Why is Log1 / 3 (3x-2) defined in (2 / 3,1) instead of (2 / 3. Positive infinity) under the logarithm function y = root

1. The formula under the root sign must be greater than or equal to 0, so 1 / 3 (3x-2) ≥ 1
2. The real number must be greater than 0
If you have any questions, you can ask again. Anyway, it's OK to stay at home during the holiday^_^

Finding the definition field of y = in (25-x ^ 2) / root sign 2sinx

25-x ^ 2 > 0 and SiNx > 0
The solution is (- 5,5) and wait until the interval (- 2 π, - π) (0, π), take the intersection of the two, and get as
(- 5, - π) and (0, π)

f(x)=3/(x^2-8x+15)(2≤x

It is known that the sum of the first n terms of the arithmetic sequence {an} is Sn, and A3 = 7, S11 = 143. (1) find the general term formula an of the sequence {an}, (2) let BN = 4 / an * an-1 (n ∈ n *), find the first n terms and TN of the sequence {BN}

Sn=（A1+An）*n/2
S11=（A1+A11）*11/2
=（A3-2d+A3+8d）*11/2
=（A3+3d）*11
=（7+3d）*11
=143
So, d = 2, A1 = a3-2d = 7-4 = 3
General formula an = a1 + (n-1) d
=3+2（n-1）
=2n+1
Bn=4/(An^2-1)
=4/［(2n+1)^2-1］
=4/(4n^2+4n+1-1)
=1/(n^2+n)
=1/［n*(n+1)］
=1/n-1/(n+1)
Tn=B1+B2+B3+…… +Bn
=1/1-1/2+1/2-1/3+1/3-1/4+…… +1/（n-1）-1/n
=1-1/n

There are two cars a and B on the straight road. A starts to drive from a standstill at an acceleration of 0.5m/s2, and B moves at a constant speed in the same direction at a speed of 5m / s 200m in front of A. question: (1) when will a catch up with B? How fast does a catch up with B? How far is a from the starting point? (2) In the process of catching up, when is the maximum distance between a and B? What is the distance?

(1) When a overtakes B, the difference of their displacements is x0 = 200m, & nbsp; x a = x0 + X B. let a overtake B with time t, then x a = 12a a T2, x B = v b T. according to the condition of pursuit, there is 12a T2 = v b t + 200, and the solution is t = 40 & nbsp; s or T = - 20 & nbsp; s (omit)

Xiao Ming and Xiao Hua practice running on a 400 meter circular track. They start from the same point at the same time and walk in reverse direction. Xiao Ming runs 4.5 meters per second, and Xiao Hua runs 4.5 meters per second
If you want to solve the equation
Xiao Ming and Xiao Hua practice running on a 400 meter circular track. They started from the same point at the same time and went in opposite directions. Xiaoming runs 4.5 meters per second and Xiaohua runs 5.5 meters per second. After a few seconds, they meet for the second time? (if it's the solution of the equation)

Suppose that after x seconds, two people meet for the second time
4.5x+5.5x=400
The solution is x = 40
A
What grade are you in?

If there are four integer solutions to the inequality system 2x < 3 (x-3) + 1 of X, then the value range of a is?
3X+2/4＞X+a

From 2x < 3 (x-3) + 1 we get x > 8
From 3x + 2 / 4 ＞ x + a we get X

On the number axis, point a represents - 6 and point B represents + 4. Divide AB into five equal parts and get points c, D, e and f respectively. What do they represent?

First draw a number axis, draw a scale with 1 as the unit, and then mark ab. you will find that the distance between a and B is 10, that is, 10 unit lengths, divided into five parts. Then each distance should be 2, that is, 2 unit lengths. Then mark a point every 2 distances from a to B on the number axis, which is C, D, ef

The soldiers are determined to break the enemy's blockhouse
Don't add too many words

The soldiers have made up their mind to break the enemy's blockhouse!

1、-0.2（5x^2+1）
2、-3（2x-1)+7X
3、-3(2x-2/3Y^2)+2(-3/2x+Y^2)
3. First simplify, then evaluate
(T + 3T ^ 2-3) - (- t + 4T ^ 2), where t = - 1
4. 2 (x + y) - 2 / 3 (X-Y) - 3 (x + y) + 2 / 3 (X-Y), where x = - 2, y = 1
Thank you very much!

1、-0.2（5x^2+1）
=-x²-0.2
2、-3（2x-1)+7X
=-6x+3+7x
=x+3
3、-3(2x-2/3Y^2)+2(-3/2x+Y^2)
=-6x+2y²-3x+2y²
=-9x
3. First simplify, then evaluate
(T + 3T ^ 2-3) - (- t + 4T ^ 2), where t = - 1
（t+3t^2-3)-(-t+4t^2)
=t+3t²-3+t-4t²
=-t²+2t-3
When t = - 1, the original formula = - 1-2-3 = - 6
4. 2 (x + y) - 2 / 3 (X-Y) - 3 (x + y) + 2 / 3 (X-Y), where x = - 2, y = 1
2(x+y)-2/3(x-y)-3(x+y)+2/3(x-y)
=-（x+y)
=-x-y
When x = - 2, y = 1
Original formula = 2-1 = 1

Why is Log1 / 3 (3x-2) defined in (2 / 3,1) instead of (2 / 3. Positive infinity) under the logarithm function y = root