(Originais Teachy 2024) - Question Medium of Mathematics

During the cleaning of the cooling system of a factory, a technician must adjust a light reflector fixed on the ceiling of the room. The reflector has the shape of a right circular cone with the vertex pointing upwards and an opening angle of 75º. The technician wants to calculate the height and the radius of the base of the cone to determine the ideal dimensions of the mirrors that will be installed on the inner surface of the cone, so that the reflected light follows a beam parallel to the floor. Consider that the angle of incidence of light on the inner surface of the cone should be 15º with the normal to the surface at the point of incidence to ensure total reflection of light. Based on this configuration, determine the height and the radius of the base of the cone, and additionally, identify the value of the sine and cosine of 22.5º, an angle that arises in the resolution of the problem.

Imagine you are helping your younger brother with a Math assignment. He asked you what a rational number is. Explain to him, in a simple way, what a rational number is. Remember to mention the different ways a rational number can be written, such as fractions, decimal numbers, and recurring decimals.

Pedro and Maria are playing a race. Pedro ran for 15 minutes and Maria ran for 1/4 of an hour. Who ran for a longer time? Justify your answer. In addition, they measured the distance they ran with a tape measure. If Pedro ran 300 meters and Maria ran 0.3 kilometers, who ran a longer distance? Explain your answer using what you know about units of length and time measurement.