(Originais Teachy 2022) - Question Easy of Mathematics

Imagine you have 432 candies and want to separate them into containers of 100, 10, and individual units to facilitate counting. How would you make this separation? Explain your answer by showing how the number 432 can be decomposed into powers of 10.

In a large engineering system, a building is being designed and energy efficiency is a major concern. To ensure the efficiency of heating and cooling, the air conditioning system must be sized according to the specific needs of the building. The engineer in charge of the project must solve a system of linear equations to determine the ideal operating temperatures. Let the following be the system of equations that models the thermal behavior of the building: 2x + y + 3z = 10, 4x - 6y + 8z = 5, 3x + 7y + 5z = 18. The engineer must rewrite this system of equations in the matrix form Ax = b, where A is the matrix of coefficients, x is the vector of unknowns, and b is the vector of constant terms.

In a renovation, an architect decides to completely cover a right prism with a square base with ceramic tiles that are in the shape of squares. The prism is 3 meters high and the edge of the base measures 2 meters. The tiles are 20 cm on each side. The architect will need to calculate the amount of tiles to cover the entire surface of the prism. How many tiles will be needed to completely cover the prism?