a) Let T be the plane 3x-y-2z=9. Find the shortest distance d
from the point P0...
a) Let T be the plane 3x-y-2z=9. Find the shortest distance d
from the point P0 = (5, 2, 1) to T, and the point Q in T that is
closest to P0. Use the square root symbol where needed.
d=
Q= ( , , )
b) Find all values of X so that the triangle with vertices A =
(X, 4, 2), B = (3, 2, 0) and C = (2, 0 , -2) has area (5/2).
Let P be the plane given by the equation 2x + y − 3z = 2....
Let P be the plane given by the equation 2x + y − 3z = 2. The
point Q(1, 2, 3) is not on the plane P, the point R is on the plane
P, and the line L1 through Q and R is orthogonal to the plane P.
Let W be another point (1, 1, 3). Find parametric equations of the
line L2 that passes through points W and R.
Let ?C be the vertically oriented helix with radius of 33 that
starts at (3,0,0)(3,0,0) and...
Let ?C be the vertically oriented helix with radius of 33 that
starts at (3,0,0)(3,0,0) and ends at (3,0,3)(3,0,3) after two
revolutions on [0,1][0,1].
a) Find a vector-valued function ?⃗:[0,1]→ℝ3r→:[0,1]→R3 whose
graph is ?C.
Hint: The projection of ?C onto the ??xy-plane
is the circle with radius 33 centred at (0,0,0)(0,0,0); the
projection of ?C onto the ?z-axis is the line segment from
(0,0,0)(0,0,0) to (0,0,3)(0,0,3).
b) Compute the first derivative ?⃗˙r→˙ of ?⃗r→.
c) Compute the length of ?.
Let X be a random proportion. Given X=p, let T be the number of
tosses till...
Let X be a random proportion. Given X=p, let T be the number of
tosses till a p-coin lands heads.
a) Let P(X=1/10)=1/4, P(X=1/7)=1/4, and
P(X=1/3)=1/2. Find E(T).
b) Find E(T) if X has the beta(r,s) density for
some r>1. Simplify all integrals and Gamma functions in your
answer.
c) Let X have the beta(r,s) density. For fixed
k>0, find the posterior density of X given T=k. Identify it as
one of the famous ones and state its name and...