Forever comic book

Forever comic book

What kind of thoughts and feelings does "Miscellaneous Poems in the mountains" express

The poem describes the poet's interesting life in the mountains: surrounded by mountains, luxuriant bamboo and wood, birds flying on the eaves of other people's houses, and clouds floating out of the window. This secluded residence has exhausted the dust of the human world, freely and divinely expressing the poet's comfortable and leisurely mood

As shown in the figure, quadrilateral ABCD is a rectangle, ab = a, BC = 2A, point F is on ad, quadrilateral aefg ∽ quadrilateral ABCD, and AE = 2 / 3a
(1) Seeking the length of Ag
(2) Verification: △ Abe ∽ ADG
(3) If s rectangle ABCD = 630cm square, calculate s rectangle aefg
Remember that the process is complete

∵ quadrilateral aefg ∵ quadrilateral ABCD
∴AE:AB=AG:AD
And ∵ AB = a, ad = BC = 2A, AE = 2 / 3a
∴2/3a:a=AG:2a
∴AG=4/3a
(2) It is proved that ∵ GAD = ∵ gae - ∵ DAE, ∵ EAB = ∵ bad - ∵ DAE
And ∵ in rectangular aefg and rectangular ABCD, ∠ gae = ∠ bad = 90 °
∴∠GAD=∠EAB
And ∵ AE: ab = Ag: AD, that is AE: Ag = AB: ad
∴△ABE∽△ADG
∵ rectangle aefg ∵ rectangle ABCD
S rectangle ABCD: s rectangle aefg = (AB: AE) ^ 2 = (A: 2 / 3a) ^ 2 = 9 / 4
And ∵ s rectangle ABCD = 630cm square
S rectangle aefg = s rectangle ABCD / (9 / 4) = 630 × 4 / 9 = 280cm square

Fractional multiplication 10-3 / 8 × 20 / 27-13 / 18
It's easy to calculate

Original formula = 10-5 / 18-13 / 18 = 10 - (5 / 18 + 13 / 18) = 10-1 = 9
Using the law of Association

Ion equation of reaction between concentrated sulfuric acid and copper

No. sulfuric acid in concentrated sulfuric acid exists in molecular form, and the generated copper sulfate cannot be separated into ionic form, because the generated water is not enough to dissolve the generated copper sulfate. Therefore, the reaction of copper and concentrated sulfuric acid is not an ionic reaction, and of course, the ionic reaction equation cannot be written

As shown in the figure, it is known that the square ABCD is above the line Mn, the edge BC is on the line Mn, and E is a point on the line BC. Take AE as the edge and make the square aefg above the line Mn, where AE = 2, denote ∠ Fen = α, and the area of △ EFC is S. (I) find the functional relationship between S and α; (II) when the angle α takes what value, s is the largest? And find the maximum value of S

(I) FH ⊥ Mn is the crossing point F, and H is the perpendicular foot In RT △ Abe, EB = aesin α = 2Sin α, BC = AB = aecos α = 2cos α, so EC = bc-eb = 2cos α - 2Sin α So the area of △ FCE is s = 12 (2cos α − 2Sin α)

The ratio of 2 / 8 to 4 / 5 is (), and the ratio is ()

The ratio of 2 / 8 to 4 / 5 is (5:16) and the ratio is (5 / 16)
2/8：4/5＝10：32＝5：16＝5/16

An operation on quadratic radical
-The third power of 1 / M radical - M=

-m^3>=0 m

In the rectangle ABCD, ab = 8 cm, BC = 10 cm, now move the rectangle ABCD to the right x cm, and then down x + 1 cm to get the rectangle a'b'c'd '
In the rectangle ABCD (a in the upper left corner, B in the lower left corner, C in the lower right corner, D in the upper right corner), ab = 8 cm, BC = 10 cm, now translate the rectangle ABCD to the right x cm, and then down x + 1 cm to get the rectangle a'b'c'd '
(1) Using the algebraic expression of X to express the area of the overlapping part of rectangle ABCD and a'b'c'd ', what conditions should x satisfy
(2) Expressing the area of hexagon abb'c'd'd with the algebraic expression of X
(3) When there is no overlap between the two rectangles, whether the conclusion of question 2 has changed, and why
There are also reasons for the third question

When there is no overlap between the two rectangles, the conclusion of sub question (2) does not change
[if (2) is solved by this method, it only needs to be explained that the solution method is the same; if it is solved by area graph division method, it needs to be explained in two cases.]

If n is a positive integer, is the value of integer n & # 178; + N + 11 necessarily prime?
Such as the title

The skill of judging prime number
According to the definition of prime number, when judging whether a number n is a prime number, we only need to use 1 to n-1 to remove N and see if it can be divisible. But we have a better way. First, find a number m so that the square of M is greater than N, and then use 1993. Then we just need to divide 1993 by n