Find the dimensions of a rectangle with perimeter 112 m whose area is as large as...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Find the dimensions of a rectangle with perimeter 112 m whose area is as large as possible. Part 1 of 4 If a rectangle has dimensions x and y, then we must maximize the area A = xy. 56-X. Since the perimeter is 2x + 2y = 112, then y= 56 Part 2 of 4 We must maximize the area A = xy = x(56-x) = 56x - x2, where 0<x< 56✔ Part 3 of 4 Solving 0 = A'(x) gives us x = (No Response) 28 4 Part 4 of 4 56 Since A"(x) = 56 The other dimension of this rectangle is y= Thus, the dimensions of the rectangle with perimeter 112 and maximum area are as follows. m (smaller value) m (larger value) x. then A has an absolute maximum at x = 28. Find the dimensions of a rectangle with perimeter 112 m whose area is as large as possible. Part 1 of 4 If a rectangle has dimensions x and y, then we must maximize the area A = xy. 56-X. Since the perimeter is 2x + 2y = 112, then y= 56 Part 2 of 4 We must maximize the area A = xy = x(56-x) = 56x - x2, where 0<x< 56✔ Part 3 of 4 Solving 0 = A'(x) gives us x = (No Response) 28 4 Part 4 of 4 56 Since A"(x) = 56 The other dimension of this rectangle is y= Thus, the dimensions of the rectangle with perimeter 112 and maximum area are as follows. m (smaller value) m (larger value) x. then A has an absolute maximum at x = 28.
Expert Answer:
Answer rating: 100% (QA)
Soln Also for Given perimeter 7 2n2y112 xy Area A A maxm ... View the full answer
Related Book For
College Mathematics for Business Economics Life Sciences and Social Sciences
ISBN: 978-0321614001
12th edition
Authors: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
Posted Date:
Students also viewed these mathematics questions
-
Find the dimensions of a rectangle with perimeter 100 ft whose area is as large as possible. What is the Main formula to use? What do the variables in the Main formula represent? What is the...
-
Find the dimensions of a rectangle with perimeter 100 m whose area is as large as possible.
-
Find the dimensions of a rectangle with area 1000m2 whose perimeter is as small as possible.
-
Find the exact value of sin(x - y) if sin(x) = 3T 3T T
-
The yield to maturity (YTM) on 1-year zero-coupon bonds is 5% and the YTM on 2-year zeros is 6%. The yield to maturity on 2-year-maturity coupon bonds with coupon rates of 12% (paid annually) is...
-
How do marketers customize pricing with pricing segmentation, peak load pricing, and surge pricing? How can marketers price to meet the need of bottom of the pyramid consumers?
-
The coefficient of determination R2 measures the percentage of variation in the outcome that is explained by the model. In Exercises 9 and 10, determine whether the statement is true or false. If the...
-
1. Woodbine had petitioned the INS to allow Filipinos as RNs, committing to pay them the same wages, but did not do so. What factors may have led to this failure? 2. Some of the Filipino RNs were...
-
Samsung Electronics Company is a global leader in semiconductor, telecommunication, digital media and digital convergence technologies with 2012 consolidated sales of US $181.7 billion. Employing...
-
1. Display the age and name for the pilot who was the oldest when HIRED. 2. Using a SET OPERATOR, display the pilots and the number of miles flown as "Miles Flown", include pilots who have not yet...
-
1. The capital market is a market prepared for trading stocks, securities. The capital market acts as a liaison between investors and companies or government institutions through long-term trading...
-
The gas mixture contains 3 2 0 mg of methane CH 4 , 1 7 5 mg of argon Ar and 2 2 5 mg of neon Ne . Neon partial pressure at 3 0 0 K is 8 . 8 7 kPa. Calculate a ) the volume of the gas mixture b )...
-
Spiller Corporation plans to issue 10%, 15-year, $500,000 par value bonds payable that pay interest semiannually on June 30 and December 31. The bonds are dated January 1 of the current year and are...
-
3. What is the sale price of a $1600 laptop that is 20% off? Write a model, s(r), for the sale price of a $1600 laptop if it is r% off. (Careful with the percent to decimal conversion here.) s(r) =...
-
Prophet At Once, By Force Ltd has Maintenance and Canteen Departments that support the four production departments A , B , C , and D . Details of the total overheads for the first quarter of 2 0 1 8...
-
Boron trifluoride gas is collected at 8.0C in an evacuated flask with a measured volume of 40.0%. When all the gas has been collected, the pressure in the flask is measured to be 0.190atm. Calculate...
-
Several friends use simple rope and pulley to raise a tree house from the ground into a tree. The moss of the tree heuse is 150kg. By pulling together, the friends manage exert an everage force of...
-
Before the latest financial crisis and recession, when was the largest recession of the past 50 years, and what was the cumulative loss in output over the course of the slowdown?
-
point of diminishing returns. A baseball cap manufacturer is planning to expand its workforce. It estimates that the number of baseball caps produced by hiring x new workers is given by T(x)=-0.25x4...
-
Solve Problems 13-30 by using any method. 14. x2 = -3/4x 16. 9y2 - 25 = 0 18. 9x2 - 6 = 15x 20. m2 = 1 - 3m 22. 2x2 = 4x - 1 24. x2 -2x = -3 26. (5x - 2)2 = 7 30. 2
-
In Problem, sketch a possible graph of a function that satisfies the given conditions at x = 1 and discuss the continuity off at x = l. f(1)- 2 and lim f(x 2
-
Your medical terminology instructor listed the following grades for the class out of a 75-point test: 34, 36, 41 , 43, 44,49,50, 55,57, 60,64, 66, 67,67, 67,68,68,69, 70, 73 a. Find the 90th...
-
From the following list of number of discharges each day in September, compute the mean, median, mode, and range. Round the mean and median to one decimal point. University Hospital Number of...
-
Use the following information to compute the ALOS and median LOS and range for Community Nursing Center. The discharge date is June 2, 20XX (a non-leap year). Round the ALOS to one decimal place....
Study smarter with the SolutionInn App