Question M04 | FUVEST 2024 | Mathematics Second Round | Special Function
Question M04 | FUVEST 2024 | Second Phase Mathematics | Special Function
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Come see the solution to question M04 from the second phase of the Fuvest 2024 entrance exam. In this math question, we will work with a very interesting function, formed by the sum of two exponential functions.
We will assume that a rope attached to the ends of two parallel rods of the same height describes a curve that is given by the equation 𝑦 = 2^x + 2^{-x}. A graphical representation of this equation, bounded by two vertical lines parallel to the 𝑂𝑦 axis and where the 𝑂𝑥 axis indicates the ground, is given in the figure. The unit of measurement is the meter (m).
a) What is the minimum height that the rope assumes?
b) What will be the height of the rods if the distance between them is 3 m?
c) What is the distance between two points on the string that are 4 m above the ground?
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Question M04 | FUVEST 2024 | Second Phase Mathematics | Special Function