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MaplePrimes Activity

These are questions asked by minhthien2016

I am trying to draw this pictures in LaTeX, then I need to find their parametric equations. How can I get them?

I want to construct a quadrilateral ABCD with A = 120 degrees, B = 80 degrees, C = 110degrees. I do know how to start. How do I construct one option of a quadrilateral with measure of its four angles?

I am trying to solve the equation: 
solve(cos(3*x - Pi/12) = cos(2*x + Pi/7), x, allsolutions).
It is difficult for me to get the resullt. 
Solve by my hand. I tried
a := 3*x - Pi/12;
b := 2*x + Pi/7;
S1 := solve(a = 2*Pi*k + b, x);
S2 := solve(a = 2*Pi*k - b, x);
S := ((S1 union S2) assuming k::integer);

I get the answer

Can I get the result by command 
solve(cos(3*x - Pi/12) = cos(2*x + Pi/7), x, allsolutions).

I am trying to find three integer a, b, c so that equation (x-a)^4 + (x-b)^4 = c has four different solutions integer x. I tried

k := 0;
for a from -10 to 10 do
    for b from -10 to 10 do
for c from -10 to 10 do
if a*b*c <> 0 and igcd(a, b) = 1 then X := [solve((x - a)^4 + (x - b)^4 = c, x)]; if type(X[1], integer) and type(X[2], integer) and type(X[3], integer) and type(X[4], integer) and nops({X[1], X[2], X[3], X[4]}) = 4 then k := k + 1; L[k] := [a, b, c, X[]]; end if; end if; end do; end do;
end do;
L := convert(L, list);


I do not get any solution

I have a polyhedron with A(1,1,0), B(-1,1,0), C(-1,-1,0), H(-1/2,0,1), K(1/2,-1/2,0). How can I calculate volume of polyhedron ABCHK?

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