If the exponential function y = (2-A) x is a decreasing function in the domain of definition, then the value range of a is______ ．

Because the exponential function y = (2-A) x is a decreasing function in the domain of definition, 0 < 2-A < 1, the solution is 1 < a < 2, so the answer is (1,2)

If the exponential function y = (A-2) ^ x is a decreasing function on X ∈ R, what is the value range of a

If the exponential function y = (A-2) ^ x is a decreasing function on X ∈ R,
So 0

1/18+1/54+1/108+…… +What is 1 / 810 + 1 / 990?

1/18+1/54+1/108+…… +1/810+1/990
=（1/3-1/6+1/6-1/9+1/9-1/12+…… +1/27-1/30+1/30-1/33）÷3
=（1/3-1/33）÷3
=10/33÷3
=10/99

If a 2 + 2 ab-35 B 2 = 0 (AB ≠ 0), find the value of AB + ba

∵ ab ≠ 0, ∵ a ≠ 0, B ≠ 0, ∵ A2 + 2ab-35b2 = 0, ∵ (a + 7b) (a-5b) = 0, ∵ a + 7b = 0, a-5b = 0, ∵ a = - 7b or 5b, when a = - 7b, AB + Ba = - 7-17 = - 717; when a = 5b, AB + Ba = 5 + 15 = 515

A cuboid container measuring 5 decimeters in length and 5 decimeters in width is filled with water 10 cm deep. Now a cylinder iron block with a diameter of 2 decimeters on the bottom is put into the container. The iron block completely intrudes into the water, and the water surface rises by 1 cm. What is the height of the cylinder iron block?

5 × 5 × 0.1 = 2.5 (cubic decimeter)
2.5 ÷ (3.14 × 1 square)
About 0.8 (decimeter)

By solving the fractional equation 5x − 96x − 19 + X − 8x − 9 = 4x − 19x − 6 + 2x − 21x − 8, X is obtained=______ ．

The original formula can be changed into (5-1 x − 19) + (1 + 1 x − 9) = (4 + 5 x − 6) + (2 + 5 x − 8), that is, 1 x − 9-1 x − 19 = 5 x − 6 + 5 x − 8, ■ − 10 (x − 9) (x − 19) = − 10 (x − 6) (x − 8), (X-6) (X-8) = (X-9) (X-19), that is, 14 x = 123, 12 314

71 1 / 6 * 7 / 6 + 61 1 / 5 * 6 / 5 + 51 1 / 4 * 5 / 4

The general solution is to change the fraction into a false fraction, (427 / 6) × (6 / 7) + (306 / 5) × (5 / 6) + (205 / 4) × (4 / 5) = (427 / 7) + (306 / 6) + (205 / 5) = 61 + 51 + 41 = 153. The special solution does not need to be completely changed into a false fraction, but only needs to be changed into a part of (70 + 7 / 6) × (6 / 7) + (60 + 6 / 5) × (5 / 6) + (50 + 5 / 4) × (4 / 5) = 60

The intersection of image and coordinate axis of quadratic function y = AX2 + BX + C is a, B, C. when the triangle ABC is a right triangle, the condition must be satisfied
Process must be attached
What we seek is a condition, not an analytical expression that satisfies the condition

y=ax^2+bx+c
1. When x = 0, the solution is y = C,
That is to say, the intersection of function and y-axis is (0, c);
2. When y = 0, there is ax ^ 2 + BX + C = 0, and the solution is: x = [- B ± √ (b ^ 2-4ac)] / (2a)
That is to say, the intersection of function and X axis is ([- B - √ (b ^ 2-4ac)] / (2a), 0), ([- B + √ (b ^ 2-4ac)] / (2a), 0). Let the former be B and the latter be c
If △ ABC is a right triangle, it must satisfy: ab ⊥ AC
Suppose the slope of AB is m and the slope of AC is n, then: Mn = - 1
m=(c-0)/{0-[-b-√(b^2-4ac)]/(2a)}=2ac/[b+√(b^2-4ac)]
n=(c-0)/{0-[-b+√(b^2-4ac)]/(2a)}=2ac/[b-√(b^2-4ac)]
mn=-1
{2ac/[b+√(b^2-4ac)]}{2ac/[b-√(b^2-4ac)]}=-1
{4(a^2)(c^2)/[b^2-(b^2-4ac)]=-1
{4(a^2)(c^2)/(4ac)=-1
ac=-1
That is, when △ ABC is a right triangle, the condition that must be satisfied is: AC = - 1

How to calculate 4322 times 1233 minus 4321 times 1234

4322×1233-4321×1234
=(4321+1)×1233-4321×(1233+1)
=4321×1233+1×1233-4321×1233-4321×1
=1233-4321
=-3088

It is known that the parabola y = ax & # 178; + BX + C passes through a (- 1,0), and passes through the intersection B of the line y = x-3 and the X axis and the intersection C of the line y = x-3 and the Y axis
The analytic formula of parabola
Finding the vertex coordinates of parabola
If point m is on the parabola in the fourth quadrant, and OM ⊥ BC, the perpendicular foot is D, the coordinates of point m are obtained

Intersection B of line y = x-3 and X axis and intersection C of line y = x-3 and Y axis
For B, y = 0, we can get: 0 = x-3, that is: x = 3
For C, if x = 0, then y = 0-3, that is, y = - 3
So for the parabola y = ax & # 178; + BX + C, we can get:
9a+3b+c=0
a-b+c=0
c=-3
In conclusion, a = 1, B = - 2, C = - 3
So there are: y = x & # 178; - 2x-3
Vertex coordinates of parabola
Y = x & # 178; - 2x-3 = (x-1) &# 178; - 4, so the vertex coordinates are: (1, - 4)
If point m is on the parabola in the fourth quadrant, and OM ⊥ BC, the perpendicular foot is D, the coordinates of point m are obtained
Let the coordinates of point m be (a, b)
B = (A-1) & # - 4
B / a = - 1 in conclusion, a = (1 + √ 13) / 2, B = (- 1 - √ 13) / 2

If the exponential function y = (2-A) x is a decreasing function in the domain of definition, then the value range of a is______ ．