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A rectangle in the first quadrant has can be made with its lower left vertex at the origin, one side along the x-axis, one side along the y-axis, and upper right vertex on the graph of y = 8 – x³. Denote the upper right vertex of the rectangle as (x, y), with x and y measured in meters.

A rectangle in the first quadrant has can be made with its lower left vertex at the origin, one side along the x-axis, one side along the y-axis, and upper right vertex on the graph of y = 8 – x³. Denote the upper right vertex of the rectangle as (x, y), with x and y measured in meters.

Intermediate Algebra
Intermediate Algebra
19th Edition
ISBN:9780998625720
Author:Lynn Marecek
Publisher:Lynn Marecek
Chapter11: Conics
Section11.1: Distance And Midpoint Formulas; Circles
Problem 11.7TI: Use the Midpoint Formula to find the midpoint of the line segments whose endpoints are (3,5) and...
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4) A rectangle in the first quadrant has can be made with its lower left vertex at the origin, one side along the x-axis, one side along the y-axis, and upper right vertex on the graph of y = 8 – x3. Denote the upper right vertex of the rectangle as (x, y), with x and y measured in meters. 10 y = 8 – x3 6. (x, y) 4 2 1 3 a) (3 points) Find a formula for P(x) the perimeter of the rectangle with right side at location x (as a function of x). P(x) : b) (4 points) What is the interval of interest for P(x)? Explain. x in c) (8 points) Find the x-value that gives the maximum perimeter over all such rectangles. (Don't forget to JUSTIFY your answer.) X =
Transcribed Image Text:4) A rectangle in the first quadrant has can be made with its lower left vertex at the origin, one side along the x-axis, one side along the y-axis, and upper right vertex on the graph of y = 8 – x3. Denote the upper right vertex of the rectangle as (x, y), with x and y measured in meters. 10 y = 8 – x3 6. (x, y) 4 2 1 3 a) (3 points) Find a formula for P(x) the perimeter of the rectangle with right side at location x (as a function of x). P(x) : b) (4 points) What is the interval of interest for P(x)? Explain. x in c) (8 points) Find the x-value that gives the maximum perimeter over all such rectangles. (Don't forget to JUSTIFY your answer.) X =
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