Solve the problem.Find the derivative of the function 
at the point 
in the direction in which the function increases most rapidly.
A. 
B. 
C. 
D. 
Answer: C
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Animal type A and animal Type B compete for the same resources. Suppose there are a animals of type A and b animals of type B. Both a and b are measured in thousands. Then the growth rates of the two types of animals are given by
Growth rate for Type A: 
Growth rate for Type B: 
A: Equilibrium occurs when both growth rates are 0. Find two expressions of ?b in terms of ?a when equilibrium occurs. Round your answers to two decimal places, if necessary.B: Plot the graphs of ?b versus ?a for both the expressions you found in part A. Be sure your graph shows the crossing point.C: How many of each type of animal is present when equilibrium occurs? Round your answers to two decimal places, if necessary.
What will be an ideal response?
Solve the problem.Escott used the formula n2 - 79n + 1601 to generate prime numbers for whole numbers n. The formula fails to produce a prime for n = 80. Evaluate Escott's formula for n = 81 and determine whether this is a prime number. If it is not a prime number, give its prime factors.
What will be an ideal response?
Select from the list of numbers all that belong to the specified set.Real numbers4, 
, -2, 0, 
, 
, 
A. 4, -2, 0, 
B. 4, -2, 0, 
, 
C. 4, -2, 0, 
, 
D. 4, 
, -2, 0, 
, 
Solve the formula for the specified variable.S = 2?rh + 2?r2 for h
A. h = 
B. h = S - r
C. h = 2?(S - r)
D. h = 
- 1