Towns A and B are located near a straight river as shown in Figure 1 (not...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Towns A and B are located near a straight river as shown in Figure 1 (not drawn to scale). A pumping station is to be built on the river's edge with pipes extending straight to the two towns. Your task is to find where the pumping station should be built (i.e. what is the value of x) to minimize the total length of the pipe required to connect both towns to the pumping station. 15 km 7 km x km Pumping station Figure 1: Proposed pumping station. B 4 km (a) Find a function, f(x), for the the total length of the pipe required as a function of x. (8 marks) (b) Using calculus and the expression found in (a) to determine, algebraically, the value of a (in kilometres) that gives the minimum total length of the pipes needed. What is the minimum total length of the pipes required? Check your value of a by substitution into the derivative. Also verify that you have found the minimum by using an appropriate calculus test. (42 marks) Towns A and B are located near a straight river as shown in Figure 1 (not drawn to scale). A pumping station is to be built on the river's edge with pipes extending straight to the two towns. Your task is to find where the pumping station should be built (i.e. what is the value of x) to minimize the total length of the pipe required to connect both towns to the pumping station. 15 km 7 km x km Pumping station Figure 1: Proposed pumping station. B 4 km (a) Find a function, f(x), for the the total length of the pipe required as a function of x. (8 marks) (b) Using calculus and the expression found in (a) to determine, algebraically, the value of a (in kilometres) that gives the minimum total length of the pipes needed. What is the minimum total length of the pipes required? Check your value of a by substitution into the derivative. Also verify that you have found the minimum by using an appropriate calculus test. (42 marks)
Expert Answer:
Answer rating: 100% (QA)
LUS a 6 7 LI n 27 154 L 7 2 2 54 42 LLithz 2 49 4 For I to be mpossun... View the full answer
Related Book For
Posted Date:
Students also viewed these accounting questions
-
A large embankment is to be built on the surface of a 15-ft clay layer. Before the embankment is built, the initial 'v at the middle of the clay layer is 480 psf. The results from a 1-D consolidation...
-
A large embankment is to be built on the surface of a 15-ft clay layer. Before the embankment is built, the initial 'v at the middle of the clay layer is 480 psf. The results from a 1-D consolidation...
-
In Drosophila, genes a and b are located at positions 22.0 and 42.0 on chromosome 2, and genes c and d are located at positions 10.0 and 25.0 on chromosome 3. A fly homozygous for the wild type...
-
Suppose that we are at time 0 and the interest rate is 10% (d) What is the PV of an asset that pays 20 installments of $5 a year starting today?
-
Oceanview School, a private high school, is preparing a planned income statement for the coming academic year ending August 31, 2013. Tuition revenues for the past two years ending August 31 were as...
-
Determine the resultant of the three forces of Prob. 2.22. Problem 2.22: Determine the x and y components of each of the forces shown. 5 kips 50 9 kips 40 20
-
North Shore Architectural Stone, Inc., a company that installs limestone in residential and commercial buildings, agreed to supply and install limestone for a property owned by Joseph Vitacco. North...
-
The Waygate Corporation makes five different types of metal casing for personal computers. The company is in the process of replacing its machinery with three different new models of metal stamping...
-
Research Web-based database technologies and identify a database management system (other than SQL Server, MySQL, or Oracle) that is used to deploy applications to the Web and the cloud. Discuss the...
-
Download the Applying Excel form and enter formulas in all cells that contain question marks. The Chapter 2 Form worksheet is to be used to create your own worksheet version of the example in the...
-
SNC Lavalin (SNC) is one of the worlds largest engineering firms that has been embroiled in bribery and other questionable ethical activities It is the main contractor for Ottawas new LRT line and...
-
Jessica paid $1,500 for electricity during the tax year. She used one-third of the electricity for personal purposes and two-thirds for farming. Under these circumstances, Jessica can deduct what...
-
What are the advantages and disadvantages of using virtual reality interface for interaction?
-
Homer Simpson finds himself in a panic attempting to meet the April 15th tax deadline. If Homer and his wife have an income of $60,000, earned $1200 in interest, invested $2500 in a tax-deferred...
-
Jonas Company has the following information related to its manufacturing and selling of decorative vases. What are the variable costs and fixed costs that Jonas Company will use to calculate the...
-
What is the DECIDE framework for evaluation and how does it facilitate advanced assessment processes?
-
The table shows values of a force function f(x), where x is measured in meters and f(x) in newtons. Use the Midpoint Rule with n = 4 to estimate the work W done by the force in moving an object from...
-
Prairie Outfitters, Inc., a retailer, accepts paymnent through credit cards. During August, credit card sales amounted to $12,000. The processor charges a 3% fee. Assuming that the credit card...
-
Consider the region R (Figure 8). Set up an integral for the volume of the solid obtained when R is revolved about the given line using the indicated method. (a) The x-axis (washers) (b) The y-axis...
-
Use the Comparison Test of Problem 46 to show that Converges. e-x2 ( e-x on [1, (]? e da
-
Determine the escape velocity for an object launched from each of the following celestial bodies. Here g 32 feet per second per second. Acceleration of Gravity -0.165g -0.85g -2.6g -28g Radius...
-
When translating Acceletrons fi nancial statements into US dollars, Redline is least likely to use an exchange rate of USD per SGD: A . 0.671. B . 0.588. C . 0.654.
-
Yus determination regarding Transaction 2 should be based on the currency of the: A . loan. B . bank. C . borrower.
-
In response to the boards fourth question, the balance sheet exposure (in C$ millions) would be closest to: A . 19. B . 148. C . 400.
Study smarter with the SolutionInn App