Combination of number and shape Known 0

Combination of number and shape Known 0

Verification: (x, 0) and (0,1) distance + (x, 0) and (1,1) distance > 2 √ 2-1
Let a (0,1), B (1,1), m (x, 0)
Let a (0,1) be symmetric about the y-axis a '(0, - 1)
|Ma '| + | MB | > = | a'B | = √ 5 > 2 √ 2-1
The proof is complete

A real estate in Guang'an City is going to be sold at an average price of 6000 yuan per square meter. After the introduction of the new policy of the State Council on real estate, buyers hold their money to wait and see. In order to speed up the capital turnover, the real estate developers decided to sell at an average price of 4860 yuan per square meter after two price reductions

Suppose that the average percentage of each price reduction is X. according to the equation, 6000 (1-x) 2 = 4860, the solution is: X1 = 10%, X2 = 1910 (not suitable, rounding off); answer: the average percentage of each price reduction is 10%

Mathematics problem in Grade Three: a building is going to be sold at 5000 yuan per square meter
After two price adjustments, it was decided to sell it at 4050 yuan per square meter. 1: ask the developer for the average percentage of each reduction. 2: Xiaoming bought 100 square meters. The discount is as follows: A. give a 9.8% discount; B. give three years' property management fee, 1 yuan per square meter per month. Which discount

Answer: (1) 10% reduction, which is the original 90% (10% discount)
(2) A is suitable
(1) If the percentage of downward adjustment is x, then the equation can be listed: 5000 * (1-x) ^ 2 = 4050, then x = 0.1
(2) A: discount = 4050 * (1-0.98) * 100 = 8100
B：3600

In August 2011, a real estate in Hangzhou was ready to be sold at an average price of 14500 yuan. Due to the introduction of the State Council's new policy on real estate, buyers held money to wait and see. In order to speed up the capital turnover, after two price reductions, the real estate developers decided to sell at an average price of 7105 yuan per square meter in June 2012 8 square meters to 138 square meters of house, someone is ready to buy a house at the average opening price in June 2012, the developer also gives the following two preferential schemes to choose from: 1. Give a 9.8% discount; 2. No discount, give three years of property management fee, the property management fee is 2 yuan per square meter per month. Which scheme is more preferential?

(1) Suppose the average percentage of each reduction is x, then 14500 (1-x) 2 = 7105, and the solution is X1 = 0.3, X2 = 1.7 (rounding off). The average percentage of each reduction is 30%. (2) if a square meter of house is purchased, then: scheme 1 is preferential: 7105a × 0.02 = 142.1a (88 ≤ a ≤ 138) scheme 2 is preferential: 12 × 3 × 2A = 72A (88 ≤ a ≤ 138) 142.1a-72a = 70.1a > 0, so scheme 1 is more preferential

Is 50 a perfect square? Why

If a number is the complete square of another integer, then we call it a complete square
0,1,4,9,16,25,36,49,64,81,100
{50} is not a perfect square
±√50=±5√2

Find all four complete squares!

32, 33, 34, 35, 36,..., 99. The square of these numbers is the complete square of four digits

Perfect square in 10000

0,1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400,441,484,529,576,625,676,729,784,841,900,961,1024,1089,1156,1225,1296,1369,1444,1521,1600,1681,1764,1849,1936,2025,2116,2209,2304,2501,2500,2601,2704,2809,2916,3025,3136,3249,3364,3481,3600,3721,3844,3969,4096,4225,4356,4489,4624,4761,4900,5041,5184,5329,5476,5625,5776,5929, 6084,6241,6400,6561,6724,6889,7056,7225,7396,7569,7744,7921,8100,8381,8564,8749,8936,9125,9316,9509,9704,9901,10000

Is 1 a perfect square

Properties and corollaries of complete square numbers
For example: 0,1,4,9,16,25,36,49,64,811001211441691962256289324361400441484 By observing these perfect square numbers, we can get the understanding of the regularity of their single digit, ten digit, digit sum, etc
Property 1: the last digit of a complete square number can only be 0,1,4,5,6,9
Property 2: odd number of square is odd number, ten number is even number
1 is a perfect square

What are the complete squares
The sooner the better, the more the better! Urgent!

0,1,4,9,16,25,36,49,64,81,100,121,144,169,196,225,256,289,324,361,400,441,484,529… Property 1: the last digit can only be 0,1,4,5,6,9

Nine out of nine equals one dozen
It must be an idiom!

Nine to one