I wish you progress in your study!
1. One of the messages of Expo 2010 is that a low-carbon life is a necessary condition for sustainable development. Low-carbon life requires everyone to change their living habits and start from every little thing in life. For example, instead of buying two pairs of socks with different styles and colors as in the past, buy two pairs (four pairs of the same socks) to wear in turn. For these two pairs of socks, according to the previous habit, as long as one sock is broken, this pair of socks will be scrapped; After changing your habits, you should rotate three socks when one sock is broken, and then consider buying socks until the third sock is broken.
1) Please tell people to buy n pairs (N> 1) of socks. What's the difference between the service life of socks that are worn in rotation and those that are not (one pair is worn out and then replaced)?
2) Write your comprehensive report.
2. During the closing of the Hangzhou World Expo, the Carnival Playground invested 6.5438+0.5 million yuan to introduce large-scale amusement facilities. If the maintenance fee is not included, it is estimated that it will generate 330,000 income every month after opening. After the amusement facilities are opened, the cumulative maintenance cost from 654.38+0 to X is Y (ten thousand yuan), Y = AX2+BX；; If the net income of amusement park after deducting investment and maintenance expenses is called G (ten thousand yuan), G is also a quadratic function about X 。
(1) If 1 month's maintenance cost is 20,000 yuan, and the next month's maintenance cost is 40,000 yuan, find the analytical formula of Y about X;
(2) Find the analytical formula of the net income g of X;
(3) Q: After the facilities were opened for several months, the net income of the playground reached the maximum? In a few months, you can recover your investment.
Solution: (1) y = x2+x;
(2) Net income G =-x2+32x-150;
(3)g=-(x- 16)2+ 106, that is, the net income of the amusement park reaches the maximum after the design opening 16 months; At 0
3. Regarding the 20 10 Shanghai World Expo, there is a report in China News Online: "There is no complimentary ticket for the Shanghai World Expo, and children under 1.2 meters (including 1.2 meters) can get free tickets. Discount tickets for designated days and working days are applicable to disabled people, people born years ago, and students in general higher education, high school education and compulsory education.
The designated daily ticket ordered by Teacher Wang of A school is RMB, and the weekday ticket ordered by Teacher Li of B school is RMB. It turns out that they booked the same number of tickets. As we all know, there are more tickets for designated days than for weekdays. According to the existing information, can you calculate the price of the designated day ticket and the flat day ticket for the 20 10 Shanghai World Expo? Give it a try!
Solution: If the weekday ticket price of 20 10 Shanghai World Expo is RMB, the daily ticket price is RMB.
6000/(X+40-80)=5000/(X-60), that is, 6/(X-40)=5/(x-60).
Solve the equation and get X= 160.
x= 160，x+40=200
A: On 20 10, if the ticket price for the Shanghai World Expo is RMB on weekdays, the ticket for the designated day will be 200 yuan.