Given that the function f (x) = 2 to the power of X (4) f (x) = f (x) + AF (2x), X belongs to the maximum value of (- ∝, 0)

F(x)=f(x)+af(2x)=2^x +a*2^2x
Let t = 2 ^ X;
Because x belongs to (∝, 0), t belongs to (0,1)
Then f (x) = a * T ^ 2 + t
When a = 0, f (x) = t, the maximum is 1
When 0

Let f (x) = (2x + 1) / (x ^ 2 + 2) for all x belonging to R, AF (x) + B, greater than or equal to - 3, less than or equal to 3, find the maximum value of a-b

For reference only:
F (x) = (2x + 1) / (x ^ 2 + 2) belongs to R for all x, and the value range is - 1 / 2

1. On the first day, the store bought 20 pieces of A-type goods at the price of a yuan per piece, and on the second day, it bought 30 pieces of B-type goods at the price of (A-2) yuan per piece, and then sold them all at a 20% increase in price. How many yuan did the store sell in total?
2. A group of students go to a construction site for social practice activities. Boys wear white helmets and girls wear red helmets. They sit together during the rest. We find an interesting phenomenon. Every boy sees as many white helmets as red helmets, and every girl sees twice as many white helmets as red helmets. According to these information, how many students are there in this group?
3. Jiangnan ecological food processing factory has purchased a batch of mountain goods with a mass of 10000 kg, and rough and finish them according to the market demand. It is known that the mass of the mountain goods with finish processing is 2000 kg more than 3 times of that with rough processing, so the mass of the mountain goods with rough processing can be calculated
4. A "harmony" EMU running on Hainan east ring high-speed railway has 6 first-class and second-class carriages, with a total of 496 seats, including 64 seats in each first-class carriage and 92 seats in each second-class carriage. How many first-class carriages and second-class carriages are there?
5. One day, mother bear went out to do business and told little bear to take care of the fruit shop for her. He liked the little fox who was greedy to buy fruit. He chose a total of 8 kg Yali and grapes, which were sold for 3 yuan per kg Yali and 5 yuan per kg grapes. But when calculating the accounts, the careless little bear made a mistake in the price of Yali and grapes, and sold them for 28 yuan at 5 yuan per kg Yali and 3 yuan per kg grapes, Little fox left happily after paying. Please calculate. How much did little bear lose when the price was wrong?
6. Master Zhao drives a truck and master Qian drives a bus. They start from a and B at the same time. After 4 hours, they meet on the way. After meeting, the two cars continue to move forward at the same speed. After another 3.2 hours, master Zhao just arrives at B. He uses his mobile phone to contact master Qian. He asks how far is the distance between a and B. master Qian only says that there are 108 kilometers from a now. After hanging up, master Zhao can get back to B, The two masters and Xiao Ming in the car have worked out the distance between the two places at the same time. Please work out the distance between the two places

1.(20a+30(a-2))(1+20%)=1.2(50a-60)
2. Girl x
X + 1 = 2 (x-1) x = 3 students have 3 + 3 + 1 = 7
3.x+3x+2000=10000 x=2000
4. First class carriage x
64x + 92 (6-x) = 496 x = 2 second class car 6-2 = 4
5. Design and buy pear XKG
5x+3(8-x)=28
x=2
3 * 2 + 5 * (8-2) - 28 = 8 yuan
6. Set X speed of freight car and Y speed of passenger car
4(x+y)=x(3.2+4)=y(3.2+4)+108
x=75 y=60
Distance between the two places 4 (75 + 60) = 540

On a square board with a circumference of 80 cm, saw the largest circle. What is the area of the circle in square cm?

The side length of the square is: 80 △ 4 = 20 (CM), the area of the circle is: 3.14 × (20 △ 2) 2, = 3.14 × 102, = 3.14 × 100, = 314 (square cm). Answer: the area of the circle is 314 square cm

It is known that: ab ≠ 0, A2 + ab-2b2 = 0, then the value of 2A − B2A + B is______ ．

The area problem and answer of mathematics circle in Grade 6 Volume 1

What about the problem? No problem, no solution

There is a rectangle. The width increases by 5 meters and the length decreases by 3 meters to form a square. The square area is 75 square meters larger than that of the rectangle
I am a primary school student, can only use the formula, can't use XY to bring, hope can give me the formula and formula together!

You can draw a picture
The side length of the square is (75-3 * 5) / (5-3) = 30
The area is 30 * 30 = 900 square meters

The sun light reaches the earth after 500 seconds, and the radius of the earth is 6.4 × 10 cubic meters

A:
The period of the earth's revolution around the sun is t = 365 * 24 * 3600s, t = 500s, and the distance between the sun and the earth is x = CT,
M1 and M2 are the mass of the sun and the earth respectively, C = 3 * 10 ^ 8m / S is the speed of light, G is the acceleration of gravity,
R is the radius of the earth, G is the gravitational constant,
GM1M2/x^2=mx(2π/T)^2
Gold substitution
GM2=gR^2
Division of two forms
M1/M2≈3.3*10^5,
The mass of the sun is about 330000 times that of the earth

Calculation of sound phenomenon in junior high school
Want some classic (not too simple) questions. Thank you! More is better!

The concept and formula are not found, but help you find some test questions of sound phenomenon, hope to be useful to you

The area of a circle and a square is 2 π cm2. Which of them has a larger perimeter? What can you learn from it?

(1) Let the radius of the circle be RCM, then π R2 = 2 π, the solution is r = 2, then the circumference of the circle is 2 π r = 2 π × 2 ≈ 8.88; let the side length of the square be ACM, then A2 = 2 π a = 2 π≈ 2.506, then the circumference of the square is 4A ≈ 10.02 ＞ 8.88, then the circumference of the square is larger. (2) enlightenment: when the surface product of the circle and the square is equal, the circumference of the square is larger

Given that the function f (x) = 2 to the power of X (4) f (x) = f (x) + AF (2x), X belongs to the maximum value of (- ∝, 0)