It is known that the center of the ellipse C is at the coordinate origin, the focus is on the y-axis, and the eccentricity is √ 2 / 2. Take one vertex and two focuses of its minor axis as the vertex, and the triangle area = 0.5 1) Solving elliptic equation 2) If there are two points a and B, which are the intersection and difference between the line L passing through the point P (0, m) and the ellipse, and satisfy AP vector = λ Pb vector, OA vector + λ ob vector = 4op vector, calculate the value of λ and the value range of M

(1) It is easy to get that the elliptic equation is
2X^2+Y^2=1
⑵
Let a (x1, Y1) B (X2, Y2)
From vector AP = λ vector PB
-X1=λX2
m-Y1=λ(Y2-m)
From the vector OA + λ vector ob = 4 vector op
X1+λX2=0
Y1+λY2=4m
The above four styles
λ=3
That is, X1 ^ 2 = 9x2 ^ 2 Y1 ^ 2 = (4m-3y2) ^ 2 ①
From elliptic equation
2X1^2+Y1^2=1 2X2^2+Y2^2=1
Substituting (1) into the solution
2m^2-3mY2+1=0
Y2=(2m^2+1)/3m
Because Y2 ∈ [- 1,1]
(2m^2+1)/3m∈[-1,1]
Solution
m∈[-1,-1/2]∪[1/2,1]
[[not clear, ask again; satisfied, good luck to you!]]

Fourth grade bracket exercise 200

1、 Teacher: do you know the order of the following two questions? Teacher: if the first question is to add and the second question is to subtract, is there any way to achieve it? Student: add parentheses. Choose a student to write on the blackboard: 360 ÷ (12 + 6) × 5120 ÷ (8-4)

The minimum distance from the point on the ellipse x ^ / 16 + y ^ / 9 = 1 to the straight line x-y-40 = 0 is?

Ellipse X & # 178 / 16 + Y & # 178 / 9 = 1
Let x = 4cos θ, y = 3sin θ
Then the distance from the point on the ellipse to the straight line is d = | 4cos θ - 3sin θ - 40 | / √ (1 + 1) = | - 5sin (θ - α) - 40 | / √ 2 = | 5sin (θ - α) + 40 | / √ 2
The auxiliary angle formula is used in the middle, where Tan α = 4 / 3
So the minimum value of D is | - 5 + 40 | / √ 2 = 35 √ 2 / 2
Similarly, we can know that the maximum value is | 5 + 40 | / √ 2 = 45 √ 2 / 2

Simple arithmetic problems in Grade Four

1.
9999×1111+3333×6667
=3333 ×3333+3333×6667
=3333×（3333+6667）
=3333×10000
=33330000
two
1005*10061006+1066*10051005
=1005*1006*10001+1005*1006*10001
=2*1005*1006*10001
=2010*1006*10001
=20222622060

For the equations of X and Y {2x + y = a 1}, {3x-y = 4A 2}, the solution satisfies X-Y ＞ 2, and the value range of a is obtained

2x+y=a①,3x-y=4a②
The sum of the two formulas gives 5x = 5a, x = a
Substituting Formula 1, we get 2A + y = A and y = - A
x-y=a-(-a)=2a>2
A > 1

The problem of special relativity
The length of a train at rest is longer than that of a tunnel. When it passes through the tunnel at high speed, two lightning strikes at both ends of the tunnel at the same time. Due to the relativistic effect, the length shrinks to shorter than the length of the tunnel, so that two people standing at both ends of the train avoid the damage of lightning. But the movement is relative. In the view of people on the train, the tunnel is moving in the opposite direction, Now ask: in the view of the people on the train, can the people on both ends of the train avoid the damage of lightning?

In the s system (tunnel), two lightning flashes appear at the same time. But in the s' system (train), people see the lightning in front first flash, and then pass through safely. After the tail of the train enters the tunnel, the lightning in the back flash, so the people on the train are safe. So, the causality you see still holds in other coordinate systems. Do you understand? I guess you may not understand the formula, So it's only written

There is a rectangular sheet of iron 40 cm long and 30 cm wide, which can be folded into an 8 cm deep sheet after subtracting the square of equal area from the four corners
Find the volume of this iron box

It's eight centimeters deep
So the side length of the minus small square is 8 cm
So the length of the bottom is 40-8-8 = 24 cm
Width 30-8-8 = 14 cm
So the volume is 24 × 14 × 8 = 2688 ml

What are the main components of the alternator?

The alternator is mainly composed of three-phase alternator and silicon diode rectifier. The three-phase alternator is mainly composed of rotor, stator, front and rear end cover, fan, pulley, etc, The inner space is equipped with steel magnetic choke and excitation winding. The two ends of the excitation winding are respectively welded on the mutually insulated slip ring, and the two brush bows are respectively connected with the "ground" connection post and "magnetic field" connection post on the rear end cover of the generator. When the excitation current passes through, six pairs of magnetic poles are formed. ② the stator is also called armature, The main function is to generate three-phase alternating current. It is composed of iron core and three-phase winding. The stator iron core is composed of five phase insulated circular silicon steel sheets with slots. The stator slots are wound with three-phase symmetrical windings for star connection, The silicon diode rectifier is used to rectify the three-phase alternating current generated by the generator into direct current. It is composed of six diodes, which are respectively pressed on the aluminum alloy element plate and the rear end cover to form a three-phase bridge rectifier circuit. For the generator with negative grounding, the three diodes installed on the rear end cover are negative tubes, and the shell is positive, The three diode shells connected together become the negative pole of the generator, and the center lead is the negative pole of the tube; the three diodes installed on the component board are the positive pole, and the shell is the negative pole, and the three diode shells connected together become the positive pole of the generator, and the center lead is the positive pole of the tube

A rectangular cardboard, cut a square with side length of 5cm from each corner, and then fold it along the dotted line into a cuboid box without cover. What's the volume of this box?

(35-10)x(20-10)x5=1250

It takes 8 days for Party A and Party B to complete a work together. It is known that the work efficiency of Party A is twice that of Party B. how many days does it take for Party A and Party B to complete this work alone?

It takes 8 days for Party A and Party B to complete a work together, so their work efficiency is 1 / 8
The working efficiency of Party B is: 1 / 8 (2 + 1) = 1 / 24
The efficiency of a is: 1 / 24 * 2 = 1 / 12
The number of days a uses is: 1 △ 1 / 12 = 12 (days)
The number of days used by Party B is: 1 / 24 = 24 (days)