What is the normal vector of a curve

What is the normal vector of a curve

Let the curve be r (s) = (x (s), y (s), Z (s)), and s be the arc length parameter. T (s) = R '(s) = (x', y ', Z') is called the unit tangent vector of R (s). It is easy to verify that | t (s) | = 1t '(s) = K (s) n (s) = (x' ', y' ', Z' ') where n (s) is called the one bit normal vector of the curve

How to judge the inner and outer normal vectors of a curve
When doing a question, the outer normal vector of a certain surface often appears. When two normal vectors are obtained, how to judge whether it is the outer normal vector or the inner normal vector?

There is no specific judgment standard. The idea is as follows: set the normal vector at the point m (x0, Y0, Z0) as n (I, J, K), find out that the point n (x0 + I, Y0 + J, Z0 + k) is located inside or outside the surface, that is, the inner normal vector is located inside the surface, and that is, the outer normal vector is located outside the surface

Proposition a, if x is greater than 0, then the x power of a is less than 1. Proposition B, the function y = xsquare - 4ax is a decreasing function in (- infinity, 1), if at least one of a and B is true
Proposition, then the value range of real number a is

You can use reverse thinking to solve this problem, that is, none of a and B is true. To find out the range of a, and then find out its complement is not the answer. Simplify the calculation
A proposition is incorrect: if x is greater than 0, then the x power of a is greater than or equal to 1, and a is greater than or equal to 1
Proposition B is wrong: the function y = x square - 4ax is a non decreasing function in (- infinity, 1), that is to say, there is a decrease and an increase or an increase. As long as it is not a simple decreasing function, the opening of the function is upward, then the value of a must make it decrease and increase, so as long as 2a is greater than 1 line, then a is greater than 1 / 2
We get that a is greater than or equal to 1
Then find the complement, that is, a less than 1 is the answer

It is known that a and B are reciprocal to each other. The calculation result of a divided by 5 of B is

If a and B are reciprocal, then
AB=1
therefore
A/3÷5/B
=A/3×B/5
=AB/15
=1 / 15 (1 / 15)

It is known that the sum of the polynomial 2x ^ + my-12 and the polynomial NX ^ - 3Y + 6 does not contain x.y. try to find the value of Mn

①2x^+my-12
②nx^-3y+6
① + 2 = (2 + n) x ^ + (M-3) y-6, excluding X and y, that is, 2 + n = 0, M-3 = 0
M = 3, n = - 2

Please write songs about summer, words about autumn and famous poems about wine
It's the song of summer, the word of autumn, the famous poem of sprinkling, not too much, just two or three sentences

The song of summer: [double tune] Qingjiang leads yuan Qianlin to dream of returning to the day. The curtain is half rolled, and the door covers the courtyard. The spider silk hangs willow cotton, and the swallow's beak sticks flower pieces. The song of spring goes far away. The words of autumn: 1. The autumn wind is bleak, and the flood surges. (Cao Cao: watching the sea) 2. The leaves fall, and the flowers bloom in February. (Li Qiao: the wind) 3

M is a negative integer greater than - 1 and 1 / 3, | n | = 2, find the cubic power of 1 / 4m - the quadratic power of 2n * the quadratic power of M + the cubic power of 6N * M. if you can't get the answer, tomorrow is ten questions! 5555 ~ you can also send it to the website!

∵ m is a negative integer greater than - 1 and 1 / 3, | n | = 2
∴m=-1 n=±2
1 / 4m-2n * m + 6N * m
=1/4*(-1)³-2(±2)²*(-1)²+6*(±2)³*(-1)
=-1/4-8±48
=39 and 3 / 4
Or = - 56 and 1 / 4

(7 out of 8 plus 13 out of 16) divided by 9 out of 16, 3 out of 5 plus 3 out of 4 divided by 3 out of 5, 7 out of 13 divided by 7 out of 7 plus 1 out of 7 multiplied by 5 out of 13

(7 out of 8 plus 13 out of 16) divided by 9 out of 16
=（7/8+13/16）x16/9
=(14/16+13/16)x16/9
=27/16x16/9
=3
Three fifths plus three fourths divided by three fifths
=3/5+5/4
=12/20+25/20
=37/20
Seven out of thirteen divided by seven plus one out of seven multiplied by five out of thirteen
=7/13x1/7+1/7x5/13
=(7/13+5/13)x1/7
=12/13x1/7
=12/91

⊙ o: X & sup2; + Y & sup2; = 1, ⊙ C: (x-4) & sup2; + Y & sup2; = 4, the moving circle P and ⊙ o sum are circumscribed, and the trajectory equation of the moving circle center P is

Center O (0,0) R1 = 1
Center C (4,0) R2 = 2
Let P (x, y)
=√（x^2+y^2）-1=√(（x-4)^2+(y-0)^2)-2
√（x^2+y^2）+1=√(（x-4)^2+(y-0)^2）
Simultaneous square of both sides
x^2+y^2+1+2√(x^2+y^2)=(x-4)^2+y^2
1+2√(x^2+y^2)=-8x+16
2√(x^2+y^2)=-8x+15
Simultaneous square of both sides
4(x^2+y^2)=(-8x+15)^2
4x^2+4y^2=64x^2-240x+225
60x^2-4y^2-240x+225=0

What's the answer to 30 days divided by 2?

The word "fat"
30 days is the month, 30 days divided by 2 is half of the month!