Mathematics in Second Year: Functions, Multiples and Geometry Exercise Solutions
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Functions, multiples, geometry, linear functions, affine functions, parallelograms, revenue maximization, mathematics exercises, second-year students
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Solutions to exercises on functions, multiples, and geometry for second-year mathematics students, covering topics such as linear and affine functions, parallelograms, and revenue maximization.
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[...] Mathematics in Second Year: Functions, Multiples and Geometry Exercise 1 : The number of subscribers is not proportional to the price of the magazine because the function which associates the price of the magazine with the number of subscribers, is not a linear function. It is not a function of the type y = ax. We can read from the graph that if the price of the magazine is 5 euros, then the number of subscribers is 1000. If we multiply the price of the magazine by i.e euros, the number of subscribers is 750 and not 1000*2, i.e. [...]
[...] Let's take a counter-example: 4 is a multiple of 4 and 12 is a multiple of but 4+12 =16 is not a multiple of 10. Exercise 3 : We have, according to the statement : According to Chasles' relation : We therefore have : ABCD is a parallelogram, we then have : We therefore have : and the quadrilateral ABEC is therefore a parallelogram. F is the symmetric of B with respect to therefore: ABEC is a parallelogram therefore: We therefore have: The quadrilateral FAEC is therefore a parallelogram. [...]
[...] The function R is not an affine function because it is not of the type y = ax + b. In fact, there is the term x². The magazine must be sold for 12.50 euros to maximize revenue. To find this result, we look at the maximum revenue on the graph, which is 7800 euros. We then draw a line parallel to the y-axis passing through this maximum point and look at the intersection of this line with the x-axis. [...]
