versions. Problem 1(a) - Fall 2008 Find parametric equations for the line L which contains A(1, 2, 3) and B(4, 6, 5). Solution: To get the parametric equations of L you need a point through which the line passes and a vector parallel to the line. −→ Take the point to be A and the vector to be the AB. The vector equation of L is −→ −→ r(t) = OA + t AB = 1, 2, 3 + t 3, 4, 2 = 1 + 3t, 2 + 4t, 3 + 2t , where O is the origin. The parametric equations are: x = 1 + 3t y = 2 + 4t, z = 3 + 2t t ∈ R. Problem
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PHYSIC AL CONSTANTS CONSTANT Speed of light Elementary charge Electron mass Proton mass Gravitational constant Permeability constant Permittivity constant Boltzmann’s constant Universal gas constant Stefan–Boltzmann constant Planck’s constant Avogadro’s number Bohr radius SYMBOL c e me mp G m0 P0 k R s h 15 2p"2 NA a0 THREE-FIGURE VALUE 3.003108 m/s 1.60310219 C 9.11310231 kg 1.67310227 kg 6.67310211 N # m2/kg 2 1.2631026 N/A2 1H/m2 8.85310212 C 2/N # m2 1F/m2
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Example 1 Equation with Rational Roots Solve 2x2 – 36x + 162 = 32 by using the Square Root Property. 2x2 – 36x + 162 = 32 Original equation 2(x2 – 18x + 81) = 2(16) Factor out the GCF. x2 – 18x + 81 = 16 Divide each side by 2. (x – 9)2 = 16 Factor the perfect trinomial square. x – 9 = Square Root Property x – 9 = ±4 = 4 x = 9 ± 4 Add 9 to each side. x = 9 + 4 or x = 9 – 4 Write as two equations. x
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Surface Reconstruction from Medical Imaging for Use in a Computer-AidedDesign (CAD) Environment A thesis by Gregory M. Sturgeon M.S.E. Presented January 2005 In partial fulfillment of the requirements for the Masters of Science in Engineering degree Padnos School of Engineering Grand Valley State University Advisor: Dr. Jeff Ray Grand Valley State University Padnos School of Engineering Certificate of Examination Advisor ________________________ Dr. J. Ray Examining Board ________________________
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TLFeBOOK WHAT READERS ARE SAYIN6 "I wish I had had this book when I needed it most, which was during my pre-med classes. I t could have also been a great tool for me in a few medical school courses." Or. Kellie Aosley8 Recent Hedical school &a&ate "CALCULUS FOR THE UTTERLY CONFUSED has proven to be a wonderful review enabling me t o move forward in application of calculus and advanced topics in mathematics. I found it easy t o use and great as a reference for those darker aspects of calculus
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Second Order Reaction Kinetics Abstract The objective of this experiment was to determine if the specific rate constant of the reduction reaction of hexacyanoferrate (III) ion with ascorbic acid (C6H8O6) is affected by the ionic strength of the solution and the charges of the ion species within the solution. A Cary Bio 50 Spectrophotometer and its associated software was used to measure the absorbance of the solution at a wavelength of 418 nm. Analysis of the data collected supports the conclusion
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ICTON 2013 Th.A2.2 Optimizing Silicon-on-Oxide 2D-Grating Couplers Lee Carroll,1 Dario Gerace,1 Ilaria Cristiani,2 Lucio Claudio Andreani1 Department of Physics, University of Pavia, via Bassi 6, 27100 Pavia, Italy 2 Department of Industrial and Information Engineering, University of Pavia, via Ferrata, 27100 Pavia, Italy Tel: (39) 0382 987491, Fax: (39) 0382 987563, e-mail: lee.carroll@unipv.it 1 ABSTRACT 3D finite difference time domain calculations are used to optimize the coupling
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Stakeholders * James Windham: manager of JBS and Company * Organization * Muslim Workers * Other Workers * Community Presenting Problems * Because Muslim workers needed to take breaks at very precise times, focus and momentum were often lost, resulting inn loss of productivity. * Because of the constant shift of both sunrise and sunset, Windham was faced with the logistical problem of planning the factory workday * While he viewed the decision
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CASE STUDY SOLUTION A. The table or spreadsheet for CSI's unit sales quantity (Q), price (P), optimal advertising level (A), advertising intensity (A/S), and sales revenue (S) is: Quantity Price 5,500 $0 5,570 5 5,631 10 5,683 15 5,725 20 5,758 25 5,781 30 5,795 35 5,800 40 5,795 45 5,781 50 5,758 55 5,725 60 5,683 65 5,631 70 5,570 75 5,500 80 5,420 85 5,331 90 5,233 95 5,125 100 Advertising $25.000 28.125 31.250 34.375 37.500 40.625 43.750
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Date of Sale Seal of Bank / Institution with Address Initial of authorized sale clerk CONTENTS Sl. No. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. Appendix I. II. III. IV . V . VI. VII. VIII. IX. List of Institutions participated in CCB(AIEEE) -2010-Counseling .......................................................... 007 Nomenclature of Disciplines in Degree Engineering & Technology/ Architecture/Town Planning (Approved by AICTE) ................................................
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