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1.
) (x+y)/(x-1/2)-(x-z)/(x*y); ) (1+z)*(x+y/z)/(a-1/(1+x*x)); ) x**(n*(m+2)) + x**(n**m); ) (a+b)**n/(1+a/(a**m-b**(m-n))); ) (a[i]**(2*l) + b[j+1]**(2*k)) * (3**n-x*x*y)/(z-(d[i,j+1]+1)/(z+ y/sqrt(t*t+x*y*z))); ) sqrt(abs(sin(x)**2))/(3.01*x - exp(2*x)); ) abs(cos(x**3) - sin(y)**2) / (abs(ln(x))**(1/4) + x*y); ) ln(y**(-sqrt(abs(x+1)))) * sin(arctg(z))**2; ) r[i,j]**abs(x-y) - 0.15*abs(sin(exp(-z**8))); ) a**((x+y)/2) - ((x-1)/(abs(y)+1))**(1/3)*exp(-(y+u/2)).
2. ) ; ) ;
) ; ) ;
) ; ) ;
) ; ) ;
) ; ) ;
) ; ) ;
) ; ) ;
) ; ) ;
) ; ) ;
) ; ) .
3. ) 16; ) 5,5; ) -256; ) 3; ) -2; ) 1.8.
4. ) : (a+b+c+d)/4; : (a*b*c*d)**(1/4); ) sqrt(x*x+y*y); ) sin(x*3.14/180); ) 6*a*a; ) sqrt(3)*a/2; ) : (c1*b2-c2*b1)/(b1*a2-b2*a1); : (c2*a1-c1*a2)/(b1*a2-b2*a1).
5. ) ; ) ; ) ; ) ; ) ;
6.
) (x < a) (x > b); ) ((x>=a) (x<=b)) ((x>=c) (x<=d)); ) ((x < a) (x > b)) ((x < c) (x > d)); ) mod(k,2)=1; ) (mod(k,5)=0) (k > 99) (k < 1000); ) (mod(i,2)=1) (mod(j,2)=0); ) a1*b2=a2*b1; ) (c < a) (b > a); ) (a=-b) (a=-c) (a=-d) (b=-c) (b=-d) (c=-d); ) ((mod(a,2)=0) (mod(b,2)=0)) ((mod(a,2)=0) (mod(c,2)=0)) ((mod(b,2)=0) (mod(,2)=0)); ) (a>0) (b>0) (c>0) (a+b>c) (a+c>b) (b+c>a); ) ((a1*b2=a2*b1) (a1*c2=a2*c1)) ((a1*c2=a2*b1) (a1*b2=a2*c1)) ((a1*c2=b2*b1) (a1*a2=b2*c1)) ((a1*a2=b2*b1) (a1*c2=b2*c1)) ((a1*a2=c2*b1) (a1*b2=c2*c1)) ((a1*b2=c2*b1) (a1*a2=c2*c1)); ) (y>5-5*x) (y<5-x) (y>0); ) (y<5-5*x)) (y>5-x) (y<0); ) (a=b) (c=d) (b=c).
7. )
)
)
)
)
)
)
)
8.
) (y>=1-x) ((y<=0) (x<=0));
) (y<1) (y>=x) (y>=-x) ( : (y<1) (y>=abs(x)));
) (abs(x)<=1) (abs(y)<1);
) ((x-1)*(x-1)+y*y<=4) (y<=3-x) (y>=x-3);
) (abs(x)<=3) (abs(y)<=3) (x*x+y*y>=9) ((x>=0) (y<=0));
) (abs(x)+abs(y)<=2) (sign(x)<>sign(y)) (x*x+y*y<=4)
((y>=2-x) (y<=-x-2));
) ((y>=x*x) (y<=-x*x)) ((x>=y*y) (x<=-y*y));
) (((x+2)*(x+2)+y*y<=4) ((x+2)*(x+2)+y*y>=1)) (x>=-1);
) (((y<=0)=(y>=-x)) ((x>=0)=(y>=x))) (x*x+y*y<=1).
9. ) a=-19; b=-114; c=17; ) a=3; b=1,875; c=15; ) a=7; b=3; c=735; ) a=10; b=2; c=120; ) a=4; b=7; c=3; ) a=16; b=100, c=11200.
10. ) c:=x[1]; x[1]:=x[2]; x[2]:=c; ) a[i]:=(a[i-1]+a[i+1])/2; a[i+1]:=0; a[i-1]:=a[i-1]+0.5; ) u:=max(max(x, y), z) + min(min(x-z,y+z), min(y,z)).
11.
) x <= -100 ) x*x+y*y <= 1
y:=sign(x)*abs(x)**(1/7) z:=x*x+y*y
x < 100 y>=x
y:=sign(x)*abs(x)**(1/3) z:=x+y
y:=sqrt(x) z:=0.5
) x < 0 )
z:=lg(-x) =0 : z:=1
z:=sqrt(x+1) =1 : z:=x
=2 : z:=3*x*x - 1/2
z>=0 =3 : z:=x*x*x - 3*x/2
F:=2*z+1 z:=2*x**4 - 3*x/2
F:=sin(z)
) abs(x)+abs(y) < r ) x>1
z:=sqrt(x*x+y*y) y>1
z:=max(abs(x), abs(y)) v:=x+y
v:=x-y
) (x-a)**2 +(y-b)**2 < r*r y>0
z:=abs(x)+abs(y) v:=y-x
z:=x+y v:=-x-y
12. )
)
)
)
13. ) 81; ) 21; ) 11; ) 44.
14. ) 0; ) 13; ) 52; ) 14.
15.
) 1( a,b,UgolC, c, UgolA, UgolB, S)
a, b, UgolC
c:=sqrt(a*a+b*b-2*a*b*cos(UgolC))
UgolA:=arcsin(a*sin(UgolC)/c)
UgolB:=arcsin(b*sin(UgolC)/c)
S:=b*c*sin(UgolA)/2
c, UgolA, UgolB, S
) 2( a,b,c, Radius,UgolA)
p
a,b,c
p:=(a+b+c)/2
UgolA:=2*arctg(sqrt((p-b)*(p-c)/(p*(p-a))))*180/3.14
Radius:=a*b*c/(4*sqrt(p*(p-a)*(p-b)*(p-c)))
Radius, UgolA
) ( a,UgolAGrad, V, S)
H,SBase,UgolARad
| H - ; SBase -
a,UgolAGrad
UgolARad:=UgolAGrad*3.14/180
SBase:=a*a*sqrt(3)/4
H:=a*sqrt(3)/6*tg(UgolARad)
V:=SBase*H/3
S:=SBase*(1+1/cos(UgolARad))
V, S
) ( RBig,RSmall,Ugol, V, S)
H,L
RBig,RSmall,Ugol
H:=(RBig-RSmall)*tg(Ugol)
L:=(RBig-RadSmall)/cos(Ugol)
V:=1/3*3.14*H*(RSmall**2 + RBig**2 + RSmall*RBig)
S:=3.14*L*(RBig+RSmall)
V, S
) ( a,UgolA, V, S, Stion)
H
a,UgolA
H:=a*sqrt(2)/2*tg(UgolA)
V:=1/3*a*a*H
Stion:=a*H*sqrt(2)/2
S:=a*a*(1+sqrt(2*tg(UgolA)**2+1))
V, S, Stion
16.
) ( a,b,c, k)
| k - a,b,c
a,b,c; k:=0
a>0
k:=k+1
b>0
k:=k+1
c>0
k:=k+1
k
) ( a,b)
| a,b
a,b
a>b
b:=b*2
a:=a*2
a,b
) ( a,b,c,d, Otvet)
| a,b c,d -
| Otvet=,
a,b,c,d
(a*d=*b) (a*c=d*b)
Otvet:=
Otvet:=
Otvet
) ( xA,yA,xB,yB,xC,yC, Otvet)
DistA,DistB,DistC
xA,yA,xB,yB,xC,yC
DistA:=sqrt(xA**2 + yA**2)
DistB:=sqrt(xB**2 + yB**2)
DistC:=sqrt(xC**2 + yC**2)
(DistA < DistB) (DistA < DistC)
Otvet:=" "
DistB < DistC
Otvet:=" B"
Otvet:=" C"
Otvet
) ( x,y,r1,r2, Otvet)
| r2>r1
| Otvet=, (x,y)
| c r1 r2
x,y,r1,r2
(x*x+y*y<=r2*r2) (x*x+y*y>=r1*r1)
Otvet:=
Otvet:=
Otvet
) ( a, b, c)
| a, b, c
t
a, b, c
a>b
t:=a; a:=b; b:=t | a b
a>c
t:=a; a:=c; c:=t | a c
b>c
t:=b; b:=c; c:=t | b c
a, b, c
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