,       3GL   4GL   5GL   .

1. :

a) e)
) )
) )
) )
) )

[ ]

2. :

) a / b ** 2;
) a+b/c+1;
) 1/a*b/c;
) a**b**c/2;
) (a**b)**c/2;
) a/b/c/d*p*q;
) x**y**z/a/b;
) 4/3*3.14*r**3;
) b/sqrt(a*a+b);
) d*c/2/R+a**3;
) 5*arctg(x)-arctg(y)/4;
) lg(u*(1/3)+sqrt(v)+z);
) ln(y*(-sqrt(abs(x))));
) abs(x**(y/x)-(y/x)**(1/3));
) sqrt((x1-x2)**2+(y1-y2)**2);
) exp(abs(x-y))*(tg(z)**2+1)**x;
c) lg(sqrt(exp(x-y))+x**abs(y)+z);
) sqrt(exp(a*x)*sin(x)**n)/cos(x)**2;
) sqrt(sin(arctg(u))**2+abs(cos(v)));
) abs(cos(x)+cos(y))**(1+sin(y)**2);

[ ]

3. x=1:
) abs(x-3)/ln(exp(3))*2/lg(10000);
   : abs(1-3)=2; ln(exp(3))=3; lg(10000)=4; 2/3*2/4=0.33;
 
) sign(sqrt(sqrt(x+15)))*2**2**2;
) int(-2.1)*int(-2.9)/int(2.9)+x;
) -sqrt(x+3)**2**(sign(x+0.5)*3)+tg(0);
) lg(x)+cos(x**2-1)*sqrt(x+8)-div(2,5);
) sign(x-2)*sqrt(int(4.3))/abs(min(2,-1));
) div(10,x+2)*mod(10,x+6)/max(10,x)*mod(2,5).
[ ]

4. , :
) a, b, c (a, b, c>0) p;
   : sqrt(p*(p-a)*(p-b)*(p-c));

) a, b, c, d;
) (x,y) (0,0);
) x ;
) ( );
) ( );
) ,
   a1x+b1y+c1=0 a2x+b2y+c2=0 ( ).
[ ]

5. :
) x*x+y*y<=9 x=1, y=-2
   : ;
 
) b*b-4*a*c<0 a=2, b=1, c=-2;
) (a>=1) (a<=2) a=1.5;
) (a<1) (a>1.2) a=1.5;
) (mod(a,7)=1) (div(a,7)=1) a=8;
) ((a>b) (a<9) (*=4)) a=5, b=4.
[ ]

6. , :
)   x [a, b]
   : (x>=a) (x<=b);
 
)   x [a, b];
)   x [a, b] [c, d];
)   x [a, b] [c, d];
)   k ;
)   k , ;
)   ai,j ;
)   a1x+b1y+c1=0 a2x+b2y+c2=0 ;
)   a, b, c , b;
)   a, b, c, d ;
)   a, b, c ;
)   a, b, c ;
)   a1, b1, c1 a2, b2, c2 ;
)   (x,y) A(0,5), B(5,0) C(1,0);
)   (x,y) , A(0,5), B(1,0) C(5,0);
)   a, b, c d .
[ ]

7. (x,y) , . , , .
 

) (x<=0) (y>=0)
   :
 
) ((x-2)**2+y*y<=4) (y>x/2)
   :
 
) (x>=0) (y<=0)
) x+y>=0
) (x+y>0) (y<0)
) abs(x)+abs(y)>=1
) (x*x+y*y<1) (y>x*x);
) (y>=x) (y+x>=0) (y<=1);
) (abs(x)<=1) (y<2);
) (x**2+y**2<4) (x**2+y**2>1);

[ ]

8. , "" , (x, y) .


[ ]

9. a=3, b=5, c=7. :
)   a:=a+1; b:=a+b; c:=a+b; a:=sqrt(a)
   : a=3+1=4, b=4+5=9, c=4+9=13, a= { } 4 =2.
   : =2, b=9, c=13;
)   :=a*b+2; b:=b+1; a:=c-b**2; b:=b*a;
)   b:=b+a; c:=c+b; b:=1/b*c;
)   p:=c; c:=b; b:=a; a:=p; c:=a*b*c*p;
)   c:=a**(b-3); b:=b-3; a:=(c+1)/2*b; c:=(a+b)*a;
)   x:=a; a:=b; b:=c; c:=x; a:=sqrt(a+b+c+x-2);
)   b:=(a+c)**2; a:=lg(b**2)**2; c:=c*a*b.
[ ]

10. :
) X=(x1, x2) : x1 , 2 - ;
   : c:=x[1]; x[1]:=x[1]+x[2]; x[2]:=c*x[2]
) X=(x1, x2);
) A(N) i (1<i<N) , , 0.5;
) u = max(x, y, z) + min(x-z, y+z, y, z);
[ ]

11. :

a)
)
)  
 
)
)
)
) r (r>0) (a,b) 


[ ]

12. y(x), :

)   x<=-1
      y:=1/x**2
     
        x<=2
          y:=x*x
          y:=4
       
   
)   x<-0.5
       y:=1/abs(x)
      
         x<1
            y:=2
            y:=1/(x-0.5)
        
    
    
)   x<0
        y:=1
       
           x<3.14
              y:=cos(x)
              y:=-1
          
    
)   x<-5
        y:=-5
       
           x<0
              y:=x
             
                 x<3
                    y:=2*x
                    y:=6
                
          
    
)   abs(x)>2
        y:=x*x
       
           x<0
              y:=-2*x
             
                 x>=1
                    y:=4
                    y:=4*x*x 
                
          
    

[ ]

13. S :

) S:=128
     i  1  4
      S:=div(S,2)
   

i S
  128
1 128/2=64
2 64/2=32
3 32/2=16
4 16/2=8
: S=8
) S:=0
     i  1  2
        j  2  3
       S:=S+i+j
      
   

i j S
    0
1 2 0+1+2=3
  3 3+1+3=7
2 2 7+2+2=11
  3 11+2+3=16
: S=16
)  S:=1; a:=1
      i  1  3
      S:=S+i*(i+1)*a
      a:=a+2
    
)    i  1  3
       S:=0
         j  2  3
         S:=S+i+j
       
    
)  S:=1; a:=1
      i  1  3
      S := S+i
        j o 2  3
        S := S+j
      
    
)    i  1  2
      S := 0
        j o 2  3
           k o 1  2
           S := S+i+j+k
         
      
    

[ ]

14. S :

)  i:=0; S:=0
      i<3
      i:=i+1;
      S:=S+i*i
    
)  S:=0; N:=125
      N>0
      S:=S+mod(N,10) | S -  
      N:=div(N,10)   |      N
    
i < 3 i S
  0 0
0 < 3? 1 0+12=1
1 < 3? 2 1+22=5
2 < 3? 3 5+32=14
3 < 3? ()    
: S=14
N > 0 S N
  0 125
125 > 0? 0+5=5 12
12 > 0? 5+2=7 1
1 > 0? 7+1=8 0
0 > 0? ()    
: S=8
)  S:=0; i:=1
      i>1
      S:=S+1/i
      i:=i-1
    
)  :=1; b:=1; S:=0;
      a<=5
      a:=a+b; b:=b+a;
      S:=S+a+b
    
) S:=0; i:=1; j:=5
     i<j
     S:=S+i*j
     i:=i+1
     j:=j-1
   
)  a:=1; b:=1
      a+b<10
      a:=a+1
      b:=b+a
    
    S:=a+b

[ ]

15. ( .. , .. .. " ", 1989):

 a,  b    c; ( ) , :

=180o-(+).
. ,  arccos   arcsin   .
:
  (  a,b,c,   UgolA,UgolB,UgolC)
  RadGr,UgolARad
    | RadGr - .       
    | UgolARad -  A ( )
  RadGr:=180/3.14
  UgolARad:=ArcCos((b*b+c*c-a*a)/(2*b*c))
  UgolA:=UgolARad*RadGr
  UgolB:=ArcSin(b*sin(UgolARad)/a)*RadGr
  UgolC:=180-(UgolA+UgolB)

 a,  b    C ( ) ;  c,   A   B  ( ) , :

 
  2 = a2 + b2 - 2ab cos C.
.  c , ;

) a, b c;  A  ( ), :

     

)  a   A  ( ) ; , :

V=Soc H/2;

)  R   r   A  ( ) ; , :

e)   a ,  A ; ,  d ; :


[ ]

16. :

,  a,  b,  c  ;
:

 (  a,b,c,   Otvet)
   | a>0, b>0, c>0, a+b>c, a+c>b, b+c>a
   | Otvet = ,   
       | Otvet = ,    

   (a=b)  (a=c)  (b=c)
     Otvet:= 
     Otvet:= 
  

 a,  b    c;

, ;

 a   b  - ,  c   d  - ; , ;

; , ;

,  (x, y)  , ,  r1   r2 ;

 a,  b   c.
[ ]

  ,       3GL   4GL   5GL   .

, - , . , push .




 18.01.2021 - 11:33: - Personalias -> WHO IS WHO - - _.
18.01.2021 - 09:05: , - War, Politics and Science -> . - _.
18.01.2021 - 08:21: , , - Upbringing, Inlightening, Education -> - _.
18.01.2021 - 07:41: , , - Upbringing, Inlightening, Education -> - _.
17.01.2021 - 17:59: , - War, Politics and Science -> - _.
17.01.2021 - 16:46: , , - Upbringing, Inlightening, Education -> - _.
17.01.2021 - 16:00: - Ecology -> - _.
16.01.2021 - 08:30: - Conscience -> . ? - _.
15.01.2021 - 09:03: , - War, Politics and Science -> - _.
15.01.2021 - 09:03: , , - Upbringing, Inlightening, Education -> - _.
15.01.2021 - 08:20: - Theorizing and Mathematical Design -> - - _.
15.01.2021 - 08:19: , , - Upbringing, Inlightening, Education -> - _.
Bourabai Research -  XXI Bourabai Research Institution