Let the coordinates of the three vertices of the triangle ABC be (x1, Y1), (X2, Y2), (X3, Y3) respectively, and find the coordinates of the center of gravity g of the triangle ABC The coordinates of the three vertices of the triangle ABC are (x1, Y1), (X2, Y2), (X3, Y3). Find the coordinates of the center of gravity g of the triangle ABC, set up the design algorithm, and draw the flow chart,

Center of gravity g of triangle ABC
G[(X1+X2+X3)/3,(Y1+Y2+Y3)/3]
Let the midpoint of AB be d
So D abscissa {X1 + x2} / 2, and gravity theorem tells us ad = 3gd, so X3 - {X1 + x2} / 2 = 3 {X - {X1 + x2} / 2}, x = {X1 + x2 + X3} / 3? Y

Senior one mathematics increase and decrease function question, seeks the solution, the process is careful, divides into 10 points
1. The function y = negative √ X & # 178; on the interval (- ∞, + ∞) is:
A increasing function B is neither increasing nor decreasing function C decreasing function D is both increasing and decreasing function
2. The monotone increasing interval of function y = - 2x & # 178; + 3x + 1 is:
A（-∞,3/4】 B【3/4,+∞） C（-∞,-3/4】 D【-3/4,+∞）

1.y=-|x|
It is known that (- ∞, 0) increases monotonically and (0, + ∞) decreases monotonically
Choose B
2. This is a parabola with a downward opening, and the axis of symmetry x = - 3 / 4
The increasing range is (- ∞, - 3 / 4]
Choose C

The coordinates of the three vertices of the triangle ABC are a (x1, Y1), B (X2, Y2), C (X3, Y3), and the △ ABC is placed on the horizontal plane
emergency
The coordinates of the three vertices of the triangle ABC are a (x1, Y1), B (X2, Y2), C (X3, Y3). Put △ ABC on the horizontal plane, and hang small balls with mass of M1, M2, m3 at a, B, C, and find the coordinates of the center of gravity g at this time

G（x,y）,x＝（m1x1+m2x2+m3x3）/（m1+m2+m3）*
y＝（m1y1+m2y2+m3y3）/（m1+m2+m3）
*: the force (M1 + M2 + m3) is placed upward at g (x, y). It should be balanced. Take the y-axis as the branch line
(M1 + M2 + m3) x = m1x1 + m2x2 + m3x3. That is the first formula. Similarly, taking X-axis as branch line, the second formula is obtained

High school mathematics, will help! Thank you! 2
Insert 3 numbers between 3 and 48, make these 5 numbers into an equal proportion sequence, find these 3 numbers!

Because it is proportional, the third number is:
Root (3 * 48) = 12
Furthermore, the product of the other two numbers is 12 ^ 2 = 144
144=2^4*3^2
The other two numbers can be:
8 and 18, 6 and 24, 4 and 36
If you want five numbers to be equal, only 3, 6, 12, 24 and 48 are verified
So the three numbers are 6, 12, 24

If the coordinates of ABC three vertices a X1 Y1, B x2 Y2 and C X3 Y3 are known, then the area of the triangle is (expressed in three-point coordinates)

G (x, y), x = (m1x1 + m2x2 + m3x3) / (M1 + M2 + m3) * y = (m1y1 + m2y2 + m3y3) / (M1 + M2 + m3) *: the force (M1 + M2 + m3) is placed upward at g (x, y). It should be balanced. Take the y-axis as the branch line

It is known that if a ∈ m, then 1 / A-1 ∈ m, then M=
If the nonempty set a = {x | 2A + 1 ≤ x ≤ 3a-5}, B = {x | 13 ≤ x ≤ 22}, then a can be included in the set C composed of all a that B holds
Given a = {x | x = 3K-2, K ∈ Z}, B = {y | y = 3L + 1, l ∈ Z}, C = {Z | z = 6m + 1, m ∈ Z}, then the relationship among a, B and C is
The relation between a = {x | x = k π / 2 + π / 4, K ∈ Z}, B = {x | x = k π / 4 + π / 2, K ∈ Z} is
(A) A = B (b) a contains B (c) a contains B (d) a ∩ B = φ

1. Because the set is a single element set, that is, there is only one element in the set
a=1/a-1,
Because a is not equal to 0,
A ^ 2 + A-1 = 0, (a ^ 2 is the square of a)
We obtain a = (- 1 + radical 5) / 2, or a = (- 1-radical 5) / 2,
So set M has two upper solutions
2. Because a is contained in B, 3a-5 = 13,
Moreover, set a is nonempty, so 3a-5 > = 2A + 1,
The simultaneous solution is: 6

What is the nature of the center of gravity of a triangle?

1) The center of gravity is divided into two sections with the length ratio of 2:1
2) Three middle lines divide the triangle into six small pieces, and the area of the six small pieces is equal. That is to say, the line between the center of gravity and the three vertices divides the area of the triangle into three equal parts
2) The center of gravity of a triangle with uniform material is on the geometric center of gravity. That is to say, you can pass through a line from the center of gravity and hold the line while the triangle remains horizontal

Let cos (A-1 / 2b) = - 1 / 9, sin (1 / 2a-b) = 2 / 3, and π / 2

∵π/2

In triangle ABC, it is known that (B + C): (c + a): (a + b) = 4:5:6 to judge the shape of triangle ABC

The proportional relations of a, B and C can be obtained by solving the following equations
b+c=4
c+a=5
a+b=6
The solution is as follows
a=3.5
b=2.5
c=1.5
a:b:c=7:5:3
5^2+3^2

(1) The function f (x) over (- 1,1) is a decreasing function and satisfies f (1-A)

1、
f(1-a)a²-1
Domain of definition
1>1-a>a²-1>-1
There are three parts
1>1-a
a>0
1-a>a²-1
a²+a-2

High school mathematics, will help! Thank you! 2 Insert 3 numbers between 3 and 48, make these 5 numbers into an equal proportion sequence, find these 3 numbers!