LG2, lg10000, etc. is LG2 equal to log2 fast return

LG2, lg10000, etc. is LG2 equal to log2 fast return

lg2 =0.301
lg10000
=lg10^4
=4
LG2 = log10 (2) LG2 is based on 10,

Prove a (B & # 178; + C & # 178;) + B (C & # 178; + A & # 178;) ≥ 4ac

∴b²+c²≥2bc,∴a（b²+c²）≥2abc
∵c²+a²≥2ac,∴b（c²+a²）≥2abc
∴ a（b²+c²）+b（c²+a²）≥4abc

Inside the brackets are the addition and subtraction of numbers and letters. After the brackets are numbers. Do you want a multiplier sign in the middle? For example: (6-A) 9, do you want a multiplier sign? If so, why?

What are the pronunciations of "Meng" and what are the words of each pronunciation

M ē ng m é ng m ě ng m é ng
Deceiving m ē ngpi à n
Blinding m é NGB ì
Understanding m ě NGD ǒ ng
Meng m é ng
Detailed meaning
Name
1. Ancient water name [Meng River]
2. A tributary of Tuojiang River in Pengxian County, Sichuan Province
3. Mengjiang River in Wuzhou, Guangxi

1 known circle C: (x-1) square + (Y-2) square = 25 and straight line (2m + 1) x + (M + 1) y = 7m + 4
Proof: no matter what real number m takes, the line L intersects the circle
Find the shortest chord length of line L cut by circle C and the equation of line at this time
2 known point P (0,5) and circle C x + y + 4x-12y + 24 = 0
Find the trajectory equation of the middle point of the chord of the circle C passing through point P
Given that the circle x + y + x-6y + M = 0 and the line x + 2y-3 = 0 intersect at P and Q, and the point product of vector OP and vector OQ = 0 (o is the origin), the center coordinates and radius of the circle can be obtained

A: the first question of the first question is very simple. You can solve two equations together and prove that the discriminant is always greater than 0. However, this kind of problem is solved in this way. It must be that the straight line passes through the fixed point and the fixed point is in the circle. The fixed point is (2mx + X + my + y-7m-4 = 0), that is, m * (2x + Y-7) + X + y-4 = 0) has x + y = 4 and 2x + Y-7 = 0, and the fixed point coordinate is (3,1) in the circle
When the shortest cut is vertical, the slope k from the center of the circle (1,2) to (3,1) can be calculated
When k * - (2m + 1) / (M + 1) = - 1, the shortest time is when the slope does not exist!
The circular C equation can be reduced to: (x + 2) ^ 2 + (X-6) ^ 2 = 16
Let the midpoint coordinate of the chord of the circle C passing through p be q (x, y), then OQ ⊥ PQ is obtained,
[(y+2)/(x-6)]*[(y-5)/(x-0)]=-1
(y-3/2)^2=73/4-x
The equation of circle can be (x + 1 / 2) ^ 2 + (Y-3) ^ 2 = (37-4m) / 4
The center coordinates are (- 1 / 2,3)
Y = (- x + 3) / 2 is substituted into the equation of circle
x^2+(x^2-6x+9)/4+x-(9-3x)+m=0
5x^2/4+5x/2-27/4+m=0
You can calculate the coordinates of P and Q points by using the algebraic formula containing M
Let P point coordinate be (x1, Y1) and Q point coordinate be (X2, Y2)
Vector OP = (x1 - (- 1 / 2), y1-3) vector OQ = (X2 - (- 1 / 2), y2-3)
Vector op · vector OQ = (x1 + 1 / 2) * (x2 + 1 / 2) + (y1-3) * (y2-3) = 0
Y1, Y2 are replaced by x1, X2 (using the straight line x + 2y-3 = 0, Y1 = (3-x1) / 2)
Re simultaneous
The relationship between x 1 + x 2 and x 1 * x 2 and M is obtained by Weida theorem
After substituting the data, we can get the value of M
Then the radius is obtained by substituting the value of m into √ (37-4m) / 2
This method is more general, that is, (x1, Y1) (X2, Y2) is set out, and then transformed into a relation (equation) related to m, and then M is solved

Who has the written arithmetic problem in Volume 1 of grade 4?
The more, the better!
The more the better! Just write!

1、 Write the number directly. (10 points in total)
760-403= 300÷12= 0.5+7.61= 2.56-0.37=
25×40= 132÷100= 36.3×100= 98+125=
7.2+2.8= 321-99= 4.13-2.8= 31×4=
3600÷18= 50×60= 26+84= (14+25) ×4=
5.4-2.5-1.4= 8×99+8= 1.7+0.43+3.3= 320×5×2=
2、 Fill in the blanks. (22 points in total)
1. (3 points) 80560320000 read as (); use "100 million" as a unit to equal (); omit the mantissa after "100 million" to equal ()
2. (2 points) 8.06 is composed of () one and () 0.01
3. (6 points) 3 square kilometers = () square meters
12:00 on the 5th = ():00
3 square meters 8 square centimeters = () square centimeters
600 cm = () M
2060g = () kg () g
86 square meters 60 square decimeters = () square meters
4. (4 points) fill in the form as required
3.5164 12.5048 10 2.015
Keep two decimal places and enlarge by 100 times
Keep three decimal places, reduce 1000 times
5. (5 points) fill in "" or "="
786005 ○ 786015 150.28 ○ 15.029 4.56 ○ 4.560
4.9 yuan 0.4 yuan 9 Jiao 1 Fen 3.6 tons 0.3406 kg
6. (2 points) 40 ^ () = 20 ^ () = 200 ^ () = () 50 = 1.2 + ()
3、 Calculation. (32 points in total)
1. Write and check the following questions: (6 points)
3250÷25 100-74.5 5.84+3.7
2. Find the unknowns χ: (8 points)
3.96+χ=10.9 χ÷134=27
χ-158=230-138 15×χ=240
3. How to simplify and calculate: (12 points)
25×32×125 47×（45+225÷45）
（100-1456÷26）×78 48.14-2.43-7.57
4. Formula calculation: (6 points)
① What is the sum of 532 minus 379 plus the quotient of 192 divided by 4?
② What is the quotient of the product of 104 and 12 minus 258 and then divided by 33?
4、 Measure and draw: (7 points)
1. Use a protractor to measure the degrees of ∠ 1, ∠ 2, ∠ 3 and ∠ 4 to see what you find. (3 points)
2. Draw the height of the triangle, and then draw a straight line parallel to the line AC through point B. (4 points)
A
B C
bottom
5、 Judgment: (mark "√" in brackets for right and "×" for wrong). (5 points)
1. Decimals must be smaller than integers
2.5kg 27g = 5.27kg ()
3. In division with remainder, divisor must be larger than remainder
4. A ray is 546 km long
5. A parallelogram is a rectangle ()
6、 Practical questions. (24 points in total)
1. One flour grinder can grind 62 kg of flour per hour. According to this calculation, how many kg of flour can five flour grinders grind in six hours?
2. Xiaoming's score in the five tests of mathematics is 96, 100, 98, 100 and 96. What's his average score?
3. Xiaoying bought two books at 7.5 yuan and 9.8 yuan respectively. She paid 20 yuan. How much should she get back?
4. The school donated books for the hope project. The third grade donated 256 books, and the fourth grade donated twice as many as the third grade. The fifth grade donated 300 less books than the third and fourth grade. How many books did the fifth grade donate?

It is known that F 1 and F 2 are the two focal points of ellipse x ^ 2 / M + 1 + y ^ 2 / M = 1, P is the moving point on the circle, and the maximum area of △ f 1pf 2 is 2

The maximum area of △ f1pf2 is 2
The bottom edge is 2c, and if you want to make the largest area, the height is equal to B
So s = 1 / 2 * b * 2C = 2
b^2=m,c^2=1
S^2=1/4 * m *4 =4
m=4
So a ^ 2 = 5, e = √ 5 / 5

Insert a bamboo pole vertically into the bottom of a reservoir. The wetted part is 1.2 meters. Turn around and insert the other end vertically into the bottom of the reservoir. In this way, the non wetted part is 0.4 meters less than half of the total length. The non wetted part of the bamboo pole is long______ Rice

Suppose that the length of the bamboo pole is x m, then x-2.4 = x2-0.4, X2 = 2, x = 4; the wetted part is 4 △ 2-0.4 = 1.6 (m); a: the length of the non wetted part of the bamboo pole is 1.6 M

The minimum value of the distance from the point on the ellipse x ^ / 16 + y ^ / 9 = 1 to the straight line x-y-10 = 0

Let a point (x, y) on the ellipse be x = 4cosa
y=3sinA
The formula of distance from point to line
L = (4cosa-3sina-10) / radical 2
=(5sin (a + b) - 10) / radical 2
So the minimum is 5 root 2 / 2

20 practical questions about simple calculation
Hurry!

(1) there are three baskets of pears with a total weight of 70 kg, one basket of 20 kg and one basket of 26 kg. How many kg is there? (use two methods to answer) 540 fluorescent lamps need to be installed in the teaching building. There are four floors in the teaching building with 15 classrooms on each floor. How many fluorescent lamps should be installed in each classroom? (use two methods to answer)