A farmer is planning to build a rectangular enclosure for sheep, using an existing straight fence as one side of the enclosure. The farmer has 100 meters of fencing available for the other three sides. Let $x$ be the length of the sides perpendicular to the existing fence, and let $y$ be the length of the side parallel to the existing fence. The area of the enclosure is given by the function $A(x, y) = xy$.
b. Show that the area of the enclosure can be expressed as a function of $x$ only, $A(x) = 100x - 2x^2$. State the implied domain of $A(x)$ in the context of this problem.
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Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 3 marks, testing your understanding of Solution of Equations f(x) = g(x). It falls under Algebra, number and structure in Unit 3: Mathematical Methods Unit 3. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Extend introductory study of functions, algebra, calculus. Focus on functions, relations, graphs, algebra, and applications of derivatives.
Covers algebra of functions, inverse functions, and solutions of equations and systems of equations.
solution of equations of the form $f(x)=g(x)$ over a specified interval, where $f$ and $g$ are functions of the type specified in the 'Functions, relations and graphs' area of study, by graphical, numerical and algebraic methods, as applicable
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