The ratio of science and technology books to story books was 2:3. In the morning, a batch of new science and technology books were put into the library, The ratio of science and technology books to story books is 10:9. In the afternoon, there are 100 more known science and technology books than story books. How many science and technology books and story books are there in the original library? When a batch of new story books are put into the library, the ratio of science and technology books to story books is 5:6. There are 100 more known science and technology books than story books. How many science and technology books and story books are there in the original library

Primary school mathematics is so difficult, no wonder it should be shouldered by primary school students

There are 400 science and technology books in the library, 38 less than story books. How many story books are there?

A: there are 640 story books

There are 500 science and technology books in the library, three eighth less than story books. How many story books are there?

Suppose there are x storybooks
X-3/8X=500
5/8X=500
X=800
A: there are 800 story books

Using dichotomy to design an algorithm for finding approximate solution of equation x ^ 2-2 = 0

F (0) = - 20, so there are real roots in [0,2],
k a b x f(a) f(b) f(x)
0 0 2 1 -2 2 -1
1 1 2 1.5 -1 2 0.25
2 1 1.5 1.25 -1 0.25 -0.4375
3 1.25 1.5 1.375 -0.4375 0.25 -0.109375
4 1.375 1.5 1.4375 -0.1094 0.25 -0.66
And so on: the question should be less than a precision requirements of the conditions, right?

The problem of linear algebra in College Mathematics and the selection of free variables
As the problem. AX = 0, find the general solution of A
How to select the free variable after Gaussian elimination of a coefficient matrix into the simplest matrix? Is it the first non-zero variable in each row? Is the selection of free variable unique?
I see a method in the reference book: delete each column separately. If the rank of the deleted matrix is equal to the rank of the original coefficient matrix, then the variables in this column can be free variables
What is the principle of this method?

Let me give you a simple example, the system of equations x + y = 1, y + Z = 1, then if you choose to use X to represent the solution of the system of linear equations, it is x = x.y = 1-x, z = x, if you use y to represent its solution, it is x = 1-y, y = y, z = 1-y, similarly using Z to represent it; then the coordinate forms of the above solutions are (0,1,0) ^ t + X (1, - 1,1) ^ t respectively

2 (5x-1) square = 3 (| 5x) how to do? Emergency?

If you put forward a sign in the bracket on the left, there will be the same number of drops on both sides. Eliminate it, and then you can do it

Let u = R, a = {x XM}
(1) If the complement of a in U is contained in B, find the value range of real number M
(2) If the complement of a in U contains B, find the value range of real number M

① Because the complete set u = R
So the complement of a in U is {x ｜ x ≥ 1}
Because the complement of a in U is contained in B, B = {x | x > m}
So the maximum value of M should be 1
So m ≤ 1
② From one knowledge,
The complement of a in U is {x ｜ x ≥ 1}
Because the complement of a in U contains B
So m > 1
If you don't understand, draw the number axis

It is known that when x = 2, the value of the cubic power + nx-5 of the algebraic formula MX is 8, then when x = - 2, what is the value of the algebraic formula?
To standardize the problem-solving process!
Yes, there will be a reward!

When x = 2, the cubic power of MX + nx-5
=8m+2n-5=8
So 8m + 2n = 13
-8m-2n=-13
When x = - 2
The third power of MX + nx-5
=-8m-2n-5
=-13-5
=-18

The function f (x) = ax + B / 1 + X2 is an odd function defined on [- 1,1], and f (1) = 1 / 2 (3) solves the inequality f (x-1) + F (x) less than 0

f(x)=(ax+b)/(1+x^2)
From F (- x) = - f (x), B = 0
From F (1) = 1 / 2 = A / 2, a = 1
So f (x) = x / (1 + x ^ 2)
The domain of F (x-1) is: - 1=

Given the three vertices a (3,3), B (2, - 2), C (- 7,1) of a triangle, we can find the equation of the straight line where the bisector ad of ∠ a lies

The slope of AB is K1 = 5
The slope of AC is K2 = 1 / 5
Then the slope of the angular bisector is k, (k-k1) / (1 + K1 * k) = (k2-k) / (1 + K2 * k) and 26k ^ 2 = 26, then k = 1 or K = - 1
From the three coordinates of the triangle, k = 1
Then the slope of ad is 1, and a (3,3) is on ad, then the linear equation of ad is Y-3 = x-3, that is y = X