If the sum of squares of several consecutive odd numbers is equal to the square of a certain number, we can find the four consecutive odd numbers and do it by factorization

If the sum of squares of several consecutive odd numbers is equal to the square of a certain number, we can find the four consecutive odd numbers and do it by factorization

Let four odd numbers be 2n-3,2n-1,2n + 1,2n + 3 (2n-3) 2 + (2n-1) 2 + (2n + 1) 2 + (2n + 3) 2 = m2, which is reduced to 16n2 + 20 = S2; therefore, (s-4n) (s + 4N) = 20 = 1x20 = 2x10 = 4X5, because s-4n and S + 4N are odd and even, so s-4n = 2 and S + 4N = 10 or s-4n = 10 and S + 4N = 2

This is a square made of tangram. The side of the square is 20 cm long. What's the area of a parallelogram (as shown in the shadow) in the tangram?

20 × 20 × 18 = 400 × 18 = 50 (square centimeter); answer: the area of shadow is 50 square centimeter

What are the strange phenomena in the desert
We need to be more detailed

Looking out on the shore of the sea, or sailing on the sea, sometimes in calm and windless conditions, you will suddenly see strange phenomena in the air, such as ships, islands, buildings and city outlines. When the wind blows together, this kind of scene will disappear immediately. This is a kind of mirage in the atmosphere, which is called mirage, or mirage for short

(X-Y of x) - (x + y of Y) + (square of X of 2XY - square of Y)

(X-Y of x) - (x + y of Y) + (square of X of 2XY - square of Y)
=1-y/x-1-x/y+(x^2-y^2)/2xy
=-2(y^2+x^2)/2xy+(x^2-y^2)/2xy
=-(x^2+3y^2)/2xy

Where the row vector group of a matrix is linearly related, its column vector group is also linearly related?
Please give reasons

Wrong
Take a counterexample
1 0
0 1
0 1
This 3 × 2 matrix is linearly related to row vectors, but not to column vectors

In equilateral △ ABC, D is the midpoint of AC, e is a point on the extension line of BC, and CE = CD. Please explain the reason why DB = De

∵ equilateral triangle three lines in one, ∵ BD is the angle bisector of ∠ ABC, ∵ CBD = 30 °, ACB = 60 °, ∵ CD = CE, ∵ CDE = ∠ CED, ∵ CDE + ∠ CED = ∠ ACB, ∵ CDE = ∠ CED = 30 °, ∵ CBD = ∠ CED = 30 ° and ∵ BD = De

Given the function f (x) = (2x + 3) / (3x) (x > 0), the sequence {an} satisfies A1 = 1, an = f (1 / an-1) (n ∈ n *, and N ＞ 2)
Is there a common ratio of Q (0) with A1 as the first term

f(x))=(2x+3)/(3x)=2/3+1/x
an=f(1/an-1)=2/3+an-1 → an-an-1=2/3 → an=1+2/3(n-1)=(2n-1)/3
If {ank} exists, then q ^ (k-1) = (2nk-1) / 3 → NK = (3Q ^ (k-1) + 1) / 2
If NK is an integer, then q must be odd
By the condition: each item in the sequence {an} is a different item in the sequence {an}
Only q = 3 satisfies the condition
So: there is an ank = 3 ^ (k-1) to satisfy the problem

Is the method to determine whether two vectors are collinear and parallel? What is the method

Yes, two vectors are collinear and two vectors are parallel

In RT △ ABC, ∠ ACB = 90 ° CD ⊥ AB, the foot drop is D, e is a point on BC, and the circle crossing AE of points c, e and D is at point F. it is proved that ∠ DFE = ∠ BAC

According to the answer from upstairs, I'll give you the details
Connect de
∵ in the circle, the circular angles of arc DG are ∠ DFE and ∠ DCE
In the new textbook, we have deleted the theorem ﹥ DFE = ﹥ DCE
∵∠ DCE = ∠ BAC (similar) is obtained from △ BCD similar to △ BAC
∴∠DFE=∠BAC

Fifth grade mathematics problem [urgent! ~ ~ ~ use equation to solve! Find process!] (use equation with only one unknown number to solve!)
1、 Xiao Ming said, "the number of white rabbits is five times that of black rabbits."
Xiao Hong said, "there are 20 more white rabbits than black rabbits."
How many white rabbits and how many black rabbits are there?
2、 According to today's calculation, 12 cases were sold in the morning, and 1.5 times of that in the afternoon. A total of 360 kg of apples were sold in the whole day. How many kg of apples per case?
3、 There were two piles of cement in the warehouse, 280 tons in pile a and 245 tons in pile B. every day, 18 tons were transported from pile a and 11 tons were transported from pile B. how many days later, the quality of the two pairs of cement was exactly the same?

Suppose the number of black rabbits is x, then the number of white rabbits is 5x.5x-x = 204x = 20x = 55x = 25, so there are 5 black rabbits and 25 white rabbits. Suppose each box of apples is x kg 12x + 12 × 1.5x = 36030x = 360x = 20, so the mass of two piles of cement is exactly the same after each box of apples is 20 kg. 280-18x = 245-11x280-18x + 11x = 245-11x