be true because 2!3! โ 4!5!
lapis marten
$3 \cdot 2 = 6 \cdot 1$, but $3! \cdot 2! \neq 6! \cdot 1!$
twin meteorBOT
Jelle
vast shale
how to simpilfy this eq
lapis marten
is r an integer?
vast shale
is r an integer?
yes
lapis marten
Well 25 - 4r >= 0
and you can probably do some more bounding
(r + 20)! seems large
also look at primes like 17, 19 or 23
vast shale
thats the original question
dapper crater
Bro
there could be only 2 cases
4r=5-r
or 4r+5-r=25
From 4r+5-r=25 we get r=20/3 not possibld
lapis marten
Just look at 19
dapper crater
hence 4r=5-r , r=1
lapis marten
it has to appear in LHS, so in the RHS as well
vast shale
why
vast shale
<enumitem>
\usetikzlibrary{angles, shapes}
Suppose a second-order casual LTI system has been designed with real impulse response $\bm{h_1}n$ and a rational system function $\m{H_1}z$. The pole-zero plot for $\m{H_1}z$ is shown in Figure (a). Now consider another casual second-order system with impulse response $\bm{h_2}n$ and rational system function $\m{H_2}z$. The pole-zero plot for $\m{H_2}z$ is shown in Figure (b). Determine a sequence $\bm gn$ such that the following three conditions are held:
\env{enumerate}{
\ii $\bm{h_2}n = \bm gn \bm{h_1}n$
\ii $\bm gn = 0 \tqs{for} n > 0$
\ii $\ds \sum_{k=0}^\infty \abs{\bm gk} = 3$
}
\env{center}{
\env{tikzpicture}{
\foreach \a/\b/\n in {0/0/A, 3/0/B, 1.414/1.414/C, -1.414/1.414/D, -3/0/E, 1.414/-1.414/F, -1.414/-1.414/G} {
\coordinate (\n) at (\a,\b);
\ifthenelse{\NOT\equal{\n}{F} \AND \NOT\equal{\n}{G} \AND \NOT\equal{\a}{0} \AND \NOT\equal{\a}{3} \AND \NOT\equal{\a}{-3}}{
\draw [dotted, thick] (0,0) -- (\n);
}{}
}
\draw[->] (-5,0) -- (5,0) node[right] {$\mathfrak{Re}$};
\draw[->] (0,-5) -- (0,5) node[above] {$\mathfrak{Im}$};
\draw [thick] (0,0) circle [radius=3];
\draw [dotted, thick] (0,0) circle [radius=2];
\pic [draw, <->, "$\frac{\pi}{4}$", angle eccentricity=1.5, angle radius=1cm] {angle = B--A--C};
\pic [draw, <->, "$\frac{\pi}{4}$", angle eccentricity=1.5, angle radius=1cm] {angle = D--A--E};
\node[draw, cross out, thick, inner sep=3pt] at (D) {};
\node[draw, circle, thick, inner sep=3pt] at (C) {};
\node[draw, cross out , thick, inner sep=3pt] at (G) {};
\node[draw, circle, thick, inner sep=3pt] at (F) {};
\node at (1.7,-0.4) {$\frac{3}{4}$};
\node at (3.2,0.2) {$1$};
\node at (0,-5.5) {Figure (a)};
\begin{scope}[shift={(13,0)}]
\foreach \a/\b/\n in {0/0/A, 3/0/B, 1.0605/1.0605/C, -1.0605/1.0605/D, -3/0/E, 1.0605/-1.0605/F, -1.0605/-1.0605/G} {
\coordinate (\n) at (\a,\b);
\ifthenelse{\NOT\equal{\n}{F} \AND \NOT\equal{\n}{G} \AND \NOT\equal{\a}{0} \AND \NOT\equal{\a}{3} \AND \NOT\equal{\a}{-3}}{
\draw [dotted, thick] (0,0) -- (\n);
}{}
}
\draw[->] (-5,0) -- (5,0) node[right] {$\mathfrak{Re}$};
\draw[->] (0,-5) -- (0,5) node[above] {$\mathfrak{Im}$};
\draw [thick] (0,0) circle [radius=3];
\draw [dotted, thick] (0,0) circle [radius=1.5];
\pic [draw, <->, "$\frac{\pi}{4}$", angle eccentricity=1.5, angle radius=0.8cm] {angle = B--A--C};
\pic [draw, <->, "$\frac{\pi}{4}$", angle eccentricity=1.5, angle radius=0.8cm] {angle = D--A--E};
\node[draw, cross out, thick, inner sep=3pt] at (D) {};
\node[draw, circle, thick, inner sep=3pt] at (C) {};
\node[draw, cross out , thick, inner sep=3pt] at (G) {};
\node[draw, circle, thick, inner sep=3pt] at (F) {};
\node at (1.2,-0.4) {$\frac{1}{2}$};
\node at (3.2,0.2) {$1$};
\node at (0,-5.5) {Figure (b)};
\end{scope}
}
}
vast shale
But I am unsure how to go from here. how do i recover the sequence?
idk how u r meant to satisfy the conditions
vast shale
A and B are arbtrary constants
dapper crater
you wrote that much
cobalt crypt
typoh 
twin meteorBOT
cobalt crypt
[ H_2(z) = (G * H_1)(z) ]
twin meteorBOT
cobalt crypt
you get this then i guess?
vast shale
yeah already did that
cobalt crypt
can you find G from that 
cobalt crypt
,w expand (z - 3/4 e^(ipi/4))(z - 3/4 e^(-ipi/4))
wtf it doesnt give me the real form
[ \f {16 - 12\s2 z^{-1} + 9z^{-2}} {16 + 12\s2 z^{-1} + 9z^{-2}} ]
vast shale
ok back sorry
flat whale
smh using j
cobalt crypt
its signal processing smh
twin meteorBOT
vast shale
like uh
cobalt crypt
vast shale
what's happening here
flat whale
im an electrical engineer come on <:Xd:1080574714939965471>
Blocked /s
cobalt crypt
[
H(z) = \sum_{n \in \Z} h[n] , z^{-n}
\Implies
z^{-m} , H(z) = \sum_{n \in \Z} h[n - m] , z^{-n}
]
twin meteorBOT
twin meteorBOT
vast shale
wair
wair
snow
doesnr it simplify to like
[
\m{H_2}z = \f BA\m{H_1}{\f32 z e^{j\pi}} = \f BA \m{H_1}{-\f32 z}
]
twin meteorBOT
cobalt crypt
[
\sum_{n \in \Z} h_2[n] , z^{-n} = H_2(z) = k \map {H_1} {\f32z} = \sum_{n \in \Z} h_1[n] , k \parens {\f23}^n z^{-n}
]
vast shale
i think it does something to this
vast shale
\[
\sum_{n \in \Z} h_2[n] \, z^{-n} = H_2(z) = k \map {H_1} {\f32z} = \sum_{n ...
[
\bm {h_2}{n}= \f BA \p{-\f23}^n\bm{h_1}n
]
twin meteorBOT
median crane
vocal sleetBOT
@vast shale Has your question been resolved?
vast shale
wait ill read in a b8t
worthy citrus
still tying his shoelace
vocal sleetBOT
@vast shale Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
civic viper
vocal sleetBOT
civic viper
pls help w/ this question
lapis marten
try substituting a_n = Bb_n + Cc_n
dull bear
You know that $b_n = \alpha b_{n-1} + \beta b_{n-2}$ and $c_n = \alpha c_{n-1} + \beta c_{n-2}$. Setting $a_n = B b_n + C c_n$, then do you get similarly $a_n = \alpha a_{n-1} + \beta a_{n-2}$
twin meteorBOT
@dull bear
civic viper
Does ${b_n}$ indicate that $b_n = \alpha b_{n-1} + \beta b_{n-2}$?
lapis marten
yes
lapis marten
If you replace a_n with b_n the first equation should hold
twin meteorBOT
anirudh
civic viper
If you replace a_n with b_n the first equation should hold
Cool thanks
vocal sleetBOT
@civic viper Has your question been resolved?
hushed quest
When dealing with domain and range of a function, Iโm having trouble understanding when it is either 0 or -/+ infinity. Specifically range.
For example, take f(x) = 4e^x
I know domain deals with the x axis and range y, and so the domain is (-infinity, infinity) and the range is (0, infinity)
But why is it (0, infinity) and not (-infinity, infinity)?
Is it because when the line touches 0 you stop it there? Why instead of keep going?
Or take g(x) = 3(1/2)^x
Yes, the range is (0,infinity)
Is it again 0 because it touches the y-axis at (0,3)? Then shouldnโt the infinity also be zero (0,0) by following the logic of the previous functionโs first zero? Since it will eventually cross the x-axis and stop?
vocal sleetBOT
When dealing with domain and range of a function, Iโm having trouble understandi...
hushed pewter
When dealing with domain and range of a function, Iโm having trouble understandi...
Because the y value of y=e^x will never 0 or negative
The function never touches zero
river wagon
The range of 4e^x is all the values 4e^x can take. Give me a positive number y and I can give you a number x such that 4e^x=y. However, if you give me a negative number, I wont be able to do that.
hushed pewter
That's why the range is (0, infty), not [0, infty)
hushed pewter
The range of 4e^x is all the values 4e^x can take. Give me a positive number y a...
Or 0
royal grotto
44/378
vocal sleetBOT
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vast shale
are truth tables a valid way in proving boolean algebra theorems?
vast shale
my book says they are, but idk if they r just waffling
worthy citrus
Why wouldn't they be
vast shale
dunno doesnt seem like they are relying on the axioms/postulates
urban edge
Proof by casework basically
solar barn
boolean algebra can be said to be propositional logic. Propositional logic is decidable, meaning that each theorem in it can be determined true or false by using an algorithm, namely the truth tables.
river minnow
Sometimes you can do it with just consideration of cases for just one variable rather than all
vast shale
aight thanks yall
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wide sundial
Hii, could someone help me with this?
vocal sleetBOT
Hii, could someone help me with this?
wide sundial
I guess A works because 2 is the lowest value so "at least 2" would imply that all values are >= 2
I guess C works otherwise the highest value wouldn't be 10
How to show B? 
solar barn
If I remember correctly, the line at the middle of the box marks the median. If that is the case, then the median amount of eggs laid daily is 6.
The median is computed by ordering all elements in ascending (or descending) order and 'picking' the one on the middle.
Since there are 30 days (an even amount of data inputs), then the median is computed by taking amount laid in day 15 + laid in day 16 divided by 2. This means that either 6 were laid on both days or more than 6 were laid on day 16.
Regardless of this, at least the 15 biggest inputs are at least 6. This would make B. true by my reasoning.
brisk moss
sounds good to me
wide sundial
If I remember correctly, the line at the middle of the box marks the median. If ...
oh yeah that's a decent reasoning
thanks
livid turtle
vocal sleetBOT
livid turtle
i dont know what to do
solar barn
What does it entail for both triangles KJM and OPR to be similar?
Similar is basically that they have the same proportions.
solar barn
yes
solar barn
you can do the same for the angle at the vertex M (matches with R) and K (matches with O).
livid turtle
but there is nothing at O
solar barn
It is not explicit in the image what O is, but you can find out. There is a property the the inner angles of all triangles fulfill, which you need to use to find out what O is.
livid turtle
what do i do when i alr found at that 60/x+10=40/0.3-20
solar barn
How did you get that equality?
livid turtle
rations
solar barn
ratios work for the sides, not angles. For x you solve x + 10 = 60, for z you solve 0.3z-20=40
livid turtle
oh wait i can do them alone
solar barn
Yes.
solar barn
After solving them, you need to find out what the angle at O is.
solar barn
Indeed.
solar barn
So now you find y.
livid turtle
Which is 200
solar barn
Okay, you've got x, y and z, now input those in the fraction.
livid turtle
450/2
solar barn
which is...
livid turtle
225
solar barn
Yes, correct, that would be the answer to the problem.
livid turtle
wait i did it wrong
livid turtle
180-100
Right here
i accidentally did 1/2y=100 not 1/2y=80 which is correct
so its 205
mb
.close
austere dagger
Is there any easy way to study maths
vocal sleetBOT
Is there any easy way to study maths
austere dagger
Can everyone suggest something
median harbor
trim walrus
sup
vocal sleetBOT
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vocal sleetBOT
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hollow thorn
vocal sleetBOT
hollow thorn
Hi there can somebody teach me this part ?
paper depot
!status
vocal sleetBOT
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
empty dove
i don't understand ur question do you have other corrected exercises about this? @hollow thorn
hollow thorn
i don't understand ur question do you have other corrected exercises about this?...
How bout this?
river minnow
Have you tried doing the polynomial division?
hollow thorn
hollow thorn
Have you tried doing the polynomial division?
Yup i did this so far
river minnow
I am talking about the first problem that you have sent
hollow thorn
Am i correct? I have no ans for this ๐ข
empty dove
equals to what ? 0 i guess
hollow thorn
I am talking about the first problem that you have sent
owh that one i have no idea where to begin first at all
river minnow
,w polynomial division 2x^5 + 6x^4 + x^3 + 4x - 2 by x^2 + 3x - 1
twin meteorBOT
river minnow
Let's see
hollow thorn
let me try
hollow thorn
does this question able to solve by synthetic division method ?
river minnow
The first or second?
hollow thorn
Oh i did it quotient is 2xยณ + 3x -9 , remainder is 34x - 11
hollow thorn
alright left one more question for it
river minnow
Right, try doing polynomial division here too
hollow thorn
Im here
hollow thorn
Right, try doing polynomial division here too
hollow thorn
Should be -16x^2
alright i recheck everything
river minnow
Right, so you are getting the remainder (m - 43)x + n + 52
Since 4x^4 - 11x^3 + mx + n should be divisible by x^2 - 3x + 4, the remainder should be zero
river minnow
Right, so you are getting the remainder (m - 43)x + n + 52
Meaning both of the coefficients here should be 0
hollow thorn
Meaning both of the coefficients here should be 0
first , 4xโด-11xยณ+ mx + n = 0 second , (m - 43)x + n + 52 = 0 ?
river minnow
4xโด-11xยณ+ mx + n = 0 is true modulo x^2 - 3x + 4, yeah, but you can forget about that
Just focus on the fact that (m - 43)x + n + 52 should be the zero polynomial
hollow thorn
Just focus on the fact that (m - 43)x + n + 52 should be the zero polynomial
i should do simul equation ?
river minnow
Yeah, m-43 = 0 and n+52 = 0
merry flame
A = {( (3n+2) / (n+5) ) โฃ nโN}
Sup(A) = ?
max(A) = ?
how do I explain that the equation approaches 3 and use that to prove that 3 is the least upper bound?
vocal sleetBOT
A = {( (3n+2) / (n+5) ) โฃ nโN}
Sup(A) = ?
max(A) = ?
how do I explain that the ...
dry yacht
Using limits.
merry flame
cant
we didnt cover that in any lecture
dry yacht
Do you mean that you haven't learned limits from the lectures, or that limits aren't mentioned in lectures?
Since natural numbers goes to infinity.
lucid bane
you can rewrite A more clearly to see it is a monotone function from N to Q
worthy citrus
Yeah you don't need limits to find a supremum
worthy citrus
Yeah you don't need limits to find a supremum
Atleast not explicitly. One option for you is to rewrite the expression into a form where its easier to see what happens as n gets big
lucid bane
$\f{3n+2}{n+5}=\f{3n+15-13}{n+5}=$
twin meteorBOT
๐ซMฮฟฮฟsey๐ซ:
lucid bane
a first step :)
merry flame
you can rewrite A more clearly to see it is a monotone function from N to Q
im not sure if i know how to do that
since the only time I heard teh term was at discrete so far
$\f{3n+2}{n+5}=\f{3n+15-13}{n+5}=$\f{3{n+5}{n+5} - \f{13}{n+5}=$\f{3{n+5}{n+5} - \f{13}{n+5} tried
twin meteorBOT
RainbowFireBeast
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
merry flame
3 - (13)/(n+5)
then bcs n is in the denominator -> therefore, - (13)/(n+5) is insegnificent? no matter how big n is bcs the "sub-equasion" approaches 0?
therefore the equation approaches 3 but will never be 3
=> 3 is an upper bound but not the max element
merry flame
a first step :)
is that enough to show that sup(A) = 3?
vocal sleetBOT
@merry flame Has your question been resolved?
merry flame
<@&286206848099549185>
vocal sleetBOT
@merry flame Has your question been resolved?
vocal sleetBOT
@merry flame Has your question been resolved?
amber kraken
**๐ซMฮฟฮฟsey๐ซ:**
using this , we have $3-\frac{13}{n+5}$ to frame A .
twin meteorBOT
Natural7
vocal sleetBOT
@merry flame Has your question been resolved?
strong jetty
vocal sleetBOT
strong jetty
which way is correct for integral?
tawny nacelle
you need to factor the constant 1/2 out before integrating the polynomial x^4
strong jetty
what does this mean
tawny nacelle
int(1/2 * x^4) = 1/2 * int(x^4) = 1/2 (1/5 * x^5) + C
strong jetty
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
misty surge
near vault
hi, im a little confused on this proof... could someone please explain the steps in detail?
https://math.stackexchange.com/questions/1825222/trigonometry-geometry
vocal sleetBOT
hi, im a little confused on this proof... could someone please explain the steps...
vocal sleetBOT
misty surge
can anyone explain why the integral was broken down to two integrals
near vault
.close
vocal sleetBOT
Available help channel!
mighty stone
help?
flat whale
Show your work, and if possible, explain where you are stuck.
Explain where you are stuck
mighty stone
> Explain where you are stuck
is my answer correct?
mighty stone
An answer would be a number
ohh yea let me solve it rq
@flat whale is it .3?
wait but thaat makes no sense
acoustic herald
8+x = 0.4(25+x)
twin meteorBOT
Result:
0.41379310344828
Did you check
mighty stone
Did you check
i did but still, ur making me double check
flat whale
i did but still, ur making me double check
You didn't answer me
mighty stone
You didn't answer me
yea i checked
flat whale
Then yes
misty siren
hi
misty siren
not yet
hushed pewter
not yet
Open a channel when you have a question
If you want to talk casually, go to #chill
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
keen plank
I need help because I'm not sure if I'm finding the area of this triangle correctly
vocal sleetBOT
I need help because I'm not sure if I'm finding the area of this triangle correc...
keen plank
so I know I have to multiply the base with the height (has to be perpendicular), but I'm not sure if multiplying 7ft and 7ft getting 49 then dividing by 2 would be the answer. Mostly because it comes back with a decimal
can anyone confirm if I did that wrong or not
lone linden
yeah, it's just $\frac{7 \cdot 7}{2}$
twin meteorBOT
Civil Service Pigeon
lone linden
Just because an answer is a decimal doesn't mean it's wrong
same thing with fractions, those can be valid answers too
keen plank
ok thanks for confirming Ill see if I get it right
yeah I got it righ thanks for confirming
soft walrus
just becuase a decimal shows up doesn't mean an answer is inherently more incorrect!
deciamls are not your enemies :) any integers also has decimals
7=7.0
keen plank
ok thanks, just was curious because it was the first question with an actual decimal answer
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
frail jungle
vocal sleetBOT
frail jungle
A and B are given, A/B is to be calculated
icy spear
start by writing out the first few terms
frail jungle
A = 1/2 + 1/2^3 + 1/2^5 ...) + 1/4^2 + 1/4^4 ...
icy spear
great
let's call A = A1 + A2
split the series into 2 series
A1 = 1/2 + 1/2^3 + 1/2^5
A2 = 1/4^2 + 1/4^4 + ...
let's find a closed form for A1
1/2 (1 + 1/2^2 + 1/2^4 + ...) =
1/2 (1 + 1/4 + 1/4^2 + ...)
frail jungle
let's find a closed form for A1
closed ?
sorry i was afk mb
i used sigma of GP on them
a/1-r
icy spear
a closed form for a sum is a number or formula for it
frail jungle
which becomes, 1/2 / 1-1/4 + 1/16 / 1 - 1/16 = 1/2 / 3/4 + 1/16 / 15/16
so A becomes 11/15
frail jungle
a closed form for a sum is a number or formula for it
fancy words
i got A right
but i am got B wrong so here i go
B = -1/2 - 1/2^3 - 1/2^5...) + ( 1/4^2 + 1/4^4 ...)
so
-1/2 / 1 + 1/4 ] + [ 1/15
so r for -1/2.. is -1/4
is this correct
frail jungle
-1/2 / 1 + 1/4 ] + [ 1/15
so -1/2 / 5/4 = -2/5 ] + 1/15
so B = -5/15
@icy spear can u confirm this
vocal sleetBOT
@frail jungle Has your question been resolved?
frail jungle
<@&286206848099549185>
vocal sleetBOT
@frail jungle Has your question been resolved?
vocal sleetBOT
<#903463353417072641>
void harbor
x= 75
y= 15
twin meteorBOT
void harbor
QOR is an equilateral triangle, so all its angles are 60ยฐ.
Angle PQR=90ยฐ PQO=PQR-POR=90-60=30
PQO is an isosceles triangle. Angle PQO=30ยฐ so 180-30=150 x=150/2=75
QPS=90ยฐ PQO=75ยฐ y= QPS-PQO= 90ยฐ-75ยฐ=15ยฐ
knotty pendant
@upbeat light Have you started this question at all?
vocal sleetBOT
@upbeat light Has your question been resolved?
vocal sleetBOT
desert hornet
what is Y?
scenic ravine
is that $sec^{ฯ}$?
teal apex
Yess
desert hornet
I meant, I couldn't see what is writtedn
dapper jay
looks hindi to me
scenic ravine
!occupied
vocal sleetBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #โhow-to-get-help for instructions).
teal apex
looks hindi to me
Bilkul
desert hornet
$x=\sec\theta-\cos\theta, y=\sec^n\theta-\cos^n\theta$, then find $(x^2+4)(\frac{dy}{dx})^2$
twin meteorBOT
kheerii
desert hornet
is that correct?
teal apex
Correct
twin meteorBOT
kheerii
teal apex
dy/dx = n sec(n-1) theta(tan thetaรsec theta)+n cos^(n-1) theta (sin theta)
desert hornet
dy/dx = n sec(n-1) theta(tan thetaรsec theta)+n cos^(n-1) theta (sin theta)
why arcsec?
scenic ravine
Kind of stupid, but how would I got about manually plotting $\frac{1}{x}-\frac{1}{y}=c$
vocal sleetBOT
Kind of stupid, but how would I got about manually plotting $\frac{1}{x}-\frac{1...
twin meteorBOT
Why am. I here
scenic ravine
I tried isolating variables but that didn't help much
scenic ravine
you cant get it interms of x?
I did, I got $\frac{y}{cy+1} =x$
twin meteorBOT
Why am. I here
scenic ravine
OK, that would be $\frac{x}{1-cx}$ how would I manually plot that?
twin meteorBOT
Why am. I here
scenic ravine
Don't really need the plot tbh
how do I identify the general shape
I had a similar problem in an exam todaym and I messed it up, hence the question
dapper jay
you can try decomposing it
scenic ravine
how?
dapper jay
actually you dont have to
try doing polynomial division maybe?
actually
that wont work
actually
no it will
tribal moss
how do I identify the general shape
firstly, according to the initial equation, all points from the lines x = 0 , and y = 0 should be removed, and then three cases should be considered, c=0, , c>0, and c<0. The last two concern the graph of the homographic function = a rational function that is the quotient of two linear functions,
scenic ravine
The last two concern the graph of the homographic function = a rational function that is the quotient of two linear functions,
could you explain this please
dapper jay
do you want to plot a c axis too?
tribal moss
could you explain this please
A homographic function is a function its graph is a hyperbola, it has one vertical and one horizontal asymptote, read about it
scenic ravine
I see, thanks!
scenic ravine
do you want to plot a c axis too?
no, c is a constant, thanks nonetheless
obsidian stream
The way you would usually do this problem is either using Calculus and treat it as a plot sketching problem, or to use high school function transformations to build it up from an image you already know how to draw.
teal apex
So xy=c is hyperbola
obsidian stream
In the case of c = 1, you can do the rest, you can see that 1/(x+1) - 1 = x/(1-x). If you know the graph of y = 1/x, then 1/(x+1) - 1 is just a shifted graph of that.
teal apex
If you understand hindi i would love to understand the whole thing again
scenic ravine
yes, that's the question. Unfortunately I don't know much hindi, sorry
teal apex
Hmm it's okay so what will we do next?
livid horizon
What's the question again? I'm not sure I understand
vast shale
What exactly is the benefit of representing gates of a circuit by NAND or NOR gates entirely?
vocal sleetBOT
What exactly is the benefit of representing gates of a circuit by NAND or NOR ga...
limber halo
There is no benefit
limber halo
It's neat because you can compose all other logic from nand
vast shale
well all binary logic that is right?
you still like uh
inverters for the unary operations
limber halo
You can make a not gate from nand
urban edge
you can NOT a single input by directing the signal to both inputs of a NAND
urban edge
i forget how the shapes work
vast shale
the fat one is and
the curvy one is or
the triangle is invert
the bubbles denote complementing the thing
anyways
can you classify x', y' as inputs like that?
urban edge
im probably not the right person to be saying things about this, sorry
vast shale
maybe because you can get these easily with transistors
yeah this is not the place to ask about this
thanks
.close
trim mountain
Maximize the given objective function using a genetic algorithm
f(x)=x^2+2 where x ฯต (0,22)
vast shale
!show
vocal sleetBOT
Show your work, and if possible, explain where you are stuck.
trim mountain
i am not able to comprehend this well
vast shale
do you know how a genetic algorithm work
trim mountain
yes
vast shale
okay so whats the confusion
also is there more information
crossover type for example
trim mountain
okay
so how will i be choosing the population for this
like from 1 or 0 should i begin
vocal sleetBOT
@trim mountain Has your question been resolved?
teal apex
vocal sleetBOT
solar barn
A vector space needs to fulfill some properties, which are those?
teal apex
Additive, multiplicative
solar barn
Okay, what are the additive properties to be fullfilled?
Or rather, there is another property which you haven't mentioned
which is connected to the addition in the vector space
teal apex
you meant internal external operations
twin meteorBOT
Crystopher
teal apex
So we need to look up that vector in this question too
solar barn
It should be straightforward, can you come up with a vector $\vec{u}$ sucht that $\vec{v}+\vec{u}=\vec{v}$ if $\vec{u}, \vec{v}\in \mathbb R^3$?
twin meteorBOT
Crystopher
teal apex
Here you meant vector u is 0
solar barn
yes
teal apex
2x1-x2+3x2 =k
Actually i am not understanding x1, x2,x3 and what i have to do it
Should i add x1+x2
2(x1+x2)-(x1+x2)+3(x1+x2)=k
solar barn
Imagine $\vec{x}=\begin{pmatrix}x_1\x_2\x_3\end{pmatrix}$
twin meteorBOT
Crystopher
teal apex
Ohh then there will be (0,0,0) for sure
solar barn
If we wanted $W$ to be a vector space, then $\vec{0}=\begin{pmatrix}0\0\0\end{pmatrix}\in W$, yes
twin meteorBOT
Crystopher
solar barn
How do we know if $\vec{0}$ is in $W$?
twin meteorBOT
Crystopher
teal apex
How do we know if $\vec{0}$ is in $W$?
Umm no idea
Should i put 0,0,0 in the equations
And k=0 too
twin meteorBOT
Crystopher
solar barn
Ye, assumming $W$ is a vector space, then we need some additive neutral element $\vec{0}$ that fullfills the equation.
twin meteorBOT
Crystopher
solar barn
Correct, if $k \neq 0$, then $\vec{0}$ would never satisfy the equation.
twin meteorBOT
Crystopher
teal apex
Absoultely
So here we strictly want k=0 to vector space
2x1-x2+3x3=0 create a vector space
I guess yes. If we put any x1,x2,x3 it will make a space
solar barn
yes, all other properties are basically trivially true. To sum up, to know if a set of vectors is a vector space you most likely need to check if a zero vector exists and if vector addition and scalar multiplication fullfill the desired properties.
The multiplicative and additive properties are generally always true in $\mathbb R^n$ so at most you may need to see if $\vec{0}$ is in the set.
twin meteorBOT
Crystopher
teal apex
You explained it to me so easily
I only read definitions
But I understand now how they ask questions
May i know which book did you read for linear algebra?
Or you wathed video
solar barn
I have already read linear algebra at uni, I mostly attended lectures and didn't touch the books. What I did start watching, but never finished, was 3blue1brown linear algebra series.
They were quite good, explained the intuitive side of linear algebra.
hoary cypress
what is lim (1/n)^n (n tends to 0)?
vocal sleetBOT
what is lim (1/n)^n (n tends to 0)?
sullen mural
vast shale
!occupied
vocal sleetBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #โhow-to-get-help for instructions).
vast shale
what is lim (1/n)^n (n tends to 0)?
it's 1
vocal sleetBOT
it's 1
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
sullen mural
Someone else is already using this help channel. If you need help with a questio...
I donโt need help
vast shale
replace t = 1/n and you will get lim (t-> inf) t^(1/t) which is easy to prove
teal apex
It is infinity^0 term
vast shale
yes
teal apex
My method is right?
vocal sleetBOT
@hoary cypress Has your question been resolved?
vast shale
replace t = 1/n and you will get lim (t-> inf) t^(1/t) which is easy to prove
here is explanation
teal apex
replace t = 1/n and you will get lim (t-> inf) t^(1/t) which is easy to prove
How to prove it?
vast shale
if @hoary cypress doesn't understand, i will tell
vast shale
replace t = 1/n and you will get lim (t-> inf) t^(1/t) which is easy to prove
? idk what you are getting at here because i dont see how you are meant to bound that (using squeeze theorem before you edited)
easiest way is to solve it is [
\lim_{t \to \infty} \exp \parens [\bigg] {\f1t \log t} ]
twin meteorBOT
vast shale
which then you can substitute u = log(t) and the convergence of the limit becomes clear
(this is assuming you dont want to use either Taylor or l'hopital, both being very direct solutions)
vocal sleetBOT
@hoary cypress Has your question been resolved?
teal apex
d=0
c=+-6
a=+-5
b=+-1
vocal sleetBOT
d=0
c=+-6
a=+-5
b=+-1
vast shale
how many do you think
gritty sage
