This idea is not limited just to two point masses. In general, if
n masses,
${m}_{1},{m}_{2}\text{,\u2026},{m}_{n},$ are placed on a number line at points
${x}_{1},{x}_{2}\text{,\u2026},{x}_{n},$ respectively, then the center of mass of the system is given by
Let
${m}_{1},{m}_{2}\text{,\u2026},{m}_{n}$ be point masses placed on a number line at points
${x}_{1},{x}_{2}\text{,\u2026},{x}_{n},$ respectively, and let
$m={\displaystyle \sum _{i=1}^{n}{m}_{i}}$ denote the total mass of the system. Then, the moment of the system with respect to the origin is given by
$M={\displaystyle \sum}_{i=1}^{n}{m}_{i}{x}_{i}$
and the center of mass of the system is given by
$\stackrel{\u2013}{x}=\frac{M}{m}.$
We apply this theorem in the following example.
Finding the center of mass of objects along a line
Suppose four point masses are placed on a number line as follows:
We can generalize this concept to find the center of mass of a system of point masses in a plane. Let
${m}_{1}$ be a point mass located at point
$\left({x}_{1},{y}_{1}\right)$ in the plane. Then the moment
${M}_{x}$ of the mass with respect to the
x -axis is given by
${M}_{x}={m}_{1}{y}_{1}.$ Similarly, the moment
${M}_{y}$ with respect to the
y -axis is given by
${M}_{y}={m}_{1}{x}_{1}.$ Notice that the
x -coordinate of the point is used to calculate the moment with respect to the
y -axis, and vice versa. The reason is that the
x -coordinate gives the distance from the point mass to the
y -axis, and the
y -coordinate gives the distance to the
x -axis (see the following figure).
If we have several point masses in the
xy -plane, we can use the moments with respect to the
x - and
y -axes to calculate the
x - and
y -coordinates of the center of mass of the system.
Center of mass of objects in a plane
Let
${m}_{1},{m}_{2}\text{,\u2026},{m}_{n}$ be point masses located in the
xy -plane at points
$\left({x}_{1},{y}_{1}\right),\left({x}_{2},{y}_{2}\right)\text{,\u2026},\left({x}_{n},{y}_{n}\right),$ respectively, and let
$m={\displaystyle \sum _{i=1}^{n}{m}_{i}}$ denote the total mass of the system. Then the moments
${M}_{x}$ and
${M}_{y}$ of the system with respect to the
x - and
y -axes, respectively, are given by
If you tell me how can I Know about engineering math 1( sugh as any lecture or tutorial)
Faysal
I don't know either i am also new,first year college ,taking computer engineer,and.trying to advance learning
Amor
if you want some help on l hospital rule ask me
Jawad
it's spelled hopital
Connor
hi
BERNANDINO
you are correct Connor Angeli, the L'Hospital was the old one but the modern way to say is L 'Hôpital.
Leo
I had no clue this was an online app
Connor
Total online shopping during the Christmas holidays has increased dramatically during the past 5 years. In 2012 (t=0), total online holiday sales were $42.3 billion, whereas in 2013 they were $48.1 billion. Find a linear function S that estimates the total online holiday sales in the year t . Interpret the slope of the graph of S . Use part a. to predict the year when online shopping during Christmas will reach $60 billion?
you have to apply the function arcsin in both sides and you get
arcsin y = acrsin (sin x)
the the function arcsin and function sin cancel each other so the ecuation becomes
arcsin y = x
you can also write
x= arcsin y
Ioana
what is the question ? what is the answer?
Suman
there is an equation that should be solve for x
Ioana
ok solve it
Suman
are you saying y is of sin(x)
y=sin(x)/sin of both sides to solve for x... therefore y/sin =x
Tyron
or solve for sin(x) via the unit circle
Tyron
what is unit circle
Suman
a circle whose radius is 1.
Darnell
the unit circle is covered in pre cal...and or trigonometry. it is the multipcation table of upper level mathematics.
You can factorize the numerator of an expression. What's the problem there? here's an example.
f(x)=((x^2)-(y^2))/2
Then numerator is x squared minus y squared. It's factorized as (x+y)(x-y).
so the overall function becomes :
((x+y)(x-y))/2
The
The problem is the question, is not a problem where it is, but what it is
Antonio
I think you should first know the basics man: PS
Vishal
Yes, what factorization is
Antonio
Antonio bro is x=2 a function?
The
Yes, and no.... Its a function if for every x, y=2.... If not is a single value constant
Antonio
you could define it as a constant function if you wanted where a function of "y" defines x f(y) = 2 no real use to doing that though
zach
Why y, if domain its usually defined as x, bro, so you creates confusion
Antonio
Its f(x) =y=2 for every x
Antonio
Yes but he said could you put x = 2 as a function you put y = 2 as a function
zach
F(y) in this case is not a function since for every value of y you have not a single point but many ones, so there is not f(y)
Antonio
x = 2 defined as a function of f(y) = 2 says for every y x will equal 2 this silly creates a vertical line and is equivalent to saying x = 2 just in a function notation as the user above asked. you put f(x) = 2 this means for every x y is 2 this creates a horizontal line and is not equivalent
zach
The said x=2 and that 2 is y
Antonio
that 2 is not y, y is a variable 2 is a constant
zach
So 2 is defined as f(x) =2
Antonio
No y its constant =2
Antonio
what variable does that function define
zach
the function f(x) =2 takes every input of x within it's domain and gives 2 if for instance f:x -> y then for every x, y =2 giving a horizontal line this is NOT equivalent to the expression x = 2
zach
Yes true, y=2 its a constant, so a line parallel to y axix as function of y
Antonio
Sorry x=2
Antonio
And you are right, but os not a function of x, its a function of y
Antonio
As function of x is meaningless, is not a finction
Antonio
yeah you mean what I said in my first post, smh
zach
I mean (0xY) +x = 2 so y can be as you want, the result its 2 every time
Antonio
OK you can call this "function" on a set {2}, but its a single value function, a constant
Antonio
well as long as you got there eventually
zach
2x^3+6xy-4y^2)^2 solve this
femi
follow algebraic method. look under factoring numerator from Khan academy