Find the unit vector in the direction of the given vector. Write your answer in the indicated form.Let u = -2i - 3j. Find the unit vector in the direction of u, and write your answer as a linear combination of the standard unit vectors i and j.
A. - 
i - 
j
B. 
i - 
j
C. - 
i - 
j
D. 
i + 
j
Answer: B
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Solve the problem.Consider the pair of differential equations that model a predator-prey system with populations x and y. x'(t) = -5x + xy y'(t) = 2y - xy(a) Find the lines along which x'(t) = 0,(b) find the lines along which y'(t) = 0,(c) find the equilibrium points for the system.
A. (a) x' = 0 along the lines x = 
and y = 0
(b) y' = 0 along the lines y = 
and x = 0
(c) (0, 0) and 
B. (a) x' = 0 along the lines x = 0 and y = 5
(b) y' = 0 along the lines y = 0 and x = 2
(c) (0, 0) and (2, 5)
C. (a) x' = 0 along the lines x = 5 and y = 0
(b) y' = 0 along the lines y = 2 and x = 0
(c) (0, 0) and (5, 2)
D. (a) x' = 0 along the lines x = 0 and y = 
(b) y' = 0 along the lines y = 0 and x = 
(c) (0, 0) and 
Solve the problem.A measure of diversity of species in an ecological community is given by the formula 
where P1, P2, ... ,Pn are the proportions of a sample belonging to each of n species found in the sample. A bog in northeastern Illinois has 5 species of birds with these proportions: cardinal, 0.204; robin, 0.28, sparrow, 0.217; oriole, 0.248; woodpecker, 0.051. Find the index of diversity, H.
A. 2.1782193 B. -2.1782193 C. -2.3299917 D. 2.3299917
If possible, find the slope of the line passing through the two points.
, 
A. 
B. 
C. 
D. 
Fill in the blank with one of the words or phrases listed below. 
Two numbers that are the same distance from 0 on the number line but are on opposite sides of 0 are called 
.
A. inequality symbols B. integers C. average D. opposites