20 12
20 1 1 year
20 10 year
In 2009
the year of 2008
In 2007
In 2006
In 2005
In 2004
24. An enterprise invested 1 10,000 yuan to introduce an agricultural product processing production line. If maintenance costs are not included, it is estimated that the annual profit of the production line will be 330,000 yuan after it is put into production. After the production line is put into production, the cumulative maintenance cost from 1 year to x years is y (ten thousand yuan), and y=ax2+bx. If it remains at 1 year,
(1) Find the analytical formula of y;
(2) In what year will the enterprise recover its investment after it is put into production?
In 2003
24. A scenic spot adjusts the ticket prices of five tourist attractions. According to statistics, the number of tourists in various scenic spots remained basically unchanged before and after the price adjustment. Relevant data are shown in the following table:
Attractions? A b? C D？ E
Original price (RMB)101015 20 25
Current price (yuan)? 5 5 ? 15 25? 30
Average number of people per day (thousands) 1 1? 2 ? 3 2
(1) The scenic spot indicated that the average ticket fees of these five scenic spots remained unchanged before and after the adjustment, and the average daily gross income was flat. How is the scenic spot calculated?
(2) On the other hand, tourists think that the average daily gross income of scenic spots has actually increased by about 9.4% after adjusting the fees. How do tourists count?
(3) Which statement do you think can better reflect the overall reality, scenic spots or tourists?
25. (Innovative learning) As shown in the figure, the shape of an isosceles triangle is different from that of a regular triangle. We call the closeness between isosceles triangle and regular triangle "positive degree". When studying the "positive degree", we should ensure that similar triangles's "positive degree" is equal.
Let the base and waist of an isosceles triangle be A and B respectively, and the base angle and vertex angle are α and β respectively. The value of "Positive Degree" must be non-negative.
Classmate A thinks that the formula |a-b| can be used to express "positive degree", and the smaller the value of |a-b|, the closer the isosceles triangle is to the regular triangle;
Classmate B thinks that "positive degree" can be expressed by the formula | α-β |, and the smaller the value of | α-β |, the closer the isosceles triangle is to the regular triangle.
Inquiry: (1) Which of their schemes is more reasonable and why?
(2) Please improve the scheme you think is not reasonable enough (just give the formula);
(3) Please give another expression to measure "correctness".
26. Other issues:
To allocate the places of 29 math competitions to 10 schools, each school must allocate at least one place.
(1) Try to propose an allocation scheme so that less than four schools can be allocated the same number of places;
(2) Proof: No matter how it is allocated, at least three schools get the same number of places;
(3) Proof: If less than 4 schools allocate the same quota, at least 5 of the 29 contestants are from the same school.