Reference no: EM131005856
Explain and sketch whenever possible. Put final answer in a frame. Each problem carries the same weight.
1) Give the point A = (1, 2, 3) and the straight line (x+1/1) = (y-1/2) = z/2. Determine:
a) The (shortest) distance between the point A and the line.
b) An equation of the plane containing A and the given line.
2) Given two lines L1 and L2
L1 = (x+2/0) = (y-4/-2) = (z+1/4), L2 = x/1 = y/3 = z/4.
Determine:
a) Whether or not the two lines intersect.
b) The point of intersection of L1 above and the plane x - y - z =1.
3) Do the two planes-
x - 2y + z =1, x + y + z = 9.
Intersect? If they intersect find an equation of the line of intersection. What is the distance between the two planes?
4) A parallel piped has the following four adjacent vertices A = (0, 0, 0), B = (1, 1, 1), C = (1, 2, 3) and D = (1, 0, 1). Determine:
a) The coordinate of the point Q that makes ABCQ a parallelogram.
b) The area of the triangle ABC.
c) The volume of the parallelepiped.
d) The length of the height that extends from the point D to the plane that contains the three points A, B, C.
|
Distributed according to a poisson process
: Policyholders of a certain insurance company have accidents at times distributed according to a Poisson process with rate λ. The amount of time from when the accident occurs until a claim is made has distribution G.
|
|
Number of customers in the system
: 1. Consider an in?nite server queuing system in which customers arrive in accordance with a Poisson process with rate λ, and where the service distribution is exponential with rate μ. Let X(t) denote the number of customers in the system at time t..
|
|
Problem regarding the independent increments
: (a) Find P{N(t) = n}. (b) Is {N(t)} a Poisson process? (c) Does {N(t)} have stationary increments? Why or why not? (d) Does it have independent increments? Why or why not?
|
|
Exponential distribution with rate
: (a) If F is the exponential distribution with rate λ, which, if any, of the processes {Xn}, {Yn} is a Markov chain? (b) If G is the exponential distribution with rate μ, which, if any, of the processes {Xn}, {Yn} is a Markov chain?
|
|
Determine the distance between the point and the line
: Give the point A = (1, 2, 3) and the straight line (x+1/1) = (y-1/2) = z/2. Determine: The (shortest) distance between the point A and the line
|
|
Find the laplace transform of each of the given function
: Find the Laplace transform of each function below. f(t)= 2 δ (t) + u3(t); f(t) = δ (t - π) (t2 +t4) sin(t); f(t) = δ (t - 1) tet.
|
|
Distribution of the time
: What is the distribution of the time at which the last rider departs the car? Suppose the last rider departs the car at time t. What is the probability that all the other riders are home at that time?
|
|
Determine the velocity and acceleration vectors
: Given a position vector r(t) = [t, t2, t3], Find the velocity and acceleration vectors and the speed at time t. Find the equation of the line passing through the points P (3,5,7) and Q (6,5,4).
|
|
Implement a simple relational dbms
: In Problem Set, you began to implement a simple relational DBMS by taking the code base that we gave you and adding support for INSERT commands and for SELECT * commands involving a single table.
|