toandhsp

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9 years, 205 days

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These are questions asked by toandhsp

I wrote a program in order to find coordinates orthocenter of the triangle. Please comment for me. This is my code:

restart;

with(geom3d);

point(A,1,-3,0);

point(B,-2,1,1);

point(C,3,1,2);

line(AB,[A,B],t);

line(BC,[B,C],t);

ab:=ParallelVector(AB); 

bc:=ParallelVector(BC);

eq1:=Equation(plane(P,[C,ab],[x,y,z]));

eq2:=Equation(plane(Q,[A,bc],[x,y,z]));

eq3:=Equation(plane(ABC,[A,B,C],[x,y,z]));

I wrote a program to find the coordinates of thecenter circle circumscribed triangle

I find the least value of the function h(x) = 1+2*cos(2*x)+3*cos(4*x)+4*cos(8*x). I did

h:=x->1+2*cos(2*x)+3*cos(4*x)+4*cos(8*x);

minimize(h(x),x=-Pi/12..5*Pi/12,location=true);

But i received 1/2-3^(1/2), {[{x = 5/12*Pi}, 1/2-3^(1/2)]}. This is wrong answer. This is shown by

plot(h(x),x=-Pi/12..5*Pi/12); 

I have a problem:" Write the  equation of all lines passing through the point M(19/12,4) and tangent to the graph of the function f(x) = 2*x^3 - 3*x^2 + 5. I did the following:

restart; 
[> f:=x->2*x^3 - 3*x^2 + 5;                    

[> g:=x->k*(x-19/12)+4;

[> solve([f(x) = g(x), diff(f(x),x) = diff(g(x),x)],[x,k]);

[> h:=k->k*(x-19/12)+4;
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