Let a = (cosx, SiNx), B = (cosy, siny), if | √ 2A + B | = √ 3 | - A - √ 2B |, then cos (X-Y)

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• 1. As shown in the figure, in ladder ABCD, ad ‖ BC, ad = 2, BC = 4, point m is the midpoint of AD, and △ MBC is an equilateral triangle (1) Prove: the trapezoid ABCD is isosceles trapezoid; (2) the moving points P and Q move on the line BC and MC respectively, and ∠ MPQ = 60 ° remains unchanged. Let PC = x, MQ = y, find the functional relationship between Y and X; (3) in (2): when the moving points P and Q move to where, the quadrilateral with points P, m and two points in points a, B, C and D as the vertex is a parallelogram? It also points out the number of parallelograms that meet the conditions. ② when y is the minimum, the shape of △ PQC is judged and the reason is given
• 2. The taxi charging standards in a city are as follows: (1) the starting price is 8 yuan for less than 3 km; (2) for 3 km or more and less than 10 km, an additional 1.7 yuan will be charged for every additional 1 km; for less than 1 km, it will be calculated as 1 km; (3) for 10 km or more, an additional 50% return fee will be charged for every extra kilometer. A person who takes a taxi for 8.2 km will be charged () yuan
• 3. CD / / EF / / AB, CD = 2, ab = 4. EF bisects the area of trapezoid ABCD and finds the length of EF CD / / EF / / AB, CD = 2, ab = 4. EF bisects the area of the trapezoid ABCD to find the length of EF (requires a problem-solving process)
• 4. If A-B = B-A and a = 4, B = 3, find the value of a + B
• 5. As shown in the figure, it is known that in the quadrilateral ABCD, ad ‖ BC, ad > BC, ab = DC, EA = ed, EB and EC intersect ad at points F and g respectively to prove that the quadrilateral fbgc is isosceles trapezoid
• 6. A mathematics application problem urgent I! Fang Hua's family has a 40 cm long and 25 cm wide glass fish tank with a water depth of 20 cm. One day, Fang Hua accidentally dropped a 10 cm square iron block into the tank. How many cm will the water surface rise? But also the solution ideas and the meaning of each formula! It's up to, remember, it doesn't seem to be up to how many centimeters!
• 7. Know the area of a circle, how to find its perimeter, diameter, radius
• 8. A copper wire is 12.56 meters long. It is wound on a circular coil for 100 turns. What is the radius of the coil?
• 9. Cut off a rectangle 2cm wide from the square sheet, and the remaining area is 48cm2. Then the area of the original square sheet is () A. 9cm2B. 68cm2C. 8cm2D. 64cm2
• 10. Some problems of physical atmospheric pressure in the second year of junior high school 1. Insert the straw into the bottle filled with water and suck the straw with your mouth. Can you suck the incoming water? Why? 2. Pour some hot water into the bottle, pour out the hot water, and then quickly close the cap. Why is the bottle shriveled? 3. After boiling water, the flask is fixed on the iron platform, and the peeled quail eggs are quickly put into the bottle mouth. You can see the quail eggs from the bottle mouth under the action of () thank you!
• 11. F1 (x) = f (x) + F (- x) is even function, F2 (x) = f (x) - f (- x) is odd function, right
• 12. How to prove that F1 (x) = f (x) + F (- x) is an even function and F2 (x) = f (x) - f (- x) is an odd function?
• 13. It is known that f (x) is an even function on R. if the image of F (x) is shifted one unit to the right, then the image of an odd function is obtained. If f (2) = - 1, then f (1) + F (2) + F (3) + +The value of F (2011) is () A. - 1B. 0C. 1D. Not sure
• 14. It is known that f (x) is an even function on R. if the image of F (x) is shifted one unit to the right, then the image of an odd function is obtained. If f (2) = - 1, then f (1) + F (2) + F (3) + +The value of F (2011) is () A. - 1B. 0C. 1D. Not sure
• 15. It is known that f (x) is an even function on R, f (0) = 2. If the image of F (x) is shifted one unit to the right, then the image of an odd function is obtained. Then the value of F (1) + F (3) + F (5) + F (7) + F (9) is () A. 1B. 0C. -1D. −92
• 16. It is known that f (x) is an odd function defined on R, and f (1) = 1. If the image of F (x) is shifted one unit to the right, the image of an even function is obtained, Then f (1) + F (2) + F (3) f (4) + F (2011) is equal to
• 17. As shown in the figure, it is a part of the graph of quadratic function & nbsp; y = AX2 + BX + C (a ≠ 0). The following propositions are given: ① a + B + C = 0; ② b > 2A; ③ two of AX2 + BX + C = 0 are - 3 and 1 respectively; ④ a-2b + C > 0. The correct proposition is () A. ①②B. ②③C. ①③D. ①②③④
• 18. The graph of quadratic function y = AX2 + BX + C is shown in the figure, then the error in the following relation is A.a＜0 B.c＞0 C.b2-4ac＞0 D.a+b+c＞0 The opening direction is downward, the symmetry axis is x = - 1, and the intersection point with y axis is in the positive half axis
• 19. Urgently seeking the image of quadratic function y = ax ^ 2 + BX + A ^ 2 + B (a is not equal to 0)
• 20. Given that the image of quadratic function y = AX2 + BX + 4 intersects with X axis at a and B, two points intersect with y axis at C angle ACB = angle ABC AB = 5, find the analytic expression of the quadratic function