Solutions to Selected Homework Problems
Math 311-501
Assignment 1.
- Problem 1.1.7(b) (page 6):
We have x=i+j, by inspection. Also, y=2j. Using the
second equation to replace j by y/2 in the first, we get
x=i+y/2. Solving for i yields i=x-y/2
- Problem 1.1.11 (page 7):
Part (a). Let R be the total revenue, and let n1, n3, n5 be the number of
1000's, 3000's, and 5000's sold in a year. If n=(n1,n3,n5), and
p=(1000, 3000, 5000), then R=n · p. Part
(b). Assume that all Nerdstations produced are sold. The profit is
then P=n · p - n · c - $100,000.
- Problem 1.2.8 (page 13): Two vectors lying in the plane are
a=i+3j and b=4(i+j+k). The cross product of
a and b is N=12i-4j-8k. This
is normal to the plane, so the desired equation is 12x-4y-8z=4. The
parametric version is x=(s+2t+1)/3, y=s, z=t.
- Problem 1.4.3 (page 20): The tangent line in vector
parametric form is x(t)=(t-2)h'(2) + h(2). At
t=3, the particle is at x(3)=h'(2) +
h(2)=(8,10,3e4).
Updated on 28 January 1998