The formula of application problem A company selects three people from 152 employees to participate in the year-end friendship competition. Any three of them are required to perform on the stage and choose the best three people combination that can represent the company's image. How many three people groups are there in total? Find the formula!

three
C =152!/3!*（152-3）!=573800
one hundred and fifty-two

Application of sum difference formula

If we know that there are 264 tons of grain in the two warehouses of a and B, the grain stored by a is 10 times that of B, and the grain stored by a and B is how many tons? Formula: decimal = sum / (multiple + 1) = 264 / (10 + 1) = = 24 tons, 24 * 10 = 240 tons

For a project, Party A, Party B and Party C need 10 days, 12 days and 15 days respectively to complete. Now it is planned to start the project in 7 days, and Party B and Party C will work together for 3 days. Team B will leave and be replaced by team A. under the condition that the work efficiency of each team remains unchanged, can the project be completed as planned?

Suppose that it will take X days for teams a and C to complete the project. The equation is: X10 + 312 + 3 + x15 = 1, and the solution is: x = 3.3. Because 3 + 3.3 = 6.3 < 7, it can be completed within the time specified in the plan. Therefore, the project can be completed according to the plan with the same work efficiency of each team

Let a be a positive definite matrix and prove that for any positive integer m, there exists a positive definite matrix B such that B ^ m = a
If the problem, mainly to prove that the matrix B is a positive definite matrix, how to prove?

It is proved that a is a positive definite matrix = > A is a symmetric matrix, so a can be diagonalized, that is, there exists an orthogonal matrix P and a diagonal matrix C such that a = (P ^ t) CP, where p ^ t represents the transpose of P. (note that P is an orthogonal matrix, so the inverse of P and the transpose of P are the same.)

There is a two digit number. The ten digit number is 2 larger than the one digit number. The two digit number is between 50 and 70. Can you work out the two digit number

Suppose the single digit of the two digit is x, then the ten digit is (x + 2). According to the meaning of the question, we get 50 < 10 (x + 2) + x < 70, and the solution is 2811 < x < 4611. Because the single digit should be an integer, so x = 3 or x = 4, and the ten digit is x + 2 = 3 + 2 = 5 or 4 + 2 = 6, so the two digit is 53 or 64

The matrix that can find the value of determinant can only be a square matrix?
Is there no determinant for a matrix with different number of rows and columns?
What's the difference between the above two sentences?

Yes, determinants only define matrices

20% of a number is 6 less than 18. What's the number? (solve the equation)

Let this number be X
20%x+6=18
0.2x=12
x=12÷0.2
x=60

What are the causes of sandstorm and desertification?

It can be divided into natural causes and man-made causes, but man-made causes are more important natural causes: low vegetation coverage and prevailing wind and weathering
Coupled with the destruction of human vegetation, overuse of water resources leads to the destruction of vegetation, lack of water resources, dry surface and prevailing wind, it is easy to cause dust storms and land desertification

3. Xiaoxiao read a story book. On the first day, he read more than 2 pages of 1 / 6 of the whole book. On the second day, he read less than 1 page of 1 / 2 of the whole book. There are still 10 pages left
3 Xiaoxiao read a story book. On the first day, he read more than two pages of one third of the whole book. On the second day, he read less than one page of one half of the whole book. There are still 10 pages left

54 pages
With X pages
1 / 3x-2 first day
1 / 2x + 1 the next day
There are 10 left
The sum is equal to the total number of pages X of the book
That is 1 / 3x-2 + 1 / 2x + 1 + 10 = X

Proof: the product of four consecutive integers plus 1 is the square of an integer

Let the four consecutive integers be n-1, N, N + 1, N + 2, then (n-1) n (n + 1) (n + 2) + 1, = [(n-1) (n + 2)] [n (n + 1)] + 1 = (N2 + n-2) (N2 + n) + 1 = (N2 + n) 2-2 (N2 + n) + 1 = (N2 + n-1) 2. Therefore, the product of four consecutive integers plus 1 is the square of an integer