Tie a cylindrical cake box with plastic rope (as shown in the figure below). The knot is just the center of the bottom. The length of the knot is 25cm (1) How many centimeters does it take to tie this box? (2) How many square centimeters is the area of this part at least?

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• 1. How to do this math problem Solving the equation of first degree with one variable One sixth of his life is childhood; He lived one twelfth of his life and grew a beard; He got married and spent another seventh of his life; Five years later, I have a son; But the son lived only half of his father's age; After his son died, he lived for another four years and died 1: His life span 2: The age of a father 3: Age at the time of his son's death
• 2. 1: F (5) = 1, f (1) = 0 for f (x) 2: F (5) = 0, f (1) = 5
• 3. It is known that no matter what value x takes, the algebraic formula a (X-2) - 2x + 5 is the same, and the value of a is obtained. Because no matter what value x takes, the value of the algebraic formula a (X-2) - 2x + 5 is the same, so we might as well take x = 0 and get a (X-2) - 2x + 5. That is to say, no matter what value x takes, the value of the algebraic formula a (X-2) - 2x + 5 is equal to - 2A + 5, The values of the algebraic formula ax + 2 / bx-5 are the same, so what kind of equivalence relationship should a and B satisfy. (2) no matter what value x takes, the equation x ^ 3 + MX + 2 = (x + 2) (x ^ 2 + ax + b) always holds, and the value of M can be obtained
• 4. The decimal point of 9.20 is removed, and the integer is () times of the original, which is () more than the original
• 5. How to calculate the indefinite integral of D / DX ln (x ^ 2 + 1), where a is 1b and E?
• 6. A rectangular piece of paper, which is 10 cm long and 8 cm wide, is cut into the largest circle with its surface
• 7. Given the function f (x) = 2sinxcosx-2cos ^ 2x, find the minimum positive period of the function. When x belongs to o, the value range of F (x) is 0,
• 8. The perimeter of a square is 12 cm. Put two such squares together into a rectangle. How many cm is the perimeter of the rectangle?
• 9. In Cartesian coordinates, the inclination angle of the line x + 3y-3 = 0 is () A. π6B. π3C. 5π6D. 2π3
• 10. Z = arctan (XY), and y = e ^ x, find DZ / dy
• 11. 1. Given that the absolute value of equation x = ax + 1 has a negative number solution but no positive number solution, find the value range of A 2. If a, B and C are all integers, and the absolute value of A-B to the 19th power plus the absolute value of C-A = 1, then what is the absolute value of C-A plus the absolute value of B-C plus the absolute value of B-A
• 12. There are 10000 hectares of cultivated land in a certain place. After 10 years of planning, the grain yield per unit area will increase by 20% and the per capita grain share will increase by 10%. If the annual population growth rate is 1%, how many hectares of cultivated land can be reduced at most every year? (accurate to 1 hectare) We should use the permutation and combination quadratic term theorem to solve the problem
• 13. Solving mathematical problems! The process of solving problems is required 1. Given that CD is the middle line of triangle ABC, BC = 10cm, AC = 7cm, what is the perimeter difference between triangle BCD and triangle ACD? 2. The perimeter of an isosceles triangle is 25cm. The median line on one waist divides the perimeter into two parts: 3:2? 3. If one internal angle of an isosceles triangle is 80 degrees, then the degrees of the other two internal angles are -? 4. In the triangle ABC, if the angle a is 90 degrees, BD is the bisector of the angle, De is perpendicular to BC and E is the midpoint of BC, then the angle ABC is equal to -? 5. The length of the base of an isosceles triangle is 5cm. If the difference between the two parts is 3cm, the waist length is -? How many significant numbers are there in the approximate number of 24000, accurate to - digits? 7. The 1998 power of minus 2 times its 1999 power equals? 8. Given that the lengths of three sides of a triangle are 14, 4x and 3x respectively, the value range of X is -? 9. For a piece of land with a triangle (acute angle or right angle), it is required to draw a line segment through a certain vertex of the triangle and divide its area into two parts equally. How do you think this line segment should be drawn? How much is the 2005 power of 10.2 multiplied by the 2006 power of 0.5?
• 14. A mathematical problem about probability, the process of solving the problem At present, a, B, C three people participate in a competition, three people have similar strength, and the probability of winning or losing is 50% Q1: A's chance to win two games in a row Probability of Q2: B continuous transmission of two fields Q3: the probability of a losing two games in a row and B losing two games in a row AB AC BA BC CA CB
• 15. There are 10 products in three grades, including 4 first-class products, 3 second-class products and 3 third-class products. If any 2 products are selected from 10 products, the probability of taking out 2 products of the same grade is 0______ ．
• 16. In order to reduce the number of matches, 20 teams are divided into two groups (10 teams in each group) for competition, and the probability of (1) the strongest two teams being divided into different groups and (2) the probability of being divided into the same group is calculated.
• 17. Two mathematical problems of probability, When a store holds a celebration activity, customers can randomly select 2 different gifts from the 4 kinds of gifts when their consumption reaches a certain amount. The probability that one of the gifts selected by any two customers has the same variety is zero___ . The startup password of a device is composed of three different numbers from 0 to 9. If the wrong password is input three times in a row, the device will be shut down permanently. The probability that a person who only remembers that the password is composed of three different numbers can start some devices is 0___ .
• 18. Finding the minimum value of a2-2a-6 Given that the value of the algebraic formula x2 + y2-14x + 2Y + 50 is 0, find the value of X and y Given x (x + 1) - (x2 + y) = - 3, find the value of x2 + y2-xy ——— two X2 = x square y2 = y square The third problem is known as X (x + 1) - (x2 + y) = - 3 to find (2 / 2 x2 = Y2) - XY
• 19. 1. There is a group of numbers arranged according to a certain rule. The order is 2, - 5,9, - 14,20, x, 35 Can you find the value of X? What's the value of X? 2. An ant crawls on a straight line of a chessboard, and the right is the positive direction. For the first time, it climbs one unit to the right from point a, for the second time, it climbs two units to the left to point B, and for the third time, it climbs three units to the right to point C In this way, it has been climbing 20 times to A. point. Given that A. point represents - 18, what number does a point represent? 3. Given that the number represented by point a is - 27 and point B is - 15 on the number axis, find the distance between two points ab To solve this problem, several students put forward the following calculation schemes: A: The larger number minus the smaller number, that is - 15 - (- 27) = 12 B: Subtract the larger number from the smaller number, i.e. - 27 - (- 15) = - 12 C: The absolute value of the difference between the preceding number and the following number, that is | - 27 - (- 15) | = 12 D: The absolute value of the difference between the latter and the former, that is | - 15 - (- 27) | = 12 E: Draw the number axis, actually count the number, that is (here is the number axis), the distance is 12 Which plan do you think is not correct, and explain the reason. Can you think of other plans? What else do you think you should pay attention to the distance between the two points of the ball?
• 20. [1/3-(-1/9)+5/12]×(-36) 19 and 15 / 16 × (- 8) (1 and 1 / 2) × (- 1 and 1 / 3) × (- 1 and 1 / 4) × 1 and 1 / 5) × (- 1 and 1 / 6) × (- 1 and 1 / 7)