very good question
#help-19
odd edgeBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
zenith jasper
what **is** (dx)^3?
does that exist mathematically?
wooden python
i personally know of no such notation in common use
zenith jasper
i think ive only seen that notation in physics
wooden python
@outer saffron show us a picture of the original problem
odd edgeBOT
@outer saffron Has your question been resolved?
outer saffron
tender lagoon
,rotate
clever fjordBOT
tender lagoon
Then diff both side with respect to x^3
You get
dx^3 = dt
Then
x^3 = t => x = t^(1/3) => (x)^(1/2) = (t)^(1/6)
Then sub in
int from 0 to 3 of t^1/6 dt ```Should do it 
zenith jasper
```you can let x^3 = t
Then diff both side with respect to x^3
You get
dx^3 = ...
just curious, does that mean d(x^3)
tender lagoon
Yes
wooden python
so then 3x^2 dx
outer saffron
Yes true
6/7× {t^7/6}
6/7 ×{3^7/6}
Ohh no i am wrong
Limit will be changed
0 to 27
6/7 × 27 × 27^(1/6)
162√3/7
Thanks basudev
.close
echo knot
odd edgeBOT
echo knot
I have to prove this limit using the epsilon delta definition
Basically I did it like this
I am getting (e/2)-5
While the textbook says it's just e/2
Where did I go wrong?
Ahh wait shit nvm
.close
mystic saffron
not really understanding the lemma here
odd edgeBOT
not really understanding the lemma here
mystic saffron
if w1.. wm are LI how are they in the span of v1 .. vn ?
i thought if a vector is in the span of some vectors they must be LD?
open onyx
i thought if a vector is in the span of some vectors they must be LD?
this sounds like you're confusing ideas
if a vector v is in the span of some set of vectors S then S U {v} (adding v to the set S) would become linearly dependent set
it does not mean v itself is linearly dependent, in fact that's usually a crazy claim to say a single vector is linearly dependent
odd edgeBOT
@mystic saffron Has your question been resolved?
mystic saffron
this sounds like you're confusing ideas
if a vector **v** is in the span of som...
but if all of w1.. wm exist in the span of v1 to vn
then would w1... wm not be linearly dependant with each other? or would each vector be linearly dependant with v1... vn
open onyx
then would w1... wm not be linearly dependant with each other? or would each vec...
the set of vectors {w1, w2, ..., wm} are linearly dependent as an assumption given by the lemma
the important part is that the set {v1, ..., vn} is not assumed to be a linearly independent set
mystic saffron
ohh
i think im following now
also do all non square matrices have a row of 0s in RREF form
mystic saffron
no, the matrix [0 1] does not
is there a reason why?
odd edgeBOT
is there a reason why?
mystic saffron
cz like if u had lots of more vectors than the basis vectors needed to span a vector space then wont they be linearly dependant to each other?
odd edgeBOT
@mystic saffron Has your question been resolved?
gleaming hedge
If we have this matrix
odd edgeBOT
If we have this matrix
devout sapphire
f(x) = ax^2 + 9x + 12, what is a if the minimum of f(x) = -8. i think my answer of 81/80 is right.
devout sapphire
Just wanna see if someone can double check as i often dont notice the mistakes in my own work
devout sapphire
Ty
zenith jasper
d/dx f(x) = 0, x = -9/2a, sub that in the function and set that to = -8
devout sapphire
.close
hazy furnace
This dont make sense, isnt d supposed to be 3,6
odd edgeBOT
This dont make sense, isnt d supposed to be 3,6
dull fossil
hazy furnace
ohhhhhhhhhhhhhhhhhhhhhhhhhhh
cyka
i didnt see the not divide
thank u .
.close
ember moth
Are all the fractals continuous but non-differentiable (when they viewed as functions)?
odd edgeBOT
Are all the fractals continuous but non-differentiable (when they viewed as func...
@ember moth Has your question been resolved?
ember moth
<@&286206848099549185>
slow sandal
@ember moth google the weirstrass function
odd edgeBOT
@ember moth Has your question been resolved?
shut wigeon
Helloo guys can you give me an example of a word problem about rational equation? I'm having troubles on solving it and there is no enough examples in the internet please provide the solutions as well, tnxx in advance!
wooden python
here is a somewhat silly one:
What number must be added to the numerator and denominator of the fraction 1/7 to get a fraction equal to 1/2?
Should the numbers be the same when adding them to the numerator and denominator?
shut wigeon
Thanks!
shut wigeon
here is a somewhat silly one:
```
What number must be added to the numerator and...
I think I got the answer to this question
Is it 5?
wooden python
Should the numbers be the same when adding them to the numerator and denominator...
that is what i intended yes
wooden python
https://www.mathsisfun.com/fractions_addition.html
not actually relevant to my problem
yes the answer is 5
odd edgeBOT
@shut wigeon Has your question been resolved?
mental forge
what is happening here? 2c + c²
wooden python
close prev?
mental forge
you can close it
wooden python
wdym by "what's happening" tho
2c + c^2 is an expression
what do you want to do with it
plain badge
c(c+2) = 2c+c^2
mental forge
i understood it already in the other channel
mental forge
yes
distant umbra
how can I find theta?
odd edgeBOT
how can I find theta?
distant umbra
its basically a triangle with base L and height L
and its rotated by an angle theta
distant umbra
So it's 45-45-90?
yeaaa
basically this triangle is being rotated and we have some conditions
its a COM question but i fulfilled the conditions
quasi sparrow
how can I find theta?
What's the number inside the triangle
distant umbra
What's the number inside the triangle
you can ignore that. it shows the height of COM
distant umbra
What's the number inside the triangle
wait sorry
i thought you meant something else
its
quasi sparrow
Theta can be anything then
distant umbra
sqrt13/6 L
quasi sparrow
Find complementary angles inside the triangle in terms of theta
distant umbra
Find complementary angles inside the triangle in terms of theta
do you mean like this?
quasi sparrow
I'm not seeing enough information to determine theta precisely
distant umbra
I'm not seeing enough information to determine theta precisely
okay wait i will share the entire question and my working
if you have a generic triangle of base length L and height L
and its rotating about the point a
what would be the angle theta for the CoM (L/3 in the y direction) to be directly over point A
quasi sparrow
Well yea that's what you should have sent from the beginning
distant umbra
Well yea that's what you should have sent from the beginning
i am so sorry about that
this is what I did
i thought after this i had to do some geometry trick
to get theta
odd edgeBOT
@distant umbra Has your question been resolved?
distant umbra
<@&286206848099549185>
odd edgeBOT
@distant umbra Has your question been resolved?
distant umbra
@quasi sparrow I had a question. if we take the vector from A to COM then initially its L/2,L/3. then it becomes 0,sqrt13/6L. So can we say the angle with which it has rotated = angle with which the triangle has rotated?
odd edgeBOT
@distant umbra Has your question been resolved?
jovial bridge
so if the variable has those absolute lines around it, that means you need the negative and positive answer?
jovial bridge
i'm thinking the answer is 9, -9
idle violet
You’d be right
storm narwhal
hello
storm narwhal
i don't really know how to solve this question
im just kinda confused to how i should solve this
clever fjordBOT
storm narwhal
3389.5km is the radius of mars
and venus is 78.5% larger than mars
so i don't know if this works or not
but like 3389.5 times 0.785
then add the result with 3389.5?
oh
hallow pelican
that works but it's faster if you do it times 1.785
and then you don't have to add anything
hallow pelican
yes
hallow pelican
yes
storm narwhal
then it would be **6050.2575 times 1.053
hallow pelican
yep
odd edgeBOT
@storm narwhal Has your question been resolved?
untold kayak
odd edgeBOT
untold kayak
Need help understanding this don’t really get what’s going on was absent this day
<@&286206848099549185>
odd edgeBOT
@untold kayak Has your question been resolved?
silk ibex
any ideas?
odd edgeBOT
any ideas?
silk ibex
<@&286206848099549185>
odd edgeBOT
@silk ibex Has your question been resolved?
silk ibex
<@&286206848099549185> can anyone help?
odd edgeBOT
@silk ibex Has your question been resolved?
silk ibex
<@&286206848099549185> help!
odd edgeBOT
@silk ibex Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
odd edgeBOT
silk ibex
Im just totally helpless with this one, could anyone help?
quasi prairie
yes
wait
so
20% from 1125 is 225
that are the money you spend on energy
this money you can partially replace with use of renewable energy
and it will double
for example
200 for non-ren, and 25 you had will turn into 50 for renewable
and manufacturing price will be 1150
and share of non-ren energy will be 200/1150
second example, 150 for non-ren, 75 turn into 150 for renewable
price is 1200
share is 150/1200 = 1/8
and you want this number to be 1/10
silk ibex
Does this take the needed energy into account too? 🤔 I think you cant have excess energy
quasi prairie
and you don't have it
you had 225 euro worth of non-ren energy
and you want to spend x for non-ren
and (225-x)*2 for ren
quasi prairie
you have to spend more money on renewable energy
numbers are a little bit tought in this problem, as i counted
these are the numbers you should have as an answer
where 225 was the amount of money on energy, 1350/11 on non-renewable, 1125*2=2250 on renewable
and you get 13500/11 as manufacturing price, and 1350 is 1/10 of it
silk ibex
hmm the price seems too high since original price is 1125 though, i think it should be around 1125-2000 in the end
is it possible to form some sort of equation out of this? 225-x*2 sounds like it could be part of it
quasi prairie
silk ibex
ohh
quasi prairie
final price is 1227 3/11
yes, i had an equation, of course
x+2y+900 is final price
x+y is 225, amount of money you have on energy
but y multiplies by 2 for the final price
silk ibex
and y is the amount of money on renewable energy right?
silk ibex
how do you go on after x+2y+900=10x?
odd edgeBOT
@silk ibex Has your question been resolved?
tiny bobcat
This question has really thrown me, I know area of prism is 2(lw+lh+hw) but the height is a squared form and in cm and the length and width are in feet , I converted the feet to cm and it got messy
brittle beacon
This question has really thrown me, I know area of prism is 2(lw+lh+hw) but the ...
How did you do the conversions from ft to cm?
tiny bobcat
Chartbit!
Your alive
I did it down the bottom
Unit conversion
1 foot is 30.48 cm
And then I multiplied
Divided by one
Cha Ching im rich
brittle beacon
Ahh I see 
I'm happy with that then 
mind you, interesting they give you the sides in ft, maybe that is deliberate 
tiny bobcat
I didn’t think I could multiply cm with feet
brittle beacon
Becomes a bit more difficult to simplify if so, so I'm wondering 
brittle beacon
I didn’t think I could multiply cm with feet
Not without converting them first, but I suspect that the problem meant for the units to be the same, unless they've given stuff like that before(?) 
tiny bobcat
Well I can convert it it any style they want
But the numbers got really big so I stopped to check if I’m doing everything correctly
brittle beacon
But the numbers got really big so I stopped to check if I’m doing everything cor...
are you like supposed to type in an answer for this question?
tiny bobcat
Is has 4 options
brittle beacon
could you show the options please? 
tiny bobcat
brittle beacon
@copper quarry 
tiny bobcat
It’s not just me yea
brittle beacon
Thank you give me a second
brittle beacon
It’s not just me yea
yep 
I think they probably meant that height to be in ft rather than cm
Considering they indicate it as an equilateral triangle the height of that triangle would work out to be 4sqrt{3} ft
@tiny bobcat 
odd edgeBOT
@tiny bobcat Has your question been resolved?
tiny bobcat
Considering they indicate it as an equilateral triangle the height of that trian...
Ummm
brittle beacon
Ummm
Yea gonna say that they miswrote and it’s ft in the question throughout (so you don’t need to do any unit converting!)
Taking it that way you will also find one of the answers there too
tiny bobcat
Yea gonna say that they miswrote and it’s ft in the question throughout (so you ...
Thank you chartbit
brittle beacon
Yea they played you 
I was also wondering that it was pretty strange too they gave that 
tiny bobcat
Ahhh well you kno what atleast I was on the right path and used unit conversion
brittle beacon
Yep you could have done it both ways if it was different hopefully with that it’s easier to do now!
outer saffron
odd edgeBOT
outer saffron
i changed cos into sin
(1+cosx)1-cos^2x
1+cosx-cos^2x- cos^3x
What should I do next?
odd edgeBOT
@outer saffron Has your question been resolved?
timber dome
I would draw the graphs on each side.
lost helm
You don't actually need to solve anything I guess. Observe that $x+\frac{1}{x}\geq 2$, and $x^2+\frac{1}{x^2}=(x+\frac{1}{x})^2-2\geq 2$. But both $\sin$ and $\cos$ are less than or equal to $1$, so the equation can only hold where the equality holds, hence at $x=1$. Just check there
clever fjordBOT
Tardis
lost helm
Since it does not hold at x=1, there are no real solutions
outer saffron
For theta=90°
lost helm
cos(x/2) is not 1 there
outer saffron
Yes
Right
So both cos and sin will be max at 45°
Which will not equal to 2
So no real solution
odd edgeBOT
@outer saffron Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
odd edgeBOT
iron orchid
odd edgeBOT
iron orchid
please help me prove this
leaden karma
this should come directly from RMS>=AM
iron orchid
huh
leaden karma
do you know of the AM-GM inequality?
iron orchid
do you know of the AM-GM inequality?
not really
leaden karma
hmm.
iron orchid
but it is given that x,y,z are real numbers
leaden karma
that's one of the most fundamental inequalities you should know..
iron orchid
that's one of the most fundamental inequalities you should know..
so can u give the formula for that?
leaden karma
this is the extended version of the AM-GM inequality
it's known as the QM-AM-GM-HM inequality
iron orchid
I see
leaden karma
this only works for positive real numbers, except for the QM-AM inequality which is true for all reals
iron orchid
oh
leaden karma
you need to use this part of the inequality (the LHS is the AM (arithmetic mean) and the RHS is the QM or RMS (quadratic mean or root mean square))
leaden karma
no
iron orchid
then
leaden karma
take n=3, then $\frac{x+y+z}{3}\le \sqrt{\frac{x^2+y^2+z^2}{3}}$ by the RMS-AM inequality
clever fjordBOT
kheerii
leaden karma
squaring both sides and multiplying by 9 gives you your inequality
oblique rapids
ln2e^5= ln2 +lne^5 =ln(2)+5 how does lne^5 become 5 cus 1^5 isn’t 5
crisp wadi
Can you recall the definition of ln?
oblique rapids
Lne=1
crisp wadi
That's not the entire definition, but, sure, if you recall the log property that log(a^n) = n * log(a), then you have ln(e^5) = 5 * lne = 5 * 1 = 5
odd edgeBOT
@oblique rapids Has your question been resolved?
mystic saffron
is a linear model just a graph?
odd edgeBOT
is a linear model just a graph?
quasi sparrow
is a linear model just a graph?
No
quasi sparrow
what is it then?
Depends on the context
odd edgeBOT
@mystic saffron Has your question been resolved?
graceful zodiac
.close
rich crane
my question is a small part from a question so it's really short
wooden python
might wanna show the full question for context just in case tho
rich crane
in the solution they have written $\arg z=\text{Im}(\text{Log } z)=\text{Re}(-i \text{Log } z)$
clever fjordBOT
acex
rich crane
might wanna show the full question for context just in case tho
was writing it lmao
i do understand the first step
since $\text{Log }z=\log |z|+i\arg z$ but i don't understand how they did the second step
clever fjordBOT
acex
rich crane
if the full question is needed i'll show it but I think it's unnecessary
wet aspen
well what would $-i \text{Log } z$ equal
clever fjordBOT
Foxos
rich crane
it would equal $-i\log |z|+\arg z$ wouldn't it?
clever fjordBOT
acex
wet aspen
yeah
odd edgeBOT
odd edgeBOT
Available help channel!
mystic saffron
odd edgeBOT
mystic saffron
I kind of cheesed it for a) and just said [
F = A'BC+AB'C'+AB'C+ABC'+ABC
]
but is this fine or should i simplify it via a K-map first and then write out the thing
clever fjordBOT
crisp wadi
I mean you can simplify that without the K-map
mystic saffron
yeah but i guess its best to stick to a standardised method
oh well its not that bad its just a 2 by 4 k map ill just do it
mystic saffron
shouldnt it be C + AB
oh i mean arbtrary variables
doesnt matter
for b
i get like
[
F = C' + C'B' + CB
]
clever fjordBOT
mystic saffron
Oh wait
i included 0
<karnaugh-map>
\begin{karnaugh-map}[4][2][1][$AB$][$C$]
\minterms{1, 2, 4, 5, 7}
\implicant{4}{5}
\implicant{1}{5}
\implicant{2}{2}
\implicant{5}{7}
\end{karnaugh-map}
mystic saffron
this is kinda cursed
crisp wadi
Yeah
clever fjordBOT
mystic saffron
Hopefully i didnt fuck it up
crisp wadi
AB' + AC + A'BC' + B'C 
Let's see
,w truth table of ((not A) and C) or ((not A) or B) or (C and B) or ((not C) and A and (not B))
clever fjordBOT
mystic saffron
man K-maps feel like the l'hopital of boolean algebras i swear 
they make everything easier
crisp wadi
,w truth table of (A and (not B)) or (A and C) or ((not A) and B and (not C)) or ((not B) and C)
clever fjordBOT
mystic saffron
shy smelt
nvm
shy smelt
,w truth table of ((not A) and C) or ((not A) or B) or (C and B) or ((not C) and...
Isn't there a typo here?
should be ((not A) and B)
crisp wadi
Oh yeah there is
shy smelt
instead of ((not A) or B)
crisp wadi
,w truth table of ((not A) and C) or ((not A) and B) or (C and B) or ((not C) and A and (not B))
clever fjordBOT
crisp wadi
shy smelt
Why is 011 true?
crisp wadi
The green implicant, shouldn't it be AB rather than A'B?
shy smelt
and 101 false
mystic saffron
well i structured it as CAB really
shy smelt
Aah, that explains why this looks wrong
indigo vortex
Got this wrong, here is my setup
indigo vortex
<@&286206848099549185>
odd edgeBOT
@indigo vortex Has your question been resolved?
cosmic island
the work required to pump all the water out of the tank is $10000 \frac{N}{m^{3}} \times \frac{1}{3}\pi (3^2)(11) \times 9.8 \times 11$.
clever fjordBOT
clovercat.
indigo vortex
That's not right
boreal saffron
Hi
odd edgeBOT
@boreal saffron Has your question been resolved?
odd edgeBOT
@boreal saffron Has your question been resolved?
timber atlas
fast whale
odd edgeBOT
fast whale
ans is B , 0 but i dont understand how is there some identity used here that idk?
stark elbow
You can simplify sec^-1 I think
Well not really actually
not in a useful way
I do think you can simplify this somehow though
You can write arcsec(x) as arccos(1/x)
Ah ok
After you change it to arccos, try using a variable to help you see what's going on
stark elbow
Wait what happened?
fast whale
And try getting arccos from that
so the arccos and arcsin diff will be inverses of each other and cancel
fast whale
Wait what happened?
someone wrote a slur which got removed
stark elbow
so the arccos and arcsin diff will be inverses of each other and cancel
Well not exactly
But stuff will cancel out, yes
fast whale
ok ill try this out on paper thx
zinc glacier
Oh that wasnt you
fast whale
i got the idea
wispy tendon
odd edgeBOT
wispy tendon
i do not know hwat i am doing wrong with this problem
i will show my work in a bit
here is my work i am not entirly sure where i have made a mistake
any help is greatly appreciated
it is about antiderevatives
zinc glacier
cos(0)=?
zinc glacier
Youre welcome
burnt grove
Can someone help with this question?
odd edgeBOT
Can someone help with this question?
burnt gazelle
do you what what it means for a function to be continuous
burnt grove
this is my first day trying to figure this sorta thing out so I think so but take that with a grain of salt
im pretty sure it means that the -9 or 5 in this example equal the same things at the end
in this case 21?
burnt gazelle
yes sort of, it means that at x=-9, the function should take on the same value whether your approaching it from the left or from the right
burnt grove
hm alr
burnt gazelle
so for x<-9, the function approaches 21
so it must be that for x>-9, the function ax+b approaches 21 too
a similar idea holds for 5 and you will end up with a simultaneous equation to solve
burnt grove
hm ok
kinda messy way to do it but I plugged in the 3rd and 5th option and got 21 for both
not sure if this is the right way to do it or not but this is what I tried
burnt gazelle
yes so you want the function that at x=-9 is 21 and when x=5 is -21
burnt gazelle
kinda messy way to do it but I plugged in the 3rd and 5th option and got 21 for ...
only one of these has this property
burnt gazelle
yes
burnt grove
ah okay tysm
burnt gazelle
Can someone help with this question?
but typically we solve osmething liek this by doing $a(-9)+b=21$ and $a(5)+b=-21$ and do abit of simultaneous equation
clever fjordBOT
Iusgnol
burnt grove
but typically we solve osmething liek this by doing $a(-9)+b=21$ and $a(5)+b=-21...
hm alr well ty :)
uh do I have to close this chat or smthn
.close
lament cargo
yo
lament cargo
yeah
pastel orbit
where are you stuck
lament cargo
at the 7+2 part
pastel orbit
what do you mean?
pastel orbit
oh, then you should use the distributive law
pastel orbit
hm
if you have any three numbers a,b, and c
then a(b+c) = ab + ac and (b+c)a = ab + ac
for example, 7*(5+3) = 7*5 + 7*3 = 56
pastel orbit
you have 2 numbers and a variable x
but the property is still the same
2(2x + 5) = 2*2x + 2*5
brisk creek
Can anyone help?
meager juniper
!occupied @brisk creek
odd edgeBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
@lament cargo Has your question been resolved?
lament cargo
i got it already thanks
odd edgeBOT
Available help channel!
reef night
I was wondering if i could get some help with differential equations formula, dP/dt= (birth rate- death rate)(Population at that point) I dont really get why its not just birth rate- death rate
odd edgeBOT
I was wondering if i could get some help with differential equations formula, dP...
@reef night Has your question been resolved?
reef night
<@&286206848099549185>
clever fjordBOT
Why am. I here
reef night
**Why am. I here**
Yeah
The population change
Rate of change of population
Change in population per some time, let’s say t years
I don’t get why it’s P(birth rate- death rate)
Why isn’t it just birth rate- death rate
@frigid canopy
frigid canopy
<@796939110815629322>
P*(birth rate- death rate)?
yeah, I'm not too sure, sorry
this may help
odd edgeBOT
@reef night Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
high nebula
help
livid mica
so basically
marble laurel
Hmm
wicked kestrel
<@165914200332304394>
!noping
odd edgeBOT
<@165914200332304394>
Please do not ping individual helpers unprompted.
odd edgeBOT
<@1000057838007226480>
Please do not ping individual helpers unprompted.
high nebula
sorry i need help
marble laurel
Do not ping people for no reason even if you need help
There were people willing to help you
high nebula
high nebula
hmm
marble laurel
It tells you you need an equation represented by the slope and intercept
Do you know how to get the slope?
high nebula
thanks
marble laurel
<@&268886789983436800>
marble laurel
Alright
high nebula
how do i get that
marble laurel
Do you recall its formula?
high nebula
im confused
ember salmon
<@&268886789983436800>
?
marble laurel
?
@livid mica was doing some trouble before deleting his/her messages
In this channel
marble laurel
im confused
Hmm...do you know what is a slope?
high nebula
uh na whats that
clever fjordBOT
VulcanOne
hushed swift
why am I being pinged
Don't troll other help channels
livid mica
Don't troll other help channels
?
stop pinging me
but since i respect discord moderators igu
dont worry
high nebula
how do i get the y and x?
marble laurel
how do i get the y and x?
That will be by choosing 2 points from the graph you have.
marble laurel
From this graph, choose 2 points
high nebula
6 and 6
livid mica
your explaining it wrong this is 7th grade math explain it to him in 7th grade language
high nebula
yea
marble laurel
Alright. Here's the notation to describe a point
hushed swift
timed out the troll
clever fjordBOT
VulcanOne
high nebula
ok
marble laurel
So let's say you want to refer to the point that is hitting the y-axis at 6
Since it is on the y-axis, that means that the x coordinate is 0
marble laurel
Correct
odd edgeBOT
@high nebula Has your question been resolved?
odd edgeBOT
odd edgeBOT
Available help channel!
stark veldt
odd edgeBOT
white basin
yes the cardinality is 3
stark veldt
<@&286206848099549185>
stark veldt
yes the cardinality is 3
thanks
white basin
no problem
white basin
do you still need help with this?
white basin
maybe you can represent it as a union of two sets in set builder form, but I feel like the "correct" answer will be a little contextual on what you've discussed in class
also for a unit step function you can have it as
$(-1)^{1-u(n)}$
clever fjordBOT
keto11
narrow chasm
for the first set, we can see that this is a set of odd numbers. So you can write is as:
S = {x|x = 2n+1, n∈Z}
Here this "|" is such that
stark veldt
for the first set, we can see that this is a set of odd numbers. So you can writ...
thanks
but part d
stark veldt
Here this "|" is such that
then what is :
white basin
it really means the same thing
stark veldt
dope
thorn palm
what about ${x|x^2=\left(\frac{2}{3}\right)^{2n}, n \in \mathbb{Z}}?$
clever fjordBOT
Dri111
stark veldt
damm
thorn palm
srry no -1
white basin
**Dri111**
genius
narrow chasm
**Dri111**
Wait that actually works out
thorn palm
would it be dirty to add $x \ne -1$
clever fjordBOT
Dri111
stark veldt
set subtraction is taught in my course
that is
A/B
no reverse slash
could use that to subtract -1
,close
.close
chilly narwhal
An ant is on one of the vertices of a cube of length 1. The ant has to travel to the opposite corner of the cube while staying on the cube. What is the shortest distance the ant can travel to the opposite corner? The second question is, in an icosahedron, what is the largest distance between a vertex and another?
odd edgeBOT
@chilly narwhal Has your question been resolved?
low locust
what have you tried
chilly narwhal
i have tried maybe looking at the net of the cube
low locust
and then? how would the ant have to travel on the net?
chilly narwhal
oh wait i get it
its root(5)
what about for an icosahedron?
wait let me close this and reword my question (now i understand for a cube but im sill quite unsure about an icosahedron/dodecahedron
.close
chilly narwhal
In an icosahedron, what is the largest distance between a vertex and another?
odd edgeBOT
In an icosahedron, what is the largest distance between a vertex and another?
@chilly narwhal Has your question been resolved?
frigid canopy
This may help https://math.stackexchange.com/questions/2333033/what-is-the-maximum-diagonal-length-of-a-icosahedron
odd edgeBOT
Available help channel!
azure kindle
where do I start here? writing the binomial expanded form?
azure kindle
after the base case, obv
neat oxide
write out the inductive hypothesis, then the inductive step, and then try to substitute the hypothesis into the inductive step
azure kindle
yes but any hints for the induction step?
neat oxide
what's the formula for A choose B, and whats the formula for expanding out the summation into a single expression
oh
you might want to use pascal's rule
azure kindle
neat oxide
ok then turn that into 2 sums
azure kindle
why two sums?
neat oxide
because you can then turn the first one into our inductive hypothesis
remember, $$\sum_{k=0}^{n}{(x+y)} = \sum_{k=0}^{n}{x}+\sum_{k=0}^{n}{y}$$
azure kindle
okay yes
clever fjordBOT
hhhapz
neat oxide
you cant just swap the k for a 0
im assuming thats just a mistake and if so, then yes
azure kindle
neat oxide
yea
azure kindle
this is my inductive step'?
azure kindle
what do you mean?
that the first sum is not equal so a 2^n+1
h
ah
the first therm of the sum is equal to my starting sum
azure kindle
neat oxide
yeap
now the last part of it is a bit more tricky, but, consider what the value of $(^{n}_{-1})$ would be
clever fjordBOT
hhhapz
neat oxide
n choose -1 is always 0
azure kindle
ah really?
neat oxide
also note that n choose n+1 is also 0
so see if you can adjust the limit and starting value of the sum
azure kindle
to see this I need to expand the binomial coefficent right?
azure kindle
proving this sum by induction
neat oxide
lol
yeah
a bit more specifically, what is the end goal of the inductive step specifically
we are trying to prove that P(k+1) = ?
what should it equal?
neat oxide
what exactly should it equal
azure kindle
2^n + sum n choose k-1
azure kindle
this is the base case?
neat oxide
yeah sec
clever fjordBOT
hhhapz
neat oxide
i copied the wrong thing
azure kindle
okay this is my inductive step
azure kindle
$$ \sum_{k=0}^{n} \binom{n+1}{k} = 2^(n+1)$$
clever fjordBOT
schufi73
neat oxide
yep, show 2^{n+1}
azure kindle
okay I dunno how to use this
clever fjordBOT
hhhapz
neat oxide
thats your end goal here
azure kindle
2^n * 2 ?
clever fjordBOT
hhhapz
neat oxide
that other term is equal to what
neat oxide
but then you're only left with $2^n$
clever fjordBOT
hhhapz
azure kindle
then it needs to be also 2^n
clever fjordBOT
hhhapz
neat oxide
if you do that, then you can complete the proof
neat oxide
n choose -1 is always 0
use the information that $\binom{n}{-1} = \binom{n}{n+1} = 0$
clever fjordBOT
hhhapz
azure kindle
**hhhapz**
I mean this is also equal to 0 if k =0
I can rewrite
n choose k-1 with n choose n+1
but I don't see how it can help me
neat oxide
can you show that $\sum_{k=0}^{n} \binom{n}{k} = \sum_{k=0}^{n+1} \binom{n}{k-1}$
clever fjordBOT
hhhapz
neat oxide
fixed it
odd edgeBOT
@azure kindle Has your question been resolved?
queen zephyr
hi i'm shufi's friend i think this is the right solution do you agree or did i do something wrong
sorry about my hand writing
am i right to assume that the first case of the sum is equal to zero since $\binom{0}{-1}=0$
clever fjordBOT
tommy
odd edgeBOT
queen zephyr
.reopen
odd edgeBOT
Available help channel!
queen zephyr
is this correct?
odd edgeBOT
is this correct?
queen zephyr
this is the original exercise
odd magnet
it's uh, not the easiest to follow
zinc glacier
Youre missing the +1 for the m+1 at the end of the third to last line
queen zephyr
if you see my friend was in this channel before and asked the same question but didnt understand i wanted to check if what i wrote is right
zinc glacier
At the top of the sum, it should be m+1, not m
queen zephyr
in the inductive hypothesis?
queen zephyr
so this is wrong
queen zephyr
so if the sums are still n+1 i need to write $\sum{k=0}^{n} \binom{n}{k}+\binom{n+1}{k} = \sum{k=0}^{n+1} \binom{n}{k}$
i canrt use the bot sorry
zinc glacier
Should be $\sum_{k=0}^{m+1} \binom {m}{k-1} + \binom mk = \sum {k=0}^{m+1} \binom {m}{k-1} + \sum{k=0}^{m+1} \binom mk$
clever fjordBOT
Ajito
zinc glacier
The rest of the proof is fine, youre just missing some +1s
queen zephyr
like this?
zinc glacier
Not quite
The term you took out of the sum is wrong in both cases
Remember, the m in the m choose k does not change
For the top sum, if you plug in k=0, what happens then?
queen zephyr
the first case is =0 ?
zinc glacier
What do you mean
queen zephyr
$\sum{k=0}^{n} \binom{n}{k} = \sum{k=0}^{n} \binom{n}{k-1}$
queen zephyr
where?
zinc glacier
The upper bounds of the sums
queen zephyr
so like this?
zinc glacier
Yeah sure
queen zephyr
but then how do i substitute the sum with 2^n
zinc glacier
$\left(\sum_{k=0}^m \binom mk \right) + \binom {m}{m+1}$
clever fjordBOT
Ajito
zinc glacier
m choose m+1 =?
zinc glacier
Youre welcome
odd edgeBOT
@queen zephyr Has your question been resolved?
odd edgeBOT
clever fjordBOT
The following error occured while calculating:
Error: Undefined symbol ulate
cosmic island
💀
odd edgeBOT
@kind wyvern Has your question been resolved?
viscid flint
mystic saffron
<karnaugh-map>
\begin{karnaugh-map}[4][4][1][$CD$][$AB$]
\minterms{0,1, 3, 4, 5, 6, 7 , 8 ,9}
\implicant{4}{6}
\implicantedge{0}{1}{8}{9}
\implicant{3}{7}
\end{karnaugh-map}
is this the best simplification of this k map
just a quick check
what the fuck deleted that
tall veldt
mystic saffron
LOL no worries
clever fjordBOT
mystic saffron
thats kinda funny
oh wait
i can do ```latex
<karnaugh-map>
\begin{karnaugh-map}[4][4][1][$CD$][$AB$]
\minterms{0,1, 3, 4, 5, 6, 7 , 8 ,9}
\implicant{4}{6}
\implicantedge{0}{1}{8}{9}
\implicant{1}{7}
\end{karnaugh-map}
paper kelp
For figure 6 is A1 X^3 and A2 6X ?
odd edgeBOT
For figure 6 is A1 X^3 and A2 6X ?