minhthien2016

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7 years, 52 days

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These are questions asked by minhthien2016

I calculate volume of tetrahedron SABC by this way. Now, I want to find one option  of coordinates of all vertices of this tetrahedron. How can I get the coordinates of the points S, A, B, C so that coordinates  center of circumcircle of the triangle ABC is (0,0,0)?

 

restart:
SA := 3: 
SB := 5: 
SC := 7:
AB := 3:
BC := 4: 
AC := 5:
V := (1/12)*sqrt(SA^2*BC^2*(AB^2+AC^2-BC^2-SA^2+SB^2+SC^2)+SB^2*AC^2*(AB^2-AC^2+BC^2+SA^2-SB^2+SC^2)+SC^2*AB^2*(-AB^2+AC^2+BC^2+SA^2+SB^2-SC^2)-SA^2*AB^2*SB^2-SB^2*BC^2*SC^2-SA^2*AC^2*SC^2-AB^2*BC^2*AC^2);

From here https://www.mapleprimes.com/questions/227573-How-To-Get-Coordinates-Of-Triangle-ABC
I find coordinates of the point A, B, C. Now I tried
 

with(geom3d):
point(A, -3/2, -2, 0):
point(B, 3/2, -2, 0):
point(C, -3/2, 2, 0):
point(S, x, y, z):
solve([distance(S, A) = 3, distance(S, B) = 5, distance(S, C) = 7], [x, y, z], explicit);
with(geom3d):
point(A, -3/2, -2, 0):
point(B, 3/2, -2, 0):
point(C, -3/2, 2, 0):
point(S, x, y, z):
solve([distance(S, A) = 5, distance(S, B) = 3, distance(S, C) = 7], [x, y, z], explicit);

Use the above code, I obtain the result.

How to get correct result this equation
restart; with(Student:-MultivariateCalculus);
A := [0, 0, 0];
B := [c, 0, 0];
S := [x, 0, z];
solve([Distance(S, A) = a, Distance(S, B) = b], [x, z]) assuming and(a > 0, b > 0, c > 0);

I want to find one option of coodiantes of vertices A, B, C of the triangle ABC, knowing that coordinates centre of circumcircle is O(0,0) and length of sides are 3, 5, 7. 
How can I get the result?

How to get the result of this limit? I don't get the result.
 

limit(sum(1/(i*sqrt(i+1)+(i+1)*sqrt(i)), i = 1 .. n), n = infinity);

With Mathematica, I got the output is 1.

I want to solve the equation (-2*cos(x)^2+2*sin(x+(1/4)*Pi)^2-1)/sqrt(-x^2+4*x) = 0 in RealDomain. I tried
 

restart; 
RealDomain:-solve({(-2*cos(x)^2+2*sin(x+(1/4)*Pi)^2-1)/sqrt(-x^2+4*x) = 0}, {x});

I got four solutions

If I work around

restart;
 RealDomain:-solve({-x^2+4*x > 0, (-2*cos(x)^2+2*sin(x+(1/4)*Pi)^2-1)/sqrt(-x^2+4*x) = 0}, x);

I only got two solutions

With Mathematica, I got three solutions 

That is mean, Maple lost the solution x = 5*Pi/4. I check this thing

f:= x-> (-2*cos(x)^2+2*sin(x+(1/4)*Pi)^2-1)/sqrt(4*x-x^2) ;
f(5*Pi/4);


and got the result 0. 

Are these bugs?

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