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A cuboid glass jar is 40 cm long, 25 cm wide and 12 cm deep. After a stone is immersed in water, the water surface rises to 16 cm and the volume of the stone is calculated
40 × 25 × (16-12) = 1000 × 4, = 4000 (CC); a: the volume of stone is 4000 CC
A cuboid glass jar is 5 decimeters long and 3 decimeters wide from the inside. The current water depth is 1.5 decimeters,
The depth of water is 2 decimeters. What is the volume of this stone
5 × 3 × (2-1.5) = 7.5 cubic decimeter
What is a nonsingular matrix? What is the eigenvalue of a matrix? What are the steps to solve the eigenvalue?
If the determinant of matrix A of order n is not zero, that is | a | ≠ 0, then a is called a nonsingular matrix, otherwise a is called a singular matrix. Let a be a square matrix of order n. if there exists a number m and a nonzero n-dimensional column vector & nbsp; X such that ax = MX holds, then M is an eigenvalue of A. AX = MX is equivalent to finding m such that (me-a) x = 0, where e is the unit
If x > 0y > 0,2 / x + 8 / y = 1, what is the minimum value of XY?
2/x+8/y=1 =>xy=2y+8x
According to Cauchy inequality,
(2 / x + 8 / y) (8x + 2Y) > = [radical (2 / X * 8x) + radical (8 / y * 2Y)] ^ 2 = 64
=>xy=2y+8x>=64
Absolute definite integral?
∫ upper limit 2, lower limit - 1 | 2x | DX
∫ upper limit 2, lower limit - 1 | 2x | DX
=∫[-1,2]|2x|dx
=∫[-1,0]-2xdx+∫[0,2]2xdx
=-x^2|[-1,0]+x^2|[0,2]
=-[0^2-(-1)^2]+2^2-0^2
=-(0-1)+4-0
=1+4
=5
It is an interesting phenomenon that the product of multiplication of two numbers equals the difference between them
For example: one by two = 1-2 / 1, 2 / 1 * 1 / 3 = 1 / 2 minus 1 / 3, 2 / 3 * 2 / 5 = 2 / 3-2 / 5
One third * one fourth = one fourth minus one fourth
1 / 99 * 1 / 100 = 1 / 99 minus 1 / 100
Calculation formula of cylinder volume
Side area of cylinder = circumference of bottom circle × height
Surface area of cylinder = area of upper and lower bottom surface + side area
Volume of cylinder = bottom area × height
How many natural numbers (including 0) less than 1000 without repeated numbers can be composed of numbers 0, 1, 2, 3 and 4?
Because the hundreds cannot be 0, there are 48 positive integers with three digits less than 1000. Because the tens cannot be 0, there are 16 positive integers with two digits less than 1000, and there are 5 positive integers with one digit less than 1000. Therefore, there are 48 + 16 + 5 = 69. A: 69 natural numbers less than 1000 can be composed of 0, 1, 2, 3 and 4
Given that the solution set of inequality x + 8 ＞ 4x + m (M is a constant) is x ＜ 3, find M
Because x + 8 ＞ 4x + m, x-4x ＞ M-8, - 3x ＞ M-8, X ＜ - 13 (M-8). Because its solution set is x ＜ 3, so - 13 (M-8) = 3. The solution is m = - 1
The municipal company plans to purchase 500 seedlings of a and B for greening a section of the light splitting belt along the river, 50 yuan for each seedling of a and 80 yuan for each seedling of B. relevant statistics show that the survival rates of a and B are 90% and 95% respectively. It is hoped that the survival rate of these seedlings is not less than 92%, and the cost of purchasing seedlings is the lowest. How to purchase seedlings
1: If x seedlings of type A were purchased, then 500-x seedlings of type B were purchased
50x+80(500-x)=28000
x=400
There are 400 seedlings of type A and 100 seedlings of type B
2: If x seedlings of type A were purchased, then 500-x seedlings of type B were purchased
50x+80(500-x)≤34000
x≥200
When a is 200, it costs 34000 yuan to buy 500 trees
When a is 0, B is 425, which costs 34000 yuan;
When a is 200 strains, B is 300 strains, a total of 500 strains, cost 34000 yuan;
When a is 500, B is 0, and the cost is 25000 yuan;
3: If we hope that the survival rate of this batch of seedlings is not less than 92% and the cost of purchasing seedlings is the lowest, how to purchase seedlings?
If x seedlings of type A were purchased, then 500-x seedlings of type B were purchased
If x seedlings of type a can survive 0.9x, then 500-x seedlings of type B and 0.95 (500-x) seedlings of type B can survive
Total survival number = 0.9x + 0.95 (500-x) = 475-0.05x
Survival rate = (475-0.05x) / 500 ≥ 0.92
x≤300
The lowest cost is 50 * 300 + 80 * 200 = 31000 yuan
RELATED INFORMATIONS
- 1. The length, width and height of a cuboid are 12.5 cm, 8 cm and 3 cm respectively. In this cuboid, what is the sum of the areas of the largest two?
- 2. A rectangular glass with water has a bottom area of 60 square centimeters and a water depth of 8 centimeters. Now, after a cylinder iron block with a bottom area of 12 square centimeters is vertically placed in the water, some iron blocks are still exposed on the water. How many centimeters is the water depth now?
- 3. A cuboid glass can is 12 cm long, 8 cm wide and 5 cm high. When it is placed horizontally, the water depth is 3 cm. When it is placed vertically, how many cm is the water depth?
- 4. The newly built teaching building needs 150 cuboid drainage pipes with a length of 3 meters, a width of 1 decimeter and a height of 8 cm. The surface of the drainage pipe is a layer of iron sheet, which needs iron sheet How many square meters?
- 5. A piece of 8 cm long and 6 decimeter wide rectangular iron sheet is rolled into a cuboid with a square bottom. What is the maximum volume of this cuboid?
- 6. In order to measure the volume of a potato, Xiao Ming carried out an experiment according to the following steps: (1) put a certain amount of water into a cylindrical glass with a bottom diameter of 12 cm, and the height of the water surface is 7 cm; (2) put the potato into the water, and then measure the height of the water surface is 8 cm. If the thickness of the glass is ignored, what is the volume of the potato Centimeter? (the number obtained keeps the whole number)
- 7. In order to measure the volume of potatoes, Xiao Ming carried out an experiment as follows: Put a certain amount of water into a cylindrical glass with a bottom diameter of 8 cm, and the height of the water surface is 6 cm. Put the potato into the water, and then measure the height of the water surface again, which is 10 cm. If the thickness of the glass is ignored, how many cubic centimeters is the volume of the potato?
- 8. Cast a rectangular iron block of 10 cm long, 8 cm wide and 5 cm high into a cylinder iron block of 20 cm in diameter, and calculate the height of the cylinder iron block Two decimal places are reserved for the loss result
- 9. A cuboid with a length of 8 cm, a width of 5 cm and a height of 3 cm and a cube iron block with an edge length of 6 cm are melted and cast into a cylinder with a height of 10 cm to find a circle What is the area of the bottom of the column?
- 10. A rectangular iron block with a length of 10 cm, a width of 8 cm and a height of 7.85 cm is fused into a cylinder with a diameter of 8 cm at the bottom What is the height of this cylinder?
- 11. A cuboid glass jar is 40 cm long, 30 cm wide and 8 cm deep What is the volume of this stone in cubic decimeter?
- 12. A cuboid glass container is 20dm long and 15dm wide. The water depth in the container is 3.8dm Ask for guidance
- 13. A cuboid glass container is 20dm long and 15dm wide, and the water depth in the container is 3.8dm. After a cube iron block with 3DM edge length is put into the container, how much DM does the water surface in the container rise?
- 14. In a cuboid glass jar with a length of 50 cm and a width of 40 cm, put a cube iron block with an edge length of 10 cm. At this time, the water depth is 20 cm A piece of iron is taken out of the cylinder. What is the depth of water in the cylinder?
- 15. In a 12 cm long and 8 cm high rectangular water tank, submerge a cube with an edge length of 6 cm, and the water surface rises by 2 cm. What is the width of the rectangular water tank?
- 16. Fill a 15 cm square glass fish tank with water, then pour the water into a 20 cm long, 15 cm wide and 12 cm high rectangular tank
- 17. Fill a square glass jar with water whose edge length is 8 cm. Pour the water into another cuboid glass jar, which is 16 cm long and 10 cm wide The height is 5cm. How high is the poured water? There are three oil drums of a, B and C. the volume of B is 12 cubic decimeters larger than that of A. the volume of C is 13 cubic decimeters larger than that of B. the volume of C is twice that of A. what are the volumes of the three oil drums of a, B and C?
- 18. 1. A square glass tank with an edge length of 8cm is filled with water. Pour it into another cuboid glass tank with a larger volume. The length of glass fiber reinforced plastic is 16cm and the width is 10cm How many centimeters is the water poured in? 2. There are 51 students in class A and 49 students in class B. in a math test, the average score of all the students in the two classes is 81 points. It is known that the average score of class B is 7 points higher than that of class A. then the average score of class B is? Two questions need to be solved in detail
- 19. There is a cuboid glass tank with a bottom of 2 square decimeters. It contains 16 cm high water, which just accounts for 80% of the capacity of the glass fiber reinforced plastic. If it is filled with water, the glass tank will be empty How many liters of water can be added to the glass jar?
- 20. How many square decimeters of glass does it need to make a goldfish tank (without cover) 12 decimeters long, 5 decimeters wide and 8 decimeters high The price of glass is 0.8 yuan. How much does it cost to make this goldfish?