to have an even/odd asymptote
#help-36
grim nebula
void crest
same
tranquil pine
I am behind on class trying to catchup
void crest
LOL
grim nebula
consider something like
1/x^n
just graph it on desmos or something
when n is odd
the asymptote at 0 goes off in different directions
as in
it goes down to -inf in the left
and +inf on the right
but when n is even
it just goes straight up
,w plot 1/x
soft zealotBOT
grim nebula
,w plot 1/x^2
soft zealotBOT
grim nebula
see the difference?
grim nebula
yes
void crest
is this the same as a func bein even or odd
grim nebula
so you can look at in your question
the two one-sided limits at 6
go to opposite infinities
tranquil pine
odd
grim nebula
which means you want it to be an odd power of (x - 6) on denominator
and
the other one you want an even power of (x - 2) i think it was
and so
just see how you can tweak the values of p and q
to make the necessary cancellations/multiplications etc
so that the powers are what you need them to be
tranquil pine
om so my job is to make the 22 into an odd number
grim nebula
indeed
so either adding or subtracting 1
depending on if you make p or q into the same factor
but remember at the same time
you need to make the (x - 2) be an even power
and there still needs to be an asymptote at x=2
you can't just delete the factor
grim nebula
issokay
you might want to just
plug the equation into desmos and try some numbers
but also
make the 22 into a smaller even number
like 2
so just graph (x - p)/(x - 2)(x - 6)^2(x - q) on desmos
and just set p and q to either of 2 or 6
and see what happens
grim nebula
i think you'll want to type out the
fraction again
don't just copy paste cuz desmos won't do the division correctly
grim nebula
yep
but you don't want to change the 2 to a 3
that's already been given to you
what you can change is the p and the q
so like for example
if you have q = 6
then in the denom
you have both (x - 6)^2 and (x - 6)
so that means together they form (x - 6)^3
multiplication
final saddleBOT
@tranquil pine Has your question been resolved?
knotty otter
I have to solve the derivative i used in ye power rule
final saddleBOT
I have to solve the derivative i used in ye power rule
knotty otter
I’m kind of confused with the 5t is there supposed to be a t behind it?
wanton python
the t goes away because the power goes to 0 via power rule
final saddleBOT
Available help channel!
honest osprey
final saddleBOT
honest osprey
I don't know how to find dy/dx in terms of anything but x
I was thinking it might have been 6y=56x^6
strange shore
first derivative :
$3y'y^2 = 8x^7$
honest osprey
Why are you multiplying by the deriv of y?
strange shore
chain rule
soft zealotBOT
Ｈｅｒｅｌｓ
honest osprey
Is (y) the chain?
strange shore
wdym ?
honest osprey
Sorry can you write out the entire chain for the left side
strange shore
huh, thats what I did
honest osprey
im just confused where the y' came from
strange shore
do you know chain rule ?
honest osprey
I thought I did
deriv of outside * deriv of inside
and ofc you can have multiple chain rules
y' * 3()^2
ok i got it
how come you dont do that with x though?
honest osprey
alright
strange shore
now differentiate a second time
soft zealotBOT
Kivi
strange shore
wrong
honest osprey
$6y''+6yy'=56x^7$
soft zealotBOT
Kivi
strange shore
$(y'y^2)' = y''y^2 + 2y'^2 y$
soft zealotBOT
Ｈｅｒｅｌｓ
honest osprey
@strange shore Whats that?
soft zealotBOT
Ｈｅｒｅｌｓ
final saddleBOT
@honest osprey Has your question been resolved?
vital crag
D FROM 3
this channel's occupied. read #❓how-to-get-help
safe oak
I'm attempting b) for the relative velocity question posted, and after redoing my answer, I still get the same result (5.0 x 10^2)km/h which is wrong, as it lists (6.0 x 10^2)km/h as the speed.
final saddleBOT
I'm attempting b) for the relative velocity question posted, and after redoing m...
safe oak
I got 500km/h by doing Vpgx = 550cos(12) + 80cos(145) Vpgy = 550sin(12) + 80sin(145)
which makes Vpgx = 474.45 and Vpgy = 160.24, giving us the overall speed of 500km/h after we add them together
final saddleBOT
@safe oak Has your question been resolved?
safe oak
<@&286206848099549185>
final saddleBOT
@safe oak Has your question been resolved?
safe oak
<@&286206848099549185>
final saddleBOT
Available help channel!
plain radish
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plain radish
hi
for 2.2 would a good proof be the inverse of I + A being I - A
or is that incorrect
dusky lichen
that is a surprisingly elegant proof i think
tranquil pine
I need some help with some linear and quadratic equations
final saddleBOT
I need some help with some linear and quadratic equations
tranquil pine
Hi there. I'm taking a functions class currently, and due to covid and the gap that it caused in my learning,
I'm quite foggy on how to carry out some of the linear/quadratic questions and graphing them.
We have a review sheet to work on currently, which consists of some factoring and some equations that we
are required to graph. This is some review as we need to have this stuff down pat for the content that we will be
expanding upon after this introductory period of the unit.
y=-2x+3
-3x+2y+16=0
y=(x+6)^2-2
y=-(x+8)^2
Firstly, how would I determine whether these equations are linear or quadratic? Is there any stand-out features
that would help?
Secondly, how would I go about obtaining x and y plot point values from these questions?
The only one I'm semi-confident with is y= -2x+3, which I believe gives a starting y-intercept of 3,
and a Rise/Run of -2/1. If anybody here could break this down for me based on these examples, I'd really
appreciate it.
frigid sierra
linear—> degree of x is 1
quadratic—> degree of x is 2
are u suppose to only sketch the graphs with essential features
or have like accurate plot points
apart from the x,y int and stuff
tranquil pine
We're supposed to take the four equations, plot the points, and graph each equation, be it either linear or quadratic, with clear labels
tranquil pine
quadratic—> degree of x is 2
So x compared to x^2?
frigid sierra
yesh
if u see an x^2 as the hifhest power
it’s a quad
if highest is only x
it’s linear
tranquil pine
Alrighty, I'll jot that down for future reference
frigid sierra
okiee
tranquil pine
But what about actually getting the points I would need out of the equations?
frigid sierra
okie so
tranquil pine
Like with the -2x+3
frigid sierra
essentially what u wld need
when plotting linear graphs
are just the x and y intercepts
tranquil pine
Cause straight lines, right?
frigid sierra
and of course u need to know the gradient
frigid sierra
Cause straight lines, right?
yepp
frigid sierra
and of course u need to know the gradient
the grad tells u the direction
the left is for a positive grad
right is for negative grad
tranquil pine
Ok, so then A and B questions are linear, C and D are Quadratic, I figured out the first one but kinda stumped on the others
Ye, I remember some of that
tranquil pine
Yeah, they're all combined onto one graph, but yeah I drew the line and plotted the points for -2x+3 since I was able to get the y-int=3 and Rise/run =-2/1
Sure
Gimme a sec
frigid sierra
okiee
tranquil pine
That's what I've established so far, I tried to do a bit of C but then just went back cause confused
frigid sierra
yepp seems good!
okie so when plotting linear graphs
it can help to express
ur equation
as y= something
so for ur B,, u have $-3x +2y +16=0$
soft zealotBOT
swaggofishballs
frigid sierra
on the left hand side of ur equal sign
u only want y
everything else u would move to the right hand side
tranquil pine
And then they change signs, I believe? I recall hearing something about that
tranquil pine
Ok, so now I've got 2y = 3x -16?
tranquil pine
but we only want y on the left hand side
Like in the first equation?
frigid sierra
yepp!
tranquil pine
Divide to cancel out the 2?
tranquil pine
But then that would result in 1.5x for the 3, right? Don't you ideally want to have whole numbers?
frigid sierra
not necessarily
tranquil pine
Because everything would need to be divided?
frigid sierra
we do this to help us see the gradient and y-int easier
essentially u can also sub x=0 to find y-int and y=0 for the x-int
tranquil pine
Ok, so that would result in y = 1.5x -8?
tranquil pine
Then it would be a y-int of -8 and a Rise/run of 1.5/1 because there's an assumed 1 when there's no fraction, right?
tranquil pine
Oh okay, so when I can't divide to get a whole number in the case of 3/2, I can still rewrite the equation as 1.5, but need to use 3/2 as the rise/run?
tranquil pine
Alrighty, let me try to draw this on the graph
frigid sierra
if u need to graph very accurately
soft zealotBOT
tranquil pine
Sorry, lil blurry in top there but I just wrote the equation at the end of the line
tranquil pine
Alrighty
tranquil pine
x+6 in the question, sorry
soft zealotBOT
swaggofishballs
tranquil pine
ye
frigid sierra
do u know what a vertex is
tranquil pine
I believe the point at which the parabola goes in the opposite direction?
Or was that something else
frigid sierra
yes basically the turning point
tranquil pine
ah alrighty
frigid sierra
or we can call it the maximum/minimum point
because that’s the lowest/highest point of the graph
if ur coefficient of x^2 is positive ull have the graph on the left
the vertex will be a minimum point
if it’s negative it’ll be the graph on the right
and the vertex is a maximum point
tranquil pine
Opening up for + and down for -
frigid sierra
ya
tranquil pine
alrighty
frigid sierra
so u have $(x+6)^{2} -2$
soft zealotBOT
swaggofishballs
frigid sierra
this is the vertex form
it helps u find the coordinates of ur vertex
u know for coordinates we have (x, y) yes?
tranquil pine
yeah
soft zealotBOT
swaggofishballs
frigid sierra
what’s x?
tranquil pine
Positive x? Because we're changing the signs and isolating x on the left, right?
tranquil pine
+6
frigid sierra
yepp
so that’s ur x-coordinate
now for the y-coordinate
u just take the last number
in this case what’s the last number
tranquil pine
-2
tranquil pine
(6,-2)
tranquil pine
So 6 and -2 would be plotted on 6x axis and -2 y axis, right?
frigid sierra
no u plot at the point (6,-2)
tranquil pine
Both on x axis?
frigid sierra
no
tranquil pine
Ye
frigid sierra
now how would u find the y-int
y-intercept is basically when the graph cuts the y-axis yes?
tranquil pine
yeah
frigid sierra
at the y-axis what’s the x-coordinate
tranquil pine
0
soft zealotBOT
swaggofishballs
frigid sierra
so $y=(0+6)^{2} -2$
soft zealotBOT
swaggofishballs
frigid sierra
what do u get for y?
tranquil pine
y=36-2?
tranquil pine
Ah, alrighty, my graph doesn't go that far up on the page
But that helps for finding the y-int
frigid sierra
oh that means u need to adjust the scaling
now for the x-intercept
at the x-int what is the y-coord
tranquil pine
0
soft zealotBOT
swaggofishballs
frigid sierra
now solve for x
tranquil pine
How would I isolate x when it's part of a bracket?
frigid sierra
okay so
tranquil pine
I wouldn't think I could just pull the 6^2 out and switch sides
frigid sierra
first thing u would do is move the -2 over yes?
tranquil pine
ye
frigid sierra
I wouldn't think I could just pull the 6^2 out and switch sides
oh u can’t
okay so u have $(x+6)^{2} = 2$
soft zealotBOT
swaggofishballs
frigid sierra
what’s the opposite of a square
tranquil pine
square root
soft zealotBOT
swaggofishballs
tranquil pine
**swaggofishballs**
No, honestly that expression is a little confusing tbh
frigid sierra
okay ya
it can look scary
but as u practice more ull get used to it HAHAH
okay so
the reason we put a plus minus there
is because
take the number 4 for example
we can write it as
$2^{2}$
soft zealotBOT
swaggofishballs
soft zealotBOT
swaggofishballs
frigid sierra
both gives us 4
tranquil pine
I see
frigid sierra
so we take $\pm{\sqrt{4}}$
soft zealotBOT
swaggofishballs
soft zealotBOT
swaggofishballs
frigid sierra
what do u do to isolate x?
tranquil pine
switch 6 to opposite side, resulting in -6
soft zealotBOT
swaggofishballs
soft zealotBOT
swaggofishballs
frigid sierra
this is what we call the exact form
if the question wants us to give our coordinates as exact form, it’s like this
but do u want to work with decimals or this?
tranquil pine
This
soft zealotBOT
swaggofishballs
soft zealotBOT
soft zealotBOT
tranquil pine
I can round, right?
frigid sierra
um if ure allowed to then sure
tranquil pine
Since this isn't a super exact graph
frigid sierra
ya just approximate
frigid sierra
HAHAH a okie
so now u can graph ur quadratic
when u graph a quad u always need
x-int
y-int
vertex
and the direction
direction is seen by coefficient of x^2 ya
tranquil pine
The signs would be switched though, right? For the zeros, cause currently the plotted vertex is 6,-2
frigid sierra
wdym?
tranquil pine
I plot at 6,-2 for the vertex, yeah?
tranquil pine
Up 6, left 2?
Or right 6, down 2
I'm sorry, it's been so long since I've done this stuff man
tranquil pine
I went right 6, then down 2
frigid sierra
yepp
tranquil pine
But if that's the vertex, how can our zeros be -4.59 and -7.41?
That would be on the opposite side of the y axis, right?
frigid sierra
oh wait ur vertex isn’t (6,-2)
sry I thought ur equation was $(x-6)^{2} -2$ HAHAHA
soft zealotBOT
swaggofishballs
tranquil pine
So by looking at the initial equation of y= (x+6)^2 -2, I can just find the vertex by reversing the charge of the bracketed number and combining with the -2?
frigid sierra
yepp!
tranquil pine
Ahhhh ok
Alright, first things I can tell by looking at D. (I think)
y = -(x+8)^2
The parabola is going to be negative and the vertex is going to be -8, 1?
frigid sierra
close
tranquil pine
Or is it still going to be 8, 1
frigid sierra
what’s the number at the end?
tranquil pine
There isn't one
tranquil pine
Oh, okay
I thought nothing there was just an assumed 1 like in factoring n whatnot
But okay yeah that makes sense with graphs
frigid sierra
yepp!
tranquil pine
And then is there a more simplified version of finding the zeros from the equation, or should I go through the process as you showed me above? I thank you for detailing it cause it makes sense to me now, but for when I need to get that information quicker as my teacher said we should be working on doing
frigid sierra
ya essentially when u do my method,, u shd be able to do it fast
on the side
with practice that’ll come naturally
that’s actually the only process here
but for D it’s actually easier than C
for y-int what do u do?
tranquil pine
let x = 0, then find the sum of the remaining right side, right?
soft zealotBOT
swaggofishballs
tranquil pine
y=-64
tranquil pine
let y = 0, then square root
soft zealotBOT
swaggofishballs
frigid sierra
but first
before u square root
u need to move the negative over ya
essentially nothing will change here
since 0/-1 is still 0
now when u square root
it’ll give u $x+8 =0$
soft zealotBOT
swaggofishballs
frigid sierra
what’s x
tranquil pine
-8?
frigid sierra
yesh
a difference between C and D
is that D has one x-intercept only
this is what we call touching the x-axis
now are u able to graph it?
tranquil pine
Oh yeah, it's the same as vertex with -8,0
tranquil pine
But so, I have the xint and vertex at -8,0, and my y-int at -64, but how would I know where to plot the other two points that would allow me to completely form the parabola? In question c, the vertex wasn't on the x-axis, and so I was able to get the other 2 points and continue the parabola from there
frigid sierra
in this case the vertex and x-int are the same
if u want to see how the graph roughly looks like
,w plot -(x+8)^2
soft zealotBOT
frigid sierra
as u can see
it touches the x-axis at (-8,0)
u can use a graphing tool called desmos
it helps a lot
tranquil pine
So would I just want to start from the y-int of -64 and roughly make a parabola towards -8 on the x-axis?
frigid sierra
yepp
tranquil pine
Ah, alrighty
Alright, thanks a bunch, this helped a lot! It'll probs take me a bit of time to get used to the process of the quadratics again, but I appreciate the explanations! My Math teachers don't bother explaining the process again, just assume you know how to do it and continue forth, but this is starting to jog my memory
tranquil pine
,tex \color{purple} There are four club cards and m heart or diamond cards on a table. You now reveal two cards. Calculate the value of m for which the probability that there is exactly one club card among the revealed cards is (\frac{2}{5}) .
final saddleBOT
,tex \color{purple} There are four club cards and m heart or diamond cards on a ...
soft zealotBOT
/\
final saddleBOT
@tranquil pine Has your question been resolved?
dusky lichen
try calculating this probability using the variable m, than solve for it.
celest crane
Given the possibility of P(C and N) or P(N and C), are each of those probabilities dependent or independent events?
tranquil pine
Given the possibility of P(C and N) or P(N and C), are each of those probabiliti...
The probability doesn't change after you reveal a card, oh whait it does actually
tranquil pine
try calculating this probability using the variable m, than solve for it.
,w 2x(1-x)=0.4
soft zealotBOT
celest crane
$P(\clubsuit \cap \neg \clubsuit) = P(\clubsuit) \cdot P(\neg \clubsuit | \clubsuit)$
soft zealotBOT
Kookiemon
celest crane
That's for dependent events.
tranquil pine
I didn't consider that the probability change when you revealed the first card
Why should this be a dependent event?
You either draw club first or second
dusky lichen
it is dependent
the probability of you getting a club your second shot is dependent on if you took a club the first shot
the probabilities changed
celest crane
The number of cards in the deck decrease by one after the first card draw.
There are 4 + m cards on the first draw and 3 + m cards on the second draw.
tranquil pine
I found the answer now with playing a bit around with the numbers
$\frac{4}{16}\cdot\frac{12}{15}+\frac{12}{16}\cdot\frac{4}{15}=\underline{0.4}$
soft zealotBOT
/\
tranquil pine
but how can you calculate it
celest crane
You should have a linear expression in the denominators because you don't know how many total cards there are. That is what you are trying to determine.
$P(\clubsuit \cap \neg \clubsuit) = P(\clubsuit) \cdot P(\neg \clubsuit | \clubsuit)\
P(\clubsuit \cap \neg \clubsuit) = \frac{4}{4+x} \cdot \frac{x}{3+x}$
soft zealotBOT
Kookiemon
celest crane
I'll give you a moment to let that sink in how I got that.
Once you have figured that out, try to calculate
$P(\neg \clubsuit \cap \clubsuit)$
soft zealotBOT
Kookiemon
final saddleBOT
@tranquil pine Has your question been resolved?
tranquil pine
I'll give you a moment to let that sink in how I got that.
thanks I figured it out
celest crane
👍
old rune
final saddleBOT
old rune
Can anyone help me with this?
final saddleBOT
@old rune Has your question been resolved?
old rune
I got 3 and 4 which is
x=6
y=3
how do i get x and y intercept?
nowbi got the y intercept
dawn elk
@old rune what do you need help with now?
final saddleBOT
@old rune Has your question been resolved?
old rune
uhh so did you find answers to all 4 previous questions?
So I think I graphed it correctly
Is this correct ?
dawn elk
yes @old rune looks good
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@old rune Has your question been resolved?
pulsar wind
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pulsar wind
When the discriminate=0 isn’t there only 1 real solution, so when they bounded with the equal to inequalities doesn’t it only yield 2 roots not 4?
scarlet sequoia
A quartic equation has 4 complex solutions counted with multiplicity. If all solutions of the quartic are real, then the solutions of the quadratics are real as well.
thus the discriminants of both quartics have to be non-negative
torpid sequoia
a polynomial with real coefficients can only have paired complex roots, so a quartic (which has four roots) with real coefficients will always have 0, 2, or 4 non-real roots, never 1 or 3
which seemed important to me for some reason but really is not, ignore me
for a quartic to have four real roots, it must be a product of two quadratics each of which has two real roots
(some of which might be identical to one another)
final saddleBOT
@pulsar wind Has your question been resolved?
onyx lake
Is this some mathematical joke that I'm too non-mathmatician to understand?
dawn elk
no
torpid sequoia
no, that's pretty much standard definitions in physics
dawn elk
it’s not joke ig
torpid sequoia
jerk is the rate at which acceleration changes
the fourth derivative is sometimes called "snap" or "jounce"
final saddleBOT
torpid sequoia
the fifth and sixth are sometiomes called "crackle" and "pop", but that is a joke
tranquil pine
this isn't a joke like has been said already
onyx lake
cool
dawn elk
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Available help channel!
ember nebula
Sup everyone,
I'm trying to place a point in front of the camera knowing the xyz of the camera, the camera angles and the distance to the point such as shown on the example below
final saddleBOT
Sup everyone,
I'm trying to place a point in front of the camera knowing the xyz...
ember nebula
this corresponds to placing a point on a sphere, so i'm using this formula :
x′=rcosθcosα
y′=rsinθ
z′=rcosθsinα```
but i'm not getting the results i'm expectingfor r = 2.83 I should be getting something like x = -2, y = 0, z = 2, but i'm getting 0, 2.83, 0
Does anyone have an idea of what i'm doing wrong ?
my implem is basically the same as the formula above, c being the camera and th being the vector containing the view angles
desert mantle
Is angle.cos() the correct syntax? I would have assumed it should be cos(angle)
ember nebula
That's the syntax in Rust 😄
desert mantle
Well that's disgusting
ember nebula
I like this better tbh. The math is implemented directed in the f64 type which is more convenient
final saddleBOT
@ember nebula Has your question been resolved?
final saddleBOT
@ember nebula Has your question been resolved?
candid vine
I have a problem in number theory where I have to show this: look image. I think of showing it with induction, showing for k=1 and (k+1), then it would be the case for all k. Don't know if this is the way to do it, and I'm just stuck with the algebra or if there is another way to go about it?
final saddleBOT
I have a problem in number theory where I have to show this: look image. I think...
@candid vine Has your question been resolved?
candid vine
<@&286206848099549185> 🙂
muted prairie
I have a problem in number theory where I have to show this: look image. I think...
This is cool
$\ncr12$
$\nCr12$
$\choose12$
soft zealotBOT
monikanicity
muted prairie
$4\choose12$
soft zealotBOT
monikanicity
dawn elk
hmm 🤔
soft zealotBOT
monikanicity
final saddleBOT
@candid vine Has your question been resolved?
candid vine
Hmm I tried to calculate it and got to this, did not see how to simplify it more
final saddleBOT
@candid vine Has your question been resolved?
dawn elk
Hmm I tried to calculate it and got to this, did not see how to simplify it more
wha-
thats just pascal’s identity
arctic estuary
The LHS counts subsets of {1,2,...n} of size k. The first term on the right counts subsets that do contain 1 and the second that don't contain 1.
grim nebula
this is just calculating (p-1 c k) in terms of (p-1 c k-1)
grim nebula
then you can just write like
soft zealotBOT
grim nebula
by applying fermat's little theorem
the RHS simplifies into (-1)^k mod p
and the case for k=1 is easy
final saddleBOT
@candid vine Has your question been resolved?
void crest
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Available help channel!
subtle flower
I’m confused how to set up for b
final saddleBOT
I’m confused how to set up for b
subtle flower
I think I’m supposed to multiple the face by how many times it landed there
Im not sure if that’s right or if I would divide by the 600 for the mean or by the total like normal
final saddleBOT
@subtle flower Has your question been resolved?
subtle flower
<@&286206848099549185>
final saddleBOT
@subtle flower Has your question been resolved?
final saddleBOT
@subtle flower Has your question been resolved?
final saddleBOT
@subtle flower Has your question been resolved?
pine valley
Im not sure if that’s right or if I would divide by the 600 for the mean or by t...
do you still need help?
the mean is just the average
so, it's the sum of all the face * number
divided by 600
final saddleBOT
final saddleBOT
Available help channel!
cinder isle
How do I convert this general form 9x^2 - y^2 = 81 to standard form
final saddleBOT
How do I convert this general form 9x^2 - y^2 = 81 to standard form
honest cloud
It appears that you have the equation of a circle, so recall the equation of a circle
Or the “standard” equation of a circle
gleaming bramble
How do I convert this general form 9x^2 - y^2 = 81 to standard form
- divide each term by 81 in the equation to make the right side to be 1
- simplify
cinder isle
1) divide each term by 81 in the equation to make the right side to be 1
2) sim...
No more completing the square
?
gleaming bramble
Just cancel out the 9 and divide the 81 by 9 then u have the form alr
cinder isle
damn. i was used to completing the square first and with this equation i couldnt do that so i got confused
.close
rare helm
final saddleBOT
honest glacier
slope is rise over run
that means 0.25 slope is 0.25 up for every 1 to the right
thats means $0.25 for every minute
the y intercept is where the graph hits the y axis
meaning the cost at 0 minutes
which would be the initial cost
the y intercept is when you plug in 0 for x which is 0 minutes
do you understand?
honest glacier
yw
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@rare helm Has your question been resolved?
turbid agate
guys i just realized, why is 100 / 3 not 100 if you times the answer of 100 / 3 to 3
final saddleBOT
guys i just realized, why is 100 / 3 not 100 if you times the answer of 100 / 3 ...
void crest
it is?
void crest
um
tawny pike
turbid agate
.close
final saddleBOT
tranquil pine
do you know any trigonometric functions that can help us here?
,w sqrt(100²-1.5²)
yes but we want b not c
not sure what you mean by that but yes b=sqrt(c²-a²)
lmao okay
but do you know how to find ?°?
or any ideas?
it is true that ?1°+?2°=90° as you said but that still can't help us get it
circle arc? this isn't a circle
why would i get a mod in here?
well i'm trying to help you
do you not know any trig functions at all?
.. the trigonometric functions would help you solve it but if you don't know any it's impossible to solve those angles
not sure why you are overthinking this
that's what i've been saying all the time.
you could've answered my questions and if you said no, i don't know them, i would've probably introduced you to them
anyways, if that's new to you, i'd recommend watching a video of it
or doing some research on websites like khan academy
that trigonometric identity only works on angles between 0 and 90°
without including 90°
so try using it on a ?° angle
that's not correct
remember sine of an angle is opposite side divided by the hypothenuse
not the adjacent side
,tex \sohcahtoa
soft zealotBOT
Al3dium
tranquil pine
maybe this helps, ignore the missing side
adj is the side that's "touching" the angle you're dealing with
excluding the hypothenuse of course
,w arcsin(1.5/100)
doesn't matter, as long as if you put it in degrees, you put the calculator in degrees mode and same for radians
tranquil pine
I gotta prove that the left is equal to the right by expanding and simplifying.
I’ve got sinx/sqrt2 - cosx/sqrt2.
final saddleBOT
I gotta prove that the left is equal to the right by expanding and simplifying. ...
void valley
,rccw
soft zealotBOT
tranquil pine
I gotta prove that the left is equal to the right by expanding and simplifying. ...
sin(a-b) formula
I used that to get to where am I. Did I do something wrong?
vale silo
where did you get to?
void valley
you forgot to multiply by sqrt(2)
tranquil pine
Where?
void valley
whole thing
loud knot
Why is the probability of failing considered as NOT probability? Couldn't we use the formula P(AUBUC) = P(A) + P (B) + P(C) - P(AnBnC)
final saddleBOT
Why is the probability of failing considered as NOT probability? Couldn't we use...
loud knot
The question is a bit wrong from beginning, its written that if a machine operates on all if its three functions
which means that machine operates if all functions are working
void crest
um
its just how they defined the machine as working
that all 3 parts need to work
its like to bake my cake i need all 3 of my ingredients
i need my
loud knot
Yea so why did they considered the prob as prob not?
void crest
flower, water, soil
loud knot
flower?
loud knot
pretty normal cake ingredients I see
loud knot
for the part failing
But we have to find the prob of machine not working, then why cant we just add the three probs of not working and use the formula?
Why we have to do it that way?
void crest
so
let
| be working
- be not working
so
essentially
the top row is the prob of machine working
loud knot
Okay
void crest
the other 7 rows are prob of machine not working
its a bit harder to calc the other 7
thus they calc the prob of the fist
first
then took
1-that first one
yay?
loud knot
oh so they have to calc every prob individually?
void crest
um
loud knot
To find the prob of failing that way?
void crest
if u wanted to u could
loud knot
Btw did you jsut made that pic?
void crest
yesh
final saddleBOT
void crest
yes
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Available help channel!
worn latch
Hey! I need help with proving this: If a matrix A is diagonally dominant, then it is also invertible
final saddleBOT
Hey! I need help with proving this: If a matrix A is diagonally dominant, then i...
strange shore
look for Hadamard's lemma
strange shore
look for Hadamard's lemma
maybe there is a proof on google
strange shore
pls fast :(
dont care
dense fable
fuck :(
final saddleBOT
@worn latch Has your question been resolved?
maiden basin
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maiden basin
What are the steps to this?
dawn elk
n=0?
final saddleBOT
@maiden basin Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
gleaming mantle
final saddleBOT
dawn elk
you are given $y= \frac k {\sqrt x}$
soft zealotBOT
soft zealotBOT
dawn elk
$y’= \frac k {\sqrt {25x}}$
soft zealotBOT
soft zealotBOT
dawn elk
now can you solve it?
dawn elk
k is right there
dawn elk
$\textcolor{red}{y= \frac k {\sqrt x}}$
$y’= \frac 15\cdot \textcolor{red}{\qty(\frac k {\sqrt {x}})}$
lets see
nooo
grim nebula
LOL
vale silo
oh my
soft zealotBOT
grim nebula
get better eyes 
dawn elk
vale silo
gleaming mantle
After?
grim nebula
solve for the value of k
using both equations
k should be a number
not in terms of x or y
soft zealotBOT
grim nebula
you can take the 25 out of the square root
gleaming mantle
After? What do i do
soft zealotBOT
grim nebula
do you see how the right hand side is just dividing y by 5
grim nebula
dividing this by 5
grim nebula
yk
soft zealotBOT
gleaming mantle
After that just k=5?
grim nebula
thats not right
soft zealotBOT
soft zealotBOT
gleaming mantle
K equal negative 5?
grim nebula
how did you get -5?
gleaming mantle
Cancel both k?
gleaming mantle
Y
soft zealotBOT
gleaming mantle
So ans is 1/5?
grim nebula
yes
grim nebula
your friend is incorrect
grim nebula
thanks chris
grim nebula
polar wing
😅
grim nebula
dont put your actual face onto your pfps
polar wing
i was gonna ditch snow and love you instead
grim nebula
because people like chris exist
final saddleBOT
@gleaming mantle Has your question been resolved?
final saddleBOT
final saddleBOT
@tranquil pine Has your question been resolved?
cerulean relic
Consider three sequences (an), (bn) and (sn) such that an ≤
sn ≤ bn for all n and lim an = lim bn = s. Prove lim sn = s.
This is called the “squeeze lemma.”
final saddleBOT
Consider three sequences (an), (bn) and (sn) such that an ≤
sn ≤ bn for all n an...
cerulean relic
(a) Let e > 0. Our goal is to show s − e<sn < s + e for large
n. Since lim an = s, there exists N1 so that |an − s| < e for
n>N1. In particular,
n>N1 implies s − e<an. (1)
Likewise there exists N2 so that |bn − s| < e for n>N2, so
n>N2 implies bn < s + e. (2)
Now
n > max{N1, N2} implies s − e<an ≤ sn ≤ bn < s + e
This was the provided proof, I am curious to whether it suffices to say that if lim an = a and lim bn = b that a = b = s, so that if for n>N1 and n>N2 respectively follows |an - a| < |sn-s| < |bn - s| < e (epsilon). So that we get lim sn = s.
hollow iron
Yes that's good. But you need to show that |s_n - s| < |b_n - s|
If you can do that, that's fine
cerulean relic
How if may ask, I thought it followed directly out of the given sn < or equal to bn?
hollow iron
But it seems more complicated than the proof you gave
No it doesn't. a < b doesn't imply |a| < |b|
-3 < 1
But |-3| = 3 > |1|
final saddleBOT
hollow iron
No problem!
final saddleBOT
Available help channel!
oak kraken
final saddleBOT
oak kraken
tired walrus
it is often (but not always) convenient to define 0^0 to be 1. not all calculators actually do that if you ask them directly to compute 0^0.
oak kraken
Is this like quantum bits where both are correct? 0 and a 1
amber holly
Still, irrelevant
oak kraken
.close
fallen reef
$\frac{3x-4}{2} = \frac{3x}{2} -2$
final saddleBOT
$\frac{3x-4}{2} = \frac{3x}{2} -2$
soft zealotBOT
dopediscorduser
