Inspired by the production of fried dough sticks, Mr. Li designed a mathematical problem. He intercepted the line AB from the origin to the corresponding point of 1 on the number axis, folded it in half (point a and B coincide) and then evenly pulled it into a line segment of unit length. This process is called one operation (for example, after the first operation, 1 / 4, 3 / 4 on the original line AB become 1 / 2, 1 / 2 become 1, etc.), After the nth operation, what is the sum of the numbers corresponding to the point exactly pulled to coincide with 1?

Inspired by the production of fried dough sticks, Mr. Li designed a mathematical problem. He intercepted the line AB from the origin to the corresponding point of 1 on the number axis, folded it in half (point a and B coincide) and then evenly pulled it into a line segment of unit length. This process is called one operation (for example, after the first operation, 1 / 4, 3 / 4 on the original line AB become 1 / 2, 1 / 2 become 1, etc.), After the nth operation, what is the sum of the numbers corresponding to the point exactly pulled to coincide with 1?

There is a rule to follow. In one operation, one point of AB is pulled to unit 1,
In the second operation, two points (AC midpoint, BC midpoint) are pulled to unit 1,
And so on, the third time, 4 points, the fourth time, 8 points
The nth time is 2 ^ (n-1) points
Sum = 1 + 2 + 4 + 8 + +2^（n-1）
This is the sum of an equal ratio sequence
Sn=a1(1-q^n)/(1-q) =1(1-2^n)/(1-2) =2^n-1

There is a square cloth with an area of 16 square meters. My mother cut a triangle from each side of it. How many square decimeters is the area of the remaining cloth?
emergency

If the title is not clear, see if it is wrong? Less conditions

First simplify, then evaluate
7a-2 [3A & # 178; + (2 + 3a-a & # 178;)], where a = - 1
(2x & # 178; y-2xy & # 178;) - (3x & # 178; Y & # 178; + 3x & # 178; y) + (3x & # 178; Y & # 178; - XY & # 178;), where x = - 1, y = 2
It is known that X-Y = 2, xy = - 3,
Find the algebraic formula (2x + 3y-2xy) - (x + 4Y + XY) - (3xy + 2y-2x)

The original formula = 7a-2 [3A ^ 2 + 2 + 3a-a ^ 2] = 7a-2 [2A ^ 2 + 3A + 2] = 7a-4a ^ 2-6a-4 = a-4a ^ 2-4, substituting a = - 1 to get - 1-4 × (- 1) ^ 2-4 = - 1-4-4 = - 9
The original formula = 2x ^ 2y-2xy ^ 2-3x ^ 2Y ^ 2-3x ^ 2Y + 3x ^ 2Y ^ 2-xy ^ 2 = - x ^ 2y-3xy ^ 2 = - XY (x + 3Y), substituting the values of X and y, we get 10
The original formula = 2x + 3y-2xy-x-4y-xy-3xy-2y + 2x = 3x-3y-6xy = 3 (x-y-2xy). Substituting the values of X and y, we get 24

Remember a thousand natural numbers x, x + 1, x + 2 The sum of X + 999 is a. if the sum of a is equal to 50, what is the minimum value of X?

x+（x+1）+（x+2）+… +(x + 999) = (x + X + 999) × 1000 ÷ 2, = (2x + 999) × 500 = 1000x + 499500, we can see that when the number of 1000x is less than 7, the condition can not be satisfied; 4 + 9 + 9 + 5 = 27, 50-27 = 23, but the title says the minimum x, so we need to complete from the highest order of 499500, so the minimum value of condition a is: 99999500, that is: 1000x = 999999500-4995001000x = 99500000, & nbsp; & nbsp;   x=99500．

The passenger car and the freight car set out from the two places at the same time and went opposite each other. They met in five hours. After meeting, the passenger car went another three hours to reach the second place. It is known that the freight car travels 72 kilometers per hour. How many kilometers are there between the two places?

A: the distance between a and B is 960 km

The maximum value of function y = (1 / 3) ^ x3-3 ^ X in interval [- 1,1] is-

y'=x^2-6x
Let y '= 0, x = 0 or x = 6
x=-1 y=-10/3
x=0 y=0
x=1 y=-8/3
The maximum value of function y = (1 / 3) ^ x3-3 ^ X in interval [- 1,1] is 0

√3X^2+(5√3-3)(x-3)=6√3X-9√3

√3X^2+(5√3-3)(x-3)=6√3X-9√3
√3X^2+(5√3-3)x-3(5√3-3)=6√3X-9√3
√3X^2+5√3x-3x-15√3+9=6√3X-9√3
√3X^2+5√3x-6√3X-3x-15√3+9+9√3=0
√3X^2-√3X-6√3-3x+9=0
(√3X^2-√3X-6√3)-3(x-3)=0
√3(X^2-X-6)-3(x-3)=0
√3(X+2)(X-3)-3(x-3)=0
(x-3)[√3(X+2)-3]=0
(x-3)[√3X+2√3-3]=0
√3X+2√3-3=0
√3X=3-2√3
X①=(3-2√3)/√3=(3-2√3)√3/3=(3√3-6)/3=√3-2
x②=3

The side area of a cylinder is 18.84 square decimeters, the bottom diameter is 2 decimeters, what is its height? What is the surface area of the cylinder?

The radius is one decimeter
The bottom area is 1 × 1 × 3.14 = 3.14 square decimeters
18.84 - 3.14 × 2 = 12.56 square decimeters, which is the lateral area
12.56 ÷ (2 × 3.14) = 2 decimeters, which is the height of the cylinder
Surface area 3.14 * 2 + 12.56 = 18.84
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The sum of ten natural numbers is equal to 1001. What is the maximum value of the greatest common divisor of these ten natural numbers___ ．

1001 is the sum of these ten natural numbers, that is, the multiple of the greatest common divisor of these ten natural numbers; 1001 = 7 × 11 × 13, so there are eight factors of 1001: 1, 7, 11, 13, 77, 91, 143, 1001.1001 △ 10 = 100.1, so the greatest common divisor of these ten natural numbers must be less than 100.1. Obviously, the greatest factor less than or equal to 100.1 is 91 The maximum value is 91

Factorization factor x-4x-12x factorization factor

Is the title wrong?
If you want to do that
X²-4X-12X=
=X²-16X
=X(X-16)
It should be x-178; - 4x-12, right
Multiplication by cross
1 -6
1 2
Get (X-6) (x + 2)
What is the rule of cross multiplication
aX²+bX+c
a1 a2
b1 b2
a1*b1=a
a2*b2=c
a1*b2+b1*a2=b