1 Q: What is the maximum number of parts that 5 straight lines divide into planes?

1 Q: What is the maximum number of parts that 5 straight lines divide into planes?

16 servings. 2. When the sun sets on the western slope, the ducks quack into the nest. A quarter of the shore goes forward, half and half with the waves; There are eight ducks behind me, how many ducks are there in my house?

3. 9 trees in 10 rows, 3 in each row, how to plant?

4. Math riddles: ("is the score line").

The reciprocal of 3 4 7 8

3 4 1 to any power.

Each of the above is an idiom.

No. 5. A number, after removing the percent sign, it is increased compared with the original number, what is the original number?

No. 6. A, B and C invested 550,000 yuan to set up a store. 1 5 of the total investment of A, and the rest shall be borne by B and C, and B will invest 20% more than C. How much does B invest?

55*(1-1 5)*2 5=10,000 yuan.

7. Fold the rope three times to measure, and there are 4 meters outside the well; Fold the rope four times to measure, and there is 1 meter outside the well. What is the depth of the well and the rope?

Rope length: (4-1) (1 3-1 4) = 36 meters.

Well Depth: (36-4) 3

8. A basket of apples is divided between A, B and C. A gets 1 5 plus 5 apples of all apples, B gets 1 4 plus 7 apples of all apples, C gets half of the remaining apples, and finally 1 8 of a basket of apples. 40 pcs.

9. There are 180 people in three workshops of a factory, the number of people in the second workshop is more than 3 times the number of people in the first workshop, and the number of people in the third workshop is half of the number of people in the first workshop. How many people are there in each of the three workshops?

The first workshop: 40 people, the second workshop "121 people, the third workshop: 19 people.

10. Some people use a car to transport rice from place A to place B, and the heavy truck loaded with rice travels 50 kilometers a day, and the empty car travels 70 kilometers a day, and goes back and forth three times in 5 days. How many kilometers are A and B apart?

No. 11. The age of the two brothers three years later is 26 years old, and the younger brother's age this year is exactly twice the age difference between the two brothers. Q: How old will the brothers be in 3 years?

Three years later, the elder brother was "15 years old, and the younger brother: 11 years old."

This problem can be solved using inductive reasoning.

Inference based on the fact that some objects of a class of things have a certain property and that all objects of such things have such properties are called inductive reasoning (referred to as induction). Induction is the process from the particular to the general, and it belongs to logical reasoning.

When a straight line passes through a section on a plane, the original area will be divided into 2 parts, i.e. 1 part will be added.

Begin to see the plane as 1 area, i.e., 1 part;

The first straight line is regarded as passing through 1 area, adding 1 part, and dividing the plane into 1+1 parts at most;

The second straight line can pass through a maximum of 2 regions, add 2 parts, and divide the plane into a maximum of 1+1+2 parts;

The third straight line can pass through up to 3 regions, add 3 parts, and divide the plane into 1+1+2+3 parts at most;

The fourth straight line can pass through up to 4 regions, add 4 parts, and divide the plane into 1+1+2+3+4 parts at most;

The 5th line can pass through up to 4 regions, add 4 parts, and divide the plane into up to 1+1+2+3+4+5 parts.

In this way, the maximum number of parts that n (n n*) lines divide into planes can be obtained, and the conclusion can be proved by mathematical induction.

In this question, the 5 straight lines divide the plane into 1+1+2+3+4+5=16 parts at most.

Answer]: C is solved by induction: when there is 1 straight line, there are 2 parts in the plane; When there are 2 straight lines, there are 4 (2+2) parts in the sub-plane; When there are 3 straight lines, there are 7 (2+2+3) annihilation parts in the plane of division; When there are 4 straight lines, there are 11 straight lines (2+2+3+4) in the flat noodles.

It can be seen that for each additional straight line, the multi-division plane part increases one by one, that is, the maximum fractional plane part of n straight lines is 2+2+3+4+....+n=1+n(n+1) 2, which is the formula for the bisector of a straight line. Therefore, when n=100, the maximum fractional plane is 1+100 (100+1) 2=5051 part. Therefore, C.

Article 1 is divided into 2, Article 2 is divided into 4, Article 3 is divided into 7, Article 4 is divided into 11, Article 2 is divided into 2 more than Article 1, Article 3 is divided into 3 more than Article 2, Article 4 is divided into 4 more than Article 3 Therefore, Article n is divided into n more than Article N-1. Number of Article 2: 4 = 2 + 2 Number of Article 3:

7 = 2 + 2 + 3 Number of Article 4: 11 = 2 + 2 + 3 ...

How many planes can be divided into 211 planes at most for 21 lines. According to the relevant knowledge, it can be seen that any other bridge intersects with straight lines and any three straight lines are incompatible with the same point. It can be seen that when the number of straight lines is n(n 3), the fluttering of these lines divides the plane into (n+n)+1 parts at most.

1 straight line divides the plane into up to 2 parts;

2 straight lines divide the plane into up to 4 parts;

3 straight lines divide the plane into up to 7 parts;

Now add the 4th straight line It has a maximum of 3 intersections with the previous 3 straight lines, and these 3 intersections divide the 4th straight line into 4 sections, each of which divides the original plane part into two, as shown in the figure, so the 4 straight lines divide the plane into 7 + 4 = 11 parts at most

Exactly in a similar way, 5 straight lines divide the plane into a maximum of 11+5=16 parts; 6 straight lines divide the plane into a maximum of 16+6=22 parts; 7 straight lines do not divide the plane into 22+7=29 parts at most; 8 straight lines divide the plane into a maximum of 29 + 8 = 37 parts

So, 8 straight lines divide the plane into a maximum of 37 parts

In a plane, there are n straight lines, and how many parts can the plane be divided into at most?

1st line: Divide the plane into 1+1 parts.

Add 1 straight line: intersect with the 1st straight line into 2 sections, and each segment divides the original part into 2 parts, that is: total number of parts + 2--- total share opening index = (1 + 1) + 2 plus 1 straight line:

Intersect with the first 2 straight lines into 3 segments, and each segment divides the original part into 2 parts, namely: the total number of copies + 3--- total number of copies = (1 + 1 + 2) + 3 The nth straight line: intersects with the first n-1 straight line into n segments, and divides the original part into 2 parts for each trembling early section, that is:

Total number of copies + n--- total number of copies = [1 + 1 + 2 + 3 + ..n-1)] +n-->Total number of copies=[1+1+2+3+..n-1)]+n1+n(n+1)/2

n��+n+2)/2

The 5 straight lines are up to the width of the cavity and divide the circle into 16 parts

So the answer is; 16．

1. If the five straight lines do not intersect at one point, at most 10 intersection points, then the core part should be a five-pointed star, so that a plane can be divided into 16 parts.

2. If five straight lines intersect at one point, then they can be divided into up to 10 parts.

If there is 1 straight line, then the plane is divided into 2 parts at most;

If there are 2 straight lines, then the plane is divided into a maximum of 4 parts;

If there are 3 straight lines, then the plane is divided into a maximum of 7 parts;

If there are 4 straight lines, then the plane is divided into a maximum of 11 parts;

1=1, 2=1+1, 4=1+1+2, 7=1+1+2+3, 11=1+1+2+3+4,......

The formula for dividing the plane of a straight line is obtained: n straight lines can divide the plane into 1+1+2+3+...... at mostn parts, that is, the plane can be divided into (n(n+1)+2) 2 parts at most, which is reduced to (n 2) 2+n 2+1.

When n is equal to 10, it can be divided into (10 2) 2+10 2+1=56 parts.

0 straight lines, 1+0=1, the plane is up to 1 block;

1 straight line, 1+1=2, the plane is up to 2 pieces;

2 straight lines, 2+2=4, the plane is up to 4 pieces;

3 straight lines, 4+3=7, the plane is up to 7 pieces;

4 straight lines, 7+4=11, the plane is up to 11 pieces;

5 straight lines, 11+5=16, the plane is up to 16 pieces; , n straight lines, 1+n(1+n) 2=(n +n+2) 2, the plane is up to (n +n+2) 2 blocks.

So 10 straight lines, (10 +10+2) 2=56, the plane is up to 56 blocks.

, n straight lines, 1+n(1+n) 2=(n +n+2) 2, the plane is up to (n +n+2) 2 blocks.

So 10 straight lines, (10 +10+2) 2=56, the plane is up to 56 blocks.