There is water in a sealed rectangular glass fiber reinforced plastic. The lengths of the three edges intersecting one vertex of the glass jar are 10 cm, 6 cm and 5 cm respectively. Put the glass jar on the water surface in three different ways. The minimum height of water is 2 cm. What is the maximum height of water? (please draw a sketch and calculate it.)

There is water in a sealed rectangular glass fiber reinforced plastic. The lengths of the three edges intersecting one vertex of the glass jar are 10 cm, 6 cm and 5 cm respectively. Put the glass jar on the water surface in three different ways. The minimum height of water is 2 cm. What is the maximum height of water? (please draw a sketch and calculate it.)

The length, width and height are 10, 6 and 5 respectively. When the water surface is the lowest, the surface of 10X6 must be at the bottom, so the volume of water is 10x6x2 = 120. When the water surface is the highest, the surface of 6X5 must be at the bottom, so the water surface height is 120 / (6X5) = 4, and the maximum is 4cm

A sealed cuboid glass jar, 18 cm long, 12 cm wide and 20 cm high, contains 15 cm deep water. Now turn the glass jar over to make it clean
How many meters is the water depth? If you know, answer quickly!

The volume of water does not change
Volume of water = 18 × 12 × 15 = 3240 (cm3)
Current water depth = 3240 ÷ (20 × 12) = 13.5 (CM)

A sealed cuboid glass jar is partially filled with water. The glass jar is 20 cm long, 12 cm wide and 8 cm high My kind brother and sister help me
1. A sealed cuboid glass jar is filled with some water. The glass jar is 20 cm long, 12 cm wide and 8 cm high. Put the different sides of the glass jar on the table as the bottom. The minimum height of water is 5 cm. How many cubic centimeters of water is in the glass jar?
2. The school electricity classroom is 10 meters long, 8 meters wide and 2 meters wide. How many pieces of square wooden floor should be laid on the ground with a side length of 1.6 decimeters? If a 0.8 meter wide coating is applied around the wall, how many square centimeters is the area of the coating?
3. A cuboid wood block. After sawing off a small cuboid with a volume of 200 cubic centimeters, the remaining part is a cube with an edge length of 5 cm. What is the surface area of the original cuboid in square centimeters?

The larger the surface is, the lower the height is. The largest surface is 20 * 12 = 240 square centimeters, so the volume of water is 240 * 5 = 1200 cubic centimeters
210 meters = 100 decimeters, 8 meters = 80 decimeters, 3.2 meters = 32 decimeters, 100 * 80 / (1.6 * 1.6) = 3125
10 * 0.8 * 2 + 8 * 0.8 * 2 = 28.8 square meters = 288000 square centimeters
The two sides of the small cuboid sawn by 3 are square, so the length is 200 / (5 * 5) = 8 cm, so the surface area of the original cuboid is 5 * 5 * 2 + 5 * (5 + 8) * 4 = 310 square cm

The least common multiple of 56 and 60

4*14*15=840

Now there are three numbers 2, 6 and 8. Please make this number proportion. The ratio of the two ratios is 1 and one third. What is this number?

8：6=2：1.5

Judge whether the following propositions are true or false? If false, give counter examples; if true, give proof
An angle must be less than its complement
If two lines are parallel, the inner angles of the same side must not be equal

1 is a false proposition. If the obtuse angle is larger than its complement angle
When a straight line is perpendicular to the two parallel lines, the inner angles of the same side are 90 degrees

The sum of the three positive numbers in the arithmetic sequence is equal to 15, and the three numbers are added with 2, 5 and 13 to form the arithmetic sequence

(1) Let the three positive numbers of arithmetic sequence be A-D, a, a + D respectively
a-d+a+a+d=15,a=5
So the order of {BN} is 7-d, 10,18 + D
Have (7-d) (18 + D) = 100, d = 2 or D = - 13 (rounding off)
So the third term of {BN} is 5 and the common ratio is 2
From B3 = B1 &; 22, that is 5 = 4b1, B1 = 5 / 4
So {BN} is an equal ratio sequence with the first term of 5 / 4 and the common ratio of 2. The general formula is BN = 5 * 2 ^ (n-1) / 4
(2) The first sum of sequence {BN} Sn = (5 / 4) * (1-2 ^ n) / (1-2) = 5 * 2 ^ n / 4-5 / 4
Sn + 5 / 4 = 5 * 2 ^ (n-2), so S1 + 5 / 4 = 5 / 2,
[(Sn+1)+5/4]]/ [Sn+5/4]]=[5*2^(n-1)]/[ 5*2^(n-2)]=2
So {Sn + 5 / 4} is an equal ratio sequence with 5 / 2 as the first term and 2 as the common ratio

The function f (x) = - x ^ 2 + (m-2) x + 2-m is known, where m is a constant
(1) Prove that the image of function f (x) must pass through a fixed point
(2) If y = ∣ f (x) ∣ is a monotone decreasing function on [- 1,0], find the value range of real number M
(3) Is there a positive integer a such that the solution set of a ≤ f (x) ≤ B is exactly [a, b]? If there is, the value of a and B is requested. If not, the reason is given

(1) Let x = - 1, then y = - 1
Constant passing point (- 1, - 1)
(2)
(a) If discriminant (m-2) ^ 2 + 4 (2-m)

The monkey king has changed into two. One of the two has become two. There are four in all. The four have changed into eight. Suppose the monkey king has changed 80 times in a row, How many Wukongs are there in total? If we know that the mass of the earth is about 5.9 * 10 to the 24th power kilogram, please list the formula to estimate how many earths the total weight of these Wukongs equals? (suppose each Wukong weighs 50 kilogram)

There are 2 ^ 1 at a time,
There are 2 ^ 2 quadratic variables,
The total weight is 2 ^ 80 * 50kg,
Is equivalent to the number of the earth
(2 ^ 80 * 50) / (5.9 * 10 ^ 24) ≈ 10.245 ≈ 10 (pieces)

The number of a regular array: 2,4,6,8,10,12... Each of its numbers can be expressed by the formula 2n (n is a positive integer)
The number of regularly arranged columns: - 2,4, - 8,16, - 32,64
(1) Each number is represented by a formula containing a positive integer n
(2) What's the 2014 number?
(3) Is 2014 the number in this column? Why?

The law is the nth power of negative two
（-2）^1=-2
（-2）^2=4
（-2）^3=-8
（-2）^4=16
（-2）^5=-32
（-2）^6=64
The number of 2014 is {(- 2) ^ 2014 =?} take your calculator and press it. I don't have a calculator at hand