A farmer divides a rectangular piece of land into 8 equal-sized rectangular sheep pens as shown in the diagram. Each sheep pen measures x m by y m and is fully enclosed by metal fencing. The farmer uses 480 m of fencing. (i) Show that the total area of land used for the sheep pens, A m2 , is given by ? = 384x − 9.6x2 (ii) Given that x and y can vary, find the dimensions of each sheep pen for which the value of A is a maximum. (There is no need to verify that the value of A is a maximum.)
A farmer divides a rectangular piece of land into 8 equal-sized rectangular sheep pens as shown in the diagram. Each sheep pen measures x m by y m and is fully enclosed by metal fencing. The farmer uses 480 m of fencing. (i) Show that the total area of land used for the sheep pens, A m2 , is given by ? = 384x − 9.6x2 (ii) Given that x and y can vary, find the dimensions of each sheep pen for which the value of A is a maximum. (There is no need to verify that the value of A is a maximum.)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterA: Appendix
SectionA.7: Quadratic Functions And Complex Numbers
Problem 4P: Write x2+12x+1 in the form a(xp)2+q.
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A farmer divides a rectangular piece of land into 8 equal-sized rectangular sheep pens as shown in the diagram.
Each sheep pen measures x m by y m and is fully enclosed by metal fencing. The farmer uses 480 m of fencing.
(i) Show that the total area of land used for the sheep pens, A m2
, is given by
? = 384x − 9.6x2
(ii) Given that x and y can vary, find the dimensions of each sheep pen for which the value of A is a
maximum. (There is no need to verify that the value of A is a maximum.)
Transcribed Image Text:-xm -
ym
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