Test questions for Fill in the blanks: 1. If a and B are reciprocal, then a is proportional to B 2. The thickness of a water cup is uniform, and the depth of water is proportional to the volume of water 3. A precision part is drawn by 5:1 on the drawing, the length is one centimeter, the actual length is 5cm, if the actual width is 0.1cm, then the width on the drawing is () cm 4. The rectangle has a certain area, and its length and width are in proportion 5. 3cm on a map represents the actual 60km. The scale of this map is (), the actual distance is 150km, the distance on the map is (), the distance on the map is 4.5cm. The actual distance is () km 6. When a circle is enlarged by 3:1, the perimeter is () times of the original perimeter and the area is () times of the original area 7. After a kind of rice is rolled into rice, the ratio of rice to rice bran is 7:3. At present, 400 kg of rice is rolled into () kg of rice and () kg of rice bran 8. When a triangle is enlarged by 3:1, the three sides are 9cm, 12cm and 15cm respectively, then the original lengths of the three sides are () () () 9. Draw a circle with a circumference of 6.28 meters on a scale of 1:100 with a radius of () 10. The area of a triangle is 12 square centimeters. What's the area of a figure when you put it under a magnifying glass that can magnify 4 times 11. In the scale of 3.6: x = 4:5, the value of X is () 1. A book on page a has read page B in 5 days, and the rest will be finished in X days A.B:5=A：X B.B:5=(A-B):X C.A:5=B:X 2. About the perimeter, side length and area of a square, the following description is correct () A. The area is proportional to the side length B. Perimeter is in direct proportion to area C. Perimeter is in direct proportion to side length 3. The following two quantities are inversely proportional () A. Circumference and diameter of a circle B. Volume and height of cylinder C. Total price is fixed, quantity and unit price

Test questions for Fill in the blanks: 1. If a and B are reciprocal, then a is proportional to B 2. The thickness of a water cup is uniform, and the depth of water is proportional to the volume of water 3. A precision part is drawn by 5:1 on the drawing, the length is one centimeter, the actual length is 5cm, if the actual width is 0.1cm, then the width on the drawing is () cm 4. The rectangle has a certain area, and its length and width are in proportion 5. 3cm on a map represents the actual 60km. The scale of this map is (), the actual distance is 150km, the distance on the map is (), the distance on the map is 4.5cm. The actual distance is () km 6. When a circle is enlarged by 3:1, the perimeter is () times of the original perimeter and the area is () times of the original area 7. After a kind of rice is rolled into rice, the ratio of rice to rice bran is 7:3. At present, 400 kg of rice is rolled into () kg of rice and () kg of rice bran 8. When a triangle is enlarged by 3:1, the three sides are 9cm, 12cm and 15cm respectively, then the original lengths of the three sides are () () () 9. Draw a circle with a circumference of 6.28 meters on a scale of 1:100 with a radius of () 10. The area of a triangle is 12 square centimeters. What's the area of a figure when you put it under a magnifying glass that can magnify 4 times 11. In the scale of 3.6: x = 4:5, the value of X is () 1. A book on page a has read page B in 5 days, and the rest will be finished in X days A.B:5=A：X B.B:5=(A-B):X C.A:5=B:X 2. About the perimeter, side length and area of a square, the following description is correct () A. The area is proportional to the side length B. Perimeter is in direct proportion to area C. Perimeter is in direct proportion to side length 3. The following two quantities are inversely proportional () A. Circumference and diameter of a circle B. Volume and height of cylinder C. Total price is fixed, quantity and unit price

Fill in the blanks:
1. If a and B are reciprocal, then a and B are in inverse proportion
2. The inner thickness of a water cup is uniform, and the depth of water is proportional to the volume of water
3. A precision part is drawn by 5:1 on the drawing, the length is one centimeter, the actual length is 5cm, if the actual width is 0.1cm, then the width on the drawing is (0.02) cm
4. A rectangle has a certain area, and its length and width are in inverse proportion
5. On a map, 3cm represents the actual 60km, the scale of this map is (1:20000), the actual distance is 150km, the distance on the map is (7.5cm), the distance on the map is 4.5cm, and the actual distance is (90km)
6. When a circle is enlarged by 3:1, the perimeter is (3) times of the original perimeter and the area is (9) times of the original area
7. After a kind of rice is rolled into rice, the ratio of rice to rice bran is 7:3. At present, 400 kg of rice is rolled into 280 kg of rice and 120 kg of rice bran
8. When a triangle is enlarged by 3:1, the three sides are 9cm, 12cm and 15cm respectively, then the original lengths of the three sides are (3cm) (4cm) (5cm)
9. Draw a circle with a circumference of 6.28 meters on a scale of 1:100 with a radius of (1cm)
10. The area of a triangle is 12 square centimeters, and the area of the figure seen under a magnifying glass that can magnify 4 times is? (12cm & sup2;)
11. In the scale of 3.6: x = 4:5, the value of X is (4.5)
choice question:
1. A book on page a reads page B in 5 days, and the rest will be finished in X days. The correct proportion is (b)
A.B:5=A：X
B.B:5=(A-B):X
C.A:5=B:X
2. About the perimeter, side length and area of a square, the following description is correct (c)
A. The area is proportional to the side length
B. Perimeter is in direct proportion to area
C. Perimeter is in direct proportion to side length
3. The following two quantities are inversely proportional to (c)
A. Circumference and diameter of a circle
B. Volume and height of cylinder
C. Total price is fixed, quantity and unit price

In 2002, the Chinese Academy of Sciences and the Chinese Academy of engineering had 1263 academicians, including 1185 male academicians. What percentage of academicians were female academicians?

(1263-1185) △ 1263, = 78 △ 1263, ≈ 0.062, = 6.2%; a: female academicians account for 6.2% of the total number of academicians

An application problem of inverse proportion function that can't be solved
A unit spent 500000 yuan to buy back a high-tech equipment. According to the follow-up investigation of this type of equipment, if the maintenance and repair costs are shared equally to one day after the equipment is put into use, the conclusion is that the maintenance and repair costs payable on the x day are [1 / 4 * (x-1) + 500] yuan
(1) If the sum of the maintenance and repair cost and the purchase cost of the equipment from the beginning of use to the end of life is shared equally to each day, it is called the average daily loss. Please express the average daily loss y (yuan) as a function of the service days x (days)
(2) According to the technical and safety management requirements of the industry, when the average loss of the equipment reaches the minimum, it should be scrapped. How many days should the equipment be scrapped?
Note: A. for any positive integer n, the following equation must hold 1 + 2 + 3 + 4 + '+ n = n (n + 1) / 2
B. For certain normal numbers a, B and variable x in the range of positive real number, there must be
A / x + X / B is greater than or equal to 2 times the root sign ax / BX and = 2 times the root sign a / b holds
The root sign a / b of 2 times is a constant, that is to say, the function y = A / x + X / B has the minimum value of 2 times
And when a / x = x / B, y gets the minimum value} (can be directly referenced if necessary)
A. (conclusion in B)
I've been thinking about it for more than an hour

(1) The total cost of maintenance and repair for X days: [(1-1) + (2-1) +... + (x-1)] / 4 + 500X = [(1 + 2 + 3 +... + x) - x] / 4 + 500X = [x (x + 1) / 2-x] / 4 + 500X = x (x-1) / 8 + 500X y = 500000 / x + (x-1) / 8 + 500 = 500000 / x + X / 8 + 3999 / 8, which is the function

An applied problem of inverse proportion function
A unit spent 500000 yuan to buy back a high-tech equipment. According to the follow-up investigation of this type of equipment, if the maintenance and repair costs are shared equally to one day after the equipment is put into use, the conclusion is that the maintenance and repair costs payable on the x day are [1 / 4 * (x-1) + 500] yuan
(1) If the sum of the maintenance and repair cost and the purchase cost of the equipment from the beginning of use to the end of life is shared equally to each day, it is called the average daily loss. Please express the average daily loss y (yuan) as a function of the service days x (days)
(2) Will the average loss reach 1124 and 7 / 8?

(1)
Total cost of maintenance and repair for X days:
[(1-1)+(2-1)+...+(x-1)]/4+500x
=[(1+2+3+...+x)-x]/4+500x
=[x(x+1)/2-x]/4+500x
=x(x-1)/8+500x
y=500000/x +(x-1)/8+500
=500000/x+x/8+3999/8
This is the function
(2) When y = 1124 and 7 / 8
500000 / x + X / 8 + 3999 / 8 = 1124 and 7 / 8
x1=1000,x2=4000
So it will
I wish you study every day, come on!

Application of inverse proportion function in grade two of junior high school
If the images of the inverse scale function y = - 6 / X and the first-order function y = mx-2 pass through the point P (a, 1) (1), find the coordinates of the point P (2), find the expression of the first-order function y = mx-2 and its intersection with the X axis

If y = - 6 / X passes through P (a, 1), 1 = - 6 / a leads to a = - 6, and the coordinate of P is (- 6,1)
The image of y = mx-2 passes through the point P (- 6,1) to get 1 = m (- 6) - 2 1 + 2 = - 6m-2 + 2 = - 6m M = 3 / (- 6) = - 1 / 2 note negative half
The expression of linear function y = mx-2 is y = - X / 2-2
Let y = - (1 / 2) X-2 = 0 to get x = - 4, and let the intersection of y = - (1 / 2) X-2 and X-axis be (- 4,0)

Solving practical problems with quadratic equations of two variables,
A city regulation: the farthest distance allowed for taxi starting price is 3km, and the part over 3km will be charged for each kilometer. A said: "I took this taxi for 11km and paid 17 yuan." B said, "I took this taxi for 23 km and paid 35 yuan. "Please calculate the starting price of this kind of taxi, and how much is the fare per kilometer after the distance exceeds 3km?

Let the starting price of taxi be x and the fare per kilometer be y. The equations are as follows:
A: x + (11-3) y = 17
B: x + (23-3) y = 35
The solution is: x = 5, y = 1.5
So the starting price of a taxi is 5 yuan, and the fare per kilometer is 1.5 yuan

Application problems of quadratic equation of two variables
How many bolts and nuts can each worker produce an average of 20 bolts and nuts per day?

Suppose x people should be assigned to produce bolts and y people to produce nuts
x+y=60
14*2x=20y
The solution is: x = 25
y=60-x=35
A: 25 people should be assigned to produce bolts and 35 people to produce nuts, so that the bolts and nuts can be just matched

Apply the problem to get the answer,
A train is 230 meters long and a slow train is 220 meters long. If two trains are running in the same direction, it takes 90 seconds for the express train to catch up with the slow train and leave the slow train. If two trains are running in the opposite direction, it only takes 18 seconds for the express train to leave the slow train when the slow train meets. What are the speeds of the express train and the slow train?
The distance between the two wharves is 240km. A ship sails between the two wharves for four hours downstream and six hours upstream. The speed of the ship in still water and the speed of water flow can be calculated

Let the slow train speed be x m / s and the fast train speed be y m / s
（y-x）×90=220+230
（y+x)×18=230+220
Solution
x=10
y=15
(2) The speed of the ship in still water is x km / h, and the speed of the water is y km / h
(x+y)*4=240
(x-y)*6=240
The solution is: x = 50, y = 10
You can understand, agree

Application problem! Binary linear equation! Solution! Process and result!
There is only one car for a class to go for an outing in Beishan, which is 18 kilometers away. They need to be divided into two groups. Group A takes the car first, and group B walks. When the car goes to a, group A gets off the car and walks, and the car returns to group B. the last two groups arrive at Beishan at the same time. The known speed of the car is 60 km / h, and the walking speed is 4 km / h

Suppose that the first passenger gets off at point a on the way and the car runs for X hours, then the first passenger gets off at point a and then has to walk (18-60x) km to Beishan station. The walking time is: (18-60x) / 4 hours. Group a needs a total of time: X + (18-60x) / 4 hours. When the car returns, the last passenger has walked 4x km

1. Party A and Party B set out from AB, with a car of 50 kilometers per hour and an art car of 75 kilometers. After 1.4 hours, the ratio of the distance traveled to the rest is 5:6. How many kilometers are there between AB and Party A
2. The sum of a number and its own sum, difference and quotient is 12.2. What's the number
3. The circumference of a semicircle with an area of () square meters is 15.42 meters

1. After 1.4 hours, the distance of line a is 50x1.4 = 70km, and that of line B is 75x1.4 = 105km, so the total distance of the two vehicles is 105 + 7 = 175km
The ratio of the distance traveled to the distance left is 5:6, so the distance left is 175x6 / 5 = 210km
The distance between a and B is 175 + 210 = 385km
2. If the sum of a number and itself is twice, the difference between the number and itself is 0, and the quotient between the number and itself is 1, so the original number = (12.2-1-0) / 2 = 5.6
3. The circumference of semicircle = (π * r + 2 * r) = 15.42 m, and the radius r = 15.42 / (π + 2) = 3 m
Area of semicircle = π * r * r / 2 = 3.14 * 3 * 3 / 2 = 14.13 square meters