Three hours later, the bus and freight car travel 36 kilometers more than 3 / 8 of the whole journey, and the freight car 5 / 12 of the whole journey, Know that the speed ratio of passenger cars and freight cars is 6:5. How many kilometers is the distance between a and B? (detailed formula)

After 3 hours, the distance ratio of the two vehicles is 6:5
Due to the freight car running 5 / 12
So the bus line is 5 / 12 * 6 / 5 = 1 / 2
Then the whole journey = 36 ÷ (1 / 2-3 / 8) = 288 (km)

Let the quadratic function y = ax ^ 2 + BX + C (a)

A ＜ 0, parabolic opening downward. X = 2 maximum, that is, X ＜ 2 is monotonically increasing
So, monotone increasing interval
（-∞,2]

A pile of soil, if it takes 30 days to transport 360 vehicles a day, now it needs to complete the task five days in advance, how many vehicles a day?

Suppose x cars are transported every day, (30-5) x = 360 × 30, the solution is x = 432

Cylinder side area 12.56 square decimeters, volume

The side area is divided by the perimeter of the bottom surface
12.56÷2=6.28
The radius of the bottom surface is determined by the perimeter of the bottom surface △ 2
6.28÷3.14÷2=1
Bottom area = 3.14x1 ^ 2 = 3.14
Volume = bottom area x height = 3.14x2 = 6.28cubic decimeter

What is the largest number that can divide both 18 and 24?
Calculation process

The greatest common divisor of 18 and 24 is 6, so it's 6

On the polynomial of X (5-2a) the square of X + (2b-1) X-1
(1) When the values of a and B are, the polynomial is quadratic
(2) When the values of a and B are the same, the polynomial is of degree one

1) 5-2a ≠ 0, a ≠ 5 / 2. B is any value
2) When 5-2a = 0, a = 5 / 2, 2b-1 ≠ 0, B ≠ 1 / 2

How many digits "7" can I count from 1 to 100?

There are 10 out of 7
7,17,27,37.97
There are ten on the tenth
70,71,72,.79
therefore
From 1 to 100, you can count to 20 digits "7"

To solve the equations 2008x-2009y = 1 2010x-2011y = 3

2008X-2009Y=1 (1)
2010X-2011Y=3 (2)
(2) (1) get 2x-2y = 2
X-Y=1
X=Y+1 (3)
From (1), there is 2008x = 2009y + 1
X=(2009Y+1)/2008 (4)
(3) Together with (4), we find that x = 2008
Y=2007

The rules of 1, 7, 19, 37, 61 and 91 are represented by letters

Cubic power of 1 - cubic power of 0 = 1
The third power of 2 - the third power of 1 = 7
The third power of 3 - the third power of 2 = 19
The third power of 4-3 = 37
The third power of 5-4 = 61
.
According to this, the rule is: the nth number is [the third power of N - (the third power of n-1)]
The answer is over

General solution of homogeneous equation XY '- Y - √ (y ^ 2-x ^ 2) = 0

∵ XY '- Y - √ (Y-X) = 0 = = > y' - Y / X - √ (Y / x-1) = 0 ∵ let y = XT, then y '= XT' + T is substituted into the equation to get XT '- √ (t-1) = 0 = = > DT / √ (t-1) = DX / x = = > ln (T + √ (t-1)) = ln │ x │ + ln │ C │ (C is an integral constant) = = = > t + √ (t-1) = CX = = > y / x + √ (Y / x-1) = CX = = > y + √ (Y-X) = Cx

Three hours later, the bus and freight car travel 36 kilometers more than 3 / 8 of the whole journey, and the freight car 5 / 12 of the whole journey, Know that the speed ratio of passenger cars and freight cars is 6:5. How many kilometers is the distance between a and B? (detailed formula)