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# ch11 - Chapter 11 Solved Problems Problem 1 Script file...

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1 Chapter 11 Solved Problems Problem 1 Script file: syms x S1=(x-4)^2-(x+3)^2+16*x-4 S2=x^3-6*x^2-x+30 disp( 'Part (a)' ) a=simple(S1*S2) disp( 'Part (b)' ) b=simple(S1/S2) disp( 'Part (c)' ) c=simple(S1+S2) disp( 'Part (d)' ) d=subs(c,2) Command Window: S1 = (x-4)^2-(x+3)^2+16*x-4 S2 = x^3-6*x^2-x+30 Part (a) a = (2*x+3)*(x^3-6*x^2-x+30) Part (b) b = (2*x+3)/(x^3-6*x^2-x+30) Part (c) c = x+33+x^3-6*x^2 Part (d) d = 19

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2 Chapter 11: Solved Problems Problem 2 Script File: syms x S1=(sqrt(3)+x)^2-2*(sqrt(3)*x+x/2+x^2/2) S2=9+3*x+x^2 disp( 'Part (a)' ) a=simple(S1*S2) disp( 'Part (b)' ) b=simple(S1/S2) disp( 'Part (c)' ) c=simple(S1+S2) disp( 'Part (d)' ) d=subs(c,4) Command Window: S1 = (3^(1/2)+x)^2-2*3^(1/2)*x-x-x^2 S2 = 9+3*x+x^2 Part (a) a = 27-x^3 Part (b) b = (3-x)/(9+3*x+x^2) Part (c) c = 12+2*x+x^2 Part (d) d = 36
Chapter 11: Solved Problems 3 Problem 3 >> syms u >> Q = u^3+2*u^2-25*u-50 Q = u^3+2*u^2-25*u-50 >> R = 3*u^3+4*u^2-75*u-100 R = 3*u^3+4*u^2-75*u-100 >> simplify(Q/R) ans = (u+2)/(3*u+4)

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4 Chapter 11: Solved Problems Problem 4 >> syms x >> % Part a >> Sa=x^5-x^4-27*x^3+13*x^2+134*x-120 Sa = x^5-x^4-27*x^3+13*x^2+134*x-120 >> SaF=factor(Sa) SaF = (x-1)*(x-2)*(x-5)*(x+4)*(x+3) >> % Part b >> Sb=(x-5)*(x+3)*(x+2)*(x-4) Sb = (x-5)*(x+3)*(x+2)*(x-4) >> SbE=expand(Sb) SbE = x^4-4*x^3-19*x^2+46*x+120
Chapter 11: Solved Problems 5 Problem 5 >> syms x y z >> % Part (a) >> aS=4*cos(x)^3-3*cos(x) aS = 4*cos(x)^3-3*cos(x) >> a=simple(aS) a = cos(3*x) >> % Part b >> bS=(sin(x-y)+sin(x+y))/2 bS = 1/2*sin(x-y)+1/2*sin(x+y) >> b=simple(bS) b = sin(x)*cos(y) >> % Part c >> cS=cos(x)*cos(y)*cos(z)-sin(x)*sin(y)*cos(z)- sin(x)*cos(y)*sin(z)-cos(x)*sin(y)*sin(z) cS = cos(x)*cos(y)*cos(z)-sin(x)*sin(y)*cos(z)- sin(x)*cos(y)*sin(z)-cos(x)*sin(y)*sin(z) >> c=simple(cS) c = cos(z+x+y)

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6 Chapter 11: Solved Problems Problem 6 Script File: syms xs ys t xs=3*t/(1+t^3) ys=3*t^2/(1+t^3) fL=xs^3+ys^3 fLS=simple(fL) fR=3*xs*ys ezplot( 'x^3+y^3-3*x*y' ,[-2,2,-3,2]) Command Window: xs = 3*t/(1+t^3) ys = 3*t^2/(1+t^3) fL = 27*t^3/(1+t^3)^3+27*t^6/(1+t^3)^3 fLS = 27*t^3/(1+t^3)^2 fR = 27*t^3/(1+t^3)^2 Figure Window: -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x y x 3 +y 3 -3 x y = 0
Chapter 11: Solved Problems 7 Problem 7 Script file: syms h R S S = pi*R*sqrt(4*h^2+R^2)+2*pi*h*R S=subs(S,h,8) Rs=double(solve(S-370,R)) Command Window: S = pi*R*(4*h^2+R^2)^(1/2)+2*pi*h*R S = pi*R*(256+R^2)^(1/2)+16*pi*R Rs = 3.6342

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8 Chapter 11: Solved Problems Problem 8 Script file: clear eqn1= '(T+a)*(v+b)=(T0+a)*b' eqn2=subs(eqn1, 'T' ,0) disp( 'Answer to part a:' ) vmax=solve(eqn2, 'v' ) eqn3=subs(eqn1, 'b' , 'vmax*a/T0' ) disp( 'Answer to part b:' ) v=solve(eqn3, 'v' ) Command Window: eqn1 = (T+a)*(v+b)=(T0+a)*b eqn2 = a*(v+b) = (T0+a)*b Answer to part a: vmax = b*T0/a eqn3 = (T+a)*(v+(vmax*a/T0))=(T0+a)*(vmax*a/T0) Answer to part b: v = -vmax*a*(T-T0)/T0/(T+a)
Chapter 11: Solved Problems 9 Problem 9 Script File: syms x y ezplot( '(x-2)^2+(y-3)^2=16' ,[-8,8,-8,8]) hold on ezplot( 'x^2+y^2=25' ,[-8,8,-8,8]) axis square xlabel( 'x' ) ylabel( 'y' ) [xs,ys]=solve(

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