Solve the value using Lagrangian Interpolation,using cubic interpolation To find how much heat is required to bring a kettle of water to its boiling point, you areasked to calculate the specific heat of water at 61°C. The specific heat of water is given as afunction of time in Table 1.Table 1 Specific heat of water as a function of temperature.Temperature, T Specific heat, C(°C)Jkg-°C2241814241795241868241991004217Determine the value of the specific heat at T = 61°C using the direct method of interpolation

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Answered: To find how much heat is required to…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.4: Composition Of Functions

Problem 97SE: The number of bacteria in a refrigerated food product is given by N(T)=23T256T+1,3T33 ,where T is...

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Use your schools library, the Internet, or some other reference source to find real-life applications of approximations of functions.
Growth in Length of Haddock D.S. Raitt found that the length L of haddock in centimeters as a function of the age t in years is given approximately by the formula L=5342.820.82t a. Calculate L(4) and explain what it means. b. Compare the average yearly rate of growth in length from age 5 to age 10 years with the average yearly rate of growth from age 15 to age 20 years. Explain in practical terms what this tells you about the way haddock grow. c. What is the longest haddock you would expect to find anywhere?
The number of bacteria in a refrigerated food product is given by N(T)=23T256T+1,3T33 ,where T is the temperature of the food. When the food is removed from the refrigerator, the temperature is given by T(t)=5t+1.5 , where t is the time in hours. a. Find the composite function N(T(t)) . b. Find the time (round to two decimal places) when the bacteria count reaches 6,752.
Focal Length A refracting telescope has a main lens, or objective lens, and a second lens, the eyepiece see Figure 3.42. For a given magnification M of the telescope, the focal length F of the objective lens is a linear function of the focal length Fe of the eyepiece. For example, a telescope with magnification M=80 times can be constructed using various combinations of lenses. The following table gives some samples of focal length for telescopes with magnification M=80. Here focal lengths are in centimeters. Fe 0.3 0.5 0.7 0.9 F 24 40 56 72 a. Construct a linear model for the data. b. In this example, the magnification M is 80. In general, F is proportional to Fe, and the constant of proportionality is M. Use this relation to write a formula for F in terms of Fe and M. c. Solve the equation you obtained in part b for M and thus obtain a formula for magnification as a function of objective lens focal length and eyepiece focal length. d. To achieve a large magnification, how should the objective and eyepiece lenses be selected? FIGURE 3.42
Hydroplaning On wet roads, under certain conditions the front tires of a car will hydroplane, or run along the surface of the water. The critical speed V at which hydroplaning occurs is a function of p, the tire inflation pressure. The following table shows hypothetical data for p, in pounds per square inch, and V, in miles per hour. Tire inflation pressure p Critical speed V for hydroplaning 20 46.3 25 51.8 30 56.7 35 61.2 a Find a formula that models V as a power function of p. b In the rain, a car with tires inflated to 35pound per square inch is travelling behind a bus with tires inflated to 60 pounds per square inch, and both are moving at 65 miles per hour. If they both hit their brakes, what might happen?
The half-life of plutonium-244 is 80,000,000 years. Find function gives the amount of carbon-14 remaining as a function of time, measured in years.

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