are you sure youre typing it right
#help-27
dense jay
steep cipher
No
devout snowBOT
devout snowBOT
Available help channel!
tight ibex
Find the derivative of this equation.
devout snowBOT
Find the derivative of this equation.
tight ibex
Red equation aka #1 is the given answer in the answer key.
Blue aka #2 is what I got, graphically the same, but I don't understand how they solved it to that. I just used quotient rule.
t!15
^ worked it out making sure I kept the same line
pulsar sand
It's often better to rewrite your function to use the product rule instead, but in this case you really just need to simplify your answer in blue
tight ibex
Yeah, I did and got the one that was purple.
olive jasper
Red equation aka #1 is the given answer in the answer key.
Blue aka #2 is what ...
Your way is correct, but you can do some modifications to reach t the red equation
olive jasper
Red equation aka #1 is the given answer in the answer key.
Blue aka #2 is what ...
Divide numerator and denominator by x½
devout snowBOT
devout snowBOT
Available help channel!
mortal aspen
how to find idk how to factorise it while finding the critical numbers
pastel pasture
mortal aspen
yess
vapid nest
how to find idk how to factorise it while finding the critical numbers
I would expand
mortal aspen
I would expand
even after expanding we need to take the common factor to simplify it right?
vapid nest
even after expanding we need to take the common factor to simplify it right?
expand take the derivative
simplify
vapid nest
factor out x^{-2/3} (and 4/3) if you want
vapid nest
that looks good
mortal aspen
i am getting -2,0 as critical numbers but its showing as incorrect answer
vapid nest
i am getting -2,0 as critical numbers but its showing as incorrect answer
why 0??
mortal aspen
idk whts critical numbersss tbh
vapid nest
and 4/{x^{2/3}} = 0
mortal aspen
idk whts critical numbersss tbh
i am just solving by guess from a long time
mortal aspen
and 4/{x^{2/3}} = 0
soo its gonna be -2 nd 4?
mortal aspen
and 4/{x^{2/3}} = 0
how did u get this?
vapid nest
btw x = 0 is a critical point but not for the reason you think
(it's undefined at x = 0)
vapid nest
where did you get 4
vapid nest
0 and -2??
mortal aspen
yupp tried bothh
uhmmm
omgg it came as correct apparently it wanted the correct order
soo basically critical numbers r the points where its udefined?
mortal aspen
ohhhh
vapid nest
omgg it came as correct apparently it wanted the correct order
yayyy
mortal aspen
0 or undefined
but for few questions 0 will not be a critical number
vapid nest
but for few questions 0 will not be a critical number
no where the derivative at the function
is 0
mortal aspen
no where the derivative at the function
huh
vapid nest
huh
uhhh
consider finding the critical points of x^2 - x
the derivative is 2x - 1
we wanna find where f'(x) = 0
x = 1/2
vapid nest
YAY
mortal aspen
thnkk uuu
vapid nest
OF COURSE
mortal aspen
.close
devout snowBOT
devout snowBOT
Available help channel!
vestal gazelle
devout snowBOT
vestal gazelle
can someone remind me how to find the magnitude of this complex number
i can times both the numerator and denominator by the conjugate of R + jwL
looking for help on next step
i just realized that | a / b | = |a| / |b|
devout snowBOT
devout snowBOT
Available help channel!
restive river
does this make sense ? i feel like i said random stuff to try and make it work
crude wasp
does this make sense ? i feel like i said random stuff to try and make it work
yeah seems fine but tbh it feels like u've written more than u needed to
probably enough just to set beta = -a - bi and then show they add to 0
pulsar sand
The problem I have with this response is that you should really be stating that since a,b, are real, -a and -b exist hence beta as you defined it exists. Some of your phrasing is a bit long-winded and avoids explicitly stating this.
devout snowBOT
@restive river Has your question been resolved?
restive river
probably enough just to set beta = -a - bi and then show they add to 0
i don’t think i get it, are you saying the negative alpha was unnecessary?
crude wasp
as in
restive river
The problem I have with this response is that you should really be stating that ...
I’m new to this i’m self studying so i’m still trying to figure it out
crude wasp
Let $\alpha = a+bi \in \mathbb{C}$. Then, let $\beta = -a - bi$. Then
$$\alpha + \beta = a + bi - a - bi = 0$$
so inverses exist in $\mathbb{C}$
woven radishBOT
LY
restive river
Oh
crude wasp
The problem I have with this response is that you should really be stating that ...
depending on how detailed u need to be u might wanna mention i.e. a,b, real so -a -b exist etc.
crude wasp
yeah
crude wasp
nw
sullen meadow
deicde x and y intercepts algerbracically
y=5x+10
x=?
y?
devout snowBOT
deicde x and y intercepts algerbracically
y=5x+10
x=?
y?
sullen meadow
hi can someone help me
shrewd thistle
Do you have another equation?
sullen meadow
no..'
junior chasm
Do you have another equation?
you dont need second equation here
junior chasm
deicde x and y intercepts algerbracically
y=5x+10
x=?
y?
for x intercept
shrewd thistle
No, you don't.. just noticed, that's just a line
junior chasm
that means where the line cuts the x axis
and where the line cuts the x axis, y's value is?
sullen meadow
that means where the line cuts the x axis
yep
sullen meadow
and where the line cuts the x axis, y's value is?
0
junior chasm
so put y=0 in the equation
shrewd thistle
Do you know the basic formula of a line, yxy? y = mx+b? Remember what b is?
sullen meadow
Do you know the basic formula of a line, yxy? y = mx+b? Remember what b is?
no i havent learnt that yet.
shrewd thistle
It's called the "slope-intercept" formula.. b is literally your y-intercept (where x=0)
sullen meadow
oh
sullen meadow
whats m
shrewd thistle
m is the slope of the line.. rise over run
sullen meadow
Okay
but like i stil dont get how to solve it if Y=5x+10
to find x and y
algerbracically
shrewd thistle
So, if your y-intercept is where x=0...
sullen meadow
yeah
shrewd thistle
Your x-intercept is going to be where y=0
sullen meadow
yeah
shrewd thistle
... plug & chug
sullen meadow
0+10 is 10
shrewd thistle
ergo.. your y-intercept is 10
sullen meadow
Oh
shrewd thistle
So.. think of it this way
shrewd thistle
Yes, you have to isolate x.. so subtract 10 from both sides, then divide by 5
WHEN x = 0, y = what? That's your y-intercept
WHEN y = 0, x = what? That's your x-intercept
sullen meadow
ohhh
shrewd thistle
The zeroes are your known values that you have to plug in (unless you recognize the format of the equation, but you said you guys hadn't gotten there yet)
restive river
you can go by this:
y=mx+b, where b is the y-intercept, so 10 is the y-intercept
that works for when x is equal to 0, so y=5(0)+10 => y=10
then you can replace y with 0 to find the x intercept, so:
0=5x+10 => -10=5x => x=-2 ; that being the x-intercept.
so the y-intercept is 10, and the x-intercept is -2.
M means the slope, essentially rise over run. It’s how much your line moves up or down while moving to the right. i.e. when M=1, that means going up 1 and going right 1. When M=-2, that means a rise of -2, or going down by 2 units, and going right by 1. When M=-3/2, that means a rise of -3 (going down by 3 units) and going right by 2 units.
I tried writing this
sullen meadow
thanks i get it now
sullen meadow
you can go by this:
y=mx+b, where b is the y-intercept, so 10 is the y-interce...
thanks also
but i do have another questio
shrewd thistle
ok
shrewd thistle
It should be both -infinity to -4 and -2 to 5
And -infinity to -4 is also on the paper..
shrewd thistle
It's where the y-values are positive
sullen meadow
the -2 to 5
shrewd thistle
Anything "above" the x-axis
sullen meadow
yeah so -2 to 5
shrewd thistle
Is above the x-axis
sullen meadow
-inf ,-4 U -2 , 5
shrewd thistle
Yep
shrewd thistle
Both have to be present to have the correct answer.. it's not an "or" - it's an "and"
sullen meadow
yes'
shrewd thistle
shrewd thistle
It's the same reason why this section is the only negative interval
Because that's the only portion of the graph BELOW the x-axis
shrewd thistle
We're not looking at the slope of the line.. where it's increasing or decreasing.. we're looking at where the graph is in relation to the x-axis
(-inf, -4] U [-2, 5]
sullen meadow
bruh
shrewd thistle
Look at the blue shaded section
sullen meadow
-2 to 1 is above the x axis..
shrewd thistle
Yes.. and above the x axis is positive..
sullen meadow
YES
and tehy are saying
to find postive
Soo -2 to 1
is positive
its above
the x axix
shrewd thistle
It's not just -2 to 1.. it's -2 to 5
it doesn't "stop" at 1, and then immediately "start" at 1 again
shrewd thistle
Trying to think of a different way to explain this..
So.. let me ask this.. what is it about x = +1 that seems unique when answering this question?
Because I don't understand why that's important to you..
sullen meadow
becuas
they say to find the postive
and -2 to 1
and is above x-axdis
so its coonsidered a postive
shrewd thistle
There's no need to break the group up at 1, though
(-inf, -4] U [-2, 5] is sufficient
sullen meadow
why
shrewd thistle
Because there's no discontinuity at 1
shrewd thistle
So.. a discontinuity is where the graph "disappears"
shrewd thistle
Yes!
sullen meadow
okay then -2 to inf
shrewd thistle
Not quite! See that black dot on the line at 5? That means the line stops at (and includes) 5
shrewd thistle
If it were just a hollow circle, it would mean the graph stops at (but does NOT include) 5
sullen meadow
you could have said that earlier
shrewd thistle
LOL
shrewd thistle
np, glad we got that sorted out
sullen meadow
and i wanted to be prepared
sullen meadow
if closed then the [] if not then brackert
shrewd thistle
[a, b] includes both a and b
(a, b) includes neither a nor b
(a, b] does not include a, but includes b
shrewd thistle
infinity always gets a parenthesis
sullen meadow
shrewd thistle
Yep
shrewd thistle
If there's no dot or circle, you can assume the graph is continuous.. so it includes x=-2
That being said, [-2 is correct
So.. for example..
shrewd thistle
A circle on the graph means that there's a discontinuity.. -2 "doesn't exist" (it's undefined)
So in this case, you'd use (-2
shrewd thistle
Because -2 is defined.. it actually exists
sullen meadow
so why is it here bracket
if theres no circle
or anything
on it
just the number
shrewd thistle
That's technically incorrect
But honestly, if you guys are just getting into this material, your instructor may not be super-strict on it..
Other than that, I'm not sure what to tell you.. it should be [-1, inf)
Because that arrow on the left? That means the graph continues off the page
And it continues forever
shrewd thistle
Yep
sullen meadow
so if theres no circle on the number then we put a bracket
shrewd thistle
So.. for the domain, you put -inf, right? Because that arrow goes off to the left for infinity
For range, it should work the same way.. the arrow goes up for infinity, too.. so the range technically goes up to infinity
sullen meadow
the thing i dont get is
what do we put if theres nothing on the nunber
the square or the bracket
i think its bracket
becuase
in inf
we put bracket
and theres no circle on it bc we dont know when it will end
so its bracket
shrewd thistle
inf gets a parenthesis, because "infinity" isn't actually a number
sullen meadow
and if a number?
shrewd thistle
If it's actually a number, like what I showed you with -2 earlier, it depends on what the graph is showing
If it's a solid dot, like on x = +5, then it's included, and it gets a bracket ]
If it's a circle, it's not included and it gets a parenthesis
shrewd thistle
Then the number is included in the upper and lower bounds. Like, x = +2 doesn't have anything on it except the line of the graph, right?
So it's included in [-2, 5]
Because [-2, 5] includes every number from -2 to 5... -1, 0, 1, 2.23428438765982.. everything
sullen meadow
oh
sullen meadow
look at the range
for
both
graphs
theres one with brackets
and one with square
why??
shrewd thistle
That looks like an inconsistency in how you guys are being taught =/
Which is extremely confusing
shrewd thistle
Assuming the graph on top actually goes to y=-25, it should have a bracket, like the [3 on the bottom graph does
Without knowing the equation, it's impossible to know if the graph actually reaches y = -25 or y = +3, so in this case it's a "if it looks like it reaches a number, then it does"
sullen meadow
it does what?
shrewd thistle
On the other hand, it's possible that the equation defining the upper graph only goes to y = -24.9999999 but since there's no way you'd ever know that just by looking at a low resolution graph, you can call it "y = -25" and you're fine
Unless your instructor is being pedantic
sullen meadow
no we ned to give weather its a square or bracket
shrewd thistle
Right, but it appears as though your instructor isn't being consistent in that regard.. either both should be [-25 and [3 or both should be (-25 and (3
There's no way to know from the graph exactly what the values are, so in order to teach the material, "close enough" should matter, at least until you guys have these concepts down pat
sullen meadow
ah
shrewd thistle
I don't know if your instructor has a reason to do it this way.. you should ask and get clarification, because I'm not the one grading your test..
sullen meadow
true
shrewd thistle
But in my opinion, I think the material could be taught.. more consistently.
I know that's a lot to digest, but hopefully it helped clear things up?
shrewd thistle
np - good luck!
shrewd thistle
.close
sullen meadow
.close
devout snowBOT
devout snowBOT
Available help channel!
radiant anvil
devout snowBOT
radiant anvil
could someone elucidate what is happening in the conversely part. I presume we are trying to show that given a k-cycle tao and a sigma, mew is a k-cycle. I am most uncertain about the part I shall highlight.
torn bane
The notation is saying that if we take some ai and then take the next one a(i+1), then mu(first) =second
The point of the mod expression is that we need to wrap back to a1 if the first is a_n
radiant anvil
could u illustrate it
torn bane
I’m not sure how I would, what exactly is confusing you
radiant anvil
like what exactly does b' represent?
I do understand the terms separately but put together, it is harder to understand
radiant anvil
it seems to be that b' is b right shifted 1?
but wouldnt that just mean they are they same as it is a cycle afterall
torn bane
Err well the relation is b=sigma(a_i), and b’=sigma(a_i+1), so mu(b) = sigma tau sigma^-1 (b)= b’
So we get that for each consecutive pair a_i, a_i+1 in the tau cycle, there are b and b’ consecutive in the mu cycle
radiant anvil
sorry
can we clear up some notation first?
sigma(ai) = b, is b the set of values as shown above? from b1 to bn?
torn bane
B is some index from 1 to n, we don’t know what it is yet
Later we make the b_is from b
radiant anvil
is it in a similar way that we constructed sigma earlier?
devout snowBOT
@radiant anvil Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
atomic herald
devout snowBOT
serene lance
devout snowBOT
@atomic herald Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
cyan dagger
I’m not sure what to do next
devout snowBOT
I’m not sure what to do next
dense lynx
I’m not sure what to do next
you can make use of the inductive hypothesis here
dense lynx
you already have it, you have to make use of it
cyan dagger
yeah sorry that’s what I tried to say my bad 😭
dense lynx
oh i see
cyan dagger
I’m not sure how to reach there
cyan dagger
so you currently have:
1296\*6^4k + 38\*38^k - 2
I mean uhh idk under exam conditions idk how I would ever manage to figure that out
wheat pawn
divide 1296 by 74. You got 17 as quotient, 38 as remainder
cyan dagger
divide 1296 by 74. You got 17 as quotient, 38 as remainder
yh but like I use a scientific calculator it don’t give remainder 😭💔
wheat pawn
...
dense lynx
I mean uhh idk under exam conditions idk how I would ever manage to figure that ...
alternatively what u can do is take this expression here
and remove a multiple of 6^(4k) + 38^k - 2 (which you assume to be divisible by 74) until the 6^(4k) term disappears
cyan dagger
and remove a multiple of 6^(4k) + 38^k - 2 (which you assume to be divisible by ...
How do I go about doing that?
wheat pawn
yh but like I use a scientific calculator it don’t give remainder 😭💔
scientific calculator would give you 17.51....
Which means that 17*74 < 1296.
Specifically, 17*74 = 1258.
And 1296 - 1258 = 38
cyan dagger
scientific calculator would give you 17.51....
Which means that 17\*74 < 1296.
S...
okay okay
cyan dagger
this is thr mark scheme though
what abt this method
can yall just show me the working out I am really really tired I’ll try learn it from working
wheat pawn
I wanna know this method
what he's doing here is taking this expression:
1296*6^4k + 38*38^k - 2
now, from the hypothesis of induction, you know that:
1*6^4k + 1*38^k - 2
is divisible by 74
so you're left with two parts:
(1295*6^4k + 37*38^k) + (1*6^4k + 1*38^k - 2)
37*38^k = 37*(2^k)*(19^k); Since 37*2 = 74, and k>=1, that part is divisible by 74.
devout snowBOT
devout snowBOT
Available help channel!
restive river
how do i do ratio test here
devout snowBOT
how do i do ratio test here
restive river
i get $\lim_{n\to\infty} \dfrac{(4\cdot9\cdot14\dotsb(5n-1))(3\cdot7\cdot11\dotsb(4n+3))}{(3\cdot7\cdot11\dotsb(4n-1))(4\cdot9\cdot14\dotsb(5n+4))}$
ah fuck
random helm
just cansel out multipliers in numerator and denominator
woven radishBOT
Derivative
random helm
no. you will be left with (4n+3)/(5n+4) -> 4/5
restive river
how?
oh right
you are right
yes
i am sorry for my incompetence
have a good day!
random helm
you too !
restive river
.close
devout snowBOT
devout snowBOT
Available help channel!
radiant anvil
describe the left cosets of SL2(R) in GL2(R). what is the index of SL2(R) in GL2(R)?
devout snowBOT
describe the left cosets of SL2(R) in GL2(R). what is the index of SL2(R) in GL2...
radiant anvil
all elements of SL2 are invertible so each left coset would be the all matrices with the same determinant right?
the index of a subgroup would be the number of cosets. in this case it is infinity
devout snowBOT
@radiant anvil Has your question been resolved?
crude wasp
all elements of SL2 are invertible so each left coset would be the all matrices ...
yeah
crude wasp
the index of a subgroup would be the number of cosets. in this case it is infini...
yeah
radiant anvil
thanks
halcyon yew
Help
storm gyro
Identify what'll be different about the graphs and what'll be the same
it might help to draw them first to do so.
halcyon yew
Would a just be horizontal reflection and y intercept down 3 @storm gyro
O wait i drew it and see that it is just a vertical reflection but how do i know this without drawing
<@&286206848099549185>
Or @storm gyro
halcyon yew
So y is always f(x)?
halcyon yew
Wait so whenever i do a question y is f(x)?
neon zephyr
you can assume the case, yes
neon zephyr
so the first equation was $y=4x+3$
woven radishBOT
🌸Anthea of the Flowers🌸
neon zephyr
you can assume $f(x)=y=4x+3$,
which means that for the second equation,$ y=-4x-3=-(4x+3)=-f(x)$
woven radishBOT
🌸Anthea of the Flowers🌸
neon zephyr
yes
halcyon yew
Ok ok that makes a lot more sense thx @neon zephyr
devout snowBOT
@halcyon yew Has your question been resolved?
wanton harness
10lb*seconds to kg, how do I solve this
devout snowBOT
10lb*seconds to kg, how do I solve this
acoustic leaf
those are not compatible units
wanton harness
those are not compatible units
I was given this by my teacher
crap
wrong
conversions
10lb/seconds to N
acoustic leaf
those still aren't compatible units
worn heath
this might be dumb question but isnt "equilibrium solutions" just values where y' = 0?? so i dont need to solve the differential equation at all for this question right?
devout snowBOT
this might be dumb question but isnt "equilibrium solutions" just values where y...
timber pebble
this might be dumb question but isnt "equilibrium solutions" just values where y...
yes
devout snowBOT
timber pebble
np 
devout snowBOT
Available help channel!
weak finch
devout snowBOT
weak finch
can anyone help me out? dunno why this is wrong
upper schooner
can anyone help me out? dunno why this is wrong
What did you mean here? Why do you have two commas?
weak finch
What did you mean here? Why do you have two commas?
I tried writing it with union as well but it didnt work
idk how im supposed to format it if thats the right answer
😭
OH
oops theres a comma in between the 2
wtf
upper schooner
Yeaaa 
devout snowBOT
devout snowBOT
Available help channel!
mild basin
devout snowBOT
mild basin
Why does x_i = i/n?
What math is being being done to calculate this?
x_i is just referencing a point on the domain, and I get that. But how do we know it’s i/n? Is there a calculation with delta x somehow to find this?
like if delta x was different would x_i be different too?
late flint
$a=0$, so in the context of $x_i$, $b-a$ would be the same as $i-0$ I think
woven radishBOT
solaris
mild basin
I thought delta x is the width of the interval
late flint
yeah it is
mild basin
The interval (delta x) is calculated using (b-a)/n
acoustic leaf
x_i is just referencing a point on the domain, and I get that. But how do we kno...
we are making the choice that x_i should be the right endpoint of the interval
late flint
it's the same as integrating from 0 to $i$ I believe
woven radishBOT
solaris
mild basin
we are making the choice that x_i should be the right endpoint of the interval
Where does it tell you that?
Because of sigma?
acoustic leaf
x_i can be anywhere in the interval but the left or right endpoints are usually easier to calculate
mild basin
x_i can be anywhere in the interval but the left or right endpoints are usually ...
But you said it starts at right endpoint for each rectangle.. how do you know?
I can only assume sigma in top right is what says that?
acoustic leaf
based on the endpoints and arithmetic
mild basin
based on the endpoints and arithmetic
Wdym? If endpoint was left side the equations would be different?
acoustic leaf
well we could still use x_i = i/n if the sum went from i = 0 to n-1
mild basin
I’m so confused right now.
mild basin
we are making the choice that x_i should be the right endpoint of the interval
So it is the sigma that tells you we are working with right side, not left side
acoustic leaf
or we could use the same summation limits and use (i-1)/n for the left endpoints
mild basin
or we could use the same summation limits and use (i-1)/n for the left endpoints
Ya but it doesn’t say that. You wrote we are working with right side. How do you know it’s right side?
supple knot
Avid you should do simpler problems
mild basin
This is intro to Riemann sun
supple knot
Like with specific n that's small
acoustic leaf
draw a number line and figure out what the end points of a partition of 0 to 1 into 5 equal subdivisions should look like
mild basin
supple knot
Example 5.3.4
supple knot
From https://youtu.be/IDl701RaNYk?si=yRCoJFGHEJAIdLkL
Yea don't
Read a simpler example
mild basin
https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/05%3A_Integr...
For me personally, I can’t read through all of this. It’s like reading through terms of service, I find math concepts way easier with video to explain so that I understand. Unfortunately he didn’t explain the x_i part he just wrote it
supple knot
https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_(Apex)/05%3A_Integr...
Also defined in here
acoustic leaf
draw a number line and figure out what the end points of a partition of 0 to 1 i...
have you tried this?
supple knot
For me personally, I can’t read through all of this. It’s like reading through t...
Under figure 5.3.7
devout snowBOT
@mild basin Has your question been resolved?
devout snowBOT
vast violet
ok i work it out and show
woven radishBOT
Astar777
junior chasm
its the same as this, right?
junior chasm
yeah its same
vast violet
oh
upper schooner
(it is: "suvat" is another form of these, but instead, e.g. u is the initial velocity, with v being the final velocity, and s being displacement)
@faint gorge hiii 
vast violet
so 0=(16)^2+2(9.8)(-25-0) is good for this so far?
junior chasm
why is v = 0
vast violet
o
junior chasm
v is what u have to find
vast violet
ok
Oops
Makes sense
-234?!?
uhhhhh
i made some dumb mistake somewhere
oh ok square root
upper schooner
so 0=(16)^2+2(9.8)(-25-0) is good for this so far?
Be careful of the units on the RHS as well, if you choose gravity acceleration as positive, then choose choose the position change to be positive
vast violet
like that yellow lne
Oh ok
so if 9.8 is negative
what is s
what should change here
v^2=16^2+2(-9.8)(-25-0)
i got 27.3
Oh i get it
So the y must match with G
in term of signs?
junior chasm
in term of signs?
it depend on the situation
here u were throwing the ball downwards
which we took as negative
so the s (displacement) was negative
but if u threw the ball upwards (which we took as positive) then s would be positive
devout snowBOT
Available help channel!
vast violet
sorry
vast violet
but
In the organge he wrong
Vox= V0
and Voy = 0
he wrote**
Is it because we start at the origin or
idk the reason for that sry ):
ohhh
Ok tell me if im wrong
I will try
So V0x = the horizontal and it is initial velcoity as the word problem says 2.7m horizontal
I hope i donnt sound dumb
And V0y = 0 is for the vertical but idk why 0
id assume cuz we start at origin but
soft umbra
idk the reason for that sry ):
At the very moment the ball was shot, the ball only had horizontal speed, do you agree?
vast violet
yep
soft umbra
So, the initial speed is Vx, which is also V0
vast violet
Oh ok
soft umbra
And V0y = 0 is for the vertical but idk why 0
Because the ball was shot horizontally
There was no vertical force applied to the ball
vast violet
ohhhhh
soft umbra
It takes a little moment for gravity to realize that "oh, the ball isn’t on the table now"
devout snowBOT
soft umbra
No problem
devout snowBOT
Available help channel!
quartz rivet
devout snowBOT
upper schooner
Why do you have 5h - 7 in the denominator 
quartz rivet
oh crap
i didnt
seem to notice that h is not f(h)
so its just h right
yea
5
ok ty
upper schooner
quartz rivet
.close
devout snowBOT
devout snowBOT
Available help channel!
cosmic lodge
devout snowBOT
cosmic lodge
ok so im dumping this into the formula but im not getting it.
im getting -6(x+3)-4(y-3)-6(z) = 0
cosmic lodge
its saying its equal to 18 so maybe im just doing the distributions wrong
mystic scarab
-6(x+3)-4(y-3)-6(z) = 0
==> -6x - 18 -4y + 12 -6z = 0
==> -6x -4y -6z - 6 = 0
==> 3x + 2y + 3z + 3 = 0
cosmic lodge
oh maybe i do need to simplify it
mystic scarab
I don't know, but this final form and what you got are both correct
cosmic lodge
cool way to show that it and the positive are equal
oh wait i might have a dumb idea
the idea worked
had to do -18x-12y-18z = 18
ty
.close
devout snowBOT
mystic scarab
had to do -18x-12y-18z = 18
Lol instead of simplifying they wanted you to complicate it 🙈
devout snowBOT
Available help channel!
upbeat marten
devout snowBOT
upbeat marten
I get stuck there
if i simplify the numerator would it not just be 0?
but i cant seem to find a zero so im just lost
mystic scarab
Multiply num and den by the conjugate of the denominator
You should recognize double angle formula of cosine
soft umbra
Just consider cos(theta) = x, and x approach 1/sqrt2
Substitution works well here
@upbeat marten
mystic scarab
,w lim as x \to \pi/4 of cos(2x)/(-1 + √2 cosx)
woven radishBOT
mystic scarab
Yep, 2 Is the correct answer
devout snowBOT
devout snowBOT
Available help channel!
sour spire
guys, if the standard deviation of 20 values is 4, does that mean its variance is 4^2 = 16?
devout snowBOT
guys, if the standard deviation of 20 values is 4, does that mean its variance i...
sour spire
ooohhh
okk thank youuu
btw i don't really understand why some questions say this
wait holdon, what about sum of x and sum of x^2,
can we just square the sum of x to find sum of x^2?
fervent hornet
no
upper schooner
E.g. compare, say, a^2 + b^2 to (a + b)^2 = a^2 + 2ab + b^2
upper schooner
Most likely you'll need to find other ways to find the sums (which hopefully don't end up being too bad) 
upper schooner
Hopefully it stays that way 
fervent hornet
Hopefully it stays that way <:catLove:1081177781452419082>
hopefully....
sour spire
Hopefully it stays that way <:catLove:1081177781452419082>
i hope so
my statistics teacher is very unexpected
i hope weird questions won't appear during the exam
thank you again guys
.close
devout snowBOT
devout snowBOT
Available help channel!
vernal grail
$\sum^{\infty}_{n=0} \frac{x^{n^2}}{n!}$
devout snowBOT
$\sum^{\infty}_{n=0} \frac{x^{n^2}}{n!}$
woven radishBOT
alee
vernal grail
Determine the interval I of convergence of the series
I wrote t = n² , so n = √t
Then I used the ratio criterion
devout snowBOT
@vernal grail Has your question been resolved?
devout snowBOT
devout snowBOT
@visual breach Has your question been resolved?
lament schooner
devout snowBOT
lament schooner
for the 2x^2
do i just need to multiple the matrix by 2 after multiplying it by itself once
zealous scroll
Yes
fervent hornet
do i just need to multiple the matrix by 2 after multiplying it by itself once
yes
lament schooner
yes
turns out i looked at the wrong answer so im like
wtf how is my answer so far
💀
.close
devout snowBOT
devout snowBOT
Available help channel!
worldly latch
devout snowBOT
misty crest
,rotate
worldly latch
I get it’s an element of all real numbers except for the numbers in between 2 and 3 so I’m just curious how to write it
woven radishBOT
twin thunder
if you can't directly find the domain, find the function's inverse and then find it's range
misty crest
domain is just all reals
woven radishBOT
misty crest
| means such that
in english you essentially are saying "the range is the set of real numbers y, such that y is between 2 and 3"
also
2>y>3?
worldly latch
Yeah that what I’m confused abt
misty crest
if 2>y then how is y>3 sir
worldly latch
Dyk how to state the domain then?
woven radishBOT
knief
misty crest
not E
worldly latch
You’re right
misty crest
so consider the portion of the graph for x<0
2^x + 1 has a maximum of 2 for x<0
what is its minimum
in other words
as x-> -inf
worldly latch
Approaches 1
misty crest
mhm
so then it’s between 1 and 2 for x<0
now how about the other portion
what’s the minimum
worldly latch
Y approaches infinity as well
worldly latch
1 and everything below that and between 2 and 3
worldly latch
Tru
misty crest
you’re welcome
worldly latch
.close
lament schooner
devout snowBOT
lament schooner
very much idk how to determine that
robust dust
multiply out AB and BA
misty crest
find AB and BA
robust dust
then equate entries
fervent hornet
yes A can be multiplied with B
lament schooner
what does it mean by commute
like it can multipled?
okay thing is i dont see what value abcd can have
that can prevent a commute
or multiplication
robust dust
commuting means you can swap the ordering
e.g. addition is commutative, so a + b = b + a, but e.g. subtraction is non-commutative, since a - b is not equal to b - a in general
lament schooner
ah
robust dust
matrix multiplication is not commutative
lament schooner
i know that
robust dust
the question is asking for which values of a,b,c,d make it so that AB = BA
lament schooner
actually i thjink if theres a row or column of zero then its non communable?
am i mistaken
robust dust
no, counterexample: zero matrix commutes with everything
since zero matrix times any matrix is the zero matrix
lament schooner
since zero matrix times any matrix is the zero matrix
so at what
time is it not commutable
i know the size of the matrix changes a lot of things
but idk
what the entries have to do with commutability
robust dust
can you multiply out AB and BA
as in, write out the resulting 2x2 matrices in terms of a,b,c, and d
lament schooner
as in, write out the resulting 2x2 matrices in terms of a,b,c, and d
using abcd
or replace them with a nonzero/zero value
robust dust
using a,b,c,d
lament schooner
oh okay ty
robust dust
I think the first entry of AB may be mistaken
robust dust
yes
lament schooner
I think the first entry of AB may be mistaken
okay here i fixed it oops
robust dust
yeah
devout snowBOT
devout snowBOT
Available help channel!
odd prism
This isn’t same technique as solutionnaire but it gives the same answer… Anything wrong with it?
devout snowBOT
This isn’t same technique as solutionnaire but it gives the same answer… Anythin...
odd prism
This is for power series
devout snowBOT
@odd prism Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
restive river
Find an approximation to √3 correct to within 10−4 using the Bisection Algorithm.
devout snowBOT
Find an approximation to √3 correct to within 10−4 using the Bisection Algorithm...
restive river
I understand how to use the bisection method on a function
how would this be applied to a number
gray fern
Assume the function is x^2 - 3
gray fern
It's a function that has a root at exactly sqrt(3)
devout snowBOT
devout snowBOT
Available help channel!
dusty robin
Could someone explain what like a free variable is
devout snowBOT
Could someone explain what like a free variable is
@dusty robin Has your question been resolved?
faint gorge
Could someone explain what like a free variable is
A variable that can be any number
See this results from looking at the last row where you can see 0y = 0 and this is always true for any value of y.
So y is a free variable.
x will then depend on the free variable basically
devout snowBOT
@dusty robin Has your question been resolved?
acoustic leaf
the number of free variables given by the number of variable columns without a pivot
ashen carbon
hi i need help
devout snowBOT
hi i need help
limber kernel
ashen carbon
apologise if this is confusing, but i wanted to know something probability related. if i flip a coin heads or tails with 50% random odds of course , and i want heads 3 times in a row how likely is this to happen?
tried asking chatgpt but it keeps breaking down on math related stuff 💀
also, if i am constained to only being able to flip 5 times, 10 times, and 15 times, does this affect the final answer?
ashen carbon
i meant like could someone figure out the %'s for this?
if i flip 5 times, i want 3 heads in a row , if i flip 10 times
etc
so far i know the odds are 1 in 8 overall, or 12.5%
but if im looking for it to happen within x amount of flips, i wanted to know how that affects the answer
uncut crow
if you want like the expected number of flips before some particular string of flips is seen, you can usually do that with conditioning
for probability some particular string is seen in a fixed amount of flips, well, tough to answer that in general
ashen carbon
12.5 is actually if you flip 3 times
wdym
ashen carbon
if you want like the expected number of flips before some particular string of f...
yeah thats what i want
like if on a coin flip the odds are naturally 50/50, what is the expected number of flips to land at 3 heads in a row
% wise probability of that happening
topaz axle
it depends on how many times you flip
ashen carbon
it depends on how many times you flip
it would not just be a increasing % number over flips?
ok so what if i flip 5 times, can you give a %
or 10 times