palm_ch4 - Solutions to Problems in Chapter Four Test Your...

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Solutions to Problems in Chapter Four Test Your Understanding Problems T4.2-1 The session is x = [5,-3,18,4];y = [-9,13,7,4]; z = ~y>x z = 0 1 0 0 z = x&y z = 1 1 1 1 z = x|y z = 1 1 1 1 z = xor(x,y) z = 0 0 0 0 T4.2-2 The script file is identical to that used in Example 4.2-1 except for the line u = find(~(h<4|v>17)); . v0 = 20;g = 9.81;A = 40*pi/180; t_hit = 2*v0*sin(A)/g; t = [0:t_hit/100:t_hit]; h = v0*t*sin(A)-0.5*g*t.^2; v = sqrt(v0^2-2*v0*g*sin(A)*t+g^2*t.^2); u = find(~(h<4|v>17)); t_1 = (u(1)-1)*(t_hit/100) t_2 = u(length(u)-1)*(t_hit/100) The results are t 1 = 0 . 5766 and t 2 = 2 . 0443. Thus h < 4 or v > 17 for t < t 1 and for t > t 2 . T4.3-1 x = 13; if x>10 y = log(x) if y>= 3 z = 4*y elseif y >2.5 z = 2*y 4-1
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else z = 0 end else y = 5*x z = 7*x end T4.3-2 Note that the asin(x) function returns the correct value (in radians) only if x is in the first or fourth quadrant. Note also that it is possible to give incompatible values for q and x . For example, q cannot equal 1 if x < 0. The following script file protects against this error. if x> = 0&x<1 if q==1 y = asin(x)*180/pi; elseif q==2 y = asin(x)*180/pi + 270; end if q==3|q==4 disp( 0 Incompatible values of x and q 0 ) else disp(y) end elseif x<0&x>-1 if q==4 y = asin(x)*180/pi; else y = asin(x)*180/pi -90; end if q==1|q==2 disp( 0 Incompatible values of x and q 0 ) else disp(y) end else disp( 0 The magnitude of x is greater than 1 0 ) end 4-2
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T4.4-1 The script file is m = 0; for q = 0:6:18 m = m+1; n = 0; for r = 4:4:12 n = n+1; A(m,n) = r+q; end end T4.4-2 The script file is [m,n] = size(A); for c = 1:n x = 0; for r = 1:m x = x + A(r,c); end sum_A(c) = x; end disp(sum_A) T4.4-3 The script file is x = 49; k = 1; while x>0 y = sqrt(x) k = k+1; x = 50 - k^2; end T4.4-4 The script file is error = 0; x = 0; while error < 1 x = x + .01; approx = 1 + x + x^2/2 + x^3/6; error = 100*(exp(x) - approx)/exp(x); 4-3
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end disp(x) T4.5-1 The script file is angle = input( 0 Enter an angle in degrees. 0 ) switch angle case 45 disp( 0 Angle is in first quadrant 0 ) case -45 disp( 0 Angle is in second quadrant 0 ) case 135 disp( 0 Angle is in third quadrant 0 ) case -135 disp( 0 Angle is in fourth quadrant 0 ) otherwise disp( 0 Quadrant is unknown. 0 ) end T4.7-1 The 0.75 in the matrix should be replaced with 0.70. T4.7-2 Initial values of a and d are needed in case the statements following the else statement are executed (these statements are a(k) = a(k-1) , d(k) = d(k-1) ). End-of-Chapter Problems 1. The answers are (a) z = 1 , (b) z = 0 , (c) z = 1 , (d) z = 1 2. The answers are (a) z = 0 , (b) z = 1 , (c) z = 0 , (d) z = 4 , (e) z = 1 , (f) z = 5 , (g) z = 1 , (h) z = 0 3. The answers are (a) z = [ 0,1,0,1,1] , (b) z = [ 0,0,0,1,1 ] , (c) z = [0,0,0,1,0] , (d) z = [1,1,1,0,1] , 4. The session is x = [-3,0,0,2,6,8]; y = [-5,-2,0,3,4,10]; n = find(x>y) n = 1 2 5 Thus the first, second, and fifth elements of x are greater than the corresponding elements in y . 4-4
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5. The session is price = [19,18,22,21,25,19,17,21,27,29]; length(find(price>20)) ans = 6 Thus the price was over $20 on six days. 6. The session is price_A = [19,18,22,21,25,19,17,21,27,29]; price_B = [22,17,20,19,24,18,16,25,28,27]; length(find(price_A>price_B)) ans = 7 7. (a) The session is price_A = [19,18,22,21,25,19,17,21,27,29]; price_B = [22,17,20,19,24,18,16,25,28,27]; price_C = [17,13,22,23,19,17,20,21,24,28]; length(find(price_A>price_B&price_A>price_C)) ans = 4 Thus the price of stock A was above both B and C on four days. (b) Replace the fourth line in the above session with length(find(price_A>price_B|price_A>price_C)) ans = 9 The answer is nine days.
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