There is a cylinder centered at (0,0) and extending in the direction of the z-axis. Then there is a 3D surface represented by some z=f(x,y). I want to express the equation of the intersection of these two by z=g(x,y). Please show me how to do this calculation.
I executed the following code, but I do not know what the calculated value indicates. I would appreciate it if you could tell me this as well.
———————————-
% シンボリック変数の定義
syms x y z
% 円筒と平面の方程式
r = 5; % 円筒の半径
cylinder_eq = x^2 + y^2 == r^2; % 円筒の方程式
plane_eq = z == x * y + 3; % 平面の方程式
z_range = z < 1000;
% 連立方程式を解く
sol = solve([cylinder_eq, plane_eq, z_range], [x, y, z]);
% 解の表示
disp(sol)
disp(sol.x)
disp(sol.y)
disp(sol.z)
———————————-
x: [7×1 sym]
y: [7×1 sym]
z: [7×1 sym]

(25/2 – 589^(1/2)/2)^(3/2)/3 – (25*(25/2 – 589^(1/2)/2)^(1/2))/3
(589^(1/2)/2 + 25/2)^(3/2)/3 – (25*(589^(1/2)/2 + 25/2)^(1/2))/3
0
0
0
(25*(25/2 – 589^(1/2)/2)^(1/2))/3 – (25/2 – 589^(1/2)/2)^(3/2)/3
(25*(589^(1/2)/2 + 25/2)^(1/2))/3 – (589^(1/2)/2 + 25/2)^(3/2)/3

(25/2 – 589^(1/2)/2)^(1/2)
(589^(1/2)/2 + 25/2)^(1/2)
0
-5
5
-(25/2 – 589^(1/2)/2)^(1/2)
-(589^(1/2)/2 + 25/2)^(1/2)

0
0
3
3
3
0
0There is a cylinder centered at (0,0) and extending in the direction of the z-axis. Then there is a 3D surface represented by some z=f(x,y). I want to express the equation of the intersection of these two by z=g(x,y). Please show me how to do this calculation.
I executed the following code, but I do not know what the calculated value indicates. I would appreciate it if you could tell me this as well.
———————————-
% シンボリック変数の定義
syms x y z
% 円筒と平面の方程式
r = 5; % 円筒の半径
cylinder_eq = x^2 + y^2 == r^2; % 円筒の方程式
plane_eq = z == x * y + 3; % 平面の方程式
z_range = z < 1000;
% 連立方程式を解く
sol = solve([cylinder_eq, plane_eq, z_range], [x, y, z]);
% 解の表示
disp(sol)
disp(sol.x)
disp(sol.y)
disp(sol.z)
———————————-
x: [7×1 sym]
y: [7×1 sym]
z: [7×1 sym]

(25/2 – 589^(1/2)/2)^(3/2)/3 – (25*(25/2 – 589^(1/2)/2)^(1/2))/3
(589^(1/2)/2 + 25/2)^(3/2)/3 – (25*(589^(1/2)/2 + 25/2)^(1/2))/3
0
0
0
(25*(25/2 – 589^(1/2)/2)^(1/2))/3 – (25/2 – 589^(1/2)/2)^(3/2)/3
(25*(589^(1/2)/2 + 25/2)^(1/2))/3 – (589^(1/2)/2 + 25/2)^(3/2)/3

(25/2 – 589^(1/2)/2)^(1/2)
(589^(1/2)/2 + 25/2)^(1/2)
0
-5
5
-(25/2 – 589^(1/2)/2)^(1/2)
-(589^(1/2)/2 + 25/2)^(1/2)

0
0
3
3
3
0
0 There is a cylinder centered at (0,0) and extending in the direction of the z-axis. Then there is a 3D surface represented by some z=f(x,y). I want to express the equation of the intersection of these two by z=g(x,y). Please show me how to do this calculation.
I executed the following code, but I do not know what the calculated value indicates. I would appreciate it if you could tell me this as well.
———————————-
% シンボリック変数の定義
syms x y z
% 円筒と平面の方程式
r = 5; % 円筒の半径
cylinder_eq = x^2 + y^2 == r^2; % 円筒の方程式
plane_eq = z == x * y + 3; % 平面の方程式
z_range = z < 1000;
% 連立方程式を解く
sol = solve([cylinder_eq, plane_eq, z_range], [x, y, z]);
% 解の表示
disp(sol)
disp(sol.x)
disp(sol.y)
disp(sol.z)
———————————-
x: [7×1 sym]
y: [7×1 sym]
z: [7×1 sym]

(25/2 – 589^(1/2)/2)^(3/2)/3 – (25*(25/2 – 589^(1/2)/2)^(1/2))/3
(589^(1/2)/2 + 25/2)^(3/2)/3 – (25*(589^(1/2)/2 + 25/2)^(1/2))/3
0
0
0
(25*(25/2 – 589^(1/2)/2)^(1/2))/3 – (25/2 – 589^(1/2)/2)^(3/2)/3
(25*(589^(1/2)/2 + 25/2)^(1/2))/3 – (589^(1/2)/2 + 25/2)^(3/2)/3

(25/2 – 589^(1/2)/2)^(1/2)
(589^(1/2)/2 + 25/2)^(1/2)
0
-5
5
-(25/2 – 589^(1/2)/2)^(1/2)
-(589^(1/2)/2 + 25/2)^(1/2)

0
0
3
3
3
0
0 3d, cylinder, intersection, equation MATLAB Answers — New Questions

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