The circumference of the bottom of a cuboid is 36 cm, and the height is 8 cm. What is the total length of the edges of the cuboid?

The circumference of the bottom of a cuboid is 36 cm, and the height is 8 cm. What is the total length of the edges of the cuboid?

The sum is 36 × 2 + 8 × 4 = = 104 cm

How to convert liquid oxygen and gaseous oxygen

The mass is the same. When the mass is fixed, the quantity n of matter is fixed. In the gas state, only three of the four quantities can determine the state. In the liquid state, only two of the three quantities can be determined when the density and volume are considered

Given a + B = 10, ab = - 2, then (3a-2b) - (- 5B + AB)=______ ．

(3a-2b) - (- 5B + AB) = 3a-2b + 5b-ab = 3 (a + b) - AB, ∵ a + B = 10, ab = - 2, the original formula = 3 × 10 - (- 2) = 32

It is proved that the volume bounded by the tangent plane of any point on the cubic (a > o) of the surface XYZ = A and three coordinate planes is a certain number

Let the coordinates (x0, Y0, Z0) of any point on the surface satisfy x0 * Y0 * Z0 = a ^ 3, and the normal vector at the point = (Y0 * Z0, x0 * Z0, x0 * Y0) tangent plane equation is: Y0 * Z0 * (x-x0) + x0 * Z0 * (y-y0) + x0 * Y0 * (z-z0) = 0. The plane intersects the X, y and Z axes to get a tetrahedron. Substituting x0 = 0, Y0 = 0 to get z = 3 * Z0

How many centimeters is a unit of length?

33.3 cm or 33 1 / 3 cm

It is known that the two sum of the equation (a + b) x + 2bx - (C-A) = 0 is – 1, two difference 1, where ABC is the trilateral length of △ ABC. 1. Find the root of the equation. 2. What is the shape of triangle ABC

Let two roots be x 1 x 2. From the known x 1 + x 2 = - 1 (1) x 1-x 2 = 1 (2)
(1)+(2) 2x1=0 x1=0 (1)-(2) 2x2=-2 x2=-1
x=0 0+0 -(c-a)=0 c-a=0 c=a x=-1 a+b-2b=0 a-b=0 a=b
A = b = C △ ABC is an equilateral triangle

Find the tangent plane of the sphere x ^ 2 + y ^ 2 + Z ^ 2 = 1 in the first trigram, so that it has the minimum volume of the tetrahedron surrounded by the plane of the three coordinate axis

The normal vector of the sphere in the first hexagram is (x0, Y0, Z0), and the tangent plane equation is (x-x0) x0 + (y-y0) Y0 + (z-z0) Z0 = 0, that is, xX0 + yy0 + zz0 = 1. The intersection point with the three coordinate axis is (1 / x0,1 / y0,1 / Z0), and the volume of the tetrahedron is 1 / (6x0y0z0). Therefore, the problem is to find the maximum value of x0y0z0, if x0 ^ 2 + Y0

Factorization 9-x2 + 13x2 + 36
2 is the square

Square difference formula

a1.a2.…… An n integers prove the existence of I, k such that a (I + 1) + a (I + 2) + +A (I + k) can be divisible by n

Let SJ = a1 + +aj;j=1,2,…… n;
Then 1. For any J, n does not divide SJ;
In this way, we can get a better result The remainder of Sn divided by N is only 1,2 N-1 this n-1
So there must be two Si, Si + K, (I + k)

It is known that F1 and F2 are the left and right focus of the ellipse x ^ 2 / 16 + y ^ 2 / 7 = 1 respectively. If P is on the ellipse and Pf1 * PF2 = 0, find the value of | vector Pf1 | - | vector PF2 |

Let Pf1 be x and PF2 be y
x+y=2a=8 c^2=16-7=9
F1F2=2c=6
Because Pf1 * PF2 = 0
therefore
x^2+y^2=36
(x-y)^2=x^2+y^2-2xy=x^2+y^2-[(x+y)^2-(x^2+y^2)]=36-(64-36)=8
||Vector Pf1 | - | vector PF2 | = 2 times root 2