(ESPCEX 2022) - Question Medium of Mathematics

A store decides to reward its customers. Each customer will receive one of the six possible gifts available, according to their arrival order at the store. The gifts to be distributed are: a ball, a keychain, a pen, a soda, an ice cream, and a CD, in that order. The first customer at the store receives a ball, the second receives a keychain, the third receives a pen, the fourth receives a soda, the fifth receives an ice cream, and the sixth receives a CD. The seventh receives a ball, the eighth receives a keychain, and so on, according to the order of the gifts. The one-thousandth customer will receive as a gift a:

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.

The image presented in the figure is a black and white copy of the square canvas titled The Fish, by Marcos Pinto, which was placed on a wall for exhibition and fixed at points A and B (figure 1). Due to a problem in fixing one of the points, the canvas detached and rotated close to the wall. After the rotation, it was positioned as illustrated in figure 2, forming a 45° angle with the horizon line. Figure 1 Figure 2 To put the canvas back in its original position, it should be rotated, close to the wall, at the smallest possible angle less than 360°. The way to put the canvas back in the original position, following what was established, is by rotating it at an angle of

The Science class is learning about vegetable gardens and decided to plant a small rectangular garden at school, where they will grow lettuce and carrots. The garden's rectangle measures 3 meters in length and 2 meters in width. To find out how many plants will fit in the garden, they need to calculate the perimeter. Help the students calculate the perimeter of this rectangular garden.