There are only three story books and five undergraduate teaching books in the bookcase. How many books should we take out at least to ensure that we take out two identical books at a time?

There are only three story books and five undergraduate teaching books in the bookcase. How many books should we take out at least to ensure that we take out two identical books at a time?

2 + 1 = 3 A: make sure to take out two identical books at a time, at least 3 books

There are three story books and seven science and technology books in the bookcase. We should ensure that we can take out two science and technology books at a time. How many books should we take out at least?
I have my own urgent need --- Ke Hongru

2 + 3 = 5
A: at least five books should be taken out

There are several different ways for a student to choose one of the two science and technology books, two political books and three literature and art books

2 + 2 + 3 = 7 species

There are three different story books and two different popular science books on the bookshelf. How many different ways can you take two books out of them?

There are only three kinds of story books
Only one popular science book
3 * 2 = 6 kinds
So there are 3 + 1 + 6 = 10

P is the point on the line AB, PA = 2 / 5ab, M is the midpoint of AB, if PM = 16cm, then AB =?

Let AB = x, then 1 / 2x-2 / 5x = 16
The solution is x = 160
That is ab = 160cm

20%x-5/1=5/4 3/1x+4/3x=5/26

20%x-5/1=5/4
0.2x-5 / 1 = 5 / 4 multiply by 5
0.2X*5-1=4
X=4+1=5
3 / 1 x + 4 / 3 x = 5 / 26 double 60
20X+45X=312
65X=312
X=4.8

It is known that the radius of the bottom of the cone is 2cm and the length of the generatrix is 4cm, then the area of the cone is CM & sup2;
What is a bus?

The generatrix is the distance from the vertex to the point on the circumference of the bottom, that is, the radius of the sector in the side view
The arc length of this sector is the circumference 4Pi of the bottom circle
Let the central angle of the sector be a (radians), 4A = 4Pi, so a = Pi
The side area is 1 / 2a4 ^ 2 = 8pi
The formula is: side area = pi * bottom radius * generatrix
PI is the PI

Given that s = 1 divided by (fifty-one plus fifty-two plus fifty-nine plus sixty one), then the integral part of S is ()

S=1*51+1*52+1*53+...+1*60
=50*10+1+2+3+4+5+6+7+8+9+10
=555

It is known that the circle C: x2 + Y2 + 2x-4y + 1 = 0,0 is the coordinate origin, the moving point P is outside the circle C, and the tangent of the circle C is made through P, and the tangent point is m
(1) If point P moves to (1,3), the equation of tangent L is obtained
(2) Find the trajectory equation of point P satisfying the condition | PM | = | Po |

1
Circle C: (x + 1) ^ 2 + (Y-2) ^ 2 = 4
When l slope does not exist, l: x = 1 is tangent to circle C
When the slope of L exists, it is set to K,
Then l: Y-3 = K (x-1), that is kx-y + 3-K = 0
The distance d from C to L is equal to the radius
∴|-k-2+3-k|/√(k^2+1)=2
The solution is k = - 3 / 4
The equation of tangent L is x = 1 or 3x + 4y-15 = 0
two
Make the tangent of circle C through P, and set the tangent point as M
∴CM⊥PM
∴|PM|²=|PC|²-4,
∵|PM|=|PO|
∴|PO|²=|PC|²-4
Let P (x, y)
∴x²+y²=（x+1)^2+(y-2)^2-4
∴2x-4y+1=0
The trajectory equation of point P 2x-4y + 1 = 0
(satisfy (x + 1) ^ 2 + (Y-2) ^ 2 > 4)

4 / 5 + 7 / 12 + 9 / 10 4 / 5 - (3 / 5 + 2 / 5) 3 / 8 + 4 / 15 + 5 / 8 + 7 / 15

4/5+7/12+9/10=48/60+35/60+54/60=137/60 4/5-(3/5+2/5)*3/8+4/15+5/8+7/15=4/5-3/8+4/15+5/8+7/15=4/5+1/4+11/15=107/60