F (x) = (x ^ 2) / (3 ^ x) and X is a positive integer. Prove that f (x) is less than or equal to 4 / 9,

F (x) = (x ^ 2) / (3 ^ x) and X is a positive integer. Prove that f (x) is less than or equal to 4 / 9,

F (x) = (x ^ 2) / (3 ^ x), X is a positive integer
f(1)=1/3,f(2)=4/9,
It is proved that when x ≥ 2, X ∈ n *, the,
F (x + 1) 0 is constant
f(x+1)/f(x)
=[(x+1)^2/3^(x+1)]/(x^2/3^x)
=(x+1)^2/(3x^2)
=(x^2+2x+1)/(3x^2)
(x^2+2x+1)/(3x^2)-1
=（-2x^2+2x+1)/(3x^2)
=[-2(x-1/2)^2+3/2]/(3x^2)
Molecule g (x) = - 2 (x-1 / 2) ^ 2 + 3 / 2
In (1 / 2, + ∞) is a decreasing function
∵x≥2
∴g(x)≤g(2)=-3

-How to solve 4x + X & # 178; = - 1.75

-4x+x²=-1.75
x²-4x=-1.75
x²-4x+4=-1.75+4
(x-2)²=2.25
x-2=±1.5
X = 3.5 or x = 0.5

What is the solution of X & # 178; - 4x + 1 = 0?

x²-4x+1=0
x²-4x+4=3
(x-2)²=3
x-2=±√3
x1=2+√3, x2=2-√3

When x = 4, the value of the algebraic formula a = ax2-4x-6a is - 1, then when x = - 5, what is the value of a?

So the algebra of X is a = 1.5x2-4x-9, so when x = - 5, there is a = 1.5 × (- 5) 2-4 × (- 5) - 9 = 37.5 + 20-9 = 48.5

When x = 4, the value of the algebraic formula a = ax2-4x-6a is - 1, then when x = - 5, what is the value of a?

So the algebra of X is a = 1.5x2-4x-9, so when x = - 5, there is a = 1.5 × (- 5) 2-4 × (- 5) - 9 = 37.5 + 20-9 = 48.5

1. In a chess match, each player has just one match with the other players. The winner of each game gets 2 points and the loser gets 0 points. If the game is tied, each player gets 1 point. Today, four students have counted the total scores of all the players in the game, which are 365 points, 380 points, 381 points and 400 points respectively. After verification, only one student has counted correctly. How many players have participated in the game?
2. According to the market survey, when a bag with a purchase price of 30 yuan is sold at a price of 40 yuan, an average of 600 bags can be sold every month, and every 1 yuan increase in the selling price of the bag will reduce the monthly sales by 10. A shopping mall plans to buy a batch of such bags. When the shopping mall has a monthly sales profit of 10000 yuan, the sales volume of the bag will be reduced,
(1) What is the price of the schoolbag?
(2) What is the monthly sales volume of schoolbags?
(3) In order to embody the sales principle of "small profit but quick turnover", how much do you think the sales price should be set?

The main ideas are as follows: (1) first analyze the total number of the competition, assuming that there are x players participating in the competition, there will be a total of Competition Bureau; (2) then analyze the characteristics of the total score, because no matter win, lose or draw, 2 points are recorded in each game, then the total score of the competition bureau is the total score of all the players

It is known that in the quadratic equation AX2 + BX + 1 = 0, B = A-M + M-A + m + 1; (1) if a = 4, find the value of B; (2) if the equation AX2 + BX + 1 = 0 has two equal real roots, find the root of the equation

(1) ∵ A-M ≥ 0 and M-A ≥ 0, ∵ a = M = 4, ∵ B = m + 1 = 5; (2) according to the meaning of the title, we get △ = b2-4a × 1 = 0, ∵ a = m, ∵ B = m + 1 = a + 1, ∵ (a + 1) 2-4a = 0, the solution is a = 1, ∵ B = 2, the original equation is changed to x2 + 2x + 1 = 0, the solution is X1 = x2 = - 1

Seek the third day mathematics problem, the process is detailed
As shown in the figure, points a, C and B are all on ⊙ o, and the quadrilateral acbo is a diamond
We need it now! Speed, urgent

AC=CB,AO=BO
Point C and point o are on the middle vertical line of AB (the distance from the point on the middle vertical line to both ends of the line break is equal)
The straight line where CO is located is the vertical line of AB (two points determine a straight line)
OC bisector AB (vertical diameter theorem)
I don't know if I didn't speak clearly enough

23. (2010, Shantou) read the following materials:
1×2 = (1×2×3－0×1×2),
2×3 = (2×3×4－1×2×3),
3×4 = (3×4×5－2×3×4),
By adding the above three equations, we can get
1×2＋2×3＋3×4= ×3×4×5 = 20．
After reading the above materials, please calculate the following questions:
(1) 1 × 2 ＋ 2 × 3 ＋ 3 × 4 ＋ &; &; &; + 10 × 11 (writing process);
(2) 1×2＋2×3＋3×4＋•••＋n×(n＋1) = _________ ；
(3) 1×2×3＋2×3×4＋3×4×5＋•••＋7×8×9 = _________ ．
(1) and (2) do not write the third directly

You are wrong! It should be 1 × 2 = 1 / 3 (1 × 2 × 3-0 × 1 × 2) = 1 × 2 × 3 * 1 / 3, multiply by 1 / 3 in front of it, I don't believe you can calculate it by yourself
(3) 1 × 2 × 3 + 2 × 3 × 4 + 3 × 4 × 5 +? + 7 × 8 × 9 = 1 / 4 [(1 × 2 × 3 × 4-0 * 1 * 2 * 3) + (2 × 3 × 4 × 5-1 × 2 × 3 × 4) + (7 × 8 × 9 × 10-6 × 7 × 8 × 9) = 1 / 4 (7 × 8 × 9 × 10-0 * 1 * 2 * 3) = 1260 (split term)

Three math problems in junior high school,
1. In a basketball championship, after each team has played three games, six teams have been eliminated, and the remaining teams have played 33 games in a single round robin?
2. A county originally planned to use several days to complete the greening task of 120 mu of wasteland. In order to speed up the speed, the actual daily greening is 3 mu more than the original plan, and the result is 2 days ahead of the original plan. How many days should the original plan be completed?
3. A shopping mall bought a batch of daily necessities with a unit price of 16 yuan. After a period of time, the investigation found that if the price of each commodity is 20 yuan, 360 pieces can be sold each month; if the price of each commodity is 25 yuan, 210 pieces can be sold each month. If the number of pieces sold each month y (pieces) and the price x (yuan / piece) satisfy the relationship y = KX + B
(1) The functional relationship between Y and X is determined, and the value range of X is pointed out;
(2) In order to make a profit of 1800 yuan per month, how much is the price of each product?
(3) In order to get the maximum profit, how many yuan should the goods be set for each piece?

The first 12,
I don't know the second one, right,
The original plan was to take X days,
one hundred and twenty
(- + 3) x (X-2) = 120, the result is not calculated,
x
(X-10)(X+8)=0
X 1 = 10, x 2 = - 8 because x > 0, so x = - 8, x = 10 is consistent with the fact
The one behind didn't write it's time to stop our