Homework $3\mathrm{.}1$

$1.[$Submit on zyLabs$]$ We are trying to write a function that implements a piecewise scheme for

determining whether the size of a widget is acceptable to send further along for production. Widgets for

our production line are flat, wide pieces that we use to construct a larger device. The following plot

illustrates acceptable widgets:

Where the areas in black are acceptable widgets, the gray areas are widgets that can be reprocessed,

and the areas in white are unacceptable widgets that need to be discarded. The black area is bounded by:

$=2$

$100$

At the top, and:

$=0\mathrm{.}5$

$100$

At the bottom. The upper gray area is bounded by:

$=5$

$100$

While the lower gray area is bounded by:

$=0\mathrm{.}2$

$100$

Write an equation that takes two inputs:

$-$ The area of a widget, a double that you can assume is greater than $0$

$-$ The thickness of a widget, a double that you can assume is greater than $0$

It should return one output:

$-$ A double with one of $3$ different values:

o $0$ for unacceptable widgets

o $1$ for widgets to be reprocessed

o $2$ for acceptable widgets

You can use the chart above to come up with test case numbers. For instance, an area of $30$ with a

thickness of $0\mathrm{.}01$ would be unacceptable, an area of $35$ with a thickness of $0\mathrm{.}1$ would be reprocessed, and

an area of $20$ with a thickness of $0\mathrm{.}04$ would be accepHomework $3\mathrm{.}1$

$[$Submit on zyLabs$]$ We are trying to write a function that implements a piecewise scheme for determining whether the size of a widget is acceptable to send further along for production. Widgets for our production line are flat, wide pieces that we use to construct a larger device. The following plot illustrates acceptable widgets:

Area or wiaget in $m^{-}$

Where the areas in black are acceptable widgets, the gray areas are widgets that can be reprocessed, and the areas in white are unacceptable widgets that need to be discarded. The black area is bounded by:

thickness $=\frac{\sqrt[\phantom{2}]{2*area}}{100}$

At the top, and:

thickness $=\frac{\sqrt[\phantom{2}]{0\mathrm{.}5*\text{a}\text{r}\text{e}\text{a}}}{100}$

At the bottom. The upper gray area is bounded by:

thickness $=\frac{\sqrt[\phantom{2}]{5*\text{a}\text{r}\text{e}\text{a}}}{100}$

While the lower gray area is bounded by: thickness $=\frac{\sqrt[\phantom{2}]{0\mathrm{.}2*\text{a}\text{r}\text{e}\text{a}}}{100}$

Write an equation that takes two inputs:

The area of a widget, a double that you can assume is greater than $0$

The thickness of a widget, a double that you can assume is greater than $0$

It should return one output:

A double with one of $3$ different values:

$0$ for unacceptable widgets

$1$ for widgets to be reprocessed

$2$ for acceptable widgets

You can use the chart above to come up with test case numbers. For instance, an area of $30$ with a

thickness of $0\mathrm{.}01$ would be unacceptable, an area of $35$ with a thickness of $0\mathrm{.}1$ would be reprocessed, and

an area of $20$ with a thiekness of $0\mathrm{.}04$ would be acceptable.table.