Let f (x) = LG (1 + 2 ^ x + (4 ^ x) * a) (a belongs to R). If f (x) is always meaningful when x belongs to (negative infinity, 1), find the value range of A

Obviously 1 + 2 ^ x + (4 ^ x) * a, then a > = 0 holds
When a

Master! Find the minimum value of u = √ (2x ^ 2-6x + 5) + √ (y ^ 2-4y + 5) + √ (2x ^ 2-2xy + y ^ 2)

Did you learn calculus? Find partial differential, then find extremum,
X = 8 / 7, y = 11 / 7, minimum 3 / 7

Exercises of binary linear equations (simple point)

X + y = 5, ① 6x + 13y = 89, ② get x = 5-y from ①, ③ substitute into ②, get 6 (5-y) + 13y = 89, i.e. y = 59 / 7, and y = 59 / 7 substitute into ③, get x = 5-59 / 7, i.e. x = - 24 / 7, x = - 24 / 7, y = 59 / 7 as the solution of the equations
X + y = 9, ① X-Y = 5, ② ① + ② 2x = 14, that is, x = 7, substituting x = 7 into ①, 7 + y = 9 solution is obtained, and y = 2  x = 7, y = 2 is the solution of the system of equations

Derivative of complex function
The analytic region of this function is pointed out and its derivative is obtained
F (z) = (x + y) / (x ^ 2 + y ^ 2) + (X-Y) / (x ^ 2 + y ^ 2) I, I am a beginner,
Let u = (x + y) / (x ^ 2 + y ^ 2), v = (X-Y) / (x ^ 2 + y ^ 2), using Cauchy Riemann condition, f '(z) = u partial derivative of X + V partial derivative of X, after reduction, we get: f (z) derivative = (y ^ 2-x ^ 2-2 * x * y) / (x ^ 2 + y ^ 2) ^ 2 + (y ^ 2-x ^ 2 + 2 * x * y) I / (x ^ 2 + y ^ 2) ^ 2, how can we continue to simplify this formula, please master's advice, or there is a mistake in finding the partial derivative, we really can't work it out
But the answer is not like this, the derivative of F (z) = - (1 + I) / Z ^ 2, would you please look at the next sign for me? This is the exercise at the back of the self-taught textbook, but I just can't simplify it

If you do it right, it's OK to calculate. This formula doesn't need to be changed. This is the answer. But you also need to point out that the analytic region is to use the Cauchy Riemann condition, U's partial derivative of x = V's partial derivative of Y, U's partial derivative of y = - V's partial derivative of X to find the range of X and Y. this is the analytic region. In the answer, z = x + iy

It is known that a, B, a + B are equal difference sequence, a, B, AB are equal ratio sequence, and 0

a. B, a + B is equal difference sequence, a, B, AB is equal ratio sequence
2b=a+a+b
b=2a
b²=a*ab=a²b
So 4A & sup2; = A & sup2; * (2a)
A ≠ 0
So a = 2
b=4
So 0

In the xoy plane of the static reference frame K, the inner side length is a square. The other reference frame a moves uniformly along the X direction of the static reference frame at the speed of 0.8C. The area of the thin plate measured from a is 0.6A square. Why, I want to know the calculation principle

The length of the moving direction becomes shorter (0.6A), and the length of the other direction remains unchanged as a. the moving square looks like a rectangle with an area of 0.6 * a * a

Calculation (x ^ 3 + 3x-2) (5-x + 2x ^ 2)

（x^3+3x-2)(5-x+2x^2)
=5x^3-x^4+2x^5+15x-3x^2+6x^3-10+2x-4x^2
=2x^5-x^4+11x^3-7x^2+17x-10

A square is divided into five equal long shapes. The circumference of each rectangle is 60 cm. What is the area of this square?

Because the side length of a square is divided by 5, one side of the rectangle is x, the other side is 5x, the perimeter is 12x, 12x = 60, x = 5, the side length of the square is 5x = 25, and the area is 625 square meters

What is slip related to? What factors will make slip change? And what impact does slip have on motor?

Slip = (synchronous speed asynchronous speed) / synchronous speed
Synchronous speed = 60 * power frequency / number of poles
Asynchronous speed is the speed of the motor
Frequency conversion energy saving means frequency conversion speed regulation
The basic principle of variable frequency speed regulation technology is based on the direct proportion between the motor speed and the input frequency of the working power supply: n = 60 f (1-s) / P (where N, F, s and P represent the speed, input frequency, motor slip and motor pole pairs respectively); the purpose of changing the motor speed is achieved by changing the working power frequency of the motor
The speed formula of three-phase asynchronous motor is: n = 60F / P (1-s). It can be seen from the above formula that the purpose of changing the speed can be achieved by changing the power supply frequency f, the number of poles P and slip s, Different speed regulation methods are to change the synchronous speed of AC motor or not The speed control methods without changing synchronous speed are widely used in production machinery, such as rotor series resistance speed control, chopper speed control, cascade speed control of wound motor, and speed control with electromagnetic slip clutch, hydraulic coupling, oil film clutch, etc, From the point of view of energy consumption, there are two methods: high efficiency speed regulation and low efficiency speed regulation: high efficiency speed regulation means that the time slip is constant, so there is no slip loss, For example, multi speed motor, frequency conversion speed regulation and speed regulation methods (such as cascade speed regulation) that can recover slip loss. Speed regulation methods with slip loss are low efficiency speed regulation, such as rotor resistance speed regulation method, energy loss is in the rotor circuit; speed regulation method of electromagnetic clutch, energy loss is in the clutch coil; speed regulation method of hydraulic coupling, energy loss is in the rotor circuit, The energy loss is in the oil of the hydraulic coupling. Generally speaking, the slip loss increases with the expansion of the speed range. If the speed range is small, the energy loss is very small

To solve the quadratic equation of two variables (using the method of addition and subtraction,
1.4x+3y=-1①2x-y=7②
2.6s=27-5t①3s=18-4t②
3. Third x + fourth y = 2 ① 3x-4y = - 7 ②
4. Half x-third y + 1 ① 3x + 2Y = 10 ②

1.4x+3y=-1①2x-y=7②
From (1) + 3 (2), we get
10x=20
x=2
Substituting in 2, we get
y=-3
2.6s=27-5t①3s=18-4t②
From (1) - 2 (2), it is concluded that
0=-9+3t
t=3
Substituting in (1), we get
s=2
3.x/3+y/4=2①3x-4y=-7②
From 16 (1) + 2 (2), we get
25x/3=25
x=3
Substituting in 2, we get
y=4
Question 4 is wrong

Let f (x) = LG (1 + 2 ^ x + (4 ^ x) * a) (a belongs to R). If f (x) is always meaningful when x belongs to (negative infinity, 1), find the value range of A