1 . Find the exact length of the curre : X = 1+3+2 9= 4+245 ost= 1 answer: 2(252 - 1 ) 2. ) Find the slope of the tangent line to the given polar curve at the point specified value of 0 ' r= cos20, 0 = I answer : 1 3.) Find the area of the region enclosed by one loop of the cure: r= 4cos 30 answer : 4 TT 4. ) Find the exact length of the polar curve, r= 2( 1+cose) answer : 16 5 . ) Find the orthogonal trajectories of the family of curves . x 2 + 24 2 = KZ answer : 4 = cx2 * also try # 31 6 .) A tank contains loool of brine with 15 kg of dissolved salt . Pure water enters the tank at a rate of 10 6 / min . The solution is kept thouroughly mixed and drains from the tank at the same rate. How much salt is in the tank ( a) after t min ? ( b ) after 20 min? answer : y = 15 e -/100 kq ( b) 12.3 kg 7.) Solve: xy'= y + x2 sinx y (TT)=0 answer : 4= - xcosx - X other Problems : 9.5 # 15 , 10.2 # 9 , 11