#help-36
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the answrs wrong idk what i did wrong
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70% of the vehicles driving on a street are cars, 30% are buses. the probability of parking for a car is 0.1, for a bus 0.2. what is the probability that a vehicle taken at random will stop?
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hello, I'm in statistics, and I was wondering if there's a way to calculate the area from a z-score without the z-score chart
You're essentially using a calculator, or you're not getting the values in any practical way
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is the equivalence class of x equal to the equivalence class of y if x and y are equivalent?
[x] = [y] if x~y
i think this is iff condition i.e [x]=[y] iff x belong [y] or y belong [x]
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how ive tried to prove it is by drawing matrix A and B and adding them together
I don’t think this is a sufficient proof though
If you wanted to make it more formal you would just convert your picture to notation
You would say something like, A is diagonal so aij =0 whenever i !=j, B is diagonal so bij = 0 whenever i != j and then compute (A+B)ij = aij + bij
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There is any proof that
Please don't occupy multiple help channels.
@hushed wagon Has your question been resolved?
just divergence theorem no?
Idk how to apply it
is the line in 3d or 2d
i mean it gets a bit hairy to do in 3d
but in 2d
say you let f = grad g
and then n ds = (-dy, dx)
if you expand out f . n ds you get like
-f1 dy + f2 dx
and you can apply greens theorem on that
then laplacian of g = 0 means div f = 0
Could you draw it ? Still a little bit confusing to me
@hushed wagon Has your question been resolved?
@hushed wagon Has your question been resolved?
guys 😭😭😭
@hushed wagon Has your question been resolved?
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can someone help
Do you know what it means if two quantities vary directly as each other / are proportional?
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Can someone help me with this problem
For the equation x^2/x^2-16
- Find the critical numbers
- Find all the relative extremas
- On the open intervals, list the domain of the function where it’s increasing and decreasing
that is not an equation
f(x)=
This was on my quiz
So I’m wondering what I did wrong
Derivative is this is -32x/(x^2-16)^2
Then there are discontinuity’s at x=+-4
And critical number at x=0
The discontinuity can’t be critical numbers cause if you plug them into the original equation they will be undefined
Then I drew a number line
Lemme draw one really quick
ok, wikipedia says a critical point is a point at which f' is not defined or at which f'=0
is that the definition you use?
or only the undefined part
Yes
F’ is 0 at x=0
But someone has told me that it’s not a critical point even though it’s not defined
why do you think you did something wrong
Wdym?
.
Cause I got 7/10
A critical point typically needs to be in the domain of the original function itself. That is an easy part of definition to miss.
was that 7/10 just for part 1)
There r 2 questions I’m pretty sure I got the 2nd one wrong
5 each
How do you find domain?
That’s something I don’t really know how to do either
can you take a pic of your work
Cuz for number 3 here I only listed 1 increasing and 1 decreasing pair, but there’s 2 of each
Uhhh
Well I saw my score online so I don’t have the paper with me
,W graph y = x^2/(x^2-16) from -10 to 10
well you could first consider the asymptotes
Yea asymptotes at x=4,-4
horizontal asymptotes as well
So ig I know one domain is (-inf,-4)
And another (4,inf)
Uhh
We just finding x value domains
it's mainly to give you a better idea of how the graph will look
if you did the work in part 2, you should've been able to determine that the would be a local max at the critical location in part 1)
Uhhh
So how I did my work
Is using the first derivative test theorem
Our teacher used a number line for this
that's fine too I suppose
Let me show u
But I don’t understand really much
My friends got different number lines
U put numbers at each interval
anyway the local max tells you that the function would be increasing on (-4,0) and the decrease again after that, (0,4)
as seen on that graph
What’s the difference between local relative absolute max/min?
Absolute is the highest/lowest right
Idk how to see that without a graph
you should be able to deduce it from what you determined in part 2)
any it'd help you a lot to look up graphing rational functions
I have done that last year and they are kind of the similar difficulty in understanding as these extremas and critical numbers
Actually they r harder than this
Hmmmm I kind of see it now
There are asymptotes at x=+-4 and if you plug them into the original equations, they are positive
So they both curve up
Which means in between the asymptotes it’s the domain (-4,4)
And since the lines on (-inf,-4) (4,inf) curve up, the line in between that should be curving down
I don’t think horizontal asymptotes really matter in this situation
And also there is a critical number at x=0
I’m assuming that itself counts as sort of an asymptote
Which means that there’s no way to make the left side (-4,0) decrease if you draw an upside down curve so it’s increase and since it’s curving the other side too at (0,4), it is decreasing
@ripe gull Has your question been resolved?
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how do i get the percentage of a number? give me the easiest formula
value/total value)×100%
ok so if i want to get 20% of 70 its 20/70*100?
*100 (not 100%)
sorry yes
oui
and remember
10% you move the decimal one place
1 % you move the decimal 2 places
5% is half of 10%
and with that you can find anything
it gave me different results
i did 20/70 *100 and it gave me 28
i did 20% of 70 and it gave me 14
ok well 20% of 70 is 10% twice
so 7 x2
so 20% of 70 is 14-70
ok well 20% of 70 is 14
what if i need to find the percentage of something?
like i have 50 and i have the number 238
50 is how much % of 238?
@frail badger Has your question been resolved?
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how to intergrate \int \frac{3}{:\sqrt{x}} ?
I split it to get 3 x 1/root x
then made the 1/root x into x^1/2
then i times 3 by the x^1/2
1/root x into x^1/2?
oh why's that
well sqrt(x) = x^(1/2)
is it supposed to be negative
yep haha
np ^-^
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Hey, I'm asked to sketch the region of non zero probability of a pdf exp(-(x+y)) defined on x,y greater than or equal to 0
Is this sketch essentially the area enclosed between the curves exp(-x) and exp(-y) in the first quadrant
sounds like it
Perfect thanks
the area enclosed between the curves exp(-x) and exp(-y)?
that sounds awfully suspicious
is this your distribution?
This is multivariable yes
what do you mean by
the area enclosed between the curves exp(-x) and exp(-y)
the distribution assigns probability to all of x,y>0
So it's the entire first quadrant?
that is where the density is positive
So it's not so much about the pdf itself it's more so down to the given conditions for x and y?
and then you just need to pick when its nonzero
Okay okay thats making much more sense now
Okay so it's the entire first quadrant including the x and y axes then
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Hi!, what is the percentual decrease in 160 000 · 0,95^x, and how do you calculate it
wow thats a new word for me
gonna need to see the problem statement
"percentual decrease in 160000 * 0.95^x" is vague
well, lets say 160000 is a price of a car, and it loses its value every year
x stands for number of years
0.95 is how much it depreciates
so you want to find the percentage by which the price goes down every year?
that's 1 - 0.95, i.e. 5%
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does anyone have an outstanding link for understanding Big O notation regarding formulas?
I'm having a difficult time understanding "Show that n^2 + 1 is O(n^2)"
Isn’t it 1/n= O
the answer?
Yeah
according to my teacher's explanation, the answer is:
Is?
Let c = 2, k = 1. Assume n > 1.
Then, cn^2 = 2n^2 = n^2 + n^2 > n^2 + 1, or n^2 + 1 < cn^2.
But I want to know why
I don't understand this at all
so, I'd like to break this down as if you are explaining things to an average 5th grader
not the super bright ones on TV
How is that the answer
ah, you're not good at Big O also?
Yeah I’m just looking around
we can wait until someone proficient comes along
Yeah. What is big O
Oh it’s a program very cool
it's not a program
Is it functions
let's just await a proficient user and then, hopefully it will be more clear
Ok. Maybe you could help my math question?
please post in a different channel since I'm waiting for assistance in this specific channel
Ok
<@&286206848099549185>
the goal is to show that you can choose some c and some minimal n, and then cn^2 is always more than n^2 + 1
they do it by choosing c = 2 and n > 1, I don;t know what they meant by k
it's the goal because it's the definition
so, I know what Big O is in a nutshell
ok
it's a way to obtain an approximation of the speed of an algorithm
and how it scales
depending on input
it's actually more like the upper bound
wait
it's not that you;re saying that it's roughly cn^2, but that it's less
before we get to technical terms, i'd like to keep things VERY simple
so any O(n^2) is also O(n^888)
"upper bound" is too technical currently
because it's less than n^888 too
if it's ok, let's start slowly
i've tried discussing this with five math enthusiasts so far and all the explanations have been far too technical
Some hard math there
@full birch Has your question been resolved?
<@&286206848099549185>
@full birch Has your question been resolved?
O(n^2) means smaller than some n^2 function
so basically, to sort something u got an algorithm
and algorithm works in different speed
big O notation basically means the speed of growth per term of that algorithm is bounded by some other function
so lets say you inputted n and it took p amount of work to compute
if you input n+1 and it takes np amount of work to compute
it grows in the speed of (n-1)!
so O(n!) is the upper bound of the growing speed
as if my understanding
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how do i find order of $SL_2(\mbb{F}_p)$
Arkos
in the first answer, i don't get how every matrix with determinant can be mapped to a matrix with det 1
ping please
@tranquil pine Has your question been resolved?
You could quotient $GL_{2}(\mathbb{F}{p})$ by the kernel of the determinant that is $SL{2}(\mathbb{F}_{p})$
black_couscous
@tranquil pine Has your question been resolved?
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lets suppose we have 2 vectors a and b how would you go on about writing the perpendicular component of a on b?(in terms of a and b)
sounds like you need a dot product
but how idk how to write the unit vector
but i want a vector perpendicular to that
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Hi, can someone help me understand why these 2 integral calculators are giving me two different answers for the same integrals ?
The first one showed me the steps, and they make sense, but the second one doesn't let me see them unless I have a premium subscription. Thus I'm confused how the second one added an extra -2/3 to it
Why did the second one feel the need to separate the -2/3 though ? That's the first time Symbolab does something weird like that in my experience
It decided to use the identity sec^2(x) = 1+tan^(x) and integrate them individually instead of directly integrating sec^2(x)
As to why I don’t know
Alright, well thanks for clearing that up. I was going mad on that one x)

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yeah looks about right
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ok to find this out i have to do
answer 12?
i did x=4 and got g(x) =2
then i went x=2 then got f(x)=12
Ye
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can you provide a mwe and screenshots?
as you can see it starts to duplicate after the chunk
<@&286206848099549185>
It was not the chunk i deleted it and the problem stayed
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why can't I plot a function like f(x)=(-2)^x
,w plot (-2)^x
I mean. You technically can but there will be a bunch of points where it is imaginary
What’s (-2)^1/2 say
if i try doing it on maple or some other program it just doesnt show anything
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I just need help finding b or the vertical axis
i think my answer is right but i just want to check
@carmine plaza Has your question been resolved?
It's correct but it'd be nice to get it explained
I don't quite understand the eccentricity
The formula for eccentricity is e = c/a.
And another formula for a, b, and c is b^2 = a^2 - c^2.
You use substitution for a and c for eccentricity to allow you to solve for b in the second equation.
$e = \frac{c}{a} = \frac{3}{5}\\
b^{2} = 5^{2} - 3^{2}$
Kookiemon
a will be your major axis and b will be your minor axis.
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Im given a centre of a circumference C(-3, 1) and asked to find the equation of the circumference with that centre and to the line 4x +3y +4 = 0
At the moment I have only put the line equation in explicit form (y = -4/3 x - 4/3)
I don't know the rest
Do you know how to calculate the distance from a line to a point not on the line?
Yea
That will be your radius for the circle.
d = | Axp + Byp + c | / sqrt(A^2 + B^2)
Ok
I don't know the radius though
d will be the radius.
(x-h)^2 + (y-k)^2 = r^2
Are you calculating the length of the circumference or the equation of the circle?
equation
Then use the formula you wrote.
Ok
Thx
Lemme do the calculus real quick
Ok it comes out
Thanks a lot man, you are a life saver!
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@ripe sonnet Has your question been resolved?
@ripe sonnet Has your question been resolved?
@ripe sonnet Has your question been resolved?
@ripe sonnet Has your question been resolved?
Draw the right triangle with opposite length h and adjacent side R-r
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Hey there, what is the formula for finding the area of a sector of a circle, given the diameter and angle in radians?
or rather, is the formula: (1/2) * r^2 * theta
yes
okay, thank you
@tranquil pine Has your question been resolved?
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Idk if im right or wrong, i did the equation twice but i still think its wrong
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Ok so I'm trying to figure out how to find the value of x in an ordered pair so that two lines are parallel or perpendicular. The way my math teacher explained it was really convoluted. The specific problems I'm working on are "Given C(x, 16), D(2, -4), E(-6, 14), and F(-2, 4), find the value of x so that CD and EF are parallel" and "Given P(12, -2), Q(5, -10), R(-4, 10), and S(4, y), find the value of y so that PQ is perpendicular to RS
Yes I knew that
the slope of CD is
(x-2)/(16-(-4))
.
the slope of EF is
(-6-(-2))/(14-4)
.
since slope of CD and EF are the same
we can set up an equation:
(x-2)/(16-(-4)) = (-6-(-2))/(14-4)
.
now we just have to solve for x
then u get the answer
for the second question
since they are perpendicular
MPQ x MRS = -1
try to set up an equation and solve for y
Wait so if x2-x1 is negative, does that make the slope negative?
@shrewd glacier Has your question been resolved?
No
well it depends on y2 - y1
if both y2 - y1 and x2 - x1 is negative then the slope can be positive
Got it
cool
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What’s the difference between these two fractions?
One has the subtract sign beside the line and one has it beside both numbers
What’s the difference
that's a minus sign, not a subtract sign
$\frac{-52}{-8}$ means you divide $-52$ by $-8$, while $-\frac{130}{20}$ means you divide 130 by 20 and take the negative of the result
...bot's slow today
you sounded like you were asking for the difference in meaning between these two fractions
as far as simplification goes, in (-52)/(-8) you can "cancel out" the minuses (which really are just multiplications by -1 and should be thought of as such) and get 52/8
no
-13/-2 is correct simplification but incomplete
and yes it changes everything
my point about cancelling out the multiplications by -1 still stands.
13/1?
you sure you didn't typo that
so you definitely absolutely got 13/1 and not 13/2 as one would expect you to get
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How do I multiply this? Do I treat it like both numbers are negative for the second fraction or do I make the negative positive and the positive negative or something else entirely?
negatives would cancel each other out and become positive
which top number?
nah the fraction is one number
its like how 2/1 is one number
so is 1/2
But the bottom number is already negative and the top isn’t
So it just both becomes positive?
yeah
i think itll help you to think of it as one number
its either positive or negative
they arent two different numbers
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Can someone pls help me identify what else can be x
dont forget you cyclical quadrilateral theroem
What u mean?
I used angle b= x for cyclic quad
<@&286206848099549185> pls can someone help me
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- Represent the following numbers as being members of set K: -2, -1, -4, -1, -3,
-1, -5, -3.
set k?
yeah ig
K = {-2, -4, -1, -3, -5,}
..? how is that right.. gosh I'm lost
the set
K must denote
distinct elements
via the definition fo cardinality
say I had the function f(x) = 2
and the domain was all real numbers
the set f(x) would just be {2}
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yes your work is correct
final answer is correct right
it’s like 10% of my grade just wanna double check💀💀
kk
lmk if final answer is correct
yeah I checked
so your fs is correct
and your dr/dt
is correct
still checking the rest lol
kk lmk before i submit if i made a dumb mistake or smth
okay yes your final calculation is correct
in your fs * dr/dt
wow that was one hell of a calc 3 refresher
frr calc 3 makes my brain fucking die
u gotta think of like problems in a whole different ass way than calc 1
calc 1 was super easy
but calc 3 is pretty fun once you get into partial differential equations
advanced multivariable calc(math major specific course) where you prove calc 3 is hard as hell
bc i wasn't paying attention
in the very beginning
not paying attention in lecture and studying 3 all nighters in a row for an exam
still gotta take mathematical methods for engineers 2
and my studying was just doing practeice problems over and over and over
OHHHH haha
prolly gonna take a gap semester or smth LMAOO
engineering mathematics right?
yeah this is math 1
yeah imma take all the easy small classes
this semester
so last semester i finish math 2
w like easy classes
Yeah for sure
your calculations are precise tho
and I like your organization while doing the problems
I think you got this just do a few more in your own time
to gain confidence
yeah gotta get prepared for the final in like 6 days
thank u tho haha
i'm not that organized but i understand my work lmaoo
most people write all over the place in math
i'm kinda proud of myself
Yeah I'm all over the place
even in analysis my proofs are so messy I get points off for bad handwriting
- illegible solution
yeah everybody has their strenghts and weaknesses i guess hhah
thank u very much for ur help tho i appreciate it @slate phoenix
everybody needs an extra set of eyes sometimes especially in calc 3 lmaoo
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35,45 = (x . 75,77 + 36,97 . 24,23) / 100
yes they are
so i translate:
35.45 = (75,77 * x + 36.97 * 24,23)/100 ?
And you want x
Am i correct?
ye
alright let's get rid of the parenthesis they're useless now
And we substract both side by 36.97 * 24,23
Then we divide both side by 75,77
why cant i do 36.97 * 24,23
3545 = 75,77 * x + 895.7831
i need more help
substract 895.7831 from both side
Then we divide both side by 75,77
And we found x
.close
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How can I find out if a stochastic matrix is not regular? Do I have to check every power of the matrix until infinity?
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what is monte carlo?
in math
fancy word for generating random data for some purpose
for example to calculate the expected value of some distribution, you just let the computer pick a million samples and then calculate the mean of that
theres no way to calculate the ev by hand?
offer?
without a computer
well not always
might be too hard
and even if it might be possible, it's definitely faster to just code it and let the computer run for five minutes
(oversimplification of course but you get the idea)
ic
roll three dice and square the middle value roll
can you help me with this question?
that's not a question
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This would simplify to cos(t)/sin(t) *9t/t 1/cosine(t), right?
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how would I go about setting this problem up
I understand L hopitals rule but I don't know how to change this to infiniti over infiniti or 0 over 0
you could try finding a common denominator. $\\frac{1}{x-2} - \frac{1}{ln(x-1)} = \frac{ln(x-1) - (x - 2)}{(x-2)(ln(x-1)}$. Then when you check for the limit it should be $\frac{0}{0}$.
MellowDramaLlama
nah it's okay. Don't worry it's easy to miss stuff like that
@sweet summit thanks man I really appreciate the help. Hopefully one day I will be smart enough to help people with questions like this 🤣
don't worry you can do these in your sleep in no time flat!
yeah the concept is easy to me, its just the weird setups
what this is getting you prepped for is algebraic manipulation
that's all calculus is
it's algebraic manipulation on steroids
so you'll be happy you've gone through these lol
calc2 is still one of my favorite courses I've taken in my undergrad
makes sense. I think calculus is very fascinating
it depends. What I"ve heard from people is that they either struggle in Calc2 or Calc3 (of course this set in stone, but seems to be a trend)
I found Calc3 much harder than Calc2
but that's just me
I know someone who had the opposite effect haha
hopefully I find calc 2 easier because I am in Texas A&M engineering and you have to get a 3.75 gpa or higher in freshman year if you want to be able to choose whichever engineering major you want
oh hey we're close by
I'm at Texas State in San Marcos
here let me give you a few resources
oh cool, good for you. Although I am not in college station. I am in a program where you go to dallas community college for all classes except my programming class (that is taught by A&M).
I can move to college station once I finish calc 3
so I am going to try and get it done over the summer
I wish I was in college station cause I have a bunch of friends there but this is way cheaper and easier to get a 3.75 gpa in
This website will help you from calc 1 to calc3 and diff eq: https://tutorial.math.lamar.edu/
This YT channel will give you full lectures over what you're going over. He's a great teacher. I would watch his videos sped through outside of lecture to get another perspective on the subject material: https://www.youtube.com/watch?v=fYyARMqiaag&list=PLF797E961509B4EB5&ab_channel=ProfessorLeonard
Welcome to my math notes site. Contained in this site are the notes (free and downloadable) that I use to teach Algebra, Calculus (I, II and III) as well as Differential Equations at Lamar University. The notes contain the usual topics that are taught in those courses as well as a few extra topics that I decided to include just because I wante...
https://www.patreon.com/ProfessorLeonard
Calculus 1 Lecture 0.1: Lines, Angle of Inclination, and the Distance Formula
oh I have seen professor leonard
he is good
although personally I prefer organic chemistry tutor
yeah partly that. That and vector fields and all 3D calculus stuff
although professor leanord is my backup
oh lord they just fucked the ui on youtube
wdym
honestly you'll be glad once that you did CC when all is said and done (at least financially haha)
I loved my CC experience (at ACC in Austin)
this was how it was just an hour ago
I agree
this is how youtube looks now
it gives me a bit of time to get used to college before I go live on my own
oh yeah sure enough
I think I have some Firefox settings on my end because nothing has changed lol
oh I hate this
Yeah absolutely!! Regardless it doesn't matter what road you take to get your education
yeah in the long run I view it as more of a product that I am buying rather than an experience
I just want to get a well paying job that and I thought engineering was the best way to do that
plus engineering really appeals to me
That's what I did 🙂
Yo, can someone help me on this 2 step equation word problem please?
I know some people who are doing it just because it will make them a lot of money and I am like, "you are not going to have a fun time at all"
@tranquil pine Hi there. Can you head to #❓how-to-get-help to open a free channel?
Okay thanks
some people can learn to love it
but yeah mostly its a terrible idea i agree
a better idea than studying communication though
it's a fine balance between good income and at least somewhat enjoying the job. I'm a big proponent that you don't have to love your work to be in a field, but it helps to at least like it a little lol
I like programming but I don't think I could do it for a living. I am either going to major in computer engineering, electrical, or industrial.
preference in that order
not a fan of programming but still wanting to major in computer engineering sounds funny lol
computer engineering is computer hardware pretty much right
I am a fan, but I don't want it to be the only thing I do
I am more interested in hardware than software
more focus on hardware design
yeah that is exactly what I am interested in
but like as an example you're making the processors so you might need to know, for example, some assembly shudders
lmaoo
but yeah basic understanding of data structures n whatnot is typically required
not hard
just annoying if you're not much into the programming part of it lol
yeah assembly code sounds kind of scary
rollercoaster tycoon was built in assembly : )
WHAT?!??!!?
that's wild
yeah lol
madlad dev
but it allowed for some crazy cpu optimisations
so the game could render lots of stuff at once
and the creator made like 50 million so
worth it
the definition of masochism
hahah yeah
Assembly isn't scary. But it's kind of... verbose? Like to do a for loop, even in a RISC architecture is like 10 instructions
I thought java was a pain in the ass bro
i think it would really help understanding how a computer words
worst ive done so far is python like a true math scrub
yeah A&M's introduction to engineering class is just python programming
its super easy
I had to write a program that converted english to pig latin today
yeah
igpay atinlay
although it only makes you do one word
cant you just disregard grammar and use that to translate entire sentences
I suppose, but that is not the assignment
I have more important things to be doing lol
lol
and if I do have freetime then usually it is spent playing apex legends or metal hellsinger
fair enough
def pig_latin(string):
return string[1:] + '-' + string[0] + 'ay'
Bam
not a lot of free time in engineering though haha
is that all pig latin is
ive never heard of it lol
yeah you take the first letter, put it at the end of the word, and add 'ay" to it
this makes more sense now
if it starts with a vowel you put yay on the end
that is for if you have one that starts with a consanent
although your code is a lot more efficient than mine lol
im still not great at python
💀
lol yeah
you are right
I should do that next time
this is why I am not a professional engineer 🤣
lmao
alright nice talking to yall I had better be getting home
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This would simplify to cos(t)/sin(t) *9t/t 1/cosine(t), right?
!15m
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I see on online calculator the next step would be to transform the fraction into this:
Intuitively this doesn't make sense to me, because I thought tan = sin/cos, here they completely disregarded the cos and substituted a 1 in it's place. Isn't it supposed to read: sin(9t)/cos/1/cos?
tan(9t) = sin(9t)/cos(9t)
The cos isn't disregarded, it's in the denominator
The denominator of the big fraction
Why would they put it as the final denominator in that expression..doesn't it belong as the denominator of the sin(9t) on top?
I don't know their exact reasons for doing it, but $\frac{\frac{sin(9t)}{cos(9t)}}{\frac{t}{cos(t)}}$ is identical to what they had
Gamer Dio
I have to be right back I'm going to my lab for better internet connection. Thanks for this clarification. I will be back.
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Need help
@median delta Has your question been resolved?
<@&286206848099549185>
@median delta Has your question been resolved?
you should google these, theyre common proofs and probably better written elsewhere
image and null space
.close
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I solved it out and get that it's [0, 1) U (1, +inf)
but why isn't it **(**0, 1) U (1, +inf)?
isn't the derivative 0 at x=0?
sorry for being so particular I just don't wanna mess this up on exams lol
you are right at 0 the derivative is 0
but now two things
technically a constant function is both increasing and decreasing
because for any a>=b
f(a)>=f(b)
just not strictly increasing
for the other thing,
your function is strictly increasing over the interval [0,1)
basically it has a constant part
if its flat on a whole interval
not on only isolated points
like for example
the function f(x) =x^3
has derivative 0 at 0
but its still strictly increasing on R
@supple copper Has your question been resolved?
ohh
hmm
so basically determining where it's increasing isn't solely based on the derivative being positive?
i mean like
if the beginning point has a slope of 0, it's still part of the interval that increasing?
if theres only isolated points
at which the derivative is 0
its not flat
at that point
like its not constant
so if its strictly increasing around
its strictly increasing even counting the point in
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how do i translate this into a first order predicate formula?
"If some farmers are right-handed and some right-handed people have blue eyes, then some farmers have blue eyes"
A is the set farmers, C is the set of right handed people, D is the set of blue eyed people
P(x) is 'x is a farmer', R(x) is 'x is right handed', S(x) is 'x has blue eyes'
my initial guess would be: $$\exists_{x \ \in \ U}((P(x) \ \land \ R(x)) \land (R(x) \ \land \ S(x)) \implies (P(x) \land S(x)))$$
yotta
but idk seems wrong and verbose
<@&286206848099549185>
ive simplified it to: $$(\exists_{x \ \in \ A}(R(x)) \land \exists_{x \ \in \ C}(S(x))) \implies \exists_{x \ \in \ A}(S(x))$$
yotta
is that right ^^ ?
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I need help with this related rates problem. I am not sure how to do this problem for my hw
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,rotate
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