yeah but you did it wrong on the last step
#help-10
cursive forge
covert kestrel
so this is the correct one?
cursive forge
4x-16 = 4x-8
then you get 4x-4x = 16-8
0 = 8
why did you add 4x?
@covert kestrel ?
cursive forge
x has no real solution
covert kestrel
forget that solution
cursive forge
because no value of x can satisfy this equation
covert kestrel
covert kestrel
i mean yeah the topic is figuring out wether its a solution or extraneous
im figuring out the value of x
covert kestrel
but we need to show solution 😭
cursive forge
just write there is no solution
covert kestrel
im figuring out the value of x
this, so we can prove its not a solution
cursive forge
solve till last
and then jus write that for no value of x is the equation true, so there is no real solution of this equation
you're done with the question
covert kestrel
alright thanks
cursive forge
yw
covert kestrel
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
viscid kelp
How were they able to turn this into a polynomial?
obtuse pebbleBOT
How were they able to turn this into a polynomial?
viscid kelp
it does seem that taking the second derivative of the first line gives the same result though, 2.
obtuse pebbleBOT
@viscid kelp Has your question been resolved?
hidden compass
i'm not sure why the two are set equal here
Me neither
lavish sand
obtuse pebbleBOT
restive gorge
alter
lavish sand
guten abend
lavish sand
ja. aber wie sollte ich es lösen
lavish sand
l hopital
lavish sand
ln(1) ist 0 oder
lavish sand
unbestimte form
restive gorge
eine vertikale asymptote hätte man
von beiden seiten wenn x sich der 1 nähert
wird x/ln(x)² immer größer weil der nenner immer kleiner wird
0.25/ln(0.25)²
0.5/ln(0.5)²
0.75/ln(0.75)²
1.75/ln(1.75)²
1.5/ln(1.5)²
1.25/ln(1.25)²
lavish sand
inf?
restive gorge
ya
lavish sand
aber was sollte ich auf dem Papier schreiben
lavish sand
wie?
restive gorge
1/0 ist in der Hinsicht unbestimmt, da es inf oder -inf sein kann, bsp. 1/x
Aber das hängt davon ab, ob die x-Werte davor negativ oder positiv waren
bei x/ln(x)² ist es so wenn x gegen 1 geht
Der Zähler bleibt positiv von beiden Seiten aus
ln(x)² quadriert ist auch immer positiv, also geht der beidseitige Grenzwert gegen unendlich
lavish sand
danke schön
restive gorge
bitte schön
lavish sand
.solved
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
violet stump
Solve without l'hopital rule
$$ \lim{x\rightarrow 0}\frac{\frac{1}{2+x}-\frac{1}{2}}{x} $$
obtuse pebbleBOT
Solve without l'hopital rule
$$ \lim{x\rightarrow 0}\frac{\frac{1}{2+x}-\frac{1...
violet stump
I'm not sure how to do this
$$ \lim_{x\rightarrow 0} \frac{\frac{1}{2+x}-\frac{1}{2}}{x} $$
warm shaleBOT
Astro648
hidden compass
It's the limit definition of the derivative of a function, which one?
violet stump
It's the limit definition of the derivative of a function, which one?
In our math class, we haven't gotten to derivatives yet
That's the next unit
So we have to only use what we know about limits
hidden compass
Ah sorry
hidden compass
Don't worry, all good 👍
You could combine the fractions on top, making common denominator
violet stump
You could combine the fractions on top, making common denominator
Yeah I tried that
All my attempts came out to -1/2 when the actual answer was -1/4
according to teh textbook answer key
hidden compass
Which gives you $$\frac{\frac{2 - (2 + x)}{2 (2 + x)}}{x}$$
warm shaleBOT
Alberto Z.
violet stump
Give me a minute, let me try to get that
Ok, I was able to simplify to
$$\frac{-x}{4+2x^2}$$
warm shaleBOT
Astro648
hidden compass
**Alberto Z.**
And this becomes $$\frac{\frac{- x}{2 (2 + x)}}{x} = \frac{- x}{2x (2 + x)}= \frac{-\cancel{x}}{2\cancel{x}(2 + x)} = \frac{-1}{2(2 + x)} $$
warm shaleBOT
Alberto Z.
hidden compass
You're welcome 🤗
violet stump
omg bruh this took so long
the teacher requires credits for any math help, should I just credit you as Alberto Z from Mathematics Discord?
hidden compass
omg bruh this took so long
I know you'd probably have the right answer, I just wanted to write it in Latex since I like when it's written in a nice format
violet stump
I know you'd probably have the right answer, I just wanted to write it in Latex ...
Yessir understandable
hidden compass
omg bruh this took so long
It was long because I'm a bit slow at typing, but after a little practice it becomes quite quick
violet stump
It was long because I'm a bit slow at typing, but after a little practice it bec...
Nono
I mean
It took me so long to do this
and you just explained it like that
hidden compass
Ahhnn alright I get it now
violet stump
I took at least 30 minutes to try to solve this 😭
hidden compass
Yeah I remember my hard times when learning these things, it took me a while to grasp everything and take confidence
violet stump
Yeah I remember my hard times when learning these things, it took me a while to ...
Understandable, calculus is hard 😅
How bad is integration?
i am very worried about it
hidden compass
How bad is integration?
I liked it more than derivatives actually, but for doing integrals you need to know 100% (more or less) of the derivatives topic
violet stump
I liked it more than derivatives actually, but for doing integrals you need to k...
Oh i see i see
hidden compass
That's why a lot of students struggle
Because they didn't grasp/study at a good level derivatives
violet stump
Because they didn't grasp/study at a good level derivatives
Oh ok, i see
so I should put lots of effort into derivatives and I will understand integration?
hidden compass
And you need a lot more of creativity with integration
hidden compass
so I should put lots of effort into derivatives and I will understand integratio...
Derivatives are necessary but not sufficient, unfortunately
violet stump
Derivatives are necessary but not sufficient, unfortunately
Damn, what else do i need to know?
hidden compass
Revise algebra (like polynomial division and factorisation)
hidden compass
Damn, what else do i need to know?
But I was referring to the fact that integration isn't as straightforward as derivatives
violet stump
Revise algebra (like polynomial division and factorisation)
Kk thanks]
violet stump
But I was referring to the fact that integration isn't as straightforward as der...
Oh icic
hidden compass
I would also say trigonometry rules (mostly double angle formulas and the relationship between tangent and secant)
violet stump
I would also say trigonometry rules (mostly double angle formulas and the relati...
Okay, thank you
I appreciate your help @hidden compass
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
umbral robin
obtuse pebbleBOT
umbral robin
how can number 2 be done
I have the following sketch:
but I'm not sure my expression for r is correct
hardy widget
What was your original proportion from the similar triangles
umbral robin
Well I'm guessing the triangle would be the one formed by the radius, the height, and the slanted 'edge' of the cone
like this
hardy widget
Yeah it’s just these two
umbral robin
👍
hardy widget
What was your original proportion from the similar triangles
?
umbral robin
the original proportion is the one with sides 10 & 3
the 'new' proportions are he ones of the smaller triangle
umbral robin
all the info I have comes from the here
hardy widget
So what’s the equation you had from that
Because your final answer is wrong
But the triangles are right
hardy widget
Yeah
ebon shard
Can someone explain why the answer is 3 and not -3?
We created the augmented matrix
[
\begin{bmatrix}
1 & -3 & 0 \
-2 & 6 & 0 \
\end{bmatrix}
]
and row reduced it to
[
\begin{bmatrix}
1 & -3 & 0 \
0 & 0 & 0 \
\end{bmatrix}
]
and so if $c_2$ is 1, why is $c_1$ equal to 3 and not -3?
obtuse pebbleBOT
Can someone explain why the answer is 3 and not -3?
We created the augmented ma...
warm shaleBOT
Ryan (The Cat Collective)
worn yoke
because we want a linear combination so that they add to 0 so:
c1(1) + 1(-3) = 0
ebon shard
ohhhhh I think I get it
okay so like if we consider c1(1) to be x, then it's the same as x-3 = 0 so then x =3
ahhhhhh
okay I think I get it
ebon shard
because we want a linear combination so that they add to 0 so:
c1(1) + 1(-3) = ...
also how can you treat the vector as a single element, is there no difference between (excuse the row vector notation) [3, 0] and just 3?
worn yoke
i am only considering the first entry in the vectors because the second entries sum to 0 no matter what c1 and c2 are
ebon shard
ahh okay
that makes sense
TYSM :3
Genuinely feel so happy rn bc I think we finally are understanding how this stuff works
.close
obtuse pebbleBOT
ebon shard
.reopen
obtuse pebbleBOT
✅
ebon shard
Actually got one more question; in something like this, when doing row reduction, do we want to get the 0 in A_{1, 1} to be a 1 or do we just go the next column and check pivots from there?
worn yoke
if there are any nonzero entries in the column you need to row swap one of them to the pivot position
ebon shard
okay thanks
realizing we shouldn't have skipped the row reduction pset in week 1
Also would it be appropriate to keep this channel open for any other questions we have or should we close ane open a new channel as need-be?
obtuse pebbleBOT
@ebon shard Has your question been resolved?
sinful falcon
For number 5, once I have my linerization equation do I plug in 0.9? For x
warm shaleBOT
Result:
0.98304757249156
,calc 1-(1/2)(0.95)
warm shaleBOT
Result:
0.525
,calc 1-(1/2)(0.9)^(1/3)
warm shaleBOT
Result:
0.51725530769719
Ok this doesn’t really help
restive gorge
Ok this doesn’t really help
sorry
restive gorge
Or do I plug in square root 0.9
you plug in 0.9 and 0.99 for x
sinful falcon
you plug in 0.9 and 0.99 for x
Thbank you
sinful falcon
sorry
It’s ok I tried using the calc to see if it gave me a hint
But it didn’t really work
Thank
🙏
.close
sinful falcon
How do I approximate the values square root 0.9 and 0.99? I know my linear approximation function is 1-(1/2)x but if I plug 0.9 in I get a wrong answer.
obtuse pebbleBOT
How do I approximate the values square root 0.9 and 0.99? I know my linear appro...
worn yoke
we are approximating the function sqrt(1-x), so we are saying
sqrt(1-x) = sqrt(0.9) what is x then?
sinful falcon
we are approximating the function sqrt(1-x), so we are saying
sqrt(1-x) = sqrt(0...
0.1?
worn yoke
yes
obtuse pebbleBOT
sinful falcon
,calc 1-(1/2)(0.01)
warm shaleBOT
Result:
0.995
obtuse pebbleBOT
Available help channel!
sinful falcon
Can someone explain the questions at 27? I know I find the find the derivative of the function in given but what does it mean when it say compare values of delta y. Ok I think I’m just dumb but I KNOW I need to find the derivative the question is just confusing me (probably because I’m dumb or stupid)
obtuse pebbleBOT
Can someone explain the questions at 27? I know I find the find the derivative o...
@sinful falcon Has your question been resolved?
restive gorge
Can someone explain the questions at 27? I know I find the find the derivative o...
,, \frac{\Delta y}{\Delta x} = \frac{f(1.05)-f(1)}{1.05-1}
warm shaleBOT
bacc
restive gorge
Delta really means here difference
dy/dx is basically the best approximation, the d stands now for infinitesimal change
sinful falcon
dy/dx is basically the best approximation, the d stands now for infinitesimal ch...
I’m a bit confused still, so am I suppose to find the linerizatio of two things over the x values?
obtuse pebbleBOT
I’m a bit confused still, so am I suppose to find the linerizatio of two things ...
restive gorge
I’m a bit confused still, so am I suppose to find the linerizatio of two things ...
,, \frac{\dd y}{\dd x} = y' \Leftrightarrow \dd y = y' \cdot \dd x
warm shaleBOT
bacc
restive gorge
You can use the derivative y'
warm shaleBOT
bacc
restive gorge
They want you to compare Delta y to dy.
dy can be calculated by what I showed above
sinful falcon
Yes
sinful falcon
dy can be calculated by what I showed above
So for the first one dy is 4(1)-1 * dx minus 4(1.05) * dx over 1-1.05….?
restive gorge
y' = 4x-1 right
sinful falcon
Yea
restive gorge
So I guess we do now
(4(1.05)-1) * (1.05-1) and (4(1)-1) * (1.05-1)
,calc (4(1.05)-1) * (1.05-1)
warm shaleBOT
Result:
0.16
,calc (4(1)-1) * (1.05-1)
warm shaleBOT
Result:
0.15
Result:
1.16550625
Is (1.05-1) dx
restive gorge
,calc (1)^4-1+1
warm shaleBOT
Result:
1
,calc 1.16550625 - 1
warm shaleBOT
Result:
0.16550625
yes
sinful falcon
oka
restive gorge
oka
It's basically if Delta x becomes really small, here like 1.05-1 = 0.05 we can treat it as dx
warm shaleBOT
bacc
restive gorge
numerator is equal lol
warm shaleBOT
Result:
0.060606060606061
does dy become better
restive gorge
dy = y'(1.01) (1.01-1)
sinful falcon
And by does the approximation delta y ~ dy become better as delta x gets smaller just means is it closer to 0 right
warm shaleBOT
Result:
0.0304
,calc (4*1-1)*0.01
warm shaleBOT
Result:
0.03
,calc (0.0304 - 0.15)/(1.01-1)
warm shaleBOT
Result:
-11.96
Result:
0.04
.reopen
obtuse pebbleBOT
✅
sinful falcon
How do I do linear approximation to estimate? (31)
Not really sure how
To think about this really
Sorry
restive gorge
How do I do linear approximation to estimate? (31)
- Look at the power
What function could that be?
sinful falcon
What function could that be?
16
restive gorge
😂
You can estimate it using the function y = x^4
and then its linearization
at x = 1.999
sinful falcon
Oh I see
Thank you
🙏
May god bless you (if you think there’s a god) if you don’t then uh I bless you myself
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
pearl horizon
Anyone know how to solve this proof? I figure I only need to show that n is perpendicular to vectors in the plane. I could use the dot product to do that but I think I'm running into trouble understanding how to work with a hyperplane.
obtuse pebbleBOT
Anyone know how to solve this proof? I figure I only need to show that n is perp...
@pearl horizon Has your question been resolved?
pearl horizon
<@&286206848099549185>
warm shaleBOT
DexNip
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
pearl horizon
Im not sure if this is on track.
I believe this would show that n is perpendicular but i'd like a second opinion
obtuse pebbleBOT
@pearl horizon Has your question been resolved?
obtuse pebbleBOT
@pearl horizon Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
The problem is: an order of 5 variables where i can choose from a, b, c, d, e, f, g and h.
every single variable can be reused except for a
how many probabilities are there for this array of 5 variables
obtuse pebbleBOT
The problem is: an order of 5 variables where i can choose from a, b, c, d, e, f...
timid silo
the answer is 5(1x7x7x7x7) + 7^5
N(arrays with a) + N(arrays without a)
I still don't totally understand why its like that
zenith raft
there are 5 ways to choose a position among the 5 to be a. then 7^4 ways to fill in the last positions with the other 7 letters
without any a’s, similar thing
timid silo
there are 5 ways to choose a position among the 5 to be a. then 7^4 ways to fill...
that's what i thought too but with N(arrways without a) 5(7x7x7x7x7)?
zenith raft
5 positions to assign letters to, 7 options for each
timid silo
because theres 5 positions and in each position there are 7 choices
but why is it wrong here
orrrrrr because the N(with a) can be a in only one spot thats why 5(1x7x7x7x7)
timid silo
why would it be that?
because when i apply the same logic from the N(with a) it kind of seems right
zenith raft
timid silo
orrrrrr because the N(with a) can be a in only one spot thats why 5(1x7x7x7x7)
but it wouldnt work becuase of this right?
timid silo
5 places to place a
1 of 4 places to place one of 7 variables
so on?
zenith raft
counting arrangements where a is in the 1st position, counting arrangements where a is in the 2nd position, …, counting arrangements where a is in the 5th position
when you fix a in the first position there are 7^4 ways to fill in the others
similar when you fix a in the second position and so on
timid silo
counting arrangements where a is in the 1st position, counting arrangements wher...
so its like 1x7x7x7x7 + 7x1x7x7x7 + ...
zenith raft
sure
timid silo
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
unborn epoch
ngineers are trying to determine where to locate a mine. At one site, 70% of the ore samples
are below the minimum size needed for studying. If we randomly select 4 ore samples from
all the available samples at this site, what is the probability that:
a) all four samples will be undersized?
b) none of the samples will be undersized?
c) Three of the samples will be undersized?
obtuse pebbleBOT
ngineers are trying to determine where to locate a mine. At one site, 70% of the...
unborn epoch
guys for part c
i got 0.7^3 * 0.3
but its wrong
3 samples undersize * 1 sample oversize
what am i doing wrong
plain stag
you've undercounted
unborn epoch
?
plain stag
perhaps it would help to think about precisely what your sample space is for this situation
unborn epoch
would this be a permutation or combination problem?
unborn epoch
perhaps it would help to think about precisely what your sample space is for thi...
meaning?
unborn epoch
meaning?
plain stag
what do you need me to elaborate on?
unborn epoch
you mean how many ways i can get 3 of my samples undersized?
unborn epoch
0.7^3
plain stag
that's not a "number of ways"
plain stag
you dodging my question isn't really appreciated
unborn epoch
123 or 132 or 231 or 321
plain stag
your experiment can be explained as follows: you have 4 samples of ore, each of which can either be undersized or not undersized
unborn epoch
4 ways
plain stag
your experiment can be explained as follows: you have 4 samples of ore, each of ...
with this in mind, what is the sample space of your experiment?
unborn epoch
what does sample space mean
plain stag
the set of all possible outcomes
unborn epoch
ok
unborn epoch
with this in mind, what is the sample space of your experiment?
hmmm not sure how i can find that
4^4
256
plain stag
for example, if we let 0 represent an ore that is undersized and 1 represent an ore that isn't, we could write 0000 to mean "all 4 ores are undersized" or 1111 to mean "none of the 4 ores are undersized"
unborn epoch
yes
plain stag
so how can we write "3 of the 4 ores are undersized"?
plain stag
quite so
so then the probability of 3 of the 4 ores being undersized is the probability of (1000 or 0100 or 0010 or 0001)
unborn epoch
ok
plain stag
hopefully you were introduced to some strategy to calculate probabilities of "or"s
unborn epoch
you are saying or because its mutually exclusive
plain stag
i wouldn't say because, but yes they are mutually exclusive
unborn epoch
how do i find total outcome
plain stag
total outcome?
plain stag
indeed
unborn epoch
so we just multiply by 4
to get 4 outcomes
can we use permutation here to solve
like xPy ?
since order matters in this question
plain stag
does order matter?
plain stag
all four of those satisfy "3 of the 4 ores are undersized"
i would argue order doesn't matter
unborn epoch
oh right it doesnt specifically say the first one of the 4 has to be undersize
so order doesnt matter
so would we use combination then?
plain stag
sure
you could say that you have 4 ores and choose 3 of them to be undersized
how many ways can you do this?
unborn epoch
4
plain stag
4
plain stag
so then the probability of 3 of the 4 ores being undersized is the probability o...
thus your ultimate answer to this is what
plain stag
4C3
unborn epoch
oh ok
hmm
if the number was high like proabbiluty of 10 of the 50 ores being undersize
how would we find the ways
is there a formula?
unborn epoch
it will obviouslt take me a long time to write it down
drifting basalt
Hello there
obtuse pebbleBOT
Hello there
safe haven
which question do you need help with
drifting basalt
drifting basalt
Isn't it -3b + a?
safe haven
indeed
drifting basalt
How do you determine whether a line is straight or not using vectors?
Uh you there>
safe haven
How do you determine whether a line is straight or not using vectors?
you need to find out whether a segment of the line is a scalar multiple of another segment of the same line
safe haven
same thing
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
surreal grotto
how to solve this
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
vital junco
vital junco
For 2 and 3 I got different answers
obtuse pebbleBOT
@vital junco Has your question been resolved?
hardy gate
yo can anyone help me out
obtuse pebbleBOT
yo can anyone help me out
hardy gate
im making an animation about the unit circle and it get faster when its about to flip
i know why
its bc its moving along the x axis at a constant speed
but i want to change it so that the hypotenuse moves around at a constant speed
the probelem is tho i draw the hypotenuse based on the x-axis
^increasing i steadily
LEN is the diameter
timid silo
hardy gate
surely someone helps
timid silo
yup, just be patient
rose scroll
RAYS is the number of frames for covering 180 degrees of that unit circle right?
So, if im reading this right, the hypotenuse is (a,b)
so you can set a as a = (LEN/2)*sin(pi*i/RAYS)
should work I think
also why do you use only the variable b in the line(), and not the variable a as well?
as in HEIGHT/2 - (b) and not a corresponding WIDTH/2 - (a)
hardy gate
RAYS is the number of frames for covering 180 degrees of that unit circle right?...
rays would be the divisor of LEN
basically what im doing is i'm diving len by how accurate and fast i want it to be and at each point along the x-axis i find the y point using pythag
hardy gate
also why do you use only the variable b in the line(), and not the variable a as...
cuz i'm stupid
hardy gate
rays would be the divisor of LEN
rays bc i was going to make a raycaster and the amount of times i divided len is the amount of hypotenuses i got
but i changed my mind midway
and kept the variable names
rose scroll
yeah, so number of different hypotenuses is the number of angles you have split from horizontal in -x to horizontal in +x right?
hardy gate
i didnt understand please repeat
hardy gate
RAYS is the number of frames for covering 180 degrees of that unit circle right?...
can you please explain why this works i shouldnt be making this project im not smart enough
rose scroll
so, the horizontal speed that you need is just the speed of the sin component of the hypotenuse on x axis
if you tweak the sin component instead of the angle, it should work
hardy gate
so, the horizontal speed that you need is just the speed of the sin component of...
does this need me to change the horizantal speed dynamically
obtuse pebbleBOT
@hardy gate Has your question been resolved?
rose scroll
also why do you use only the variable b in the line(), and not the variable a as...
thats coz you only use b and not a like I said before I think...
dim moon
why are there two product symbols
obtuse pebbleBOT
why are there two product symbols
hardy gate
thats coz you only use b and not a like I said before I think...
no i put a into it
its fine i did it
surreal forge
why are there two product symbols
the two product symbols are there to indicate you are multiplying across every possible ordered pair of positive integers (m, n)
obtuse pebbleBOT
@dim moon Has your question been resolved?
dim moon
the two product symbols are there to indicate you are multiplying across every p...
ok
thank you
dim moon
the two product symbols are there to indicate you are multiplying across every p...
but there is no upper bound upto which we have to take m and n
surreal forge
yes it just means product to infinity
dim moon
.close
fading stream
Variables:
D : Number of days to count
n : number of binary clocks
N : amount of time when a binary clock is in on state (1) (in seconds)
F : amount of time when a binary clock is in off state (0) (in seconds)
c : offset for the binary clock (when it turns on or off)
f : lowest frequency such that N + F is lower than 200000, or floor (86400D/200000)
Base question:
Use the lowest amount of binary clocks with the lowest amount of combinations such that it's able to differentiate between each day
Example from image: 3 day counter
There's 12 combinations: which is
Day 1: 0000 0001 0011 1110
Day 2: 1100 1001 0011 0010
Day 3: 0100 1101 1111 1010
The Clocks values are:
1st bit: N = 64800 F = 64800 c = 0
2nd bit: N = 64800 F = 64800 c = 21600
3rd bit: N = 43200 F = 43200 c = 0
4th bit: N = 43200 F = 43200 c = 21600
There's no overlap of combinations between each days
And as for personal reasons, I need help for these constraints:
D is prime, N < 100000, F < 100000, c < 100000
Therefore (f to n)Π(2-|(N-F)/(N+F)|) ≥ between 2(n-f) to n(n+1) - f(f+1)
or 2^(n-f) ≥ between 2(n-f) to n(n+1) - f(f+1)
If N = F
It gets harder the more days you have, I want to know a good way to find the solutions and whether it has a mathematical solution or have to be solved computationally using search algorithms like depth first search
also what field of maths is this
obtuse pebbleBOT
Variables:
D : Number of days to count
n : number of binary clocks
N : amount of...
kind hawk
I am confused about your f and what you mean with floor(n/200000). cause that will be 0 most of the time
just my feeling tells me this wont have a nice solution
fading stream
I am confused about your f and what you mean with floor(n/200000). cause that wi...
oops i put wrong thing
done look at it again
yea its not so nice
obtuse pebbleBOT
@fading stream Has your question been resolved?
fading stream
a
obtuse pebbleBOT
@fading stream Has your question been resolved?
obtuse pebbleBOT
@fading stream Has your question been resolved?
fading stream
bru
echo osprey
Is this a legitimate proof of sqrt(3) being irrational?
obtuse pebbleBOT
Is this a legitimate proof of sqrt(3) being irrational?
@echo osprey Has your question been resolved?
obtuse pebbleBOT
@echo osprey Has your question been resolved?
prisma pasture
z=x+yi
it's given that z^2+1/z^2 is a real number
Prove that z is located on the unit circle
My idea was to rewrite z^2+1/z^2 as a+bi, using z=x+yi, and then solve the question b=0
But I can't rewrite z^2+1/z^2 as a+bi, can someone help?
obtuse pebbleBOT
z=x+yi
it's given that z^2+1/z^2 is a real number
Prove that z is located on the...
tardy epoch
z=x+yi
it's given that z^2+1/z^2 is a real number
Prove that z is located on the...
Just plug in x+iy for z
(x+iy)^2 = x^2 + 2ixy + y^2
obtuse pebbleBOT
@prisma pasture Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
harsh scaffold
obtuse pebbleBOT
iron edge
How can we help you?
harsh scaffold
Can u give me an example of each, and maybe explain difference squares a little bit
iron edge
Can u give me an example of each, and maybe explain difference squares a little ...
a^2 -b^2 = (a+b)(a-b)
astral steeple
How can I solve this limit?
obtuse pebbleBOT
How can I solve this limit?
astral steeple
$\lim_{x \to 0}\frac{sin(x^2+\frac{1}{x})-sin(\frac{1}{x})}{x}$
warm shaleBOT
Douglas Fanucchi
astral steeple
I was able to get this far:
$$\lim_{x \to 0}\frac{sin(x^2+\frac{1}{x})-sin(\frac{1}{x})}{x} = \lim_{x \to 0}\frac{2\cdot sin\left(\frac{x^2+\frac{1}{x} - \frac{1}{x}}{2}\right)cos\left(\frac{x^2+\frac{1}{x}+\frac{1}{x}}{2}\right)}{x}$$
$$\lim_{x \to 0}\frac{2\cdot sin(\frac{x^2}{2})cos(\frac{x^2}{2}+\frac{1}{x})}{x} = \lim_{x \to 0} \frac{2\cdot sin(\frac{x^2}{2})cos(\frac{x^2}{2})cos(\frac{x^2}{2}+\frac{1}{x})}{cos(\frac{x^2}{2})x}$$
$$\lim_{x \to 0}\frac{sin(x^2)cos(\frac{x^2}{2} + \frac{1}{x})}{cos(\frac{x^2}{2})x}$$
warm shaleBOT
Douglas Fanucchi
agile patio
2+2! ?
astral steeple
i don't speak your language
agile patio
sorry
obtuse pebbleBOT
2+2! ?
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).
astral steeple
.close
plucky trail
sqrt(|x|) always assumes a positive value?
obtuse pebbleBOT
sqrt(|x|) always assumes a positive value?
median dome
no
plucky trail
okay
median dome
it's bounded from below but not from above
usually by bounded we mean that it has to be bounded within a finite interval
plucky trail
If I have a bounded function * a function bound from above/below
would the result be a bounded function?
My prof said if I have a bounded function divided by infinity it would equal 0
I can't remember him mentioning anything about bound from below or bound from above so that's new to me
idle pond
if two functions f(x) and g(x) have the exact same natural domain, say R for both or (0,infinity) does that mean the composition of them will have that same domain?
obtuse pebbleBOT
if two functions f(x) and g(x) have the exact same natural domain, say R for bot...
gilded needle
what if some value of f(x) isn't in the domain of g?
idle pond
would it matter cause im talking abotu like the maximal domain? or
like if each function can take the same range of inputs wouldnt their composition be that range
marsh geyser
I would not use the word range
idle pond
how would i better say this
idle pond
oh yeah my bad
marsh geyser
I would say yes to your question but i am not sure if I understand totally your question
Can you provide an example?
idle pond
say let f(x)= 2x, g(x) =x^2 with their maximal domain being (-inf,inf) then their composition (fog)(x) =2(x^2) and (gof)(x)=(2x)^2 would have the same maximal domain ?
idle pond
thanks
restive gorge
say let f(x)= 2x, g(x) =x^2 with their maximal domain being (-inf,inf) then thei...
I wonder about f(x) = 1/x and if you do f(f(x)) 
warm shaleBOT
restive gorge
x = 1/(1/x)
marsh geyser
For x different of 0
obtuse pebbleBOT
@idle pond Has your question been resolved?
sinful falcon
Hello, can I take advantage of your guys knowledge please even though this is a Math server.
How would I determine if (NH_4)_(2)SO_4 is an ionic, polar, or non polar bond?
obtuse pebbleBOT
Hello, can I take advantage of your guys knowledge please even though this is a ...
tranquil geyser
Hello, can I take advantage of your guys knowledge please even though this is a ...
If electron exchange occurs then it is ionic
iron edge
Hello, can I take advantage of your guys knowledge please even though this is a ...
Just check if those are symmetry
The circles stand for lp
Because the shape of SO4^2- looks like tetrahedron
And its outer atoms are the same
Therefore, it should be non polar
Let’s take another example, CO2
It looks like
O=C=O, which is also symmetry
sinful falcon
Yea
iron edge
Does that clear your doubts?
sinful falcon
Does that clear your doubts?
Am I suppose to know Lewis Structures? We haven’t touched on the topic yet
iron edge
Ofc you should
iron edge
Without that, all you can do is memorize what is given on the textbook
There’s no way for you to verify
sinful falcon
There’s no way for you to verify
These are all my notes on the bonds am I suppose to know how to find out if it’s ionic polar or non polar with this? (I was absent for the day but he gives out stuff we’re suppose to read and touch on)
But I might just be stupid too
iron edge
There are two options
First, learn Lewis structure
Second, memorize
There is no alternative for Lewis structure
tranquil geyser
Almost all ionic compounds are polar
Then for covalent compounds you probably have to analyze the arrangement of elements or radicals around the central element
obtuse pebbleBOT
@sinful falcon Has your question been resolved?
dusky cedar
I need help on this asap 🙏🙏
I cant understand Gauss method
obtuse pebbleBOT
I need help on this asap 🙏🙏
I cant understand Gauss method
restive gorge
I need help on this asap 🙏🙏
I cant understand Gauss method
What is your doubt on Gauss
dusky cedar
What is your doubt on Gauss
Idk i just dont get it
Well
Actually
I can find the two zeros
But i cant find third
surreal forge
<@&268886789983436800>
dusky cedar
Bro
restive gorge
lol
Let me check
From here you use the 2nd row
to continue
It's actually easier to do -R2 + R3 -> R3
dusky cedar
What i need to do with 2nd row?
restive gorge
Add the negative of it onto the 3rd row
dusky cedar
It's general formula i can use everywhere or it's specific for this one example?
unreal musk
"formula" 
restive gorge
But here we make an exception and we let 8 stay
cause removing -1 is way simpler than introducing fractions
dusky cedar
It's actually easier to do -R2 + R3 -> R3
So the new third row is 0 5 0?
restive gorge
-(-5)-10?
warm shaleBOT
bacc
restive gorge
Now you are basically done
You can deduce what the solution is starting from the last row
dusky cedar
5z = -5
restive gorge
ye
dusky cedar
So y = -1 right
dusky cedar
OOOOH
restive gorge
🧑🏻🍳
restive gorge
ye
marsh geyser
No
dusky cedar
Hold on
marsh geyser
You made a double mistake
dusky cedar
Where?
marsh geyser
Mistake in your subtitution and mistake in your resolution
dusky cedar
Mistake in your subtitution and mistake in your resolution
I don't understand, can u explain?
marsh geyser
x - 2 + 2 = 4
Mistake in your resolution: this is never x=2
Mistake in your substitution: -2(-1) = 2, not -2
dusky cedar
0 -1 2
dusky cedar
x=0
y=-1
z=2
The answer is right tho
restive gorge
You basically work you way down
dusky cedar
Im so weak at math
dusky cedar
You basically work you way down
Yeah i got it
But im struggling with getting those 0s
restive gorge
your work tools are your diagonal element
dusky cedar
I remembered it need staircase-like form
restive gorge
for 1st column you use a_11
for 2nd column a_22
for 3rd column a_33 etc
restive gorge
You wanna turn $d,g$ and $h$ to 0's with the diagonal elements (it's of best interest if we manage to get clean numbers like 1 on the diagonals)
[ \left ( \begin{array}{ccc|c} \textcolor{cyan}{a} & b & c & u \ \textcolor{red}{d} & \textcolor{cyan}{e} & f & v \ \textcolor{red}{g} & \textcolor{red}{h} & i & w\end{array} \right ) ]
You do this by making use of scalar multiplication on rows and adding them to the others.
dusky cedar
dusky cedar
You wanna turn $d,g$ and $h$ to 0's with the diagonal elements (it's of best int...
What
warm shaleBOT
bacc
restive gorge
I need to multiply r1 by -4
yes
restive gorge
ye
restive gorge
ye
dusky cedar
Alright what's next
restive gorge
the rest should be trivial
2nd and 3rd row are identical
what does that mean for your system
dusky cedar
y and z have same value?
restive gorge
yes
mellow meteor
hello
mellow meteor
is (-x) = x?
obtuse pebbleBOT
@mellow meteor Has your question been resolved?
wary badger
if it’s an even function then yes
uneven flame
so its a rule?
not really no
more context would really be appreciated
for example, it's true for f(x) = x^2 but not f(x) = x^3
mellow meteor
what
mellow meteor
for example, it's true for f(x) = x^2 but not f(x) = x^3
what does that mean?
obtuse pebbleBOT
uneven flame
more context would really be appreciated
seriously, more context please
.reopen
uh, can you send the .reopen?
mellow meteor
exercice?
uneven flame
I think it needs to be the person who opened the channel
mellow meteor
.reopen
obtuse pebbleBOT
✅
mellow meteor
but it's in arabic..
uneven flame
but it's in arabic..
Even so
obtuse pebbleBOT
@mellow meteor Has your question been resolved?
mellow meteor
obtuse pebbleBOT
@mellow meteor Has your question been resolved?
echo forum
what did i do wrong here?
void quartz
search and read about total differential of multivariable functions
obtuse pebbleBOT
@echo forum Has your question been resolved?
echo forum
like this?
obtuse pebbleBOT
@echo forum Has your question been resolved?
void quartz
like this?
yess
echo forum
ok, i can try that. but whats wrong with the 1.5-(1.5*38)/40.5?
void quartz
i dont know how you got that, its wrong
but somehow, its close to the right answer, when you evaluate it lol
echo forum
i remembered the gas laws. P1V1=nRT. n is the number of mols. R is a constant. and in this case T is constant too. which gives P1V1=P2V2
void quartz
youre clearly asked to use part (a)... 😛
but it should work though
void quartz
<:pain:1157895315878322197> but it should work though
yeah its correct though, definitely
except you swapped signs of two terms
echo forum
ok yeah i just got the same answer using a
echo forum
-1.5 + fraction
why should it be like that?
void quartz
ok yeah i just got the same answer using a
using part (a), you got -0.09
and not +0.09
isnt it 😛
echo forum
no i got 0.09
void quartz
nope, its -0.09
pressure has to decrease by 0.09, not increase by 0.09
,w 0=(-16.574/38² + 2* 0.52754/38^3 + 1.5*12.187)2.5 + (-0.3879 + 12.18738)*x
warm shaleBOT
void quartz
yep, watch the signs!
i dont blame you, this problem makes you lose focus
so many numbers and terms and decimal places
echo forum
it said -0.09 is wrong
echo forum
ok thats hilarious'
when i put in the equation that gives -0.09 for its answer, it gets marked wrong. But as soon as i just type in -0.0987 its right?
void quartz
lol
echo forum
thats kinda ridiculous
void quartz
it is xD
thats why i dont like these too much
they dont replace the teacher's eyes
when they are checking result/answer
echo forum
the funniest thing is that im technically supposed to solve this without a calculator
i didnt
because half the questions couldnt be solved without one
but thats still hilarious
echo forum
agreed. its why i hate these math classes. SoLvE tHiS wItHoUt A cAlCuLaToR. yeah right buddy
i also hate when physics classes do it. or really any class that requires a lot of calculations. But i'm getting off tpic now. Thanks for the help
void quartz
my pleasure, thank you too!
edgy needle
for part d
obtuse pebbleBOT
for part d
unreal musk
why they do 4+2
4 + 2? 
unreal musk
Oh, I see what you mean now 
edgy needle
rose scroll
I think thats because the object is at rest at 1 sec
so the net displacement would be different from the distance covered
coz distance cares about the path and displacement is just the difference between the locations at two times
rose scroll
if you see, at t=2, x=1, so displacement is only 2
rose scroll
is it a trick question
not really. It just checks whether you understand the concept of distance and displacement properly and can distinguish between the two
edgy needle
):
edgy needle
not really. It just checks whether you understand the concept of distance and di...
oh
distance doesnt care ab the negative
s
ohh
edgy needle
not really. It just checks whether you understand the concept of distance and di...
i dont get how they got the first value
4
rose scroll
x(1) = 3
x(0) = -1
you take the difference, which is the distance/displacement (both are same in this case) which equals 4
rose scroll
yep
rose scroll
np
edgy needle
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
fathom mural
could anyone explain why this is wrong please
obtuse pebbleBOT
could anyone explain why this is wrong please
warped aspen
i have no clue what cylindrical shells is but I would integrate using volume form
fathom mural
according to the graph
the red is the original region shaded
and then rotating it around the y-axis, the grey region would be covered as well
fathom mural
i have no clue what cylindrical shells is but I would integrate using volume for...
i did
i used the following formula
V = pi * int [0,9] (x) dx
warped aspen
Yes
fathom mural
thats the formula i solved for giving me (81/2)pi
and as u can see thats wrong according to the question
unless im supposed to use the shell method which im not sure if i am supposed to
that is
V = 2 pi * int [ a , b ] (point radius) ( f ( x ) - g ( x ) )dx
fathom mural
I got 81/2 pi aswell
yep
are my bounds correct btw
im pretty sure its frm 0 to 9 right
fathom mural
could anyone explain why this is wrong please
anyone know why this is wrong?
<@&286206848099549185>
is it bc i didnt use shell method?
timid silo
<@&286206848099549185>
what area did you find for the flat shape,
imma try even though ive never done it before
fathom mural
what area did you find for the flat shape,
even if u find the area, its different
like thats not how u find the volume in these types of problems
idk how to explain myself but the area has nothing to do w finding the volume 😭
solved it
obtuse pebbleBOT
timid silo
like thats not how u find the volume in these types of problems
idk how to expla...
bro i just need to find the area and rotate it
thats the volume
do you know the correct answer?
i got something
@fathom mural whats the given answer?
fathom mural
<@972573098861822032> whats the given answer?
i got (972pi)/5
and thats the correct answer
fathom mural
i got something
what was it
obtuse pebbleBOT
Available help channel!
empty maple
How do I find inverse of a function like $f(x) = ax^2 + bx$
obtuse pebbleBOT
How do I find inverse of a function like $f(x) = ax^2 + bx$
warm shaleBOT
MetuMortis
deft magnet