The graph of the linear function

It considers the function f: R — R >, f (x) = p x + q, where p and q are real numbers.

a)     find the real numbers p and q knowing that

f (1) = 1 and f (2) =-1

b)     for p = -2 and q = 3, graph the function using xOy coordinates system. 

Geometry - an Aquarium a right prism

The figure is represented schematically an Aquarium in the form of a right prism with square floor, which features 8 dm floor side and the lateral edge of Aquarium of 5 dm. The faces of the Aquarium are made of glass. The Aquarium floor is made from a different material. Aquarium is not covered. Into Aquarium is located water up to a height of 4dm (glass thickness neglect).

a) Calculate how many litres of water are in the Aquarium,

b) Calculate how many square metres of glass are needed to into 100 pcs. of Aquarium, having the dimensions given in the hypotesis,

c) Show that, at any time, the distance between two fish is less than or equal to 12 dm.

Geometry - congruent triangles

The triangle ABC has the measure of 90 degrees of the angle A, the bisector of the angle ABC intersects in point D the side AC and DE is the altitude of the triangle BDC. Find that:

a)  AE is perpendicular to BD ; 

b)  AE is parallel to FC,  where F is the intersecting point of AB and DE: 
 {F} = AB ∩ DE.