Five colors make people blind; five sounds make people deaf; five tastes make people cool; galloping and hunting make people crazy; rare goods make people do harm

Five colors make people blind; five sounds make people deaf; five tastes make people cool; galloping and hunting make people crazy; rare goods make people do harm

This sentence comes from Laozi's Tao Te Ching, which means: colorful makes people dazzled; too much music makes people deaf; too much delicious makes people hurt; indulging in horse hunting makes people loose and crazy; saving precious things makes people nervous. Therefore, saints only want to eat enough, not for the enjoyment of the ears and eyes, so they should abandon those who get these things

English translation
Hi Ms Wang,
Attached is the particular design and quantity i want to order,please make provision as soo

Hello, Ms. Wang
According to the quantity I want, please attach the design I want and provide it as soon as possible Incomplete /

English translation
I do hope that the music of a creek from me ,will echoing the deep of valley of you .
Finally, I can express the meaning, such as blessing, love, etc~

It's a very elegant sentence
I wish the concert of my news would reverberate in your valley
It's like a love sentence~

If all items of the proportional sequence {an} are positive, a1 + A2 + a3 + A4 + A5 + A6 = 1, 1 / A1 + 1 / A2 + 1 / A3 + 1 / A4 + 1 / A5 + 1 / A6 = 10, then A1 * A2 * A3 * A4 * A5 * A6 =?

A1 + A2 + a3 + A4 + A5 + A6 = 1, A1 (1-Q ^ 6) / 1-Q = 1. Similarly, 1 / A1 + 1 / A2 + 1 / A3 + 1 / A4 + 1 / A5 + 1 / A6 = 10, 1 / A1 * (1-1 / Q ^ 6) / (1-1 / Q) = 10, A1 ^ 2 * q ^ 5 = 1 / 10, and A1 * A2 * A3 * A4 * A5 * A6 = A1 ^ 6 * q ^ 15 = (A1 ^ 2 * q ^ 5) ^ 3 = 1 / 1000

If the sum of the top and bottom of the isosceles triangle ABCD is 4, and the acute angle between the two diagonals is 60 degrees, the shape of the isosceles trapezoid is right

The area of isosceles trapezoid ABCD = 1 / 2 * 4 * 4 * sin60 = 4 times root 3
The area of isosceles trapezoid ABCD = 1 / 2 * 4 * 1 / root 3 = 2 times root 3 / 3
So the area of isosceles trapezoid is 4 times root number 3, or 2 times root number 3 / 3

If LG (x + y) + LG (2x + 3Y) = LG12 + lgx + lgY, then=

lg(x+y)+lg(2x+3y)=lg12+lgx+lgy
lg[(x+y)(2x+3y)]=lg(12xy)
(x+y)(2x+3y)=12xy
2x^2+5xy+3y^2=12xy=0
2x^2-7xy+3y^2=0
(2x-y)(x-3y)=0
2X = y or x = 3Y
X / y = 1 / 2 or X / y = 3

How many days does a snail climb a tree 9 meters high, climbing 1 meter up in the daytime and 1 / 3 meter down at night

On the thirteenth day, we could climb there by day
On the 12th day, I climbed to the 8m position, and on the 13th day, I climbed up 1m

The right focus of ellipse C is f (2,0) and passes through point P (2, √ 2). Line L passes through point F and intersects ellipse C at two points a and B
The intersection point of axis is m (1 / 2,0), and the equation of line L is obtained

It is known that C = 2, so a ^ 2-B ^ 2 = C ^ 2 = 4,
And the ellipse goes through P (2, √ 2), so 4 / A ^ 2 + 2 / b ^ 2 = 1,
A ^ 2 = 8, B ^ 2 = 4,
So the elliptic equation is x ^ 2 / 8 + y ^ 2 / 4 = 1
Line L passes through point F
Let I: y = K (X-2)
A (x1, Y1) B (X2, Y2), AB midpoint (x0, Y0)
x1^2/8+y1^2/4=1-----------①
x2^2/8+y2^2/4=1-----------②
②-①
(x2+x1)/8+k(y2+y1)/4=0
2x0/8+2ky0/4=0
x0+2ky0=0
The intersection of the vertical bisector of line AB and X axis is m (1 / 2,0)
Let the vertical bisector of AB y = - 1 / K (x-1 / 2)
y0=-1/k(x0-1/2)
y0=k(x0-2)
x0+2ky0=0
Three simultaneous
Get k ^ 2 = 1 / 2
k=±√2/2
The equation of line L
y=±√2/2(x-2)
Simplification
x-√2y-2=0
Or x + √ 2y-2 = 0

If the height of a parallelogram is 10 meters, the height of a triangle is () meters

20 meters
Principle: triangle area = bottom x height / 2 parallelogram area = bottom x height

Given two points m (- 1,0), n (1,0), and the moving point P makes the vector Mn ^ 2 = 2, the vector PM &; the vector PN, find the value range of the angle between the vector PM and PN

Let P (x, y)
PM=(-1-x,-y),PN=(1-x,-y)
PM*PN=(1-x^2)+y^2=MN^2/2=2
y^2-x^2=1
The trajectory of point P is a hyperbola with y axis as symmetry axis
Let the angle between PM and PN be α
PM*PN=|PM|*|PN|cosα
cosα =2/√[(1+x)^2+y^2][(1-x)^2+y^2]
It is concluded that cos α = 1 / √ [x ^ 4 + x ^ 2 + 1]
Let f (x) = 1 / √ [x ^ 4 + x ^ 2 + 1]
f'(x)=(-1/2)(4x^3+2x)√[x^4+x^2+1]^3
Let f '(x) = 0, x = 0
x>0,f'(x)