In △ ABC, a = 108 ° and C - B = 28 ° are used to calculate the degrees of B and C

In △ ABC, a = 108 ° and C - B = 28 ° are used to calculate the degrees of B and C

According to the theorem of the sum of internal angles of triangles, we can get ∠ B + ∠ C = 180 ° - 108 °, then ∠ B + ∠ C = 72 °

Subtract (13-x) square from the square of 12 under the root sign = the square of 5 under the root sign - the square of X

The two sides are square
12^2-(13-x)^2=5^2-x^2
144-169+26x-x^2=25-x^2
26x=50
x=25/13
It is proved that x = 25 / 13 is the root of the original equation

As shown in the figure, in ladder ABCD, ad ‖ BC, e and F are the midpoint of diagonal AC and BD respectively, ad = 3, BC = 5, and ef?

In OBC, Fe is parallel to BC. In ABC, e is the midpoint of AC, so G is the midpoint of ab. similarly, h is the midpoint of CD, so ad = 2gf = 3 in abd. Similarly, ad = 2eh = 3 and GH = (3 + 5

Is there A.B.C such that equation 1 & # 178; + 3 & # 178; + 5 & # 178; +. + (2n-1) &# 178; = an ^ 3 + BN & # 178; + CN holds for any positive integer n

This is the formula that can be used in the formula: 1: the formula: 1: the formula: 1: the formula: 1: the formula: 1: the formula: 1: the formula: 1: 1 (n-1) \35\\\\\\\\\\\\\\\\\\\\\\\;;;;;;;;;;;;;;;;;;;;;;;;;;; \\\\\\\\\\\\\\\\58853; 178; + 6 &  178; +. + (2n-2) &  178;] = 2n (2n-1)

Summary of knowledge points of mathematics unit 2 (cylinder and cone)

1、 Cylinder
Definition of cylinder
1. The space geometry obtained by rotating one side of the rectangle 360 ° around the other side is called a cylinder, that is, Ag. One side of the rectangle is the axis, and the geometry obtained by rotating 360 ° is a cylinder. AG is called the axis of the cylinder, the length of Ag is called the height of the cylinder, all line segments parallel to Ag are called the generatrix of the cylinder, and the two circles formed by Da and d'g rotation are called the bottom surface of the cylinder, The surface formed by DD 'rotation is called the side of the cylinder
2. In the same plane, there is a fixed line and a moving line. When the plane rotates around the fixed line, the surface formed by the moving line is called the rotating surface, the fixed line is called the axis of the rotating surface, and the moving line is called the generatrix of the rotating surface, If two planes perpendicular to the axis are used to truncate the cylindrical surface, then the geometry enclosed by the two sections and the cylindrical surface is called a straight cylinder
Surface area of a cylinder
The surface area of a cylinder is called the surface area of the cylinder
Surface area of cylinder = 2 × bottom area + side area
After the side of the cylinder is expanded, it is a square (rectangle). After the side is expanded, the length is the perimeter of the bottom, and the width is the height, so the side area = the perimeter of the bottom × the height
Let R be the bottom radius and H be the height of a cylinder
S = 2 * s bottom + s side
=2*πr2+CH
Volume of cylinder
The amount of space a cylinder occupies is called the volume of the cylinder
The volume of a cylinder is the same as that of a cuboid or a cube, which is base area × height: let the radius of the bottom of a cylinder be r and the height be h, then the volume V: v = π r2h
If s is the bottom area, h is the height, and V: v = SH is the volume
Side area of cylinder
Side area of cylinder = perimeter of bottom multiplied by height s side = Ch
Note: C is π D
The name of each part of the cylinder
The two circular surfaces of a cylinder are called the bottom (also divided into upper and lower bottoms); the surrounding surfaces are called the sides; and the distance between the two bottom surfaces is called the height (there are innumerable lines of height)
2、 Cone
Volume of cone
The space occupied by a cone is called the volume of the cone
The volume of a cone is equal to 1 / 3 of the volume of a cylinder with the same base and height
According to the cylinder volume formula v = sh (v = RR π h), the cone volume formula is obtained
V＝1/3Sh（V＝1/3SH）
S is the bottom area, h is the height, and R is the bottom radius
prove:
Divide the cone into k parts along the height
Per serving, H / K,
The nth radius: n * r / K
The nth bottom area: pi * n ^ 2 * R ^ 2 / K ^ 2
The nth volume: pi * h * n ^ 2 * R ^ 2 / K ^ 3
Total volume (1 + 2 + 3 + 4 + 5 +... + n): pi * h * (1 ^ 2 + 2 ^ 2 + 3 ^ 2 + 4 ^ 2 +... + K ^ 2) * R ^ 2 / K ^ 3
because
1^2+2^2+3^2+4^2+...+k^2=k*(k+1)*(2k+1)/6
therefore
Total volume (1 + 2 + 3 + 4 + 5 +... + n): pi * h * (1 ^ 2 + 2 ^ 2 + 3 ^ 2 + 4 ^ 2 +... + K ^ 2) * R ^ 2 / K ^ 3
=pi*h*r^2* k*(k+1)*(2k+1)/6k^3
=pi*h*r^2*(1+1/k)*(2+1/k)/6
Because when n is larger and larger, the total volume is closer to the cone volume, and 1 / K is closer to 0
So pi * h * R ^ 2 * (1 + 1 / k) * (2 + 1 / k) / 6 = pi * h * R ^ 2 / 3
Because v-column = pi * h * R ^ 2
therefore
The V-cone is 1 / 3 of the volume of the v-column with the same base and height
The surface area of a cone
The surface area of a cone is called the surface area of the cone
Calculation formula of cone
The side area of the cone = the square of the height * π * percent of the degree of the sector
Side area of cone = 1 / 2 * generatrix length * bottom circumference
Surface area of cone = bottom area + side area s = square of π R + π RA (note a = generatrix)
Volume of cone = 1 / 3 sh or 1 / 3 π r square H
If the cone is connected with its sector, then n = A / R * 360
Other concepts of cone
Height of cone:
The distance between the apex of the cone and the center of the bottom of the cone is called the height of the cone;
Side area of cone:
When the side of the cone is expanded along the generatrix, it is a sector; when it is not expanded, it is a curved surface
Bus bar of cone:
The radius of the sector formed by the expansion of the side of the cone and the distance from the bottom circle to the apex
A cone has a bottom, a side, a vertex, a height and numerous generatrix
The relationship between cylinder and cone
The volume of a cone with the same base and height as a cylinder is one third of that of a cylinder
Between a cylinder and a cone of equal volume and height, the base area of the cone is three times that of the cylinder
Between a cylinder and a cone of equal volume and base area, the height of the cone is three times that of the cylinder
Unequal cylinders and cones are unequal

The perimeter of a rectangle is 54 cm, and the ratio of length to width is 7:2. What is the area of the rectangle?

The sum of length and width is 54 / 2 = 27, length is 7 / 9 × 27 = 21, width is 2 / 9 * 27 = 6, area is 6 × 21 = 126cm & sup2;

There is a seven digit number. The sum of the numbers on each digit is 55. If you add 2 to this number, you will get a new seven digit number. At this time, the sum of the numbers on each digit of the new number is 3, and the original number is 3______ ．

According to the meaning of the title, the sum of the new seven digit numbers is 3. It can be concluded that each digit in the new seven digit number only contains 3, 6 zeros, or 1, 2, 5 zeros, or 1, 1, 1, 4 zeros. Because the sum of each digit in the new seven digit number is 3, which is much smaller than the original 55, it shows that there is a continuous carry when adding 2

Does it take 45 seconds for a train to cross the 860 meter long bridge? It takes 35 seconds for a train to cross the 610 meter long tunnel at the same speed
Formula!
It's a bus!

860-610 = 250 250 ÷ [45-35] = 25 speed 25 × 45 = 1125 1125-860 = 265 car length

In rectangular ABCD, the intersection of diagonal lines AC and BD is O, AE bisecting angle bad, angle AOD = 120 degrees, and the degree of angle AEO is calculated

∵ in isosceles △ AOB, ∵ ABO = 60 °, ∵ BAE = 45 ° in △ Abe, ∵ AOB is equilateral triangle, ∵ Abe is isosceles right triangle, ∵ be = AB = Bo, ∵ BOE is isosceles triangle, ∵ EBO = ∵ ADB = 30 °, ∵ BeO = (180-30) / 2 = 75 °, ∵ AEO = 75 ° - 45 ° = 30 °

The speed of light in vacuum is 300000 kilometers per second. How many million kilometers is a light year calculated by computer (365 days per year)

3 × 10 ^ (5) km × 365 days × 24 hours × 60 minutes × 60 seconds = 9.46 × 10 ^ (12) km