2. A supply ship found that the cargo ship was sailing at the speed of 12 nautical miles per hour from Island A to northwest 10 degrees. What speed and direction does the supply ship need to sail in order to catch up with the cargo ship for nourishment within 2 hours?
3. Solve the triangle in △ABC ∠ A = 120 AB = 5BC = 7.
4. Solve the triangle of a = 4b = 3a = 45° in △ABC.
5. In △ABC, if asinA=bsinB, what is the shape of △ ABC?
Isosceles, right angles, isosceles right angles or equilateral?
How to prove it?
6. If someone invests 865,438+00,000 yuan to buy a storefront, the decoration fee in the first year is 654,38+00,000 yuan, and it will increase by 20,000 yuan every year. After renting out the store, the annual income is 300 thousand. (654,38+0) How many years did this person start to make a net profit after deducting investment and various decoration expenses? (2) This person needs several years, and when the average annual profit is the largest, he decides to sell the store for 460,000 yuan. How much does this person make at this time?
7. If A 1, A2, A3 and A4 are in geometric series and the common ratio is 2, find 2a 1+a2/2a3+a4.
8. In the geometric series {an}, it is known that A 1+A2+A3 = 7 and A 1A2a3 = 8 find the sequence {an}.
9. As we all know, a.b.c is a real number that is not equal to each other. If a, b and c are geometric series, find a/b.
10. known function f (x) = a * x2bx1(a >; 0, b is a real number) Let the equation f(x)=x have two real roots x 1, x2.
(1) If x; - 1
(2) If it is 0
1 1. in triangle a.b.c, a, b and c are opposite sides of angle a, angle b and angle c respectively. It is known that A, B and C form geometric series in turn, and a2-c2=ac-bc. Find the size of (1)A (2) (b sin b)/
12. Let 0 < a < 1 and the function f (x) = loga (a (2x)-2a x-2) find the value range of x that makes f (x) < 0.
13. As we all know, when f (2-a)+f (2a-3), odd function f(x) is a monotonically decreasing function defined on (-2,2).
14. In order to strengthen the macro-management of wine production, the state implements the policy of levying additional tax. It is known that each bottle of a certain wine in 70 yuan sells about/kloc-0.000000 bottles a year without tax. If the government levies additional tax, it will be taxed at R% for every sales of 100 yuan, and the annual sales will be reduced by 100 million yuan.
15. In triangle ABC, sinA+cosA= root number 2/2, AC=2, AB=3, find the area of triangle ABC.
16. in triangle ABC, a+b= 10, and the value of cosC follows the equation 2x square -3x-2=0. Find the minimum value of triangle perimeter.
17. In acute triangle ABC, A, B and C are opposite sides of angles A, B and C, respectively, and the root number is 3=2csinA. Determine the size of angle C.
18. In the triangle ABC, A, B and C are opposite sides of A, B and C respectively, 1+cos(π+2A)=2sin squared (B+C)/2.
(1) Find the size of angle A (is it 45? If so, you don't need to go through the detailed process and ask the second question directly)
(2) When a=6, find the maximum area and judge the shape of triangle ABC at this time.
19. In △ABC, b? -bc-2c？ =0, a= root 6, cosA=7/8, so what is the area of triangle ABC?
20. Find the sum of all integers between 1 and 100 that are not divisible by 3 and 5.
2 1。 It is known that f(x)=x2-2(n+ 1)x+n2+5n-7. Let the distance between the vertex of the image of f(x) and the X axis constitute {an}, and find the sum of the first n terms of {an}.
22. Set the quadratic equation anx? -A (n+1) x+1= 0 (n =1,2,3 ...) has two α and β, and satisfies 6α-2αβ+6β=3.
(1) try an on A (n+ 1);
(2) Verification: {an-2/3} is a geometric series;
(3) Find the general formula of the sequence {an}.
23. the sequence {an} satisfies a 1= 1, and an=3an- 1-4n+6(n≥2, n ∈ n *).
(1) Let bn=an-2n, and prove that the sequence {bn} is geometric progression;
(2) Find the first n terms of the sequence {an} and sn.
24. it is known that the quadratic function f (x) = ax 2-2x+2 (a is a constant) about x has f (x) > 0 for all values of x that satisfy 1 < x < 4, and the value range of constant a is found.
25. in triangle ABC, (tanA-tanB)/(tanA+tanB)=(c+b)/c, find the range of angles a and (b+c)/a.
26. If {an+ 1-an} is arithmetic progression and {bn+ 1 -bn} is geometric progression, find the general formula of {an}{bn} respectively.
27. What is the value of the equation k about x?
The two real roots of x squared -kx+k-2=0 are more than half.
28. There are two points A +(Y-4 1 0) and B (1 0) on the plane, and point P is on the square of the circle (X-3)+ square (Y-4) =4. What is the coordinate of the point P with the smallest square of AP +BP?
Please forgive me if there is any duplication.