Given that f (x-1) is odd, f (x + 3) is even, f (0) = 1, then f (8)=______ ．

Given that f (x-1) is odd, f (x + 3) is even, f (0) = 1, then f (8)=______ ．

∵ the function f (x + 3) is even, ∵ f (x + 3) = f (- x + 3), ∵ f (8) = f (5 + 3) = f (- 5 + 3) = f (- 2); the function f (x-1) is odd, f (0) = 1, ∵ f (- 2) = f (- 1-1) = - f (1-1) = - f (0) = - 1, ∵ f (8) = - 1

If f (x) is odd and f (x + 1) is even, then f (1) + F (3) +... F (19) = f (2) + F (4) +... F (20)

If f (x + 1) is an even function, then f (- x + 1) = f (x + 1), that is, f (x) = f (2-x), and f (x) is an odd function, then f (- x) + F (x) = 0, f (0) = 0, f (x) = f (2-x) = - f (X-2) = - f (4-x) = f (x-4), so f (x) is a periodic function with period 4. So f (1) + F (3) = f (1) + f (4-1) = f (1) + F (- 1) = 0, f (...)

The waterworks has a cylindrical pool with a bottom diameter of 10 meters and a depth of 2.5 meters. What is its floor area? How many cubic meters is its volumetric type?
Keep integers

Floor area = π * r square = 25 π
Volume is volume = bottom area times height = 25 π times 2.5 = 62.5 π

24 points: 3 4 - 6 10; 3 - 5 7 - 13; 7 7 3 4; 3 5 7 - 13

3,4,-6,10=10+(-6)+4*3=24
7,7,3,4=7*3+(7-4)=24
3,-5,7,-13=[(-5)*(-13)+7]/3=24
The last one is really not. I'm sorry

Application of definite integral, volume calculation of rotating body,

Draw a sketch, the straight line y = 2x-1 is the tangent of the curve y = x ^ 2 at (1,1), and the intersection of y = 2x-1 and X axis is (1 / 2,0). Because the cross section of the rotating body is circular, the volume differential element DV = π y ^ 2DX. Therefore, the volume to be calculated is ∫ (0,1) π (x ^ 2) ^ 2DX - ∫ (1 / 2,1) π (2x-1) ^ 2DX = π / 30 ((0,1) and (1 / 2,1) are the upper and lower limits of the integral)

A certain number multiplied by 3 is a square number, multiplied by 4 is a cubic number, multiplied by 5 is a fifth power number, so what is the remainder of this number divided by?
A multi digit number multiplied by 3 is a square number, multiplied by 4 is a cubic number, and multiplied by 5 is a fifth power number. Then what is the remainder of this number divided by? List all the possibilities
one
Sorry, is the remainder of 7

This number is the 24th power of 5 times the 15th power of 3 times the 10th power of 2! Maybe there is 0
I don't know, right

As shown in the figure, the front view (or the main view) and the side view (or the left view) of an empty geometry are congruent equilateral triangles, and the top view is a circle with a radius of 1, then the total area of the geometry is ()
A. πB. 3πC. 2πD. π+3

Carefully observing the main view and side view of the geometry, we can see that the geometry is a cone. From the image, we can see that the center angle of the cone is 60 ° and the length of the generatrix l of the cone is 2 and the radius is 1. According to the calculation method of the cone surface area formula: S = π RL + π RR = π × 1 × 2 + π × 1 × 1 = 3 π, we choose B

It is known that the vertex coordinates of the square of parabola y = ax + BX are tangent to the point (4,0) on the line y = Fu half X-1
It is known that the vertex coordinates of the square of parabola y = ax + BX are tangent to the point (4,0) on the line y = Fu half X-1
(1) No, I'll write it
(2) Let p be the vertex of the parabola. Is there a point B on the parabola, a quadrilateral and opab a trapezoid? If so, find out the coordinates of point B. if not, explain the reason
(3) Let point C be (1, - 3), please determine a point D on the symmetry axis of the parabola, which is the maximum value of | ad-cd | and write the coordinates of point d directly
Please teach me how to write the last two questions

I don't know what point a is. I think point a is (4,0)
For the second question, since we know the parabolic equation, we know the coordinates of P
1. If op / / AB, the slope k of OP can be calculated first, and then the coordinates of B can be obtained by combining the linear point oblique equation y = K (x-4) with the parabolic equation
2. If ob / / AP, the same is true
Third, there is a theorem that when two line segments are collinear, the difference between them is the largest
Therefore, as long as a, D and C are collinear, the linear equation of AC can be obtained, and then x = 2, the D coordinate can be obtained

How many tons is a cubic meter of sand?

1.2t, sand can not reach the so-called 2.4t compactness. In the natural state, it is only so heavy, and a certain value in the middle is reasonable

X square-200x + 5000 = 0
Simple quadratic equation of one variable

Equation x ^ 2-200x + 5000 = 0 can be written as x ^ 2-200x + 10000-5000 = 0, that is, (X-100) ^ 2-5000 = 0, that is, (X-100) ^ 2 = 5000, then X-100 = ± 50 √ 2, so x = 100 ± 50 √ 2