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Chapter 5 Solutions
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Thomas' Calculus: Early Transcendentals (14th Edition)
University Calculus: Early Transcendentals (4th Edition)
Glencoe Math Accelerated, Student Edition
Calculus, Single Variable: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals (3rd Edition)
- (Statics) An annulus is a cylindrical rod with a hollow center, as shown in Figure 6.7. Its second moment of inertia is given by this formula: I4(r24r14) I is the second moment of inertia (m4). r2 is the outer radius (m). r1 is the inner radius (m). a. Using this formula, write a function called annulusMoment ( ) that accepts two double-precision numbers as parameters (one for the outer radius and one for the inner radius), calculates the corresponding second moment of inertia, and displays the result. b. Include the function written in Exercise 5a in a working program. Make sure your function is called from main(). Test the function by passing various data to it.arrow_forward(Automotive) a. An automobile engine’s performance can be determined by monitoring its rotations per minute (rpm). Determine the conversion factors that can be used to convert rpm to frequency in hertz (Hz), given that 1rotation=1cycle,1minute=60seconds,and1Hz=1cycle/sec. b. Using the conversion factors you determined in Exercise 7a, convert 2000 rpm into hertz.arrow_forward(Mechanics) The deflection at any point along the centerline of a cantilevered beam, such as the one used for a balcony (see Figure 5.15), when a load is distributed evenly along the beam is given by this formula: d=wx224EI(x2+6l24lx) d is the deflection at location x (ft). xisthedistancefromthesecuredend( ft).wistheweightplacedattheendofthebeam( lbs/ft).listhebeamlength( ft). Eisthemodulesofelasticity( lbs/f t 2 ).Iisthesecondmomentofinertia( f t 4 ). For the beam shown in Figure 5.15, the second moment of inertia is determined as follows: l=bh312 b is the beam’s base. h is the beam’s height. Using these formulas, write, compile, and run a C++ program that determines and displays a table of the deflection for a cantilevered pine beam at half-foot increments along its length, using the following data: w=200lbs/ftl=3ftE=187.2106lb/ft2b=.2fth=.3ftarrow_forward
- (Statics) A beam’s second moment of inertia, also known as its area moment of inertia, is used to determine its resistance to bending and deflection. For a rectangular beam (see Figure 6.6), the second moment of inertia is given by this formula: Ibh3/12 I is the second moment of inertia (m4). b is the base (m). h is the height (m). a. Using this formula, write a function called beamMoment() that accepts two double- precision numbers as parameters (one for the base and one for the height), calculates the corresponding second moment of inertia, and displays the result. b. Include the function written in Exercise 4a in a working program. Make sure your function is called from main(). Test the function by passing various data to it.arrow_forwardODU2MTQ4/a/MjkwNjEwMTAyODU1/details Problem: 1 A company want to raise the salary of its employee. The raise rate is given as following: The raise rate is 20% of the salary if the employee have 15 years in work or more The raise rate is 10% of the salary if the employee have 7 years in work or more Otherwise, the raise rate is 5% of the salary. The new salary is computed by the formula: new salary=old salary x(1+ raise rate) Write a main program that prompts the user to enter n of employees then enter their salary and years in work of each of them. It displays the new salary for each employee and finally, it displays the average salaries of all employees after raising as shown in the following sample run. Sample run Enter the number of employees: 2 Enter the salary and the number of years of Employee 1: 1500 Enter the salary and the number of years of Employee 2. 800 16 8. The New Salary of Employee 1 is: 1800 The New Salary of Employee 2 is: 880 The average Salary of all employees is:…arrow_forwardHeat capacity of a solid: Debye's theory of solids gives the heat capacity of a solid at temperature T to be 3 T rOp/T Cy = 9VpkB (e* – 1)2 dx, - where V is the volume of the solid, p is the number density of atoms, kg is Boltzmann's constant, and 0D is the so-called Debye temperature, a property of solids that depends on their density and speed of sound. Develop a computer code to evaluate Cy (T) for a given value of the temperature, for a sample consisting of 1000 cubic centimeters of solid aluminum, which has a number density of p = 6.022 x 1028m-3 and a Debye temperature of 0p = 428K. The Boltzmann's constant kg = 1.380649 x 10-23 J · K-1. Please evaluate the integral with the following methods: (a) MATLAB adaptive Simpson quadrature, [Q.FCNT] = QUAD(FUN,A,B,TOL) with TOL =le-10.arrow_forward
- (x² If h(x) X 2 , then 2arrow_forward5. The function y = a + b ·x² is a solution to one of these differential equations for all a and all b. Using dsolve, find the DE. a. y y" (y)² = 0 b. xy'-y (1 + x) = 0 c. xy" - y' = 0 d. xy" + y = 0arrow_forwardHandwork problem (also includes MATLAB applications): HW10_1 First, compute the integral analytically. Then estimate the integral to 6 decimal places, as instructed. a) handwork Use multiple applications of the trapezoid rule, with n=6. .3 dx b) handwork Apply the composite trapezoid rule, with n=6. (3x + 1)3 c) MATLAB Apply the composite trapezoid rule, with n=6, 12 & 24 d) handwork Use multiple applications of Simpson's 1/3 rule, with n=6. e) handwork Apply the composite Simpson's 1/3 rule, with n=6. f) MATLAB Apply the composite Simpson's 1/3 rule, with n= 6, 12 & 24 for all cases, handwork & MATLAB: Compare all results with the exact integral, and compute the relative errors using MATLAB and publish as pdf.arrow_forward
- Question The refractive index of Sodium Chloride is 1.54. Make a function by which user can Find the critical angle of diamond by taking Air as a rare medium (Refractive index of Air is 1). Note: (User Take different incident Angles as a Input)arrow_forwardProblem: The third side of the triangle is 8 less than twice the sum of the two other sides and the first side is 5 more than the thrice the second side. If the perimeter is given, how long are its sides?arrow_forward(8). If L₁ and L2 are in D, then L₁ - L2 must be in D. True Falsearrow_forward
- C++ for Engineers and ScientistsComputer ScienceISBN:9781133187844Author:Bronson, Gary J.Publisher:Course Technology Ptr
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