loud falcon
#help-13
cedar kilnBOT
young quail
cedar kilnBOT
Available help channel!
dreamy cove
I'd like assistance. How would I go about finding the values on the right and plotting the sin function?
royal loom
What do you know about the period of a trig function?
Do you know for example what the period of just sin(x) is?
dreamy cove
What do you know about the period of a trig function?
little.
dreamy cove
Do you know for example what the period of just sin(x) is?
no. Wouldn't it be just one?
the graph would start at (0,0) right?
royal loom
not one. The period is how often the function repeats itself
yes the graph would have a point at the origin
dreamy cove
okay.
royal loom
so what is special about trigonometric functions is that they are periodic, basically they repeat themselves after some distance (which we call the period)
dreamy cove
okayyy
dreamy cove
yes because it repeats itself and starts at zero.
royal loom
well, that doesn't necessarily mean that it is sin(x), but I agree that it is so we can move on
looking at that graph
how often does it repeat itself?
dreamy cove
it repeats twice
royal loom
say for example, how often does it have a point where y=0
but what is the distance in between each of those points?
royal loom
okay so
the first point where y=0
the graph goes up
the next point
it goes down
so we aren't yet repeating, because at the next y=0 the graph doesn't do the same thing
so we move on to the next point where y=0
dreamy cove
ohhh okay
royal loom
here you can see that it goes up again
so it started at 0 going up, and then it went some distance (what distance?) and was at 0 going up again
dreamy cove
so it started at 0 going up, and then it went some distance (**what distance?**)...
The distance is pi
royal loom
check that again
royal loom
No, look at the graph. We start at (0,0), we go over pi units, we are now at (pi, 0) is the graph behaving the same at this point as it was at the beginning?
the answer is no, because after (pi, 0) it goes downwards, instead of upwards like at the beginning
dreamy cove
okay
dreamy cove
the function still isn't repeating itself though.
wraith daggerBOT
royal loom
this is the same graph of sin(x), just a little bit bigger
can you see now that it is repeating itself?
For example look at the left side of that graph, to the left of the y-axis. Isn't this the exact same as the right side of the y-axis?
dreamy cove
yes because at both points y = 0
royal loom
but again I would point out that, just because y=0 again doesn't mean that it is repeating. Look at the graph I just plotted in the chat
Do you see that it has y=0 at x=-pi, and also at x=0 ?
but at x=-pi the graph is going down
and at x=0 it is going up
so it hasn't started repeating itself
So you want to find two points where y is the same, but also the graph continues in the same direction from those points
So where are two points where y=0 and they both are going up afterwards
royal loom
-2pi is going up, pi going down. So no
royal loom
So where are two points where y=0 **and** they both are going *up* afterwards
This is the key question
dreamy cove
-2pi and 0?
dreamy cove
-2pi?
royal loom
does it make sense for distance to be negative?
royal loom
yeah
okay so what you just figured out is
sin(x) , repeats itself every 2pi
does that make sense?
wraith daggerBOT
royal loom
take another look to verify
choose any point you want
move to the left or right by 2pi
you will be at the same point
dreamy cove
-pi / 2pi
how come at the 2pi point the graph is going up but at the -pi point it's going down?
royal loom
that is moving by 3pi, so that is why
dreamy cove
okay
royal loom
going from -pi to 2pi is a distance of 3pi
it repeats every 2pi
not every 3pi
So we would say that, 2pi is the period of sin(x)
dreamy cove
So we would say that, 2pi is the *period* of sin(x)
because at 2pi the graph repeats.
royal loom
because every 2pi the graph repeats
dreamy cove
every* thanks.
royal loom
and I also mean like this
say we start at x=pi
and we go to x=3pi
this was a distance of 2pi
the graph will be the same then
at x=pi
and at x=3pi
So, does all of this sound good to you so far?
the talk about the period of the functions?
royal loom
Okay, now that we spent all the time talking about sin(x), I figure I should just tell you that it works the same for cos(x)
the period of cos(x) is 2pi also
Now I'll ask you this
,w plot tan(x)
wraith daggerBOT
dreamy cove
pi
royal loom
perfect
Okay
So
if instead we had something like
sin(2x)
when we put in x=0 we get sin(0)
right?
dreamy cove
yeah
dreamy cove
the period would be 4pi?
dreamy cove
yes
royal loom
but we went from sin(0) to sin(4pi)
so, like you know about sin(x), that means it repeated itself twice
right?
dreamy cove
right.
royal loom
but we only changed x from 0 to 2pi
and it did 2 repititons
so what does this tell you about the period of sin(2x)
it isn't still 2pi
we only care about 1 repetition
going from 0 to 2pi gives us 2
so we can divide this distance by 2
and go from 0 to pi
that will give us a repetition
dreamy cove
the period is 1pi?
wraith daggerBOT
royal loom
verify with your eyes
dreamy cove
at -pi and 0 the graph is going up
dreamy cove
and 0 and pi the graph is also going up.
dreamy cove
is there an equation to find the period?
royal loom
So let me put what we have gathered together now, and see if you can tie it all together
sin(x) has period 2pi and sin(2x) has period pi
dreamy cove
**sin(x)** has period **2pi** and **sin(2x)** has period **pi**
right.
royal loom
what might the period of sin(3x) be? And once you have found that, what might the period of sin(L x) be, for any L
I'll brb while you work on that
Think about how the multiple on the 'x' changes how fast/slow 'x' travels compared to how just normal sin(x) does
dreamy cove
the greater the x the more faster it travels?
would the period of sin(3x) be 3/2? and would the period of sin(L x) be x/2 (x being any given period)?
royal loom
So, like we did for sin(2x) we took the period of normal sin(x) and we divided it by 2
for sin(3x)
we would take the period of normal sin(x)
and divide it by what?
dreamy cove
2 right?
royal loom
why would we still do 2?
for sin(2x) it was traveling 2 times faster
now for sin(3x) it is traveling 3 times faster
shouldn't we instead divide by 3?
dreamy cove
yeah you're right.
royal loom
we would divide by L
dreamy cove
okay L.
dreamy cove
wait I thought you said divide by 3?
dreamy cove
if the equation is 2pi wouldn't we divide by 2?
royal loom
we divide the normal period of sin(x) by 3
and the normal period of sin(x), is 2pi
so we divide 2pi, by 3
does that make sense?
Just like for sin(2x)
we divided 2pi, by 2
and got pi.
dreamy cove
okay
royal loom
Feel free to ask a specific question if you have any confusions so far
dreamy cove
How would we translate this into the problem I posted? Or Did we already solve for it?
royal loom
So, looking at your problem
does the 2 on the outside change how fast the 'x' is changing?
dreamy cove
no
royal loom
Okay
and what about adding 3pi/2
does this change how 'fast' x changes?
or does it just start 'x' 3pi/2 larger
and the speed doesn't change
dreamy cove
it starts 'x' 3pi/2 larger
it would have to directly multiply the variable, x, to change it's speed.
royal loom
Perfect
so the 'x' in , $2sin(x+\frac{3\pi }{2})$ doesn't change any faster than the 'x' in $sin(x)$
wraith daggerBOT
AustinU
royal loom
so what's its period?
dreamy cove
2pi?
dreamy cove
yes as the X isn't directly affected by the 3pi/2 so it wouldn't change. It's the same as saying sin(x)
royal loom
Okay cool nice job. I see you already have the amplitude done, do you know why it is "2" ?
dreamy cove
Wait before we go onto the amplitude, what if the x was something like 4x?
dreamy cove
sin(x) = 2pi
royal loom
'x' changes 4 times faster
not 4pi times faster
so we only divide 2pi by 4
not 2pi by 4pi
dreamy cove
okay.
royal loom
Tell me when you're ready to move onto a different part
royal loom
exactly
dreamy cove
because it's infront on the sin
royal loom
but what does a 2 being infront of the sin actually mean
what does it mean for the graph
dreamy cove
it's 2x as big?
dreamy cove
alright
royal loom
Okay, and you already identified the vertical shift to be none
I assume you know why this is?
royal loom
yup
we just have the sine function
it's scaled
but it isn't shifted upward (or downward)
dreamy cove
nor downward
dreamy cove
no.
wraith daggerBOT
royal loom
taking a look at this
we can say that it 'starts' at (0,0)
really it could start wherever, but imagine that it starts at (0,0)
dreamy cove
right.
royal loom
you know that we can move the function up or down
by adding/subtracting on the outside
but what if we wanted to instead move the function left or right?
the distance that the function is moved left/right is called the phase shift
dreamy cove
okay.
wraith daggerBOT
royal loom
what would we do to move this over, say 1 to the right?
dreamy cove
y=x^2+1
royal loom
,w plot y=x^2 +1
dreamy cove
,w plot x^2 + 1
dreamy cove
great minds think alike 😆
royal loom
why not?
dreamy cove
the 1 is the K and that affects the up/down value
royal loom
because we added the '1' not to the 'x' but to the function itself
we shifted it up instead of shifting it right
,w plot y=x^2
wraith daggerBOT
royal loom
so what does moving this 1 to the right do?
well
instead of having x=0 having y=0
instead of having (0, 0)
we want x=1 has y=0
(1, 0)
how can we make it go from 'x' to something that when we put x=1 is still 0
dreamy cove
I don't really know.
royal loom
,w plot (x-1)^2
wraith daggerBOT
royal loom
see how that worked out for us?
that is the graph of (x-1)^2
when we plug in x=1 into this, we get (1-1)^2=0
which is what we wanted
we started with (0, 0)
and we wanted it shifted 1 to the right
we wanted (1, 0)
so, this gave us what we wanted.
,w plot y=x^2, y=(x-1)^2
wraith daggerBOT
royal loom
Let me know what you think about all of that.
dreamy cove
I feel good about it
royal loom
okay so a quick test would be, how can we shift y=x^2, 5 to the left?
dreamy cove
to change the parabola to move one point to the right, we would keep the ^2 the same and do the inverse of what we actually want so it cancels out.
(x+5)^2
dreamy cove
it's moving it 3pi/2 away from the origin at (0,0)
royal loom
yes, but in which direction
royal loom
yes
dreamy cove
because it's +3pi/2
dreamy cove
if it was -3pi/2 it would be positive
royal loom
mhm
Okay so
the 2 is scaling our function vertically by 2
the period is unchanged
the 3pi/2 is shifting us left 3pi/2
(which is the phase shift)
dreamy cove
-3pi/2 or 3pi/2?
royal loom
seems like you have everything you need
royal loom
-3pi/2 or 3pi/2?
I'll look into what would be the right way of saying it, I'm not really familiar with like the actual semantics of it.
1 sec
I think you would say the phase shift is -3pi/2
but you could also say the phase shift is 3pi/2 to the left
to be more clear
or say both
dreamy cove
I said -3pi/2(left)
is that fine?
what about the midline?
and it wants us to graph the line.
royal loom
I'm not sure if I would say it like that
-3pi/2 to the left
implies 3pi/2 to the right
don't use the negative and the left
in the same statement
because the negative means left
and if you just left it as positive, you could say (left) to indicate that shift is to the left
but I wouldn't do both
The midline is just the line through the middle of the function (horizontally) this should be pretty easy to find once you have graphed the function itself
dreamy cove
and if you just left it as positive, you could say (left) to indicate that shift...
I wrote this then added an indicator that the X=-3pi/2
Alright then how would we go about graphing this function?
royal loom
I'd write, phase shift is -3pi/2, or phase shift is 3pi/2 to the left
and I wouldn't write it any other way
dreamy cove
alright
royal loom
Alright then how would we go about graphing this function?
just use all of the knowledge that we just picked up about it
graph sin(x) first as a reference
and then use what we just found out
it should be 2x taller
dreamy cove
,w sin(x)
royal loom
it should be shifted 3pi/2 to the left
wraith daggerBOT
royal loom
,w plot sin(x)
wraith daggerBOT
dreamy cove
2x taller would be 2sin(x)
period would be 2pi
phase shift is -3pi/2
no vertical shift
and midline is ehh for right now.
royal loom
take this plot, move it over to the left 3pi/2, and make it 2x taller. Then you have the plot of your function, 2sin(x+3pi/2)
dreamy cove
,w plot f(x) = 2sin(x+3pi/2)
wraith daggerBOT
dreamy cove
viola
royal loom
well that's not really the point, you should be able to do it yourself without seeing it
that's why we gathered all of that information
royal loom
This is how
dreamy cove
could you teach me how to do it w/o calculator?
royal loom
I'll give you the steps
- Plot y=sin(x)
- Scale it vertically by 2
- Shift it over 3pi/2 to the left
- Celebrate
dreamy cove
could you plot it on the paper so I could see your thinking process?
just draw on it?
dreamy cove
okay
dreamy cove
okay
royal loom
making it 2x taller
dreamy cove
right
royal loom
step 3 shifting it over 3pi/2 to the left
in greeen
so we started with sin(x) in purple
we scaled it
this gives us 2sin(x) in red
then we shifted it
this gives us 2sin(x+3pi/2) in green
dreamy cove
could you plug in points for the green step? only part i'm iffy about.
royal loom
whichever the points are for sin(x), move them over 3pi/2 to the left
I am confident that you can do that
dreamy cove
so for example; pi
moving 3pi/2, 3pi/2 units to the left = 0
pi would become -pi/2?
royal loom
yes
which you can see is the case with the green function
we had purple 0 at pi
we now have green 0 at -pi/2
because we moved pi over 3pi/2 to the left
and it's the same
so it works out
dreamy cove
okay.
i've got another problem. I want both of us to solve it then compare answers
rt, ccw 90
how do you do the rotation thing?
?
,w plot f(x) = 4cos(x-pi)
wraith daggerBOT
dreamy cove
so
for the equation I posted
I had the amplitude - 4, period is 2pi, phase shift = pi, no vertical shift and the midline at y = 0
you there? @royal loom
full karma
No
cedar kilnBOT
@dreamy cove Has your question been resolved?
inland trail
i dont have work, i just need someone to explain how to do trigonometry ratios
inland trail
yeah, i just dont know how to ratios
river ermine
the acronym helps with that
for example
youd use tan here
toa = tan opposite/adjacent
try 32tan(41
river ermine
im pretty sure it is
inland trail
tysm
river ermine
do you have answers to these questins
inland trail
no sadly
river ermine
oh alr
cedar kilnBOT
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Available help channel!
dim osprey
What did I do wrong?
storm mural
What did I do wrong?
this is really weird
nvm the arc notation confused me
if you just see WZYX as a quadrilateral that might help
cedar kilnBOT
dim osprey
.reopen
cedar kilnBOT
✅
dim osprey
if you just see WZYX as a quadrilateral that might help
Like how
storm mural
tangents to circles are perpendicular to the radius
dim osprey
So like this right
dim osprey
So like this right
.rotate
.rotate
Uhh idk how that works
But like this right
It makes a right angle at w and y?
I still don’t see how that helps tho
Wait wait wait
So like a kite?
dim osprey
well angles in quadrilateral add to 360
Ok
I still don’t understand how this helps me answer the question
I think I have to find a, and then substitute that value into 10a to get my answer, right?
storm mural
you could but my method allows you to bypass that entirely
by finding the larger angle WZY
dim osprey
What’s the method
storm mural
well angles in quadrilateral add to 360
this
dim osprey
So like…90+90+50+m<WZY = 360?
storm mural
yep
dim osprey
Ohhh so that gets me
WZY = 130
storm mural
What did I do wrong?
as for what you did wrong here im not 100% clear where you get 10a - 180 - 10a
storm mural
Ohhh so that gets me
WZY = 130
ye thats the small wzy
dim osprey
Then I subtract 360 from 130? And that gets me the the measure of arc WVY right
storm mural
as for what you did wrong here im not 100% clear where you get 10a - 180 - 10a
maybe you intended parentheses like 10a - (180 - 10a)?
dim osprey
maybe you intended parentheses like 10a - (180 - 10a)?
Yes
storm mural
ah so thats the issue
cedar kilnBOT
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Available help channel!
halcyon eagle
cedar kilnBOT
buoyant perch
why the urgency
buoyant perch
is it like worth credit
halcyon eagle
yes lol
it's worht hw points
but its the last thing i need to do
so i have like 20 mins to figure one part of this out hehe
i don't really understand how to approach d in the first place
@buoyant perch
buoyant perch
if (x(t),y(t)) are positions then surely the tangent is the derivative making it velocity
so 2t - 1 is the velocity?
so the acceleration is 2?
halcyon eagle
wdym by paramterise it? put it in terms of x and y
pls help
@cold briar
@lusty birch
<@&286206848099549185>
pls sumeone
this is due in 19 mins
amber bronze
@halcyon eagle
halcyon eagle
wdym write it out?
halcyon eagle
pls pls its due in 3 mins 😭
halcyon eagle
For t>3, the line tangent to the curve at (x(t)),y(t)) has a slope of 2t-1. Find the acceleration of the object at t=5
needs to be in vector form: <,>
@amber bronze 2 mins left pls 😭
amber bronze
waitt
WAIT
so v = sqrt(x'(3)^2+y'(3)^2)
we've already evaluated that y'(3) = -9
and x'(3) you can find by pluging 3 into dx/dt
halcyon eagle
ahhh so what is it
halcyon eagle
that's fine :/
how to do d though
i want to know how to do it regardless
@old cedar
amber bronze
um wait
Given that the slope of the tangent line at any point (x(t), y(t)) for t > 3 is 2t - 1, we can say that the velocity vector of the object is given by:
v(t) = <dx/dt, dy/dt> = <1, 2t - 1>
To find the acceleration vector of the object at time t = 5, we need to take the derivative of the velocity vector with respect to time:
a(t) = <d^2x/dt^2, d^2y/dt^2> = <0, 2>
So the acceleration vector of the object at time t = 5 is:
a(5) = <0, 2>
@halcyon eagle
cedar kilnBOT
@halcyon eagle Has your question been resolved?
cedar kilnBOT
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Available help channel!
dense cargo
why isnt option c correct
cedar kilnBOT
why isnt option c correct
fair geyser
why isn't it 1?
dense cargo
there is
fair geyser
oh yeah
dense cargo
v2 to v1 to v7 to v2
fair geyser
so the shortest path is not 1
you go around the cycle faor a bit and get −12 or something
and that's shorter even though it's longer
that's what they mean i guess
fair geyser
yes
cedar kilnBOT
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small cloak
.close
cedar kilnBOT
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supple holly
You’re in a math class of 16 students (including yourself). Your teacher has a bag of 16 chocolate bars, and says “This morning, I had exactly one golden ticket. There’s an 80% chance I put it in one of these bars, and a 20% chance I threw it away.”
She then passes the bag around, and everyone takes a bar at random. You keep your bar closed while each of the other students in the class opens theirs and discovers no golden ticket inside.
What are the chances your bar has the golden ticket in it?
tropic oxide
where is the question
woven turret
nice story whats the question tho
supple holly
Sorry, i'm sending rn
supple holly
You’re in a math class of 16 students (including yourself). Your teacher has a b...
Yes, I have edited
supple holly
I'm also stuck 😭
I thought 1/16= your chance of getting golden ticket, right?
But have no idea when there's a chance 80% the teachers put in 16 chocolate bars
mighty drift
law of total probabilities
tropic oxide
I thought 1/16= your chance of getting golden ticket, right?
But have no idea w...
no
1/16 is your chance of getting the golden ticket given that somebody from your class has got it
mighty drift
in each case (80-20) what's the probability you have the bar ?
sum them up according to the probability of each case
supple holly
in each case (80-20) what's the probability you have the bar ?
sum them up accor...
60%
fair geyser
intuitively it's like there's 20 bars, so the probability would be 1/5
supple holly
in each case (80-20) what's the probability you have the bar ?
sum them up accor...
U should logical
fair geyser
it's not the standard reasoning, but it may be valid and give the right answer
supple holly
why would that be ?
U said (80-20=60) which is the probability you have in ur hand
mighty drift
80-20 was to indicate what the split was, as in 80% vs 20%
of course you have no reason to do that subtraction. Why would that yield the result we want ?
supple holly
it's not the standard reasoning, but it may be valid and give the right answer
Unfortunately, it didn't come up with answer sheet 😞
supple holly
80-20 was to indicate what the split was, as in 80% vs 20%
I don't understand
fair geyser
yeah i'm pretty sure it's 1/5
it's sorta like monty hall, just the choice of open doors is not deliberate, so the intuitive answer is right
mighty drift
in each case (80-20) what's the probability you have the bar ?
sum them up accor...
case1: someone has the ticket. What's the probability you it ?
case2: no one has the ticket. What's the probability you have it ?
considering the probability of cases 1 and 2, what's the probability you have it ?
supple holly
I think I got the answer
fair geyser
thanks for the problem
supple holly
5%
The ticket you're getting would be 1/16 if it has it. So 0.0625 and there's 80% if the ticket includes, so 0.0625×0.8= 5% = the chance you're getting ticket
.close
cedar kilnBOT
mighty drift
case1: someone has the ticket. What's the probability you it ?
case2: no one has...
case1: 100%
case2: 0%
so it's actually 80%
cedar kilnBOT
Available help channel!
final burrow
hi, i need help with this , its 3f
cedar kilnBOT
hi, i need help with this , its 3f
final burrow
the book says its x>-0.75 snd x<-1, but I can’t get that ans
copper plinth
Also graph is wrong
cedar kilnBOT
@final burrow Has your question been resolved?
final burrow
how are you getting the (4x-3)(x+1)
ok it should be (4x+3) (x+1)
and ik the graph is wrong but
still it doesnt give x>-0.75
if the curve is below the st line
livid hound
first identify your actual roots
and sort them in ascending order
cedar kilnBOT
cedar kilnBOT
✅
livid hound
and sort them in ascending order
final burrow
yea so -0.75>-1
livid hound
consider the locations of
-1 and -0.75 and on the x-axis
and deduce from the graph when f(x) > g(x)
cedar kilnBOT
Available help channel!
livid latch
Trying to find eigenvectors for the following matrix
cedar kilnBOT
Trying to find eigenvectors for the following matrix
livid latch
[0 4 4 ] [1 0 -3] [-2 4 7]
Its a 3x3 matrix
I have found eigenvalues of 2,2 and 3
And now i have put them back into (A- lamda)x = 0
But struggling with solving this for the eigenspace/ eigenvectors
livid latch
Because apparenlty its supposed to be a Jordon normal form calculation where theres only supposed to be one Lineraly independent eigenvector
But i have solved it to find the matrix [1 0 0] [0 1 1] [0 0 0] leading to my eigenvectors being [1 0 0] and [0 1 -1] for when lambda =3
livid latch
[0 4 4 ] is the first row of A
granite knoll
ok so for lambda = 2, find a basis for the kernel/nullspace of $\begin{pmatrix} -2 & 4 & 4 \ 1 & -2 & -3 \ -2 & 4 & 5 \end{pmatrix}$
wraith daggerBOT
cwatson
livid latch
i did that to find my vectors as [1 1/2 0]x1 + [0 0 1]x3 as the vectors
But apparnelty thats wrong because there should only be one linearly independent eigenvector meaning its not diagonalisable and I need to continue the question solving with jordon normal form
granite knoll
yes that is not right. your first vector is right though
rugged tusk
how to deal with absolute value in linear programming?
// forall edge values x: r-1 >= d(x,0)
// r-1 >= |x - 0|
// r-1 >= |x|
// r - 1 - |x| >= 0
this condition must hold but i need to get rid of the abs(x) somehow
granite knoll
i think you can write it as -(r - 1) <= x <= (r - 1)
rugged tusk
hmm
granite knoll
so it'd be 2 conditions
rugged tusk
im gonna try it
granite knoll
does whatever you're programming in not do absolute values?
rugged tusk
does whatever you're programming in not do absolute values?
dont get your question
granite knoll
I'm just asking why you need to get rid of abs(x)
rugged tusk
im using lpsolve library for linear programming and it does not support abs values
granite knoll
ah, got it
I also think you can write abs(x) as sign(x)*x, if you have a "sign" function
actually having two inequalities might be better
rugged tusk
and how to write this?
r-1 >= |x| >=1
granite knoll
is r - 1 >= 1 always?
rugged tusk
it must always hold
granite knoll
ok, then I think you'd need something like (x <= -1 OR x >= 1) AND [(-(r - 1) <= x <= (r - 1)]
if I'm thinking about it correctly
the first part handles |x| >= 1, and the second handles (r - 1) >= |x|
rugged tusk
ok, thanks
weary cargo
Given a triangle ABC with area of 15 squared cm, BC = 5.66 and the angle A is 30 degrees
Fond the P of abc
grand storm
weak pecan
I need help for number 9
cedar kilnBOT
I need help for number 9
digital cliff
we had h^-1(x)=(x+1)/2, this so when you use the function ie h^-1(3) for example, you replace all the x with 3 or whatever else was in the bracket: h^-1(3)=(3+1)/2
do the same with (5m-1) and 9
weak pecan
So would it be
(5m - 1) - (9 +1)/2 = 15 ?
cedar kilnBOT
@weak pecan Has your question been resolved?
stiff gyro
Partial Sum of summation of (xi – 2)^2, i from 1 to n when n = 4
cedar kilnBOT
Partial Sum of summation of (xi – 2)^2, i from 1 to n when n = 4
@stiff gyro Has your question been resolved?
stiff gyro
<@&286206848099549185>
crimson delta
what about it. what are the xi
cedar kilnBOT
@stiff gyro Has your question been resolved?
wide patio
cedar kilnBOT
wide patio
Lemme explain my doubt
So the highlighted one is question
So the question is x(1-x)^2 dx
Then how did it got evaluated in Int of (1-x)^2 Underoot(1-(1-x)) dx?
Is there any formula for it?
<@&286206848099549185>
vague rapids
!15m
cedar kilnBOT
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.
astral bay
,rccw
wraith daggerBOT
cedar kilnBOT
@wide patio Has your question been resolved?
dire geode
after some k!, all terms are multiples of 100
so you only need to sum the first (k-1)! mod 100
vague rapids
10! onwards last two digits are always zero
dire geode
no, it doesn't
dire geode
after some k!, all terms are multiples of 100
Beard gave you k
dire geode
so you only need to sum the first (k-1)! mod 100
now you just sum 9 terms mod 100
vague rapids
now you just sum 9 terms mod 100
4
vague rapids
yes
frail thistle
2, 5, and 10 are all in there
vague rapids
we need to find last two digits and so
dire geode
10! = 10 *... * 5 *... * 2 * 1
vague rapids
mod100
frail thistle
mod 100
correct
it should be pretty straightforwards from there
correct
yea
mhm
jolly knoll
integral of [lnx]²
cedar kilnBOT
integral of [lnx]²
lyric narwhal
why do you need to u sub at all
jolly knoll
because I can't do integral of lnx squared
lyric narwhal
yes you can
jolly knoll
how
lyric narwhal
just use integration by parts
jolly knoll
yeah that's what i meant, why is it that i can't use u sub (ik i can just use integration by part)
lyric narwhal
why do you want to use u sub at all
jolly knoll
simpler?
dire geode
yeah that's what i meant, why is it that i can't use u sub (ik i can just use in...
This is a meaningless question.
Why can't you use a hammer to screw in a screw?
Why can't you use a helicopter to go to the moon?
jolly knoll
I'm sorry I'm just confused on how to recognize which technique to use
lyric narwhal
if you do try u subbing, what do you propose u should be
u sub should only be a first option if there's something obvious you can choose for your u
jolly knoll
it will come in as u squared then I'll use the rule of power and at the end I'll put ln x in u's place
ps I'm not good at math
lyric narwhal
you should revise u substitution
jolly knoll
ok
lyric narwhal
what?
jolly knoll
for u sub you replace variables and in ibp you can replace whole f(x) am I right?
lyric narwhal
i don't get what you mean'
lyric narwhal
no...
jolly knoll
well fuck me
lyric narwhal
i strongly suggest looking up a tutorial on u substitution
crimson sedge
Hi, My question is not too hard but I can't find this answer :
Two natural no. differs by 3. Find the no. if the sum of their reciprocals is 7/10
median valve
Give me better quality
median valve
.-.
crimson sedge
Better?
median valve
more closely
crimson sedge
Dude
crimson sedge
yes but in laptop is blurry right?
median valve
Mmm...
crimson sedge
wait i'll try
median valve
😄
frail thistle
i just zoomed screenshotted and sent again 💀
crimson sedge
you are in mobile right?
frail thistle
nah
frail thistle
what happened to ur 2a
crimson sedge
help me guys
frail thistle
lol
frail thistle
no problem
crimson sedge
how to close the channel now 😐 ??
frail thistle
.close
spiral badge
Is this good way of calculating this?
cedar kilnBOT
Is this good way of calculating this?
opal basin
Well 8^3 = 512, the sum is 8 and 8 - 3 = 5?
It doesn't always work
But I think it might hold for numbers below 8
I checked: It does although you need to have at least 5 to get a three-digit number
spiral badge
I checked: It does although you need to have at least 5 to get a three-digit num...
So it’s ok
But you need at least 5 digit number?
opal basin
So, it works for 5, 6 and 7
runic garnet
Is it just a coincidence that it works?
spiral badge
If there is a cube root, you need x * x * x instead of x * x?
opal basin
Is it just a coincidence that it works?
idk, maybe something with remainders stops big numbers from working
opal basin
If there is a cube root, you need x * x * x instead of x * x?
Yes
opal basin
kinda, if you cube x you need x * x * x
frail thistle
it seems like a coincidence
spiral badge
So cube root 64 is 4 cus it’s 4 * 4 * 4 = 64
But square root 64 would be 8 cus 8*8
frail thistle
yes
frail thistle
huh
spiral badge
Root 6 + root 64
spiral badge
6√64
frail thistle
6th root or 6 * root 64
spiral badge
You need to add 6 to √64
Idk
But like
3√2
To
Make delete the 3
You need to multiply √2 * √3
Right
<@&286206848099549185>
spiral badge
Oh so
6√4
Would be
2 * 3
Right
Cus
√4 = 2 and √6 = 3
<@&286206848099549185>
spiral badge
Help me
cedar kilnBOT
@spiral badge Has your question been resolved?
chilly linden
cedar kilnBOT
@spiral badge Has your question been resolved?
lucid gazelle
How do I calculate x? I think it might be something simple and I'm just not seeing it, but it's been some long days and there are a couple problems I just can't get the hang of
candid minnow
you can calculate the dotted line using the triangle ABC
lucid gazelle
you can calculate the dotted line using the triangle ABC
how? at first I thought of notable triangles but BC would have to be 4
candid minnow
what is u ?
candid minnow
do you know the pythagorean theorem ?
lucid gazelle
c squared = to b squared plus a squared?
candid minnow
c^2=a^2+b^2, where c is the hypothenuse of a right triangle. we have two right sided triangles in this case, so we can calculate the dotted line, which then allows us to calculate x
lucid gazelle
it would also mean that AB^2+BC^2=AD^2+CD^2
idk if that helps but think I can work from that on, just thought there was something that solved it easier than pythagoras but sometimes simple is better
thanks!
.close
crimson sedge
i have a question about the solution to something
cedar kilnBOT
i have a question about the solution to something
crimson sedge
like i understand the range of cos and why the sentance is true i just dont know if i understand fully why you can make that inqueality comparrison
like originally i just manually solved the intergral
mighty drift
It's a property of integrals
If f <= g then so are their integrals (over the same interval)
crimson sedge
i mean i guess it does make sense if also cos(x) will basically be less than or = 1
since youd be multiplying x^2 by that value idk if im making sense
cosmic steppe
Yeah kinda
mighty drift
If f <= g then so are their integrals (over the same interval)
x^2 cos x <= x^2
crimson sedge
also can i ask another quick q
im very confused about the intergral
i did u sub first
got rid of the deonminator
cosmic steppe
IBP after that I'm pretty sure
crimson sedge
so we have intergral of arcsin(u) my next best guess was to use ibps but idk
okay okay yeah so i chose u = arcsin(u) and dv = du
i get like arcsin(u)u - intergral u/sqrt(1 - u^2) du
but i have no clue how to do the intergral
dire geode
another sub
cosmic steppe
"Integrals are easy" I was once told
dire geode
dire geode
can i post what i got here
yes
crimson sedge
Sorry give me a second I just got kicked out of the library bc it’s closing
i need to know if this part is okay before i finish the rest of the intergrak
cedar kilnBOT
@crimson sedge Has your question been resolved?
cerulean sail
