if i calculate everything i get:
#help-33
surreal glade
$\frac{e^{\frac{1}{x}}}{(x+2)^2} \cdot -\frac{x-1}{x^3+2x^2} \cdot e^{\frac{1}{x}}$
elfin berryBOT
alee
surreal glade
but its so strange in this form
and there is a way to get this result
.
but i dont know how
surreal glade
I have to find a simple result, then make f'(x) > 0
stoic topaz
you don't get why this works?
stoic topaz
this is just simple fraction manipulation
surreal glade
can you help me
pls
we have to start from here:$\frac{1}{(x+2)^2} \cdot e^{\frac{1}{x}} + \frac{x+1}{x+2} \cdot -\frac{1}{x^2} \cdot e^{\frac{1}{x}}$
elfin berryBOT
alee
surreal glade
I have to find a simple result, then make f'(x) > 0
trying to do that
stoic topaz
yeah but make the question clear, what's f(x)? what do you want with f'(x)?
prove that f'(x)>0?
surreal glade
I just want to try to simplify what I sent you as easily as possible
then i will do f'(x) > 0 myself
:$\frac{1}{(x+2)^2} \cdot e^{\frac{1}{x}} + \frac{x+1}{x+2} \cdot -\frac{1}{x^2} \cdot e^{\frac{1}{x}}$
elfin berryBOT
alee
stoic topaz
this is correct i think
surreal glade
yes but i didnt did that
stoic topaz
just factor e^(1/x)
surreal glade
i know but how i can do that
stoic topaz
ok $$e^{1/x}\left(\frac{1}{(x+2)^2}-\frac{x+1}{x^2(x+2)}\right)$$
elfin berryBOT
moriaritie
stoic topaz
then make the denominators same
$$e^{1/x}\left(\frac{x^2}{x^2(x+2)^2}-\frac{(x+1)(x+2)}{x^2(x+2)^2}\right)$$
elfin berryBOT
moriaritie
stoic topaz
$$e^{1/x}\left(\frac{x^2-(x+1)(x+2)}{x^2(x+2)^2}\right)$$
elfin berryBOT
moriaritie
stoic topaz
$$e^{1/x}\frac{-3x-2}{x^2(x+2)^2}$$
elfin berryBOT
moriaritie
stoic topaz
that's what you wanted right?
surreal glade
yes
stoic topaz
tell me which step you didn't understand
surreal glade
**moriaritie**
ok here now i check others
stoic topaz
i dont get it 😦
just multiply top and bottom by the same thing
surreal glade
and why we do that?
stoic topaz
we can write $\frac{1}{x}=\frac{y}{yx}$
elfin berryBOT
moriaritie
stoic topaz
and why we do that?
to make the denominators (the bottom) of the two fractions equal
stoic topaz
im glad you got it
stoic topaz
yeah sure
surreal glade
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
winged idol
Is pi make able through e if you consider all the elementary operators i.e. division addition, adding other rationals?
marsh citrusBOT
Is pi make able through e if you consider all the elementary operators i.e. divi...
devout mauve
I am pretty sure we do not know
winged idol
Oh ok that's pretty interesting
What if you constrain it to e= a+b*pi
Where a and b are rationals
proper zodiac
What if you constrain it to e= a+b*pi
if you could get to here then you could get to pi (take away a, divide by b), and the other way around
static wyvern
Let $d_b(x,y)=\min(1,|x-y|)$ be a metric on $\mathbb R$. Let $X$ be the set of countable sequences of real numbers and define a metric $\varsigma_b$ on $X$ by $$\varsigma_b((x_n),(y_n))=\sup{d_b(x_n,y_n):n\geq 0}.$$ Let $S\subseteq X$ be the subset of sequences such that $\lim x_n=0$. \textbf{Is $S$ open in $X$?}
marsh citrusBOT
Let $d_b(x,y)=\min(1,|x-y|)$ be a metric on $\mathbb R$. Let $X$ be the set of c...
elfin berryBOT
Junojuno
proud ice
Isn't a sequence countable by definition?
elfin ivy
So if I’m reading this right, S is the set of sequences whose terms go to 0?
static wyvern
Yes
proud ice
Thats irrelevant
I just wanted to be sure I understood your problem correctly
elfin ivy
Do you remember the definition of open for subsets of a metric space
marsh citrusBOT
@static wyvern Has your question been resolved?
marsh citrusBOT
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twin nebula
i have a questionabout a graph wuick
marsh citrusBOT
i have a questionabout a graph wuick
twin nebula
if i have a decreasing velocity function that represents a car breaking
what is the area under curve represent?
didtsnce traveled while breaking?
trim quest
yes, since position is the antiderivative of velocity, it represents the change in position over the given time
marsh citrusBOT
@twin nebula Has your question been resolved?
twin nebula
yes, since position is the antiderivative of velocity, it represents the change ...
can you explain more what the integral is
so is it the output of b-a
of the original function
trim quest
well it's the output of the antiderivative
trim quest
where $F$ is an antiderivative of $f$: $\int_a^b f(x) dx = F(b) - F(a)$
elfin berryBOT
tatpoj
trim quest
oh, that pretty much is the fundamental theorem
trim quest
yeah
trim quest
Do you mean like an example of a problem where you might be asked to use it?
Part 1 is like: If $F(x) = \int_a^x f(t) dt$, then $\frac{d}{dx}F(x) = f(x)$
elfin berryBOT
tatpoj
trim quest
notice the variable x is one of the bounds of the integral
twin nebula
so we basivally put x instead of t?
twin nebula
so that could be any variabel
if i want to take an integral in terms of another variavle
trim quest
yes, and a could be any constant
twin nebula
ok
im learnign this today actually
so maybe ill uinderstand the use of it
i had a test today so thats why i asked the question
i wanna make sure i wrote the write thing even though it wont change anything lol
thanks tho
.solved
solved
/solved
marsh citrusBOT
twin nebula
ok thanks
trim quest
np 👍
twin nebula
i would be here all day
marsh citrusBOT
Available help channel!
boreal rose
I just need help finding a closed form expression to solve this q: "Let n be a positive integer. How many different candy bowls can you make if you must include
n pieces of candy, subject to the following conditions:
• The number of Skittles is a multiple of five.
• Any number of peanuts is possible.
• Any number of gummy bears is possible.
• There are at most two Snickers.
• There are at most four KitKat.
• There is at most one chocolate bar.
You answer should be a closed formula."
marsh citrusBOT
I just need help finding a closed form expression to solve this q: "Let n be a p...
boreal rose
I have the generating function btw
$\frac{1}{1-x^5} * \frac{1}{1-x} * \frac{1}{1-x} * \frac{1-x^3}{1-x} * \frac{1-x^5}{1-x} * \frac{1-x^2}{1-x}$
elfin berryBOT
nosqldb
boreal rose
<@&286206848099549185>
sand fable
i think just simplify this (and partial fractions) then you're good
boreal rose
i think just simplify this (and partial fractions) then you're good
huh but I need the coef
for x^n
😦
boreal rose
once you get to the partial fractions part you'll see it
huh
I did partial fractions like in high school 💀
you have to help me through this
sand fable
sure
sand fable
$\frac{1}{1-x^5} * \frac{1}{1-x} * \frac{1}{1-x} * \frac{1-x^3}{1-x} * \frac{1-x...
also i assume that plus sign should be multiplication?
boreal rose
also i assume that plus sign should be multiplication?
yes
boreal rose
yay
sand fable
do you know how to factor like (1 - x^3) and (1 - x^2) ?
boreal rose
do you know how to factor like (1 - x^3) and (1 - x^2) ?
uhh (1-x)(1-x+x^2)
or sm like that
I forgot
but 1-x^2 is ez
(1-x)(1+x)
sand fable
ye square diff
boreal rose
,w calc (1-x)(1-x+x^2)
elfin berryBOT
sand fable
(1 - x^3) factors into (1 - x)(1 + x + x^2)
boreal rose
ah I was pretty close fr
sand fable
in general, (1 - x^n) factors into (1 - x)(1 + x + x^2 + ... + x^(n - 1))
sand fable
**nosqldb**
so for now try to simplify this expression a bit
there's a lot of things you can factor and/or cancel
boreal rose
,w simplify \frac{1}{1-x^5} * \frac{1}{1-x} * \frac{1}{1-x} * \frac{1-x^3}{1-x} * \frac{1-x^5}{1-x} * \frac{1-x^2}{1-x}
elfin berryBOT
boreal rose
and it gives you the partial fraction decomp
what I do with that
sand fable
you can extract the coefficients
sand fable
you can consider each term separately
boreal rose
yes
boreal rose
you can consider each term separately
mhm and
okay so we made progress
boys
$\frac{1}{1-x^5} * \frac{1}{1-x} * \frac{1}{1-x} * \frac{1-x^3}{1-x} * \frac{1-x^5}{1-x} * \frac{1-x^2}{1-x}$ = $-\frac{5}{x-1} - \frac{9}{(x-1)^2} - \frac{6}{(x-1)^3} - 1$
elfin berryBOT
nosqldb
boreal rose
but now what to do
oh wait I'm so stupid @sand fable
why not take derivatives
.close
marsh citrusBOT
sand fable
why not take derivatives
yeah i was wondering if you were allowed to use calc
boreal rose
yeah i was wondering if you were allowed to use calc
well I can use wtv I want
sand fable
good on figuring that out. that's pretty much how to continue from there
marsh citrusBOT
Available help channel!
boreal rose
,w what's the nth derivative of $-\frac{5}{x-1} - \frac{9}{(x-1)^2} - \frac{6}{(x-1)^3} - 1$
marsh citrusBOT
,w what's the nth derivative of $-\frac{5}{x-1} - \frac{9}{(x-1)^2} - \frac{6}{(...
elfin berryBOT
marsh citrusBOT
@boreal rose Has your question been resolved?
cursive fiber
Is my homework answer key erroneous or did I make several calculation mistakes? We're asked to determine general term of arithmetic sequences:
a. -14, -11, -8, -5, ... has answer key 3n-20 and I got 3n-17
b. 0, -3, -6, -9, ... has answer key -3n+6 and I got -3n+3
c. 4, 0, -4, -8, ... has answer key 12-4n and I got 8-4n
marsh citrusBOT
Is my homework answer key erroneous or did I make several calculation mistakes? ...
runic temple
can you send a picture of your homework
cursive fiber
cursive fiber
yeah that was weird like all the other ones are off by 3
teacher probably accidentally calculated tn=a+(n-2)d or smth
thanks!
.close
marsh citrusBOT
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Available help channel!
upbeat oar
marsh citrusBOT
upbeat oar
why did they change the integral
in the second one
to 0 to pi/3
and not to the first question? - where they kept the integral the same
marsh citrusBOT
@upbeat oar Has your question been resolved?
marsh citrusBOT
@upbeat oar Has your question been resolved?
cobalt yacht
\begin{figure}[ht]
\centering
\begin{tikzpicture}[node distance={35mm}, thick, main/.style = {draw, circle}]
\node[main] (1) {1};
\node[main] (3) [right of=1] {3};
\node[main] (4) [below right of=3] {4};
\node[main] (2) [below left of=4] {2};
\node[main] (5) [left of=2] {5};
\draw (1) -- (3);
\draw (1) -- (5);
\draw (2) -- (3);
\draw (2) -- (4);
\draw (3) -- (4);
\draw (3) -- (5);
\end{tikzpicture}
\end{figure}
a) Suppose this is an electric circuit in which all edge conductances are unity.
i) By assigning columns/rows to nodes according to the numbering shown, find the graph Laplacian matrix (\mathbold K), the degree matrix (\mathbold D) and the adjacency (\mathbold W).
\textcolor{red}{\textit{\textbf{Solution}}} The degree matrix (\mathbold D) is given by a (5\times5) matrix where the (D_{ii}) entry is given by the number of nodes connecting the (i)-th node. Consequently, this is given by
$$
\mathbold D =
\begin{bmatrix}
2&0&0&0&0\
0&2&0&0&0\
0&0&4&0&0\
0&0&0&2&0\
0&0&0&0&2
\end{bmatrix}.
$$
The adjacency (\mathbold W) is given by a (5\times5) matrix where the (\mathbold D_{ij}) entry are (1) if there is an edge between node (i) and (j), and (0) otherwise. Thus, it is given by
$$
\mathbold W =
\begin{bmatrix}
0&0&1&0&1\
0&0&1&1&0\
1&1&0&1&1\
0&1&1&0&0\
1&0&1&0&0
\end{bmatrix}.
$$
The laplacian matrix (\mathbold K) is given by
$$
\mathbold K = \mathbold{D-W} =
\begin{bmatrix}
2&0&-1&0&-1\
0&2&-1&-1&0\
-1&-1&4&-1&-1\
0&-1&-1&2&0\
-1&0&-1&0&2
\end{bmatrix}.
$$
marsh citrusBOT
\begin{figure}[ht]
\centering
\begin{tikzpicture}[node distance={35mm}, thick, m...
elfin berryBOT
Faq
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
cobalt yacht
First of all, is this correct?
And how can I go about calculating the voltages in nodes 3-5 given that the voltage in node 1 is unit and node 2 is grounded?
hidden plaza
Why did you use \(…\) but $$…$$
Looks right. And just do KV=b to solve for the voltages. Are you familiar with that?
marsh citrusBOT
@cobalt yacht Has your question been resolved?
marsh citrusBOT
@cobalt yacht Has your question been resolved?
spice field
hi
i am coding a sort of google map with SDL and C but i run into a problem
i want to make a zoom function (on the cursor)
what i do for now is
scale the image.x + 100
scale the image.y + 100
deplace the image.x according to offset.x
deplace the image.y according to offset.y
mx = mouse position x relative to screen
my = mouse position x relative to screen
W = constant Width (of the screen)
H = constant Height (of the screen)
Z = constant Zoom factor (100)
d = direction of zoom (1 or -1)
offset_x = mx / W * Z * d
offset_y = my / H * Z * d
is there a better way ?
marsh citrusBOT
hi
i am coding a sort of google map with SDL and C but i run into a problem
i wa...
proud ice
You want to learn matrix algebra
spice field
i've watched some of 3blue1brown videos
do you have any other links ?
marsh citrusBOT
@spice field Has your question been resolved?
marsh citrusBOT
wheat geyser
.close
marsh citrusBOT
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Available help channel!
rough trellis
thyself need help with math problem
marsh citrusBOT
thyself need help with math problem
quaint elm
can you answer the rest of the questions? this type of quadrilateral has two pairs of parallel sides.
rough trellis
can you answer the rest of the questions? this type of quadrilateral has two pai...
I was absent during the lesson so i have no idea how to start
dire spire
would be a good idea to learn the basics of quadrilaterals
drowsy crag
I just dont get why it seems like all of its angles are same. That would mean its a rectangle
rough trellis
but heres an example
quaint elm
ohhhh ok i understand what they want now
ok so um. the capital letters are referring to the points where two sides meet (the corners)
we call those vertices (plural of vertex)
quaint elm
yeah you'll sometimes hear people say vertexes and you get to be smug if you know the fancy word
the lines in the middle of the shape (like the one going from P to N) are called diagonals because, well, they go diagonally
when we want to talk about a shape as a whole we just list out the vertices in clockwise order, so in that second example the quadrilateral is named ABCD. For yours you can start anywhere, just make sure you go in order clockwise
rough trellis
Is clockwise is going to right?
quaint elm
yes
rough trellis
oh i see then how about the second?
quaint elm
well the vertices are just the capital letters themselves
rough trellis
I mean 2) sides
quaint elm
oh right
well to name a side (or any line) we just say the endpoints
so for instance, one of your sides is NM
or you could say MN, those both refer to the same side
rough trellis
Oh so its two letters connected to each other?
quaint elm
it doesn't, that's kind of just a standard to make it easier to tell when you're talking about the same one
it does always have to be in order though, you can't jump around
but if you went the other way around (anticlockwise) it would be fine
rough trellis
oh
quaint elm
the last thing is angles. To name an angle, use this funny symbol ∠ and then three points that define the angle, you need a start point, a vertex, and an end point. so for example this is ∠ONM
quaint elm
so for instance, one of your sides is NM
oh yeah when you're talking about edges, you should put a line over top of it so like $\overline{NM}$
elfin berryBOT
hayley!
quaint elm
it's like you're drawing the line that goes from N to M
quaint elm
to be honest i don't know exactly 
i guess just to remind your reader that N and M are vertices and you're talking about a line, you're not multiplying N by M
some of this notation goes back to ancient greece
rough trellis
Oh i guess that does make sense
anywys opposite sides means Sides of the Opposites so i understand that but Consecutive Sides is the next im still wondering bout
quaint elm
consecutive means they share a vertex so they're next to each other
like NM and MP are consecutive sides
rough trellis
i mean why does it start at A not B
quaint elm
i think you could start anywhere if i understand your question right, your teacher tried to alphabetize it as much as possible i think
rough trellis
Oh so i can start anywhere then?
quaint elm
yeah it's common to start in the top left though
rough trellis
like CD & DA, CB & BA
quaint elm
yep
this exercise seems like practice in writing the same 4 letters as many ways as possible 
rough trellis
Oh i just understood on why the overlining now
its like a symbol like when looking for angles u put an angle
I think i understand it now tyvm
.close
marsh citrusBOT
quaint elm
there's a symbol for triangles as well (it's just a small triangle)
marsh citrusBOT
Available help channel!
surreal glade
ni
surreal glade
hi
marsh citrusBOT
marsh citrusBOT
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manic peak
is gaussian elimination the quickest way of solving 3 variable system of equations?
marsh citrusBOT
is gaussian elimination the quickest way of solving 3 variable system of equatio...
void elm
is gaussian elimination the quickest way of solving 3 variable system of equatio...
I believe so
do you mean for a human or for a computer?
manic peak
do you mean for a human or for a computer?
human
void elm
human
I guess it depends on the person and system then
I think for most people, it will be the fastest method
for me personally though, I find substitution quicker for most nice systems
manic peak
I guess it depends on the person and system then
can u help me with this problem? I learned gaussian elimination today, but I want to learn how to apply it. I simplified the bottom so that it is
$(\alpha -10)z= \beta - 16$
elfin berryBOT
manic peak
$2x+y+6z=0 \$
$-y-2z=-4 \$
$(\alpha -10)z=\beta -16$
This is what I have from gaussian elimination
elfin berryBOT
serene basalt
You know when you get no solution ??
manic peak
You know when you get no solution ??
idk
i forgot
when there are no intersection points between the 3 equations
i dont have a graphic calculator tho
I got a=10 and B doesnt equal 16 for the no solution
idk if this is correct
serene basalt
You know matrix form of it
Like putting in a matrix
You get no solution if your last row is like [0 0 0 b]
serene basalt
See there is no solution if coff. Of you last equation is 0
And after equal part is non zero
manic peak
And after equal part is non zero
i found a similar problem here. can u confirm the solution is correct??
marsh citrusBOT
@manic peak Has your question been resolved?
marsh citrusBOT
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Available help channel!
stoic drum
i am making a weighted average calculator for my bio class, did i use the correct weight for each unit
what i did is i took 32% of each unit and put it in the row with the the blue label that matched the unit name. then i took 48% of each unit and put it in the row with the purple label that matched the unit name
then i took 20% of each unit (in total 16%) and added it to the final exam row with the red label. i added 20% to that 16%, because the final is worth 20%
marsh citrusBOT
i am making a weighted average calculator for my bio class, did i use the correc...
@stoic drum Has your question been resolved?
limber star
i am making a weighted average calculator for my bio class, did i use the correc...
Looks right, except that I’d expect the final exam to have a weight of 20 out of the total 100
pearl granite
hi
pearl granite
marsh citrusBOT
pearl granite
Need help with this
So for this question to figure out the work do I need to calculate the force first?
static quarry
you could do it using potential energy, if you know about that
pearl granite
well this is calc 2
pearl granite
you could do it using potential energy, if you know about that
so idk how to do that
static quarry
ah ok
restive sun
can't you use work = force * distance (to avoid explictly using energy calculations)
and force is mass * gravity (I don't know what this is in imperial units)
marsh citrusBOT
@pearl granite Has your question been resolved?
pearl granite
can't you use work = force * distance (to avoid explictly using energy calculati...
so I would do 1,500 times 40?
that what I thought initally but wasnt sure
pearl granite
what gravitational acceleration?
restive sun
yes, it's the same formula
but you need force
you don't have force, you have mass
so use F=ma to find force
restive sun
we're not working with springs
pearl granite
we're not working with springs
well this was how we were taught
so i think if I just do 1,500 times 40 I should get it
pearl granite
you have a mass
the answer was 1500 times 40
thats all I needed to do
now I am not sure how to do this
marsh citrusBOT
@pearl granite Has your question been resolved?
marsh citrusBOT
@pearl granite Has your question been resolved?
trail flint
marsh citrusBOT
trail flint
felt like this one should be simple but can't seem to get it done
I tried solving for y and got y = 12 - 6x
then because its rotated about the y-axis I solved it in terms of x and got y -12 = -6x so (y-12)/-6 = x
then since I knew that for the volume of a solid region I needed to do PI * integral from a-b of [R(x)]^2
I took the (y-12)/-6 and squared it to get
Then I solved for the zero of the function, which is given by setting y to 0, so 0 = 12 - 6x so -6x = -12 so x = 2
And so if x = 0 is a bound and y = 0 is a bound and x = 2 is our zero, we can integrate from 0 to 2
Leaving us with 61/9
But the PI on the outside needs to be remembered, so 61*PI/9
Can anyone help me with this? Where is my logic wrong?
trail flint
It's not three functions
Oh I see what you mean
nvm
Sorry I misinterpreted
Yeah you get a triangle
still temple
use it to find its volume
trail flint
Yeah but I am not meant to do it by the triangle
I am supposed to integrate, that's what will be on my test
trail flint
pretty much the same, except with volume now you use the volume equation, so PI * integral of [R(x)]^2 where R(x) is your function that creates the graph
In the case of 2 functions creating a region in between them, it's [R(x)]^2 - [r(x)]^2 where R(x) is the function on top and r(x) is the function that lies below
still temple
im thinking we should get the area of the triangle and multiply by 2pi
other than that im stumped :/
you gotta wait for someone else to come help you im sorry
drowsy crag
Just use the formula for area of a cone
trail flint
Just use the formula for area of a cone
I can't
drowsy crag
Why?
trail flint
It's a requirement that I integrate
drowsy crag
Oh
late geode
bounds are wrong
you're rotating around the y-axis with disk's, / integrating wrt y
the bounds should be the y-coords
late geode
yes
trail flint
ok
you are 100% right
I didn't realize that
I only flipped the function
not the bounds lol
ty
I still get it wrong lol
I get -4 doing it from 0 to 12
And then I multiplied it by PI to get -4PI
but it's not correct
late geode
can you take a pic of your work on paper
marsh citrusBOT
@trail flint Has your question been resolved?
late geode
work on paper seems fine
you plugged your bounds into the integrand instead of the antiderivative in mathway
trail flint
Oh I see I plugged it in wrong
my work was right I worked it out by hand and got 16 * PI and it was accepted
ok one last question it's of the same type
I am guessing I messed up along the way somewhere again
I will post work
This feels good to me
But I'm not sure
trail flint
is this right?
marsh citrusBOT
@trail flint Has your question been resolved?
trail flint
<@&286206848099549185>
This question is plaguing me
I can post my work so far
I only have 2 trains of thought for it
nova solstice
Yes that looks alright to me
nova solstice
this one up here
nova solstice
this ones start and stops are still in terms of x and need to change to terms of y
trail flint
so 0-32?
nova solstice
yeah
trail flint
ok so 0-32 I tried both 0-32 and 2-6 but neither worked for me
I got (-32^2)/2+36(32) so 640
and * PI
so 640*PI
but it was not accepted
nova solstice
What if you multiplied the pi and 640? does it typically want pi left byitself?
trail flint
What if you multiplied the pi and 640? does it typically want pi left byitself?
oh I got it 🤦♂️
It is 640
but...
-4(32)
nova solstice
?
trail flint
Because the bounds are x = 2 and x = 6, but we rotate around x = 0
so we don't want from x = 0 to x = 2
therefore we subtract x = 2 function from the given function
nova solstice
ah, yeah. right minus left
late geode
.close
pure pagoda
marsh citrusBOT
pure pagoda
in this form of u substitution, the sub taken is 3-x. How is that affecting the x in the original equation if the u sub is 3-x and not just x. If this is some kind of rule, can someone explain how it works?
elfin berryBOT
pure pagoda
right i get this, but should this be done in every situation of x? for example, if there was another x somewhere in the qeuation somehow would i do it then to? do i do it to every x every time?
still temple
right i get this, but should this be done in every situation of x? for example, ...
you are changing your integration variable from x to u
so you should always accordingly change every x to be in terms of u yes
lone heart
in this form of u substitution, the sub taken is 3-x. How is that affecting the ...
You want to pick something that makes it easy for you. If you made u = x, the du = 1 dx, but that doesn't make it easy with the the 3 - x part
marsh citrusBOT
marsh citrusBOT
Available help channel!
dense oriole
Suppose that you want to have a $39,000 retirement fund after 39 years. How much will you need to deposit now if you can obtain an APR of 11.3%, compounded daily? Assume that no additional deposits are to be made to the account.
$472.47
$639.14
$475.80
$411.67
None of the above.
marsh citrusBOT
Suppose that you want to have a $39,000 retirement fund after 39 years. How much...
dry ibex
Since irl nobody would tell you which angle is the right angle, how to identify the hypotenuse, opposite and adjacent without knowing the right angle? What if the theta is placed on right angle and the hypotenuse is oppositing the theta?
main idol
Since irl nobody would tell you which angle is the right angle, how to identify ...
!occupied
marsh citrusBOT
Since irl nobody would tell you which angle is the right angle, how to identify ...
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
@dense oriole Has your question been resolved?
sturdy cradle
marsh citrusBOT
hazy lion
What have you tried?
lavish kernel
Identify the possible outcomes when two dice are rolled to get a sum of 7.
sturdy cradle
my work
hazy lion
https://www.youtube.com/watch?app=desktop&v=H02B3aMNKzE this video is an okay intro
lavish kernel
<@1073667744798621728> this is myy work could you please check it
Yeah, you corrected calculated it using the formula for conditional probability
sturdy cradle
Yeah, you corrected calculated it using the formula for conditional probability
thank you
sturdy cradle
https://www.youtube.com/watch?app=desktop&v=H02B3aMNKzE this video is an okay in...
thank you...
scarlet rune
Can I have some help?
marsh citrusBOT
Can I have some help?
scarlet rune
Oh
muted narwhal
ITS YOU
lethal bridge
?
muted narwhal
waddup
scarlet rune
If x² - 2ax + a²=0, find the value of x
-
a
scarlet rune
Yes
muted narwhal
did you leave the server and come back today lol
yea
I realised I forgot all my maths which isn't good, so revising it all again hahaa....
lavish kernel
If x² - 2ax + a²=0, find the value of x
-
a
To find the value of $\frac{x}{a}$, we will solve the given quadratic equation $x^2 - 2ax + a^2 = 0$ and then divide the solution $x$ by $a$.
elfin berryBOT
David K.
marsh citrusBOT
@scarlet rune Has your question been resolved?
marsh citrusBOT
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inland patio
I have tried converting the x denominator into x*sinx/sinx and put it in the exponent, I just got ln(1+sinx)^sinx and sat like a duck, the answer is supposed to be 1 but I kept getting 0
marsh citrusBOT
I have tried converting the x denominator into x*sinx/sinx and put it in the exp...
inland patio
I honestly thought there'd be a form of some sort for ln(1+x)^x, but nope, it is always x and 1/x and vice versa
inland patio
Hvae you tried l'hopital's rule
God I hope to learn that tomorrow because it seems really helpful. I've been asking limits in the past 3 days and I always encountered that name.
inland patio
alternatively multiply and divide by sin(x)
Which I did, I had x*sinx/sin, which is sin x/ x sin x when flipped, right?
novel juniper
you want to use the result (1+sin(x))/sin(x) at 0 is 1
inland patio
Ohhhhh, and I disect x and sin x and place eachother accordingly.
Yeah I got it, 1*1
Morning limits. haha. Thanks for the help!
.close
cunning heath
Hello
cunning heath
is there any theorem saying
how to quickly find roots of a polynomial
(write as a product of polynomials)
late geode
approach with rational root theorem i suppose
cunning heath
what is it
late geode
way of searching for candidates for rational roots
cunning heath
moreover, what does it say? like how can i use it
late geode
it'll be easier for you to look it up
cunning heath
i did
late geode
try applying it here
after you find one of the roots, you can use long division
then repeat as needed
limpid bison
marsh citrusBOT
limpid bison
Is n+1,n+2,n+3 also correct?
limpid bison
right ty
vital oracle
np
limpid bison
Do i have to state the root 11 thing
or is it implied
I never seen this before 😵💫
vital oracle
do you know why the root thing works?
limpid bison
nope
vital oracle
say you needed the factors of 100
you usually have a small number * a big number = 100
you meet in the middle with 10 * 10 = 100
then have a big number * a small number = 100
when you go through the factors in order
1 * 100 = 100
2 * 50 = 100
...
10 * 10 = 100
...
50 * 2 = 100
100 * 1 = 100
youll notice the big * small part of the list is just a repeat of the small * big part of the list
you already went through all the factors on the small side
so they have to reappear on the big side
that means the big side is redundant
the separation between them is that 10 * 10 = 100, where both are equal
and so you can stop after √100 = 10
vital oracle
.close
limpid bison
.quit
vital oracle
np
limpid bison
.close
marsh citrusBOT
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Available help channel!
void cove
i don't know how to start this, the method i used was to try and isolate R and then take the partial derivative of r1 but I got stuck when I saw dr/dr1 on both sides
marsh citrusBOT
i don't know how to start this, the method i used was to try and isolate R and t...
marsh citrusBOT
marsh citrusBOT
Available help channel!
fast needle
I don't know where to exactly start for b
marsh citrusBOT
I don't know where to exactly start for **b**
@fast needle Has your question been resolved?
hoary timber
marsh citrusBOT
hoary timber
can somone explain why as x goes to infinite
it became ln 4
from what i see its should jsut be ln(1) as infinite cancel out
novel juniper
Try writting L=ln(f(x) )so e^L=f(x)
Evaluate it now
And then Take the log of both sides
hoary timber
ok
glass silo
Seeing the second is equivalent, may be easier to see if you write
[
\ln\qty( \frac{2x^2 + 3}{(x + 1)^2 } ) = \ln\qty( \frac{2x^2 + 3}{x^2 + 2x + 1} ) = \ln\qty( \frac{2 + \frac3{x^2}}{1 + \frac2x + \frac1{x^2}} )
]
elfin berryBOT
@glass silo
hoary timber
<@788085606483361802>
oh
that make more sense
cause what i done was infinite +3 =infinite
tacit fractal
yes exactly
hoary timber
so top bottom both becames infinite
but it actully 3/infinite
so it becames 0
yeah
thgat make so much sense
glass silo
I think we forgot to square it
gilded sierra
I have been stuck on this problem for a few hours and found an online solution that I think is wrong. I've transcribed it out to make it easier to read.
marsh citrusBOT
I have been stuck on this problem for a few hours and found an online solution t...
@gilded sierra Has your question been resolved?
gilded sierra
<@&286206848099549185>
marsh citrusBOT
@gilded sierra Has your question been resolved?
marsh citrusBOT
@gilded sierra Has your question been resolved?
marsh citrusBOT
@gilded sierra Has your question been resolved?
robust notch
Why 2xy=12
marsh citrusBOT
Why 2xy=12
static quarry
divide both sides by 2x? (assuming x is not zero)
marsh citrusBOT
marsh citrusBOT
Available help channel!
tulip marsh
im not sure
marsh citrusBOT
im not sure
still temple
Are you familiar with the fundemental theorem of calculus
tulip marsh
well
next ravine
This is FTOC Part 1
tulip marsh
i know them but i dont konw how to apply them. i just learn the steps to solve problems
still temple
i know them but i dont konw how to apply them. i just learn the steps to solve p...
well okay its really two things that you need:
FTC and chain rule
so first of all we establish FTC
,, \dv x\int_a^x \m ft \dd t = \m fx
tulip marsh
for reference this is what i learned
elfin berryBOT
still temple
for reference this is what i learned
yeah the first one is all you need
tulip marsh
when do you use the second one?
still temple
the second one is basically the first in disguise
next ravine
for reference this is what i learned
Yes! Use this first one here
still temple
,, \int_{\m hx}^{\m gx} \m ft \dd t = \int_{\m hx}^a \m ft \dd t+ \int_a^{\m gx} \m ft \dd t = -\int_{a}^{\m hx} \m ft \dd t + \int_a^{\m gx} \m ft \dd t
elfin berryBOT
tulip marsh
im not good at understandn letter notation. it seems like the first intergral n's should be a to a.
since it goes from
a to hx and then gx to a
oh
i read it wrong
yes
it makes sense
tulip marsh
Yes! Use this first one here
i dont understand how to apply it. or rather, i dont understand what tells us to apply it. what part in the problem indicates to us we should use this theorem. what should i look for to know to use this
anyone??
.close
marsh citrusBOT
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Available help channel!
brazen flame
marsh citrusBOT
brazen flame
can someone explain me why 1/1 * 2 + 1/2 * 3 is equal to 1/1 - 1/2 + 1/2 - 1/3 + 1/3
vernal forge
work backwards
brazen flame
hmm?
marsh citrusBOT
@brazen flame Has your question been resolved?
vernal forge
hmm?
$\frac{1}{2} - \frac{1}{3} = \frac{3}{2\cdot 3} - \frac{2}{2\cdot 3} = \frac{3-2}{2\cdot 3} = \frac{1}{2\cdot 3}$
elfin berryBOT
artemetra
harsh vigil
how do you do this problem?
marsh citrusBOT
how do you do this problem?
still temple
split it up first
harsh vigil
idk how to apply this to this problem
still temple
,, \sum_{k=1}^n a_k + b_k = \sum_{k=1}^n a_k + \sum_{k=1}^n b_k
elfin berryBOT
still temple
idk how to apply this to this problem
well we can do it a step at a time
still temple
but do you understand how to do this
harsh vigil
no 😦 so i got n(n+1)(2n+1)/6 + 5n(n+1)/2 + 8(n) so far but idk what the next step is
still temple
okay so you do know how to do it since you implicitly did exactly that
anyways that's correct
the rest is just algebra
harsh vigil
ok yayy
like for the next part i see that they got 9n^2+9n and 24n and idk what number they mulitiplied it by?
still temple
anyways that's correct
you dont even need to do anything else. Your answer suffices. Although simplification is possible
harsh vigil
ive had several attempts at this question and they want the answer to be in the same 1/3n(n^2+...+...) form
still temple
like for the next part i see that they got 9n^2+9n and 24n and idk what number t...
are you familiar with the GCF (greatest common factor)
still temple
ok so you have [
\f{n(n+1)(2n+1)}6+5\cd\f{n(n+1)}2 + 8n
]
you want to get rid of the fractions. To do that, you can multiply and divide by the least common factor between 6 and 2 (the denominators)
elfin berryBOT
harsh vigil
sooo im multiplying by 2...?
still temple
that's not the LCM
harsh vigil
oh is it 6
still temple
yeah
so like now
[
\f{n(n+1)(2n+1)}6+5\cd\f{n(n+1)}2 + 8n = \c b{\f66\cd}\bs{\f{n(n+1)(2n+1)}6+5\cd\f{n(n+1)}2 + 8n}
]
elfin berryBOT
still temple
try distributing in like, that 6 in the numerator while keeping out the 1/6
zealous lava
harsh vigil
so 1/6[2n^3+3n^2+n]+(30n^2+30n)+48n ... ?
harsh vigil
oh sorry im really lost 
elfin berryBOT
Gamer Sans The Gamer Skeleton
it's $\frac{1}[6} \cdot n(n+1)(2n+1) + 15 \cdot n(n+1) + 48n$
if im not stoobid
```Compilation error:```! Extra }, or forgotten $.
l.49 it's $\frac{1}[6}
\cdot n(n+1)(2n+1) + 15 \cdot n(n+1) + 48n$
I've deleted a group-closing symbol because it seems to be
spurious, as in `$x}$'. But perhaps the } is legitimate and
you forgot something else, as in `\hbox{$x}'. In such cases
the way to recover is to insert both the forgotten and the
deleted material, e.g., by typing `I$}'.
Preview: Tightpage -1310720 -1310720 1310720 1310720
[1{/usr/local/texlive/2023/texmf-var/fonts/map/pdftex/updmap/pdftex.map}{/usr/l```
elfin berryBOT
Gamer Sans The Gamer Skeleton
still temple
,align
\f{n(n+1)(2n+1)}6+5\cd\f{n(n+1)}2 + 8n &= \c b{\f66\cd}\bs{\f{n(n+1)(2n+1)}6+5\cd\f{n(n+1)}2 + 8n}\
&=\f16\bs{6\cd\f{n(n+1)(2n+1)}6+6\cd5\cd\f{n(n+1)}2 + 6\cd8n}
elfin berryBOT
still temple
@harsh vigil this is what you have currently. Do you agree yes or no?
harsh vigil
yes
still temple
okay, so for now, don't distribute the parentheses
simplify the numbers only
what do you get?
harsh vigil
1/6[6n(n+1)(2n+1)/6 + 30n(n+1)/2 + 48n] ??
harsh vigil
oh 15
harsh vigil
1
still temple
so, your updated version?
harsh vigil
1/6[1n(n+1)(2n+1) + 15n(n+1) + 48n] ?
harsh vigil
15n^2+15
still temple
nuh uh
still temple
yeah
harsh vigil
okk
still temple
so, your updated version now?
harsh vigil
1/6[n(n+1)(2n+1) + 15n^2+15n + 48n]
harsh vigil
1/6[n(n+1)(2n+1) + 15n^2+63n]
still temple
yeah
so now going to the left
distribute out all three parentheses
or do you want me to guide you with that?
harsh vigil
wait so do i multiply (n+1)(2n+1) by n first then 1/6?
harsh vigil
n(n^2+n)(2n^2+n)...
still temple
pause
harsh vigil
isnt 1n = n??
still temple
n goes only once
harsh vigil
oh what
still temple
,, a(b\cd c) \c r{\ne} ab \cd ac
elfin berryBOT
harsh vigil
im sorry how do u distribute it then? i forgot most of my algebra
elfin berryBOT
still temple
so like
still temple
you have n(n+1)(2n+1) remember
distribute out n(n+1) what do you get
harsh vigil
n^2+n...?
harsh vigil
ohhhh thats what you meant
still temple
yes
harsh vigil
i thought the n goes into both parenthesis
still temple
no like
for multiplication its only once
you are confusong it with addition
for addition yes it does distribute
a(b+c) = ab + ac
a(b*c) != ab * ac
!= means not equal to
harsh vigil
ohh ok
harsh vigil
2n^3+3n^2+n
harsh vigil
FINALLY
still temple
so your updated version?
harsh vigil
1/6[(2n^3+3n^2+n)+15n^2+63n]
harsh vigil
64n?
harsh vigil
18n^2
still temple
and, at last, your updated final version is?
harsh vigil
1/6(2n^3+18n^2+64n)
harsh vigil
lmaoo were almost there at least
still temple
what's the greatest common factor between 2n^3, 18n^2 and 64n
harsh vigil
2?
still temple
i mean, yeah, but you are missing something
harsh vigil
2n
harsh vigil
1/6 2n(n^2+9n+32)
still temple
yess and whats 2 divided by 6 (in fraction)
harsh vigil
1/3
harsh vigil
so 1/3n(n^2+9n+32) ?!!?!?!
still temple
so your last thing is[
\f n3(n^2 +9n +32)
]
elfin berryBOT
still temple
so 1/3n(n^2+9n+32) ?!!?!?!
yeah although i hope you didnt mean that n to be in the denominator because it isn't
harsh vigil
so 1/3n(n^2+9n+32) ?!!?!?!
no cus this is my last attempt and i don't want to get the format wrong :(((!!
still temple
i mean
we can check for you lol
let's see
,w sum of i^2 + 5i + 8 from 1 to n =n/3(n^2+9n+32)
elfin berryBOT
harsh vigil
lifesaver fr fr
loud pagoda
.close
marsh citrusBOT
Available help channel!
hardy smelt
marsh citrusBOT
hardy smelt
I just want to understand the part why it can assume lambda to be an specific thing, and then prove the unequally for all lambda in R
It’s in spanish but ill explain the important parts:
It is trying to prove the cauchy inequality
Starting with the square of the norm of x+lambda * y, which is always > 0 because its an square
And then, it choses that one specific lambda, which will be enough to make everything work out and prove the inequality
My question is that
If you chose that one specific lambda, does it mean that the inequality will only work if the lambda is only the one you chose?
devout mauve
well the first inequality is valid for all lambdas
the actual inequality you want to prove doesnt depend on lambda at all
hardy smelt
I see
So it does work
Now if there was a lambda in the inequality (like the cauchy one)
We shouldn’t assume it works for all lambdas in R?
devout mauve
well depends on the statement of the inequality
it could be "for all lambda this inequality holds"
or "there exists a lambda for which the inequality holds"
devout mauve
the inequality is true
marsh citrusBOT
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Available help channel!
minor verge
marsh citrusBOT
bitter solstice
Can you not use the same tehod you used for a and c?
Here's a hint that may or may not help (depends on what method you use), there's one eigenvector you can kind of tell by inspection
marsh citrusBOT
@minor verge Has your question been resolved?
minor verge
Here's a hint that may or may not help (depends on what method you use), there's...
i figured out b the same way, but idk with a 3x3 matrix
bitter solstice
Whats the method you've been taught to use?
minor verge
Whats the method you've been taught to use?
this is what i did for part a
