The following data define the sea-level concentration of dissolved oxygen for freshwater as a function of temperature:T°CO81624324014.621 11.843 9.970 8.418 7.305 6.413o,mg/LEstimate o(27) using (a) Newton's interpolating polynomial, and (b) cubic splines.Note that the exact result is 7.986 mg/L.

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Answered: The following data define the sea-level…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Please see the attached image for the multiple choice quesiton in green colour. Please answer the one question.
Medical studies of obesity use the Body Mass Index (BMI), which is defined by w BMI = where w is weight in kilograms and h is height in meters. (a) Using the fact that 1 kg = 2.2 lb and 1 meter = 39.4", calculate the BMI of a 5'5" woman who weighs 150 lb. (b) Which has more effect on the BMI: a 10% weight increase or a 10% height decrease? Justify your answer.
The efficiency for a steel specimen immersed in a phosphating tank is the weight of the phosphate coating divided by the metal loss (both in mg/ft?). An article gave the accompanying data on tank temperature (x) and efficiency ratio (y). Temp. 173 175 176 177 177 178 179 180 Ratio 0.94 1.21 1.44 1.05 1.09 1.02 0.96 1.88 Temp. 183 183 183 183 183 184 184 185 Ratio 1.53 1.50 1.57 2.07 2.05 0.86 1.53 0.80 Temp. 185 185 185 187 187 188 189 191 Ratio 1.71 1.96 2.76 1.59 2.60 3.10 1.81 3.18 In USE SALT (a) Determine the equation of the estimated regression line. (Round all numerical values to four decimal places.) (b) Calculate a point estimate for true average efficiency ratio when tank temperature is 185. (Round your answer to four decimal places.) (c) Calculate the values of the residuals from the least squares line for the four observations for which temperature is 185. (Round your answers to two decimal places.) (185, 0.80) (185, 1.71) (185, 1.96) (185, 2.76) Why do they not all have…
(b) What is an approximate value for e ?
Kleiber's Law states that the metabolic needs (such as calorie requirements) of a mammal are proportional to its body weight raised to the 0.75 power.¹ Surprisingly, the daily diets of mammals conform to this relation well. Assuming Kleiber's Law holds, answer the following questions. (a) Write a formula for C, daily calorie consumption, as a function of body weight, W. NOTE: Use k for the constant of proportionality. C(W) = (b) If a human weighing 150 pounds needs to consume 1800 calories a day, estimate the daily calorie requirement of a horse weighing 740 lbs and of a rabbit weighing 11 lbs. NOTE: Round your answers to the nearest calorie. Daily calorie requirement of a horse = Daily calorie requirement of a rabbit = calories Choose one calories (c) On a per-pound basis, which animal requires more calories: a mouse or an elephant? ¹S. Strogatz. "Math and the City." The New York Times. May 20, 2009. Kleiber originally
2. As ultrasound propagates into the body, absorption and scattering result in a decrease (or attenu- ation) of the intensity. This can be described by the attenuation coefficient, a. In an experiment to investigate this attenuation in the chest wall of humans, measurements were conducted in which the attenuation of ultrasound through sample human tissue was measured as a function of the ultrasound frequency, f [1]. (a) The figure below (adapted from [1]) shows a set of measurements of the attenuation coef- ficient as a function of the frequency. Fit a linear function to the data points shown. You should draw an approximate line of best fit, determine the slope and intercept of your fit, and then quote the final equation for your line. 12 10 2 1 3 4 5 Frequency (MHz) Attenuation coefficient (dB/cm)
the sales revenue of a new mobile phone model is found to follow an AR(1) process, as shown below. what is the 3-lag AČF value? Xt =0.7*xt-1+Wt 0.700 .0.343 0.490 0.240
A sonar (Ultrasonic) sensor can be used in detecting obstacles around a robot.A robot equipped with a sonar sensor transmits a signal at T=0 seconds and receives aresponse at T = 93 milliseconds.Assuming that the speed of sound is (340m/s) calculate the distance between the robot and the potential obstacle in meters. Give your answer to an accuracy of 1 decimal place.Note: A millisecond is a thousandth (0.001 s) of a second.
A 9-foot-tall cylindrical water tank has a base of diameter 10 feet. NOTE: Enter exact answers or round to three decimal places. (a) How much water can the tank hold? ft.3 (b) How much water is in the tank if the water is 6 feet deep? V(h) = ft. 3 (c) Let h be the depth of water in the tank. Write a formula for the volume of water as a function of its depth in the tank. ft ³
The wind-chill index is modeled by the function W = 13.12 + 0.62157- 11.37v0.16 + 0.39657v0.16 where T is the temperature (°C) and v is the wind speed (in km/h). When T = -14°C and v= 35 km/h, by how much (in °C) would you expect the apparent temperature W to drop if the actual temperature decreases by 1°C? (Round your answers to two decimal places.) °C drop What if the wind speed increases by 1 km/h while the actual temperature stays constant at T = -14°C? °C drop
The data presented in the following table give the tensile strength in psi (y) of paper as a function of the percentage of hardwood content (x). Hardwood Content Tensile Strength 1.0 26.8 1.5 29.5 2.0 36.6 3.0 37.8 4.0 38.2 4.5 41.5 5.0 44.8 5.5 44.7 6.0 48.5 6.5 50.1 7.0 52.1 8.0 56.1 9.0 63.1 10.0 62.0 11.0 62.5 12.0 58.0 13.0 52.9 14.0 38.2 15.0 32.9 16.0 21.9 a. Fit polynomial models of degrees 1, 2, and so on to predict tensile strength from hardwood content. For each one, use the F test to compare it with the model of degree one less. Stop when the P-value of the F test is greater than 0.05. What is the degree of the polynomial model chosen by this method? b. Using the model from part (a), estimate the hardwood concentration that produces the highest tensile strength.

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