A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 8 - x. What are the dimensions of such a rectangle with the greatest possible area? Width = Height =
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 8 - x. What are the dimensions of such a rectangle with the greatest possible area? Width = Height =
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter4: Polynomial And Rational Functions
Section4.1: Quadratic Functions
Problem 96E
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Pls hlp.
![**Problem Statement:**
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola \( y = 8 - x^2 \). What are the dimensions of such a rectangle with the greatest possible area?
**Inputs Required:**
- Width = [Input Box]
- Height = [Input Box]
**Explanation:**
In this problem, you are asked to find the dimensions of a rectangle that is inscribed under the parabola \( y = 8 - x^2 \). The rectangle's base lies on the x-axis, and its upper corners touch the parabola. The goal is to determine the width and height of the rectangle that result in the maximum area. The problem involves using calculus or geometric reasoning to find the optimal dimensions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7bdf3309-fa76-4a47-91fb-d52ef92fe6e2%2F7e825b72-903e-4f2d-9fdc-6d68ac5161da%2F6nuv9n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola \( y = 8 - x^2 \). What are the dimensions of such a rectangle with the greatest possible area?
**Inputs Required:**
- Width = [Input Box]
- Height = [Input Box]
**Explanation:**
In this problem, you are asked to find the dimensions of a rectangle that is inscribed under the parabola \( y = 8 - x^2 \). The rectangle's base lies on the x-axis, and its upper corners touch the parabola. The goal is to determine the width and height of the rectangle that result in the maximum area. The problem involves using calculus or geometric reasoning to find the optimal dimensions.
Transcribed Image Text:**Problem Statement:**
A rancher wants to fence in an area of 3,000,000 square feet in a rectangular field and then divide it in half with a fence down the middle parallel to one side. What is the shortest length of fence that the rancher can use?
**Explanation:**
The given problem involves a rancher who needs to enclose a rectangular area of 3,000,000 square feet with additional fencing required to divide this area into two equal halves. The objective is to determine the minimum total length of fencing required, considering one of these dividing lines runs parallel to one of the sides of the rectangle.
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