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' ×
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 help me with these questions. I am really struggling to complete it correctly. i keep on getting the incorrect answer. Thank you
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
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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