### Pipeline Length Minimization Exercise1. **Function Derivation** - Derive a function of the variable $ x $ to represent the total length of the pipeline. - Include a fully labeled diagram illustrating the derivation of the function.2. **Graphing the Function** - Use technology to graph the function that was previously derived. Include the graph in the submission. - Use an appropriate window to illustrate the features of the function as relevant to the question of minimization. - The graph should be hand-drawn into the assignment.3. **Minimum Length Calculation** - Using the graph of the function, determine the minimum length of the pipeline. - State your answer to three decimal places.4. **Optimal $ x $ Value** - What is the value of $ x $ that will minimize the length of the pipeline? - State your answer to three decimal places.### Note:Ensure all diagrams and graphs are clearly labeled and accurately depict the necessary components for understanding the solutions. **Optimizing Waste Treatment Plant Location**On the same side of a straight road are two towns, and the townspeople want to build a waste treatment plant along this road. The waste treatment plant is to be built along this road with pipes extending straight to the two towns. Where should the waste treatment plant be built to minimize the total length of the pipe?**Diagram Explanation:**The diagram illustrates two towns, Town A and Town B, situated on the same side of a straight road. Town A is 1.25 miles from the road, while Town B is 2.125 miles from the road. The distance along the road between the points in line with Town A and Town B is 3.5 miles. The waste treatment plant, represented by a point on the road, is connected to both Town A and Town B by straight pipes. The variable "x" indicates the distance from the orthogonal projection of Town A to the location of the waste treatment plant.**Objective:**The objective is to determine the optimal position of the waste treatment plant along the road, minimizing the total length of the pipes required to connect both towns to the facility.

------------------------------------------------------------------------------- Total pipe line…

Answered: On the same side of a straight road are…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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A man decides which load plan is the best choice if he has an average of 1000.75 min of call in 30 days. Help him choose which plan is the best. Plan X: A fixed fee of £1000 for 30 days for unlimited calls. Plan Y: A fee of £100 for 30 days and a charge of £0.8 per minute (or fractional part) for all calls. Plan Z: A fee of £600 for 30 days, for a total of 30 hours of calls. An additional charge of £0.2 per minute (or fractional part) for all minutes exceeding 30 hours.
Many gas stations give a discount for using cash instead of a credit card. A gas station gives a discount of 10 cents per gallon. William plans to pump 14 gallons. How much will William save by paying cash instead of credit card?
A city park next to a river consists of a recreation area and its parking lot. The city is will use fencing that costs $10/foot to build a fence around the outside of the park, except that they will not build a fence on the side next to the river. They will use fencing that costs $12/foot to build a divider between the parking lot and the recreation area (shown as a dotted line on the diagram). River/No fence a. Write a simplified formula for the area of the park (including both the parking lot and the recreation area) as a function of L and W. Parking I Recreation Area Lot W- b. Write a simplified formula for the cost of all of the fence as a function of L and W. c. The total cost of all of the fencing is $3000. Find a simplified formula for the area of the park as a function of W.
Match each set of measurements with the length of material needed to fence the area. The width of a house is 115 feet, and length of the yard is 185 feet The width of a house is 100 feet, and length of the yard is 200 feet The width of a pasture is 1,000 feet, and the length of the pasture is 550 feet The length of a pasture is 800 feet and the width of the pasture is 700 feet 485 feet 500 feet 3,000 feet 3,100 feet

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