In a plan with a scale of 1 / 400, the bottom of a triangular vegetable field is 8 cm, and the height is 4.5 cm. The actual area of this triangular vegetable field is 8 cm

In a plan with a scale of 1 / 400, the bottom of a triangular vegetable field is 8 cm, and the height is 4.5 cm. The actual area of this triangular vegetable field is 8 cm

8 * 400 = 3200 cm = 32 m
4.5 * 400 = 1800 cm = 18 m
32*18=576

Seeking fairy tale composition
Please choose some of the animals such as pig, lamb, rabbit, Fox and wolf to play the leading role and make up a fairy tale

a long time ago, there was a dense forest. There lived a lovely lamb. One day, the lamb felt very lonely and decided to go and play with a friend. Before his lamb left, his mother gave him a piece of meat, a hoe and a bottle of perfume.

Proof: the square difference of two consecutive odd numbers is 8 times, and is equal to twice the sum of the two numbers

Let the two consecutive odd numbers be 2N-1, 2n + 1, n ∈ n, n > 1
Then (2n + 1) & sup2; - (2n-1) & sup2; = (2n + 1 + 2n-1) [2n + 1 - (2n-1)] = 8N, which is obviously a multiple of 8;
And (2n + 1) + (2n - 1) = 4N, 8N is obviously a multiple of 4N
The proof is complete

How to divide an isosceles right triangle into four triangles of equal area

Method 1: the isosceles right triangle can be divided into four equal area triangles by taking the middle points of the three sides of the isosceles right triangle and connecting them with each other; method 2: the isosceles right triangle can be divided into four equal area triangles by taking the middle points of the three sides of the isosceles right triangle and connecting the right vertex and the middle point of the right side with the middle point of the hypotenuse;

The following motion is translational. Why
A. The movement of kite flying with the wind
B. The movement of basketball in the process of rolling
C. The movement of a car on the ground when it brakes sharply
D. Bubble rising during ice water heating

C.
Because a doesn't have to be translational, wind direction doesn't have to be, maybe it will drift
B is also wrong, the rolling basketball, not translation, because the above pattern does not translate together, but rolling rotation
D is also wrong. Bubbles from bottom to top will grow from small to large, obviously not translational

The symmetric curve equation of circle C: X ＾ + y ＾ - 2x-6y + 9 = 0 with respect to straight line X-Y + 1 = 0

X-Y + 1 = 0 is a special line
∴ x=y-1,y=x+1
The equation of curve symmetric with respect to X-Y + 1 = 0 only needs to change x into Y-1 and Y into x + 1
The symmetric curve equation of circle C: X ＾ + y ＾ - 2x-6y + 9 = 0 with respect to straight line X-Y + 1 = 0
(y-1)²+(x+1)²-2(y-1)-6(x+1)+9=0
It is reduced to X & # 178; + Y & # 178; - 4x-4y + 7 = 0

If vectors a and B are nonzero vectors, it is necessary and sufficient to prove that | a + B | = | a | + | B |, if vectors a and B are collinear and in the same direction

Certification:
Let the angle between vectors a and B be X
∵|a+b|=|a|+|b|===>|a+b|²=(|a|+|b|)²
That is a & sup2; + B & sup2; + 2 | a | B | cosx = A & sup2; + B & sup2; + 2 | a | B | cosx = 1 = = = > x = 0 & ordm;
A vector and B vector are collinear and in the same direction
∵ a vector and B vector are collinear, x = 0 & ordm; = = = > cosx = 1
===>a²+b²+2|a||b|cosx=a²+b²+2|a||b|=(|a|+|b|)²
∴ |a+b|=|a|+|b|
The sufficiency and necessity are satisfied, the proof is over!

In △ ABC, the vertical bisectors of AB and AC intersect BC at points E and f respectively. If ∠ BAC = 115 °, then ∠ EAF=______ Degree

The vertical bisectors of AB and AC intersect BC at points E and f respectively, so: (1) ea = EB, then ∠ B = ∠ EAG, let ∠ B = ∠ EAG = x degree, (2) FA = FC, then ∠ C = ∠ FAH, let ∠ C = ∠ FAH = y, because ∠ BAC = 115 ° so x + y + ∠ EAF = 115 ° according to the triangle inner angle sum theorem, x + y + X + y + ∠ EAF = 18

Given the function f (x) = x ^ 2-x, A1 = f (x + 1), A2 = 1, A3 = f (x) in the arithmetic sequence {an},
(1) Finding the general term an of sequence {an}
(2) When finding that the sequence {an} is a decreasing sequence, find A1 absolute value + A2 absolute value + a3 absolute value + +Absolute value of an

According to the properties of arithmetic sequence and the conditions given in the title, we can get the following results
2A2 = a1 + a3, that is, 2 = (x + 1) & sup2; - (x + 1) + X & sup2; - x = 2x & sup2;, so x = ± 1, so A1 = 2 or 0, d = - 1 or 1, so the general term an = a1 + (n-1) d = 3-N or n-1
When the sequence is a decreasing sequence, A1 = 2, an = 3-N, the first three items are 2, 1 and 0 respectively, the absolute value is itself, and the absolute value of the following items is its own negative number, then the required value of the title is 3 + 1 + 2 + 3 + +n. According to the summation formula of arithmetic sequence, the above formula is 3 + (n & sup2; + n) / 2

Prove that three vectors are coplanar

The vector k1a-k2b + (k2b-k3c) = k1a-k3c = - (k3c-k1a),
The vectors K 1a-k 2B, K 2b-k 3C, K 3c-k 1A are coplanar