PLEASE ANSWER ALL QUESTIONS AND MAKE WRITING CLEAR

A square with side it is changing with time where xit] = 5t - 2. What is the iermula fer the rate at change at the area of the square? a \"A 1002) a \"it 10(5r2) s {1H 2(5r 2) e \"34 =5(5r2) A spherical balloon is expanding with time where r = 3t. What is the formula for the rate of change ofthe volume ofthe balloon with respect to time'?I O \"W = 361112 E av _ 2 o W 43:11 av _ 2 o E _ 108ml _ 2 o d! 27m' Assume that a rectangle with sides at and y is expanding with time. Let y = 3x and m) = 2*: - 1. What is the rate of change of the area when t = 1'? o=24 oiz o \"ii42 Assume that a rectangle with sides x and y is changing with time. Let y = 3x and x(t) = 2t?. What is the rate of change of the area at time t = 2? O dA di = 384 O dA dt = 192 O dA dt = 96 dA O dt = 48What function should be used to maximize the volume of an open box that has a surface area of 24 and has a square bottom? A- O V = 13(24x3] {24 .1'3 ) O = V 4x V _ .t(24+x3] O V = .t(24.t3] The area of a rectangle is A = bh. If the perimeter of the rectangle is 2b + 2h = 24. what formula will maximize the area of the rectangle? o A = (b)(12 b) o A = (1:002 2b) a A = (b)(24 b) o A = (was b) The triangle shown has base to and height h. h Assume that at: + h = 36 to find the maximum area of the triangle? 0 A = 324 O A = 103 O A = 60 O A=54 The area of a rectangle is A = bh. Assume that b + 2h = 28. What is the maximum area of the rectangle? O A = 243 O A = 162 O A = 108 O A = 98A farmer has 600 feet of fencing with which to build a rectangular corral having two internal dividers both parallel to two of the sides of the corral. What is the maximum total area of such a corral? O A = 33,570 square feet 0 A = 18.?50 square feet 0 A = 15,000 square feet 0 A = 11,250 square feet A piece of sheet metal is rectangular, 5 feet wide and 8 feet long. Congruent squares are to be cut from its four corners. The resulting piece of metal is to be folded and welded to form a box with an open top. What would be the dimensions of the box that will maximize its volume? 0- 24 cubic feet 0 18 cubic feet 0 16 cubic feet 0 12 cubic feet