It is known that the function f (x) = the cube of X + the square of AX + 3bx + C (B is not equal to 0), and G (x) = f (x) - 2 is an odd function?

It is known that the function f (x) = the cube of X + the square of AX + 3bx + C (B is not equal to 0), and G (x) = f (x) - 2 is an odd function?

G (x) = f (x) - 2 = x & sup3; + ax & sup2; + 3bx + C-2 is an odd function
g(-x)=-g(x)
-x³+ax²-3bx+c-2=-x³-ax²-3bx-c+2
2ax²+2c-4=0
This is an identity
So 2A = 0
2c-4=0
a=0,c=2

Given the function f (x) = (x ^ 2) / 2 + alnx, if a is equal to - 1, find the monotone increasing interval of F (x). When x is greater than or equal to 1
Given the function f (x) = (x ^ 2) / 2 + alnx, if a is equal to - 1, find the monotone increasing interval of F (x). When x is greater than or equal to 1, f (x) is greater than LNX, which is constant. Find the value of real number a

F '(x) = x + A / X when a = - 1, the solution set of F' (x) = X-1 / x > 0 is x > 1 (- 1lnx) constant, that is, f (x) - LNX > 0, let g (x) = f (x) - LNX = x & # 178 / / 2 + (A-1) LNX, then G (x) increases only when x ∈ [1, ∞), and G (1) > 0g '(x) = x + (A-1) / x, so x + (A-1) / x > 0 is constant when x ∈ [1, ∞)

Given f (x) = 2x + 3, X ∈ (- ∞, 0); 2x & # 178; + 1, X ∈ [0, + ∞], find the values of F (0) and f [f (x-1)]

f(0)=2*0²+1=1
1. When x

In the international system of units, the primary unit of length is______ , the symbol is______ In the international system of units, the primary unit of time is______ , the symbol is______ ．

In the international system of units, the main unit of length is meter, symbol m; the main unit of time is second, symbol s

Two materials with mass of M1 = 2kg and M2 = 3kg are placed on a smooth horizontal plane and connected by a light spring in the middle. The two materials are F1 = 30n and F2 = 20 respectively
(1) the acceleration of M1 is calculated when M1 is stable;
(2) (3) remove the acceleration of M1 at the moment of F1;
(4) Remove the acceleration of M1 at the moment of F2 removal

1)a1=a2=(F1-F2)/(m1+m2)=2m/s^2
2)m1a1=F1-T T=F1-m1a1=30-2*2=26N
3)m1a1'=T a1'=26/2=13m/s^2
4) When F2 is removed, the spring deformation remains unchanged, so t and F1 remain unchanged. A1 = 2m / S ^ 2 remains unchanged

A bulb marked with 110v10w, find its resistance, if connected in the 110V circuit, what is the actual power? The normal working current
When connected in the circuit of 220 V, how much is its actual power and what will happen?

1. Resistance R = u * U / P = 110 * 110 / 10 = 1210 Ω
2. Connected in the 110V circuit, the bulb works under the rated voltage, and the actual power is the marked power: 10W
3. Current I = P / u = 10 / 110 = 0.0909 a
4. Connected in the 220 V circuit, the actual power: P = u * U / r = 220 * 220 / 1210 = 40 W, working under overpressure, the bulb will soon burn out

There is a hollow aluminum ball with a mass of 540g and a volume of 300CM3______ Cm3, if the hollow part is filled with water, the total mass is______ g．

(1) When the aluminum ball is solid, its volume is v = m ρ al = 540g2.7g/cm3 = 200cm3; it is smaller than the current volume of the aluminum ball, so the aluminum ball is hollow; the volume of the hollow part is v = V present-v real = 300cm3-200cm3 = 100cm3; (2) the mass of the hollow part filled with water is m water = ρ water, V void = 1g / cm3 × 100cm3 = 100g; the total mass of the hollow part filled with water is m total = 540g + 100g = 640g; so the answer is: 100; 640

Formula of calculating side length of isosceles right triangle

Let the right angle side be x and the hypotenuse side be y
2x^2=y^2
^Represents square

As shown in the figure, objects a and B with equal mass are stacked on a smooth horizontal plane. One end of the two light springs is fixed on a vertical wall, and the other end is connected with a and B respectively. The original length of the two springs is the same, and the stiffness coefficient of the spring connected with a is less than that of the spring connected with B. at the beginning, a and B are in a static state. Now, a horizontal right tension is applied to object B to make a and B work together After moving to a certain position to the right, it is still (A and B have no relative sliding, and the spring is within the elastic limit)
A. The resultant force a receives is always equal to the spring force B. the resultant force a receives is always greater than the spring force B. the friction force a receives is always in the same direction as the spring force B. the friction force a receives is sometimes in the same or opposite direction as the spring force B

A. According to Hooke's law, FA = Kax, FB = kbx. According to the meaning of the title, Ka < KB, so FA < FB remains relatively static after pulling off the tension and moves to the left with acceleration A. according to Newton's second law, FA + FB = 2mA, then FA < Ma, so the elasticity of a is not stable after pulling off the tension For a, according to Newton's second law: FA + F = ma, the direction of static friction on a is horizontal to the left; for B, according to Newton's second law: fb-f = ma, so the resultant force on a is less than the spring force on B, so abd is wrong, and C is correct; so select C

Junior high school mathematics integral operation content exercises!
1. (X-Y) ^ 4 (Y-X) ^ 5 (X-Y) ^ 2 (and explain how to do it)
2. Why a ^ - P = 1 / A ^ - P

1. Transform (Y-X) ^ 5 to - (X-Y) ^ 5, and the result is - (X-Y) ^ 11
2、a^(-p)=(a^(-1))^p=1/(a^p)