Download Math 242 - Homework 9 Due Thursday, October 30

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Transcript
Math 242 - Homework 9
Due Thursday, October 30
Exercises from the Book
• Chapter 2.5# 1, 3, 5, 9, 10
• Chapter 2.7# 1, 2, 4
Additional Exercises
1. Use the level curves shown in the figure predict the locations of the critical points of
f and whether f has a saddle point or a local maximum or minimum at those points.
Then use the second derivative test to confirm your predictions.
2. Three alleles (alternative versions of a gene) A, B, and O determine the four blood types.
If someone has two A genes or an A and an O gene, they have type A blood. If they
have two B genes or a B and an O, they have type B blood. Someone with two O genes
has type O blood, and finally, someone with an A and a B gene has type AB blood.
The Hardy-Weinberg Law states that the proportion of individuals in a population who
carry two different alleles is:
P = 2pq + 2pr + 2rq
where p, q, and r are the proportions of the genes A, B, and O in the population. Use
the fact that p + q + r = 1 to show that P is at most 2/3.