How many litres of paint must you buy to paint the walls of a rectangular prism shaped room that is
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- 2.3 Vibration amplitude of a machine plotted against time shown in Fig. T2.3. is described by sin(0.8+) In(t + 2) x(t) = t + 0.5 Here, t is in seconds and x is in millimeters 0.6 0.4 0.2 ° -0.2 mmm -0.4 0 10 20 30 40 50 60 70 Time [s] Fig. T2.3: Machine vibration amplitude variation against time Obtain the vibration velocity as a function of time, x(t), if it is measured by a vibration velocity sensor.arrow_forwardO State Jordan's lemma. Calculate the following integrals using complex variable techniques. 2π do (i) 1+8 cos²0' I COS x dx x²-2x+5° Leave your answers in terms of real functions of real variables.arrow_forwardSketch to scale the orbit of Earth about the sun. Graph Icarus’ orbit on the same set of axesWhile the sun is the center of Earth’s orbit, it is a focus of Icarus’ orbit. There aretwo points of intersection on the graph. Based on the graph, what is the approximate distance between the two points of intersection (in AU)?arrow_forward
- Refer to page 138 of the shared file for the numerical methods problem. Use Newton's method to approximate the solution of the given nonlinear system of equations. Start with an initial guess provided in the problem and iterate for at least two steps. Link: [https://drive.google.com/file/d/1RQ2OZk-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Show the Jacobian matrix, iteration formulas, and each step of the computation.arrow_forwardUnknown to a medical researcher, 7 out of 24 patients have a heart problem that will result in death if they receive the test drug. 5 patients are randomly selected to receive the drug and the rest receive a placebo. What is the probability that less than 4 patients will die? Express as a fraction or a decimal number rounded to four decimal places.arrow_forwardRefer to page 128 for the heat equation problem. Solve the one-dimensional heat equation with the given initial and boundary conditions. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Use Fourier series or other appropriate methods.arrow_forward
- Go to page 137 for the real analysis problem. Determine whether the given infinite series converges or diverges using appropriate convergence tests, such as the ratio test, root test, or comparison test. Justify your choice of test and provide clear steps. Link: [https://drive.google.com/file/d/1RQ2OZk-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Explain your reasoning and show all calculations.arrow_forwardRefer to page 132 of the document for the linear algebra problem. Solve the given nonhomogeneous system of equations using Gaussian elimination or matrix inverses, and express the general solution in parametric form. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Justify each step in the elimination process and interpret the solution.arrow_forwardTum to page 134 for the vector calculus problem. Verify Stokes' theorem by calculating the surface integral of the curl of a vector field over the given surface S and comparing it to the line integral of the same field over the boundary curve C. Link: [https://drive.google.com/file/d/1RQ2OZk-LSxpRyej KEMg1t2q15dbpVLCS/view? usp=sharing] Provide all detailed steps for calculating the curl, surface integral, and line integral.arrow_forward
- The Laplace equation problem is provided on page 136. Solve the two-dimensional Laplace equation on a rectangular region using the method of separation of variables with the specified boundary conditions. Link: [https://drive.google.com/file/d/1RQ2OZk-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Include all steps, separation constants, and final solution in series form.arrow_forwardThe dynamical systems problem is on page 127. Determine the stability of the fixed points of the given nonlinear system using linearization techniques. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Provide phase plane analysis if necessary.arrow_forwardRefer to page 130 in the shared document for the differential equation problem. Solve the given second-order linear ordinary differential equation with the specified boundary conditions using the method of undetermined coefficients or variation of parameters as appropriate. Link: [https://drive.google.com/file/d/1RQ2OZK-LSxpRyejKEMg1t2q15dbpVLCS/view? usp=sharing] Show all intermediate steps, including how you satisfy the given boundary conditions.arrow_forward
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