Writing a better solution

Writing a better solution

Postby JJKD » Mon Mar 12, 2018 12:52 pm

Hey guys,

Firstly, just to give context, I'm starting an OU degree in Autumn with Math as my first module. My math is questionable so I've been given a few practise papers to prepare myself and there are a few questions I just can't grasp, even with all the materials I've been given.

The Question:

Consider the following exam question and a student’s attempt at a solution.

''Anny wants to fence off an area in the middle of a field in order to
make an enclosure for some pigs. She has 200 metres of fencing
available. Should she make the fencing in the shape of a square or a
circle, in order to enclose the greatest area?''

Annie's solution:

200 = 2πr
= πr^2 = 3183.
200 = 4l
l^2 = 2500, so circle.

(a) Criticise the solution, explaining why it is difficult to follow.

(b) Write out a better solution.

Thanks :)

EDIT: Sorry if this is the wrong place to post! Like I said, my math is questionable so I'm even unsure about the topic title!
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Re: Writing a better solution

Postby Guest » Mon Mar 12, 2018 2:47 pm

It's clear to me that Annie understanding of the problem is fine, and that therefore the only legitimate criticism of her solution pertains to its exposition.

Some people are under the mistaken impression that good mathematical writing consists of numbers and symbols and uses as few words as possible. Adding some English around the equations will make Annie's solution much more readable. Particularly critical is explaining what each variable used is intended to represent. I also isolated r and l before substituting them into the area equations and added units where appropriate.

A circle of perimeter 200m has a radius, r, satisfying
200m = 2πr
or r = 200m/(2π)
and an area given by [tex]A_{cir}= πr^2[/tex] or approximately 3183m^2.

A square of perimeter 200m has a side length, l, satisfying
200m = 4l
or l = 50m
and an area given by [tex]A_{sq}=l^2[/tex]= 2500m^2, so the circle has the greater area.

Re: Writing a better solution

Postby Guest » Wed Sep 25, 2019 12:57 pm

The first two lines are
200= 2πr
= πr^2= 3183.

The leading "=" in the second line means that it is a continuation of the first line. That is, it is saying 2πr= πr^2 which is not true! There is no mention if what "r" or "l" represent nor is there any indication where "3183" or "2500" came from.

A better form would be
"Letting r be the radius of the circle, its circumference is 2πr= 200 m of fencing. So r= 200/2π= 100/π. Then the area of the circle is πr^2= π(10000/π^2)= 10000/π which is about 3183 square meters.

Letting l be the length of a side of the square, its perimeter is 4l= 200 m so l= 50 m. The area is 50^2= 2500 square meters."

Re: Writing a better solution

Postby Guest » Wed Jun 22, 2022 1:56 am

In this advance technological world everyone want avoid losses in each firm and company etc. So nursing assignment help all of users trying to find writing better solutions. To my point of view that this solution is a good source to improve writing skills.

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