Explanation Definition used: General quadratic equation : “Given that a , b , and c are constant ( a ≠ 0 ) , the equation a x 2 + b x + c = 0 is called the general quadratic equation in x ”. Calculation: Consider the equation x 4 − 20 x 2 + 64 = 0 . In order to find the value of x , first rewrite the equation in quadratic form. Substitute y = x 2 in x 4 − 20 x 2 + 64 = 0 and simplify the equation as follows. y 2 − 20 y + 64 = 0 y 2 − 16 y − 4 y + 64 = 0 y ( y − 16 ) − 4 ( y − 16 ) = 0 ( y − 16 ) ( y − 4 ) = 0 On further simplification, y − 16 = 0 or y − 4 = 0 y = 16 or y = 4 x 2 = 16 �

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

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Chapter 14.3, Problem 29E

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To solve: The equation x4−20x2+64=0 algebraically and check the solution by using calculator

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Chapter 14.3, Problem 28E

Chapter 14.3, Problem 30E

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Answer questions 8.2.11 and 8.2.12 respectively

8.4.2 An article in Knee Surgery, Sports Traumatology, Arthroscopy [“Arthroscopic Meniscal Repair with an Absorbable Screw: Results and Surgical Technique” (2005, Vol. 13, pp. 273–279)] showed that only 25 out of 37 tears (67.6%) located between 3 and 6 mm from the meniscus rim were healed. a. Calculate a two-sided 95% confidence interval on the proportion of such tears that will heal. b. Calculate a 95% lower confidence bound on the proportion of such tears that will heal. 8.4.3 An article in the Journal of the American Statistical Association [“Illustration of Bayesian Inference in Normal Data Models Using Gibbs Sampling” (1990, Vol. 85, pp. 972–985)] measured the weight of 30 rats under experiment controls. Suppose that 12 were underweight rats. a. Calculate a 95% two-sided confidence interval on the true proportion of rats that would show underweight from the experiment. b. Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95%…

8.4.8 Use the data from Exercise 8.4.2 to compute the two-sided Agresti-Coull CI on the proportion of tears that heal. Compare and discuss the relationship of this interval to the one computed in Exercise 8.4.2.

Chapter 14 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 14.1 - In Example 7, determine how many times the rocket...Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E Ch. 14.1 - Prob. 6E Ch. 14.1 - Prob. 7E Ch. 14.1 - Prob. 8E Ch. 14.1 - Prob. 9E

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The equation x 4 − 20 x 2 + 64 = 0 algebraically and check the solution by using calculator

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Chapter 14 Solutions