Multiple choice question:
9. Coloring all vertices and diagonals of a regular hexagon requires that three sides of each triangle have different colors (the vertices of the triangle coincide with the vertices of the regular hexagon), and different triangles use different color combinations. How many colors do you need at least?
Big question:
1, in the triangle ABC, 2sin 2 ((a+b)/2)+cos2c = 1, and the circumscribed circle radius R=2.
(1) find c
(2) Find the maximum area
2. There are four ABCD points on the parabola X 2 = 4Y, of which two AD points are symmetrical about the parabola, and the D point is the tangent of the parabola, and the straight line BC is parallel to this tangent. The distance from point D to AB is d 1, the distance from point D to AC is d2, and D 1+D2 = (√ 2) | AD |
(1) triangle ABC is an acute triangle? Right triangle? Obtuse triangle? certificate
(2) The area of triangle ABC is 240. Find the coordinates of a.
3. Positive N Pyramid:
The volume of (1) regular quadrangular pyramid V=(√2)/3, and the minimum surface area of regular quadrangular pyramid satisfying this condition is found.
(2) For a regular N-pyramid with constant volume, a necessary and sufficient condition for minimizing its surface area is given.
4. The individual proportion of genotypes aa, Aa and AA in a population is w:2v:φ(w+2v+φ= 1), and the number of parents is sufficient to mate immediately:
(1) Ask the proportion of three genotypes in the first generation.
(2) Are the proportions of the three genotypes in the second generation the same as those in the second generation? Give reasons