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# Qpsk Matlab Code

QPSK modulation is also performed on MATLAB tool, which gives three types of waveforms. 5 db ,then we evaluate the coded. 8psk Matlab Code. He was trying to replicate bits, the way that the comms rectpulse() function would. Quadrature Phase Shift Keying (QPSK)/BPSK and QPSK/QPSK Waveform (Digita Modulation Techniques) [HD] - Duration: 11:02. This technique is also known as quaternary PSK, quadriphase PSK or 4-PSK. Implementing a π/4 Shift D-QPSK Baseband Modem Using the TMS320C50 9 Baseband Communications In this class of modem the modulator and demodulator functions such as signal mapping and filtering are completed at baseband frequencies as opposed to directly modulating the carrier at IF. this blog about digital communication, how to simulate code matlab for BPSK, QPSK and 8 QAM, then apply it to Rectangular pulse shaping (RPS) then simulate code matlab for Square Root Raised Cosine (SQRC) filter as pulse shaping filter and matched filter, and apply it to the system, and we found minimum number of coefficient that the loss did not exceed 0. Once the basis function are chosen, any vector in the. Generating QPSK symbols for adaptive filtering. Set useCodegen to true to run the executable generated by codegen instead of the MATLAB code. + Post New Thread. The binary code taken here is the Gold code sequence. This is because, QPSK actually consists of two orthogonal BPSK systems. The Eb/N0 Vs BER Curve for QPSK and BPSK are identical. I was responsible for the design of a general purpose adaptive SRC, developing a Matlab model, and developing a fast running c-code model of the block. Matlab code to generate QPSK. Choose a web site to get translated content where available and see local events and offers. They have designed the system using VHDL codes in Xilinx & analog filter simulation in Matlab. Generally the basis functions are orthogonal to each other. You select two bits, then increment j qpsk modulation and demodulation matlab code only 1. All About Modulation - Part I Basic Concepts, Signal Space, Constellations and Phase Shift Keying modulations (PSK, QPSK, OQPSK, M-PSK, π/4-QPSK, MSK, and GMSK) Basic Concepts of modulation Three kinds of modulations Modulation is the process of facilitating the transfer of information over a medium. QPSK uses four points on the constellation diagram, equally spaced around a circle. Wright, Michael G. The input must be a complex signal. The example uses some key algorithms in MATLAB, emphasizing textual algorithm expression over graphical algorithm expression. I have code for the generation of a bpsk signal and I want a similar one for qpsk. Matlab source codes section | Download MATLAB source code freerce-codes 1. Quadrature phase shift keying. MATLAB code for Frequency modulation (FM) with modulation index Gallery of Electronic Circuits and projects, providing lot of DIY circuit diagrams, Robotics & Microcontroller Projects, Electronic development tools. The data encoding and decoding is run on the Zynq ARM processor through code generation. Amplitude Shift Keying (ASK) Modulation Code in MATLAB Gallery of Electronic Circuits and projects, providing lot of DIY circuit diagrams, Robotics & Microcontroller Projects, Electronic development tools. equalizer is converging. MATLAB Code for QPSK Modulation and Demodulation – File Exchange – MATLAB Central. G2 QPSK Nr=1 ===== function [ser]=hcmlg2x1(snr_db) Nt=2; Nr=1; T=2; err=0; snr = 10^(snr_db/10); qpsk=[1+0i 0+1i -1+0i 0-1i]; M=2; Nb=0; while (err<10 && Nb<10^8). Create scripts with code, output, and formatted text in a single executable document. There must be something wrong in my code but I cannot figure it out what is wrong. 程序使用matlab语言设计，主要实现基于qpsk方式的调制解调，设计时，在调制端加入了成型滤波器，同时在解调端加入了匹配. The receiver addresses practical issues in wireless communications, e. MATLAB script using System. Define parameters. matlab; Saturday, January 26, 2013. Pulse code modulation is used in almost all modern communication systems and is essential for digital communication. QPSK Matlab Code. well this is basic code for matched filter to detect similarity between any two simple signals of same frequency. After that the QPSK demodulator has been developed using MATLAB tool in order to verify the functionality of the modulator. Approximate message passing (AMP) for Massive MIMO detection, MATLAB codes provided. Making a possible to send the different four every symbol. OFDM MATLAB Code. 11g matlab code 16 QAM modulation matlab code with noise baseband QPSK matlab code Source code for pulse width modulation in matlab: 2012 - 5989-1121EN. The Simulink model is shown. The following Matlab project contains the source code and Matlab examples used for ofdm with qpsk. If you find any mistake in terms of accuracy, it is also very highly likely be my fault. The transmitter includes the Bit Generation subsystem, the QPSK Modulator block, and the Raised Cosine Transmit Filter block. BPSK QPSK 16QAM 64QAM MATLAB source code. Abstract: 54916. If you are generating HDL code you will be to add Vivado to your MATLAB path. GNU Octave Scientific Programming Language. High state is represented by a M in modulated signal and low state is represented by a wave which appears like W in modulated signal DPSK encodes two distinct signals of same frequency with 180 degree phase difference between the two. Finally, it is worth briefly discussing how to generate QPSK signals for testing. So I thought it would be easier to make a matlab-file instead. QPSK Matlab Code. I have made Matlab and C program for BPSK with Sinc Pulse shaping with and without Channel at noisy environment. The transmitter includes the Bit Generation subsystem, the QPSK Modulator block, and the Raised Cosine Transmit Filter block. Any callback that is followed by a * has code in it. I have been looking at the OQPSK-block in simulink but I dont know how to use it correctly. pdf Free Download Here QPSK, 8PSK and 16QAM The following matlab program illustrates the BER calculations for BPSK over an AWGN channel. Draw the constellation diagram for QPSK. We will first load our audio signal. DOWNLOAD FSK matlab code. Understanding current loop compensation in boost PFC 2. well this is basic code for matched filter to detect similarity between any two simple signals of same frequency. C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™. this blog about digital communication, how to simulate code matlab for BPSK, QPSK and 8 QAM, then apply it to Rectangular pulse shaping (RPS) then simulate code matlab for Square Root Raised Cosine (SQRC) filter as pulse shaping filter and matched filter, and apply it to the system, and we found minimum number of coefficient that the loss did not exceed 0. You select two bits, then increment j qpsk modulation and demodulation matlab code only 1. 05 out of 5) Binary Phase Shift Keying (BPSK) Binary Phase Shift Keying (BPSK) is a two phase modulation scheme, where the 0’s and 1’s in a binary message are represented by two different phase states in the carrier signal: $$\theta=0^{\circ}$$ for binary 1 and $$\theta=180^{\circ}$$ for binary 0. ber of qPSK over AWGN noise added. QPSK uses four points on the constellation diagram, equally spaced around a circle. Setting up parameters for modulation. This post is a part of the ebook : Digital Modulations using Matlab: build simulation models from scratch - by Mathuranathan Viswanathan In the previous article we saw about how QPSK modulation and demodulation can be done. This page describes QPSK modulation basics or Quadrature Phase Shift Keying modulation. The Bit Generation subsystem uses a MATLAB workspace variable as the payload of a frame, as shown in the figure below. Engineering Made Easy 55,919 views 11:02. I don't understand a thing they do there, and I have asked them, but the answer they gave me wasn't as clear as I expected. BPSK_QPSK_OFDM-Matlab-Codes. Scribd is the world's largest social reading and. is this matlab code of 8psk ??. (21 votes, average: 4. Its syntax is as follows: [code]y = dpskmod(x,M) y = dpskmod(x,M,phaserot) y = dpskmod(x,M,phaserot,symorder) [/code]where y is output signal * x is input signal * M is modulation order * phaserot is. So I thought it would be easier to make a matlab-file instead. The binary code taken here is the Gold code sequence. Asingment QPSK use. Making a possible to send the different four every symbol. matlab code for dpsk modulation and demodulation, qpsk modulator in hardware, fonction qpsk modulation and demodulation matlab code, qpsk modulation and demodulation animation, mini project based on am modulation and demodulation, modulation techniques am fm fsk psk qpsk qam 16qam pptlation techniques am fm fsk psk qpsk qam 16qam ppt, decision. Matlab source codes section | Download MATLAB source code freerce-codes 1. Your main Matlab simulation should have the following as input variables: a. In this paper, we present a (7, 4) code which can be directly applied on the phase of the QPSK constellation points. well this is basic code for matched filter to detect similarity between any two simple signals of same frequency. Theoretical expression is 2*p-p^2, where p is BER for BPSK modulation. carrier frequency and phase offset, timing offset and frame synchronization. doc), PDF File (. See the complete profile on LinkedIn and discover Pranjali. I want to Write a code in Matlab which creates a constant envelop PSK signal waveform that generate for M=8 (M stands for modulation), so that amplitude of the signal can reach up to sqrt(2). Matlab code samples. I need to do the QPSK modualtion in MATLAB but don't really know how to !! Could anyone help me a bit? Help to make use of an. What can I change in my code below to make the results that of qpsk. Finally, it is worth briefly discussing how to generate QPSK signals for testing. In comparison to the BER vs Eb/No plot of a conventional QPSK modulation scheme. This list includes image processing projects using MATLAB, MATLAB projects for ECE students, digital signal processing projects using MATLAB, etc. average ES/N0). Each symbol’s phase is compared relative to the previous symbol; so, if there is no phase shift (0 degrees), the bits “00” are represented. Graph is displayed in figure 3. A set of random QPSK symbols can be created by generating an array of random integer numbers in 1. Abstract: vhdl code for ofdm transmitter OFDM Matlab code ofdm code in vhdl OFDM QPSK simulation OFDM matlab program CODES VHDL PROGRAM for ofdm vhdl code for 8 point ifft in xilinx simulation for prbs generator in matlab vhdl code for block interleaver Text: the mother code are G1=171OCT for X output and G2=133 OCT for Y output. Keywords Binary Phase Shift Keying, Quadrature Phase Shift Keying,. pdf), Text File (. I've delivered the following Matlab implementation of a QPSK modulator, to test it I also arrange a simple QPSK demodulator, the problems I have are the following : 1) For the noise introduced by the channel I use the relations SNR_x_bit_dB = 6 ;. MIMO OFDM using QPSK modulation matlab code Search and download MIMO OFDM using QPSK modulation matlab code open source project / source codes from CodeForge. MATLAB has inbuilt feature of DPSK Modulation. The theoretical curve was plotted/calculated with a small matlab code:. Matlab code for bpsk modulation using snr, which is function of distance. In this video we look at the performance analysis of various digital modulation schemes namely M-PSK's , M-QAM's , DPSK and DQAM by plotting BER vs Eb/N0 in Matlab. This model shows how to use the Universal Software Radio Peripheral® (USRP®) device with Simulink® to implement a QPSK receiver. Symbol Timing Recovery for QPSK (digital modulations) June 17, 2019 November 18, 2013 by Mathuranathan also MATLAB codes are in it or attached by it, please. Pulse code modulation is used in almost all modern communication systems and is essential for digital communication. verilog code for QPSK modulation Search and download verilog code for QPSK modulation open source project / source codes from CodeForge. Matlab code for qpsk demodulator with carrier and clk recovery. Create scripts with code, output, and formatted text in a single executable document. The Bit Generation subsystem uses a MATLAB workspace variable as the payload of a frame, as shown in the figure below. QPSK Modulation and Demodulation in Matlab AWGN Channel. MATLAB Code of Single Sided Band Modulation and Demodulation. See Callbacks for Customized Models for more detailed information. Each message has only two levels, ±V volt. There must be something wrong in my code but I cannot figure it out what is wrong. Then we will use quantization, QPSK modulation, QPSK demodulation and dequantization. The QPSK symbol alphabet has four complex symbols. The input test signals data and carrier are interfaced to the CPLD and FPGAs. Work on a wireless link of QPSK including the transmitter with PA, LNA, down-converter and receiver. The theoretical description of QPSK modulation and demodulation are available in the book of "communication system " by SIMON HAYKIN. This section of MATLAB source code covers BPSK,QPSK,16QAM and 64QAM modulation or data mapping matlab code. Performance Evaluation Of BPSK And QPSK Modulation With LDPC Codes in Matlab. Chapter One Introduction to the DSP-OFDM Modulator Project 1. matlab code for line coding : unipolar, polar, bip Matlab code for convolution of two signals without Mathlab code AM modulation; mathlab code QPSK modulation; mathlab code Fourier series of rectangular wave; mathlab code HDB3; Donate a Car makes donating a vehicle simple for b PAST CONTINUOUS TENSE. The Iterative Solutions Coded Modulation Library (ISCML) is an open source toolbox for simulating capacity approaching codes in Matlab. Qpsk modulation and demodulation matlab code This post is a part of the book: Can anybody please help me with that, Please guy's, my email id is onkarvpatil15 gmail. The Bit Generation subsystem uses a MATLAB workspace variable as the payload of a frame, as shown in the figure below. MIMO OFDM using QPSK modulation matlab code Search and download MIMO OFDM using QPSK modulation matlab code open source project / source codes from CodeForge. The transmitter includes the Bit Generation subsystem, the QPSK Modulator block, and the Raised Cosine Transmit Filter block. Click on Qpsk modulation and demodulation matlab code Tags link and type a new tag. The BER is then calculated by comparing the generated bits to the received bits:. Matlab codes. This gray scale image is first converted into a black and white image for processing. FSK USING MATLAB CODE. These signals are then streamed from target to Simulink via the ad9361 block. Theoretical expression is 2*p-p^2, where p is BER for BPSK modulation. This model shows how to use the Universal Software Radio Peripheral® (USRP®) device with Simulink® to implement a QPSK receiver. Can I receive this matlab code? Kylie Batt Says:. The red line is my QPSK BER curve, and the blue/lower curve is the theoretical curve. or can u give u ur personal email address plz so tht i would contact wid u if i feel some problem during doing the code. C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™. hi; i have simulated a general ofdm system but i am not having correct results. We will first load our audio signal. I am trying to generate a qpsk signal. My deliverables: I delivered a tool which accepts the design parameters, and automatically generates Matlab-model and cycle accurate c-codes of the required A-SRC block. Start the QPSK Transmitter with ADALM-PLUTO Radio example in one MATLAB session and then start the receiver script in another MATLAB session. Mo deling of QPSK transmitter and receiv er using MA TLAB y ChangGene W oo SungW ook Jung and Hw anMok Jung A bstr act This rep ort describ es fundamen tals of QPSK. The following Matlab project contains the source code and Matlab examples used for ofdm with qpsk. Modulation is achieved by varying the phase of the basis functions depending on the message symbols. this blog about digital communication, how to simulate code matlab for BPSK, QPSK and 8 QAM, then apply it to Rectangular pulse shaping (RPS) then simulate code matlab for Square Root Raised Cosine (SQRC) filter as pulse shaping filter and matched filter, and apply it to the system, and we found minimum number of coefficient that the loss did not exceed 0. In this example, the transmit and receive FPGA implementation of a QPSK system are combined into one HDL IP core and implemented on the Zynq programmable logic (PL). QAM Theoretical BER in AWGN December 8, 2011 BER Performance , LTE , WiMAX 4G , AWGN , BER , LTE , QAM , QPSK , WiMAX John (YA) Quadrature Amplitude Modulation (QAM) is an important modulation scheme as it allows for higher data rates and spectral efficiencies. Abstract: verilog code for ofdm transmitter digital IIR Filter VHDL code fir filter coding for gui in matlab digital IIR Filter verilog code qpsk modulation VHDL CODE vhdl code for ofdm transmitter vhdl code for ofdm qpsk demapper VHDL CODE turbo codes qam system matlab code. The SDR device in this model will continuously transmit indexed 'Hello world' messages that are QPSK modulated onto a carrier with a specified center frequency. QPSK Transmitter. BPSK-Binary Phase Shift Keying. Real-Time Digital Signal Processing from MATLAB to C with the TMS320C6x DSPs. average ES/N0). THEORY:- Quadrature Phase Shift Keying (QPSK) is the digital modulation technique. Figure 4: Main window of the MATLAB application for the DVB-SH simulation. this blog about digital communication, how to simulate code matlab for BPSK, QPSK and 8 QAM, then apply it to Rectangular pulse shaping (RPS) then simulate code matlab for Square Root Raised Cosine (SQRC) filter as pulse shaping filter and matched filter, and apply it to the system, and we found minimum number of coefficient that the loss did not exceed 0. Choose a web site to get translated content where available and see local events and offers. have i used correct formulas in this code? i mean does RAYLEIGHCHAN command hold for it? do i need to equalize the receiver signal? if so then how and at what stage? and have i used right command for theoritical BER of OFDM in Rayleigh channel?. MATLAB CODE FOR AMPLITUDE MODULATION; MATLAB CODE FOR FM MODULATION; MATLAB CODE FOR QPSK MODULATION TECHNIQUE; MATLAB CODE FOR ASK,FSK & PSK; Differences Between Gprs, Edge, 3g, Hsdpa, Hspa+ A Explian about Cognitive Radio Networks? what is MIMO? HOW TO INSTALL MATLAB SOFTWARE? WHAT IS OFDM? Analysis Power Allocation in Cognitive Radio Netwo. C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™. This page describes QPSK modulation basics or Quadrature Phase Shift Keying modulation. The transmitter includes the Bit Generation subsystem, the QPSK Modulator block, and the Raised Cosine Transmit Filter block. After the input is given press "ENTER" key, you will get output matlab image as below. Now two symbols per bit can be transmitted. With four phases, QPSK can encode two bits per symbol. 1) In-phase component, 2) Quadrature phase, and 3) Composite of both. The symbols are transmitted using Quadrature Phase Shift Keying (QPSK) 4-QAM. What can I change in my code below to make the results that of qpsk. binary data source,data mapping,IFFT,CP insertion. There is a helper function to make this easy as long as Vivado is installed in a default location:. MATLAB Code for QPSK Modulation and Demodulation – File Exchange – MATLAB Central. QPSK (Quadrature Phase Shift Keying) is a phase modulation algorithm. After that the QPSK demodulator has been developed using MATLAB tool in order to verify the functionality of the modulator. gives a PSK modulated signal. Then, the second stage will be the implementation of QPSK using USRP Hardware. Catalog Datasheet MFG & Type PDF Document Tags; 2001 - GSM 900 simulink matlab. In this example, the transmit and receive FPGA implementation of a QPSK system are combined into one HDL IP core and implemented on the Zynq programmable logic (PL). The HDL Optimized QPSK Transmitter example shows how Simulink blocks that support HDL code generation can be used to implement the baseband processing of a digital communications transmitter. This model shows how to use the Universal Software Radio Peripheral® (USRP®) device with Simulink® to implement a QPSK receiver. Frequency-shift keying (FSK) is a frequency modulation scheme in which digital information is transmitted. + Post New Thread. From hexa, the data will plot the graph. Explore Simple MATLAB Projects, VLSI Projects Topics, IEEE MATLAB Minor and Major Project Topics or Ideas, VHDL Based Research Mini Projects, Latest Synopsis, Abstract, Base Papers, Source Code, Thesis Ideas, PhD Dissertation for Electronics Science Students ECE, Reports in PDF, DOC and PPT for Final Year Engineering, Diploma, BSc, MSc, BTech and MTech Students for the year 2015 and 2016. The task is to plot two diagrams that show the I/Q component for each modulation scheme : BPSK, QPSK, 16 QAM, and MSK for only ONE data set which will be after the modulation, and after adding the white Gaussian noise. Work on a wireless link of QPSK including the transmitter with PA, LNA, down-converter and receiver. C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™. we have discussed how to implement an equalizer for a bursty QPSK signal. This section of MATLAB source code covers OFDM transmitter and OFDM receiver basic chain coded in matlab. Making a possible to send the different four every symbol. R (site here) is a great open-source environment for statistical analysis. Edition 3rd Edition. If you find any mistake in terms of accuracy, it is also very highly likely be my fault. This object demodulates the input signal using the quadrature phase shift keying (QPSK) method. THIS COURSE HAS BEEN DONE IN MATLAB. The receiver addresses practical issues in wireless communications, e. BPSK QPSK 16QAM 64QAM MATLAB source code. Brie y explain the procedure (what you did in the lab) 2. carrier frequency and phase offset, timing offset and frame synchronization. A set of random QPSK symbols can be created by generating an array of random integer numbers in 1. Create scripts with code, output, and formatted text in a single executable document. Then we will use quantization, QPSK modulation, QPSK demodulation and dequantization. The VHDL code is designed to use the LLR values in the LUTs by applying bi-linear interpolation to correctly determine the LLR value. Learn more about signal processing, communication, matlab compiler is there any matlab code which can be used to generate the. This section of MATLAB source code covers OFDM transmitter and OFDM receiver basic chain coded in matlab. It shows how to model several parts of the QPSK system such as modulation, frequency and phase recovery, timing recovery, and frame synchronization. This post is a part of the ebook : Digital Modulations using Matlab: build simulation models from scratch - by Mathuranathan Viswanathan In the previous article we saw about how QPSK modulation and demodulation can be done. Based on your location, we recommend that you select:. This section of MATLAB source code covers BPSK,QPSK,16QAM and 64QAM modulation or data mapping matlab code. QPSK modulation system with recover loops. I have to hand the work soon. The following Matlab project contains the source code and Matlab examples used for ofdm with qpsk. FSK USING MATLAB CODE. This post is a part of the ebook : Digital Modulations using Matlab: build simulation models from scratch - by Mathuranathan Viswanathan In the previous article we saw about how QPSK modulation and demodulation can be done. ABSTRAK Tulisan ini memberikan gambaran tentang tahapan proses yang terjadi pada sistem modulasi Orthogonal Frequency Division Multiplexing (OFDM) menggunakan teknik Quadrature Phase Shift Keying (QPSK) menggunakan program aplikasi MatLab. This page describes QPSK modulation basics or Quadrature Phase Shift Keying modulation. Can anybody please send the MATLAB code for Probability of missed detection vs Threshold and SNR under different fading channels. Define parameters. With four phases, QPSK can encode two bits per symbol. Bpsk Matlab Code - Free download as Word Doc (. QPSK Modulation-Quadrature Phase Shift Keying modulation. MATLAB code for Amplitude modulation (AM) with modulation index Gallery of Electronic Circuits and projects, providing lot of DIY circuit diagrams, Robotics & Microcontroller Projects, Electronic development tools. Examples are highly readable MATLAB code files that show you how to solve problems or accomplish tasks such as curve fitting, plotting, and image processing. RF215 transmission time on MR-O-QPSK is much slower then expected;. Download FSKModulation rar file containing matlab file>>. This page covers modulation or mapping of binary data based on modulation type bpsk,qpsk,16qam and 64qam. Code for PWM (Pulse Width Modulation) generation in MATLAB Gallery of Electronic Circuits and projects, providing lot of DIY circuit diagrams, Robotics & Microcontroller Projects, Electronic development tools. this blog about digital communication, how to simulate code matlab for BPSK, QPSK and 8 QAM, then apply it to Rectangular pulse shaping (RPS) then simulate code matlab for Square Root Raised Cosine (SQRC) filter as pulse shaping filter and matched filter, and apply it to the system, and we found minimum number of coefficient that the loss did not exceed 0. Design of 4 Bit QPSK and 256 Bit QAM Using MATLAB Poorva Mishra1, Shashank Mane2 1,2 (Electronics and communication, SBITM Betul, RGPV University Bhopal, India). That is why the BER curved for QPSK and BPSK are identical. carrier frequency and phase offset, timing offset and frame synchronization. Search for jobs related to Matlab code qpsk modulation demodulation or hire on the world's largest freelancing marketplace with 15m+ jobs. The task is to plot two diagrams that show the I/Q component for each modulation scheme : BPSK, QPSK, 16 QAM, and MSK for only ONE data set which will be after the modulation, and after adding the white Gaussian noise. The input must be a complex signal. It shows how to model several parts of the QPSK system such as modulation, frequency and phase recovery, timing recovery, and frame synchronization. However, the simulated and theoretical graph are very different. Now it is time to plot the simulation results in Matlab and compare with theory using the Matlab code below. implemented in software using MATLAB. Structure of the Example. QPSK-using-MATLAB. This object modulates the input signal using the quadrature phase shift keying (QPSK) method. Thank you very much. They have designed the system using VHDL codes in Xilinx & analog filter simulation in Matlab. Quadrature Phase Shift Keying (QPSK) is one of the most popular digital modulation techniques. The BER is then calculated by comparing the generated bits to the received bits:. as far as i know it uses two qpsk is. Then we will use quantization, QPSK modulation, QPSK demodulation and dequantization. 1 Introduction The Orthogonal Frequency Division Multiplexing (OFDM) digital communication technique has been attracting a great concern of researchers all over the world, due to its unique characteristics. I have followed the instructions to download and build the firmware but i am completely lost about how to go from there. and provide input as follows. qpsk matlab codes - Matlab code for rician fading channel - DVB-S2 LDPC Performance - Adaptive Modulation and Coding(AMC)in Matlab - how to create user defined block in OPTSIM - need a model of PCCC turbo encoder/ decoder for QPSK - Does any one have. I have code for the generation of a bpsk signal and I want a similar one for qpsk. Gray codes can be applied to higher-order modulations, as shown in this Gray-coded QPSK constellation. Luckily, it is pretty easy to run R code from Matlab. I have made Matlab and C program for BPSK with Sinc Pulse shaping with and without Channel at noisy environment. Then we will use quantization, QPSK modulation, QPSK demodulation and dequantization. A song is a combination of multiple signal( voice+ musical instruments) with a wide frequency range so this simple matched filter code will not provide you reliable results for finding out similarity between two songs. I need to do the QPSK modualtion in MATLAB but don't really know how to !! Could anyone help me a bit? Help to make use of an. In this example, FMCOMMS3 is used as RF front-end, which captures the modulated QPSK signals over the air. March 3, 2013 by prabhath6. Constellation Diagram of QPSK also uses both an in-phase carrier and quadrature [7]. QPSK MATLAB SIMULATION A simple MATLAB code was implemented to simulate the basic working of the modulator and the demodulator. The following Matlab project contains the source code and Matlab examples used for matlab code for qpsk modulation and demodulation. We will use MatLab 7. © 2001, Cisco Systems, Inc. You either need to delete or modify that code. 11g matlab code 16 QAM modulation matlab code with noise baseband QPSK matlab code Source code for pulse width modulation in matlab: 2012 - 5989-1121EN. IMPLEMENTING QPSK USING MATLAB Firstly an integer generator is used to generate random uniformly distributed integer in the range [0, M-1], where m is the M-ary number (Fig 7). ECG MATLAB code Simulation m file ; MATLAB Simulation Program to implement BPSK system ; MATLAB Simulation Program to implement QPSK system ; MATLAB code for Discrete Fourier transform (DFT) MATLAB Simulation of BCH code and decode ; MATLAB Simulation Program to implement TRELLIS CODE m file ; MATLAB Simulation of Perceptron Learning. Hello, You should search on Mathworks community before posting on Quora, the community is meant for this purpose only you just create a student account on Mathworks then you can post your own questions on it and as it is the community is so develo. Thousands of code examples are available online and within MATLAB to get you started with your work project or homework assignment. The SDR device in this model will continuously transmit indexed 'Hello world' messages that are QPSK modulated onto a carrier with a specified center frequency. QPSK Matlab Code. The Bit Generation subsystem uses a MATLAB workspace variable as the payload of a frame, as shown in the figure below. I haven't made any effort for effiecient code. 4 and mapping these numbers to complex symbols:. After my friend submitted his code, I sent him my solution, which is the content of this File Exchange submission. The theoretical description of QPSK modulation and demodulation are available in the book of "communication system " by SIMON HAYKIN. Symbol Timing Recovery for QPSK (digital modulations) June 17, 2019 November 18, 2013 by Mathuranathan also MATLAB codes are in it or attached by it, please. If you are generating HDL code you will be to add Vivado to your MATLAB path. QPSK MODULATOR EQUATION Principle of QPSK modulation – In Quadrature Phase Shift Keying (QPSK), the information is send by changing the phase of the carrier wave. View Pranjali Chumbhale’s profile on LinkedIn, the world's largest professional community. (21 votes, average: 4. Discover Live Editor. Can anybody please send the MATLAB code for Probability of missed detection vs Threshold and SNR under different fading channels. QPSK MODULATOR EQUATION Principle of QPSK modulation - In Quadrature Phase Shift Keying (QPSK), the information is send by changing the phase of the carrier wave. I am trying to generate a qpsk signal. Notice the use of the colon (:) operator in MATLAB to select a portion of the vector. MATLAB CODE FOR AMPLITUDE MODULATION; MATLAB CODE FOR FM MODULATION; MATLAB CODE FOR QPSK MODULATION TECHNIQUE; MATLAB CODE FOR ASK,FSK & PSK; Differences Between Gprs, Edge, 3g, Hsdpa, Hspa+ A Explian about Cognitive Radio Networks? what is MIMO? HOW TO INSTALL MATLAB SOFTWARE? WHAT IS OFDM? Analysis Power Allocation in Cognitive Radio Netwo. Matlab code to generate QPSK waveform for the given binary sequence. Performance Evaluation Of BPSK And QPSK Modulation With LDPC Codes in Matlab. A song is a combination of multiple signal( voice+ musical instruments) with a wide frequency range so this simple matched filter code will not provide you reliable results for finding out similarity between two songs. The Compute Delay subsystem correlates the data input with the QPSK modulated Barker code, and uses the index of the peak amplitude to find the delay. 5 db ,then we evaluate the coded. QPSK uses four points on the constellation diagram, equally spaced around a circle. The code is based on the fundamental. In this video we look at the performance analysis of various digital modulation schemes namely M-PSK's , M-QAM's , DPSK and DQAM by plotting BER vs Eb/N0 in Matlab. QAM becomes QPSK: The QAM modulator is so named because, in analog applications, the messages do in fact vary the amplitude of each of the DSBSC signals. Based on your location, we recommend that you select:. TurboEqualization Matlab programs for turbo equalization. Click on that callback to see the code. Results 1 to 2 of 2 MATLAB Code of Single Sided Band Modulation and Demodulation. qpsk matlab codes - Matlab code for rician fading channel - DVB-S2 LDPC Performance - Adaptive Modulation and Coding(AMC)in Matlab - how to create user defined block in OPTSIM - need a model of PCCC turbo encoder/ decoder for QPSK - Does any one have. Quadrature Phase Shift Keying (QPSK)/BPSK and QPSK/QPSK Waveform (Digita Modulation Techniques) [HD] - Duration: 11:02. It uses four points on the constellation diagram, equispaced around a circle. I want to Write a code in Matlab which creates a constant envelop PSK signal waveform that generate for M=8 (M stands for modulation), so that amplitude of the signal can reach up to sqrt(2). 4 and mapping these numbers to complex symbols:. 5 db ,then we evaluate the coded. Engineering Made Easy 59,096 views. This section of MATLAB source code covers BPSK,QPSK,16QAM and 64QAM modulation or data mapping matlab code. Generating QPSK symbols for adaptive filtering. Matlab code to generate QPSK waveform for the given binary sequence. Modulation is achieved by varying the phase of the basis functions depending on the message symbols. or can u give u ur personal email address plz so tht i would contact wid u if i feel some problem during doing the code. QPSK modulation is also performed on MATLAB tool, which gives three types of waveforms. The example uses some key algorithms in MATLAB, emphasizing textual algorithm expression over graphical algorithm expression. doc), PDF File (. The code of QPSK modulation and demodulation technique has been developed according to the theory. written in MATLAB. The top-level structure of the model is shown in the following figure. This object demodulates the input signal using the quadrature phase shift keying (QPSK) method. C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™. Connect two ADALM-PLUTO Radios to the computer. Graph is displayed in figure 3. Discover Live Editor. Thank you very much. Which includes a USRP receiver block, a QPSK Receiver subsystem and a BER Display blocks. The power of the spread QPSK data stream can be calculated using the following MATLAB command: Solution: The power of the spread QPSK data stream is calculated using the command in the line number 23 of the appended MATLAB code. Engineering Made Easy 55,919 views 11:02. fm modulation and demodulation with digital pll pdf, qpsk modulator in hardware, matlab code for pm qpsk modulation, matlab code for dpsk modulation and demodulation, modulation techniques am fm fsk psk qpsk qam 16qam ppt telugu language, mc1496 modulator qpsk, matlab code for qpsk modulation and demodulation free download,.


text:
Curved momentum spaces from quantum groups with cosmological constant

2017, August 8
Physics Letters B, vol. 773 (2017) 47

We bring the concept that quantum symmetries describe theories with nontrivial momentum space properties one step further, looking at quantum symmetries of spacetime in presence of a nonvanishing cosmological constant $\Lambda$. In particular, the momentum space associated to the $\kappa$-deformation of the de Sitter algebra in (1+1) and (2+1) dimensions is explicitly constructed as a dual Poisson-Lie group manifold parametrized by $\Lambda$. Such momentum space includes both the momenta associated to spacetime translations and the `hyperbolic’ momenta associated to boost transformations, and has the geometry of (half of) a de Sitter manifold. Known results for the momentum space of the $\kappa$-Poincaré algebra are smoothly recovered in the limit $\Lambda\to 0$, where hyperbolic momenta decouple from translational momenta. The approach here presented is general and can be applied to other quantum deformations of kinematical symmetries, including (3+1)-dimensional ones.

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text:
# In search of "strange" plant

SMeissne at AOL.COM SMeissne at AOL.COM
Fri Oct 16 22:40:10 EST 1998

There has been some discussion about finding a plant that could respond to
sound.

I wanted to first point out that responses to sound by biological systems have
been published in
the scientific literature.  Here are two examples, one at the subcellular
level and the
other on the whole plant level:

Pohl P., E. Rosenfeld, R. Millner- 1993-Effects of ultrasound on the steady-
state
transmembrane pH gradient and the permeability of acetic acid through bilayer
lipid
membranes- Biochem et Biophys Acta  1145:  279-283

Weinberger P., M. Measures- 1968-The effect of two audible sound frequencies
on the
germination and growth of a spring and winter wheat- Canadian J. of Botany 46:
1151-1158

I think that the Canadian Journal of Botany is a "reputable science journal".
article and am convinced by the data presented that a response to different
sound treatments could
be concluded.  Sadly this sort of good controled work has not been done in
other species, or under
under conditions.  This seems just the sort of thing that make for some fun
class experiments.
Several experiments could be done modeled on the methods used in the above
article.  I'd encourage
the observations in wheat or
other species.

Second:
One suggested plant to test for sensitivity to sound was Mimosa pudica, the
sensitive plant.
One thing that this plant displays in its response to stimuli is habituation.
This was demonstrated in
Mimosa pudica quite dramatically when some specimens became so used to being
buffetted by
typhoon winds that they simply did not respond any more.  This was reported in
the following
article:

Toriyama H- 1966-The behaviour of the sensitive plant in a typhoon-  The
botanical magazine  79:  427-428

So if you are going to test for response to sound be careful that the plant
has not habituated to the
stimulus.  And allow enough time between tests for it to recover fully.  For
more on habituation in
Mimosa pudica you might wish to look at the following:

Simons P- 1992-The action plant.  Movement and nervous behaviour in plants.
Blackwell Press, Cambridge.  323 pgs.  ISBN:  0-631-13899-4

Hope that helps,....
but really, aren't ALL plants somewhat strange??
;)

Scott T. Meissner

smeissne at aol.com

Aure Entuluva!

On 10/16/98 Ross Koning (koning at ecsu.ctstateu.edu) wrote:

\The suggestions about Mimosa pudica are on target...
\if the vibrations are of sufficient magnitude, the
\leaflets will fold.  Crank up the bass and volume
\and those plants will respond!

\As for the TV shows and Mr. Baker, well not all
\"science" is good science. Except for seismonasty
\in species like M. pudica, there are no articles
\on sound perception or musical tastes of plants
\in reputable science journals.  Some trade books
\and even some educational texts and software have
\given projects on musical appreciation by plants
\more respectability that is deserved.  It is a good
\example of "not everything you read in print is
\to be believed."

\If any of you are teachers out there on this
\mail-list, PLEASE do not direct students toward
\class projects or science fair studies on the
\effect of music on plants.  There is so much more
\interesting to test...and much of it really works!
\David Hershey has a good book on Plant Biology
\Science Projects (J Wiley)...it contains much

\ross

At 8:38 AM -0400 10/15/98, Jeremy Lee iment
>involving plants and music.  The basis of the experiment was to have several
>groups of the same plant (forget which one, but I don't think it mattered
>to the
>experiment) and play different types of music to each.  Other than the music,
>each plant group had identical soil, water, light, and fertilizer.
>
>As I recall, the plant group that was played Rock 'N Roll did the best.  The
>group that had no music at all (the control group) did worst.  I can't
>remember
>if Jazz beat Classical....
>
>Anyway, I don't think that this is exactly what you're looking for (you
>want an
>"immediate" plant reaction, not "long-term", right?), but it does show plants
>are sensative to sound vibrations.
>
>Cheers,
>Jeremy
>
>Derek H. wrote:
>
>> I am searching for any type of plant that is sensitive to sound waves. I am
>> doing science experiments to demonstrate sound vibrations.
>>
>> I don't know if such a plant exists...I am hoping it does.
>>
>> The ideal plant would be one that would pick up sensitive sounds (much like
>> a microphone), and vibrate the sounds with a delayed reaction.
>>
>> Any and all help/comments are greatly appreciated.
>>
>> Thanks
>> Derek H.
>> derekh at aloha.net


text:
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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeJul 27th 2016

edits and edit discussion on the entry conformal compactification is going on here

• CommentRowNumber2.
• CommentAuthorDavidRoberts
• CommentTimeJul 27th 2016

Thanks. It seems that’s a better place to engage Willie than here, but I may copy over any insights if they are warranted.

• CommentRowNumber3.
• CommentAuthorDavidRoberts
• CommentTimeJul 27th 2016

I added that the Klein quadric conformally compactifies complexified $\mathbb{R}^{3,1}$, with a sketchy reference as really I have to go offline now. (Lecturing in 8.5 hours and need to sleep first…)

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJul 27th 2016

I have added the brief remark that the example of complexified Minkowski spacetimes conformally compactifying to the Klein quadric is key in the twistor correspondence.

And thereby this discussion connects to the solitonic M5-dicussion here. Is that the reason why you are looking into conformal compactification at the moment? Still building that explicit String 2-bundle for Christian?

• CommentRowNumber5.
• CommentAuthorDavidRoberts
• CommentTimeJul 28th 2016

I added the equation, and the reference to Klein’s thesis.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeJul 28th 2016

• CommentRowNumber7.
• CommentAuthorDavidRoberts
• CommentTimeJul 28th 2016

Whoops, thanks.

• CommentRowNumber8.
• CommentAuthorDavidRoberts
• CommentTimeJul 29th 2016

Added link to Klein quadric to published version of Klein’s thesis (is Springer hiding results from Google? I could only get it by searching the journal website itself, once I discovered where it was published) in German, and a link to a pdf of the English translation, not sure where that pdf is from, searching its title gives only that one result.

• CommentRowNumber9.
• CommentAuthorDavidRoberts
• CommentTimeAug 2nd 2016

I added to conformal compactification the actual formula for the embedding $\mathbb{R}^{n,1}\hookrightarrow \mathbb{R}^{n+1,2}\setminus \{0\}$. In fact this is a diffeomorphism with the intersection of the real points of the Klein quadric with a particular hyperplane (the original Minkowski space times one of the null planes in the extra $\mathbb{R}^{1,1}$ factor – there’s another disjoint embedding using the other null plane). I need to calculate the correct normalisation factor that means this will land in $S^n\times S^1$ instead, but not now.

• CommentRowNumber10.
• CommentAuthorDavidRoberts
• CommentTimeAug 2nd 2016
• (edited Aug 2nd 2016)

Well, as a first stab, I think with the normalising factor the map $\mathbb{R}^{n,1} \to S^n\times S^1 \subset \mathbb{R}^{n,1}\times\mathbb{R}^{1,1}$ looks like

$\frac{1}{\sqrt{q(x,t)^2 + 2(|x|^2+t^2)+1}}(2x,2t,1-q(x,t),-1-q(x,t))$

in the notation of conformal compactification.


text:
• # Last digit of 13-digit ISBN forced to second line in pull-down list of order rec

• Article Type: General
• Product: Aleph
• Product Version: 18.01

Description:
The display of ISBN numbers in the pull-down list of the order record can't display the last digit of 13-digit ISBN numbers on the same line. The last digit shows at the beginning of the next line. It is even worse when there is something else after the number.

I have attached 2 snapshots to show the scenario. Is this something that could be fixed easily locally or is it something that Ex Libris would have to fix?

Resolution:
The percentage of the 2 columns of the expand list is defined in the abc01 pc_tab_col.eng, entry PC_TABLE. We distribute it as 30/70:

PC_TABLE L Code 01 030 01 C01 Expand Table Code
PC_TABLE L Info 02 070 02 C02 Expand Table Text

Changing it to 35/65:

PC_TABLE L Code 01 035 01 C01 Expand Table Code
PC_TABLE L Info 02 065 02 C02 Expand Table Text

and restarting the pc_server lets the entire 13-digit ISBN be displayed on a single line.

Note that this affects all the multi-field dropdowns in the GUI.

• Article last edited: 10/8/2013


text:
## Section6.3Rational Exponents

### Subsection6.3.1Powers of the Form $$a^{m/n}$$

In the last section, we considered powers of the form $$a^{1/n}\text{,}$$ such as $$x^{1/3}$$ and $$x^{-1/4}\text{,}$$ and saw that $$a^{1/n}$$ is equivalent to the root $$\sqrt[n]{a}\text{.}$$ What about other fractional exponents? What meaning can we attach to a power of the form $$a^{m /n}\text{?}$$

Consider the power $$x^{3/2}\text{.}$$ Notice that the exponent $$\dfrac{3}{2}= 3(\dfrac{1}{2})\text{,}$$ and thus by the third law of exponents, we can write

\begin{equation*} (x^{1/2})^3 = x^{(1/2)^3} = x^{3/2} \end{equation*}

In other words, we can compute $$x^{3/2}$$ by first taking the square root of $$x$$ and then cubing the result. For example,

\begin{align*} 100^{3/2} \amp = (\alert{100^{1/2}})^3 \amp\amp \blert{\text{Take the square root of 100.}}\\ \amp= \alert{10^3} = 1000 \amp\amp \blert{\text{Cube the result.}} \end{align*}

True or false.

1. When we raise a power to a power, we multiply the exponents; in symbols

\begin{equation*} \begin{gathered} (a^m)^n = a^{mn} \end{gathered} \end{equation*}

• True

• False

2. $$\dfrac{4}{3} = 4\left(\dfrac{1}{3}\right)\text{,}$$ and in general $$\dfrac{p}{q} = p\left(\dfrac{1}{q}\right)\text{.}$$

• True

• False

3. To compute $$(25^{1/2})^3\text{,}$$ we first take the square root of 25, then cube the result.

• True

• False

4. The notation $$16^{3/4}$$ means to multipy 16 by $$\dfrac{3}{4}\text{.}$$

• True

• False

$$\text{True}$$

$$\text{True}$$

$$\text{True}$$

$$\text{False}$$

Solution.
1. True

2. True

3. True

4. False

A fractional exponent represents a power and a root. The denominator of the exponent is the root, and the numerator of the exponent is the power. We will define fractional powers only when the base is a positive number.

#### Rational Exponents.

\begin{equation*} \blert{a^{m/n} = (a^{1/n})^m = (a^m)^{1/n},~~~~a \gt 0\text,~~ n \ne 0} \end{equation*}

To compute $$a^{m/n}\text{,}$$ we can compute the $$n$$th root first, or the $$m$$th power, whichever is easier. For example,

\begin{equation*} 8^{2/3} = \left(8^{1/3}\right)^2 = 2^2 = 4 \end{equation*}

or

\begin{equation*} 8^{2/3} = \left(8^2\right)^{1/3} = 64^{1/3} = 4 \end{equation*}
1. $$\displaystyle 81^{3/4} = \left(81^{1/4}\right)^3 = 3^3 = 27$$

2. $$\displaystyle -27^{5/3} = -\left(27^{1/3}\right)^5 = -3^5 = -243$$

3. $$\displaystyle 27^{-2/3} = \frac{1}{\left(27^{1/3}\right)^2} = \frac{1}{3^2}= \frac{1}{9}$$

4. $$\displaystyle 5^{3/2} = \left(5^{1/2}\right)^3 \approx (2.236)^3 \approx 11.180$$

#### Note6.3.3.

You can verify all the calculations in Example 6.3.2 on your calculator. For example, to evaluate $$81^{3/4}\text{,}$$ key in

81 ^ ( 3 ÷ 4 ) ENTER

or simply

81 ^ 0.75 ENTER

#### Caution6.3.4.

When computing $$81^{3/4}$$ on a calculator, do not forget the parentheses around the exponent, $$\dfrac{3}{4}\text{.}$$ The keying sequence

$$\qquad\qquad 81$$ ^ $$3$$ ÷ ENTER gives us the value of $$\dfrac{81^3}{4}\text{,}$$ or $$132,860.25\text{.}$$ The parentheses tell the calculator to include all of the quotient $$3 \div 4$$ in the exponent, not just the 3.

Evaluate each power.

1. $$32^{-3/5}=$$

2. $$-81^{1.25}=$$

$${\textstyle\frac{1}{8}}$$

$$-243$$

Solution.
1. $$\displaystyle \dfrac{1}{8}$$

2. $$\displaystyle -243$$

### Subsection6.3.2Power Functions

Perhaps the single most useful piece of information a scientist can have about an animal is its metabolic rate. The metabolic rate is the amount of energy the animal uses per unit of time for its usual activities, including locomotion, growth, and reproduction.

The basal metabolic rate, or BMR, sometimes called the resting metabolic rate, is the minimum amount of energy the animal can expend in order to survive.

A revised form of Kleiber's rule states that the basal metabolic rate for many groups of animals is given by

\begin{equation*} B(m) = 70m^{0.75} \end{equation*}

where $$m$$ is the mass of the animal in kilograms and the BMR is measured in kilocalories per day.

1. Calculate the BMR for various animals whose masses are given in the table.

 Animal Bat Squirrel Raccoon Lynx Human Moose Rhinoceros Weight (kg) $$0.1$$ $$0.6$$ $$8$$ $$30$$ $$70$$ $$360$$ $$3500$$ BMR (kcal/day)
2. Sketch a graph of Kleiber’s rule for $$0 \lt m \le 400\text{.}$$

3. Do larger species eat more or less, relative to their body mass, than smaller ones?

Solution.
1. We evaluate the function for the values of $$m$$ given. For example, to calculate the BMR of a bat, we compute

\begin{equation*} B(0.1) = 70(0.1)^{0.75} = 12.4 \end{equation*}

A bat expends, and hence must consume, at least 12 kilocalories per day. We evaluate the function to complete the rest of the table. The values of BMR are rounded to the nearest whole number.

 Animal Bat Squirrel Raccoon Lynx Human Moose Rhinoceros Weight (kg) $$0.1$$ $$0.6$$ $$8$$ $$30$$ $$70$$ $$360$$ $$3500$$ BMR (kcal/day) $$12$$ $$48$$ $$333$$ $$897$$ $$1694$$ $$5785$$ $$31,853$$
2. We plot the data from the table to obtain the graph below.

3. If energy consumption were proportional to body weight, the graph would be a straight line. But this graph is concave down, or bends downward. Larger species eat less than smaller ones, relative to their body weight. For example, a moose weighs 600 times as much as a squirrel, but its energy requirement is only 121 times the squirrel's.

True or false.

1. The graph of $$f(x)=70x^{3/4}$$ is concave down.

• True

• False

2. Energy consumption is not directly proportional to body weight.

• True

• False

3. An animal twice as heavy as a squirrel uses twice as much energy as a squirrel.

• True

• False

4. The graph of $$f(x)=70x^{3/4}$$ passes through the origin.

• True

• False

$$\text{True}$$

$$\text{True}$$

$$\text{False}$$

$$\text{True}$$

Solution.
1. True

2. True

3. False

4. True

1. Complete the table of values for the function $$f (x) = x^{-3/4}\text{.}$$

 $$x$$ $$0.1$$ $$0.2$$ $$0.5$$ $$1$$ $$f (x)$$
 $$x$$ $$2$$ $$5$$ $$8$$ $$10$$ $$f (x)$$
2. Sketch the graph of the function.

$$5.62341$$

$$3.3437$$

$$1.68179$$

$$1$$

$$0.594604$$

$$0.29907$$

$$0.210224$$

$$0.177828$$

Solution.
1.  $$x$$ $$0.1$$ $$0.2$$ $$0.5$$ $$1$$ $$f (x)$$ $$5.623$$ $$3.344$$ $$1.682$$ $$1$$
 $$x$$ $$2$$ $$5$$ $$8$$ $$10$$ $$f (x)$$ $$0.595$$ $$0.299$$ $$0.210$$ $$0.178$$
1. A graph is below.

Because $$a^{1/n} = \sqrt[n]{a}\text{,}$$ we can write any power with a fractional exponent in radical form as follows.

\begin{equation*} \blert{a^{m/n} = \sqrt[n]{a^m} =\left( \sqrt[n]{a}\right)^m} \end{equation*}
1. $$\displaystyle 125^{4/3} = \sqrt[3]{125^4} \text{ or } \left(\sqrt[3]{125}\right)^4$$

2. $$\displaystyle x^{0.4} = x^{2/5} = \sqrt[5]{x^2}$$

3. $$\displaystyle 6w^{-3/4} = \dfrac{6}{\sqrt[4]{w^3}}$$

Write each expression in radical notation.

1. $$5t^{1.25}$$

• $$\displaystyle \sqrt[4]{5t^{5}}$$

• $$\displaystyle \sqrt[4]{(5t)^{5}}$$

• $$\displaystyle 5\sqrt[4]{t^{5}}$$

• $$\displaystyle 5\sqrt{(t/4)^{5}}$$

2. $$3m^{-5/3}$$

• $$\displaystyle \dfrac{3}{\sqrt[3]{m^{5}}}$$

• $$\displaystyle \dfrac{1}{\sqrt[3]{3m^{5}}}$$

• $$\displaystyle \dfrac{1}{3\sqrt[3]{m^{5}}}$$

• $$\displaystyle -3 \sqrt[3]{m^{5}}$$

$$\text{Choice 3}$$

$$\text{Choice 1}$$

Solution.
1. $$\displaystyle 5\sqrt[4]{t^5}$$

2. $$\displaystyle \dfrac{3}{\sqrt[3]{m^5} }$$

Usually, we will want to convert from radical notation to fractional exponents, since exponential notation is easier to use.

1. $$\displaystyle \sqrt{x^5} = x^{5/2}$$

2. $$\displaystyle 5 \sqrt[4]{p^3} = 5p^{3/4}$$

3. $$\displaystyle \dfrac{3}{\sqrt[5]{t^2}}= 3t^{-2/5}$$

4. $$\displaystyle \sqrt[3]{2y^2} = \left(2y^2\right)^{1/3} = 2^{1/3} y^{2/3}$$

Convert to exponential notation.

1. $$\sqrt[3]{6w^2}=$$

2. $$\sqrt[4]{\dfrac{v^3}{s^5}}=$$

$$1.81712w^{\left({\textstyle\frac{2}{3}}\right)}$$

$$v^{\left({\textstyle\frac{3}{4}}\right)}s^{\left(-{\textstyle\frac{5}{4}}\right)}$$

Solution.
1. $$\displaystyle 6^{1/3} w^{2/3}$$

2. $$\displaystyle v^{3/4} s^{-5/4}$$

True or false.

1. $$x^{3/5}$$ represents the cube root of $$x$$ to the fifth power.

• True

• False

2. We can simplify $$2x^{4/3}$$ as $$\sqrt[3]{2x^4}\text{.}$$

• True

• False

3. The notation $$a^{-1/4}$$ means $$-a^4\text{.}$$

• True

• False

4. We can simplify $$5b^{-3/2}$$ as $$\dfrac{1}{5b^{3/2}}\text{.}$$

• True

• False

$$\text{False}$$

$$\text{False}$$

$$\text{False}$$

$$\text{False}$$

Solution.
1. False

2. False

3. False

4. False

### Subsection6.3.4Operations with Rational Exponents

Powers with rational exponents—positive, negative, or zero—obey the laws of exponents, which we discussed in Section 6.1. You may want to review those laws before studying the following examples.

1. \begin{align*} \frac{7^{0.75}}{7^{0.5}}\amp= 7^{0.75-0.5} = 7^{0.25} \amp\amp \blert{\text{Apply the second law of exponents.}} \end{align*}
2. \begin{align*} v \cdot v^{-2/3}\amp= v^{1+(-2/3)} \amp\amp \blert{\text{Apply the first law of exponents.}}\\ \amp = v^{1/3} \end{align*}
3. \begin{align*} \left(x^8\right)^{0.5}\amp= x^{8(0.5))} = x^4 \amp\amp \blert{\text{Apply the third law of exponents.}} \end{align*}
4. \begin{align*} \frac{\left(5^{1/2}y^2\right)^2}{\left(5^{2/3} y\right)^3} \amp= \frac{5y^4}{5^2 y^3} \amp\amp \blert{\text{Apply the fourth law of exponents.}}\\ \amp = \frac{y^{4-3}}{5^{2-1}}=\frac{y}{5} \amp\amp \blert{\text{Apply the second law of exponents.}} \end{align*}

Simplify by applying the laws of exponents.

1. $$x^{1/3}\left(x + x^{2/3}\right)=$$

2. $$\dfrac{n^{9/4}}{4n^{3/4}}=$$

$$x^{\frac{4}{3}}+x$$

$$\frac{n^{\frac{3}{2}}}{4}$$

Solution.
1. $$\displaystyle x^{4/3}+x$$

2. $$\displaystyle \dfrac{n^{3/2}}{4}$$

### Subsection6.3.5Solving Equations

According to the third law of exponents, when we raise a power to another power, we multiply the exponents together. In particular, if the two exponents are reciprocals, then their product is $$1\text{.}$$ For example,

\begin{equation*} \left(x^{2/3}\right)^{3/2} = x^{(2/3) (3/2)} = x^1 = x \end{equation*}

This observation can help us to solve equations involving fractional exponents. For instance, to solve the equation

\begin{equation*} x^{2/3} = 4 \end{equation*}

we raise both sides of the equation to the reciprocal power, $$3/2\text{.}$$ This gives us

\begin{align*} \left(x^{2/3}\right)^{3/2} \amp = 4^{3/2} \\ x \amp = 8 \end{align*}

The solution is $$8\text{.}$$

Solve $$~~(2x + 1)^{3/4} = 27$$

Solution.

We raise both sides of the equation to the reciprocal power, $$\dfrac{4}{3}\text{.}$$

\begin{align*} \left[(2x + 1)^{3/4}\right]^{4/3} \amp= 27^{4/3} \amp\amp \blert{\text{Apply the third law of exponents.}}\\ 2x + 1 \amp = 81 \amp\amp \blert{\text{Solve as usual.}}\\ x \amp = 40 \end{align*}

Solve the equation $$3.2z^{0.6} - 9.7 = 8.7\text{.}$$ Round your answer to two decimal places.

Hint.

$$\blert{\text{Isolate the power.}}$$

$$\blert{\text{Raise both sides to the reciprocal power}}.$$

$$\left(\frac{18.4}{3.2}\right)^{\frac{1}{0.6}}$$

Solution.

$$18.45$$

True or false.

1. The first step in solving an equation with a fractional exponent is to isolate the power.

• True

• False

2. Then we raise both sides to the reciprocal of the exponent.

• True

• False

3. We can use the laws of exponents to simplify expressions involving fractional exponents.

• True

• False

4. The reciprocal of 0.6 is $$\dfrac{1}{0.6}\text{.}$$

• True

• False

$$\text{True}$$

$$\text{True}$$

$$\text{True}$$

$$\text{True}$$

Solution.
1. True

2. True

3. True

4. True

### Exercises6.3.6Problem Set 6.3

#### Warm Up

##### 1.

Combining powers and roots

1. Start with 8, square it, and then take the cube root of the result. That is:

\begin{equation*} \sqrt[3]{8^2} = \sqrt[3]{?}= \end{equation*}

Now start with 8, take the cube root, then square the result. That is:

\begin{equation*} (\sqrt[3]{8})^2 = (?)^2= \end{equation*}
2. Do you get the same answers for parts (a) and (b)? You should! Now try the same thing with some irrational numbers. Use your calculator, and round your answers to two decimal places.

\begin{align*} \sqrt{3^5} \amp = \amp \amp (\sqrt{3})^5 = \\ (\sqrt[3]{58})^4\amp = \amp \amp \sqrt[3]{58^4}= \end{align*}
3. Choose the most convenient order of operations to evaluate each root without using a calculator.

1. $$\displaystyle \sqrt[5]{32^3}$$

2. $$\displaystyle -\sqrt[3]{27^4}$$

1. 4; 4

2. 15.59; 15.59

3. $$\displaystyle 8;~-81$$

##### 2.

Using exponents

1. Simplify $$(\sqrt[3]{8})^2$$ using exponents as follows. Fill in the blanks with the correct exponents.

\begin{equation*} (\sqrt[3]{8})^2 = (8^{\fillinmath{XX}})^2 = 8^{\fillinmath{XX}} \end{equation*}
2. Use your calculator to compute $$8^{2/3}\text{.}$$ Don't forget to put parentheses around the exponent.

3. Approximate each power to the nearest thousandth.

1. $$\displaystyle 12^{5/6}$$

2. $$\displaystyle \sqrt[3]{6^4}$$

3. $$\displaystyle 37^{-2/3}$$

4. $$\displaystyle 4.7^{2.3}$$

##### 3.

Evaluate each root without using a calculator.

1. $$\displaystyle \sqrt[4]{16y^{12}}$$

2. $$\displaystyle \sqrt[5]{243x^{10}}$$

3. $$\displaystyle \sqrt[3]{8x^9y^{27}}$$

4. $$\displaystyle -\sqrt[4]{81a^8b^{12}}$$

5. $$\displaystyle \sqrt[3]{64x^6 y^{18}}$$

6. $$\displaystyle -\sqrt[5]{32x^{25}y^{5}}$$

1. $$\displaystyle 2y^3$$

2. $$\displaystyle 3x^2$$

3. $$\displaystyle 2x^2y^9$$

4. $$\displaystyle -3a^2b^3$$

5. $$\displaystyle 4x^2y^6$$

6. $$\displaystyle -2x^5y$$

##### 4.

Evaluate each power without using a calculator.

1. $$\displaystyle 81^{3/4}$$

2. $$\displaystyle 125^{2/3}$$

3. $$\displaystyle 625^{0.75}$$

4. $$\displaystyle 16^{-3/2}$$

5. $$\displaystyle 8^{-4/3}$$

6. $$\displaystyle 32^{-1.6}$$

#### Skills Practice

##### Exercise Group.

For Problems 5 and 6, write each power in radical form.

###### 5.
1. $$\displaystyle y^{3/4}$$

2. $$\displaystyle a^{-2/7}$$

3. $$\displaystyle (st)^{-3/5}$$

1. $$\displaystyle \sqrt[4]{y^3}$$

2. $$\displaystyle \dfrac{1}{\sqrt[7]{a^2}}$$

3. $$\displaystyle \dfrac{1}{\sqrt[5]{s^3t^3}}$$

###### 6.
1. $$\displaystyle 5y^{2/3}$$

2. $$\displaystyle 6w^{-1.5}$$

3. $$\displaystyle -3x^{0.4}y^{0.6}$$

##### Exercise Group.

For Problems 7 and 8, write each expression with fractional exponents.

###### 7.
1. $$\displaystyle \sqrt{y^3}$$

2. $$\displaystyle 6\sqrt[5]{(ab)^3}$$

3. $$\displaystyle \dfrac{-2n}{\sqrt[8]{q^{11}}}$$

1. $$\displaystyle y^{3/2}$$

2. $$\displaystyle 6a^{3/5}b^{3/5}$$

3. $$\displaystyle -2nq^{-11/8}$$

###### 8.
1. $$\displaystyle \sqrt[3]{ab^2}$$

2. $$\displaystyle \dfrac{5}{\sqrt[3]{y^2}}$$

3. $$\displaystyle \dfrac{S}{4\sqrt{VH^3}}$$

##### Exercise Group.

For Problems 9–14, simplify by applying the laws of exponents. Write your answers with positive exponents only.

###### 9.

$$4a^{6/5}a^{4/5}$$

$$4a^2$$

###### 10.

$$(-2m^{2/3})^4$$

###### 11.

$$\dfrac{8w^{9/4}}{2w^{3/4}}$$

$$4w^{3/2}$$

###### 12.

$$(-3u^{5/3}) (5u^{-2/3})$$

###### 13.

$$\dfrac{k^{3/4}}{2k}$$

$$\dfrac{1}{2k^{1/4}}$$

###### 14.

$$c^{-2/3}\left(\dfrac{2}{3}c^2 \right)$$

##### Exercise Group.

For Problems 15–20, solve. Round your answers to the nearest thousandth if necessary.

###### 15.

$$x^{2/3} - 1 = 15$$

$$x = 64$$

###### 16.

$$x^{-2/5} = 9$$

###### 17.

$$6-2.4x^{-5/4} = 8$$

$$x = 1.157$$

###### 18.

$$2(5.2 - x^{5/3}) = 1.4$$

###### 19.

$$\dfrac{2}{3}(2y+1)^{0.2} = 6$$

$$29.524$$

###### 20.

$$1.3w^{0.3} + 4.7 = 5.2$$

##### 21.

If $$f (x) = (3x - 4)^{3/2}\text{,}$$ find $$x$$ so that $$f (x) = 27\text{.}$$

$$\dfrac{13}{3}$$

##### 22.

If $$S(x) = 12x^{-5/4}\text{,}$$ find $$x$$ so that $$S(x) = 20\text{.}$$

##### Exercise Group.

For Problems 23–26, use the distributive law to find the product.

###### 23.

$$x^{1/3} (2x^{2/3} - x^{1/3})$$

$$2x-x^{2/3}$$

###### 24.

$$3y^{-3/8}\left(\dfrac{1}{4}y^{-1/4} + y^{3/4} \right)$$

###### 25.

$$(2x^{1/4} + 1) (x^{1/4} - 1)$$

$$2x^{1/2} - x^{1/4} - 1$$

###### 26.

$$(a^{3/4}-2)^2$$

##### Exercise Group.

For Problems 27–30, factor out the smallest power from each expression. Write your answers with positive exponents only.

###### 27.

$$x^{3/2} + x = x(~~\text{?}~~)$$

$$x(x^{1/2} + 1)$$

###### 28.

$$y^{3/4} - y^{-1/4} = y^{-1/4}(~~\text{?}~~)$$

###### 29.

$$a^{1/3} + 3 - a^{-1/3} = a^{-1/3}(~~\text{?}~~)$$

$$\dfrac{a^{2/3}+a^{1/3}-1}{a^{1/3}}$$

###### 30.

$$4b-6+4b^{-2/3} = 2b^{-2/3}(~~\text{?}~~)$$

##### 31.
1. Complete the table of values, then graph both functions on the grid, along with the graph of $$y=x\text{.}$$

\begin{equation*} f(x) = x^{4/3},\quad g(x)=x^{3/2} \end{equation*}
 $$x$$ $$0$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$f(x)$$ $$\qquad$$ $$\qquad$$ $$\qquad$$ $$\qquad$$ $$\qquad$$ $$\qquad$$ $$\qquad$$ $$g(x)$$ $$~~~$$ $$~~~$$ $$~~~$$ $$~~~$$ $$~~~$$ $$~~~$$ $$~~~$$
2. Check your work by graphing the functions in the suggested window, and compare the graphs.

\begin{align*} \text{Xmin} \amp = 0 \amp\amp \text{Xmax} = 6\\ \text{Ymin} \amp = 0 \amp\amp \text{Ymax} = 10 \end{align*}
 $$x$$ $$0$$ $$1$$ $$2$$ $$3$$ $$4$$ $$5$$ $$6$$ $$f(x)$$ $$0$$ $$1$$ $$2.5$$ $$4.3$$ $$6.4$$ $$8.5$$ $$10.9$$ $$g(x)$$ $$0$$ $$1$$ $$2.8$$ $$5.2$$ $$8$$ $$11.2$$ $$14.7$$
##### 32.
1. Complete the table of values, then graph both functions on the grid, along with the graph of $$y=x\text{.}$$

\begin{equation*} f(x) = x^{3/4}, \quad g(x)=x^{2/3} \end{equation*}
 $$x$$ $$0$$ $$2$$ $$4$$ $$6$$ $$8$$ $$10$$ $$f(x)$$ $$~~~$$ $$~~~$$ $$~~~$$ $$~~~$$ $$~~~$$ $$~~~$$ $$g(x)$$ $$~~~$$ $$~~~$$ $$~~~$$ $$~~~$$ $$~~~$$ $$~~~$$
2. Check your work by graphing the functions in the suggested window, and compare the graphs.

\begin{align*} \text{Xmin} \amp = 0 \amp\amp \text{Xmax} = 10\\ \text{Ymin} \amp = 0 \amp\amp \text{Ymax} = 4 \end{align*}
##### Exercise Group.

For Problems 33 and 34, solve the equations, and locate the corresponding points on the graphs in Problems 31 and 32.

###### 33.
1. $$\displaystyle x^{4/3}=4$$

2. $$\displaystyle x^{3/2}=6$$

1. $$\displaystyle 2.83$$

2. $$\displaystyle 3.30$$

###### 34.
1. $$\displaystyle x^{3/4}=4$$

2. $$\displaystyle x^{2/3}=6$$

#### Applications

##### 35.

During a flu epidemic in a small town, health officials estimate that the number of people infected $$t$$ days after the first case was discovered is given by

\begin{equation*} I(t) = 50 t^{3/5} \end{equation*}
1. Complete the table of values.

 $$t$$ $$5$$ $$10$$ $$15$$ $$20$$ $$I(t)$$
2. How long will it be before 300 people are ill?

3. Graph the function $$I(t)$$ on your calculator, and verify your answer to part (b) on your graph.

1.  $$t$$ $$5$$ $$10$$ $$15$$ $$20$$ $$I(t)$$ $$131$$ $$199$$ $$254$$ $$302$$
2. 20 days

##### 36.

The research division of an advertising firm estimates that the number of people who have seen their ads $$t$$ days after the campaign begins is given by the function

\begin{equation*} N(t) = 2000 t^{5/4} \end{equation*}
1. Complete the table of values.

 $$t$$ $$6$$ $$10$$ $$14$$ $$20$$ $$N(t)$$
2. How long will it be before 75,000 people have seen the ads?

3. Graph the function $$n(t)$$ on your calculator, and verify your answer to part (b) on your graph.

##### 37.

In the 1970s, Jared Diamond studied the number of bird species on small islands near New Guinea. He found that larger islands support a larger number of different species, according to the formula

\begin{equation*} S = 15.1A^{0.22} \end{equation*}

where $$S$$ is the number of species on an island of area $$A$$ square kilometers. (Source: Chapman and Reiss, 1992)

1. Fill in the table.

 $$A$$ $$10$$ $$100$$ $$1000$$ $$5000$$ $$10,000$$ $$S$$ $$\hphantom{000000}$$ $$\hphantom{000000}$$ $$\hphantom{000000}$$ $$\hphantom{000000}$$ $$\hphantom{000000}$$
2. Graph the function on your calculator for $$0\lt A\le 10,000\text{.}$$

3. How many species of birds would you expect to find on Manus Island, with an area of 2100 square kilometers? On Lavongai, which bird's area is 1140 square kilometers?

4. How large must an island be in order to support 200 different species of bird?

1.  $$A$$ $$10$$ $$100$$ $$1000$$ $$5000$$ $$10,000$$ $$S$$ $$25$$ $$42$$ $$69$$ $$98$$ $$115$$
2. 81, 71

3. 126,000 sq km

##### 38.

The climate of a region has a great influence on the types of animals that can survive there. Extreme temperatures create difficult living conditions, so the diversity of wildlife decreases as the annual temperature range increases. Along the west coast of North America, the number of species of mammals, $$M\text{,}$$ is approximately related to the temperature range, $$R\text{,}$$ (in degrees Celsius) by the function

\begin{equation*} M = f(R) = 433.8R^{-0.742} \end{equation*}

(Source: Chapman and Reiss, 1992)

1. Graph the function for temperature ranges up to $$30\degree$$C.

2. How many species would you expect to find in a region where the temperature range is $$10\degree$$C? Label the corresponding point on your graph.

3. If 50 different species are found in a certain region, what temperature range would you expect the region to experience? Label the corresponding point on your graph.

4. Evaluate the function to find $$f(9)\text{,}$$ $$f(10)\text{,}$$ $$f(19)\text{,}$$ and $$f(20)\text{.}$$ What do these values represent? Calculate the change in the number of species as the temperature range increases from $$9\degree$$C to $$10\degree$$C and from $$19\degree$$C to $$20\degree$$C. Which $$1\degree$$ increase results in a greater decrease in diversity? Explain your answer in terms of slopes on your graph.

##### 39.

The table at right shows the exponent, $$p\text{,}$$ in the allometric equation

\begin{gather*} \text{variable} = k (\text{body mass})^p \end{gather*}

for some variables related to mammals. (Source: Chapman and Reiss, 1992)

 Variable Exponent, $$p$$ Home range size $$1.26$$ Lung volume $$1.02$$ Brain mass $$0.70$$ Heart rate $$-0.25$$
1. The average body mass of a dolphin is about 140 kilograms, twice the body mass of an average human male. Using the allometric equation above, calculate the ratio of the brain mass of a dolphin to that of a human.

2. A good-sized brown bear weighs about 280 kilograms, twice the weight of a dolphin. Calculate the ratio of the brain mass of a brown bear to that of a dolphin.

3. Use a ratio to compare the heartbeat frequencies of a dolphin and a human, and those of a brown bear and a dolphin.

1. 1.62

2. 1.62

3. 0.84; 0.84

##### 40.

A bicycle ergometer is used to measure the amount of power generated by a cyclist. The scatterplot shows how long an athlete was able to sustain variouslevels of power output. The curve is the graph of

\begin{equation*} y = 500x^{0.29} \end{equation*}

which approximately models the data. (Source: Alexander, 1992)

1. As represented by the graph, which variable is the input, and which is the output?

2. The athlete maintained 650 watts of power for 40 seconds. What power output does the equation predict for 40 seconds?

3. The athlete maintained 300 watts of power for 10 minutes. How long does the equation predict that power output can be maintained?

4. In 1979 a remarkable pedal-powered aircraft called the Gossamer Albatross was successfully flown across the English Channel. The flight took 3 hours. According to the equation, what level of power can be maintained for 3 hours?

5. The Gossamer Albatross needed 250 watts of power to keep it airborne. For how long can 250 watts be maintained, according to the equation?

##### 41.

Birds’ eggs typically lose 10%–20% of their mass during incubation. The embryo metabolizes lipid during growth, and this process releases water vapor through the porous shell. The incubation time for birds’ eggs is a function of the mass of the egg and has been experimentally determined as

\begin{equation*} I(m) = 12.0 m^{0.217} \end{equation*}

where $$m$$ is measured in grams and $$I$$ in days. (Source: Burton, 1998)

1. Calculate the incubation time (to the nearest day) for the wren, whose eggs weigh about 2.5 grams, and the greylag goose, whose eggs weigh 46 grams.

2. The rate of water loss from the egg is also a function of its mass and appears to follow the rule

\begin{equation*} W(m) = 0.015 m^{0.742} \end{equation*}
Combine the functions $$I(m)$$ and $$W(m)$$ to calculate the fraction of the initial egg mass that is lost during the entire incubation period.

3. Explain why your result shows that most eggs lose about 18% of their mass during incubation.

1. 15 days, 28 days

2. $$\displaystyle \dfrac{I(m)\times W(m)}{m} = 0.18 m^{-0.041}$$

3. $$m^{-0.041}$$ is close to 1

##### 42.

The incubation time for birds’ eggs is given by

\begin{equation*} I(m) = 12.0 m^{0.217} \end{equation*}

where $$m$$ is measured in grams and $$I$$ in days. (See Problem 41.) Before hatching, the eggs take in oxygen at the rate of

\begin{equation*} O(m) = 22.2 m^{0.77} \end{equation*}

in milliliters per day. (Source: Burton, 1998)

1. Combine the functions $$I(m)$$ and $$O(m)$$ to calculate the total amount of oxygen taken in by the egg during its incubation.

2. Use your result from part (a) to explain why total oxygen consumption per unit mass is approximately inversely proportional to incubation time. (Oxygen consumption is a reliable indicator of metabolic rate, and it is reasonable that incubation time should be inversely proportional to metabolic rate.)

3. Predict the oxygen consumption per gram of a herring gull’s eggs, given that their incubation time is 26 days. (The actual value is 11 milliliters per day.)

##### 43.

Kepler’s law gives a relation between the period, $$p\text{,}$$ of a planet’s revolution and its average distance, $$a\text{,}$$ from the Sun:

\begin{equation*} p^2 = Ka^3 \end{equation*}

where $$K = 1.243 \times 10^{24}\text{,}$$ $$a$$ is measured in miles, and $$p$$ is measured in years.

1. Solve Kepler’s law for $$p$$ in terms of $$a\text{.}$$

2. Find the period of Mars if its average distance from the Sun is $$1.417 \times 10^8$$ miles.

1. $$\displaystyle p=K^{1/2}a^{3/2}$$
Refer to Kepler's law, $$p^2=Ka^3\text{,}$$ in Problem 43.
1. Solve Kepler’s law for $$a$$ in terms of $$p\text{.}$$


text:
# Traffic management

• Tables
• Figures

### 5.2.2 Absorption Capacities

An important value for road traffic applications is the theoretical maximum rate at which minor traffic stream vehicles can cross or be absorbed into the major traffic stream in a gap acceptance situation. This maximum rate is known as the theoretical absorption capacity.

The formula for theoretical absorption capacity in gap acceptance situations with random arrivals in both the major and minor traffic streams is derived in Commentary 8.

This formula is as follows.

 $C = \frac{q e^{-qT} }{1 - e^{-qT_{0} } }$ 5.4 where q and T = defined in Section 5.2.1 T0 = the follow-up headway, in s/veh C = the theoretical absorption capacity in veh/s (multiply by 3600 for veh/h).

It is observed that the absorption capacity C is a theoretical upper limit, which may not be achieved in practice. It is common practice in traffic analysis to define a practical absorption capacity as

 $C_{p} = \alpha . C$ 5.5

where the factor $$\alpha$$ is typically taken to be in the range 0.80 to 0.85.


text:
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Found in: Page 370

### Essential Calculus: Early Transcendentals

Book edition 2nd
Author(s) James Stewart
Pages 830 pages
ISBN 9781133112280

# A water storage tank has the shape of a cylinder with diameter $$10{\rm{ft}}$$. It is mounted so that the circular cross-sections are vertical. If the depth of the water is $$7{\rm{ft}}$$, what percentage of the total capacity is being used?

The percentage of usage capacity of water storage tank is $$74.7\%$$.

See the step by step solution

## Equation of circle and Pythagorean Theorem

The equation of circular tank is $${x^2} + {y^2} = r{}^2$$

Pythagorean Theorem $$A{B^2} + B{C^2} = A{C^2}$$

## Find area of cross section of tank

Consider the cross section of the tank as circular shape.

Draw the cross section of storage tank as in figure 1

The equation of circular tank is as follows:

$${x^2} + {y^2} = 25{\rm{ }}$$ $${\rm{(1) }}$$

Rearrange Equation (1)

\begin{aligned}{l}{x^2} = 25 - {y^2}\\x = \sqrt {25 - {y^2}} \end{aligned}

Calculate the area of cross section of circle tank:

$$A = \int_a^b x dy$$ $$(2)$$

Substitute $$( - 5)$$ for a, 2 for $$b$$, and $$\left( {\sqrt {25 - {y^2}} } \right)$$ for $$x$$ in Equation (2).

$$A = \int_{ - 5}^2 {\sqrt {25 - {y^2}} } dy$$ $$(3)$$

Consider $$y = 5\sin \theta$$ (4)

Differentiate both sides of the Equation (4).

$$dy = 5\cos \theta d\theta$$

Substitute $$(5\sin \theta )$$ for $$y$$ and $$(5\cos \theta d\theta )$$ for in Equation (3).

\begin{aligned}A&= \int_{ - 5}^2 {\sqrt {25 - {{(5\sin \theta )}^2}} } (5\cos \theta d\theta )\\&= 5\int_{ - 5}^2 {\sqrt {25 - 25{{\sin }^2}\theta } } \cos \theta d\theta \\&= 5\int_{ - 5}^2 {\sqrt {25\left( {1 - {{\sin }^2}\theta } \right)} } \cos \theta d\theta \\&= 5\int_{ - 5}^2 5 \sqrt {{{\cos }^2}\theta } \cos \theta d\theta \\&= 5 \times 5\int_{ - 5}^2 {\cos } \theta \cos \theta d\theta \\&= 25\int_{ - 5}^2 {{{\cos }^2}} \theta d\theta \\&= 25\int_{ - 5}^2 {\left( {1 + {{\sin }^2}\theta } \right)} d\theta \,\end{aligned}

Integrate Equation

\begin{aligned}A&= 25\left[ {\theta + \frac{1}{2}\sin 2\theta } \right]_{ - 5}^2\\&= 25\left[ {\theta + \frac{1}{2}(2\sin \theta \cos \theta )} \right]_{ - 5}^2\end{aligned}

$$= (25\theta + 25\sin \theta \cos \theta )_{ - 5}^2$$

Rearrange Equation (4).

\begin{aligned}\sin \theta&= \frac{y}{5}\\\theta&= {\sin ^{ - 1}}\left( {\frac{y}{5}} \right)\end{aligned}

## Use Pythagorean Theorem and solve

Represent Equation (7) with Pythagorean Theorem as shown in Figure 2.

$$A{B^2} + B{C^2} = A{C^2}$$

Refer to Figure 2.

\begin{aligned}A{B^2} + {y^2}&= {5^2}\\A{B^2} + {y^2}&= 25\\A{B^2}&= 25 - {y^2}\\AB&= \sqrt {25 - {y^2}} \end{aligned}

Calculate the value of $$\cos \theta$$ from Figure 2.

\begin{aligned}\cos \theta &= \frac{{AB}}{{AC}}\\ &= \frac{{\sqrt {25 - {y^2}} }}{5}\end{aligned}

Substitute $${\sin ^{ - 1}}\left( {\frac{y}{5}} \right)$$ for $$\theta ,\frac{y}{5}$$ for $$\sin \theta$$, and $$\frac{{\sqrt {25 - {y^2}} }}{5}$$ for $$\cos \theta$$ in Equation (6).

\begin{aligned}A&= \left[ {25{{\sin }^{ - 1}}\left( {\frac{y}{5}} \right) + 25 \times \frac{y}{5}\frac{{\sqrt {25 - {y^2}} }}{5}} \right]_{ - 5}^2\\&= \left[ {25{{\sin }^{ - 1}}\left( {\frac{y}{5}} \right) + \frac{{25y\sqrt {25 - {y^2}} }}{{25}}} \right]_{ - 5}^2\\&= \left[ {25{{\sin }^{ - 1}}\left( {\frac{2}{5}} \right) + 2\sqrt {25 - {2^2}} } \right] - \left[ {25{{\sin }^{ - 1}}\left( {\frac{{ - 5}}{5}} \right) + ( - 5)\sqrt {25 - {{( - 5)}^2}} } \right]\\&= (10.29 + 9.16) - ( - 39.25 - 0)\\&= 58.7{\rm{f}}{{\rm{t}}^2}\end{aligned}

## The percentage of usage capacity of water storage tank.

Calculate the area of cross section of circle tank:

$$a = \pi {r^2}{\rm{ (8) }}$$

Substitute 5 for $$r$$ in Equation (8).

\begin{aligned}a = \pi {(5)^2}\\ = 25\pi {\rm{f}}{{\rm{t}}^2}\end{aligned}

Calculate the percentage of the total capacity in used:

$$Pt = \frac{A}{a} \times 100{\rm{ (9) }}$$

Substitute $$58.7{\rm{f}}{{\rm{t}}^2}$$ for $$A$$ and $$25\pi {\rm{f}}{{\rm{t}}^2}$$ for $$a$$ in Equation (8).

$$Pt{\rm{ }} = \frac{{58.7}}{{25\pi }} \times 100 = 74.7\%$$

Hence, the percentage of usage capacity of water storage tank is $$74.7\%$$.