As shown in the figure, the line AB passes through the origin and the hyperbola y = K / X (k)

As shown in the figure, the line AB passes through the origin and the hyperbola y = K / X (k)

AB cross the origin hyperbola, a, B two points must be symmetrical two points of the origin, so AC = BC, in the question that ac * BC = 2 * 8 = 16, so AC = BC = 4, a (- 2,2), B (2, - 2), into the hyperbola to get k = - 4

Finding the derivative of y = ln (Tan ^ 2x) + ln (SiNx)
This is a composite function. It's better to set it separately

y=lnU+lnM
Derivation of u = Tan ^ 2x, derivation of M = SiNx
T = the derivative of 2x, so we can find the derivative of Tan ^ 2x separately. Forget it, it seems to be a fraction
Y = 1 / Tan ^ 2x * (derivative of Tan ^ 2x) * 2 + 1 / SiNx * cosx

Write the reduplication as required
To describe having a bright luster
1: It is used to describe a bright and shining object
2: It describes the loose appearance of grass, leaves and hair
3: It is used to describe the appearance of tufted animals and plants
4: It describes the heavy appearance of things
5: It describes how hot gas evaporates

1. To describe an object as bright and shiny
2. Description of grass, leaf pine powder (hairy)
3. To describe the appearance of fine hairs of plants and animals
4. It's a heavy thing
5: It describes the way hot gas evaporates

In the same plane rectangular coordinate system, draw the following function images: Y1 = - 2x ^ 2-3 and y2 = - 2x ^ 2 + 2, and say the vertex, the maximum value and their values of each image
Better have a picture

In fact, Y1 and Y2 are the same, as long as you can get them by translation! You can get the vertex of Y1 by translating Y2 down 5 units
（0,-3）,y2(0,2）

Let a, B and C be the lengths of the three sides of the triangle, and the quadratic function y = (a + b) x2 + 2cx - (a-b) obtain the minimum value − A2 when x = − 12, and then calculate the degree of the three internal angles of the triangle

The function y = (a + b) x2 + 2cx - (a-b) is changed into vertex formula as: y = (x + Ca + b) 2 + − (a + b) (a − b) − C2A + B. when x = − 12, the minimum value − A2 is obtained, and Ca + B = 12, ① − (a + b) (a − b) − C2A + B = − A2, ② is obtained, a + B = 2C is obtained from ①, and a-2b + C = 0 is obtained by substituting ②, and a = b = C is obtained, so the triangle is equilateral triangle, so the degree of three internal angles is 60 °

A2 + B2 + a2b2 + 1 = 4AB, find the algebraic formula (a + 2) (b-2)

a²+b²+a²b²+1=4ab
a²-2ab+b²+a²b²-2ab+1=0
(a-b)²+(ab-1)²=0
(a-b)²=0,(ab-1)²=0
a-b=0,ab=1
a=b,ab=1
therefore
A = b = 1 or - 1
When a = b = 1
（a+2)(b-2)
=(1+2)(1-2)
=3*(-1)
=-3
When a = b = - 1
（a+2)(b-2)
=(-1+2)(-1-2)
=1*(-3)
=-3
therefore
（a+2)(b-2)=-3

As shown in the figure, be and CF are the heights of △ ABC, M is the midpoint of BC, BC = 10, EF = 52, and the area of △ EFM is calculated

Let m be MD ⊥ EF to D, ∵ be, CF are the height of △ ABC, respectively, ∵ BFC = ∠ BEC = 90 °, ∵ m is the midpoint of BC, BC = 10, ∵ me = MF = 5, ∵ EF = 52, ∵ de = DF = 522. In △ MDE, from Pythagorean theorem, MD = 52 - (522) 2 = 522, ∵ EFM's area is 12ef · DM = 12 × 52 × 522 = 252

Is 3 / 5-6 / 8 equal to 40?

3/5-6/8=3/5-3/4=（12-15）/20=-3/20

The average length of Xiaodong's step is 0.4m. The length of his side playground is 175 steps and the width is 105 steps. How many square meters is the playground?

0.4 × 175 × (0.4 × 105) = 2940 square meters

The length of the base of an isosceles triangle is 10 cm. If the difference between the two parts is 3 cm, the waist length is 10 cm______ ．

As shown in the figure, let the waist length of an isosceles triangle be xcm. When the difference between AD + AC and BC + BD is 3cm, that is 12x + X - (12x + 10) = 3, the solution is x = 13cm; when the difference between BC + BD and AD + AC is 3cm, that is 10 + 12x - (12x + x) = 3, the solution is x = 7cm. Therefore, the waist length is 7cm or 13cm