On a round table with a diameter of 80 cm, place a square table cloth with a side length of 80 cm. What is the area of the sagging part of the square table cloth?

3.14 times the square of 40 minus 80 times 80

For the general solution and special solution of differential equation, it is known that Y1 = x, y2 = x ^ 2, Y3 = e ^ X are the three special solutions of the equation y '' + P (x) y '+ Q (x) y = f (x)

Y1 = x, y2 = x ^ 2, Y3 = e ^ X are the three special solutions of the equation y '' + P (x) y '+ Q (x) y = f (x). This second order differential equation obviously has two general solutions. Then it is obvious that x ^ 2-x and e ^ X - X are the general solutions of Y' '+ P (x) y' + Q (x) y = 0, so the general solutions of Y '' + P (x) y '+ Q (x) y = f (x) are y = a * (x ^ 2-x) + b * (e ^ X - x) + X, a

Lay a 3-meter-long and 2-meter-wide tablecloth on a rectangular tabletop. The length of each side is the same. If the tablecloth area is 3 times of the tabletop area, calculate the length of the tablecloth

Let the length of the table cloth hang down be x meters. According to the meaning of the title, we can get 3 (3-2x) (2-2x) = 3 × 2. After finishing, we can get 2x2-5x + 2 = 0. The solution is X1 = 12, X2 = 2 (rounding off). A: the length of the table cloth hang down is 12 meters

If we know that y = 1, y = x, y = x ^ 2 are three solutions of a second order non-homogeneous linear differential equation, then the general solution of the equation is
I want to ask why y = 1 is the special solution of non-homogeneous equation, and y = x, y = x ^ 2 is not the special solution of non-homogeneous equation

Firstly, these three solutions are special solutions of non-homogeneous equation. Secondly, because they are linearly independent, the difference between any two solutions is the corresponding solution of homogeneous equation, Then the difference between any two solutions is taken as the general solution of the corresponding homogeneous equation. For example, C1 (1-x ^ 2) + C2 (x-x ^ 2) + x ^ 2 or C1 (x ^ 2-x) + C2 (x ^ 2-1) + X can write many similar results
This problem is an exercise in Tongji higher mathematics, the answer is only given in one form

Rectangular tabletop is 4m long and 2m wide. The area of a rectangular tablecloth is three times the volume of the tabletop. When the tablecloth is laid on the tabletop, the length of each side is the same. Q: what are the length and width of this tablecloth

The length is 6m and the width is 4m

Given three special solutions of a linear non-homogeneous differential equation, how to find its general solution?
Great. Can you explain it in the simplest and most clear way?

First of all, I don't know what order the equation is. It must be of second order. By subtracting the three special solutions, we can get the general solution of the linear homogeneous differential equation. Then, take two of them, multiply each by an arbitrary constant, add them, and then add any one of the three special solutions

Cut the largest square in a rectangle 8 decimeters long and 5 decimeters wide. The perimeter of the square is______ Decimeter

5 × 4 = 20 (decimeter), answer: the perimeter of this square is 20 decimeters, so the answer is: 20

How to find the second derivative of parametric equation?
The known parameter equation: x = arctant, y = 1-LN (1 + T & # 178;)
I find its derivative is - 2T, but I can't find its second derivative
Now I learn higher derivative

dy/dx = (dy/dt)/(dx/dt) = g(t)d²y/dx² = d/dx (dy/dx) = d/dx (g(t)) = dg(t)/dt • dt/dx = dg(t)/dt • 1/(dx/dt)x = arctant,y = 1 - ln(1 + t²)dx/dt = 1/(1 + t²),dy/dx = - 2...

Mom bought a rectangular cloth and cut the largest square from it. What's the area of the rest?

26 × 15 - 15 × 15 = 390 - 225 = 165 (square decimeters). A: the remaining area is 165 square decimeters

On a round table with a diameter of 80 cm, place a square table cloth with a side length of 80 cm. What is the area of the sagging part of the square table cloth?