barcode in excel 2007

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8.68. Fit a least-squares parabola, y a bx cx2, to the data in Table 8-34. Table 8-34 x y 0 2.4 1 2.1 2 3.2 3 5.6 4 9.3 5 14.6 6 21.9

where O is the n 1 null matrix. Now, if the matrix I A were nonsingular, only the trival solution X Y O would exist. Hence, for a nontrivial solution, the value of must be such as to make I A a singular matrix; that is, we must have a11 a21 det I A ... a n1 a12 a22 ... an2 a13 a23 ... an3 . . . a1n a2n 0 ... ... ann

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8.69. Table 8-35 gives the stopping distance d (feet) of an automobile traveling at speed v (miles per hour) at the instant danger is sighted. (a) Graph d against v. (b) Fit a least-squares parabola of the form d a bv cv2 to the data. (c) Estimate d when v 45 miles per hour and 80 miles per hour. Table 8-35 Speed, v (miles per hour) Stopping Distance, d (feet) 20 54 30 90 40 138 50 206 60 292 70 396

8.70. The number y of bacteria per unit volume present in a culture after x hours is given in Table 8-36. (a) Graph the data on semilogarithmic graph paper, with the logarithmic scale used for y and the arithmetic scale for x. (b) Fit a least-squares curve having the form y abx to the data, and explain why this particular equation should yield good results, (c) Compare the values of y obtained from this equation with the actual values. (d) Estimate the value of y when x 7. Table 8-36 Number of Hours (x) Number of Bacteria per Unit Volume (y) 0 32 1 47 2 65 3 92 4 132 5 190 6 275

The n roots of this polynomial equation in are the eigenvalues of matrix A; the corresponding nontrivial solutions X are known as the eigenvectors of A. Setting 0 in the left side of the above characteristic equation, we see that the constant term in the equation must be det A det 1 A 1 n det A Since the coe cient of n in the equation is obviously unity, the constant term is also equal to 1 n times the product of all the roots. The determinant of a square matrix is the product of all its eigenvalues an alternate, and very useful, de nition of the determinant.

8.71. Table 8-37 shows the corresponding values of three variables x, y, and z. (a) Find the linear least-squares regression equation of z on x and y. (b) Estimate z when x 10 and y 6.

ABC sequence, 250, 262 263, 266, 270 AC generator, 248, 260 AC power, 219 247 apparent, 226 230 average, 221 223, 224, 236, 245 247 complex, 226 230, 245, 247 energy exchanged between inductor/capacitor, 224 226 instantaneous, 219, 220, 224, 236 maximum power transfer, 233 234, 247 parallel-connected networks, 230 231 power factor improvement, 231 233 quadrature, 223 reactive, 223, 226 231, 243 real, 221 224 in RLC, 223 224 sinusoidal steady state, 220 221 AC wattmeter, 259, 265 Active circuits, 143 145, 175 rst-order, 143 145 higher-order, 175 Active elements, 7 8 Active lters, 282 283 Active phase shifter, 145 Admittance, 196, 205, 242, 305 combination of, 197 coupling, 201 diagram, 197 input, 201, 211 in parallel, 197 self-, 201 in series, 197 transfer, 201, 211 Admittance parameters, short-circuit (see Y-parameters) Air-core transformers, 340 Ampere, 1, 2 Ampere-hours, 5 Ampere-turn dot rule, 343 Ampere-turns, 343 Ampli ers, 64 100 di erential/di erence, 75 feedback in, 65 66 integrator/summer, 78 79 leaky integrator, 78

8.72. Find (a) sy.x, (b) sx.y for the data in Problem 8.67. 8.73. Compute (a) the total variation in y, (b) the unexplained variation in y, (c) the explained variation in y for the data of Problem 8.67. 8.74. Use the results of Problem 8.73 to find the correlation coefficient between the two sets of quiz grades of Problem 8.67. 8.75. Find the covariance for the data of Problem 8.67 (a) directly, (b) by using the formula sxy of Problem 8.74. rsxsy and the result

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