Question

According to the x-y axis set given in the figure, Calculate the center of gravity coordinates of the shaded surface?

Figure is here = https://hizliresim.com/5QRR60

Answer #1

y=6-2x-x^2 and y=x+6, about the x-axis. Draw the figure,
set up the integral needed to find the volume when the given curve
is rotated about the specified axis, find the answer. Use
calculator if needed!

Mass and coordinates of three particles are given: Mass, M1 = 3
kg, Coordinates: X = 1, Y = 1 Mass, M2 = 2 kg, Coordinates: X = -1,
Y = -1 Mass, M3 = 1 kg, Coordinates: X = 0, Y = 1 (a) Find the
Moment of Inertia of the three particles about the X-axis (axis of
rotation) (b) Find the Center of Mass of the three objects

Set-up, but do not evaluate, an iterated integral in polar
coordinates for ∬ 2x + y dA where R is the region in the xy-plane
bounded by y = −x, y = (1 /√ 3) x and x^2 + y^2 = 3x. Include a
labeled, shaded, sketch of R in your work.

Consider the following mass distribution where the x- and
y-coordinates are given in meters: 5.0 kg at (0.0, 0.0) m, 3.1 kg
at (0.0, 4.7) m, and 4.0 kg at (2.7, 0.0) m. Where should a fourth
object of 8.6 kg be placed so that the center of gravity of the
four-object arrangement will be at (0.0, 0.0) m?
x= _____m
y=______m

Consider the following mass distribution where the x-
and y-coordinates are given in meters: 5.0 kg at (0.0,
0.0) m, 2.8 kg at (0.0, 4.3) m, and 4.0 kg at (2.9, 0.0) m.Where
should a fourth object of 7.5 kg be placed so that the center of
gravity of the four-object arrangement will be at (0.0, 0.0) m?
x = m
y = m

Consider the following mass distribution where the x- and
y-coordinates are given in meters: 5.0 kg at (0.0, 0.0) m, 3.1 kg
at (0.0, 3.4) m, and 4.0 kg at (2.7, 0.0) m. Where should a fourth
object of 6.4 kg be placed so that the center of gravity of the
four-object arrangement will be at (0.0, 0.0) m?
x = _____m
y = _____m

Consider the following mass distribution where the
x-and y-coordinates are given in meters: 5.0 kg
at (0.0, 0.0) m, 3.2 kg at (0.0, 4.6) m, and 4.0 kg at (3.5, 0.0)
m. Where should a fourth object of 7.7 kg be placed so that the
center of gravity of the four-object arrangement will be at (0.0,
0.0) m?
x
= m
y
= m

Consider the following mass distribution where the x-
and y-coordinates are given in meters: 5.0 kg at (0.0,
0.0) m, 3.1 kg at (0.0, 3.6) m, and 4.0 kg at (2.7, 0.0) m. Where
should a fourth object of 7.4 kg be placed so that the center of
gravity of the four-object arrangement will be at (0.0, 0.0) m?

find the coordinates of the vertex and the equation of
the axis of symmetry for the parabola given by the equation.
y = 2x^2 - x - 5
vertex (x,y) = ( ? )
axis of symmetry ?
y = x^2 + 2x
vertex (x,y) = ( ? )
axis of symmetry ?

a) Set up the integral in cylindrical coordinates for the moment
of inertia about the z-axis for a cone bounded by z = sqrt x^2+y^2
and z = 2. The density of the cone is a constant 5.
b) Evaluate the integral by using direct method the work done by ~
F(x,y) = (y,−x) along ~r(t) = (2cos(t),2sin(t)), 0 ≤ t ≤ π.
need help on a and b

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