Answered: 4. -3→2, 1 -3-* 2 3 2.

Name: The fuel tank on a truck has trapezoidal cross sections with the dimen
Uploaded: 2024-03-20T06:47:08.000Z
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Description: The fuel tank on a truck has trapezoidal cross sections with the dimensions (in feet) shown in the figure. Assume that the engine is approximately 3 feet above the top of the fuel tank and that diesel fuel weighs approximately 53.1 pounds per cubic f

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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Question

The fuel tank on a truck has trapezoidal cross sections with the dimensions (in feet) shown in the figure. Assume that the engine is approximately 3 feet above the top of the fuel tank and that diesel fuel weighs approximately 53.1 pounds per cubic foot. Find the work done by the fuel pump in raising a full tank of fuel to the level of the engine.

Expert Solution

Step 1

Given: The fuel tank on a truck has trapezoidal cross sections with the dimensions (in feet).
To find: The work done by the fuel pump in raising a full tank of fuel to the level of the engine.

Step 2

The right side of the fuel tank is a line that contains points $(1, 0) and (2, 3) .$
The slope of the equation $y = m x + c$ consisting of these two points is given by-
$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} H e r e, (x_{1}, y_{1}) = (1, 0) a n d (x_{2}, y_{2}) = (2, 3) \Rightarrow m = \frac{3 - 0}{2 - 1} = \frac{3}{1} = 3 \Rightarrow m = 3$
Hence, the equation becomes-
$y = 3 x + c$
As seen from the graph below-

$y (1) = 0 \Rightarrow 3 (1) + c = 0 \Rightarrow c = - 3 The equation will be y = 3 x - 3 . i . e . x = \frac{y + 3}{3} \Rightarrow x = \frac{y}{3} + 1$

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