It is known that the length of each edge of a regular pyramid is 3 root sign 2, then the surface area of the circumscribed sphere of a regular pyramid is I want detailed process, don't copy

It is known that the length of each edge of a regular pyramid is 3 root sign 2, then the surface area of the circumscribed sphere of a regular pyramid is I want detailed process, don't copy

A:
The length of each edge is 3 √ 2
Complete the regular pyramid into the cube abcd-a1b1c1d1
Then the side length of cube is ab = BC = 3
So: cube diagonal BD1 = AC1 = √ 27 = 3 √ 3
So: radius of circumscribed sphere r = (BD1) / 2 = (3 √ 3) / 2
So: surface area of circumscribed sphere = 4 π R ^ 2 = 27 π

Suppose that the lengths of six edges of a tetrahedron are 1, 1, 1, 1, 2 and a respectively, and the edges with length a are different from those with length 2, then the value range of a is___ ．

Let the base of tetrahedron be BCD, BC = a, BD = CD = 1, vertex a, ad = 2. In triangle BCD, because the sum of two sides is greater than the third side, we can get: 0 ＜ a ＜ 2. ① take the midpoint e of BC, ∵ e is the midpoint, and the right triangle ace is equal to the right angle DCE. Therefore, in triangle AED, AE = ed = 1 - (A2) 2, ∵ the sum of two sides is greater than the third side ∵ 2 ＜ 21 - (A2) 2, we can get 0 ＜ a ＜ 2, (negative value 0 is rounded off) ② ② So the answer is: (0, 2)

If the length of six edges of a tetrahedron is 2,2,2,2, a and a respectively, and there are exactly two such tetrahedrons, then the value range of a is 0
The answer is: √ 6 - √ 2 ＜ A2 √ 2 and a ≠ 2

It's easy to think about it. We should draw a picture
A is not equal to 2 and a > 1, a

It is known that if the side length of the base of a regular pyramid is 2 and the side length is root 5, then the angle between the side and the base is?

The distance from the vertex to the bottom is root sign 3, that is, the height of the regular pyramid is root sign 3, so the height of the side triangle is 2. According to the cosine theorem, cos = 1 / 2 is obtained. Because it is in a triangle, the angle is 60 degrees
Just draw a picture

What is the size relationship among the three numbers a = 0.3 ^ (- 0.4), B = log (0.3) (0.4), C = log4 (0.3)

A=0.3^(-0.4)>1
B = log (0.3) (0.4) > 0 but less than 1
C=log4（0.3）

M = LG (2), n = LG (3), using m, n for log (5) 24
My final answer is 6m + 4

log(5)24
=lg24/lg5
=lg(2×2×2×3)/lg(10÷2)
=(lg2+lg2+lg2+lg3)/(lg10-lg2)
=(3m+n)/(1-m)

If log (a) 2 = m, log (a) 3 = n, then a ^ 2m + n=

12

Given log (a) (2) = m and log (a) (3) = n, what is the value of a ^ (2m + n)?

Log (a) (2) = m, a ^ m = 2, a ^ 2m = 2 ^ 2 = 4;
Log (a) (3) = n to get a ^ n = 3
From the additivity of exponential operation, (a ^ 2m) * (a ^ n) = a ^ (2m + n) = 12

① Let log а 2 = m, log a 3 = n, find the value of 2m + n power of A
Eager for answers
Requirement calculation process

Sorry, there is a symbol on the mobile phone, if the first one is: the logarithm of 2 with a as the base is m! Then the answer is 12, the mobile phone can't write down the process! This is a problem in high school mathematics!

How to calculate log (a) (m-n)

This is the simplest form. If it is log (a) (m) - log (a) (n), it can be equal to log (a) (M / N)