It is known that: as shown in the figure, △ ABC, CA = CB, point D is the midpoint of AC, and ⊙ o with diameter ad cuts BC at point E, ad = 2. (1) find the length of be; (2) make DF ∥ BC intersection ⊙ o at point F through point D, and find the length of DF

It is known that: as shown in the figure, △ ABC, CA = CB, point D is the midpoint of AC, and ⊙ o with diameter ad cuts BC at point E, ad = 2. (1) find the length of be; (2) make DF ∥ BC intersection ⊙ o at point F through point D, and find the length of DF

(1) As shown in the figure, connect OE to FD at point G, ∵ point D is the midpoint of AC, ad = 2 ∵ AC = 4 ∵ BC cuts ⊙ o to e, ∵ OE ⊥ BC, ∵ CE = 32 − 12 = 8 = 22, ∵ be = 4-22; (2) ∵ DF ∥ BC, ∵ OGD ∵ OEC, ∵ gdec = odoc, ∵ gd22 = 13, ∵ GD = 223, ∵ OE ⊥ BC, ≁ OE ⊥ FG, ∵ FD = 2Gd = 423

Change the plural
He is a student.

They are students.

Given the equation x & # 178; + Y & # 178; - 10x = 0 of the circle C, then the trajectory equation of the center P of the moving circle tangent to the Y axis and circumscribed to the circle C is__________
A.y²=20x
B. Y & # 178; = 20x (x0) and y = 0
D. Y & # 178; = 20x (x ≥ 0) and y = 0 (x ≥ 0)

The equation of circle C is: (X-5) ^ 2 + y ^ 2 = 25
The center coordinate is (5,0) and the radius is 5
The coordinates (x, y) of P satisfy:
((x-5)^2+y^2)^0.5=5+|x|
When x > = 0, y ^ 2 = 20x
When x < 0, y = 0
Therefore, choose D

Finding indefinite integral ∫ 1 / e ^ x (1 + e ^ x) DX

∫ 1 / [e ^ x (1 + e ^ x)] DX, you can understand it = ∫ e ^ X / [e ^ 2x (1 + e ^ x)] DX = ∫ (1 - e ^ 2x + e ^ 2x) / [e ^ 2x (1 + e ^ x)] de ^ x, actually you can use U = e ^ x = ∫ [(1 - e ^ x) (1 + e ^ x) + e ^ 2x] / [e ^ 2x (1 + e ^ x)] de ^ x = ∫ (1 - e ^ x

English translation
At that time the three props of their national power were the atom bomb,the dollar,and their surplus grains.

At that time, the three pillars of their country's strength were the atomic bomb, the dollar, and their surplus crops

Find an arithmetic solution to a math problem!
Uncle Wang's and Uncle Li's monthly salary income ratio is 3:2, their monthly expenditure is 1200 yuan, their monthly surplus money ratio is 9:4, how many yuan are Uncle Wang's and Uncle Li's monthly salary? (use the equation to get 3000 and 2000, now need the detailed process of arithmetic method)

Take Uncle Li's salary as unit one, Uncle Wang's salary is more than 3 / 2 and 1 / 2
The balance of Uncle Li is 1, Uncle Wang is 9 / 4 more than 5 / 4
The extra money is the same, so the ratio of two units is 5 / 2
1200 accounts for 3 / 5 of unit one
Unit one is 2000
Uncle Wang 3000

The area of a square=______ , denoted by letters______ ．

The area of a square = side length × side length. The formula for calculating the area of a square is expressed in letters: S = A2. So the answer is: side length × side length, s = A2

TaNx + tany = 25, Cotx + Coty = 30, then Tan (x + y) =?

cotx+coty=30
1/tanx +1/tany=30
(tanx+tany)/tanxtany=30
25/tanxtany=30
tanxtany=25/30=5/6,
tan(x+y)
=(tanx+tany)/(1-tanxtany)
=25/(1-5/6)
=150

The calculation process should be specified
X2-3x-4 = 0, use the method of △ = b2-4ac. Don't skip steps

The root formula of quadratic function x = [- B ± √ (b2-4ac)] / (2a) a = 1, B = - 3, C = - 4 take a = 1, B = - 3, C = - 4 into the above formula, and get two X1 = (3 + √ 5) / 2x2 = (3 - √ 5) / 2 -------- hope it can help you

Several geometric problems
1. It is known that the circumference of parallelogram ABCD is 80cm, the circumference of AC ⊥ AB and △ ABC is 60cm, and the lengths of AB and BC are calculated
2. It is known that ad ∥ BC, e, F, G and h in the isosceles trapezoid ABCD are the middle points of each side respectively. It is proved that efgh on four sides is a diamond

1. The circumference of the parallelogram ABCD is 80cm, which means that the sum of the lengths of AB and BC is 40cm,
The circumference of △ ABC is 60cm, indicating that AC = 60-40 = 20cm
AC ⊥ AB, let AB = x, then BC = 40-x
Pythagorean theorem, AC ^ 2 + AB ^ 2 = BC ^ 2
That is, 20 ^ 2 + x ^ 2 = (40-x) ^ 2
X = 15cm
That is ab = x = 15cm
BC=40-x=25cm
2. In trapezoidal ABCD, AD / / BC, ab = CD, e, F, G, h are the midpoint of each side respectively
(1) Verification: the quadrilateral efgh is a diamond
Connect AC, BD, E on AB, f on BC, G on CD, h on AD
Because e, F, G and H are the midpoint of each side
So Hg = 1 / 2Ac, EF = 1 / 2Ac
So Hg = EF, Hg ‖ EF
Similarly: eh = GF, eh ‖ GF
So hefg is a parallelogram
Because AD / / BC, ab = CD
So angle ABC = angle ADC
So be = 1 / 2Ab, CG = 1 / 2CD
Because AB = CD
So be = CG
Because f is the midpoint of BC
So BF = CF
So triangle EBF is similar to triangle CFG
So EF = FG
So Hg = EF = eh = GF
So the quadrilateral efgh is a diamond