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the question translation is below : Exercice 4 (3 points) : Une piscine a la forme d'une pyramide inversee comme indique dans la figure ci-
the question translation is below :
Exercice 4 (3 points) : Une piscine a la forme d'une pyramide inversee comme indique dans la figure ci- dessous, Cette piscine est remplie d'eau jusqu'a une hauteur de 3 metres. Le haut de la piscine est un carre de 10 metres de cote et le fond de la piscine est un carre de 2 metres de cote et la profondeur de piscine est de 4 metres. L'aire d'une tranche horizontale placee a x metres sous le niveau de l'eau de la piscine est A(x) = (8 - 2x) m. 10 Surface de l'eau Tranche horizontale 2 4 En supposant que la densite de l'eau est p km/m' et que l'acceleration de la gravite est g m/sec . Le travail, en Joules, necessaire pour pomper tout l'eau de la piscine par un orifice place a un metre au-dessus de la piscine est donne par l'integrale : (A) pgf (8 -2x) ? (2 + x) dix ; (B) pgf (8 - 2x) (2 + x) dix ; (C) pgf (8 - 2x) (2 + x ) dix ; (D) pgf (8-2x)(5-x) dx ; (E) pgf (8-2x) (1 + x) dx; (F ) pgf (8 -2x ) (1 + x ) dx.Exercise 4 (3 points) : A swimming pool has the shape of an inverted pyramid as shown in the figure below- below, This pool is filled with water up to a height of 3 meters. The top of the swimming pool is a square of 10 meters side and the bottom of the pool is a square of 2 meters side and the pool depth is 4 meters. The area of a horizontal slice placed x meters below the water level of the pool is A(x) = (8 - 2x)2 m2. 10 Water surface Horizontal slice X - 24 Assuming that the density of water is pkm/m3and that the acceleration of gravity is g m/sec2. The work, in Joules, necessary to pump all the water from the pool by a orifice placed one meter above the pool is given by the integral : (A) pgf (8-2x) *(2+x)dx; (B) pg] (8-2x) *(2+x)dx; (C) pgf (8-2x) 3(2+x) dx; (D) pgf (8-2x) (5-x)dx; (E) pg] (8-2x) 2(1+x) dx; (F) pgf (8-2x) (1+x)dx
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