237 can be composed of prime numbers

237 can be composed of prime numbers

These are the six

The function f (x) = loga (AX-1) (a ＞ 0 and a ≠ 1) is known. It is proved that: (1) the image of function f (x) is on one side of the y-axis; (2) the slope of the line between any two points on the image of function f (x) is greater than 0

It is proved that: (1) from AX-1 ＞ 0, we can get: ax ＞ 1, when a ＞ 1, X ＞ 0, that is, the definition domain of function f (x) is (0, + ∞), and the image of function f (x) is on the right side of y-axis; when 0 ＜ a ＜ 1, X ＜ 0, that is, the definition domain of function f (x) is (- ∞, 0), and the image of function f (x) is on the left side of y-axis

Find the domain of definition and monotone increasing interval of function f (x) = log α (x ^ 2-2x) (a > 0 and a ≠ 1)
Finding monotone increasing interval of function f (x) = log α (x ^ 2-2x) (a > 0 and a ≠ 1)

There is a logarithmic function: x ^ 2-2x > 0, that is, x > 2 or X

Let ABC be a three digit number, a > C, and a three digit number XYZ is obtained from ABC CBA. It is proved that XYZ + ZYX = 1089
ABC is 100A + 10B + C
CBA is 100C + 10B + a
XYZ is 100x + 10Y + Z
ZYX is 100z + 10Y + X

Calculation (ABC) - (CBA) because a > C, so we can know the bit operation: z = C - A + 10, ten bits need to abdicate, so y = (B - b) - 1 + 10 = 9, hundred bits need to abdicate, so x = a - C - 1, substituting the above into (XYZ) + (ZYX) operation, we can get (100x + 10Y + Z) + (100z + 10Y + x) = 10

Let the random variable x obey the uniform distribution on [0,1], and find the probability density FY (y) of the x power of the random variable function y = E

How to use the title function in MATLAB

A topic used to mark the shape of a drawing, for example
x = 1:0.1:100;
y = 1/2.*x.^2;
figure
plot(x,y);
Title ('parabola ');
There will be the name of the graph right above the graph. You can use the
Title ('parabola ',' color ',' R ',' fontsize ', 20');
Set the title font size, color and so on

A fraction, if the numerator plus 1 equals 1, if the denominator plus 1 equals seven eighths, what is the original fraction?

Let the numerator be equal to X and the denominator be x + 1
x/(x+2)=7/8
x=14
The denominator is x + 1 = 15
The original score was 14 / 15

For example, the area of the large parallelogram in the figure is 48 square centimeters, and a and B are the middle points of the upper and lower sides. Can you find out the area of the small parallelogram (shadow part) in the figure?

Connect CD, the area of shadow is 48 △ 2 = 24 (square centimeter); answer: the area of small parallelogram (shadow) is 24 square centimeter

The general form of quadratic function in the third grade of junior high school mathematics turns to vertex form
If a is 1 in the first case, a ＞ 1 in the second case, and a ＜ - 1 in the third case, do not use letters! For example: 2x & # 178; - 4x-6

The vertex formula of quadratic function in the course of formula is: y = a (X-B / 2a) 2 (square) + [4ac-b2 (square)] / 4A
So you just need to insert it
For example: y = 2x & # 178; - 4x-6, where a = 2, B = - 4, C = - 6
Y = 2x & # 178; - 4x-6 = 2 [x - (- 4) / 2 * 2] 2 (square) + [4 * 2 * (- 6) - (- 4) 2 (square)] / 4 * 2 = 2 (x + 1) 2 (square) - 8
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It shows that the square of polynomial x + 2mx + 2m + 1 is always greater than 0

x²+2mx+2m²+1
=(x²+2mx+m²)+m²+1
=(x+m)²+m²+1
∵(m+1)²≥0,m²+1＞0
∴(x+m)²+m²+1＞0
∴x²+2mx+2m²+1＞0