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In the triangle ABC, the opposite sides of a, B, C are a, B, C, a = π / 6, (1 + radical 3) C = 2B, find C I'll give you five points when I finish
From the cosine theorem a ^ 2 = B ^ 2 + C ^ 2-2bccosa = [(1 + radical 3) ^ 2 + 4 - (radical 3) * (1 + radical 3) * 2] * x ^ 2, we get a = (radical 2) X. from the sine theorem a / Sina = C / sinc, that is, (radical 2) x / (1 / 2) = 2x / sinc, we get sinc = (radical 2) / 2 and a
The first chapter is to solve the sine theorem and cosine theorem of triangle 1, the second chapter is to solve the sequence of numbers, and the third chapter is to solve the inequality
Ha ha, one has been sent before
Comprehensive application of mathematical inequality in Senior High School
It is known that the function f (x) = x cubic - ax square + (3-2a) x + B is an increasing function on (0. + ∞)
Find the maximum value of integer a?
Is an increasing function on (0. + ∞)
F '(x) = 3x ^ 2-2ax + 3-2a > 0 on (0. + ∞)
The axis of symmetry is x = A / 3
a/30,a
RELATED INFORMATIONS
- 1. It involves solving triangles and vectors In △ ABC, the opposite sides of ∠ a, B, C are a, B, C, vector M = (a ^ 2, B ^ 2), vector n = (Tana, tanb), and vector M / / vector n. then what is the shape of △ ABC?
- 2. 】Given that x is any number except 2, x ^ 2 + 2x + 1 / (X-2) ^ 3 = A / X-2 + B / (X-2) ^ 2 + C / (X-2) ^ 3, find the value of a, B, C Given that x is any number except 2, x ^ 2 + 2x + 1 / (X-2) ^ 3 = A / X-2 + B / (X-2) ^ 2 + C / (X-2) ^ 3, find the value of a, B, C
- 3. Given the equation x * - 5x - 1 = 0 about X, find the value of (1) x + 1 / X
- 4. There are three schools a, B, Let three schools a, B and C be located at the three vertices of an equilateral triangle. In the Internet age, to set up communication cables between the three schools, Xiao Zhang designed three connection schemes, as shown in the figure, scheme a AB + BC; scheme B AD + BC {D is the midpoint of BC}; scheme C Ao + Bo + CO (o is the intersection of the three heights of the triangle). Please help to calculate which of the following schemes has the shortest route
- 5. If the perimeter of △ ABC is 12cm and the area of △ DEF is 8cm, then the perimeter of △ DEF is ---. △ ABC If the perimeter of △ ABC is 12cm and the area of △ DEF is 8cm, then the perimeter of △ DEF is --------. The perimeter of △ ABC is ---.
- 6. If △ ABC is similar to △ def, the similarity ratio is 3:2, if their perimeter difference is 40 cm, then the perimeter of △ DEF is?
- 7. It is known that the lengths of three sides of △ ABC are a, B, C, and the perimeter is 6, and a ^ 2 + B ^ 2 + C ^ 2 = AB + BC + Ca, then the lengths of three sides of △ ABC are?
- 8. Given that a, B and C are the three sides of △ ABC, and a + B + C = 60cm, a: B: C = 3:4:5, the area of △ ABC is obtained
- 9. At RT △ ABC, ∠ C = 90 °, girth 60cm, two right angle sides, BC: AC = 5:12, find the value of s △ ABC Pythagorean theorem in Mathematics
- 10. It is known that the perimeter of △ ABC is 18cm, and a + B = 2c, a − B = C2. Find the length of a, B, C on three sides
- 11. The known vectors AB = (6,1), BC = (x, y), CD = (- 2, - 3) (1) If BC is parallel to Da and AC is perpendicular to BD, then x and y are obtained (2) Find the area of quadrilateral ABCD All AB, BC. Above are vectors
- 12. Vector representation of triangle interior If O is a triangle ABC, ab = C, AC = B, BC = a, prove a * [0A] + b * [ob] + C * [OC] = [0] ([OA] denotes vector OA) I asked why
- 13. On vectors It is known that AC vector is the sum of AB vector and Ad vector, AC vector = a, BD vector = B, AB vector and Ad vector are represented by a respectively
- 14. 1. Given the points a (2,3), B (5,4) and C (7,10), if the vector AP = AB + λ AC (λ∈ R), what is the value of λ, the point P is in the third quadrant? 2. (1) it is proved that three non parallel vectors a, B and C can form a triangle (the starting point of each vector coincides with the end point of one of the other two vectors) if and only if a + B + C = 0 (2) It is proved that three midline vectors of a triangle can form a triangle (3) In △ ABC, e and F are points on AC and AB, respectively. Be and CF intersect at point g. given CE = 1 / 3CA, BF = 2 / 3ba, calculate the constants λ and μ, such that GE = λ be, GF = μ CF & # 61549;, # 61472 3. As shown in figure 5-3-19, e and F are the edges of ABCD, ad and the midpoint of CD, and be, BF and diagonal AC intersect at points R and t respectively Verification: ar = RT = TC 4. Try to prove: the necessary and sufficient condition for the end points a, B and C of three vectors a, B and C with the origin as the starting point to be on the same straight line is that C = α a + β B (α, β ∈ R, and α + β = 1) Before 6 am on the 21st, don't look down on us
- 15. Given the direction vector a of the line L = (1,3), the direction vector of the line L 'is b = (- 1, K). If the line L' passes through the point (0,5) and l ⊥ L ', then what is the equation of the line L' Above is the original title The answer given in the book is ∵a=(1,3) ,b=(-1,k), ∴a·b=-1+3k=0 And because the line L 'passes through the point (0,5) And l ⊥ L ', then the equation of L' is X-3Y+15=0 I don't think the K in B (1, K) should represent the slope? Here's what I did, Let the equation of line L 'be y-0 = K (X-5) That is, the point oblique formula of the column. This should be OK. After multiplying it, it becomes Y = kx-5k, the slope of L 'should be the K I set! Then from the direction vector a + (1,3) of L, we know that the slope of l should be 3 The slope k of L 'should be - 1 / 3 Then we substitute y = kx-5k to get x + 3y-5 = 0 I love to go to the top, thank you very much!
- 16. In the straight triangular prism abc-a1b1c1, if ∠ BAC = 90 ° AB = AC = Aa1, then the angle between the out of plane straight line BA1 and AC1 is equal to () A. 30°B. 45°C. 60°D. 90°
- 17. In the triangle ABC, the bisector of angle B and angle c is called point O. if angle a is equal to 40 degrees, then how many degrees is angle BOC equal to Right now!
- 18. It is known that the lengths of the side edges and the bottom edges of the triangular prism abc-a1b1c1 are equal, and the projection of A1 on the bottom ABC is the midpoint of the BC edge, then the out of plane straight line AB and CC1 are formed It is known that the lengths of the side edges and the bottom edges of the triangular prism abc-a1b1c1 are equal, and the projection of A1 on the bottom ABC is the midpoint D of the BC edge, then the cosine value of the angle formed by the out of plane line AB and CC1 is: A、(√3)/4 B、(√5)/4 C、(√7)/4 D、3/4 I see from the Internet that many people's answers are d.3/4, and they all think that a1d ⊥ surface ABC, but according to my personal understanding, the projection point D of A1 on the side of BC can only explain a1d ⊥ BC, not a1d ⊥ surface ABC... What's the matter with projection?
- 19. In the triangular prism abc-a1b1c1, the length of each edge is equal, find the angle between the straight line CB1 and the plane aa1bb1
- 20. In the straight triangular prism abc-a1b1c1, ad ⊥ plane a1bc, its perpendicular foot D falls on the straight line A1B, P is the midpoint of AC, (1) Verification: B1C ‖ plane a1bp (2) Verification: BC ⊥ A1B