A natural number and its reciprocal are 101 out of 10. The natural number is () 1 5 ② 10 ③ 11

②101/10 =10+1/10

Divide 1 / 3 into the reciprocal sum of 10 natural numbers

1/3
=16/48
=1/48+2/48+3/48+4/48+6/48
=1 / 48 + 1 / 24 + 1 / 16 + 1 / 12 + 1 / 8 (because 1 / 12 = 1 / 36 + 1 / 18, 1 / 8 = 1 / 56 + 1 / 28 + 1 / 14)
=1/48+1/24+1/16+1/36+1/18+1/56+1/28+1/14(1/18=1/54+1/27、1/14=1/42+1/21）
=1/48+1/24+1/16+1/36+1/54+1/27+1/56+1/28+1/42+1/21
(it's time for you to ask, what my tutor just asked us to do, I didn't do it for long,,,, ha ha,,, this is already my limit, and I can't calculate it in small numbers.)

The sum of a natural number and its reciprocal is 10 / 3. The natural number is ()

The natural number is three
3 + 1/3 = 10/3

Car a and car B start from both places at the same time and travel in opposite directions. The distance is 900 km. The speed ratio of car a and car B is 2:3. After six hours of meeting, what are the speeds of car a and car B respectively?

900 △ 6 = 150 (km), 2 + 3 = 5150 × 25 = 60 (km), 150 × 35 = 90 (km); a: the speed of car a is 60 km / h, and that of car B is 90 km / h

The ratio of length to width of a rectangle is 5:3, and its diagonal length is root 64. Calculate the length and width (the result retains two significant numbers)

If the length is 5x, the width is 3x
Pythagorean theorem obtains 25X ^ 2 + 9x ^ 2 = 64
The solution is x = 1.37
9
The width is 4.1

Let ABC be a positive integer, and prove 1 / A ^ 3 + 1 / b ^ 3 + 1 / C ^ 3 + ABC > = 2 times root sign 3

Prove that ∵ a, B, C are positive real numbers, 1 / A ^ 3 + 1 / b ^ 3 + 1 / C ^ 3 + ABC = 1 / A ^ 3 + 1 / b ^ 3 + 1 / C ^ 3 + ABC / 3 + ABC / 3 ≥ 6 * 6 times √ (1 / A ^ 3 + 1 / b ^ 3 + 1 / C ^ 3 + ABC / 3 + ABC / 3) = 6 * 6 times √ (1 / 3 ^ 3) = 2 * 6 times √ (3 ^ 6 / 3 ^ 3) ≥ = √ 2 * 6 times ∵ (3 ^ 3) = 2 √ 1 / A ^ 3 + 1 / b ^ 3 +

Lever, pulley, bevel, 20 related application questions and fill in the blanks and the answers

1. Use the device shown in Figure 1 to lift object a with a weight of 900 n, and when the tension applied to the free end of the rope is 400 N, it can make the object rise at a uniform speed. Find out: (1) the mechanical efficiency of the pulley block at this time; (2) if the rope weight and friction are ignored, the weight of the pulley is calculated; (3) if the lifting weight is changed to 1200 n, What is the mechanical efficiency of the pulley block at this time? (4) in question (3), how much tension should be added at the free end of the rope to pull up the object at a uniform speed?
Figure 1
2. Use the moving pulley to lift the object weighing 80 n for 2 meters at a uniform speed, and the pulling force does work of 200 joules. Regardless of the rope weight and all friction. (1) calculate the mechanical efficiency of the moving pulley at this time; (2) if the moving pulley lifts a weight of 200 N at a uniform speed, and the pulling power is 11 watts, what is the lifting speed of the weight?
Figure 2
3. A man uses a pulley block to lift an object with a weight of 128n at a constant speed, and the mechanical efficiency of the pulley block is 80%. In 4S, a man uses a force of F = 40n to move the end of the rope for 4m. (1) find out the number of strands of the rope n; (2) calculate the amount of useful work and the total power
4. A pulley block with mechanical efficiency of 80% can lift an object weighing 4900n at a constant speed by pulling 1225n downward. Please draw the device diagram of this pulley block
5. Use the pulley block as shown in Figure 3 to pull an object a with a weight of 100 N to move at a constant speed along the horizontal plane, and the tension f is 40 n. (1) calculate the friction force on object a without considering the gravity and friction of the wheel and rope. (2) if the mechanical efficiency of the pulley block is 80%, calculate the friction force on object a
Figure 3
6. As shown in Figure 4, the mechanical efficiency of the whole device is 75% when the object rises at a constant speed with a pull force of 40 n, regardless of the weight of the rope and friction?
Figure 4
7. As shown in Figure 5, the object with 600 n weight was pulled by the pulley block and moved 8 meters to the right at a constant speed along the horizontal direction. The work done by the pulling force F is 1280 joules. (regardless of the weight of the rope and friction) find out: (1) the size of the pulling force; (2) if the weight of the moving pulley is 12 N, what is the mechanical efficiency?
8. Using the device as shown in Figure 7 to lift heavy objects, the maximum tension that the rope can bear is 120N, the weight of the movable pulley is 60N, and the weight of the rope and friction are not considered. The following results can be obtained: (1) using this pulley block can lift multiple objects at a uniform speed at most? (2) using this pulley block to lift an object with a weight of 240n to make it rise at a uniform speed, What is the pull force on the free end of the rope? What is the mechanical efficiency of the pulley block? What is the power of the pull force when the object rises at a speed of 0.5m/s? (3) what is the maximum mechanical efficiency of the pulley block?
9. As shown in Figure 8, use pulley block a and pulley block B to lift the weight at a constant speed. The known weight ratio of G1 to G2 is 2:1. The weight ratio of movable pulley block a to G1 is 1:5. The total weight ratio of two movable pulleys in pulley block B is 3:5 (excluding rope weight and friction). Find: 1) the ratio of mechanical efficiency of pulley block a and pulley block B? (2) the ratio of pulling force F1 and F2 used at the free end of rope?
Reference answer:
(1) 75% (2) 300N (3) 80% (4) 500 2. (1) 80% (2) 0.05m/s 3. (1) 4 (2) 128j 40W 4.5 sketch 5. (1) 120N (2) 96n 6. (1) 90N 30n (2) 80% 7. (1) 80N (2) 92.5% 8.25% 9. (1) 300N (2) 100N 150W 83.3% (3) 80% 10. (1) 4 ∶ 3 (2) 2 ∶ 1

A square piece of iron has a circumference of 80 decimeters. Cut this piece of iron into the largest circle. How many square meters is the area of the circle

Bao Yi died in Japan,
The side length of a square is the diameter of a circle
80 △ 4 = 20 (decimeter) = 2 (meter)
The area of the circle is:
3.14 × (2 △ 2) ^ 2 = 3.14 (M2)

The prime factor of a composite number is 2,5,11. The composite number is ()

110 and the multiple of 110

For a project, Party A works alone for 2 days, and then works together with Party B for 7 days, so as to complete half of the whole project. It is known that the work efficiency ratio of Party A and Party B is 2:3. If Party B works alone, how many days will it take to complete the project?

(2 + 7) × 2 ／ 3 × 2 + 7 × 2 = 18 ／ 3 × 2 + 14 = 12 + 14 = 26 (days) a: this project is done by Party B alone, and it will take 26 days to complete

A natural number and its reciprocal are 101 out of 10. The natural number is () 1 5 ② 10 ③ 11