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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?
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Chapter 1 Solutions
College Algebra (6th Edition)
- A student completed the problem below. Identify whether the student was correct or incorrect. Explain your reasoning. (identification 1 point; explanation 1 point) 4x 3x (x+7)(x+5)(x+7)(x-3) 4x (x-3) (x+7)(x+5) (x03) 3x (x+5) (x+7) (x-3)(x+5) 4x²-12x-3x²-15x (x+7) (x+5) (x-3) 2 × - 27x (x+7)(x+5) (x-3)arrow_forward2 Add the rational expressions below. Can you add them in this original form? Explain why or why not. 3x-7 5x + x² - 7x+12 4x-12 Show all steps. State your least common denominator and explain in words your process on how you determined your least common denominator. Be sure to state your claim, provide your evidence, and provide your reasoning before submitting.arrow_forwardcarol mailed a gift box to her sister the boxed gift weighed a total of 2 pounds the box alone weighed 13 ounces what was the wright of the giftarrow_forward
- Directions: Use the table below to answer the following questions and show all work. Heights of Females 50.0 51.5 53.0 53.5 54.0 1. What is the average female height? 2. What are all the differences from the mean? 3. What is the variance for the female heights? 4. What is the standard deviation of the heights of the females? 5. What does the standard deviation found in number 4 represent? Write your answer in complete sentences.arrow_forward135 metr uzunlikdagi simni 6:3 nisbatda qismlarga am eatingarrow_forwardIn circle T with m, angle, S, T, U, equals, 168, degreesm∠STU=168∘ and S, T, equals, 12ST=12, find the area of sector STU. Round to the nearest hundredth.arrow_forward
- (±³d-12) (−7+ d) = |||- \d+84arrow_forward(z- = (-2) (→ Use the FOIL Method to find (z — · -arrow_forwardMODELING REAL LIFE Your checking account has a constant balance of $500. Let the function $m$ represent the balance of your savings account after $t$ years. The table shows the total balance of the accounts over time. Year, $t$ Total balance 0 1 2 3 4 5 $2500 $2540 $2580.80 $2622.42 $2664.86 $2708.16 a. Write a function $B$ that represents the total balance after $t$ years. Round values to the nearest hundredth, if necessary. $B\left(t\right)=$ Question 2 b. Find $B\left(8\right)$ . About $ a Question 3 Interpret $B\left(8\right)$ . b represents the total balance checking and saving accounts after 8 years the balance would be 16 / 10000 Word Limit16 words written of 10000 allowed Question 4 c. Compare the savings account to the account, You deposit $9000 in a savings account that earns 3.6% annual interest compounded monthly. A = 11998.70 SINCE 9000 is the principal ( 1+0.036/12)12 times 8 gives me aproxtimately 1997 14 / 10000 Word Limit14 words written of 10000 allowed Skip to…arrow_forward
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