A: According to your question, the following is the application of junior high school algebra in life, work and science:

First, the application in life:

Since the day when human beings appeared on the earth, people have gradually gained a profound understanding of mathematics while understanding and transforming the world. As early as ancient times, there was a legend that primitive people "dabbled in counting" and "knotting a rope". This is the earliest application of algebra in life!

For example, when we shop, rent a car or stay in a hotel, operators often provide us with two or more payment schemes or preferential measures for publicity, promotion or other purposes. At this time, we should think twice, dig deep into the mathematical knowledge in our minds and make wise choices.

Preferential activities: May 1 "Give back to guests" tea set preferential activities. There are two specific preferential schemes: (1) sell one and get one free (that is, buy a teapot and send a teacup); (2) 10% discount (that is, 90% of the total purchase price). There is also a prerequisite: buy more than three teapots (teapot 20 yuan/one, teacup 5 yuan/one). From this, we should think: Is there a difference between these two preferential measures? Which is cheaper? We naturally think of functional relations and apply the learned functional knowledge to analyze this problem.

Solution: Suppose a customer bought X teacups and paid Y yuan (x>3 and x∈N), then

Pay y1= 4× 20+(x-4 )× 5 = 5x+60 according to the first method;

Use the second method to pay y2=(20×4+5x)×90%=4.5x+72.

Then compare the relative sizes of y 1y2.

Let d = y1-y2 = 5x+60-(4.5x+72) = 0.5x-12.

Discussion:

When d>0, 0.5x-12 >; 0, namely x & gt24;

When d=0, x = 24.

When d < 0, x

To sum up, when buying more than 24 teacups, method (2) saves money; When only 24 pieces are purchased, the prices of the two methods are equal; When the number of purchases is only between 4 and 23, the method (1) is cheap.

Visible, using a function to guide shopping, that is, exercise the mathematical mind, divergent thinking, but also save money, put an end to waste, really kill two birds with one stone!

Second, the application in the work:

In our work, we often encounter such a problem: under what conditions can we use the least materials to obtain the maximum profit and the highest efficiency. These problems are usually called optimization problems, but they are actually algebraic application problems:

1. What is the most material-saving problem that engineers will encounter in design: What is the ratio of the height to the diameter of cans?

Through the application of algebraic calculation, when the ratio of height to diameter is 2: 1, the materials used in cans are the least.

We have measured that the height of 355ml Coca-Cola cans is 122 and the diameter is 65 (the ratio is 2: 1.06). Other 355ml cans, such as Tsingtao Brewery, Budweiser Brewery, Uniform Iced Black Tea and Uniform Fresh Orange Blossom, have the same ratio.

Another example is Nestle Coffee 180ml, with a height of 10.5mm and a diameter of 54mm (the ratio is 2: 1.02).

2. A manufacturer produces and sells some spherical bottled drinks. The manufacturing cost of the bottle is 0.8pr2, where r is the radius of the bottle in cm. It is known that the manufacturer can make a profit of 0.2 per 1 ml of beverage, and the maximum radius of the bottle that the manufacturer can manufacture is 6 cm. When is the profit per bottle of drinks the biggest and the smallest?

Through algebraic knowledge, we can deduce that:

When the radius of the bottle is 6cm, the profit of each bottle of beverage is the largest.

When the radius of the bottle is 2cm, the profit of each bottle of beverage is the smallest.

3. Given that the daily production cost of X products in a factory is A, how many products should be produced every day to minimize the average cost?

All of the above are living examples of algebra at work!

Second, the application in science:

Mathematician Hua pointed out that "the size of the universe, the size of particles, the speed of rockets, the change of the earth, the mystery of biology and the complexity of daily life" are all inseparable from mathematics.

Without mathematics, the successful launch of Shenzhou series spacecraft is based on applied science, which is based on mathematics. In this way, mathematics will surely become the most powerful accelerator for the rapid development of society and push the society forward; Mathematics will be the golden key to open the door of science hall and help us to have a treasure house of knowledge; Mathematics will give us the most powerful wings and let us fly to a brilliant tomorrow. For the prosperity of our motherland, for our leisurely life and for our work to run according to our own expectations, there is no reason why we should not make ourselves a person with a "mathematical mind".

The future world is a modern scientific world, and future science is a mathematical science.

China's tests to develop an atomic bomb are only one-tenth that of western countries. It took only two years and three months from the atomic bomb explosion to the successful development of the hydrogen bomb, which was much shorter than that in the United States. One of the reasons is that many outstanding mathematicians have been selected to participate in the development work.

The Three Gorges Project of the Yangtze River has attracted worldwide attention. According to the design, the total installed hydropower capacity of the Three Gorges Project is 65.438+07.68 million kilowatts, and the annual power generation is 84 billion kWh. When the Three Gorges Dam is completed, it will be a concrete dam with a height of 200 meters and a length of nearly 2000 meters, which is simply a concrete hill. There are countless problems to be solved in the construction of such a grand project, and the most important one is the heat generated by the chemical reaction of mass concrete during the setting process. This huge heat will endanger the safety of the dam. The computer software developed by scientists in China can dynamically simulate the temperature, stress and creep of mass concrete construction, can be used to analyze and compare various construction schemes, design the best construction process control, and can also be used to monitor the operation period after the completion of the dam to ensure the safety of the dam. It can be said that mathematics has played an important role in the construction of the Three Gorges Dam.

Mathematics plays an important role in modern war. Some people say that World War I was a "chemical war" (gunpowder). The Second World War was a "physical war" (machinery), and the modern war was a "mathematical war" (information and computers).

During the 1998 flood in China, in order to ensure the safety of large industrial cities such as Wuhan and Nanjing, the relevant departments faced the problem of Jingjiang flood diversion. 20 tons of explosives have been loaded and the countdown to blasting has entered, but this plan was abandoned at the last minute. According to the news report at that time, the water conservancy expert group composed of many experts used the finite element method in mathematics to calculate the volume leakage of Jingjiang levee and determined a safety factor. According to this result, even if the water level in Shashi rises to 45.3 meters, the Yangtze River levee can be strictly defended without flood diversion.

Summary: The application of mathematics is very extensive, ranging from the calculation of daily life, interest rate, insurance and medical expenses to astronomical geography, environmental ecology, information network, quality control, management and prediction, large-scale engineering, agricultural economy, national defense science and aerospace industry.

Try to learn math well! You will benefit for life!