Explanation Definition used: Equation of a Hyperbola: Center at ( 0 , 0 ) ; Transverse axis along the x-axis: An equation of the hyperbola with the center at ( 0 , 0 ) , foci at ( − c , 0 ) and ( c , 0 ) , and vertices at ( − a , 0 ) and ( a , 0 ) is x 2 a 2 − y 2 b 2 = 1 where b 2 = c 2 − a 2 . The hyperbola has a transverse axis of length 2 a along x axis and a conjugate axis at ( 0 , ± b ) of length 2 b . “ Equation of a Hyperbola: Center at ( 0 , 0 ) ; Transverse axis along the y-axis An equation of the hyperbola with the center at ( 0 , 0 ) , foci at ( 0 , − c ) and ( 0 , c ) , and vertices at ( 0 , − a ) and ( 0 , a ) is y 2 a 2 − x 2 b 2 = 1 where b 2 = c 2 − a 2 . The hyperbola has a transverse axis of length 2 a along y axis and a conjugate axis at ( ± b , 0 ) of length 2 b

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Chapter 21.6, Problem 32E

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To show: The hyperbolas x2cos2θ−y2sin2θ=1 have foci at (±1,0) for all values of θ.

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Chapter 21.6, Problem 31E

Chapter 21.6, Problem 33E

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A classification study involving several classifiers was carried out. After training and the usual validation step, the following table shows results for classifiers tried. In below, classifiers are identified as M1, M2 and so on. Sensitivity Specificity M1 0.82 0.82 M2 0.92 0.72 M3 0.72 0.92 M4 0.46 0.47 M5 0.03 0.16 M6 0.13 0.02 M7 0.33 0.64 M8 0.72 0.24 M9 0.47 0.82 M10 0.06 0.84 The following list has statements about the classifiers. In the list, there is a single incorrect statement. Please identify the incorrect statement. Hint 1: recall that a classifier dominates another if both performance measures are better. Hint 2: to help you visualize and compare classifiers, you may want to plot the classifier data in a ROC graph (which will not be submitted). Select one: Qa. O b. Oc. d. By swapping zeroes and ones, M5 can be worsened M8 does not dominate M9 M1 dominates all of M4, M5 and M6 M1 is a good classifier ? e. By swapping zeroes and ones, the performance of M4 does not change…

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Chapter 21 Solutions

Basic Technical Mathematics

Ch. 21.1 - Find the distance between (−2, 6) and (5, −3). Ch. 21.1 - Prob. 2PE Ch. 21.1 - Prob. 1E Ch. 21.1 - Prob. 2E Ch. 21.1 - Prob. 5E Ch. 21.1 - In Exercises 5–14, find the distance between the...Ch. 21.1 - Prob. 7E Ch. 21.1 - Prob. 8E Ch. 21.1 - Prob. 9E Ch. 21.1 - Prob. 10E

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The hyperbolas x 2 cos 2 θ − y 2 sin 2 θ = 1 have foci at ( ± 1 , 0 ) for all values of θ .

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To show: The hyperbolas x2cos2θ−y2sin2θ=1 have foci at (±1,0) for all values of θ.

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