Divide the eight numbers 6, 4, 8, 30, 21, 35, 33 and 22 into two groups to make the product of the four numbers in each group equal. How to divide them

Divide the eight numbers 6, 4, 8, 30, 21, 35, 33 and 22 into two groups to make the product of the four numbers in each group equal. How to divide them

6=6
4=4
8=2×4
30=6×5
21=3×7
35=5×7
33=3×11
22=2×11
The first group: 35, 33, 6, 8
The second group: 21, 30, 22, 4

Xiao Ming goes to exercise with his uncle. They run on the 400 meter ring track with their own uniform speed. They start at the same place at the same time. Xiao Ming's speed is 100 meters per minute, and uncle's speed is 1.5 times of Xiao Ming's.q. (1) how long did it take Xiao Ming and uncle to meet for the first time? (2) how long did it take for them to meet for the second time?
At present, there are two porcelain shops a and B, with teapots less than 20 yuan and teacups more than 5 yuan each. It is known that the preferential scheme formulated by shop a is to buy a teapot and get a teacup free, while shop B pays 0.92% of the total price. The school office needs to buy 4 teapots and several teacups (no less than 4), (2) when you need to buy 40 cups, which store is the best choice? Why?

1. Uncle's speed is 1.5 times faster than Xiao Ming's, which means uncle's speed is 150 m / min. they both go in the same direction, so the relative speed is 50 m / min. if you want to meet him for the first time, uncle should walk 400 m more than Xiao Ming, so the time is 400 m divided by 50 m / min, which is 8 minutes. 2. The second time, uncle's speed is 400 m more than Xiao Ming's, so it takes 8 minutes, so it takes 16 minutes
2. If you buy x tea cups, you need to pay 4 * 20 + (x-4) * 5 = 60 + 5x to go to a store
If you go to store B, you need to pay 4 * 20 * 0.92 + 5 * x * 0.92 = 73.6 + 4.6x
The equation 60 + 5x = 73.6 + 4.6x, which makes the two preferential payments the same, solves x = 34 to buy 34 cups
② When you need 40 cups, you need to pay 20 * 4 + (40-4) * 5 = 260 for shop a
For store B, you need to pay 20 * 4 * 0.92 + 40 * 5 * 0.92 = 257.6
As you can see, it costs less in shop B, so it pays to go to shop B

How to find the area of a square, a rectangle, a triangle or a parallelogram,

Area of square = side length x side length s = AXA
Area of rectangle = length x width s = AXB
Area of triangle = bottom x height / 2 s = ah / 2
Area of parallelogram = base x height s = ah
Thank you (*^__ ^*)

Using monotonicity to prove the inequality arctanx / X

Let f (x) = arctanx, G (x) = x, x > 0
f(0)=0,g(0)=0
f'(x)=1/(1+x²)＞0,g'(x)=1＞0
f'(x)-g'(x)=1/(1+x²)-1=-x²/(1+x²)≤0
That is, f '(x) ≤ G' (x)
Because f (x) and G (x) on [0, + ∞) increase monotonically and f '(x) ≤ G' (x)
So x > arctan (x)
Then arctanx / X

—X+4

From - x + 4

Suppose that ABCD and abef are parallelograms, they are not in the same plane, m and N are diagonal points AC and BF respectively, and am: FN = AC: BF, we prove that Mn is parallel to bec
Want to ask the first floor, how to prove mg parallel BC, GN parallel AF

Am: AC = FN: FB is obtained from am: FN = AC: BF
Take point G on AB so that am: AC = FN: FB = Ag: ab
Then mg is parallel to BC, GN is parallel to AF
The plane MGN is parallel to the plane bec
So Mn is parallel to the plane bec

Given that a and B are positive real numbers and a + B = 1, what is the maximum value of A. B?
a. "B" means "dot by". It's not good~·

A quarter
Well, I guess you haven't learned the mean value theorem yet
I'll explain it to you with the idea of function
b=1-a
a*b=a*(1-a)
With the idea of quadratic function, it is easy to get the maximum value of a * (1-A) when a = 1 / 2

Let y power of Y + Xe = 1, and find dy of DX

dy+d(x*e^y)=d(1)
dy+xd(e^y)+e^ydx=0
dy+xe^ydy+e^ydx=0
(xe^y+1)dy=-e^ydx
dy/dx=-e^y/(xe^y+1)

Given the equation AX ^ 2 + BX + C = 0 (zero vector), where a, B, C are non-zero vectors and a, B are not collinear, then the equation ()
A. There is at most one solution B. there is at least one solution C. There are at most two solutions d. There may be innumerable solutions

Shift C = - ax ^ 2-bx
c=-x^2a-xb
Since a vector has only one base,
So - x ^ 2 and - X are unique, and - X has only one solution at most

The minimum value of function f (x) = LG (4 ^ X-2 ^ x + 1 + 11) is

1、
Y (2 ^ x + 1) = 2 ^ X-1 the method of finding the domain of the inverse function
2^x=(1+y)/(1-y)>0
∴-1