The current price of Andersen's fairy tales is 1 / 6 lower than the original price. The original price is 4 yuan higher than the current price. How much is the original price? How much is it

The current price of Andersen's fairy tales is 1 / 6 lower than the original price. The original price is 4 yuan higher than the current price. How much is the original price? How much is it

The original price is x yuan
Then 4 + x = 5x / 6
x=24

The original price of a book is 24 yuan, and the current price is 4 yuan cheaper than the original price. How much lower is the current price?

The current price is lower than the original price: 4 / 24 = 1 / 6

Passenger cars and freight cars leave from a and B at the same time and meet after 4 hours. It is known that the speed ratio of passenger cars and freight cars is 7:5, and passenger cars travel 5 kilometers more per hour than freight cars?

After the meeting, the time for the freight car to arrive at a: 75 + 7 ^ (55 + 7 ^) 4, = 712 ^ (512 × 14), = 712 ^ 548, = 712 × 485, = 5.6 (hours); the total time for the freight car from B city to a City: 5.6 + 4 = 9.6 (hours); a: the total time for the freight car from B city to a city is 9.6 hours

Given that the average of a group of numbers x, 5, 0, 3, - 1 is 1, then its median is 1______ ．

∵ (x + 5 + 0 + 3-1) △ 5 = 1, ∵ x = - 2, ∵ data from small to large are - 2, - 1, 0, 3, 5, then the median is 0

Party A and Party B walk towards each other from 810 meters away at the same time. Party A walks 50 meters per minute and Party B 40 meters per minute. After () minutes, they meet
Within 10 minutes, please

Party A and Party B walk from 810 meters to each other at the same time. Party A travels 50 meters per minute and Party B 40 meters per minute. After (9) minutes, they meet
810 (40 + 50) = 9 minutes

2/1+4/1+8/1+16/1+32/1

1/2+1/4=3/4
3/4+1/8=7/8
2/1+4/1+8/1+16/1+32/1
=31/32

On a map with a scale of 1:6000000, the distance between the two places is 2.5cm, and it takes two hours for a train to complete the whole journey,

The actual distance between the two places is: 2.5 × 6000000 = 37500000cm = 375km
Then the speed of the train is 375 △ 2 = 187.5km/h

If real numbers a, B, C, D satisfy a ^ 2-2lna / b = 1, C-4 / 3 = 1 / 3D, then the minimum value of (A-C) ^ 2 + (B-D) ^ 2 is

a^2-2lna/b=1
It should be related to derivative tangent, distance
A ^ 2-2lna / b = 1 = = > P (a, b) on the curve X & # 178; - 2lnx / y = 1
C-4 / 3 = 1 / 3D = = > Q (C, d) on the line x-4 / 3 = 1 / 3Y
（a-c)^2+(b-d)^2=|PQ|²
We should find the tangent of the curve parallel to the straight line x-4 / 3 = 1 / 3Y
Your first formula is not accurate. It's not easy to go on
If the curve (X & # 178; - 2lnx) / y = 1
y=x²-2lnx
y'=2x-2/x
The straight line x-4 / 3 = 1 / 3Y is 3x-y-4 = 0
Make a line parallel to the line y = 3x-4 and tangent to the curve
Let the tangent be t (m, n) (M > 0)
Then y '(x = m) = 2m-2 / M = 3 = = > 2m & # 178; - 3m-2 = 0, M = 2
The cut-off point is (2,4-2ln2)
∴|PQ|²min=|6-4+2ln2-4|²/10=2/5*(ln2-1)²
If you have a question, ask

2 / 3 of the number a is equal to 4 / 5 of the number B. what is the percentage of the number B? What is the percentage of the number a?

Number a = (4 / 5) / (2 / 3) = 6 / 5 = 120%
B is 5 / 6 of A

1. In the arithmetic sequence an, S8 = 100, S16 = 392, try to find S24
2. Let the square of the square (M + 1) of function f (x) - MX + M-1
(1) If the equation f (x) = 0 has a real root, the value range of the real number m is obtained
(2) If the inequality f (x) is greater than 0 and the solution set is empty, the value range of real number m is obtained
(3) If the inequality f (x) is greater than 0 and the solution set is r, the value range of real number m is obtained
If you answer the question completely, you will be rewarded with a high score. Please finish it as soon as possible,
Question 2 F (x) = (M + 1) x2 MX + M-1
2 means square
The first square in the original question is wrong. It's the = sign

1. In the arithmetic sequence an, S8 = 100, S16 = 392, try to find S24
Introduce a knowledge point: if an is an arithmetic sequence, then Sn, s (2n) - Sn, s (3n) - S (2n) S (2n) - Sn = a (n + 1) + a (n + 2) a(2n) S(2n)-2Sn=a(n+1)+a(n+2)…… a(2n)-an-a(n-1)…… -a1=nd
Similarly [S (3n) - S (2n)] - [S (2n) - Sn] = a (3n) + a (3n-1) +a(2n+1)-[a(n+1)+a(n+2)…… a(2n)]=nd
So S8, s16-s8, s24-s16 become arithmetic sequence 2 (s16-s8) = s24-s16 + S8, substituting into S24 = 876
2: The general solution is to replace S8 and S16 with A1 and D, solve the equation and obtain S24, or solve a and B in SN = an ^ 2 + BN, and then replace S24 with general formula, but it is more troublesome
3: This paper introduces a solution of analytic geometry
∵ Sn = an^2 + bn Sn/n = an + b
(8, S8 / 8), (16, S16 / 16), (24, S24 / 24) in a straight line
If you use the same slope, the vectors are collinear, you can get S24
2. Let f (x) = (M + 1) x2 MX + M-1
(1) If the equation f (x) = 0 has a real root, the value range of the real number m is obtained
(2) If the inequality f (x) is greater than 0 and the solution set is empty, the value range of real number m is obtained
(3) If the inequality f (x) is greater than 0 and the solution set is r, the value range of real number m is obtained
(1) (M + 1) x2 MX + M-1 = 0 has real roots
If M = - 1 has constant real root; if M ≠ - 1 △ ≥ 0, m ^ 2-4 (M + 1) (m-1) ≥ 0, then 2 / 3sqrt (3) ≥ m ≥ - 2 / 3sqrt (3), and m ≠ - 1, then 2 / 3sqrt (3) ≥ m ≥ - 2 / 3sqrt (3)
(2) (M + 1) x2 MX + M-1 > 0 has no real root
If M = - 1, there must be a real root; if M ≠ - 1, there must be a real root
(3) The solution set of (M + 1) x2 MX + M-1 > 0 is r
If M = - 1, the solution set is not R; if M ≠ - 1, it must be m > - 1 (opening up), △ 2 / 3sqrt (3)
To sum up the above two points, M > 2 / 3sqrt (3)