Hi I was wondering if anyone can help with this it just doesn't click with me...
A 40 cm string is cut in 2. one piece forms a square and the other a circle. find what the lengths of the pieces has to be so that the total of the areas is minimal.
Hi I was wondering if anyone can help with this it just doesn't click with me...
A 40 cm string is cut in 2. one piece forms a square and the other a circle. find what the lengths of the pieces has to be so that the total of the areas is minimal.
let one piece of string have length $\displaystyle x$ ... other piece will have length $\displaystyle 40-x$
let $\displaystyle x$ = piece forming a circle
$\displaystyle x = 2\pi r$ , derive an expression for the circle area in terms of $\displaystyle x$
$\displaystyle 40-x$ = piece forming a square
$\displaystyle 40-x$ = Perimeter of the square , derive an expression for the square area in terms of $\displaystyle x$
total area, $\displaystyle A$ = circle area as a function of $\displaystyle x$ + square area as a function of $\displaystyle x$
find $\displaystyle \frac{dA}{dx}$ and determine the value of $\displaystyle x$ that minimizes the total area