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A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s² for g. Use 1000 kg/m³ as the weight density of water.) 5m+ 3 m + ☑ 5 m 15 m Step 1 A layer of water Ax m thick which lies x m above the bottom of the tank will be rectangular with length 15 m. Using similar triangles, we can see that it will have width x m. X ब्र 3 m + 5 m 15 m 5 m X 5 Step 2 The mass of the layer of water is approximately equal to its density (1000 kg/m³) times its approximate volume. m = 15x Ax(1,000) kg 15x Step 3 The force required to lift this layer is given by the following. (Use 9.8 m/s² for g.) F = ma = 9.8 9.8 (15,000x Ax) Step 4 To be lifted to the top of the pump's piping, the layer must be lifted a distance equal to 8 -x Step 5 We can now say that the work required to move this layer is about the following. W = (147,000x Ax) 8-x (a) Find the approximations T10 and M10 for T10 M10 26.285683 = 26.152371 L √ √² 13 e¹ 1/x dx. (Round your answers to six decimal places.) (b) Estimate the errors in the approximations of part (a) using the smallest possible value for K according to the theorem about error bounds for trapezoidal and midpoint rules. (Round your answers to six decimal places.) |E| ≤0.088344 EMI 0.044172 (c) Using the values of K from part (b), how large do we have to choose n so that the approximations T and M to the integral in part (a) are accurate to within 0.0001? n For T n' n = 502 For M, n = 355 'n' ×

A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s² for g. Use 1000 kg/m³ as the weight density of water.) 5m+ 3 m + ☑ 5 m 15 m Step 1 A layer of water Ax m thick which lies x m above the bottom of the tank will be rectangular with length 15 m. Using similar triangles, we can see that it will have width x m. X ब्र 3 m + 5 m 15 m 5 m X 5 Step 2 The mass of the layer of water is approximately equal to its density (1000 kg/m³) times its approximate volume. m = 15x Ax(1,000) kg 15x Step 3 The force required to lift this layer is given by the following. (Use 9.8 m/s² for g.) F = ma = 9.8 9.8 (15,000x Ax) Step 4 To be lifted to the top of the pump's piping, the layer must be lifted a distance equal to 8 -x Step 5 We can now say that the work required to move this layer is about the following. W = (147,000x Ax) 8-x (a) Find the approximations T10 and M10 for T10 M10 26.285683 = 26.152371 L √ √² 13 e¹ 1/x dx. (Round your answers to six decimal places.) (b) Estimate the errors in the approximations of part (a) using the smallest possible value for K according to the theorem about error bounds for trapezoidal and midpoint rules. (Round your answers to six decimal places.) |E| ≤0.088344 EMI 0.044172 (c) Using the values of K from part (b), how large do we have to choose n so that the approximations T and M to the integral in part (a) are accurate to within 0.0001? n For T n' n = 502 For M, n = 355 'n' ×

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter47: Applications Of Formulas To Cutting Speed, Revolutions Per Minute, And Cutting Time
Section: Chapter Questions
Problem 40A: Compute the following problems. Express the answers to 1 decimal place. Use: T=LFN Cast iron, 312...
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A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s² for g. Use 1000 kg/m³ as the weight density of water.) 5m+ 3 m + ☑ 5 m 15 m Step 1 A layer of water Ax m thick which lies x m above the bottom of the tank will be rectangular with length 15 m. Using similar triangles, we can see that it will have width x m. X ब्र 3 m + 5 m 15 m 5 m X 5 Step 2 The mass of the layer of water is approximately equal to its density (1000 kg/m³) times its approximate volume. m = 15x Ax(1,000) kg 15x Step 3 The force required to lift this layer is given by the following. (Use 9.8 m/s² for g.) F = ma = 9.8 9.8 (15,000x Ax) Step 4 To be lifted to the top of the pump's piping, the layer must be lifted a distance equal to 8 -x Step 5 We can now say that the work required to move this layer is about the following. W = (147,000x Ax) 8-x
Transcribed Image Text:A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s² for g. Use 1000 kg/m³ as the weight density of water.) 5m+ 3 m + ☑ 5 m 15 m Step 1 A layer of water Ax m thick which lies x m above the bottom of the tank will be rectangular with length 15 m. Using similar triangles, we can see that it will have width x m. X ब्र 3 m + 5 m 15 m 5 m X 5 Step 2 The mass of the layer of water is approximately equal to its density (1000 kg/m³) times its approximate volume. m = 15x Ax(1,000) kg 15x Step 3 The force required to lift this layer is given by the following. (Use 9.8 m/s² for g.) F = ma = 9.8 9.8 (15,000x Ax) Step 4 To be lifted to the top of the pump's piping, the layer must be lifted a distance equal to 8 -x Step 5 We can now say that the work required to move this layer is about the following. W = (147,000x Ax) 8-x
(a) Find the approximations T10 and M10 for T10 M10 26.285683 = 26.152371 L √ √² 13 e¹ 1/x dx. (Round your answers to six decimal places.) (b) Estimate the errors in the approximations of part (a) using the smallest possible value for K according to the theorem about error bounds for trapezoidal and midpoint rules. (Round your answers to six decimal places.) |E| ≤0.088344 EMI 0.044172 (c) Using the values of K from part (b), how large do we have to choose n so that the approximations T and M to the integral in part (a) are accurate to within 0.0001? n For T n' n = 502 For M, n = 355 'n' ×
Transcribed Image Text:(a) Find the approximations T10 and M10 for T10 M10 26.285683 = 26.152371 L √ √² 13 e¹ 1/x dx. (Round your answers to six decimal places.) (b) Estimate the errors in the approximations of part (a) using the smallest possible value for K according to the theorem about error bounds for trapezoidal and midpoint rules. (Round your answers to six decimal places.) |E| ≤0.088344 EMI 0.044172 (c) Using the values of K from part (b), how large do we have to choose n so that the approximations T and M to the integral in part (a) are accurate to within 0.0001? n For T n' n = 502 For M, n = 355 'n' ×
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