(Originais Teachy 2024) - Question Easy of Mathematics

In Ana's lunchbox, she has 8 green grapes and 6 purple grapes. In João's lunchbox, he has 4 grapes of each color. If they combine all the grapes and divide them equally between them, who will have more grapes, Ana or João? Write two different addition equations that result in the same total number of grapes to help Ana and João divide the grapes fairly.

João is building a fence for his garden. He decided to make the fence in the shape of a rectangle and already knows that the height is 4 meters and the base is 7 meters. Help João calculate the perimeter of the fence. What is the perimeter of João's garden fence?

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.