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Assume a circle is expanding with time. where r = t + 2. What is the formula for the rate of change cf the area cf the circle with respect to time? D =(t+2) d: O % =2:r(t+2) c % =2:r(r2) O %=(t+2)2 Assume that an airplane is flying toward you at a constant helght, h miles, and at a speed %. X 1When the plane is x miles away. what is the rate of change of 19'? tan(i9) = % O @_ a a d: x2+h1dr 0 __ h a d: _ x2\"; d: 0 _ h? a d: _ x3+h3 d: 0 = _h2 a d! X2+hl (I! Assume a circle is expanding with time where r = t + 2. What is the rate of change of the area of the circle at time t = 2? O dA = 8x O dA dt = 4n O dA = 61 di O dA dt = 2nThe volume of a sphere is expanding where r = 2t + 1. What is the rate of change in volume with respect to time when t = 1? The volume of a sphere is V = 4 x7-3. O dV dt = 108AT O dV dt = 72n O dV dt = 161 O dv dt = 32nGiven the area of a rectangle is A = bh, and assuming the rectangle is open on one side with a perimeter of b + 2h = 40, what formula will maximize the area of the rectangle? O A = 40h - h2 O A = 20h - 2h2 O A = 40h - 2h2 O A = 20h - h2For the diagram shown: If the area of the inner region A = xy = 100, what equation will minimize the total area TA = (x+ 1)(y + 1)? x +1 X Y y +1 O TA = (x - 1) ( 100 + 1 ) O TA = (x + 1) ( 100 - 1) O TA = (x+ 1) (10 + 1 ) O TA = (x - 1) (100 X - 1)The area of a rectangle is A = bh. Given the perimeter of the rectangle is 2b + 2h = 32, what dimensions maximize the area of the rectangle? O b = 10, h = 10 O b = 8. h = B O b = 8. h = 6 O b=9,h=? What dimensions will maximize the lateral surface area of an inverted cone, ii 'v' = 27 cm'? 0 r = 4.50, h = 3.50 O r = 4.52, h = 3.75 O r = 2.63, h = 3.?2 O r = 4.07, h = 5.86 Sue wants to build an enclosed area behind her house for her pets. One wall of the enclosed area will be the back of her house. She needs to the total area to be 90 square feet. She wants to minimize the cost of the fence materials. For the sides. W. fence materials cost $3 fit; for the length. L they cost $5 fft. What dimensions should the fence be? W L O W = 8.435 , L = 7.0?1 ft 0 W= 11.243ft. L=12.U?1 ft 0 W=10.4ft.L=8.56 O W = 3.485 f1, L = 3.5361! Jill is building a right triangular shelf which will fit into the corner of a room. The shelf has sides x and y where x + y = 10. What is the largest area possible for the shelf given the constraints? 2 3' X o A=13.5 o A=11.5 o A=12.5 O A=9.5