Elementary Differential Equations and Boundary Value Problems, 11e WileyPLUS Registration Card + Loose-leaf Print Companion
Elementary Differential Equations and Boundary Value Problems, 11e WileyPLUS Registration Card + Loose-leaf Print Companion
11th Edition
ISBN: 9781119336617
Author: William E. Boyce, Richard C. DiPrima
Publisher: Wiley (WileyPLUS Products)
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Chapter 1.2, Problem 10P

(a)

To determine

The decay rate r from given data.

(b)

To determine

To find: The expression for the amount of thorium-234 present at any time t.

(c)

To determine

To find: The time required for the thorium-234 to decay to one-half its original amount.

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6. [10] Evaluate (2 (2+2y) ds where C is the upper half-circle centered at the origin connecting the point (2,0) to the point (-2,0). 7. [10] Show that the vector field F(x, y, z) = is conservative and integrate it along the curve П C(t) = si sin t, nt, cost,t), te [0,1] 8. [10] Use Stokes' Theorem to compute the integral curl F.dS, where F(x, y, z) = xzi+yxj+xy k I cur and S is the part of the sphere x² + y²+z² = 9 that lies inside the cylinder x2 + y² above the xy-plane. 9. [10] Use Green's theorem to evaluate So √1+x3 dx+2xy dy where C is the triangle with vertices (0,0), (1, 0) and (1, 3). 10. [10] Evaluate the surface integral (x²z + y²z) dS where S is the hemisphere x² + y²+2² = 4, z> 0. = 1 and ☐
Part 1: A linear electrical load draws 1₁ A at a 0.72 lagging power factor. See the table to find ½ for your student ID. When a capacitor is connected, the line current dropped to 122 A and the power factor improved to 0.98 lagging. Supply frequency is 50 Hz. a. Let the current drawn from the source before and after introduction of the capacitor be 1₁ and I₂ respectively. Take the source voltage as the reference and express 11 and 12 as vector quantities in polar form. b. Obtain the capacitor current, Ic = 12 − I₁, graphically as well as using complex number manipulation. Compare the results. c. Express the waveforms of the source current before (į (t)) and after (i2(t)) introduction of the capacitor in the form Im sin(2лft + 0). Hand sketch them on the same graph. Clearly label your plots. d. Analytically solve i̟2(t) − i₁ (t) using the theories of trigonometry to obtain the capacitor current in the form, ic(t) = Icm sin(2πft + 0c). Compare the result with the result in Part b.

Chapter 1 Solutions

Elementary Differential Equations and Boundary Value Problems, 11e WileyPLUS Registration Card + Loose-leaf Print Companion

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