Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 6.4, Problem 10CP
To determine
To findout the solution anderor of the given IVP using the Hodgkin −Huxley eqaution and calculate the RMSC value.
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The output of a solar panel (photovoltaic) system depends on its size. A manufacturer states that the average daily production of its 1.5 kW system is 6.6 kilowatt hours (kWh) for Perth conditions. A consumer group monitored this 1.5 kW system in 20 different Perth homes and measured the average daily production by the systems in these homes over a one month period during October. The data is provided here.
kWh 6.2, 5.8, 5.9, 6.1, 6.4, 6.3, 6.9, 5.5, 7.4, 6.7, 6.3, 6.2, 7.1, 6.8, 5.9, 5.4, 7.2, 6.7, 5.8, 6.9
1. Analyse the consumer group’s data to test if the manufacturer’s claim of an average of 6.6 kWh per day is reasonable. State appropriate hypotheses, assumptions and decision rule at α = 0.10. What conclusions would you report to the consumer group? (Hint: You will need to find Descriptive Statistics first.)
2. If 48 homes in the central Australian city of Alice Springs had this system installed and similar data was collected, in order to assess whether average daily production in…
A medical researcher says that less than 86% of adults in a certain country think that healthy children should be required to be vaccinated. In a random sample of 400 adults in that country, 84% think that healthy children should be required to be
vaccinated. At a =0.10, is there enough evidence to support the researcher's claim? Complete parts (a) through (e) below.
(a) Identify the claim and state Ho and H.
Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice.
(Type an integer or a decimal. Do not round.)
O A. The percentage of adults in the country who think that healthy children should be required to be vaccinated is not %.
O B. Less than 86 % of adults in the country think that healthy children should be required to be vaccinated.
O C. More than % of adults in the country think that healthy children should be required to be vaccinated.
O D. % of adults in the country think that healthy children should be required…
At wind speeds above 1000 centimeters per second (cm/sec), significant sand-moving events begin to occur. Wind speeds below 1000 cm/sec deposit sand and wind speeds above 1000 cm/sec move sand to new locations. The cyclic nature of wind and moving sand determines the shape and location of large dunes. At a test site, the prevailing direction of the wind did not change noticeably. However, the velocity did change. Fifty-nine wind speed readings gave an average velocity of x = 1075 cm/sec. Based on long-term experience, ? can be assumed to be 255 cm/sec.
(a)
Find a 95% confidence interval for the population mean wind speed at this site. (Round your answers to the nearest whole number.)
lower limit_________cm/sec
upper limit_________ cm/sec
(b)
Does the confidence interval indicate that the population mean wind speed is such that the sand is always moving at this site? Explain.
No. This interval indicates that the population mean wind speed is such that the sand may not always be…
Chapter 6 Solutions
Numerical Analysis
Ch. 6.1 - Show that the function y(t)=tsint is a solution of...Ch. 6.1 - Show that the function y(t)=esint is a solution of...Ch. 6.1 - Use separation of variables to find solutions of...Ch. 6.1 - Find the solutions of the IVP given by y(0)=0 and...Ch. 6.1 - Apply Eulers Method with step size h=1/4 to the...Ch. 6.1 - Apply Eulers Method with step size h=1/4 to the...Ch. 6.1 - (a) Show that y=tan(t+c) is a solution of the...Ch. 6.1 - (a) Show that y=tanh(t+c) is a solution of the...Ch. 6.1 - For which of these initial value problems on [0,...Ch. 6.1 - Sketch the slope field of the differential...
Ch. 6.1 - Find the solutions of the initial value problems...Ch. 6.1 - (a)Show that if a0, the solution of the initial...Ch. 6.1 - Use separation of variables to solve the initial...Ch. 6.1 - Find the solution of the initial value problem...Ch. 6.1 - Prob. 15ECh. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Apply Eulers Method with step size h=0.1 on [0, 1]...Ch. 6.1 - Plot the Eulers Method approximate solutions for...Ch. 6.1 - Plot the Eulers Method approximate solutions for...Ch. 6.1 - Prob. 4CPCh. 6.1 - For the IVPs in Exercise 4, make a log-log plot of...Ch. 6.1 - Prob. 6CPCh. 6.1 - Plot the Eulers Method approximate solution on [0,...Ch. 6.1 - Plot the Eulers Method approximate solution on [0,...Ch. 6.1 - Calculate the Eulers Method approximate solution...Ch. 6.1 - Calculate the Eulers Method approximate solution...Ch. 6.1 - Plot the Eulers Method approximate solution on [0,...Ch. 6.2 - Using initial condition y(0)=1 and step size...Ch. 6.2 - Using initial condition y(0)=0 and step size...Ch. 6.2 - Find the formula for the second-order Taylor...Ch. 6.2 - Apply the second-order Taylor Method to the...Ch. 6.2 - (a) Prove (6.22) (b) Prove (6.23).Ch. 6.2 - Apply the Explicit Trapezoid Method on a grid of...Ch. 6.2 - Prob. 2CPCh. 6.2 - Prob. 3CPCh. 6.2 - Prob. 4CPCh. 6.2 - Prob. 5CPCh. 6.2 - Plot the Trapezoid Method approximate solution on...Ch. 6.2 - Calculate the Trapezoid Method approximate...Ch. 6.2 - Calculate the Trapezoid Method approximate...Ch. 6.2 - Prob. 9CPCh. 6.3 - Apply the Eulers Method with step size h=1/4 to...Ch. 6.3 - Apply the Trapezoid Method with h=1/4 to the...Ch. 6.3 - Convert the higher-order ordinary differential...Ch. 6.3 - Apply the Trapezoid Method with h=1/4 to the...Ch. 6.3 - (a) Show that y(t)=(et+ett2)/21 is the solution of...Ch. 6.3 - Apply Eulers Method with step sizes h=0.1 and 0.01...Ch. 6.3 - Carry out Computer Problem 1for the Trapezoid...Ch. 6.3 - Prob. 3CPCh. 6.3 - Prob. 4CPCh. 6.3 - Prob. 5CPCh. 6.3 - Adapt pend.m to build a damped pendulum with...Ch. 6.3 - Prob. 7CPCh. 6.3 - Prob. 8CPCh. 6.3 - Prob. 9CPCh. 6.3 - Prob. 10CPCh. 6.3 - Prob. 11CPCh. 6.3 - Prob. 12CPCh. 6.3 - Prob. 13CPCh. 6.3 - Prob. 14CPCh. 6.3 - Prob. 15CPCh. 6.3 - A remarkable three-body figure-eight orbit was...Ch. 6.4 - Apply the Midpoint Method for the IVPs...Ch. 6.4 - Carry out the steps of Exercise 1 for the IVPs...Ch. 6.4 - Apply fourth-order Runge-Kutta Method to the IVPs...Ch. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - Consider the initial value problem y=y . The...Ch. 6.4 - Prob. 7ECh. 6.4 - Prob. 1CPCh. 6.4 - Apply the fourth-order Runge-Kutta Method solution...Ch. 6.4 - Carry out the steps of Computer Problem 2, but...Ch. 6.4 - Prob. 4CPCh. 6.4 - Plot the fourth-order Runge-Kutta Method...Ch. 6.4 - Plot the fourth-order Runge-Kutta Method...Ch. 6.4 - Prob. 7CPCh. 6.4 - Prob. 8CPCh. 6.4 - Prob. 9CPCh. 6.4 - Prob. 10CPCh. 6.4 - Adapt the orbit .m MATLABs program to animate a...Ch. 6.4 - Assess the conditioning of the Lorenz equations by...Ch. 6.4 - Follow two trajectories of the Lorenz equations...Ch. 6.4 - Prob. 14CPCh. 6.4 - Prob. 15CPCh. 6.4 - Prob. 16CPCh. 6.4 - Prob. 17CPCh. 6.4 - Prob. 18CPCh. 6.4 - Run tacoma.m with wind speed W=80km/hr and initial...Ch. 6.4 - Replace the Trapezoid Method by fourth-order...Ch. 6.4 - The system is torsionally stable for W=50km/hr ....Ch. 6.4 - Find the minimum wind speed W for which a small...Ch. 6.4 - Prob. 5SACh. 6.4 - Prob. 6SACh. 6.4 - Prob. 7SACh. 6.5 - Write a MATLAB implementation of RK23 (Example...Ch. 6.5 - Prob. 2CPCh. 6.5 - Prob. 3CPCh. 6.5 - Compare the results of Computer Problem 3 with the...Ch. 6.5 - Apply a MATLAB implementation of RKF45 to...Ch. 6.6 - Using initial condition y(0)=0 and step size...Ch. 6.6 - Find all equilibrium solutions and the value of...Ch. 6.6 - Prob. 3ECh. 6.6 - Consider the linear differential equation y=ay+b...Ch. 6.6 - Apply Backward Euler, using Newtons Method as a...Ch. 6.6 - Carry out the steps in Computer Problem1 for the...Ch. 6.7 - Apply the Adams-Bashforth Two-Step Method to the...Ch. 6.7 - Carry out the steps of Exercise 1 on the IVPs...Ch. 6.7 - Prob. 3ECh. 6.7 - Prob. 4ECh. 6.7 - Show that the Implicit Trapezoid Method (6.89) is...Ch. 6.7 - Prob. 6ECh. 6.7 - Prob. 7ECh. 6.7 - Prob. 8ECh. 6.7 - Find the order and stability type for the...Ch. 6.7 - Prob. 10ECh. 6.7 - Prob. 11ECh. 6.7 - The Mime-Simpson Method is a weakly stable...Ch. 6.7 - Prob. 13ECh. 6.7 - (a) Use the matrix formulation to find the...Ch. 6.7 - Prob. 15ECh. 6.7 - (a) Use the matrix formulation to find the...Ch. 6.7 - Adapt the exmultistep.m program to apply the...Ch. 6.7 - Adapt the exmultistep.m program to apply the...Ch. 6.7 - Prob. 3CPCh. 6.7 - Prob. 4CPCh. 6.7 - Prob. 5CPCh. 6.7 - Prob. 6CPCh. 6.7 - Prob. 7CPCh. 6.7 - Prob. 8CPCh. 6.7 - Prob. 9CPCh. 6.7 - Change Program 6.8 into a fourth-order...
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forwardThe output of a solar panel (photovoltaic) system depends on its size. A manufacturer states that the average daily production of its 1.5 kW system is 6.6 kilowatt hours (kWh) for Perth conditions. A consumer group monitored this 1.5 kW system in 20 different Perth homes and measured the average daily production by the systems in these homes over a one month period during October. The data is provided here. (a) Analyse the consumer group’s data to test if the manufacturer’s claim of an average of 6.6 kWh per day is reasonable. State appropriate hypotheses, assumptions and decision rule at α = 0.10. What conclusions would you report to the consumer group? Hint: You will need to find Descriptive Statistics first.) (b) If 48 homes in the central Australian city of Alice Springs had this system installed and similar data wascollected, in order to assess whether average daily production in Alice Springs exceeded 6.6 kWh, (i) what would the alternate hypothesis be? (ii) What would be the…arrow_forwarda) We conduct a regression of size on hhinc, owner, hhsize, hhsize2,and hhsize3. We do not include the constant. The regression output is reported in Table 3. Would you conclude that the home size increases with the household size? Interpret the sign and magnitude of the estimated coefficients of hhsize1, hhsize2, and hhsize3.arrow_forward
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- At wind speeds above 1000 centimeters per second (cm/sec), significant sand-moving events begin to occur. Wind speeds below 1000 cm/sec deposit sand and wind speeds above 1000 cm/sec move sand to new locations. The cyclic nature of wind and moving sand determines the shape and location of large dunes. At a test site, the prevailing direction of the wind did not change noticeably. However, the velocity did change. Sixty-three wind speed readings gave an average velocity of x = 1075 cm/sec. Based on long-term experience, σ can be assumed to be 275 cm/sec. (a) Find a 95% confidence interval for the population mean wind speed at this site. (Round your answers to the nearest whole number.) lower limit cm/sec upper limit cm/sec (b) Does the confidence interval indicate that the population mean wind speed is such that the sand is always moving at this site? Explain. No. This interval indicates that the population mean wind speed is such that the sand may not always be moving…arrow_forwardAt wind speeds above 1000 centimeters per second (cm/sec), significant sand-moving events begin to occur. Wind speeds below 1000 cm/sec deposit sand and wind speeds above 1000 cm/sec move sand to new locations. The cyclic nature of wind and moving sand determines the shape and location of large dunes. At a test site, the prevailing direction of the wind did not change noticeably. However, the velocity did change. Sixty-three wind speed readings gave an average velocity of x = 1075 cm/sec. Based on long-term experience, ? can be assumed to be 265 cm/sec. (a) Find a 95% confidence interval for the population mean wind speed at this site. (Round your answers to the nearest whole number.) lower limit cm/sec upper limit cm/secarrow_forwardAt wind speeds above 1000 centimeters per second (cm/sec), significant sand-moving events begin to occur. Wind speeds below 1000 cm/sec deposit sand and wind speeds above 1000 cm/sec move sand to new locations. The cyclic nature of wind and moving sand determines the shape and location of large dunes. At a test site, the prevailing direction of the wind did not change noticeably. However, the velocity did change. Sixty-three wind speed readings gave an average velocity of x = 1075 cm/sec. Based on long-term experience, σ can be assumed to be 275 cm/sec. 1. Find a 95% confidence interval for the population mean wind speed at this site. (Round your answers to the nearest whole number.) lower limit cm/sec upper limit cm/sec 2. Does the confidence interval indicate that the population mean wind speed is such that the sand is always moving at this site? Explain. (a) No. This interval indicates that the population mean wind speed is such that the sand may not always be moving…arrow_forward
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