Bottled Water Sales The rate of U.S. sales of bottled water for the period 2007-2014 could be approximated by
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Chapter 6 Solutions
Applied Calculus
- Calculating riemann sum of table v(t) below is increasing 0<t<12 t 0 3 6 9 12 v(t) 26 28 29 30 32 i n =4 and ii n=2 The total distance traveled of i = The total distance traveled of ii =arrow_forwardComputing populations The population densities in nine districtsof a rectangular county are shown in the figure.a. Use the fact that population = (population density) x (area) to estimate the population of the county.b. Explain how the calculation of part (a) is related to Riemann sums and double integrals.arrow_forwardnumerical integration use the trapezoidal rule and simpsons rule. round off to three significant digitsarrow_forward
- The rectangles in the graph below illustrate a left endpoint Riemann sum for f(x)=(x^2)/(12) f(x)=(x^2)/(12) on the interval [2,6].The value of this left endpoint Riemann sum is __________________ , the area of the region enclosed by y=f(x)y=f(x), the x-axis, and the vertical lines x = 2 and x = 6.arrow_forwardNumerical integration use multiple segments trapezoidal rule n=8, aproximate value = 2.097, Et = 0.731, abs Et = 25.85%arrow_forward(a) Find the Riemann sum for f(x) = sin x, 0<=x <= 3 pie/2 , with six terms, taking the sample points to be right end-points. (Give your answer correct to six decimal places.) Explain what the Riemann sum represents with the aidof a sketch.arrow_forward
- Tea leaves are placed in a cup of hot water. Caffeine is infused into the water at a rate of 15 −(x2/14) milligrams per minute. After 6 minutes, the tea leaves are removed. (a) Estimate the amount of caffeine in the cup of water after the tea leaves are removed using a right Riemann sum with 3 subintervals.arrow_forwardApproximating the displacement Suppose the velocity in m/s of an objectmoving along a line is given by the function v = t2, where 0 ≤ t ≤ 8. Approximate the displacement of the object by dividing the time interval [0, 8] into n subintervals of equal length. On each subinterval, approximate the velocity with a constant equal to the value of v evaluated at the midpoint of the subinterval.Divide [0, 8] into n = 8 subintervals of equal length.arrow_forwardApproximating the displacement Suppose the velocity in m/s of an objectmoving along a line is given by the function v = t2, where 0 ≤ t ≤ 8. Approximate the displacement of the object by dividing the time interval [0, 8] into n subintervals of equal length. On each subinterval, approximate the velocity with a constant equal to the value of v evaluated at the midpoint of the subinterval.Divide [0, 8] into n = 4 subintervals: [0, 2], [2, 4], [4, 6], and [6, 8].arrow_forward
- a. Use a left Riemann sum with the three subintervals indicated by the data in the table to approximate the amount of grain in the silo at 3 minutes. b. Is the approximation in part a an over or underestimate? explain your reasoning.arrow_forwardSalty Overflow A 600-gaJlon tank is filled with 300 gal of pure water. A spigot is opened and a sa1t solution containing I lb of sa1t per gallon of solution begins flowing into the tank at a rate of 3 gal/min. Simultaneously. a drain is opened at the bottom of the tank a1lowing the solution to leave the tank at a rate of I gal/min. What will be the salt content in the tank at the precise moment that the volume of solution in the tank reaches the tank's capacity of 600 ga1?arrow_forwardSolve using Calculus (Integrals). A swimming pool has the shape of a rectangular box with a base that measures 25 m by 15 m and a uniform depth of 2.5 m. Suppose that the swimming pool is filled with water to the 2 meter mark, how much work is required to pump out all the water to level 3 m above the bottom of the pool. Density of water: 1000 kg/m3 Solve using Calculus (Integrals).arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage