Solaris (firecatto)
#help-27
woven radishBOT
hexed apex
But I cannot solve this since because of the $\frac{d^2}{dt^2}(1+x)$, what can I do?
woven radishBOT
Solaris (firecatto)
supple knot
Close one of your channels
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@hexed apex Has your question been resolved?
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@hexed apex Has your question been resolved?
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@hexed apex Has your question been resolved?
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@hexed apex Has your question been resolved?
noble niche
But I cannot solve this since because of the $\frac{d^2}{dt^2}(1+x)$, what can I...
hi
i don't understand why doesn't that allow you to solve it?
you are looking for x right?
x is the function you're looking for?
if you integrate the expression two times with respect to t you will get some uglier expressions but you will get rid of derivatives
restive river
if you integrate the expression two times with respect to t you will get some ug...
Wouldn't better he use the Laplace transform or something like that?
noble niche
Wouldn't better he use the Laplace transform or something like that?
i don't know
but integrating with respect t should yield some "polynomial" looking equation in the end
restive river
But, man, you'd have a twice integration on a non-known x function in relation to t
@hexed apex
@noble niche , I think that the Laplace transform is actually better
hexed apex
Laplace transformation, what?
Turns out that the answer was to just ignore the 1 from $\frac{d^2}{dt^2}(1+x)$
woven radishBOT
Solaris (firecatto)
hexed apex
if you integrate the expression two times with respect to t you will get some ug...
Yeah but that's not how I've been taught to solve second order differential equations
We were told to get a general solution and if non-homogenous, add the complementary function
restive river
So, just do the Ae^ax substitution
restive river
Laplace transformation, what?
It's a method for solve differential equations. It's a more precise one that assume that the function has one form
You basically transform a differential equation into an algebric one
@hexed apex
mental night
How can I find V(c) using Laplace transforms ?
devout snowBOT
How can I find V(c) using Laplace transforms ?
@mental night Has your question been resolved?
weak cove
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@mental night Has your question been resolved?
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@mental night Has your question been resolved?
finite cairn
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finite cairn
Can someone do this problem and show every step they do
Im trying to compare my steps with other people because its a thing my teacher said and i js need to submit mine and someone else’s steps and we’re supposed to get partners from our class but my partner is dumb and wont do it so
Also pretty sure i got the answer right but yea would he helpful for someone to check that
<@&286206848099549185>
dense jay
$$\int{2y^2(y^3-8)^3 dy}$$
take $u=y^3-8$ then $\frac{du}{dy}=3y^2$ so $dy=\frac{du}{3y^2}$
and so:
$$\int{2y^2(y^3-8)^3 dy}=\int{2y^2\cdot u^3 \cdot \frac{du}{3y^2}}$$
$$\frac{2}{3}\int{ u^3 \cdot du}$$
$$\frac{1}{6}u^4+C$$
$$\frac{1}{6}(y^3-8)^4+C$$
woven radishBOT
AℤØ
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dense jay
(you got the same thing)
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dense jay
you wrote $\frac{u^4}{6}+C$
woven radishBOT
AℤØ
dense jay
didnt you?
finite cairn
Yea
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swift flint
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swift flint
hey was just wondering how to show that the height is equal to that
rugged sparrow
assume the height to be h, radius to be x and write an expression for surface area of the solid
Note that you must think carefully before doing so, because the question has a condition
swift flint
yes i did that and the area i got was A = 2πxh+πx = 6π
swift flint
oh yes sorry a typo
i had that but i still cant find the height to be equal to A/2πx -π/2
rugged sparrow
have you tried isolating h
rugged sparrow
well then show what you've done
oh wait
yeah it does not simplify to it
there must be a typo
sinful oasis
Hi, could someone please help me with this? Its a question in relation to the application of derivatives
devout snowBOT
Hi, could someone please help me with this? Its a question in relation to the ap...
torn vessel
how do you find the area of that rectangle?
torn vessel
you have the expression b = -2a + 1800
So you say the area funcion A = a(-2a+1800)
hasty saffron
Let the dimensions be x,y
2x+y= constant = 1800
We need to maximise area, i.e., xy
Just substitute x or y from the first equation
torn vessel
how do you find the maximum of a function?
hasty saffron
set equal to 0
You need to set the derivative equal to 0 ig
hasty saffron
It's asking dimensions
hasty saffron
Hi, could someone please help me with this? Its a question in relation to the ap...
See
hasty saffron
It's alr, happens.
hasty saffron
Np
sinful oasis
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sage socket
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sage socket
Would I just start picking values of theta?
then plot (r,theta) ?
I thought it made sense but I'm not getting a great plot there
I stopped at 5pi/4
supple knot
Did you convert to Cartesian coordinates
sage socket
no.
I think the way to do that is x = rcostheta and y = r sintheta right?
But how do I get those with the given equation?
I believe I'd need to change the given equation to be in that form for both sin and cos
supple knot
Trig identities
robust karma
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torn vessel
which equation does that point make true?
idle stag
Hello. If I have two random variables for dice, B1, B2 ~ Discrete Uniform (1...6) and then sort these as C2 and C1 such that C2 >= C1 (i.e. if B2 <= B1, then C2 = B2 and C1 = B1), then how would I describe the CDF of C1.
In case that wasn't clear, C2 is the higher value of B1 and B2, and C1 is the smaller one
devout snowBOT
Hello. If I have two random variables for dice, B1, B2 ~ Discrete Uniform (1...6...
idle stag
The event C2<=k is equivalent to the intersection of B1 <= k and B2 <= k
<@&286206848099549185>
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sweet veldt
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sweet veldt
for iii, can i just say f is a subset of Q, and Q is countable so done
<@&286206848099549185>
also i need help with this one
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sweet veldt
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ionic swift
<@&286206848099549185>
hey i think I should be able to help you with this one
let me take a closer look
so the notation f[NxN] is just the range or is it supposed to be something else ?
ionic swift
for iii, can i just say f is a subset of Q, and Q is countable so done
how did you come up with that idea ?
how would you argue that it is a subset of Q
sweet veldt
ionic swift
well but here its quite obvious since n and m are from N right ?
oh hold on
lmao
somehow I had in mind that R was the domain
my bad
sure
sounds reasonable
ionic swift
well did you try proof 2 's strategy ?
sweet veldt
how do i say An is countable for this though, since isnt there still 2 more variables
Do i just form An, then set m = fixed variable?
then Am is countable, and if Am is coutanble then An is a sum of countable sets of Am, then A is a sum of countable sets of An
like do the thing twice
ionic swift
Do i just form An, then set m = fixed variable?
I wouldve thought, that one is supposed to fix 2 of the variables and then show that the set is countable , then repeat that for the other two variables and take the union over all of them
ionic swift
but I might be mistaking
sweet veldt
ionic swift
would have to think about it for a bit longer
sweet veldt
let 2x + 2y + 1 = pk
let x + y = pj, p is prime, j and k are integers
2(pj) + 1 = pk
1 = pk - 2pj
1 = p(k-2j)
1/(k-2j) = p
p is prime
but LHS is 1/some integer
and that cant be prime
so contradiction
i just need to know if this works for it
i think it does
ionic swift
what is LHS exactly ?
sweet veldt
left hand side
ionic swift
give me a second to think about it agian
sweet veldt
ok
wise bone
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twilit swan
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scenic plume
do you know slope-intercept form?
twilit swan
yes
scenic plume
then just plug in the values
twilit swan
the answer
scenic plume
ok so slope intercept form has 4 variables
y and x aren't supposed to be changed, you need to change the m and the b
you're looking for the values of m and b. once you know them, replace m and b with those values.
twilit swan
do i put the -1 or -4 first
twilit swan
no
scenic plume
ok so m is the slope. b is the y-intercept.
scenic plume
ok so what part of the problem are you stuck on
twilit swan
the equation
scenic plume
ok so in the last problem they gave you the values for m and b. but here you need to solve for them.
let's start with slope
do you know the formula for slope?
twilit swan
rise over run?
lusty sapphire
rise over run?
Do you know what "rise over run" means?
lusty sapphire
i forgot
That's important to know
rise is how much your y value changes, and run is how much your x value changes
in functions, x is usually the input, and y is the output
so slope is change in output divided by change in input
twilit swan
are u good at graphing in slope
lusty sapphire
yes
twilit swan
can u help me with it after we finish this problem
lusty sapphire
if I have time
twilit swan
@lusty sapphire i need help
lusty sapphire
Did you understand this explanation?
lusty sapphire
This table?
twilit swan
yes
lusty sapphire
yes I know how to solve the table
twilit swan
i needed help on it
lusty sapphire
y=mx+b
m is the slope and b is the y intercept
twilit swan
where do i get the numbers to write in in a equation
lusty sapphire
you solve these
lusty sapphire
you're not "solving the table"
You're using the table to find the slope and y intercept
twilit swan
alr i got the slope and y-intercept now the last thing i need is the equation
lusty sapphire
y=mx+b
m is the slope and b is the y intercept
Use this then
twilit swan
finished
twilit swan
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verbal harbor
can someone explain?
devout snowBOT
can someone explain?
keen summit
because the amount of gold he gives her is always being divided and it continues until infinity
if I gave you a cent for 100 days, you'd have a dollar in 100 days
but if I gave you 1 cent on the first day, then 0.05, then 0.025, then 0.00125, etc, you wouldn't have a dollar by 100 days, but you'd be "close"
verbal harbor
but if I gave you 1 cent on the first day, then 0.05, then 0.025, then 0.00125, ...
tysm is their anyway toshow this with math?
or is itmore concept
keen summit
the formula given to you shows it
1(.99)^n-1
if you take a number that isn't a whole number (less than 1), and give it an exponent, it will actually get smaller
imagine doing 0.99 * 0.99 * 0.99
so (0.99)^3
verbal harbor
oh so it just keeps getting smaller
keen summit
yeah ignore my whole number rant thing
but yes
it gets smaller
any number that is less than 1
if you multiply them together, it gets smaller
keen summit
is this pre-calc?
in calculus, you'll be introduced to something called a limit
thats what that is
it goes to infinity
lusty sapphire
can someone explain?
For part a, do you want recursive rule, or explicit rule?
verbal harbor
is this pre-calc?
yeah
keen summit
okay well e is a concept question then
you just have to realize that its going to be infinitely getting smaller and smaller
verbal harbor
For part a, do you want recursive rule, or explicit rule?
I don't know either😄 thisisthe answer I just have no idea how myteacher got to this
verbal harbor
you just have to realize that its going to be infinitely getting smaller and sma...
yea thanks alot for explaning i was pretty stuck on why it smaller
lusty sapphire
I don't know either😄 thisisthe answer I just have no idea how myteacher got to...
That seems wrong. That doesn't consider the 1,000 that get added every hour.
verbal harbor
That seems wrong. That doesn't consider the 1,000 that get added every hour.
how do you think it should be written?
lusty sapphire
The recursive rule would look like $a_0=1,100$ and then $a_n=2a_{n-1}-1000$
woven radishBOT
SWR
lusty sapphire
I don't know either😄 thisisthe answer I just have no idea how myteacher got to...
Oh it's removing 1,000 not adding. Maybe this is right
Oh yeah. It's right, my mistake.
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true garden
How to do this?
devout snowBOT
How to do this?
true garden
Like you gotta rationalise in this
red viper
multiply the numerator and denominator by $\sqrt{7+2x}+(\sqrt{5}+\sqrt{2})$
woven radishBOT
Alisia
thin inlet
this is known as the conjugate of $\sqrt{7+2x}-(\sqrt{5}+\sqrt{2})$
woven radishBOT
Moosey
true garden
this is known as the conjugate of $\sqrt{7+2x}-(\sqrt{5}+\sqrt{2})$
Ok bro thanks
true garden
multiply the numerator and denominator by $\sqrt{7+2x}+(\sqrt{5}+\sqrt{2})$
Ok got it
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restive river
how do I shift a reimann sum
devout snowBOT
how do I shift a reimann sum
devout snowBOT
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acoustic leaf
if you don't want the area below the x-axis to be negative (corresponding to negative y-values) you can instead take the riemann sum of the absolute value of your function
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restive pulsar
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restive pulsar
I am not sure of where to start
I did this but with T2
the integral was very hellish
I'm unsure of how to form the bounds here
acoustic leaf
let's start by getting a graph of the region again
restive pulsar
acoustic leaf
so this time for the y-bounds we need to find the bottom and top curve
restive pulsar
so y=1/4 x^2 and y=2
graceful cosmos
Because y is first, the y-bounds will depend on x.
Because x is last, the x-bounds will be constants
acoustic leaf
so y=1/4 x^2 and y=2
yes
restive pulsar
so those are the bounds?
restive pulsar
so then x had bounds of 0 to...
acoustic leaf
since x is our outer integral they must be constant bounds
so we need to find the smallest and largest values of x in our region
restive pulsar
so 0 is the lower
acoustic leaf
yes
acoustic leaf
yes
restive pulsar
ok
hmm, and how to prove we can't integrate it
well we'd have to use imaginary numbers somewhere wouldn't we?
acoustic leaf
we have our new integral \ $\int_0^{2\sqrt{2}} \int_{\frac{1}{4}x^2}^2 5x^3 \cos\left(y^3\right) ,dy,dx$
messed up the bounds sorry
woven radishBOT
cloud
acoustic leaf
our inside integral is in terms of y, so we can treat x as a constant and bring it out to the front
restive pulsar
so bring 5x^3 out front?
acoustic leaf
yes
now we have $\int_0^{2\sqrt{2}} 5x^3 \int_{\frac{1}{4}x^2}^2 \cos\left(y^3\right) ,dy,dx$
woven radishBOT
cloud
acoustic leaf
at this point we run into a problem
restive pulsar
yeah not sure how the cos(y^3) works
acoustic leaf
that's exactly the issue, we can't find an elementary antiderivative
restive pulsar
do that's just what I would say?
acoustic leaf
yes, you can say something along the lines of "cos(y^3) has no elementary antiderivative" (meaning we couldn't express it in terms of elementary functions like polynomials, exponentials, logarithms, trig functions, etc)
note that we could still have a computer take a riemann sum or the like, but that would only give a numerical answer
median lichen
This is a translation of the question:
"17. To construct a patterns that is similar to snowflakes you can do what the mathmatician Helge von Koch did and assume you have a equilateral triangle with the sides of 3 (Look at the picture)
Divide each side of the original triangle into three equal lengths.
The middle stretch now forms the side of a new equilateral triangle.
A new figure with a larger circumference has now been formed, figure 1.
Repeat the procedure to create the next figure, figure 2.
a) The original triangle has a perimeter of 9.
Calculate the perimeter of Figure 1.
b) Calculate the perimeter of figure 2.
c) The perimeter increases for each figure.
Calculate the change factor from Figure 1 to Figure 2.
d) The perimeter increases exponentially for each figure.
Write an exact formula for the perimeter O of figure n.
e) What number does the figure with the (2^16)/(3^6) perimeter have?"
median lichen
How do I even get started solving this?
supple knot
How do I even get started solving this?
do you know the length of each triangle side?
little locust
can you see that for figure one every length is third of the figure 0?
median lichen
do you know the length of each triangle side?
The question says "divide each side of the original triangle (figure 0) into three equal lengths"
So I assume it's just the side length/3
median lichen
0.3333
supple knot
no
supple knot
do you know the length of each triangle side?
here
median lichen
12 sides
supple knot
so you got part a)
use the same pattern for part b)
find the side length, then count how many there are
supple knot
try to find a recurrence now
median lichen
12/48
supple knot
48 is the number of sides or is it the perimeter?
supple knot
find the side length, then count how many there are
i think you skipped the first part here
median lichen
its the number of sides
supple knot
yea don't skip the first part
median lichen
oh
supple knot
you need the perimeter
median lichen
so 12/3
wait
4/3..? then (4/3)*12?
16
so the perimeter is 16
or is that completely wrong?
supple knot
i don't know how you got it, but 16 sounds right
median lichen
I just thought you divide the previous one into 3
then that into 3
cause the new figure is also divided by 3
supple knot
yea i don't understand what you're saying
slate fossil
trail eagle
The first question is worded incorrectly. I suspect it should rather ask to express AC in terms of OA and OC.
For the second one, what kind of vector can satisfy BD = -2 BD?
devout snowBOT
Show your work, and if possible, explain where you are stuck.
pine rock
well, draw the end points
draw an arrow head pointing to the second letter
and you will get a nice diagram
should i provide a tutorial on how to draw a point, line and an arrowhead:
?
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slate fossil
should i provide a tutorial on how to draw a point, line and an arrowhead:
just ssend the solution
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pine rock
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wicked rover
@slate fossil we dont give full solutions here
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celest sundial
I already got dy/dx=2x+1/2y+1, but idk d^2y/dx^2
devout snowBOT
I already got dy/dx=2x+1/2y+1, but idk d^2y/dx^2
trail eagle
Take the derivative again.
trail eagle
You'll get bits in terms of dy/dx in it, but you already have an expression for that.
celest sundial
Yeah, so I just replace dy/dx with what it's worth?
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knotty citrus
Anyone know some good sources to find out how to calculate a change of basis matrix?
devout snowBOT
Anyone know some good sources to find out how to calculate a change of basis mat...
knotty citrus
Looking to find out how to do a change of basis matrix on P^3 in respect to basis B and E
I cant seem to find any helpful resources as well
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queen zealot
Can someone help me use implicit difrentiation here
devout snowBOT
Can someone help me use implicit difrentiation here
queen zealot
white meadow
Not a helper, hope it helps
derivate every term, whenever you derive y add y'
and solve for y'
every term that has y' to one side of the equation
and common factor y'
queen zealot
ok
white meadow
But its product rule
queen zealot
2x(y)
white meadow
It is a product, you need to use the rule
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crimson imp
If we have a finite-dimensional Banach space (W), an open set (U \subseteq \mathbb{R}^n), and a mapping (f: U \rightarrow W), how can we show that:\
\
If all partial derivatives of order (k) exist for (f) and are continuous on (U), then (f) is (k)-times differentiable.
woven radishBOT
Levens
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crimson imp
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crimson imp
can I do it with induction?
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fleet belfry
need some help on how to solve this equation:
$\sin(4x) = \sin(2x), 0 \le x \le \frac{\pi}{4}$
devout snowBOT
need some help on how to solve this equation:
$\sin(4x) = \sin(2x), 0 \le x \le ...
woven radishBOT
Nomzz1
fleet belfry
so far the only solution i have found is x = 0
but the question says there are two solutions
dense jay
show your work
dense jay
oh, i see
not a great solution i must say
use the double angle identity on the sin(4x)
dense jay
not quite
fleet belfry
there
dense jay
okay
2cos(2x)sin(2x)=sin(2x)
fleet belfry
sin(2x)(2cos(2x) - 1) = 0
so sin(2x) = 0
which gives x = 0
and then cos(2x) = 1/2
which giiiives 2x = pi/3?
so x = pi/6
and thats within the range
dense jay
seems fine
devout snowBOT
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summer harbor
was helping a friend out and turns out my calculator is inaccurate, why is this?
sullen island
What's that G on top of your screen
grand siren
that's exactly 10/9ths of the correct answer so i think probably some kind of unit issue
grand siren
...oh i see
so a right angle is 100 gradians
summer harbor
how should it be set up?
winter patrol
mode mode deg
grand siren
i feel like i vaguely remembered that that unit existed but had not remembered until now
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amber oriole
Does anyone know how the mean value, μ and the deviation, σ, can be found/calculated when doing a QQ-plot over observations? y = x-μ / σ
devout snowBOT
Does anyone know how the mean value, μ and the deviation, σ, can be found/calcul...
amber oriole
I've found this, but does that mean that we can always find the deviation etc. by going from 1, hitting the graph and down?
supple knot
Put y into y = mx + b form
you can find m and b from your plot
Solve for sigma and mu
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half smelt
S is the part of the sphere x² + y² + z² = 9 between the planes z = 1 and z = 2
half smelt
<@&286206848099549185>
devout snowBOT
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crisp niche
<@&286206848099549185>
that is the beginning of yoru surface integral:
$\iint_S z^{3}dS=\int_{0}^{2\pi}d\varphi\int_{\sqrt{5}}^{\sqrt{8}}\left( \sqrt{9-\varrho^{2}} \right)^{3}\sqrt{1+\frac{\varrho^{2}}{9-\varrho^{2}}}\cdot \varrho
d\varrho$
woven radishBOT
Joanna Angel
half smelt
$\iint_S z^{3}dS=\int_{0}^{2\pi}d\varphi\int_{\sqrt{5}}^{\sqrt{8}}\left( \sqrt{9...
how did you get to that?
crisp niche
first all, you have to draw the region of integraition
that is:
$5\le x^{2}+y^{2}\le 8$
woven radishBOT
Joanna Angel
crisp niche
and next we use formula
for changin surface integral into double integral
iterated of course, in polar coordiantes
half smelt
5 and 8 are the radii of the upper and lower circles?
half smelt
got it
crisp niche
so you cut off part of thsi pshere, and you prohect it into plane
0 , 2pi is clear interval too
rest is only long formula )
i ws differetiating i tin my midn and decided to write ready form with polar coords
half smelt
i ws differetiating i tin my midn and decided to write ready form with polar coo...
how did you get to this term?
crisp niche
how did you get to this term?
since
$dS=\sqrt{1+\left( \frac{\partial
z}{\partial
x} \right)^{2}+\left( \frac{\partial
z}{\partial
y} \right)^{2}}dxdy$
woven radishBOT
Joanna Angel
crisp niche
how did you get to this term?
do you know the theory ?
half smelt
not very well, as you may notice lol
i know that formula but why $\varrho d\varrho$? is it that jacobian thing? also, is the fraction term in your expression already considering the sum of (dz/dx)² + (dz/dy)²?
woven radishBOT
Kvikna
half smelt
lol
crisp niche
yes it is jacobian 🙂
and yes, radical form contains those partial derivatives
i squared them
and changed to polar too
you know, to save time 🙂
half smelt
i might need to revise transformation into polar coordinates
crisp niche
thatis constant i mean jacobian, but rest is:
$x=\varrho
cos\varphi\y=\varrho
sin\phi$
woven radishBOT
Joanna Angel
woven radishBOT
Joanna Angel
crisp niche
yvw 🙂
half smelt
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gilded nova
An item is marked up by 20%, then marked down by 15%, then marked up again by 27%. What single percentage would you have to charge to get the equivalent markup?
devout snowBOT
An item is marked up by 20%, then marked down by 15%, then marked up again by 27...
gilded nova
i was asking my dad about this and i was wondering why its like this [(C+0.20C−0.15(C+0.20C)]+0.27[(C+0.20C−0.15(C+0.20)]
like c+0.2c makes sense
oh btw c is the original cost of the item
keen nacelle
i mean thats kind of long for no reason i think
couldnt you just do 1.2 x 0.85 x 1.27 ?
i think
gilded nova
i mean thats kind of long for no reason i think
couldnt you just do 1.2 x 0.85 ...
but why
keen nacelle
ok
gilded nova
how does that work
thin inlet
ok
so assume you have an item, it has price P
Marking it up 20% means you're charging the original price, plus 20% of the price
so assuming price is 1 (for simplicity), if we charge 20% markup, then it'd be 1+.2=1.2
then, we mark this down by .15, meaning we charge the price we have, then subtract 15% from it
gilded nova
so assuming price is 1 (for simplicity), if we charge 20% markup, then it'd be 1...
yup
gilded nova
then, we mark this down by .15, meaning we charge the price we have, then subtra...
so 1-0.15?
ok wait those make sense
but how do i fin the equivalent markup
thin inlet
note if we also charge a price P, then this could be written as $P+.2P=(1.2)P$
woven radishBOT
Moosey
gilded nova
note if we also charge a price P, then this could be written as $P+.2P=(1.2)P$
so it is suppose to be 1.2*p or 1.12
wheat pawn
Call A the original price.
B after first markup
C after markdown
D after 2nd markup
B = (1+0.2)A
C = (1-0.15)B
D = (1+0.27)C
substituting backwards, you get that D = (1+0.27)(1-0.15)(1+0.2)A
near stone
Find the sum: (10+20+30+\ldots+150)
devout snowBOT
Find the sum: \(10+20+30+\ldots+150\)
woven radishBOT
Akira (fumo)
near stone
!status
devout snowBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
5
twin wedge
yes
near stone
I want to check why my teacher added 15 on n here and where did they got it from?
twin wedge
10(1+2+..+15)
near stone
arithmetic series doesn't work like that
near stone
I want to check why my teacher added 15 on n here and where did they got it from...
ok then how he got 15 here on n?
thin inlet
wait does it only go up to 130
thin inlet
OH
near stone
near stone
**Akira (fumo)**
how did he get 15 from in this example?
near stone
150 divide by 10?
thin inlet
there are 15 terms
thin inlet
- 10
- 20
- 30
- 40
- 50
- 60
- 70
- 80
- 90
- 100
- 110
- 120
- 130
- 140
- 150
royal kestrel
to find these zeroes
devout snowBOT
to find these zeroes
royal kestrel
can i just set it = to 0 then sqrt both sides
and just have x(x-2)
or will i need to simplify this first
tender lotus
$\sqrt{x^2} = |x|$
woven radishBOT
Adam Chebil
tender lotus
and just have x(x-2)
|x| = 0 or |x-2| = 0
royal kestrel
i just did this
thin inlet
can i just set it = to 0 then sqrt both sides
note that for a product, if you have two terms multipled, and they're equal to 0, one of them must be 0
royal kestrel
LMFAOO what am i doing
thin inlet
So you can have the case where x^2=0, and the case where (x-2)^2=0
royal kestrel
okay
thin inlet
what you did also works
thin inlet
yes
tender lotus
i just did this
overcomplicated but correct :p
tender lotus
yeah
royal kestrel
ok ok
tender lotus
multiply by x^2 too
royal kestrel
tender lotus
snow shore
Does anyone know how to calculate a weighted grade
devout snowBOT
Does anyone know how to calculate a weighted grade
@snow shore Has your question been resolved?
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supple knot
Does anyone know how to calculate a weighted grade
If you have values and weights, you should show them
winged hazel
Does anyone know how to calculate a weighted grade
$$\left(\frac{\text{Mark Recieved}}{\text{Total}}\right) \times \text{Weighting}$$
woven radishBOT
Nope
winged hazel
You should be able to convince yourself why this is true very easily
snow shore
alright
umbral abyss
how do i factorize 27x^3-8?
devout snowBOT
how do i factorize 27x^3-8?
winter patrol
difference of two cubes identity
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digital wren
does anybody know how I may be able to figure out e?
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does anybody know how I may be able to figure out e?
digital wren
a. 16cm , b. 10cm, c. 5cm, d. -2x+32 answers to previous questions
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severe echo
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severe echo
I dont actually need help with the binomial aspect of the question
I just dont understand how to interpret sigma notation
in (ii) of the first image it shows the definitions of the B terms
The correct interpretrations are in the answers (the second image)
i dont understand how im supposed to know how B(2n+2) and B(2n+3)'s summations go up to n+1
while B(2n+1) it only goes up to n
perhaps its linked to part (i) but i dont quite understand
severe echo
How about for the 2n+3 one
rich summit
2(n + 1) + 1
torn vessel
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torn vessel
trying to understand this
From what I can glean, it's saying that P is the ratio between the Kth term of each summation as K approaches infinity, so like the ratio of the "infinity"th terms
but I don't get how statements 1, 2, and 3 are derived
acoustic leaf
so the condition for a series to converge is that it must approach 0 (we need to add smaller and smaller terms)
but it's not enough for the sequence to approach 0, it must approach 0 "quickly"
so for example, the series of 1/n approaches 0 but doesn't get small fast enough for its sum to be finite. on the other hand, (1/2)^n gets small very quickly, so it does converge
torn vessel
right
acoustic leaf
so what the limit of sequence a / sequence b can tell us which sequence grows/shrinks "faster"
torn vessel
how can just looking at the ratio of the "last" two terms give us whether the two series converges though
acoustic leaf
what the limit tells us is, as we get very large values of n, which sequence "dominates" - i.e. gets so much bigger that the other sequence is negligible by comparison
torn vessel
Oh wait the limit of $a_k$ is always going to be either $0$ or $\infty$ right?
woven radishBOT
Vѳrtєx-
acoustic leaf
the idea is that both of them approach 0, since otherwise we could just rule them out immediately
torn vessel
what do you mean by "rule them out"
acoustic leaf
we already know that for any series to converge its sequence must approach 0
so if it didn't approach 0, we wouldn't need to use the test in the first place
torn vessel
we're not given that the sum of ak nor bk converge or diverge right
acoustic leaf
usually the way this test works is that we're looking at ak, and comparing it to some bk which has a known convergence/divergence
torn vessel
oh
i see
ok so for statement 2, if $b_k$ converges, that means that $\lim_{k\rightarrow\infty}b_k=0$ right
woven radishBOT
Vѳrtєx-
acoustic leaf
so if we're considering the limit to infinity of ak/bk, we have 3 possibilities:
- ak shrinks slower than bk -> eventually, ak will seem vastly bigger than bk, so the limit is infinity
- ak shrinks faster than bk -> eventually bk will be vastly bigger than ak, so the limit is 0
- ak and bk shrink at the same rate -> eventually ak and bk will be roughly proportional, so the limit is some nonzero constant
torn vessel
ok im gonna copy the image again sorry
acoustic leaf
**Vѳrtєx\-**
yes, although we also know that it can't "just" approach 0, it must approach 0 quickly
torn vessel
so if we're considering the limit to infinity of ak/bk, we have 3 possibilities:...
ok yeah this makes sense
ok so for #2, the only way for p=0 is for the terms of ak to shrink faster than bk, and if bk converges that means ak must converge
acoustic leaf
yes
torn vessel
ok i think i get it
its kinda like if one series converges and the other shrinks faster, then it must converge, but here it only looks at the behavior of the "k"th term
i guess it's the same idea though
ok cool thank you so much!
that helped a lot
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restive river
restive river
<@&286206848099549185>
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<@&286206848099549185>
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sweet sparrow
Could someone please explain this question
devout snowBOT
Could someone please explain this question
sweet coral
Could someone please explain this question
Do you know the binomial theorem?
sweet sparrow
Yes somewhat
sweet coral
sweet sparrow
Hm
sweet coral
try plugging your formula in there, with p instead of n of course
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calm thicket
fx,y (x,y) = { c, if 0 <= y <= x <= 1; c, if 0 <= y <= 2-x <= 1; 0, else.
(a) The value of c
(b) The marginal pdf of X and its mean, i.e., fX (x), E(X)
(c) The marginal pdf of Y and its mean, i.e., fY (y), E(Y )
(d) The MMSE E(X|Y = 0.55)
(e) The V ar(X|Y = 0.55)
(f) Are X, Y independent? Explain.
devout snowBOT
fx,y (x,y) = { c, if 0 <= y <= x <= 1; c, if 0 <= y <= 2-x <= 1; 0, else.
(a) Th...
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restive river
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restive river
i'm having trouble finding the domain of V(x)
this is my teachers notes
he got 0<x<sqrt of 300
which i dont understand
how
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restive river
i just dont understand where the sqrt of 300 came from
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zenith ether
so this question is asking me to write an explicit rule for a geometric sequence using subscript notation i know what an explicit rule is but not how to get the common ratio my math doesn’t add up. The question is the 3rd term of the sequence is 120. The firh term is 76.8 i put it into the calculator(TI-84 Plus CE) , in a table and put it into y= ax+b form then pushed y= put the equation in and pressed 2nd->table then the table said (1, 163.2),(2,141.6),(3,120)(4,98.4),(5,76.8)
devout snowBOT
so this question is asking me to write an explicit rule for a geometric sequence...
zenith ether
and heres my work so far and i got stuck
im just stuck because everytime i rework the problem o get different results
lyric isle
A common ratio can always be found by multiplying the last term by a number n to get the current term (recurrence). You can write 120n = the fourth term, and 120n^2 as the third term. Thus 120n^2 = 76.8, so you can do the algebra and have your calculator give you a result/turn it back into a fraction.
zenith ether
I’ll try that ty
4th term is 98.4 so multiply again by .82, right? But the problem says the 5th term is 76.8 not 80.688
thats where i get stuck
pale bolt
.82 isnt the right common ratio
pale bolt
this work is wrong because you are using arithmatic sequence on your calculator
you have a geometric sequence
but you should reread RA4's message and see how you can set up an equation with only the 120 and the 76.8
zenith ether
well i just did $120n^2$ in the calculator and got 6290112000 definitely not 76.8
woven radishBOT
EmberYT
pale bolt
you dont need the term in the middle to solve for the common ratio
pale bolt
well i just did $120n^2$ in the calculator and got 6290112000 definitely not 76....
why did you do this?
have you taken an algebra class?
if so, are you capable of solving 120x^2=76.8 (by hand)
zenith ether
the person above said that so i put it in the calculator
pale bolt
you are overdependent on your calculator and dont understand the core idea
you understand that if the common ratio is x, then $120x$ is equal to the term after 120 in the sequence?
zenith ether
yeah i am lol
woven radishBOT
zenith ether
wait did i make this too complicated for myself im very slow at algebra but i think i know where i messed up but im not sure, i missed this lesson in class
lyric isle
if so, are you capable of solving 120x^2=76.8 (by hand)
Get x on one side and try again in the calculator. It will turn out right.
Also sorry wrong ping lol
zenith ether
okay
I’m so confused is there any way you could dumb it down? Im kinda a step by step learner and i take tons of notes
lyric isle
Sure. So instead of calling it the common ratio, just refer to it as n. We know the third term is 120, so the fourth term will be 120 multiplied by n.
The fifth term will be the fourth term multiplied by n again, and since the fifth term is 76.8 and the fourth term will be 120•n, we know 120•n•n = 76.8.
From there, you can do a simple dividing over and square rooting to get something to plug into your calculator. The answer is quite nice actually
Basically, each time you go forward in the set you will be multiplying by this number we are trying to find, n. That’s how 120n^2 = 76.8
zenith ether
Oh um the problem says 3rd term is 120 and 5th term is 76.8 not trying to correct you because you know more than me but i wanna make sure we are on the same page
lyric isle
Ah sorry, I said it like the order was going down. It’s corrected now
lyric isle
No.
lyric isle
Now that 120n^2 = 76.8, you should be able to set n equal to something.
Don’t worry about it
Try to isolate n now, so that you can solve it
lyric isle
No, the restriction is 120n^2 = 76.8
There is only one answer here. Can you show me how you isolated n?
zenith ether
Yes
i don’t think I understand how to isolate n
i remember doing something like this in past but this may be completely different
lyric isle
You’re completely correct. You need to do the opposite of PEMDAS (order of operations). First will be division here, and then square root
lyric isle
do i just need to divide 120 from n and divide 76.8 by 120?
Yes!
Then take the square root, and plug that mess into the calculator
lyric isle
do i square it again or do i leave it .8?
Glad I could help. You got it 😄
.8 is a fraction, and that fraction is the common ratio n
zenith ether
TY i hope you didn’t bang your head against a wall too much 😂
oop didnt mean to send that XD
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keen loom
if the half-life of caffeine in your system is 6 hours, how much caffeine will be left in your system after 9 hours compared to when you initially drank it?
devout snowBOT
if the half-life of caffeine in your system is 6 hours, how much caffeine will b...
weak cove
less
keen loom
if the half-life of caffeine in your system is 6 hours, how much caffeine will b...
Where do i even start lol
I was away for this lesson, and Idk which formula to use for this scenario
mighty galleon
so there is X amount of caffeine in your system, which after 6hrs its now at X/2, I think you can use a rudimentary formula of $\frac{X}{2^y}$
woven radishBOT
dragonbreath
mighty galleon
X is initial amount of caffiene, y is how many halflives have passed
which can be solved for with $y = \frac{hrs passed}{halflife time}$
woven radishBOT
dragonbreath
mighty galleon
$\frac{9}{6}$
woven radishBOT
dragonbreath
mighty galleon
or 1.5
keen loom
Can you not write it like
y= Initial amount x (1/2) ^(9/6)