\[ \begin{align}\begin{aligned}\newcommand\blank{~\underline{\hspace{1.2cm}}~}\\% Bold symbols (vectors) \newcommand\bs[1]{\mathbf{#1}}\\% Poor man's siunitx \newcommand\unit[1]{\mathrm{#1}} \newcommand\num[1]{#1} \newcommand\qty[2]{#1~\unit{#2}}\\\newcommand\per{/} \newcommand\squared{{}^2} \newcommand\cubed{{}^3} % % Scale \newcommand\milli{\unit{m}} \newcommand\centi{\unit{c}} \newcommand\kilo{\unit{k}} \newcommand\mega{\unit{M}} % % Percent \newcommand\percent{\unit{\%}} % % Angle \newcommand\radian{\unit{rad}} \newcommand\degree{\unit{{}^\circ}} % % Time \newcommand\second{\unit{s}} \newcommand\s{\second} \newcommand\minute{\unit{min}} \newcommand\hour{\unit{h}} % % Distance \newcommand\meter{\unit{m}} \newcommand\m{\meter} \newcommand\inch{\unit{in}} \newcommand\foot{\unit{ft}} % % Force \newcommand\newton{\unit{N}} \newcommand\kip{\unit{kip}} % kilopound in "freedom" units - edit made by Sri % % Mass \newcommand\gram{\unit{g}} \newcommand\g{\gram} \newcommand\kilogram{\unit{kg}} \newcommand\kg{\kilogram} \newcommand\grain{\unit{grain}} \newcommand\ounce{\unit{oz}} % % Temperature \newcommand\kelvin{\unit{K}} \newcommand\K{\kelvin} \newcommand\celsius{\unit{{}^\circ C}} \newcommand\C{\celsius} \newcommand\fahrenheit{\unit{{}^\circ F}} \newcommand\F{\fahrenheit} % % Area \newcommand\sqft{\unit{sq\,\foot}} % square foot % % Volume \newcommand\liter{\unit{L}} \newcommand\gallon{\unit{gal}} % % Frequency \newcommand\hertz{\unit{Hz}} \newcommand\rpm{\unit{rpm}} % % Voltage \newcommand\volt{\unit{V}} \newcommand\V{\volt} \newcommand\millivolt{\milli\volt} \newcommand\mV{\milli\volt} \newcommand\kilovolt{\kilo\volt} \newcommand\kV{\kilo\volt} % % Current \newcommand\ampere{\unit{A}} \newcommand\A{\ampere} \newcommand\milliampereA{\milli\ampere} \newcommand\mA{\milli\ampere} \newcommand\kiloampereA{\kilo\ampere} \newcommand\kA{\kilo\ampere} % % Resistance \newcommand\ohm{\Omega} \newcommand\milliohm{\milli\ohm} \newcommand\kiloohm{\kilo\ohm} % correct SI spelling \newcommand\kilohm{\kilo\ohm} % "American" spelling used in siunitx \newcommand\megaohm{\mega\ohm} % correct SI spelling \newcommand\megohm{\mega\ohm} % "American" spelling used in siunitx % % Inductance \newcommand\henry{\unit{H}} \newcommand\H{\henry} \newcommand\millihenry{\milli\henry} \newcommand\mH{\milli\henry} % % Power \newcommand\watt{\unit{W}} \newcommand\W{\watt} \newcommand\milliwatt{\milli\watt} \newcommand\mW{\milli\watt} \newcommand\kilowatt{\kilo\watt} \newcommand\kW{\kilo\watt} % % Energy \newcommand\joule{\unit{J}} \newcommand\J{\joule} % % Composite units % % Torque \newcommand\ozin{\unit{\ounce}\,\unit{in}} \newcommand\newtonmeter{\unit{\newton\,\meter}} % % Pressure \newcommand\psf{\unit{psf}} % pounds per square foot \newcommand\pcf{\unit{pcf}} % pounds per cubic foot \newcommand\pascal{\unit{Pa}} \newcommand\Pa{\pascal} \newcommand\ksi{\unit{ksi}} % kilopound per square inch \newcommand\bar{\unit{bar}} \end{aligned}\end{align} \]

Dec 03, 2024 | 333 words | 3 min read

3.2.2. Task 2

Learning Objectives

By the end of this task, you will be able to identify conditions and implement conditional logic with confidence. You’ll learn how to interpret and analyze flowcharts that use conditional statements, allowing you to predict outcomes based on different inputs. Additionally, you’ll develop the skills to debug control statements, ensuring that the logic in your programs or spreadsheets accurately reflects the decisions you intend to make.

Instruction

In programming, you will often need your program to make decisions based on the conditions it is given. You can tell your programs when to make decisions by writing conditional statements into your program or spreadsheet. Conditional statements check if a condition is either True or False and then perform actions based on the outcome.

Part A

1. Below is a Flowchart. for a program that takes the variables \(x\) and \(y\) as inputs and then outputs the value of \(z\).

   Determine the output for each of the following inputs.

   1. \(x = 40, y = 40\)

   2. \(x = 20, y = 20\)

   3. \(x = 55, y = 20\)

Fig. 3.9 Flowchart.

Part B

2. You are given the task of writing a program that finds the real roots of a quadratic function of the form \(f(x) = ax^2 + bx + c\). Recall from algebra that there are three possible values for the number of real roots of a quadratic function depending on the value of the discriminant \((b^2 - 4ac)\).

3. Create a flow chart for a program that takes \(a\), \(b\), and \(c\) as inputs, uses conditional statements with the discriminant to determine how many real roots there are, and prints the value of the root(s).

   Table 3.6 Discriminant Value

   Value of Discriminant	Results
   \((b^2 - 4ac = 0)\)	one repeated rational solution
   \((b^2 - 4ac > 0)\), perfect square	two rational solutions
   \((b^2 - 4ac > 0)\), not a perfect square	two irrational solutions
   \((b^2 - 4ac < 0)\)	two complex solutions

   Note

   For \(ax^2 + bx + c =0\), where \(a\), \(b\) and \(c\) are real numbers, the discriminant, is the expression under the radical in the quadratic formula: \(b^2 - 4ac\) . It tells us whether the solutions are real numbers or complex numbers and how many solutions of each type to expect.

Task Instructions

1. One team member will open a MS Word document and name it as ex3_team_2_teamnumber.pdf. Be sure to replace teamnumber to your team’s number.

2. Record your responses and submit the file to Gradescope.