1951^2-1950^2+1953^2-1952^2+… +2011^2-2010^2

1951^2-1950^2+1953^2-1952^2+… +2011^2-2010^2

(n + 1) = (n + 1 + n) (n + 1-N) = 2n + 1, so: 1951 ^ 2-1950 ^ 2 + 1953 ^ 2-1952 ^ 2 + +2011^2-2010^2=(2*1950+1)+(2*1952+1)+...+(2*2010+1)=2(1950+1952+...+2010)+31=2*(1950+2010)*31/2+31=(1950+2010)*31+31=122791...

Solving the equation 2x + (99-x) △ 2 = 99

2x+（99-x）÷2=99
Multiply both sides by two
4x+99-x=198
4x-x=198-99
3x=99
x=99÷3
x=33

In △ ABC, the edges opposite the angles a, B and C are a, B and C respectively. If a = π / 3, a = √ 7 and B = 2, then the area of △ ABC is determined

From cosine theorem
The results are as follows
a^2=b^2+c^2-2bccosA
7=4+c^2-4c*1/2
c^2-2c-3=0
(c-3)(c+1)=0
c=3
S△ABC
=1/2bcsinA
=1/2*2*3*sinπ/3
=3√3/2

composition
You must write it yourself

With the passage of time in my sixth grade life, I became a sixth grade student in primary school. In this semester, I not only learned a lot, but also learned a lot. Every morning, four dry and boring classes are so wordy that people can't help yawning. Mathematics: "when the multiplier is greater than 1, the product is bigger than the multiplicand..." Chinese: "the way to do this problem

The wire with length of 1 is divided into two sections and enclosed into a square and a circle respectively. In order to minimize the sum of the area of the square and the circle, the perimeter of the square should be___ ．

Analysis: let the perimeter of the square be x, then the perimeter of the circle is 1-x, the radius r = 1-x2 π. S positive = (x4) 2 = x216, s circle = π · (1-x) 24 π 2. S positive + s circle = (π + 4) x2-8x + 416 π (0 < x < 1). When x = 4 π + 4, there is a minimum value. Answer: 4 π + 4

(1) It is known that the difference between the polynomial (- 2x2 + 3) and the double of a is 2x2 + 2x-7. ① find the polynomial a; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; ② When x = - 1, find the value of A. (2) the corresponding points of a, B and C on the number axis are known, as shown in the figure, and the simplification is: | a | - | a + B | + | C-A | - | C |

(1) (1) according to the meaning of the question: (- 2x2 + 3) - 2A = 2x2 + 2x-7, we can get a = 12 [(- 2x2 + 3) - (2x2 + 2x-7)] = - 2x2-x + 5; (2) when x = - 1, the original formula = - 2 + 1 + 54; (2) according to the number axis: C < B < 0 < A, | a | B |, | a + B < 0, C-A < 0, then the original formula = a + A + B + a-c + C = 3A + B

If a building needs to build a 20-year insulation layer, the construction cost per centimeter of the insulation layer is 60000 yuan. The annual energy consumption cost of the building C (unit: 10000 yuan) and the insulation layer thickness x (unit: cm) satisfy the relationship C (x) = K / (3x + 5) (0 ≤ x ≤ 10). If the insulation layer is not built, the annual energy consumption is 80000 yuan. Let f (x) be the sum of the insulation layer construction cost and the 20-year energy consumption cost
1. Find the value of K and the expression of F (x)
2. The total cost f (x) reaches the minimum when the thickness of insulation layer is built

C (0) = K / 5 = 8, then k = 40
f(x)=6x+800/(3x+5)
When x = 5, there is a minimum f (5) = 70

If the side length of a square increases by 50 decimeters, its area will increase by 125 square meters?

（125-5x5）÷2÷5=10
10x10=100

1molne contains 6.02x10 24 th power electrons. Is that right? Why?

1molne contains 6.02x10 24 th power ne atoms, and a ne contains 10 electrons, so 1molne contains 6.02x10 24 th power electrons

The difference between stress and force is conceptually significant

Stress is the force on the unit area of the cross section, and internal force is the sum of the stresses on the calculated cross section. Stress = internal force / cross section area. Stress is a kind of force. As long as it is physical mechanics, it will obey Newton's third law, such as force and reaction force