Home repairs
Characters:
Theme: Linear functions
Competencies
Mathematical competence in science, technology and engineering
Personal, social and learning to learn competence
Competence in cultural awareness and expressions
Subjects and year by Educational System
Spain > Mathematics > 2nd ESO > Algebraic sense
Spain > Mathematics > 2nd ESO > Socio-affective sense
Enunciation
Maria Gaetana Agnesi, an Italian mathematician of the 18th century, well known for the "Agnesi curve", is recognized mainly in the area of analysis, with the publication of the first complete book on Differential and Integral Calculus.
Let us suppose the situation in which Maria Gaetana Agnesi needed to make some repairs in her home and contacted a company in her city for their execution. The company provided her with the rate that would be applied:
- Travel expenses: €6
- Price per hour of work: €9
Please, answer the following questions:
- Try to find a function that connects the total number of hours of work with the total price that Maria must pay.
- What kind of function is it?
- Represent it on a graph.
- Does it make any sense to connect the points in the graph? Give reasons for your answers.
- Calculate how much Maria must pay if the repairs take 2 hours and 30 minutes.
Observations and context
- Some of Maria Gaetana Agnesi's forerunners in mathematics, philosophy and astronomy are Theano of Crotone (c. 546 BC - c. 450 BC), Hypatia of Alexandria (c. 370 – c. 416) and, in the early modern period, Sophia Brahe (1556-1643), Maria Cunitz (1610-1664), and Elena Lucrezia Cornaro Piscopia (1646 -1684).
- Some of her contemporaries were renowned scientists such as Margaretha Kirch (1703-1744), astronomer; Faustina Pignatelli Carafa (1705-1785), physicist and mathematician; Émilie du Châtelet (1706-1749), mathematician, physicist and philosopher; Laura Maria Catharina Bassi (1711-1778), scientist, poet, and philosopher; Angelique-Marguerite le Boursier du Coudray (1712-1794), midwife; Dorothea Christiane Leporin (1715-1762), doctor; Anna Morandi Manzolini (1716-1774), anatomist; Marie-Geneviève-Charlotte Thiroux d’Arconville (1720-1805), chemist, anatomist, and biologist; María Juana Rosa Andresa Casamayor de la Coma (1720-1780), mathematician; Nicole-Reine de la Brière Lepaute (1723-1788), astronomer; Marie Anne Victoire Pigeon (1724-1767), mathematician, or Maria Angela Ardinghelli (1728-1825), mathematician and physicist, among others.
- Other relevant scientists in the 18th century were Maria Christina Bruhn (1732-1808), chemist and inventor; Claudine Picardet (1735-1820), chemist, mineralogist and meteorologist; Jeanne Baret (1740-1807), botanist and explorer; Caroline Lucrecia Herschel (1750-1848), astronomer; Marie-Anne Pierrette Paulze (1758-1836), chemist; and Sophie Germain (1776-1831), mathematician and physicist.
Description
Obtaining the algebraic expression of a linear function from a statement and drawing its graphical representation.