Lemma: If n is a positive integer‚ [pic] proof: [pic] [pic] [pic] = an − bn. Theorem: If 2n + 1 is an odd prime‚ then n is a power of 2. proof: If n is a positive integer but not a power of 2‚ then n = rs where [pic]‚ [pic]and s is odd. By the preceding lemma‚ for positive integer m‚ [pic] where [pic]means "evenly divides". Substituting a = 2r‚ b = − 1‚ and m = s and using that s is odd‚ [pic] and thus [pic] Because 1
Premium Integer Mathematics Natural number
Assignment Week 4 Chapter 11 20. A parallel RL circuit has values of IL = 240 mA and IR = 180 mA. Calculate the magnitude and phase angle of the circuit current. It=√ IL^2 + IR^2= √ 240mA^2 + 180mA^2= 0.3 x 10^-3= 300mA θ= tan^-1(-IL/IR)= (-240mA/180mA)= -53° 300mA∟-53° 22. Calculate the total impedance for the circuit shown in Figure 11.38b. It= √IL^2 + IR^2= √800mA^2 + 120mA^2= 0.808949 x 10^-3= 808.95mA Zt= Vs/It= 120V/808.95mA = 148Ω θ= tan^-1(-IL/IR)= (-800mA/120mA)= -81.5= 82° 148∟82° 24
Premium Ohm's law Electric current Resistor
Laboratory Report Chong You Liang (0300915) Chong You Liang Choon Zhe Shyi Lai Li Yang Ng Yee Kai Table of Contents ABSTRACT 2 1.0 INTRODUCTION
Premium Test method Science Experiment
. Na+ and K+. K+ was more concentrated inside the cell while Na+ was more concentrated outside the cell. 2. A cell is at rest without any implications of changing the potential. 3. 4. 5. K+ is more permeable than Na+ in a resting neuron. This is because there are few sodium leakage channels. 6. Since the resting membrane potential is the potential difference between the inside and outside of the cell across the membrane‚ a change would depend on the resting permeability of the membrane to ions.
Premium
LADDER DIAGRAM: FIGURE 53 LADDER PROGRAM FOR THE SHIFT AND CLOCK PROGRAM THE SIMULATION OPTION IS SELECTED: Figure 54 SIMULATING THE LADDER PROGRAM ERROR AND DEBUGGING: Once the simulation has started it checks for the errors in the ladder diagram‚ address etc. if there is an error‚ the output cannot be processed until the error is rectified. REMOVING THE DEFECTIVE PRODUCTS: Figure 55 REMOVING THE DETECTED BOTTEL 1 Figure 56 REMOVING THE DEFECTED BOTTLE 2 INPUT
Premium Statistics Statistical hypothesis testing Regression analysis
Solve each of the following problems. Show your solution. 1. A hydraulic lift office chair has its seat attached to a piston with an area of 11.2 cm2. The chair is raised by exerting force on another piston‚ with an area of 4.12 cm2. If a person sitting on the chair exerts a downward force of 219 N‚ what force needs to be exerted on the small piston to lift the seat? Answer: a= 11.2 cm2 A= 4.12 cm2 f= 219 N F= 80.56 N F= fA / a ;
Premium Force Thermodynamics Mass
The Three Rivers Optical Case MKT 7850-60 1.1 Introduction According to Jobson Medical Information‚ as of 2008 the U.S optical retail market was a $23.5B industry. This number excludes refractive surgery‚ reader and sunglasses sales at non – optical retail locations and contact lens sales by mail/internet suppliers.
Premium Sales Strategic management
Bonus Assignment #2 COEN 233 Computer Networks Department of Computer Engineering Santa Clara University Dr. Ming-Hwa Wang Phone: (408) 525-2564 Course website: Office Hours: Fall Quarter 2012 Email address: mwang2@engr.scu.edu http://www.cse.scu.edu/~mwang2/network/ Monday & Wednesday 9:00-9:30pm Name: ID: Score: Due date: 7:10pm‚ January 14‚ 2013 Problem 1 What is the ISO OSI protocol stack? Please describe the functionality for each layer. ---------The answer is in your text book. Problem
Premium OSI model Modulation Telephone
3M Optical Systems: Case Brief As Andy Wong‚ how would you handle the authorization for expenditure for the re-launch of the privacy screen? As Andy Wong‚ I would take the proposal to one of my senior-level mentors for support. The OS unit has already tried and failed three times with the microlouvered filter and high level support would benefit both Wong and Guehler in this case. If Guehler sees that other areas of 3M are in support of the authorization for expenditure‚ then he will not have
Premium Management Marketing Strategic management
Elena Mesa Nov. 15‚ 2013 Ms. Lelacheur IB Biology HL The Effect of Temperature on Beet Root Membranes What is the affect of temperature on beetroot membranes? Hypothesis: It is hypothesized that as the temperature increases‚ the deeper red the beetroot water will be. At higher temperatures the proteins in the beetroot plasma membrane will denature‚ leaving holes in the membrane and allowing the red pigment in the cell sap to seep out into the water around it. Variables: Dependent-The
Premium Cell membrane Fahrenheit Temperature