The vector O E ⇀ as sums of scalar multiple of u and v .
The vector O E ⇀ as sums of scalar multiple of u and v .
Solution Summary: The author illustrates the parallelogram rule by connecting the tails of the vectors u and v so that it should form adjacent sides of a paralelogram.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Chapter 13.1, Problem 17E
(a)
To determine
To find: The vectorOE⇀ as sums of scalar multiple of u and v.
(b)
To determine
To find: The vector
OB⇀ as sums of scalar multiple of u and v.
(c)
To determine
To find: The vector
OF⇀ as sums of scalar multiple of u and v.
(d)
To determine
To find: The vector
OG⇀ as sums of scalar multiple of u and v.
(e)
To determine
To find: The vector
OC⇀ as sums of scalar multiple of u and v.
(f)
To determine
To find: The vector
OI⇀ as sums of scalar multiple of u and v.
(g)
To determine
To find: The vector
OJ⇀ as sums of scalar multiple of u and v.
(h)
To determine
To find: The vector
OK⇀ as sums of scalar multiple of u and v.
(i)
To determine
To find: The vector
OL⇀ as sums of scalar multiple of u and v.
The spread of an infectious disease is often modeled using the following autonomous differential equation:
dI
-
- BI(N − I) − MI,
dt
where I is the number of infected people, N is the total size of the population being modeled, ẞ is a constant determining the rate of
transmission, and μ is the rate at which people recover from infection.
Close
a) (5 points) Suppose ẞ = 0.01, N = 1000, and µ = 2. Find all equilibria.
b) (5 points) For the equilbria in part a), determine whether each is stable or unstable.
c) (3 points) Suppose ƒ(I) = d. Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the
dt
function by hand.) Identify the equilibria as stable or unstable in the graph.
d) (2 points) Explain the biological meaning of these equilibria being stable or unstable.