EBK JAVA HOW TO PROGRAM, LATE OBJECTS
EBK JAVA HOW TO PROGRAM, LATE OBJECTS
11th Edition
ISBN: 9780134763507
Author: Deitel
Publisher: VST
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Chapter 3, Problem 1.14SRE
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A “floating-point number” is a number which contains a decimal part in it, such as 7.33, 0.0975, or 1000.12345.

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Exercise III: Catalan numbers For n e N, denote by c, to be the number of ways to form a "mountain range" with n upstrokes (U) and n downstrokes (D) that all stay above a horizontal line. For instance: for n = 1, only UD is allowed, so c = 1; • for n = 2, only UUDD and UDUD are allowed, so c2 = 2. 1. Check that c3 = 5 by writing down or drawing all possible options. 2. Consider the power series +00 g(x) = 2 n=0 (by definition co = 1) called the generating function of the sequence (en). Justify that cn < 4" for each n, and deduce that the radius of convergence of g is at least 1/4. 3. It can be show that for r E (-1/4, 1/4), g(x) = 1+ xg(r)? and therefore 1- VI 4.x g(x) = 2.x Use this formula and the known power series of V1+ x to write the first terms of the power series expansion of g, in the form g(x) = co + c1x + c2x2 + C3x + c4x* + ·.. Show how you obtain a few terms, but you do not need to show all computations and you can use a calculator for fractions. Check that you recover co,…
Suppose you want to deposit a certain amount of money into a savings account, and thenleave it alone to draw interest for the next 10 years. At the end of 10 years, you would like tohave $10,000 in the account. How much do you need to deposit today to make that happen?You can use the following formula, which is known as the present value formula, to find out:The terms in the formula are as follows: [5 marks]• P is the present value, or the amount that you need to deposit today.• F is the future value that you want in the account. (In this case, F is $10,000.)• r is the annual interest rate.• n is the number of years that you plan to let the money sit in the account.Write a method named presentValue that performs this calculation. The method should accept the future value, annual interest rate, and number of years asarguments. It should return the present value, which is the amount that you need to deposit today.Demonstrate the method in a program that lets the user experiment with…
You are given an integer, N. Your task is to print an alphabet rangoli of size N. (Rangoli is a form of Indian folk art based on creation of patterns.) Different sizes of alphabet rangoli are shown below: #size 3 ----C---- --c-b-c-- c-b-a-b-c --c-b-c-- ----C---- #size 5 ------e-d-e-- ----e-d-c-d-e---- --e-d-c-b-c-d-e-- e-d-c-b-a-b-c-d-e --e-d-c-b-c-d-e-- ----e-d-c-d-e---- e-d-e---- ---- #size 10 --j- -j-i-j- --j-i-h-i-j-- ---j-i-h-g-h-i-j- --j-i-h-g-f-g-h-i-j- -j-i-h-g-f-e-f-g-h-i-j-- ------j-i-h-g-f-e-d-e-f-g-h-i-j-- ----j-i-h-g-f-e-d-c-d-e-f-g-h-i-j--- --j-i-h-g-f-e-d-c-b-c-d-e-f-g-h-i-j-- j-i-h-g-f-e-d-c-b-a-b-c-d-e-f-g-h-i-j --j-i-h-g-f-e-d-c-b-c-d-e-f-g-h-i-j-- ----j-i-h-g-f-e-d-c-d-e-f-g-h-i-j-- -j-i-h-g-f-e-d-e-f-g-h-i-j- -j-i-h-g-f-e-f-g-h-i-j- ---j-i-h-g-f-g-h-i-j- --j-i-h-g-h-i-j- -j-i-h-i-j- j-i-j- The center of the rangoli has the first alphabet letter a, and the boundary has the Nth alphabet letter (in alphabetical order). Eunction Descrintion

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EBK JAVA HOW TO PROGRAM, LATE OBJECTS

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