Question

A farmer wishes to build a pen(enclosure) to protect his chickens from predatory foxes. He wants the chicken to have as much as freedom and room to move as possible. The fencing comes in 1 meter panels (i.e. no decimal values possible, only integers) and he can afford only 100 panels. The farmer can vary the lengths of the sides of the pen, which will affect the area. Planning restrictions say that the lengths of the sides of the pen must be rectangular and must be in the form provided below.
i. Identify relevant elements of authentic real life situations.
Explain why as the length increases, the width decreases.
Explain why the sides of the pen have been labeled as x and (50-x)
Show why the area(y) is represented by the function y=-x² + 50x

Select appropriate mathematical strategies when solving authentic real-life situation.
ii. The farmer wants to know what areas he would be able to find for different lengths. By choosing different lengths(values of x) find the corresponding areas. You may use a table to show your results.

Apply the selected mathematical strategies successfully to reach a solution.
Represent the quadratic function on a graph to show how area changes with length. Calculate the optimum dimensions(both length and width) of the pen for the iv. farmer.
Justify the degree of accuracy of solution. How realistic is this problem? Would your answer help the farmer? How close to the 'real' value can you get with a function? Justify whether a solution makes sense in the context of the authentic real life situation. How does this problem relate to other situations where the resources are limited? State similar situations where you could use this strategy?​

Answer 1

Answer:

this much long question.

Step-by-step explanation:

I don't know what will be the answer.