Xiaoyong and Xiaoqiang go to the bookstore to buy books. They have a crush on a book. When they ask about the price, they know they don't have enough money. Xiaoqiang is 0.8 yuan less than Xiaoyong, and Xiaoyong is 2 yuan less than Xiaoqiang It's not enough. How much is the most for this book? How much is the minimum? Process 1

Xiaoyong and Xiaoqiang go to the bookstore to buy books. They have a crush on a book. When they ask about the price, they know they don't have enough money. Xiaoqiang is 0.8 yuan less than Xiaoyong, and Xiaoyong is 2 yuan less than Xiaoqiang It's not enough. How much is the most for this book? How much is the minimum? Process 1

Minimum 2 pieces, maximum 2.8 pieces

Xiaojun and Xiaoqiang buy the same book. The difference between Xiaojun and Xiaoqiang is 1.60 yuan and 2.10 yuan. With their money, they can just buy the book. What's the price of the book? How much did they take with them?

The most ingenious answer is:
1.6+X=Y
2.1+Z=Y
1.6+X=2.1+Z
X=2.1 Z= 1.6
The money for the book is 3.7

Xiaoming and Xiaoqiang went to the bookstore to buy the same kind of books. When they arrived at the bookstore, they found that the money Xiaoming brought was still 0.65 yuan short, and Xiaoqiang was still 0.15 yuan short
A total of 13.2 yuan. How much is the price of this book?

Price
（13.2+0.65+0.15）÷2
=14÷2
=7 yuan
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Proof: if you take any 14 natural numbers, at least two natural numbers have the same remainder divided by 13?

Let n be a natural number, we can write n as n = 13N + 1; 13N + 2; 13N + 3; 13N + 4; 13N + 5; 13N + 6; 13N + 7; 13N + 8; 13N + 9; 13N + 10; 13N + 11; 13N + 12; 13N
So the remainder of natural number divided by 13 can only be 0,1,2,3,4,5,6,7,8,9,10,11,12. There are 13 in total, and now take 14 numbers, so there must be at least two natural numbers with the same remainder divided by 13

Given that the solution set of inequality x + 8 ＞ 4x + m (M is a constant) is x ＜ 3, find M

Because x + 8 ＞ 4x + m, x-4x ＞ M-8, - 3x ＞ M-8, X ＜ - 13 (M-8). Because its solution set is x ＜ 3, so - 13 (M-8) = 3. The solution is m = - 1

1. It is known that the diagonal length of a rectangle is 13 root sign 6, and the width is 150 root sign
2. Given x ^ 2-4x-1 = 0, find the value of root x ^ 2 + 1 / x ^ 2-9

1. According to Pythagorean theorem, the length is 12 root sign 3, the perimeter is 24 root sign 3 + 10 root sign 6 2. According to the condition, X-1 / x = 4, x ^ 2-2 + 1 / x ^ 2 = 16, then x ^ 2 + 1 / x ^ 2-9 = 9

The coordinate formula of vertex a (x1, Y1), B (X2, Y2), C (X3, Y3) and triangle center of gravity g (x, y) of triangle ABC is as follows:

The coordinate formula of vertex a (x1, Y1), B (X2, Y2), C (X3, Y3) and triangle center of gravity g (x, y) of triangle ABC is as follows:
G((x1 + x2 + x3)/3,(y1 + y2 + y3)/3)

The real number a is not equal to 0, f (x) = a (x ^ 2 + 1) - (2x + 1 / a) has the minimum value - 1
Finding the value of a

f(x)=ax^2-2x+a-1/a=a(x-1/a)^2-1/a+a-1/a
There's a minimum, so the opening is up
a>0
Minimum = - 1 / A + A-1 / a = - 2 / A + a = - 1
So a ^ 2 + A-2 = 0
(a+2)(a-1)=0
a>0
So a = 1

Let f (x) = e ^ (- x), then ∫ [derivative of F (LNX) / x] DX =?
Why can't I first find f (LNX) = 1 / X and then find the derivative of F (LNX)? The derivative is - 1 / x ^ 2

f(x)=e^(-x)
therefore
f'(x)=-e^(-x)
f'(lnx)=-1/x
Integral; [f '(LNX)] / xdx
=Integral; (- 1 / x) / xdx
=Integral; - 1 / x ^ 2DX
=1/x+C
(C is a constant)

What is the difference between the standard curve method and the direct method in the determination of protein concentration by UV absorption method