Given x ^ 2 + 4Y ^ 2 = 4, find the maximum value of M = x ^ 2 + 2XY + 4Y ^ 2 + X + 2Y

x^2+4y^2=4
Let x = 2cos α, y = sin α
M＝x^2+2xy+4y^2+x+2y=4+2xy+x+2y=4sinα*cosα+2(sinα+cosα)+4
Then use the maximum value of trigonometric function to deal with it

Given 1 / 4 (x ＾ 2Y ＾ 3) ＾ m (2XY ＾ n + 1) ＾ 2 = x ＾ 4Y. Find the value of (m ＾ 2n) ＾ 3

Left = x ^ (2m + 2) y ^ (3 + 2n + 2) = x ^ 4Y
So 2m-2 = 4
3+2n+2=1
m=3,n=-2
So the original formula = 18 ^ 3 = 5832

The quadratic equation with real coefficients x ^ 2 + (a + 1) x + A + B + 1 = 0 has two real roots x1, X2, and 0

Let f (x) = x ^ 2 + (1 + a) x + A + B + 1
Satisfy the condition that the two real roots are x1, X2, and 00 f (1) 0
f(1)=2a+b+3

If f (x ^ 6) = log2x ^ 3, then f (8)=

Let x ^ 6 = t, then x ^ 3 = √ t
f(x^6)=log2x^3
That is, f (T) = log2 √ t
Then f (8) = log2 (√ 8)
=log2 [2^(3/2]
=3/2
So f (8) = 3 / 2

The radius of the earth increases by 1 meter, and the radius of table tennis increases by 1 meter
Not from the point of calculation, I think it's strange to measure. I take a small table tennis ball and a big table tennis ball to measure, and increase 1 meter. I think it's definitely not the same. Why is it the same?

If the radius of the earth r meter increases by 1 meter, and the radius of table tennis r meter increases by 1 meter, how many meters will the circumference increase?
2 π (R + 1) - 2 π r = 2 π R + 2 π - 2 π r = 2 π (m),
2 π (R + 1) - 2 π r = 2 π R + 2 π - 2 π r = 2 π (m),
The perimeter increases by 2 π M;
Sometimes people's feeling is wrong, and mathematical calculation is rigorous. So we should base on correct calculation rather than on people's feeling

On the calculation of circuit
The working principle of the diesel generator is: the air-cooled four stroke direct injection diesel engine is used as the power system to drive the generator to generate electricity. Now a diesel generator of this type is used to supply temporary emergency power to a residential area. The distance between the generator and the residential area is 400m. The fire line and zero line in the transmission line are gbcz60 single strand copper wires, The resistance per unit length of this type of conductor is 0.00025 ohm / m. The total power of household appliances in residential area is 44 kW
(1) What is the current in the transmission line?
(2) What is the power loss of transmission line?
(3) What is the actual output voltage of the generator?

(1) The current of the transmission line is the current in the trunk road, and the household appliances are in parallel with each other, with the rated voltage of 220 v
So I = 44000 / 220 = 20A
(2) Power loss P = I ^ 2R = 400 * 0.00025 * 400 = 40W
(3) The actual output voltage of generator is = 20 * 0.1 + 220 = 222v

Can you tell me the set symbol
In the derivative formula:
If f (x) = x ^ n, then f '(x) = NX ^ (n-1), (n ∈ Q )
Is that Q for "positive rational number"? If it is, is n not allowed to be negative in (x ^ n) '= NX ^ (n-1)? Since n can only be positive rational number, why is [x ^ (- 1)]' = (1 / x) '= - 1 / X & sup2; = - x ^ (- 2) Tenable?

Q * denotes the set of rational numbers without 0
The set of positive rational numbers is Q +. The set of negative rational numbers is Q -
Representation of special set C real number set R positive real number set R + negative real number set r-integer set Z positive integer set Z + negative integer set z-rational number set Q positive rational number set Q + negative rational number set q-rational number set without zero Q * natural number set n natural number set without zero n*

As shown in the figure, in ladder ABCD, ad ‖ BC, e is the midpoint of AB, de ⊥ CE

It is proved that the extension line of de-cb is extended to F, ∵ ad ≌ CF, ≌ ad = BF, de = EF, ≁ CE ⊥ DF, ≁ CD = CF = BC + BF, ≌ AD + BC = DC in △ AED and △ bef

Let a be a matrix of order n, and prove that a + at is a symmetric matrix

(a + at) t = at + (at) t = at + a = a + at, so a + at is a symmetric matrix

The square of (T-3) times the maximum of (- t square + 2T + 1)

In this problem, you can get a cubic equation with one variable by deriving it first. After finding the root of the cubic equation with one variable, you can draw a general picture and get the solution you want. The method of kaldan formula is as follows: equation x ^ 3 + PX + q = 0, (P, Q ∈ R) discriminant △ = (Q / 2) ^ 2 + (P / 3) ^ 3. X

Given x ^ 2 + 4Y ^ 2 = 4, find the maximum value of M = x ^ 2 + 2XY + 4Y ^ 2 + X + 2Y