If the four vertices of a regular triangular pyramid are on a sphere with radius 1, and the three vertices of the bottom surface are on a big circle of the sphere, then the volume of the regular triangular pyramid is___ ．

The four vertices of a regular triangular pyramid are all on a sphere with radius 1, and the three vertices of the bottom surface are on a big circle of the sphere, so the center of the sphere is the center of the triangle on the bottom surface. Let the radius of the sphere be 1, so the side length of the triangle on the bottom surface is a, 23 × 32A = 1, a = 3. The volume of the regular triangular pyramid is 13 × 34 × (3) 2 × 1 = 34, so the answer is: 34

If the four vertices of a regular triangular pyramid are on a sphere with radius 2, and the three vertices of the bottom surface are on a large circle of the sphere, then the volume of the regular triangular pyramid is?

The three vertices of the bottom surface are on a big circle of the ball, that is, the three vertices of the bottom surface are on a circle with radius 2, so the side length of the regular triangle of the bottom surface is 3 under 2, so the area of the bottom surface is 3 under 3. The height of the triangular pyramid is radius 2, so the volume is 3 under 2

Given that the planes of the three great circles of a sphere are perpendicular, the ratio of the volume of the octahedron whose vertex is the intersection of the three great circles to the volume of the sphere is ()
A. 1：πB. 1：2πC. 2：πD. 4：3π

Let the radius of the sphere be r, and divide the regular octahedron into two regular quadrangular pyramids. The diagonal length of the square at the bottom of the quadrangular pyramid is 2R. The side length of the square is 2R, the area of the square at the bottom is 2r2, the height of the quadrangular pyramid is R, and the volume of the regular octahedron is 132r2 · 2R = 43r3. Therefore, the ratio of the volume of the regular octahedron to the volume of the sphere is (43r3): (43 π R3) = 1: π, so a is selected

∫1/(x^2+2x+5)dx =∫1/[(x+1)²+4] dx =∫1/[(x+1)²+4] d(x+1) =1/2 arctan(x+1)/2 +C
Can you explain step three to step four

There is an integral formula
∫ 1/(x²+a²)dx
=1/a arctan x/a
The corresponding x is replaced by X + 1 and a by 2

Do me a favor, calculate ∫ e ^ (2x) * (Tan x + 1) ^ 2DX and ∫ (x * e ^ (arctan x)) / (1 + x ^ 2) ^ (3 / 2) DX
The indefinite integral of 2x power of e multiplied by the square of Tan x + 1 (arctan x power of X * e) starts with the indefinite integral of 3 / 2 power of (1 + x ^ 2)
Don't count the first, just the second

I didn't work it out with a calculator, did I copy it wrong

Help me figure out how much this calculus equals
six
(1/16)y^2*e^(-y/2)
0

1-(17/2)*e^(-3)
Use a few more partial integral, keep putting e ^ (- Y / 2) back
The answer is not sure, right
There's no problem with the method

How much is 0 to 0 in calculus

In calculus, 0:0 is an indeterminate formula
The derivation of numerator and denominator can be used in calculation

Calculus is not much, but this is my last point, I hope to write out the detailed process of solving the problem
Page 238: question 78: try to prove that the tangent of the curve y = x ^ 3 at any point (a, a ^ 3) must intersect the curve again, and the slope at the intersection is 4 times of that at point (a, a ^ 3)
Find the values of H, K and a such that the circle (X-H) ^ 2 + (Y-K) ^ 2 = a ^ 2 is tangent to the parabola y = x ^ 2 + 1 and the point (1,2) also makes the d ^ 2Y / DX ^ 2 of the two curves equal at this point
Question 6: a bus can hold 60 people. The relationship between the number of passengers X and the cost P (US dollars) paid for renting the bus per trip is given in P = [3 - (x / 40)] ^ 2. Write the expression of the total revenue R (x) of each trip obtained by the bus company. What is the number of passengers per trip with the marginal revenue DR / DX equal to zero? What is the corresponding cost?

After derivation, y '= 3x & # 178; y = x & # 179; at the point (a, a & # 179;) the slope is 3A & # 178;, and the tangent equation is y = 3A & # 178; X - 2A & # 179; simultaneous: y = x & # 179;, y = 3A & # 178; X - 2A & # 179; X = a, or x = - 2aX = a, so

The approximate value of cos29 & # is expressed by differential equation

Help me find some approximations····
(1) 90149 to the thousandth is ()
(2) 4030 to ()
(3) 0.02866 to 0.0001 is ()
(4) 38765 is ()
(5) 283500 to 10000 ()
(6) 3056 keep 3 significant digits is ()

0.901
zero point four zero
zero point zero two eight seven
thirty-nine thousand
two hundred and eighty thousand
zero point three zero six

If the four vertices of a regular triangular pyramid are on a sphere with radius 1, and the three vertices of the bottom surface are on a big circle of the sphere, then the volume of the regular triangular pyramid is___ ．