Given the square of function f (x) = (1 / 2a) * x + 2x, G (x) = LNX If the function y = f (x) is a monotone increasing function on [1, positive infinity], find the value range of A Is there any real number a > 0, like the equation g (x) / x = f '(x) - (2a + 1) in the interval (1 / E, e) with only two unequal real number roots? If it exists, ask for the value range of A. if it does not exist, explain the reason most urgent!

Given the square of function f (x) = (1 / 2a) * x + 2x, G (x) = LNX If the function y = f (x) is a monotone increasing function on [1, positive infinity], find the value range of A Is there any real number a > 0, like the equation g (x) / x = f '(x) - (2a + 1) in the interval (1 / E, e) with only two unequal real number roots? If it exists, ask for the value range of A. if it does not exist, explain the reason most urgent!

1. If f '(x) = ax + 2, f (x) is a monotone increasing function on X ∈ [1, + ∞), then f' (x) ≥ 0 is constant and f '(x) is not constant
If ax + 2 ≥ 0, X ∈ [1, + ∞) is constant, only a ≤ min {- 2 / X} = - 2, X ∈ [1, + ∞)
So the value range of a is (- ∞, 2]
2. If the equation g (x) / x = f '(x) - (2a + 1) has and only has two unequal real roots in the interval (1 / E, e),
The equation lnx-ax & sup2; + (2a-1) x = 0 has two different real roots in (1 / E, e)
Let g (x) = lnx-ax & sup2; + (2a-1) x, x > 0, as long as G (x) has two zeros in X ∈ (1 / E, e)
g'(x)=-2a[ x+1/(2a)](x-1)/x ,x>0
Let g '(x) = 0, then X1 = - 1 / (2a)

If the coordinate X of a particle moving on the x-axis changes with time t as x = 3t2 + 2t-4, then its acceleration a=______ And T = 0______ (x is in meters, T & nbsp; is in seconds)

According to x = v0t + 12at2 and x = 3t2 + 2t-4, we know a = 6m / S2. When t = 0, the speed is 2m / s. so the answer is: 6m / S2; 2m / s

On the problem of pinprick method in high school mathematical inequality
I don't know how to drive up and down when drawing. Just take (x + 4) (x + 7) (x-3) (X-7) > 0 as an example to give me a detailed picture. Why do you draw so

First of all, we must ensure that the coefficients of every x on the left side of the inequality are positive,
Then find out the root of the inequality, that is, change the inequality into an equation to solve. For example, the root of the above inequality is - 7, - 4,3,7, and mark it on the number axis
Then start to pierce the root. The method is: from right to left, from top to bottom,
Then according to the number axis above is positive, the number axis below is negative, write the inequality solution set, such as the above inequality solution set is: X

In the plane rectangular coordinate system, given the points a (0,1), B (- 1,0), C (1,0), if the point D and a, B, C constitute a parallelogram
Please write the coordinates of all points d that meet the conditions

Point d coordinates (2,1) of parallelogram with AB and BC as sides
Point d coordinates (0, - 1) of parallelogram with AB and AC as sides
Point d coordinates of parallelogram with AC and BC as sides (- 2,1)

X ^ 2-3x-2 = 0, find (x - 2x-1 / x) / (x ^ 2-2x)

( x - 2x-1/x )÷(x-1)/(x^2-2x)
=(x²-2x+1)/x ×x(x-2)/(x-1)
=(x-1)²/x ×x/(x-2)/(x-1)
=(x-1)(x-2)
=x²-3x+2
=x²-3x-2 +4
∵x²-3x-2=0
The original formula = 0 + 4
=4

Given that the distance from a point P to the focus f on the parabola y ^ 2 = 4x is 10, the coordinates of point P are obtained

A:
Parabola y ^ 2 = 4x = 2px
The solution is: P = 2
So: focus f (1,0), collimator x = - 1
The distance from point P to focus f on the parabola is equal to the distance from point P to the directrix
PF=x-(-1)=10
The solution is that the abscissa of point P is x = 9
Substituting into parabolic equation, y ^ 2 = 4x = 36
The solution is y = - 6 or y = 6
So: point P is (9, - 6) or (9,6)

Who can help me solve the integer solution of this binary linear equation. The equation is 4x + 7Y = 73, thank you

4x+7y=73
4x=73-7y
x=(73-7y)/4
The positive integer solution is
x=14,y=3
and
x=6,y=7

Physical experiment: in the experiment of "measuring the rated power of small light bulb" by voltammetry, the rated voltage of small light bulb is 2.5V, the resistance is about 10 Ω, and the power supply is 6V
There are two sliding rheostat R1 (10 Ω, 0.5A) and R2 (50 Ω, 0.5A). Which sliding rheostat should I choose? Why~

To make the small bulb work normally, the sliding rheostat needs 3.5V,
The current in the circuit is about I = u / r = 2.5v/10 Ω = 0.25A
The connecting resistance of the sliding rheostat is about R1 = U1 / I = 3.5v/0.25a = 14 Ω, so R2 (50 Ω, 0.5A) is selected,

Factorization of cubic equation with one variable

5X^3-24X^2+36x-16
=5x^3-10x^2-14x^2+28x+8x-16
=(5x^3-10x^2)-(14x^2-28x)+（8x-16）
=5x^2(x-2)-14x(x-2)+2(x-2)
=(x-2)(5x^2-14x+2)

How many days? How many hours? How many minutes? How many seconds did it take from April 28, 2012 to December 02, 2012?

Ha... This is simple
219 days, 5256 hours, 315360 minutes, 18921600 seconds, including the 28th and the 02TH,