LINKING
concepts... For Individual or Group Explorations
Minimizing Construction Cost
A homeowner needs to run a new water pipe from his house to a water terminal as shown in the accompanying diagram. The terminal is 30 ft down the 10–ft-wide driveway and on the other side. A contractor charges $ 3/ft alongside the driveway and $4/ ftfor underneath the driveway.
a) What will it cost if the contractor runs the pipe entirely under the driveway along the diagonal of the 30–ft by 10–ft rectangle?
b) What will it cost if the contractor runs the pipe 30 ft alongside the driveway and then 10 ft straight across?
c) The contractor claims that he can do the job for $120 by going alongside the driveway for some distance and then going under the drive diagonally to the terminal. Find x. the distance alongside the driveway.
d) Write the cost as a function of x and sketch the graph of the function.
e) Use the minimum feature of a graphing calculator to find the approximate value for x that will minimize the cost.
f) What is the minimum cost (to the nearest cent) for which the job can be done?
Want to see the full answer?
Check out a sample textbook solutionChapter 1 Solutions
College Algebra, Books a la Carte Edition, plus NEW MyLab Math- Access Card Package (6th Edition)
- A vacant lot is being converted into a community garden. The garden and a walkway around its perimeter have an area of 690 square feet. Find the width of the walkway (x) if the garden measures 14 feet wide by 18 feet long. Write answer to 2 decimal places. (Write the number without units). Hint: add 2x to each of the garden dimensions of 14 x 18 feet to get the total area for the length multiplied by width.arrow_forwardSolve x-1 x+2 = 12 3 4 Your Answer: Answerarrow_forwardFind the solutions to the following equation 21x²+5x=6 ○ a) -3/7, 3/2 ☐ b) -2/3, 3/7 ○ c) -7/3, 3/2 ○ d) -2/3, 7/3arrow_forward
- Listen Solve the quadratic equation. Write the one solution, do not write x =. 2 x²+6x+9= 0 বarrow_forwardSolve the rational equation 14 1 + x-6 x x-7 x-7 ○ a) x = 1, x = 8 ○ b) x = 1 ○ c) x = 7 ○ d) x = 1, x = 7arrow_forwardSolve the absolute inequality | x + 5 > 3 ○ a) (-∞, -8] U[-2, ∞0) ☐ b) (-8, -2) c) (-2, ∞0) ○ d) (-∞, - 8) U(-2, ∞0)arrow_forward
- 1) Listen Describe the error in the problem X 3 X x 3 - 2 = 25x = 0 25x 25 x = ±5arrow_forwardA falling object travels a distance given by the formula d = 6t + 7t² where d is in feet and t is the time in seconds. How many seconds will it take for the object to travel 115 feet? Round answer to 2 decimal places. (Write the number, not the units). Your Answer:arrow_forwardListen Solve the quadratic equation. Write the smaller answer first. 2 Xx - 5x = 24 x = Α x =arrow_forward
- Solve the absolute equation |2x = 4| = 10 ○ a) x = -7, x = 3 ○ b) x = -2, x = 6 ○ c) x = -3, x = 7 ○ d) x = 7arrow_forwardFind a rational inequality that has the solution set (-2, 5] О a) x-5 x+2 b) x+5 x-2 ΛΙ ≥ 0 < 0 VI О c) x-5 x+2 ≤0 VI ○ d) x +2 x-5 <0arrow_forward1) Listen Solve the quadratic equation by factoring. One solution is O. Find the other. (Just write the numerical answer, not x =) 2x² + 28x = 0 Your Answer:arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage LearningElementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGALElementary AlgebraAlgebraISBN:9780998625713Author:Lynn Marecek, MaryAnne Anthony-SmithPublisher:OpenStax - Rice UniversityAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning