On Sunday, Xiaoming's mother went to the street to play, and saw a billboard at the door of a shop: "all clothes in our shop are sold at a 20% discount."

On Sunday, Xiaoming's mother went to the street to play, and saw a billboard at the door of a shop: "all clothes in our shop are sold at a 20% discount."

On Sunday, Xiaoming's mother went to the street to play, and saw a billboard at the door of a shop saying "all clothes in our shop are sold at a 20% discount". Xiaoming's mother took a fancy to one of the clothes. After some bargaining, the owner agreed to give another 5% discount. As a result, Xiaoming's mother spent 150 yuan to buy it. Students, can you work out the original price of this dress?
[150 / (1-5%)] / 0.8 = 198 yuan

Let the sum of the length and width of the rectangle ABCD be 2, and rotate a circle around AB to get a geometry
Is the side area of this geometry the largest or the smallest? I want a reason. Don't just give me an answer. It's better to add some explanation. I want to be able to understand it!

Let AB be a, BC be B, a + B = 2, a + B ≥ 2 √ (AB) √ (AB) ≤ 1, ab ≤ 1. When a = B, ab = 1 2 × 3.14 × a × B = 6.28ab  the side area of this geometry has a maximum value of 6.28

F (x) = the x power of e-ax-1, (1) find its monotone interval, (2) if it increases monotonically in the domain R, find the value range of A
（3） Is there a such that it decreases monotonically on (- ∞, 0) and increases monotonically on [0, + ∞)? If it exists, the value of a will be obtained; if it does not exist, the reason will be given

Find out the derivative function: F '(x) = e ^ X - A
1、 When a = 0, it is monotonically increasing
2 e ^ x = 0 leads to a

How to do this math problem?
The average of a and B is 51, the average of a and C is 47, and the average of B and C is 55. What is the average of a, B and C?

Because the average of a and B is 51, the average of a and C is 47, and the average of B and C is 55
So the sum of a, B and C is (51 * 2 + 47 * 2 + 55 * 2) / 2 = 153
The average of a, B and C is 153 / 3 = 51

As shown in the figure, ▱ the diagonal lines AC and BD of ABCD intersect at point O, point E is the midpoint of CD, and the perimeter of △ abd is 16cm, then the perimeter of △ DOE is______ cm．

∵ quadrilateral ABCD is a parallelogram, ≌ o is the midpoint of BD, ≌ abd ≌ CDB, and ≌ e is the midpoint of CD, ≌ OE is the median line of △ BCD, ≌ OE = 12bc, that is, the perimeter of △ DOE = 12 △ BCD, ≌ DOE = 12 △ DAB. ≌ DOE = 12 × 16 = 8cm

A car drives from the east to the West. After a journey, it is 210 kilometers away from the west, and then 20% of the whole journey. At this time, the ratio of the distance traveled to the distance not traveled is 3:2. How many kilometers are there between the East and the west?

Suppose the distance between the East and the west is x km, we can get: & nbsp; x-210 + 20% x = 35x, x-210 + 0.2x = 0.6x, & nbsp; 1.2x-210 = 0.6x, & nbsp; 1.2x-0.6x = 210, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 0.6x = 210, & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; X = 3

Super difficult mathematical calculation problems
Who can calculate (? + 50000)_ (?*10_ 5) What is the unknown term in = 22122

3098.11

Saw the largest circle on a square board. It is known that the perimeter of the board is 160 decimeters. How many square decimeters is the area of this circle?

The diameter of the circle is equal to the side length of the square, which is 160 △ 4 = 40 decimeters
The area is (40 ／ 2) & 178; × 3.14 = 1256 square decimeters

Given that AB is a rational number, and satisfies (A-1) &# 178; + B-2 = 0, find the value of AB 1 + (a + 1) (B + 1) 1 + (a + 2) (B + 2) 1 + ··· + (a + 2013) (B + 2013) 1

(A-1) &# + B-2 = 0
So A-1 = 0, B-2 = 0
a=1,b=2
So the original formula = 1 / 1 × 2 + 1 / 2 × 3 + +1/2014×2015
=1-1/2+1/2-1/3+…… +1/2014-1/2015
=1-1/2015
=2014/2015

On the application of circle area
It is known that the diameter of a circular flower bed is 4 meters. A 1-meter-wide path is paved along its outer side. The area of the path is calculated (accurate to 0.1 square meter)

(4 △ 2 + 1) × 3.14 - (4 △ 2) × 3.14 = 15.7 (M2)