Answered: Using the backward divided difference… | bartleby

Trigonometry (MindTap Course List)

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section: Chapter Questions

Problem 33CT

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Using the backward divided difference approximation (e²) = 5. 5125 at x = 2.6 for a step size of 0.05. If you keep
halving the step size to find (e*)at x = 2.6, what is the step size would be to have two significant digits that can be
considered to be least correct in your answer?

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An executive conference roomof a corporation contains 4500 ft3 of air initially free of carbon monoxide. Starting at time t = 0, cigarette smoke containing 4% carbon monoxide is blown into the room at the rate of0.3 ft3/min. A ceiling fan keeps the air in the room well circulated and the air leaves the room at the same rate of 0.3 ft3./min.Find the time when the concentration of carbon monoxide in theroom reaches 0.01%.
11.Suppose that during a controlled experiment, the temperature in a test tube attime t is rising at a rate of 6t^2+2 degrees centigrade per minute. If the initialtemperature is 20°C, what is the temperature in the test tube after 10 minutes?
Find the solution to the equation 2x^2 - ln(1/3x) - 5x = 0. Use a tolerance of function error of 0.001
Total net shipments of aluminum (in billions of pounds) are approximated by g(x) = 16.2 + 2.86 In(x + 1) where x=0 corresponds to year 1990 a) How many pounds of aluminum were sipped in 2004? b) Assuming the continued accuracy of the model, when will aluminum shipments reach 27,400,000,000 pounds?
Water is running into a hemispherical bowl having a radius of 10 cm at a constant rate of 3 cu. cm/min. When the water is x cm deep, the water level is rising at the rate of 0.0149 cm/min. What is the value of x?
In a factory there is a 10,000 liter water tank that contains 0.01% colorant. From the beginning (t = 0) water with a dye content of 0.001% is pumped into the tank at a rate of 4 l/min. The water leaves the tank at the same speed. Calculate the percentage of chlorine in the tank after 60 minutes (iterations) taking time intervals of one minute: - using the approximate method of Euler and Runge Kutta of 4 order.
An executive conference room of a corporation contains 4500 ft3 of air initially free of carbon monoxide. Starting at time t = 0, cigarette smoke containing 4% carbon monoxide is blown into the room at the rate of 0.3 ft3/min. A ceiling fan keeps the air in the room well circulated and the air leaves the room at the same rate of 0.3 ft3/min. Find the time when the concentration of carbon monoxide in the room reaches 0.01%.
Total net shipments of aluminum (in billions of pounds) are approximated by g(x)=16.2+2.86ln(x+1) where x=0 corresponds to year 1990. A) How many pounds of Aluminum were shipped in 2004 B) Assuming the continued accuracy of the model when will aluminum shipments reach 247,400,000,000 pounds.
3. The radius of a circular oil slick expands at a rate of 2 m/min.a. How fast is the area of the oil slick increasing when the radius is 25m?b. If the radius is 0 at time t = 0, how fast is the area increasing after 3 min?
why does the local error increase in proportion to the square of the step size but the global error in proportion to the step size in euler's method for solving ODE’s? I am curious and have not been able to find a satisfactory answer
The rate of U.S. per capita sales of bottled water for the period 2000–2010 can be approximated by s(t) = −0.18t2 + 3t + 15 gallons per year (0 ≤ t ≤ 10), where t is the time in years since the start of 2000.† After conducting a survey of sales in your state, you estimate that consumption in gyms accounts for a fraction f(t) =√0.2 + 0.04t of all bottled water consumed in year t. Assuming that your model is correct, estimate, to the nearest gallon, the total amount of bottled water consumed per capita in gyms from the start of 2008 to the start of 2010. HINT [Rate of consumption = s(t)f(t).] ____________ gal
The rate of U.S. per capita sales of bottled water for the period 2000–2010 can be approximated by s(t) = −0.18t2 + 3t + 15 gallons per year (0 ≤ t ≤ 10), where t is the time in years since the start of 2000.† After conducting a survey of sales in your state, you estimate that consumption in gyms accounts for a fraction f(t) = 0.2 + 0.04t of all bottled water consumed in year t. Assuming that your model is correct, estimate, to the nearest gallon, the total amount of bottled water consumed per capita in gyms from the start of 2004 to the start of 2010. HINT [Rate of consumption = s(t)f(t).]

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