Prove that the 53rd power of 53 - 33rd power of 33 is a multiple of 10

Prove that the 53rd power of 53 - 33rd power of 33 is a multiple of 10

If the power is: 4K digits 14K + 1 digits 34k + 2 digits 94K + 3 digits 753 ^

What is 2.53 times 10 to the fifth power

2.53*10^5
=2.53*100000
=253000

The distance between a and B is 770 km. The passenger cars and freight cars leave from a and B at the same time. The passenger cars travel 65 km per hour and the freight cars 45 km per hour. How many hours later are the two cars 110 km apart?

(770-110) / (65 + 45) = 660 / 110, = 6 (hours). Answer: after 6 hours, the distance between the two vehicles is 110 km

Proof: there are no such four points a, B, C and D in the plane, so that △ ABC, △ DBC, △ abd and △ ADC are all acute triangles

You can get it by drawing
Here any triangle has an internal angle which is the same angle as the quadrilateral ABCD
Therefore, unless the four internal angles of a quadrilateral are less than 90 degrees, all four triangles are acute triangles
Because the sum of internal angles of quadrilateral = 360
If the four angles are all less than 90 degrees, the inner angle and

Team a will transfer one sixth of the people to team B, and the number of the two teams will be equal. It turns out that team B is a fraction of the number of team a

Take the number of the original team a as unit 1, and the team a still has: 1-1 / 6 = 5 / 6
The original number of team B is: 5 / 6-1 / 6 = 2 / 3
Therefore, the original team B is the number of team a: 2 / 3 △ 1 = 2 / 3
Test: team a: 1-1 / 6 = 5 / 6
Team B: 2 / 3 + 1 / 6 = 5 / 6
Therefore, the two teams are equal in number

The first line is 1, the second line is 2 and 3. Ask the number 2004 in which line from the left,
The order of natural numbers is as follows
one
2 3
4 5 6
7 8 9 10
.........
Find the number 2004 from the left of the first line

The number of numbers in the first n lines = (1 + n) × n / 2
There are
(1 + N)×N/2 ≤ 2004 ≤ (2 + N)×(N + 1)/2
The solution is n = 62
(1 + N)×N/2 = 1953
There are 1953 numbers in the first 62 lines
2004 on line 63, 2004-1953 from left = 51

The distance between the two cars is 50 kilometers, and they are facing each other at the same time. The car travels 120 kilometers per hour, and the truck travels 80 kilometers per hour. How many kilometers are there after two hours
Starting from one direction

It's a matter of chasing
(120-80) × 2-50 = 30 (km)

In RT △ ABC, ad is the height on the hypotenuse, ab = 4, AC = 5, then s △ ABC ∶ s △ DAC ∶ s △ DAB=
rt

BC²=25+16=41
According to the area ratio equal to the square of the similarity ratio
S △ is obtained ABC:S △ DAC:S △DAB=BC²:AC²:AB²=41：25：16

The car and bus start from two places 362.5km apart at the same time. After meeting for 2.5 hours, the car travels 75KM per hour,
How many kilometers does the bus travel per hour?

362.5÷2.5-75
=145-75
=70 km / h

(2a－3b)(4a＋6ab＋9b）

Cubic difference formula
The original formula = (2a) cubic - (3b) cubic
=8a-27b cubic