If the vertices of a cube of 8 are all on a sphere, the surface area of the sphere is______ ．

The volume of a cube is 8, so its side length is 2, and the diagonal of the cube is 4 + 4 + 4 = & nbsp; 23, which is the diameter of the ball, so the radius is 3, and the surface area of the ball is 4 π & nbsp; 32 & nbsp; = 12 π

If the surface area of a square is 24, then the volume of the ball is?
RT.. Wait
There is no mathematical answer

If the surface area of the cube is 24 and the area of one side is 24 / 6 = 4, the side length of the cube is 2 and the diagonal of the cube is 2 * root 3
The diagonal of the cube is the diameter of the ball. Therefore, the radius of the ball is root 3
The volume of the sphere is 4 / 3 * π R ^ 3 = 4 π * radical 3

If the surface area of the sphere is the same as that of the cylinder whose cross-section (cross-section through the axis of symmetry) is square, then the ratio of the volume of the cylinder to that of the sphere is ()
A. 1：1B. 1：43C. 2：3D. 3：2

Let R be the radius of the bottom of the cylinder and R be the radius of the ball. If the height of the cylinder is 2R, then the side area of the cylinder is 2 π R · 2R = 4 π R2, and the surface area of the ball is 4 π R2. Because 4 π R2 = 4 π R2, so r = R, then the volume of the cylinder is V1 = π R2 · 2R = 2 π R3, the volume of the ball is V2 = 43 π R3, and V1: V2 = 3:2

If an axial section of a cylinder is a square with side length of 4, the volume of the cylinder can be obtained

If the axial section of the cylinder is a square with side length of 4, the diameter and height of the bottom of the cylinder are 4
The radius of the bottom of the cylinder is 4 △ 2 = 2
Volume of cylinder
=3.14×2×2×4
=50.24

Solving inequality 2log2 (x-4) < log2 (X-2)

log2(x-4)²

Let f (x) = log take 1 / 2 as the base, 1-ax / X-1 as an odd function, and a as a constant
(1) Finding the value of a
(2) It is proved that f (x) increases monotonically in the interval (1, positive infinity)
(3) If the inequality f (x) > (1 / 2) ^ 2 + m holds for every value of X in the interval [3,4], the value range of real number m is obtained

1) Let f (x) = log take 1 / 2 as the base and 1-ax / X-1 as the odd function
So f (2) = f (- 2)
A = 1
2) Let x1, X2 belong to (1, positive infinity), and x1

The known function f (x) = log (a) (x ^ 2-ax + 5), (a > 0, and a ≠ 0)
When a = 2, find the minimum value of F (x)
When a = 2, let u = x ^ 2-2x + 5,
And u = x ^ 2-2x + 5 = (x-1) ^ 2 + 4 is greater than or equal to 4
And because y = log2x is an increasing function,
So f (x) = log (x ^ 2-2x + 5) is greater than or equal to log24 = 2,
That is, the minimum value of F (x) is 2
Why should it be greater than or equal to 4

Answer: because the minimum value of (x-1) ^ 2 is 0 (when x = 1), so u is greater than or equal to 4, and because the base number 2 is greater than 1, so y = log2u is an increasing function, which requires the minimum value of F (x), only the real number u takes the minimum value of 4

Given the function f (x) = log2 (AX + b), f (2) = 2. F (3) = 3, then f (5) =?

Given the function f (x) = log2 (AX + b), f (2) = 2. F (3) = 3, then f (5) =?
f(2)=log2(2a+b)=2
f(3)=log2(3a+b)=3
By definition
loga(b)=c
A ^ C (C power of a) = b
2 ^ 2 (the square of 2) = 2A + B 1
2 ^ 3 (the third power of 2) = 3A + B 2
Formula 2 minus Formula 1
a=8-4=4
b=-4

If f (x) = log2 (AX + b), f (2) = 2, f (3) = 3, then f (5) = what
Note: 2 in log2 is the base

Answer: F (2) = log2 (2a + b) = 2 ﹣ 2A + B = 4f (3) = log2 (3a + b) = 3 ﹣ 3A + B = 8A = 4 B = - 4f (x) = log2 (4x-4) f (5) = log2 (4 * 5-4) = 4 Analysis: F (2) = 2, f (3) = 3. These two formulas can be substituted into the analytical formula to get a and B. how easy it is to find f (5) again

If f (x) = log2 (AX + b), f (2) = 2, f (3) = 3, then f (5) =?
Note: 2 in log2 is the base
Please master answer, to the process, thank you!

F (2) = 2, that is, 2 ^ 2 = 2A + B 2A + B = 4
F (3) = 3, that is, 2 ^ 3 = 3A + B 3A + B = 8
The solution is a = 4, B = - 4
f(5) = log2(4*5-4) = log2(16) = 4

If the vertices of a cube of 8 are all on a sphere, the surface area of the sphere is______ ．