Two rectangular pieces of paper with equal width are stacked together to get the quadrilateral ABCD as shown in the figure. (1) prove that quadrilateral ABCD is diamond; (2) if two rectangular pieces of paper are 8 in length and 2 in width, does the perimeter of diamond ABCD have a maximum or minimum? If it does, ask for it; if it does not, give a brief reason
(1) It is proved that: as shown in the figure, ∵ ad ∥ BC, DC ∥ AB, ∥ quadrilateral ABCD is parallelogram. Passing through points a and D respectively, AE ⊥ BC is e, DF ⊥ AB is f. ∵ the width of two rectangular pieces of paper is equal, ∵ AE = DF, and ∵ AE · BC = DF · AB = s ▱ ABCD, ≁ BC = AB, ▱ ABCD is diamond; (2) there is a minimum value
RELATED INFORMATIONS
- 1. 1. There are 26 bricks, two brothers fight to choose, brother gun in front, just put bricks, brother came. Brother see brother choose too much, bring half to himself. Brother refused, and from the brother to take half. Brother refused, brother had to give brother 5, so brother than brother move 2 more, I ask: at first, how many will brother move? 2. A basket of apples, the first day to eat half more than one, the next day to eat the remaining half less than one, then there are still three. How many apples in this basket? 3. Write three scores (), (), () smaller than 3 / 4 and larger than 5 / 8 4. For a fraction, the sum of numerator and denominator is 20. If the denominator is subtracted by 8, the fraction is equal to 1. The fraction turns out to be ()
- 2. 1. The purchase price of a batch of goods is a yuan. If the gross profit (what is it?) is to account for 30% of the bid price, the bid price should be a yuan? 2. The length of one right side of a right triangle is reduced by 25%. To keep its area unchanged, the other side should be increased () A. A quarter B. a quarter of it c. a third of it D. two fifths of it
- 3. Clever calculation: 1 / 1 × 3 + 1 / 3 × 5 + 1 / 5 × 7 + +1/17×19
- 4. Calculate 2 + 4 + 6 +.. + (2n + 4)
- 5. Ask some mathematical questions about fractional equation Given that 1 / (x-1) = 2, what is the value of 2 / (x-1) + X-1? If the equation 1 / (x + 3) = 2 / (x + k) has a negative solution, then the range of K is? If (x-3) / (X-2) and (2-x) / (3x + 2) are reciprocal, what is the value of X? Given that the solution of the equation [2 (x + a)] / [a (x-1)] = - 8 / 5 is x = - 1 / 5, what is the value of a?
- 6. It is known that the two roots of the equation AX2 + BX + C = 0 are - 1 and 3 respectively. The parabola y = AX2 + BX = C has an intersection n (2, - 3) with the straight line y = kx-m passing through the point m (3,2) (1) The analytic formula of straight line and parabola (2) If the parabola passes through the point (a + 1, b2-4) and a is not equal to B, find the value of a + B Sorry, the title should be parabola y = AX2 + BX + C
- 7. Solving a mathematical problem about quadratic function Given that the image of quadratic function y = x square + ax + A-2 has two focal points with X axis, and the distance between the two focal points is 2 root sign 5, then a =? Hope to write out the answers and solutions
- 8. A mathematical problem of quadratic function in junior high school Parabola y = AX2 + BX + C, vertex coordinates of passing point a (- 3,0) B (1,0) C (0, √ 3) are d. find out whether there is a point P on the straight line BC, so that the perimeter of triangle pad is minimum. If there is, find out the coordinates of point P, and explain why there is no such point
- 9. On mathematical problems of quadratic function Fenghuang bridge on Qingjiang River in Enshi has been completed and opened to traffic. Fenghuang bridge is a half through reinforced concrete arch bridge integrating highway traffic and urban landscape. The arch of the main bridge draws a beautiful arc in the air. From a distance, it looks like a curved rainbow lying on Qingbo (as shown in the picture). The arch of the bridge is a part of parabola, The arch height and span above the bridge are about 18 meters and 112 meters respectively (1) Please establish an appropriate plane rectangular coordinate system and find an analytical formula that can approximately describe the arch shape of the main bridge; (2) Calculate the length of the vertical support 28 meters from the center of the bridge deck
- 10. It is known that the quadratic function y = 2x ^ 2 + 9x + 34, when the independent variable x takes two different values X1 and X2, the function values are equal, then the function values when the independent variable x takes X1 + x2 are equal to the function values when x is the value
- 11. The length of the rectangle is 2xcm, the width is 4cm, the length of the trapezoid is xcm, the length of the bottom is 3 times of the length of the top, and the height is 5cm? How much bigger?
- 12. I'll hand it in tomorrow! There are 1500 bags of rice in a warehouse and 3 / 5 of them are taken away. How many bags have been taken away? How many bags are left? A barrel of oil is 10 kg, 4 / 5 of which is used. How many kg are left? Zhang Jia village has 720 pigs, and the number of sheep is 1 / 8 less than that of pigs. How many sheep did Zhang Jia village have? Zhang Jun weighs 42 kg. Li Ming weighs one seventh of Zhang Jun's weight, and Wang Hai weighs one sixth of Zhang Jun's weight. What are the weights of Li Ming and Wang Hai? Bad, I'll hand it in tomorrow!
- 13. Four mathematical problems No.1 road repair team plans to build a road 150 meters a day and complete it in 12 days. If it is to be completed two days in advance, how many meters should be built every day? No.2 two trains leave from two places at the same time and run in opposite directions. After 4.5 hours, the two trains meet at a distance of 9 km from the destination. The express train runs 42 km per hour. How many kilometers are there between the two places? 2 times, how many students are there in each grade? No.4 a hospital plans to use white cloth with a length of 30 meters and a width of 1.8 meters to make triangular towel for rescue with two right angles of 0.6 meters. How many can be made?
- 14. 1. The square of the polynomial X of x.y-mxy + 2xy-y to the 2N-1 power + 1 is a cubic trinomial, and the value of the square of (M + n) can be obtained 2. Xiao Ming is doing a math problem: "two polynomials A and B, where b = the square of 3A - 5a-7. Try to find a + 2B." he mistakenly regards a + 2b as a-2b. The answer is the square of - 2A + 3A + 6. Can you help him to calculate the correct result of a + 2B?
- 15. Given the equation system x + y = 7ax + 2Y = C, try to determine the value of a and C, so that the equation system: (1) has one solution; (2) has innumerable solutions; (3) has no solution
- 16. There are 8% salt water and 5% salt water in the laboratory. Now we need to mix these two kinds of salt water to make 3kg salt water with 6% salt. How many grams of these two kinds of salt water are suitable?
- 17. A few seventh grade math problems, solving, urgent! 1. Party A and Party B set out from place a to place B at the speed of 4km per hour at the same time. After 2.5 hours, Party A returned to place a to get the documents. He rushed back to place a at the speed of 6km per hour. After getting the documents, he went back to catch up with Party B at the same speed. As a result, Party A and Party B arrived at the same time, The speed of the ship in still water is 10km / h, and the speed of the current is 2km / h. how many kilometers must the ship go to return to the original Wharf in 8 hours
- 18. Several seventh grade math problems, with a calculator solution 1) The cube root of 28 2) 345 3) Cube root of - 17.6 4) The cube root of 1 / 48 (one in 48) Accurate to 0.1
- 19. Solving a math problem in the second semester of grade seven If the inequality system A-X > 0, x + 1 > 0 has no solution, the value range of a needs to be solved
- 20. What is the zero power of (- 2) + (negative half) / (negative second power of negative half) * (negative third power of negative half)