Mathematics

Old Test 2 Answers

2(a) Region in xy-plane above and including the line x+y=0.
2(b) x+y=1, x+y=4. Both are lines.

3. 5+(-3)(-.1)+7(.2) = 6.7.

4. (2/3)*pi*6*8*1 + (1/3)*pi*36*(1/2) = 38*pi cubic feet per minute.

5(a) < 3, (3/4)*pi*root(3), (9/2)*root(3) >
5(b) < 3, (3/4)*pi*root(3), (9/2)*root(3) > dot < x-3, y-1, z-(pi/6) > = 0.

6(a) The problem is wrong. There are three points: (0,0), (1,0), (1/2, 1/8).
6(b) The first two are saddles. The last is a local maximum.

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