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How to distinguish positive proportion from negative proportion? Good points, don't break the formula, mixed points don't come
1) Positive proportion: two related quantities, one of which changes, and the other changes with it. If the ratio (quotient) of the two numbers corresponding to the two quantities is fixed, the two quantities are called positive proportion quantities, and their relationship is called positive proportion relations
What are the positive proportion and the negative proportion?
Positive proportion, positive proportion function
Inverse proportion, inverse proportion function
What is it?
Positive proportion: two related quantities, one of which changes, and the other changes with it. If the ratio (quotient) of the two numbers corresponding to the two quantities is fixed, the two quantities are called positive proportion quantities, and their relationship is called positive proportion relations. ① express with letters: if the letters x and y are used to express the two related quantities, and K is used to express their ratio, then the two quantities are called positive proportion relations, The (certain) positive proportional relationship can be expressed by the following formula:
② For example, if the speed of a car is fixed per hour, is the distance traveled in a positive proportion to the time spent?
Note: when judging whether the two related quantities are in a positive proportion, we should pay attention to the two related quantities. Although they are also one quantity and change with the change of the other, the ratio of the two corresponding quantities is not necessarily, For example, a person's age is not directly proportional to his weight, and the side length of a square is not directly proportional to his area. Inverse proportion: one of the two related quantities changes, and the other changes with it. If the product of the two corresponding quantities is fixed, the two quantities are called inverse proportion, The relationship between them is called inverse proportional relationship. It is indicated by letters: two related quantities, respectively "X" and "Y", and "K" means constant quantity. Then the inverse proportional relationship is: xy = K (certain). ② the change law of two related quantities of inverse proportional relationship is that one quantity expands, the other quantity shrinks, one quantity shrinks and the other quantity expands, For example: if the distance on the graph is constant, whether the actual distance and the scale are inversely proportional. Because the actual distance × scale = the distance on the graph (constant), the actual distance and the scale are inversely proportional. 3. The same point of positive proportion and negative proportion: two quantities are related, one quantity changes, and the other changes with it, The law of their expansion and reduction is that the ratio of the two numbers corresponding to the two quantities remains unchanged, that is, the quotient is fixed. The inverse proportion of the two quantities means that one quantity expands, the other quantity shrinks, the other quantity shrinks and the other quantity expands. The law of their change is that in the two quantities, The product of the two corresponding numbers is invariant
Inverse proportion
The inverse proportion relationship is to help students understand through the relationship between the total number and the number of copies. In the relationship between the total number and the number of copies, it includes the total number, the number of copies and the number of copies. When the total number is fixed, the number of copies and the number of copies are two related variables. If the number of copies changes, the number of copies also changes. Similarly, if the number of copies changes, the number of copies also changes, The product of the two corresponding quantities (i.e. the total number) is fixed. Specifically, when the total number is fixed, the number of each quantity (or the number of copies) increases or decreases several times, The number of shares (or the number of each share) is reduced or expanded by the same multiple. It is called "one expansion one contraction (or one contraction one expansion)". The number of shares and the number of shares with this change relationship are in inverse proportion. The inverse proportion relationship belongs to the aggregation problem in typical application problems. Reflected in division, when the divisor is fixed, the divisor and quotient are in inverse proportion, The denominator is inversely proportional to the score. In proportion, the preceding item of the ratio is fixed, and the following item of the ratio is inversely proportional to the ratio. If we further concretize the relationship between the total number and the number of shares as follows: in the shopping problem, the total price is fixed, and the unit price is inversely proportional to the quantity. In the itinerary problem, the route is fixed, and the speed and time are inversely proportional, If the two quantities are in inverse proportion, then the ratio of any two numbers of one quantity is equal to the inverse ratio of two corresponding numbers of the other quantity. For example, the total number of processed parts must be 600. If 10 parts are processed per hour, the task can be completed in 60 hours. If 20 parts are processed per hour, the task can be completed in 30 hours, 2 ∶ 1 is the inverse ratio of 1 ∶ 2
In the beginning of teaching, the students directly write the meaning of inverse proportion according to the meaning of positive proportion
Two related quantities - → two related quantities,
A quantitative change - → a quantitative change
The other quantity changes with it
The ratio of the two numbers corresponding to these two quantities is fixed - → the product of the two numbers corresponding to these two quantities is fixed
Then, according to the meaning of the inverse proportion written by students, give examples to verify
After that, we can further understand the meaning of inverse proportion
① Analyze the significance of inverse proportion
The quantity in inverse proportion includes three quantities, one quantity and two variables. This paper studies the expanding (or shrinking) relationship between two variables. The change of one quantity causes the opposite change of the other. These two quantities are in inverse proportion, and their relationship is in inverse proportion
② Anti proportional substance
Two related quantities, one of which changes, and the other changes with it. The product of the two corresponding numbers in the two quantities is certain. These two quantities are called inverse proportional quantities. Their relationship is called inverse proportional relations
Compare positive and negative proportion
Similarities: 1. Positive proportion and negative proportion contain three quantities, in which there is one quantity and two variables
② In the two variables of positive and negative proportion, one variable changes, and the other changes with it. And the way of change is to expand (multiply by a number) or reduce (divide by a number) several times
Difference: the quantitative of positive proportion is the ratio of two corresponding numbers in two variables. The quantitative of inverse proportion is the product of two corresponding numbers in two variables
How much is 99 * 100 * 101 1 / 100 plus 1 / 100
1/(99*100*101) + 1/100= (1 + 99*101) / (99*100*101)= (1+ (100+1)*(100-1)) / (99*100*101)= (1+10000-1) / (99*100*101)= 10000 / (99*100*101)= 100/ (99*101)= 100/9999
If the line passing through the focus of the parabola and perpendicular to the axis of the parabola intersects the parabola at P and Q, the Quasilinear of the parabola intersects the axis of the parabola at m, then the angle PMQ must be (right angle)
Since it's about parabola, you must have learned the problem of vector. So let the focus of parabola be on the positive half axis of x-axis (other cases can be deduced according to my following derivation). Let the equation of parabola be y & sup2; = 2px, that is, the focus coordinate is (P / 2,0) and the Quasilinear equation is x = - (P / 2), because PQ is too
Calculation method of steel weight
Who knows how to calculate the weight of steel;
Weight of round steel (kg) = 0.00617 × diameter × diameter × length; weight of square steel (kg) = 0.00785 × side width × side width × length; weight of hexagonal steel (kg) = 0.0068 × opposite side width × opposite side width × length; weight of octagonal steel (kg) = 0.0065 × opposite side width × opposite side width
Simple calculation of 5.56 × 4-4.56 △ 0.25
5.56×4 - 4.56÷0.25
= 5.56×4 - 4.56×4
= 4×(5.56 - 4.56)
= 4×1
= 4
Given the function f (x) = 4x-1, G (x) = x + 1
1. If f [g (x)] = 15, calculate the value of X
2. The domain of definition of the Torr function g (x) is (1,2). Find the domain of definitions of functions f [g (x)] and G [f (x)]
1.f[g(x)]=f(x+1)=4(x+1)-1=4x+3=15,x=3
2. If G (x) is defined as (1,2), then G (x) ∈ (2,3)
The definition field of F [g (x)] is (2,3)
Let 1 < f (x) < 2
And 1 ＜ 4x-1 ＜ 2
That is, 1 / 2 < x < 3 / 4
The domain of definition of [f (x)] is (1 / 2,3 / 4)
What is the density of cooking oil?
Peanut oil density: 0.9110 to 0.9180
Density of soybean oil: 0.9150 to 0.9375
For rational numbers a, B, definition: a * b = 3a-2b, if x, y are rational numbers, try to calculate [(x + y) * (X-Y)] * 2x
[(x+y)*(x-y)]*2x
=[3(x+y)-2(x-y)]*2x
=(x+5y)*2x
=3(x+5y)-2*2x
=-x+15y
The problem of double integral is related to the geometric meaning of double integral,
What are the geometric meanings of the double integrals of ∫∫ DXDY and ∫∫ DS on a certain surface e (the integrand function is 1). I hope I can explain them in detail,
What's the geometric meaning of this? It's very simple. Your integrand function is all 1. Don't you calculate the area of the plane and the surface of the area to be integrated? In detail, DXDY is the tiny area element of the plane. Double integration is to accumulate all these tiny area elements. It's just a limit process of getting finer and finer points and getting more accurate
RELATED INFORMATIONS
- 1. What's the difference between positive proportion and negative proportion? I didn't get it.
- 2. 2 (X & # 179;) & # 178; · X & # 179; - (4x & # 179;) & # 179; + (- 3x) & # 8308; · x M power of (X & # 179;) / N + 2 power of X · n-2 power of X The sixth power of (-) (-) / (-) / (-) / (-) / (-) / (-) / (-) / (-) / (-) / (-) / (-) / (-) / (-) / (-) / (-) / (-) / (-) / (-) / (-) / (-) / (-) / (-) / (-) / (-) / (-) / (-); （-ab）⁴÷﹙-ab）² （-3a²﹚²
- 3. Experiment junior high school grade 8 mathematics volume 2 Chapter 7 inequality test volume 9. If the degree of an acute angle is (5x - 35) °, then the value range of X is 10. The sum of the inner angles of an n-polygon is at least 150 degrees larger than the sum of its outer angles
- 4. Who can give me 20 questions of binary linear equations and 20 questions of unitary linear equations? Don't use questions! There must be a process! I want the process! No process, I don't!
- 5. Solving practical problems with linear equation of one variable A batch of saplings will be collected by each class according to the following methods: the first class will receive 100 saplings and the remaining 1 / 10 saplings, the second class will receive 200 saplings and the remaining 1 / 10 saplings, and the third class will receive 300 saplings and the remaining 1 / 10 saplings Finally, all the saplings are collected, and the saplings of each class are equal
- 6. The application of the equation of first degree with one variable, In order to meet the increasing demand of water consumption, Kunming recently built three new waterworks a, B and C. the daily water supply of these three waterworks is 118000 cubic meters, of which the daily water supply of B waterworks is three times of that of a waterworks, and that of C waterworks is 10000 cubic meters more than half of that of a waterworks (1) How many ten thousand cubic meters of water can be supplied each day? (2) In the construction of water supply pipeline of water plant a, 600 tons of earth and rock will be transported. The transportation company will send two kinds of trucks, type A and type B, 6 vehicles of type A and 4 vehicles of type B, to transport the earth and rock for 5 times respectively; or 3 vehicles of type A and 6 vehicles of type B, to transport the earth and rock for 5 times respectively? The key is to do (2) questions, (1) questions do not do nothing, but do (1) points plus I'm sorry, but I made a mistake (2) In the construction of the water supply pipeline of water plant a, 600 tons of earth and rock will be transported. The transportation company will send two kinds of trucks, type A and type B, 6 type a trucks and 4 type B trucks, to transport the earth and rock for five times. One type a truck and one type B truck can transport 25 tons of earth and rock. How many tons of earth and rock will each type a truck and each type B truck transport each time?
- 7. Practical problems of quadratic equations with two variables A supermarket sells 20 yuan for each teapot and 3 yuan for each teacup. The supermarket puts forward a promotion method: buy a teapot and get a teacup free. Xiaoming spends 170 yuan. Buy back the teapot and 38 teacups in total. How many teapots and cups do you buy back? A series of quadratic equations with two variables
- 8. Application problem, please use 2 yuan 1 solution A basketball player scored 24 points in 12 of 23 shots in a game. The number of two-point shots is twice that of three-point shots. How many three-point shots did the basketball player hit? How many two-point shots? How many free throws did he make?
- 9. It is known that x + Y-Z = 4 x^2+y^2-z^2=12 x^3+y^3-z^3=34 Find XYZ
- 10. Make up an application problem of solving the system of linear equations of two variables, so that the solution of the system of equations is 9,10
- 11. Two proportional application problems must be solved by X, and they must be solved by X, and they must be solved by the method of proportion 1. A plane with fuel can fly for 6 hours at most. It flies 1500 kilometers an hour downwind and 1200 kilometers an hour upwind when it goes back. How many kilometers should the plane fly back? (there are many answers on the Internet, but they are not what I want. What I want is to use the method of comparison and X solution.) 2. In the first half of the year, the automobile factory produced 260 cars, accounting for 60% of the whole year
- 12. Positive proportion and negative proportion 1. A has 150 grey rabbits, white rabbits and black rabbits. The number of white rabbits is 5 / 6 of that of black rabbits. The ratio of black rabbits to white rabbits is 4:5. How many grey rabbits are there? 2. For a classroom, 800 pieces of brick with a side length of 3DM should be used. If the brick with a side length of 4dm should be used, how many pieces should be used? 3. Fill in the blanks according to the proportion A 8 12 （ ） 2 24 （ ） B 6 4 15 （） （） 48
- 13. Simple calculation: (4 / 7 * 9 / 10 * 11 / 4) / (2 / 11 * 7 / 2 * 9 / 5)
- 14. A cylinder, the side is a square, its side length is 18.84 cm, the bottom radius of the cylinder is______ ．
- 15. Make a long-distance call from a to B, and charge 2.4 yuan within 3 minutes. After 3 minutes, charge 1 yuan more for every additional minute. Someone calls from a to B for t (t ≥ 3, t is an integer) minutes, and the charge is m yuan. Please write the functional relationship between M and t
- 16. The results showed that: 1 / 2:5 / 40.8:1.73 5 / 9:0.2 ratio; 3 5:42 1 / 2:5 / 40.8:1.73 5 / 9:0.2 ratio; 3 5:42 1 / 2:5 / 4 0.8:1.73 5 / 9:0.2 ratio; Reduction ratio What is ratio? Simplify ratio!
- 17. The price of a coat will be increased by 20% first and then reduced by 20%. Compared with the original price, the price of a coat will be increased by 20%
- 18. Ask "mathematics class practice and evaluation" seventh grade (1) self-evaluation (5.5
- 19. The sum of all integers whose absolute value is less than 5 is A：7 B：-7 C：0 D：5
- 20. What is the least common multiple of 10,15,18,24