Given that the direction vector of the line L1: x + A ^ 2Y + 1 = 0 is parallel to the normal vector of the line L2: (a ^ 2 + 1) x-by + 3 = 0, and AXB is not equal to 0, find the minimum value of | ab | I get a ^ 2B = a ^ 2 + 1 Then what should we do?

Given that the direction vector of the line L1: x + A ^ 2Y + 1 = 0 is parallel to the normal vector of the line L2: (a ^ 2 + 1) x-by + 3 = 0, and AXB is not equal to 0, find the minimum value of | ab | I get a ^ 2B = a ^ 2 + 1 Then what should we do?

a^2b=a^2+1
b=1+1/a^2
ab=a+1/a
|ab|=|a+1/a|=|a|+1/|a|≥2
The minimum is 2

Additional questions: as shown in the figure, it is known that △ ABC is inscribed in ⊙ o, AB is the diameter, ∠ CAE = ∠ B. verification: AE and ⊙ o are tangent to point a

It is proved that ∵ AB is the diameter, ∵ ACB = 90 degree, ∵ BAC + ∵ B = 90 degree, and ∵ CAE = ∵ B, ∵ BAC + ∵ CAE = 90 degree, that is, ∵ BAE = 90 degree, so AE and ⊙ o are tangent to point a

If X-2 is the solution of the equation K (2x-1) = KX + 7, then what is the value of K?

Substitute X-2 into the equation

Given that the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1, (a > b > 0) intersects the positive half axis of X axis at point a, O is the origin, if there is a point m, am ⊥ om on the ellipse, calculate the range of eccentricity

M can be regarded as a point on a circle with OA as its diameter
Center coordinates (A / 2,0), radius = A / 2
The equation of circle (x-a / 2) ^ 2 + y ^ 2 = a ^ 2 / 4
And the elliptic equation, eliminate y, get the solution,
One is x = a, the other is ab ^ 2 / (a ^ 2-B ^ 2)
X = a is the largest point of intersection, so there is
0

As shown in the figure, in the triangle ABC, e is the midpoint on the edge AC, and De is parallel to BC, EF is parallel to ab. prove that the triangle ade is equal to the triangle efc

It is proved that: ∵ de ∥ BC, ∫ AED = C,
∵EF∥AB,∴∠A=∠CEF,
∵ e is the midpoint of AC, ∵ AE = CE,
In Δ ade and Δ EFC:
∠A=∠CEF,AE=CE,∠AED=∠C,
∴ΔADE≌ΔEFC(SAS).

(1) As shown in the figure, the moving pulley is used to raise the speed of 900N objects by 2m. Regardless of the friction and pulley weight, how many n is the applied tension, and how many joules is the tension f in this process?
(2) In a construction site, workers use the pulley block as shown in the figure to transport the building materials weighing 1200n from the ground to the 20m high building. The vertical upward tension of the hand is 500N. In this process, how much extra work has the workers done and what is the mechanical efficiency of the pulley block?
(3) The pulley block can not only save labor but also change the direction of force. The 600 n weight of the pulley block made by construction workers can be slowly lifted by 2 M. as shown in the figure, the tension force at the free end of the rope is f = 250 n. what is the work done by the tension force, what is the mechanical efficiency of the pulley block, and how much is the moving pulley weight of the pulley block, N, regardless of all friction and rope weight?

1.F=G/n=900N/3=300N
W=Fs=F*nh=300N×3×2m=1800J
2. W = GH = 1200n * 20m = 24000j
Wtotal = FS = f * NH = 500N × 3 × 20m = 30000j
W amount = w total - w you = 30000j-24000j = 6000J
η = w yes / W total = 24000j / 30000j = 80%
3. Wtotal = FS = f * NH = 250N × 3 × 2m = 1500j
η = w / W total = 600N × 2m / 1500j = 80%
Gdynamic = nf-g = 3 × 250n-600n = 150n
That's about it in writing

Logx 3 ＜ 0, then the value range of X

logx(3)=1/log3(x)

Given that the three sides of a triangle are 6cm, 8cm and 10cm respectively, the area of the triangle is______ ．

∵ 62 + 82 = 102, this triangle is a right triangle, the area of this right triangle is 12 × 6 × 8 = 24 (cm2), so the answer is: 24cm2

The circuit is open. Is there any indication for measuring resistance with voltmeter
A resistor is connected in series in a simple circuit. The circuit is open. Connect it to both ends of the resistor with a voltmeter. There is a digital indicator. If so, whose is it

Open circuit is also called open circuit, which means that the line can not form a closed loop. The popular point is that if you start from the positive pole of the power supply, you can not return to the negative pole. The so-called short circuit means that the positive pole of the power supply is directly connected with the negative pole, and there is no resistance in the middle, or

Given the set M = {m | M = a + B √ 2, B belongs to Q}, then the number of the following four elements belonging to the set M is
(1) M = 1 + radical 2 · π
(2) M = root 7 + 2 · root 12
(3) M = 2 under root 3 + 2 under root 3 + root 3
There are four elements. The first one is relatively simple, but it doesn't go up

(1) M = 1 + radical 2. π, because π does not belong to Q, it is not;
(2) M = root 7 + 2 · root 12 = √ 7 + 4 √ 3, so it is not;
(3) M = 2 under root 3 + 2 under root 3 = 2 √ 2 = 0 + 2 √ 2, yes
So there is only one element that belongs to M