Insert Fig 5-2 6. Note that Θ is the angle between the applied force and the displacement. 7. Work is described in Newtons x meters (force x displacement). The unit of work is the Joule (J) 8. 1 Newton meter = 1 Joule 9. Work is a vector with both direction AND magnitude. This means WORK CAN BE NEGATIVE! 10. Negative work is most commonly used to slow an object
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1.66 (34.53‚ 40.16) C20 30 39.46 10.65 1.94 (36.16‚ 42.77) C21 30 34.71 9.21 1.68 (31.85‚ 37.57) d) 1 Sample T-Test for Variable C2 n= 30 df= 29 = 36.91 SE= 1.92 α= 1-CC = 1.0.90 = 0.1 e) Apply binomial theorem for x= 16‚ 17‚18‚19‚20 p=0.9 q=0.1 n=20 16 Interval 17 Interval 18 Interval 19 Interval 20 Interval f) Mean from Part A = 37.9263 Variable N Mean StDev SE Mean 90% CI C2 30 36.91
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5 6 Bisection Method and also give comparative study of other methods for non-linear =n in the form of table 6 45 6 7 Secant Method and also give comparative study of other methods for non-linear =n in the form of table 7 46 7 8 Newton Raphson Method and also give comparative study of other methods for non-linear =n in the form of table 8 47 8 9 Method Of Successive Approximation and also give comparative study of other methods for non-linear =n in the form of table 9 48
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2σ 2 2 Discrete Distributions Distribution Binomial Probability Function p(y) = n y p y (1 − p)n−y ; Mean Variance MomentGenerating Function np np(1 − p) [ pet + (1 − p)]n 1 p 1− p pet 1 − (1 − p)et y = 0‚ 1‚ . . . ‚ n Geometric p(y) = p(1 − p) y−1 ; p y = 1‚ 2‚ . . . Hypergeometric p(y) = r y N−r n−y N n ; nr N n r N 2 N −r N N −n N −1 y = 0‚ 1‚ . . . ‚ n if n ≤ r‚ y = 0‚ 1‚ . . . ‚ r if n > r Poisson Negative binomial λ y e−λ ; y! y = 0‚ 1‚ 2‚ . . . p(y) = p(y)
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didn’t leave much time for his love of math. Since math was just his hobby‚ he never wanted any of his work to be published. When he did publish his work‚ it was always anonymously. Fermat would state theorems‚ but always neglected the proofs. For example‚ his most famous work‚ ‘Fermat’s Last Theorem‚’ didn’t include a proof until when Andrew J. Wiles provided the first in 1993. He made many contributions in the field of mathematics. For example‚ he is considered as one of the ‘fathers’ of analytic
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Eigen values and eigen vectors. Calculus: Functions of single variable‚ Limit‚ continuity and differentiability‚ Mean value theorems‚Evaluation of definite and improper integrals‚ Partial derivatives‚ Total derivative‚ Maxima and minima‚Gradient‚ Divergence and Curl‚ Vector identities‚ Directional derivatives‚ Line‚ Surface and Volume integrals‚ Stokes‚ Gauss and Green’s theorems. Differential equations: First order equations (linear and nonlinear)‚ Higher order linear differential equations with constant
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This page intentionally left blank [50] Develop computer programs for simplifying sums that involve binomial coefficients. Exercise 1.2.6.63 in The Art of Computer Programming‚ Volume 1: Fundamental Algorithms by Donald E. Knuth‚ Addison Wesley‚ Reading‚ Massachusetts‚ 1968. A=B Marko Petkovˇek s Herbert S. Wilf University of Ljubljana Ljubljana‚ Slovenia University of Pennsylvania Philadelphia‚ PA‚ USA Doron Zeilberger Temple University Philadelphia‚ PA‚ USA April
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Leonhard Euler (/ˈɔɪlər/ oil-er;[2] German pronunciation: [ˈɔʏlɐ] ( listen)‚ local pronunciation: [ˈɔɪlr̩] ( listen); 15 April 1707 – 18 September 1783) was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation‚ particularly for mathematical analysis‚ such as the notion of amathematical function.[3] He is also renowned for his work in mechanics
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Early trigonometry The ancient Egyptians and Babylonians had known of theorems on the ratios of the sides of similar triangles for many centuries. But pre-Hellenic societies lacked the concept of an angle measure and consequently‚ the sides of triangles were studied instead‚ a field that would be better called "trilaterometry".[6]The Babylonian astronomers kept detailed records on the rising and setting of stars‚ the motion of the planets‚ and the solar and lunar eclipses‚ all of which required
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between the binomial and the hypergeometric distributions? a. The sum of the outcomes can be greater than 1 for the hypergeometric. b. The probability of a success changes from trial to trial in the hypergeometric distribution. c. The number of trials changes in the hypergeometric distribution. d. The outcomes cannot be whole numbers in the hypergeometric distribution. 3. In which of the following distributions is the probability of a success usually small? a. Binomial b. Poisson
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