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complex analysis. please answer the question fully, with neat
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(5) If f(z) = u + iu is analytic on a region U, show that φ= is harmonic on U.
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Aparticle moves along the curve given by the equation: r(t)-14(2e)1+(e)k. Find the normal component of acceleration of the particle and the radius of curvature of the curve 4.
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15 Ω 30Ω 25 Ω 60 V 5Ω 10Ω In the DC circuit shown above, apply Thevenin's theorem or Kirchoff's loop current theory to calculate the current in and the voltage across the 25 Ω resistor.
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10 Evaluate the integral: + 3x3/2 dx. 14. Sketch the region whose areas is indicated by the integral: [7 dx. 18. Find the indefinite integral: dx.
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Find the particular solution for the equation. dy = 8x3-9x? +7x: y=0 when x = 1 y = Determine the location of each local extremum of the function. f(x)=x? + 6x2 - 2 What is/are the local maximum/maxima? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The local maximum/maxima is/are at x = (Use a comma to separate answers...
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Page 5 4. A tank is filled with incompressible oil to a depth of (h,) 6.43 m open tank The tank is being drained via a horizontal pipe (radius 1.92 cm), attached at a height of (h,) 0.789 m above the tank bottom Oil is flowing out through the pipe at a rate of 2.34 x 10" m%, but the tank is so large...
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5) Find the average value of the function from-110-S 0) Set up the necessary integral to find the length of the curve over the given interval. Do not evaluate the 22 M'- integral exactly. Find the arc length of the curve 3 Com x-x-3
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If 2.35 g of Cuso, is dissolved in 0.51 x 102mL of 0.380 M NH3, calculate the concentrations of the following species at equilibrium. x 10M Enter your answer in scientific notation. NH3 Cu(NH3)22+
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- For the MUST HAVE directions, you should have everything
organized and labeled by its number in the same order(Rease divide
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- This problem has 2 parts (A&B).
- Please write ALL equations before your answers.
- Summarize your answers as advised in the end and label...
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Question A cantilever box beam carrying a point load of 0.36 kN at its tip is to be constructed from 4 boards nailed together as shown in Fig 1. Assume that each Nail B can carry a maximum shear force of 0.13 kN. (a) Draw the SFD of the cantilever beam and determine the shear force at mid-span. (b) Draw the shear stress distribution across the section at mid-span...