Question

Suppose β = β(s) is a curve parametrized by arc-length. If β lies on a sphere of center c and radius r, prove β −c = −ρn−ρ0σb where ρ = 1/κ and σ = 1/τ.

Answer #1

Suppose g : (a,b) ? R^n is a differentiable
parametrized curve with the property that at each t, the position
and velocity vectors are orthogonal. Prove that g lies on a
sphere centered at the origin.

Write the curve given by r(t)=((3/2)t)i+(t^3/2)j as a function
r(s) parameterized by the arc length s from the point where t=0.
Write your answer using standard unit vector notation.

Suppose a conducting sphere, radius r2, has a spherical cavity
of radius r1 centered at the sphere's center. At the center of the
sphere is a point charge -4Q. Assuming the conducting sphere has a
net charge +Q determine the electric field,magnitude and direction,
in the following situations:
a) From r = 0 to r = r1.
b) From r = r1 to r = r2.
c) Outside of r = r2
d) find the surface charge density (charge per...

A solid nonconducting sphere of radius R = 5.82 cm has
a nonuniform charge distribution of volume charge density
ρ = (13.3 pC/m3)r/R, where r
is radial distance from the sphere's center.
(a) What is the sphere's total charge?
8.23e-15 C
(b) What is the magnitude E of the electric field at
r = 0? (Use any variable or symbol stated above along with
the following as necessary: ε0.)
E = 0
(c) What is the magnitude E of...

I need answer for this problems ! Thanks Ypu !
1. Suppose a 1.0-kg cart with low-friction wheels is traveling
at 1.0 m/s rightward just before colliding with an identical cart
at rest. If the collision interaction delivers a total rightward
impulse of 1.5 kg·m/s to the cart at rest, what is the velocity
(magnitude and direction) of the originally moving cart after the
collision is over? (Hint: Draw some arrows.)
2. A certain child's top consists of a uniform...

1. A plane curve has been parametrized with the following
vector-valued function, r(t) = (t + 2)i + (-2t2 + t + 1)j a.
Carefully make 2 sketches of the plane curve over the interval . (5
pts) b. Compute the velocity and acceleration vectors, v(t) and
a(t). (6 pts) c. On the 1st graph, sketch the position, velocity
and acceleration vectors at t=-1. (5 pts) d. Compute the unit
tangent and principal unit normal vectors, T and N at...

Assume the earth is a uniform sphere of mass M and
radius R. As strange as it may sound, if one can dig a
long tunnel from one side of the Earth straight through the center
and exit the other end, any object falling into the tunnel will
appear at the other end (i.e. the opposite side of the Earth) in
just 2530 s (42.2 min). Call that time t. Let t
be a function of G, M, and R,...

1. Given β = XT 1×nAn×nXn×1, show that the gradient of β with
respect to X has the following form: ∇β = X T (A + A T ). Also,
simplify the above result when A is symmetric. (Hint: β can be
written as Pn j=1 Pn i=1 aijxixj ).
2. In this problem, we consider a probabilistic view of linear
regression y (i) = θ T x (i)+ (i) , i = 1, . . . , n, which...

The net charge difference across the membrane, just like the
charge difference across the plates of a capacitor, is what leads
to the voltage across the membrane.
How much excess charge (in picocoulombs, where 1 pc =
1x10-12 C) must lie on either side of the membrane of an
axon of length 2 cm to provide this potential difference (0.07 V)
across the membrane? You may consider that a net positive charge
with this value lies just outside the axon...

Use Matlab to solve the following
(a) Create a plot with a sphere at the center of the graph
(origin) representing the sun with a radius of 6955000 km. Make
sure that the outside of the sphere is painted in ’autumn’ colors.
(Hint: look up the sphere() function, the colormap() function, and
the surf() function).
(b) Create a variable t ranging from 0 to 2? with increments of
0.01.
(c) The following Table gives you important values needed to
compute...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 7 minutes ago

asked 8 minutes ago

asked 8 minutes ago

asked 11 minutes ago

asked 24 minutes ago

asked 29 minutes ago

asked 30 minutes ago

asked 32 minutes ago

asked 36 minutes ago

asked 42 minutes ago

asked 1 hour ago

asked 1 hour ago