the limit is 0 because f(x) gets close to 0
#help-10
timid silo
graceful nova
thats the point
ohhhhh
oh okay
its starting to click now
the limit is equal to what it approaches
you said earlier than for continuous functions you can substitute, why can you do it there but not here?
that was a little vague
oops brb 1 minute delivery guy
timid silo
continuous functions are defined to be functions where you can substitute to get the limit
ie $f(x)$ is continuous if and only if $\lim_{x\to a}f(x)=f(a)$ for all $a$
warm shaleBOT
Toby
timid silo
examples of continuous functions are polynomials (x, x^2+2 etc), sin, cos, e^x
but if f is not continuous at a point, (such as the previous pi function), then we cant substitute because the limit at a is NOT f(a)
graceful nova
but in your previous example you just said f(a) is just some other number
instead of the regular pattern
so why wouldnt the limit be then just that number
what would that say exactly thats incorrect
timid silo
f in that example isnt continous
timid silo
graceful nova
ohhhhhhh
timid silo
yeah, but why isnt it correct when not continuous
because thats the definition of continuous :p
graceful nova
THANKS
this was so confusing
i think i kind of get it now, need to ponder about it on my own
thanks for the help, you are really kind!!!
.close
obtuse pebbleBOT
timid silo
thanks for the help, you are really kind!!!
yw, glad I could help :D
obtuse pebbleBOT
Available help channel!
slim gust
obtuse pebbleBOT
high lily
is that
$$f(x)= - x^2 + x$$
warm shaleBOT
ℝamonov
slim gust
yes
high lily
your work is wrong,
the website is correct
high lily
(order of operations)
timid silo
can anyone send me a friend request
I have a Math exam next week
I need help in equation , power , number types and use of calculator
obtuse pebbleBOT
can anyone send me a friend request
I have a Math exam next week
I need help i...
cedar lichen
Why did you ask the same thing in two channels
timid silo
sorry
brittle blaze
Not even a reason to open a help channel
timid silo
can anyone ?
misty temple
I’m confused by what “functionally complete” means. I understand using a set S that is functionally complete, prove the set R in question is functionally complete by deriving the symbols in S, but when I discussed this with my professor he said that we need to work from a general form ex. A+B, using S={+, comp.}. The set R in his example was R={complement, implication}. Why can’t I just go from A -> B === not A or B and call it functionally complete?
obtuse pebbleBOT
I’m confused by what “functionally complete” means. I understand using a set S t...
misty temple
Would another way of doing it be proving that the truth table for not A -> B is the same as A + B?
misty temple
I’m a vim fan :P are you able to lend a hand with this?
night fox
I am neovim user, previously I was using emacs but somehow apt brick it 😦
misty temple
I’m confused by what “functionally complete” means. I understand using a set S t...
<@&286206848099549185>
night fox
!15m
obtuse pebbleBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
misty temple
Oh sorry
night fox
np
obtuse pebbleBOT
@misty temple Has your question been resolved?
misty temple
<@&286206848099549185>
obtuse pebbleBOT
@misty temple Has your question been resolved?
misty temple
Nvm ig
unborn spire
How do I simplify this
obtuse pebbleBOT
How do I simplify this
final thunder
,rotate
stable rain
()
warm shaleBOT
unborn spire
Ok
stable rain
n distribute the - in
unborn spire
So make 1 negative and other plus or just 1 negative
unborn spire
One question
The first one in second bracket x power 3
Will it be positive or negative
@stable rain
stable rain
neg
obtuse pebbleBOT
@unborn spire Has your question been resolved?
unborn spire
Yes
vernal linden
What is the standard equation of the circle whose center is (-5,-4) and whose radius is 3?
A. (x+5)2 + (y+4)2 = 9
obtuse pebbleBOT
What is the standard equation of the circle whose center is (-5,-4) and whose ra...
vernal linden
(x - 5)2 + (y - 4)2 = 9
final thunder
A is right
final thunder
First one centred at -5,-4 second one 5,4
versed cave
and whose radius is 3
Nvm I didn't notice those 2s were ²
obtuse pebbleBOT
vernal linden
What are the four vertices of the ellipse whose equation is (x2)/9 + (y2)/4 = 1
will this one be (3,0) (0,-3)
oh nvm it might be (3,0),(-3,0),(0,2),(0,-2)
or am i tripping
obtuse pebbleBOT
Available help channel!
vernal linden
What are the four vertices of the ellipse whose equation is (x2)/9 + (y2)/4 = 1
will this one be (3,0) (0,-3)
oh nvm it might be (3,0),(-3,0),(0,2),(0,-2)
or am i tripping
obtuse pebbleBOT
What are the four vertices of the ellipse whose equation is (x2)/9 + (y2)/4 = 1
...
brisk grove
Yes that's correct
vernal linden
[(x2) / 25] - [(y2) / 36] = 1
ik this one opens to the sides but why does it open to the sides
is it because of y term being negative
vernal linden
The coefficient of y^2 is negative.
this one open up and down becasue the x^2 is negative right
brisk grove
Yes
obtuse pebbleBOT
@vernal linden Has your question been resolved?
vernal linden
In Matrix A, what element is in the second row, third column?
i said it was 1.5 but its wrong
brisk grove
It's 2
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
mighty sage
obtuse pebbleBOT
mighty sage
i multiplied 16/16 and got sin(16x)/16x * 16/18 which i simplified from 1 * 8/9 = 8/9 but was wrong
hot sonnet
i multiplied 16/16 and got sin(16x)/16x * 16/18 which i simplified from 1 * 8/9 ...
Hello, x is approaching inf, not 0
mighty sage
Hello, x is approaching inf, not 0
oh true
idk it keeps going up and down on graph
or should i have it in degrees?
boreal condor
couldnt u also use squeeze theorem?
warm canopy
If you know the squeeze/sandwich theorem, that can be applied here
boreal condor
im on limits and continuity rn
well try to think logically
in sinx
what is the range
try to think of what a sin(x) graph looks like, what is the maximum and minimum value
obtuse pebbleBOT
@mighty sage Has your question been resolved?
frank night
obtuse pebbleBOT
frank night
a is a real number and i need to show that f(x)<0 for every x real numbers
i started by calculating the derivative of f
but idk what to do after
timid silo
a is a real number and i need to show that f(x)<0 for every x real numbers
as in you need to put a constraint on a?
ie, find all a such that f(x)<0?
or are you saying that its true for any a (it isnt)
frank night
as in you need to put a constraint on a?
yes i need to show the a's which satisfy the condition
timid silo
what happens when (a+1)≥0?
frank night
what happens when (a+1)≥0?
f is increasing
timid silo
f is increasing
right, so f(x) must take on positive values if a≥-1. So we can disregard those and so we only need to test for a<-1
We want the vertex to be <0 as f would be decreasing and so the max is the vertex
so solve for a such that f(vertex)<0
frank night
so solve for a such that f(vertex)<0
i need to calculate f(-b/2a) and in this case f(a/2(a+1))?
timid silo
unfortunate naming convention, but yeah
frank night
so for f(vertex)<0 i get a∈(2-sqrt(28)/3,2+sqrt(28)/3)
and i need to reunite this with (-1,inf)?
so it would be a∈(-1,2+sqrt(28)/3)
timid silo
(2-sqrt(28))/3? careful of brackets
also double check your interval
I think it should be ((2-sqrt(28))/3,-inf)
we want it to be negative, so like this:
timid silo
I think it should be ((2-sqrt(28))/3,-inf)
fixed sorry
frank night
I think it should be ((2-sqrt(28))/3,-inf)
isn't actually (2-sqrt(28))/3<-1 so the interval would be -1,2+sqrt(28)/3
timid silo
no, we take intersections
so its the smaller one
play around with val of a https://www.desmos.com/calculator/otcozhmfkq
frank night
no, we take intersections
oh right
timid silo
(gtg sorry)
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
urban garnet
I literally have no idea how to do this question, so I need all the help that I can get
obtuse pebbleBOT
I literally have no idea how to do this question, so I need all the help that I ...
haughty coyote
a), b): projectors are linear
c): projections are along a direction, so you can just take the unit vector anyways
brisk matrix
$\text{proj}_uv=\frac{u\cdot v}{||u||^2}u$
warm shaleBOT
maximo
brisk matrix
if you know what theo mentioned it’s quicker to compute, but it can be shown from the definition of projection as well
urban garnet
How do I figure out what u, v, and w are, or do I not need to?
brisk matrix
you don’t need to
for example:
$\text{proj}_w(u+2v)= \frac{(u+2v)\cdot w}{||w||^2}w= \frac{u\cdot w}{||w||^2}w + 2\frac{v\cdot w}{||w||^2}w = \text{proj}_wu+2\text{proj}_wv$
warm shaleBOT
maximo
urban garnet
Why does u+2v suddenly become u
urban garnet
Oh wait I didn't see the plus and then the next line, my b
Ok I think I can do 3a and b, but for c, I get that you can distrubute the 3 out of w vector, but what about the w scalar?
would |3w|^2, be 9w^2?
<@&286206848099549185> ?
urban garnet
Also for 3b it would be 3projw_u right?
brisk matrix
yes
brisk matrix
it’s called linearity
urban garnet
Cool
brisk matrix
linear algebra is all about linear transformations
urban garnet
I haven't done linear algebra
brisk matrix
this is linear algebra
not exactly groundbreaking stuff but it’s part of the field nonetheless
urban garnet
I have no idea why this is a question in my multivariable calc class then
brisk matrix
multi variable calc is often taught through vector calc
so you’ll run into linear algebra more than likely
urban garnet
.close
obtuse pebbleBOT
cedar lichen
What have you tried
shrewd epoch
I think this calls for a case of Cramer's rule
cedar lichen
shrewd epoch
42
cedar lichen
Don't troll in help channels
nocturne minnow
Well, no one here is going to give you answers
Because we're not here to give answers
We help
And someone helped, by providing a good video
cedar lichen
What grade are you in?
grand garden
which language do you speak
cedar lichen
I'm convinced this guy is trolling
nocturne minnow
Like under 13 years old?
shrewd epoch
You probably shouldn't be on discord then
shrewd epoch
12 years old, 3rd grade. Makes total sense
nocturne minnow
Sorry can't, bye
long plinth
"Almost" 13 is not enough. You can come back in half a year.
upbeat plinth
.close
obtuse pebbleBOT
long plinth
(Whoops, preempted by quicker colleague).
obtuse pebbleBOT
Available help channel!
grizzled geyser
I'm having a bit of difficulty with a problem. I had to find mesure BC in this triangle
obtuse pebbleBOT
I'm having a bit of difficulty with a problem. I had to find mesure BC in this t...
grizzled geyser
here's what I did.
and then the following question was to find the angles of A, B and C we are already given the angle of A (10 degrees) so then I found that the angle of B was of approx 56.44 degrees and the angle of C of approx 66.43 degrees
the problem is that the angles inside the triangle don't add up to 180 degrees! (sorry the words are in french but you don't need to understand the words, just follow the steps) I don't know where I made the mistake any help would be appreciated so much. From the graph, it does not look not right angled
I dont know where I made the mistake
how is it possible that the angles do not add up to 180 degrees
tidal hawk
how is it possible that the angles do not add up to 180 degrees
I don’t think it is
was your calculator in radians mode
grizzled geyser
no it was in deg mode
grizzled geyser
I even used a website that does the calculations automically to double check
this one
nocturne minnow
,w 180 - 10 - 56.44
warm shaleBOT
nocturne minnow
I even used a website that does the calculations automically to double check
According to my calculations sin(66.43) = sin(113.56), probably some weird circle thing where you have to transform 66.43 to 113.56
grizzled geyser
is it possible that the way im supposed to find angle C is by doing 180 - (10+56.44)?
instead of using the sine rule
summer stone
u should be able to get it both ways
nocturne minnow
u should be able to get it both ways
Not really
summer stone
Not really
why not?
nocturne minnow
Because it results in 66
summer stone
Because it results in 66
right right, understand that
nocturne minnow
,w 58.35/sind(10) = 308/sind(x) solve for x
warm shaleBOT
nocturne minnow
I knew it had something to do with sine being periodic
summer stone
I knew it had something to do with sine being periodic
suppose that you didn't know thar they don't add up to 180
then how would you have known that 113.6 is the right answer and not 66.4?
tidal hawk
if u wanted 66.4
then I think the other angle
shd be
wait nvm
doesn’t add up
,w 180-56.44
warm shaleBOT
nocturne minnow
,w 180-56.44
You forgot about the 10
tidal hawk
oh I was doing smth else HAHAH
summer stone
that's not my point tho, my point was that how would one know that the law of sines would give an incorrect formula
would we have to manually check it, or is there a condition or something that it only works in these cases
grizzled geyser
sooo I'm kinda confused
how did the other guy find the correct answer
I don't understand his calculations
nocturne minnow
is it possible that the way im supposed to find angle C is by doing 180 - (10+56...
Doing this
Because you know sum of angles in a triangle equals 180
tidal hawk
,w solve sin(123.56)/280 = sin10/58.35
warm shaleBOT
nocturne minnow
And I was showing that sin(66) = sin(113)
tidal hawk
wait oops
grizzled geyser
alright then
that was way simpler than I thought
thanks all three of you
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
idle swallow
n is an integer and n is greater than or equal to 100. Ethan writes down the number n, n+1, n+2,..., 2n on each cards. He shuffles the cards and split them into 2 decks of cards. Prove that at least one deck of cards has two cards whose sum is a square number.
obtuse pebbleBOT
n is an integer and n is greater than or equal to 100. Ethan writes down the num...
idle swallow
I found that at least 2 square numbers between n and 2n
And idk what should i do next
obtuse pebbleBOT
@idle swallow Has your question been resolved?
obtuse pebbleBOT
@idle swallow Has your question been resolved?
still dirge
can someone solve and graph this inequality: x² + 9x + 14 > 0
obtuse pebbleBOT
can someone solve and graph this inequality: x² + 9x + 14 > 0
still dirge
x² + 9x + 14 > 0
i watched tutorials on yt but i still dont get it
someone help me
green plank
use a table of signs
daring rock
Do you know what we should expect the graph of y = x² + 9x + 14 to look like?
hallow mesa
pastel jackal
Do you know what we should expect the graph of y = x² + 9x + 14 to look like?
if its a quadratic its a parabola
pastel jackal
You're not the one who posted the question 🤔 lol
im stupid
i thought you were asking lmao
daring rock
Lol nah no problem, i was trying to help
pastel jackal
yeah i probably should have read more than the 2 most recent mssges
obtuse pebbleBOT
@still dirge Has your question been resolved?
idle thunder
@still dirge https://www.youtube.com/watch?v=FmVCBddNyuE
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
obtuse pebbleBOT
mossy hull
I've never done stats before and my prof didn't teach this to us
like do I just do (0+1+2+3+10)/5?
mossy hull
I'm really sorry I've never taken stats before I'm going to need a bit of hand holding here
mossy hull
so
stable rain
so u can think of it like
freq 22 of 0 is like
22 ppl excercised 0 times
in a wk
mossy hull
(22*0)+(40x1)+(21x2)...
stable rain
no its
mossy hull
what wld b the total num of ppl?
78 people
stable rain
just 100
the ppl who dont excercise
r still ppl who r part of the
survey
they just are
inactive
hahhaa
mossy hull
same
mossy hull
how do I do this in R
mossy hull
bc head empty can I just automate this
mossy hull
lol no worries
stable rain
oh
mossy hull
can I ask more questions
stable rain
just coding in general
i think that isnt too hard
but
not much diff cuz
u still gotta
enter in each val which is
-.-
sure
i might leave aft a bit
mossy hull
like for the data I gave up there is it the same process for finding stdev and median and variance?
stable rain
but ask away
um
u just
find the std n what not as u usually do
just
note that freq is like
num of ppl who exercise that amt
or like
fufil that crieteria
so if freq is 29
then just treat it as 29 times that
number appeared
when calcing std or similar
mossy hull
then do the std formula?
mossy hull
I hate stats
stable rain
think thrs a formula that counts the freq as well
mossy hull
I miss calc2
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
fickle isle
can anyone explain to me how she got the h functions in this video? https://www.youtube.com/watch?v=PzEWHH2v3TE
obtuse pebbleBOT
can anyone explain to me how she got the h functions in this video? https://www....
obtuse pebbleBOT
@fickle isle Has your question been resolved?
digital quail
Hi
digital quail
Can someone help me solve this
fair monolith
solve what
daring rock
These are separable differential equations, yes?
@digital quail
You want to manipulate the equation so all the x's and dx's are on one side, and all the y's and dy's are on the other
So for number (1) you could start like
$$xy dx - (x+2) dy = 0$$
$$xy dx = (x+2) dy$$
$$\frac{x}{x+2}dx = \frac{1}{y} dy$$
warm shaleBOT
tatpoj
warm shaleBOT
tatpoj
digital quail
a
digital quail
You want to manipulate the equation so all the x's and dx's are on one side, and...
so the positioning is not fixed right
as long as you grouped them
doesnt matter if all the x's are either on the right side or on the left side
daring rock
I'm not 100% sure what you mean
I manipulated the equation by adding/subtracting/multiplying both sides of the equation by something
digital quail
like you can group x either on the left side or on the right side
daring rock
just as you would manipulate any algebraic equation
Well, you can do anything you want, as long as you do the same thing to both sides of the equation
Just like how you would solve a typical algebraic equation
Like 3x+3=5. You'd subtract something from both sides, then divide by something on both sides
That's all i did
digital quail
oh okay got it
daring rock
**tatpoj**
I added (x+2)dy to both sides. Then divided both sides by y and divided both sides by (x+2)
So yes, that's all algebraically valid
digital quail
thank you
daring rock
You're welcome
digital quail
You're welcome
Wait can I have one last question
In integrating
How did it become t-2 in numerator
daring rock
Well
It's not easy to divide x/(x+2)
It would be easier if the denominator was only a single term
digital quail
Yeah
daring rock
So they made the substitution t = x+2
It's the same as u-substitution. They just used t instead of u for some reason
daring rock
If t = x + 2
Then t - 2 = x
daring rock
No problem lol
digital quail
Ty
daring rock
No problem 👍
This is a common theme in solving integrals, especially in differential equations, so I think you'll get used to it pretty soon
digital quail
I hope so
digital quail
If you have any other question, feel free to dm me
sure
daring rock
I may or may not be awake lol
digital quail
okay okay iam actually studying for a quiz tomorrow
obtuse pebbleBOT
@digital quail Has your question been resolved?
sudden pond
Hello
tardy epoch
,w plot y=2^x-x for -2<x<5
warm shaleBOT
tardy epoch
find a way to substitute $y$ into the equation $2^x = 2x+2$
warm shaleBOT
riemann
tardy epoch
and then find $y = f(x)$
warm shaleBOT
riemann
tardy epoch
you have $2^x$ in both equations
warm shaleBOT
riemann
tardy epoch
solve for that in terms of y and x and plug it into the second equation
$2^x = y ...$
warm shaleBOT
riemann
tardy epoch
and then that right hand side you'll plug into the second eqn
sudden pond
I don’t get it
sudden pond
So 2x= y=2*x-x
sudden pond
Ok
So what do I do know
The book doesn’t explain it very well
Can u show me the working on how to do this
cloud jungle
dit they convert it to 12-12/x = 0/1?????
obtuse pebbleBOT
dit they convert it to 12-12/x = 0/1?????
tardy epoch
algebra?
tardy epoch
👏🏻
cloud jungle
yay
why do i keep asking for help and while i am asking i figure it out lol
.close
stoic mesa
I'm converting 7y^2+8x+84y+244=0 from general form to standard form of the parabola. Do I still need to divide both side by 7 or not?
obtuse pebbleBOT
I'm converting 7y^2+8x+84y+244=0 from general form to standard form of the parab...
pine sail
It's eh but yeah divide it.
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
weak hemlock
I'm supposed to realize a function $$f_1(S, T) = \begin{cases}
0, if S = 0\
T, if S = 1
\end{cases}$$
The subject is logic so I'm supposed to realize it with the common logical expressions.
obtuse pebbleBOT
I'm supposed to realize a function $$f_1(S, T) = \begin{cases}
0, if S = 0\\
T, ...
warm shaleBOT
FelixBergman
obtuse pebbleBOT
@weak hemlock Has your question been resolved?
obtuse pebbleBOT
@weak hemlock Has your question been resolved?
kind hawk
What do you mean with realize
obtuse pebbleBOT
@weak hemlock Has your question been resolved?
worldly thorn
Help me
worldly thorn
$\frac{dy}{dx} = 3-\frac{12}{x^2}$
warm shaleBOT
ΛKT Kakashi
worldly thorn
then I found the gradient as 2
worldly thorn
$\frac{20-12}{6-2}=2$
warm shaleBOT
ΛKT Kakashi
urban glen
Why differentiate
worldly thorn
differentiation topic sir
urban glen
no?
worldly thorn
it is
urban glen
I'm doing this in class and you don't need to differentiate?
urban glen
AB gradient = 2
warm shaleBOT
ΛKT Kakashi
dusky dock
sqrt12
dusky dock
ohh never mind
worldly thorn
2x²=3x²-12
did U multiplied everything with 12?
urban glen
x is sqrt12
urban glen
did U multiplied everything with 12?
x²
worldly thorn
I mean that
obtuse pebbleBOT
@worldly thorn Has your question been resolved?
worldly thorn
<@&286206848099549185>
obtuse pebbleBOT
Available help channel!
timid silo
obtuse pebbleBOT
timid silo
Hey, can someone please help with this
So I'm guessing we have to use the (n-2) x 180 / N = X formula
not sure how to re-arrange it
.close
fickle portal
Hello can somebody tell me what is wrong here when a is from R and b is from R+?
hardy widget
Consider ||division by 0||
fickle portal
Consider ||division by 0||
so the only one right is the first?
or R+ means there is no 0
hardy widget
or R+ means there is no 0
$\mathbb{R}^{+}$ means the set of positive real numbers, so yes, it excludes $0$
warm shaleBOT
enclave wangedrocht
fickle portal
$\mathbb{R}^{+}$ means the set of positive real numbers, so yes, it excludes $0$
Thank you! So then true is only the first one, right?
but when i say the a is 0 the third doesnt make sence, when i say b is 0 the second and last. In the first one when i have a = 0 v b = 0 it is still true...
or i still dont understand
@hardy widget
hardy widget
but when i say the a is 0 the third doesnt make sence, when i say b is 0 the sec...
you're right about the third one
but we specified b=0 isn't possible
fickle portal
**enclave wangedrocht**
ah sorry ive read it includes
ok got it now, thank you
hope u have a great day!
.close
zenith jetty
zenith jetty
I need help with part C please
fossil crag
Hello, part C is about using Chasles's formula on the appropriate dots
fossil crag
Ok, Im warning you in advance that when I write XY Im referring to the vector XY (with an arrow on it)
nocturne minnow
As the bot stated, don't open multiple channels, even if you have different questions
zenith jetty
As the bot stated, don't open multiple channels, even if you have different ques...
how do i leave a channel?
fossil crag
Ill do it for you on the other channdl
swift dawn
I am having trouble finding if this group is associative in 𝑉 = {𝑎, 𝑏, 𝑐, 𝑑}, is there a way to find associative in 𝑉,∗ quicker instead of testing every operation possible
brisk grove
A quick google search tells me you can use something called "Light's associativity test"
Though I can't be of any help for this.
obtuse pebbleBOT
@swift dawn Has your question been resolved?
toxic elm
Can someone help me with part C please?
obtuse pebbleBOT
Can someone help me with part C please?
toxic elm
I don't understand the question
versed cave
Mh ok, do you know what a root of a function is?
roots are also called "zeros", they are the x values of the function that make the function = 0
If you have something like (unrelated example) f(x) = x - 2, then 2 is a root, because if I substitute x with 2, I get 2 - 2, which is 0
toxic elm
The equation from part C is =0
versed cave
To solve it you should put 27x⁶ + 26x³ - 1 = 0 and solve that (find the x values)
if that's what you mean
There's a trick to solve that equation
You can do a substitution, for example, t = x³
So that becomes
27t² + 26t - 1 = 0
And hopefully it's much easier to solve
devout sable
i need ur keyboard 
nonna
wild swallow
substitution jutsu
versed cave
i need ur keyboard <:kawaiiCat:635953356354879499> nonna
steal the linux keyboard layout, it's great, it has a lot of symbols
You can edit* the layout too, so you can have extra cool symbols which give extra cool points, of course
wild swallow
just type latex 
devout sable
<:KEK:586240877358350341> steal the linux keyboard layout, it's great, it has a ...
oh i see 
obtuse pebbleBOT
@toxic elm Has your question been resolved?
toxic elm
How to factorise this quadratic equation?
simple marsh
Replace 26t with 27t - t
crimson spoke
Have logic design midsem tomorrow, stuck on this one
obtuse pebbleBOT
Have logic design midsem tomorrow, stuck on this one
crimson spoke
My approach : equivalence for a and d is ad + a'd' , taking + with d gives a' + d (after simplification)
Then xor a b is ab' + a'b but my final answer is not matching with the key
obtuse pebbleBOT
@crimson spoke Has your question been resolved?
crimson spoke
<@&286206848099549185> anything i am missing? thanks
weary delta
(A XNOR D + D) XOR (A AND B). We are simplifying this?
crimson spoke
yep
crimson spoke
`(A XNOR D + D) XOR (A AND B)`. We are simplifying this?
.
crimson spoke
ok
weary delta
(A XNOR D + D) = (A' + D) this is what I got so far
crimson spoke
`(A XNOR D + D) = (A' + D)` this is what I got so far
yep i mentioned that
@weary delta got it thanks mate
.close
real reef
obtuse pebbleBOT
real reef
Is number 3 possible to solve with the info my prof gave me?
Or do I need some outside help
This is the most insane math ive done in my entire life
still struggling to understand parts of this when you have 2 conversions
high lily
based on just the conversions listed no,
it requires knowledge of metric conversions which are quite easy to remember
obtuse pebbleBOT
@real reef Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
stoic scroll
obtuse pebbleBOT
stoic scroll
Is this the correct answer?
covert crag
marble bane
i just need help here
obtuse pebbleBOT
i just need help here
marble bane
just with A thru H, no more
devout sable
obtuse pebbleBOT
devout sable
obtuse pebbleBOT
Available help channel!
eternal ginkgo
Can someone help me with a combinatorial proof
obtuse pebbleBOT
Can someone help me with a combinatorial proof
solar trellis
what have you tried
warm shaleBOT
scale
kind hawk
This is out of the pool of possible people if we fix the m'th person at a particular position
Why not
The m'th person has to be at some position. So we fix that position, calculate all options and then sum over all possible positions
obtuse pebbleBOT
@eternal ginkgo Has your question been resolved?
kind hawk
First let the mth person be at the mth position. Then you have m-1 choose m-1 options to fill the rest. Next let the mth person be at the m+1st position. Then you have m choose m-1 options to fill the rest. Etc
obtuse pebbleBOT
@eternal ginkgo Has your question been resolved?
serene furnace
hi guys
warm shaleBOT
Raid
serene furnace
then I must say that x != 0 and x+2 !=0 => x != -2
But can't I simply say x(x+2) !=0 ?
manic karma
The latter implies the former
violet sentinel
^^^
serene furnace
So they're equal?
violet sentinel
not necessarily equal, but they're saying the same thing.
Anything times 0 equals 0. So if x = 0, we get (0)(0 + 2) = 0. Similary, we have x = -2, so (-2)(-2 + 2) = 0
manic karma
I think you would usually write it as $\mathbb{R} \setminus {-2, 0}$
Idk how to do the exclusion symbol
Lol
obtuse pebbleBOT
warm shaleBOT
Princess Ann
obtuse pebbleBOT
Available help channel!
timid silo
Struggling a bit to finish this inner product space proof
obtuse pebbleBOT
Struggling a bit to finish this inner product space proof
timid silo
My goal is to show that $||v||=\sqrt{\langle v, v\rangle}$ is a norm
warm shaleBOT
jswatj
fervent cradle
ok, so define a norm for me rq
and then you just want to show all the properties of a norm are met by ||v||
timid silo
are the properties
||a*v|| = |a| * ||v||
||v|| = 0 <=> v = 0
||v+w|| ≤ ||v|| + ||w||
by any chance?
fervent cradle
yes
obtuse pebbleBOT
@timid silo Has your question been resolved?
gilded otter
obtuse pebbleBOT
hardy widget
I'd rewrite the left hand side as x²(...)+x(....)+(constants)
Then you can compare coefficients
@gilded otter
fervent cradle
yeah, the number of x^2 on the left has to be the same as on the right (1)
the number of x^1 on the left has to be the same as on the right (0)
the number of x^0 on the left has to be the same as on the right (0)
gilded otter
Ill do my work here just in case I go wrong somewhere
y=x²(A) + x(B) + C
and
x²=2x(A) + (B) + 2(A) - 2y
.
.
2y=2x²(A) + 2x(B) + 2C
and
2y= 2x(A) + 2(A) + B - x²
.
2x(A) + 2(A) + B - x² = 2x²(A) + 2x(B) + 2C
wait wtf
how
Am I trying to get rid of all the X's??
@hardy widget could I take your attention for this please
hardy widget
Did you ever find y' and y''
hardy widget
Ngl idk what you did
hardy widget
yeah, the number of x^2 on the left has to be the same as on the right (1)
the n...
This
If you did that then I'm high
gilded otter
Okay I guess
I guess Ill keep trying
and try to remove as many X's as I can
thank you
.close
fringe ingot
obtuse pebbleBOT
fringe ingot
how would i describe this function's range
astral ivy
The image?
Well first of all the domain is a quarter circle in the first quadrant
So that might help
But like a circle with a hole, yknow
Anyway
fringe ingot
i understand that part but i cant figure out how the actual function affects that
royal shard
when multiplying complex numbers, the angles add and the lengths multiplies
fringe ingot
so would it be like from from -4<|Z|<-16
royal shard
lime?
gilded needle
|z| is always nonnegative so no
flat rune
nothing can be more than -4, and less than -16!
royal shard
we have a ring segment
radius going from 1 to 2
angle going from 0 to pi/2
if we square z, then
radius goes from 1 to 4
angle goes from 0 to pi
so we get a bigger ring segment
the width is now broader and the angle is bigger
fringe ingot
we have a ring segment
radius going from 1 to 2
angle going from 0 to pi/2
if we...
how does the angle go from 0 to pi
wouldnt it be 0 to pi/4
gilded needle
so would it be from 4<Z<16 cuz it cant be negative
you can change the sign from - to + if you also change the angle to compensate
gilded needle
how does the angle go from 0 to pi
when you square a complex number, then the modulus is squared and the angle is doubled
e.g. i has angle pi/2, and i^2 = -1 has angle pi
fringe ingot
when you square a complex number, then the modulus is squared and the angle is d...
Did not knwo tjat
gilded needle
it's easiest to see in polar form if you know about that
if $z = re^{i\theta}$ then $z^2 = (re^{i\theta})^2 = r^2 e^{i2\theta}$
fringe ingot
|Z|E^itheta
warm shaleBOT
Bungo
gilded needle
Like this?
not quite right, removing the - sign from -4 does not change 2theta to -2theta
instead you should add pi to the angle
gilded needle
this is because $-1 = e^{i\pi}$, so therefore $-z = -re^{i\theta} = (-1)re^{i\theta} = (e^{i\pi}) r e^{i\theta} = re^{i(\theta + \pi)}$
warm shaleBOT
Bungo
fringe ingot
so if it becomes - u always add pi?
gilded needle
if you multiply by -1 (to remove the - from -4) then you also need to add pi to the angle
to compensate
or putting it another way, you're taking the -1 factor from the front of -4, and expressing it as the angle pi instead
graphically, if z is a complex number with modulus r, then it sits somewhere on the circle of radius r, and then -z sits on the same circle but opposite z
(on the other side of the circle, where it intersects the line that passes through z and the origin)
and to get from z to -z you can equivalently travel pi radians around the circle
fringe ingot
i have like 0 experience with any mathematical theoretical/proof ideas or anything so idrk know any rules like that
thank u for letting me know tho
is from 4 to 16 correct or no
fringe ingot
instead you should add pi to the angle
does that meant it goes from pi to pi/2?
obtuse pebbleBOT
@fringe ingot Has your question been resolved?
gilded needle
does that meant it goes from pi to pi/2?
the original z was in the range 0 to pi/2, so z^2 is in the range 0 to pi (because of the doubling of the angle as mentioned above)
when you multiply by -4, that's equivalent to multiplying by 4 (which does not change the angle) and then adding pi to the angle
so the final result should be in the range pi to 2pi
which is equivalent to the range -pi to 0
obtuse pebbleBOT
@fringe ingot Has your question been resolved?
gilded needle
isnt -pi to 0 the quadrents 3 & 5
yep
that's where the answer lies in this problem
fringe ingot
that's where the answer lies in this problem
so my graph was correct i just did it wrong?
gilded needle
so my graph was correct i just did it wrong?
yep your graph is right, be sure to be careful about which parts of the real axis are part of the image and which are not
fringe ingot
wdym by that
obtuse pebbleBOT
@fringe ingot Has your question been resolved?
obtuse pebbleBOT
@fringe ingot Has your question been resolved?
obtuse pebbleBOT
@fringe ingot Has your question been resolved?
little warren
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
kind flame
If u and v are three-dimensional real vectors and u × v = 0, then either u = 0 or v = 0.
This is false?
obtuse pebbleBOT
If u and v are three-dimensional real vectors and u × v = 0, then either u = 0 o...
lone kestrel
If u and v are three-dimensional real vectors and u × v = 0, then either u = 0 o...
yes
lone kestrel
in a cross product
kind flame
Let u, v and w be three-dimensional real vectors, g(u, v) = u · v, and h(u, v) = u × v. Then
one of the differences between g and h is that g : R3 × R3 → R3 while f : R3 × R3 → R.
lone kestrel
oh wait is that cross
kind flame
Would this be true?
lone kestrel
my bad I thought that is dot
kind flame
It’s cross?
kind flame
Let u, v and w be three-dimensional real vectors, g(u, v) = u · v, and h(u, v) =...
What about for this
wild swallow
If u and v are three-dimensional real vectors and u × v = 0, then either u = 0 o...
this is untrue regardless of if its cross or dot product
kind flame
Is it cuz it equals 0 when it could be something else
kind flame
.close
obtuse pebbleBOT
kind flame
.reopen
obtuse pebbleBOT
✅
kind flame
I can’t figure this one out
Let u, v and w be three-dimensional real vectors, g(u, v) = u · v, and h(u, v) = u × v. Then
one of the differences between g and h is that g : R3 × R3 → R3 while f : R3 × R3 → R.
wild swallow
what are you meant to be figuring out
that statement is problematic
somehow you have f appearing out of nowhere
obtuse pebbleBOT
@kind flame Has your question been resolved?
kind flame
what are you meant to be figuring out
If the statement is just true or false
kind flame
why is there an f
The the long italicized f
kind flame
why is there an f
kind flame
is 3. a part of a bigger problem?
It just asks if the statement is true or false
lethal sand
that's would probably be a typo there
but anyway, regardless of what f is, you can already draw a conclusion to whether or not the relation of g is true or false
dull hornet
obtuse pebbleBOT
dull hornet
what should i do next? am i doing it right?
implicit differentiation
should the y on the lhs become 1 or y’?
teal turret
I think u reversed the exponent on the last term in the denom
Other than that looks good
teal turret
Np
teal turret
Yea, they just factored out a -1 from the denom
Ig to get it in higher powers->lower powers form
dull hornet
oh right