A gardener has 100 meters of fencing to enclose two adjacent rectangular gardens, as shown in the figure. 4x + 3y = 100 %3D (a) Write the area of the enclosed region as a function of x. A(x) = (b) Use a graphing utility to generate additional rows of the table. (Round your answers to one decimal place.) y Area 92 = 30.7 368 = 122.7 2 4 28 224 6. 10 12 14 Use the table to estimate the dimensions that will produce a maximum area. (Round your answers to one decim longer side 2x = m shorter side y = E E
A gardener has 100 meters of fencing to enclose two adjacent rectangular gardens, as shown in the figure. 4x + 3y = 100 %3D (a) Write the area of the enclosed region as a function of x. A(x) = (b) Use a graphing utility to generate additional rows of the table. (Round your answers to one decimal place.) y Area 92 = 30.7 368 = 122.7 2 4 28 224 6. 10 12 14 Use the table to estimate the dimensions that will produce a maximum area. (Round your answers to one decim longer side 2x = m shorter side y = E E
Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Enclosing Rectangular Gardens with a Fixed Amount of Fencing**
A gardener has 100 meters of fencing to enclose two adjacent rectangular gardens, as shown in the figure.
**Diagram Explanation:**
The image shows two adjacent rectangular gardens. The total perimeter of the fencing is represented by the equation \(4x + 3y = 100\), where \(x\) is the width of each garden, and \(y\) is the length.
**Problem Details:**
(a) **Function for Area:**
Write the area of the enclosed region as a function of \(x\).
\[ A(x) = \_\_\_\_ \]
(b) **Use a Graphing Utility:**
Generate additional rows of the table below. (Round your answers to one decimal place.)
| x | y | Area |
|----|------------------|----------------|
| 2 | \( \frac{92}{3} \approx 30.7 \) | \( \frac{368}{3} \approx 122.7 \) |
| 4 | 28 | 224 |
| 6 | | |
| 8 | | |
| 10 | | |
| 12 | | |
| 14 | | |
**Estimate Dimensions for Maximum Area:**
Using the table, estimate the dimensions that will produce the maximum area. (Round your answers to one decimal place.)
- Longer side \(2x = \_\_\_ \) m
- Shorter side \(y = \_\_\_ \) m
Fill in missing values in the table and complete the calculation for the maximum area dimensions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94b6c74d-50b2-4ee4-ae37-0e0d67b5f1e0%2F8702464e-1343-4f63-9abd-9dc732a35180%2Fmgusfju_processed.png&w=3840&q=75)
Transcribed Image Text:**Enclosing Rectangular Gardens with a Fixed Amount of Fencing**
A gardener has 100 meters of fencing to enclose two adjacent rectangular gardens, as shown in the figure.
**Diagram Explanation:**
The image shows two adjacent rectangular gardens. The total perimeter of the fencing is represented by the equation \(4x + 3y = 100\), where \(x\) is the width of each garden, and \(y\) is the length.
**Problem Details:**
(a) **Function for Area:**
Write the area of the enclosed region as a function of \(x\).
\[ A(x) = \_\_\_\_ \]
(b) **Use a Graphing Utility:**
Generate additional rows of the table below. (Round your answers to one decimal place.)
| x | y | Area |
|----|------------------|----------------|
| 2 | \( \frac{92}{3} \approx 30.7 \) | \( \frac{368}{3} \approx 122.7 \) |
| 4 | 28 | 224 |
| 6 | | |
| 8 | | |
| 10 | | |
| 12 | | |
| 14 | | |
**Estimate Dimensions for Maximum Area:**
Using the table, estimate the dimensions that will produce the maximum area. (Round your answers to one decimal place.)
- Longer side \(2x = \_\_\_ \) m
- Shorter side \(y = \_\_\_ \) m
Fill in missing values in the table and complete the calculation for the maximum area dimensions.
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