If the center of circumscribed circle of triangle ABC is known to be o, AC = 6, BC = 7, ab = 8, then vector Ao × vector BC =?

If the center of circumscribed circle of triangle ABC is known to be o, AC = 6, BC = 7, ab = 8, then vector Ao × vector BC =?

Because o is the outer center of the triangle (the center of circumscribed circle is called the outer center), the projection of O on the three sides of the triangle is the midpoint of the three sides, so AO * AB = | Ao | * | ab | * cos ∠ OAB = (| Ao | * cos ∠ OAB) * | ab | = (1 / 2 * | ab |) * | ab | = 32. Similarly, AO * AC = 1 / 2 * | AC | ^ 2 =

If u = R, M = {x | x ≥ 1}, n = {x | x + 1x − 2 ≥ 0}, then ∁ U (m ∩ n)=______ ．

Because M = {x | x ≥ 1}, n = {x | x ＞ 2 or X ≤ - 1}, then m ∩ n = {x | x ＞ 2}, so ∁ U (m ∩ n) = {x | x ≤ 2}

It is known that, as shown in the figure, RT △ ABC and RT △ ADC, ∠ ABC = ∠ ADC = 90 ° and point E is the midpoint of AC

It is proved that: ∵ ABC = 90 ° and point E is the middle point of AC, ∵ EB = 12ac, similarly: ed = 12ac, ∵ EB = ed, ∵ EBD = EDB

Finding the solution set of inequality ax + b > 0 {A is not equal to 0}

When a > 0
∵ax+b>0
∴ax>-b
∴x>-b/a
When a

If Da = a, DC = B in the parallelogram ABCD and its diagonal intersection is O, then ob is a vector

OB=½a+½b

My father is 28 years older than Xiao Liang this year. Seven years later, my father's age is three times that of Xiao Liang. How old are my father and Xiao Liang this year?
The answer is that dad is 35 years old and Xiao Liang is 7 years old
But I use the equation to calculate, children do not understand, please master do not use the equation,

This is the problem of difference times in arithmetic
Xiaoliang: 28 / (3-1) = 14
Dad: 14 * 3 = 42
Now: 14-7 = 7 42-7 = 35
If you want to talk about it, you can do as follows:
1. The age difference between them is 28
Two or seven years later, my father was three times as old as Xiao Liang,
3, difference 28 is 2 times of Xiaoliang's age
4. Xiaoliang's age is 28 / 2 = 14, and his father's is 14 * 3 = 42
They are now 7 and 35

Why is current scalar? What is vector parallelogram rule?
be deeply grateful..

You can understand the current as a kind of matter, because the current is a beam of electrons carrying energy (electrons are a kind of matter, and energy can also be understood as a kind of matter), and the matter itself has only the size of mass and no so-called direction, while the force is a way of energy transfer, and all ways of energy transfer have vector existence, If you want to move a substance to another place, there are two necessary conditions: 1. The energy (size) required to move the substance there (energy is also a scalar with size but no direction, because energy is also a substance). 2. Where (direction) you need to move. Then only through the force with size and direction can you move the substance to another place, Another example is heat transfer. From the microscopic point of view, it is actually the displacement between molecules, which is also realized by the "force" between molecules
The parallelogram rule of vector is actually very simple. For example, if you want to push a box to the southwest for a distance of √ 2 meters (root 2 meters), you can achieve three methods: 1. Push 1 meter to the south, and then pile 1 meter to the West; 2. Push 1 meter to the west, and then push 1 meter to the South; 3. Directly push √ 2 meters to the southeast, The result of a force can be obtained by adding two other forces. You can draw with a stroke. It's easy to understand

Use the method of solving equation on five!
1. The distance between a and B is 380 km, one of which is Expressway and the other is ordinary highway. A car drives the whole journey in 4 hours. It is known that the driving speed on the expressway is 100 km / h, and the driving speed on the ordinary highway is 80 km / h. The length of the expressway can be calculated
2. A person's salary for one month's work is 1000 yuan and 4 blankets. After 17 days of work, he quits and gets 5 blankets, 430 yuan each. How much is each blanket? (30 days of this month)

1. If the car runs on the highway for X hours, it runs on the ordinary highway for (4-x) hours
100X+80（4-X）=380
100X+320-80X=380
20X=60
X=3
So (4-x) = 1
A: three hours on the highway and one hour on the ordinary highway
2. Set X Yuan for each blanket
17（1000+4X）=30（430+5X）
17000+68X=12900+150X
82X=4100
X=5
A: 5 yuan per blanket

Known function f (x) = 2 ^ X-2 ^ (- x) / 2 ^ x + 2 ^ (- x)
1. Find the definition and range of function
2. Ask if there are two different points a and B on the image of function f (x), so that the line AB is just perpendicular to the Y axis. If there are, find out the coordinates of two points a and B; if not, explain the reason and prove it

Let t = 2 ^ x, then when x ≥ 0, t ≥ 1
∴f(t)=(t-1/t)/(t+1/t )
=(t^2-1)/(t^2+1)
=1-2/(t^2+1)
T ≥ 1, then T ^ 2 + 1 ≥ 2; 0 ＜ 1 / (T ^ 2 + 1) ≤ 1 / 2; 0 ＞ - 2 / (T ^ 2 + 1) ≥ - 1; 1 ＞ 1-2 / (T ^ 2 + 1) ≥ 0
That is, when x ≥ 0, the range of F (x) is [0,1]
∵ f (- x) = (2 ^ - X-2 ^ x) / (2 ^ - x + 2 ^ x) = - (2 ^ X-2 ^ - x) / (2 ^ x + 2 ^ - x) = - f (x), if f (x) is an odd function, then the range is symmetric about the origin. Then when x ≤ 0, the range of F (x) is (- 1,0]
In conclusion, the range of F (x) = (2 ^ X-2 ^ - x) / (2 ^ x + 2 ^ - x) is (- 1,1)

Application of derivative of one variable function
F (x) and its first derivative are continuous on [a, b], the second derivative exists in (a, b), f (a) = f (b) = 0, and there are points in (a, b) such that f (c) > 0
It is proved that there is a point Q in (a, b) such that the second derivative of F (q) is less than 0
Please give me an idea. I really don't know how to start

It is known that f (a) = f (b) = 0 and f (c) > 0 (C ∈ (a, b)), and f (x) is continuous on [a, b]
So there must be a point P in (a, c) such that f '(P) > 0;
Similarly, there must be a point Q in (B, c) such that f '(q)