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Trigonometric substitutions Evaluate the following integrals.
25.
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- Use the following definitions to express each union or intersection given. You can use roster or set builder notation in your responses, put no set operations. For each definition, i e Z* • A; = {i°, i', i²} (Recall that for any number æ, xº = 1.) • B; = {x € R : -i < x <1/i} • C; = {x €R: -1/i < x <1/i}arrow_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_forward(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
- (Thermodynamics) The work, W, performed by a single piston in an engine can be determined by this formula: W=Fd F is the force provided by the piston in Newtons. d is the distance the piston moves in meters. a. Determine the units of W by calculating the units resulting from the right side of the formula. Check that your answer corresponds to the units for work listed in Table 1.1. b. Determine the work performed by a piston that provides a force of 1000 N over a distance of 15 centimeters.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_forwardDetermine the value of each of the following expressions. (1) a.staticcastchar(toupper('#'))b.staticcastchar(toupper('k'))c.staticcastchar(toupper('3'))d.staticcastchar(toupper('-'))e.staticcastchar(tolower('T'))f.staticcastchar(tolower(':'))g.staticcastchar(tolower('u'))h.staticcastchar(tolower(''))arrow_forward
- 1 Use buolenn elebre fo redluce Hhe equation nuch as F= abct ač t b ēarrow_forwardPython code for calculate the factorial with the help of function and make the program compatible with Rarrow_forwardQuestion 1: Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 4, 6, 8, 10}, and B = {1, 3, 5, 7, 8, 9}. Find:arrow_forward
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