There are 110t grain in warehouse A and 70t grain in warehouse B. after the grain is taken from warehouse A and put into warehouse B, the grain ratio of warehouse A and warehouse B is 5:13 (equation ratio)

110t a, 70t B
It can be concluded from 5:13
The total number is 18
So the remaining 50t of warehouse A is 130t of warehouse B
So 110t-50t = 60t
I took 60 tons from a to B

7(x-2)³=56

7(x-2)³=56
(x-2)³=56÷7
(x-2)³=8
x-2=2
x=2+2
x=4

, solving (simple calculation),
(2 squared by 1 * 3) * (3 squared by 2 * 4) * (4 squared by 3 * 5). (98 squared by 97 * 99) * (99 squared by 98 * 100)

If you list the above formula in the form of fractions, you can find that the square number of the molecule in the middle fraction will be divided by the denominator of the previous fraction and the following fraction. For example, in the fraction (3's Square divided by 2 * 4), the square of 3 can be divided by the two 3S in (2's Square divided by 1 * 3) and (4's Square divided by 3 * 5)
In this way, only (2 divided by 1) * (99 divided by 100) is left in the above formula, and the result is 1.98

Suppose that the common ratio of an is q = 1 / 2 and the sum of the first n terms is Sn, then S4 / A4 =?

Using general term formula and summation formula of equal ratio sequence
S4=a1(1-q^4)/1-q
a4=a1.q^3
If you take Q equal to 1 / 2, you can find that the answer is 15

Simple calculation of 8 / 13 of 21-21 * 13

21-21 * 8 / 13
=21*(1-8/13)
=21*5/13
=105/13

In square ABCD, AC and BD intersect at point O, make straight lines EF and GH through point O, and intersect AB, BC, CD and DA at points g, F, h and e respectively
Connect g, F, h and e to judge the shape of quadrilateral gfhe

∵ o is the intersection of the diagonals of a square
∴OE=OF OG=OH
The EF and GH are equally divided
Furthermore, EF and GH are diagonals of quadrilateral gfhe
The quadrilateral gfhe is a parallelogram

Add the operation symbol and bracket = 5 between the five 2 to make the equation hold
Question: 2_ 2_ 2_ 2_ 2=5

2+2+2-2/2=5

Why is the trace of a matrix the sum of eigenvalues? Why is it equal to the coefficient of the second term

The definition of matrix trace is that the main diagonal is the sum of elements
When a matrix is similar to its Jordan canonical form, the trace becomes the sum of eigenvalues,
From Vader's theorem, the sum of the roots of an equation is the inverse sign of its second coefficient
For characteristic polynomials, that's what you need

Given a four digit sum of the numbers and the four digit sum is equal to 2002

Let this four digit number be ABCD
The sum of each digit is: a + B + C + D
This four digit number: 1000A + 100b + 10C + D
All in all: 1001a + 101b + 11C + 2D
A can only be 1
b=9
Then C = 8, d = 2
The number is: 1982

Why are the ranks and determinants of similar matrices equal

The determinants of similar matrices are equal: ([denotes determinant, M is eigenvalue)
P^-1*A*P=B
[mE-B]=[mE-P^-1*A*P]=[m*p^-1*p-P^-1*A*P]=[P^-1*(mE-A)*P]=[mE-A]

There are 110t grain in warehouse A and 70t grain in warehouse B. after the grain is taken from warehouse A and put into warehouse B, the grain ratio of warehouse A and warehouse B is 5:13 (equation ratio)