Question

1.(4 pts) A rectangular tank, shown in Figure A, is 4 ft long, 2 ft wide, and 3 ft high. Initially there is 4 fts of water in the tank and water starts flowing into the tank at the time t Let V (t) denote the volume of the water in the tank at the time t. The graph of V', the derivative of V, o ft3 is given in figure B, where t is in minutes, and V'in min Figure A Figure B 3 ft 2 1 2 3 45 67 8 910 4 ft 2 ft Use the graph in Figure B to answer the questions (a) (g) (a) Find the value and explain what it represents. V'(t)dt 10 J0 (b) Solve the equation for cand mark all the solutions in figure B. V'(c)0 0V(dt (c) Circle all the correct statements about the function V or write "none" ( V() V' (s)ds i) V (t) 4V(s)ds (ii) V (t) V(0)+V(s)ds uwvn-vo-[vods.ods (ovn-v 10 10 (i v) V(t)- V (0)V (s)ds (v) V (t)-4V(s)ds (vi) V (t)-V(0)V(s)ds (d) Find the values. V(10)- : V(4) V(6) : (e) Sketch the graph of V in the figure below. 13 12 10 6 78910 (f) Find an expression for V (t), 0sts 10. 0sts1 44ts6 V (t)- , 8

Answer 1

whene v is the d t volume of wt in 莊 tonk Repsent the volume affnene 2 い(a) + (3)(1)+1(2 ) (2) to +1 (2) (25) ミ

lo for 2 2312

OSts