I have the answers, but I don't know how to get them

1) a = 75, b = -75

2) a = 20, b = 10 3) l = 25, w = 25

5) base = 20, height = 10 6) Max. Volume = .5 x 2 x 2 = 2 3 m 7) length = 1060.6, width = 707.1

8) (-10/13, 2/13)

9) (-2, 2)

10) r=³500/=5.4cm

11) All Square: Area = 2 100cm , All Circle: Area = 2 6.128 cm Square & Circle.: sq: 22.41 cm, circle: 17.59 cm

12) x=2, y=2, Area= 4cm²

1. 2. 10 . 11. 12, Find two numbers whose difference is 15o and whose product is a minimum. Find two positive numbers with product zoo such that the sum of one number and twice the second number is as small as possible. A rectangle has a perimeter of 100 cm. What length and width should it have sothat its area is a maximum? Showthat a rectangle with a given area has a minimum perimeter when It is a square. A box with a square base and open top must have a volume of too are". Find the dimensions of the box that minimizes the amount of material used. A box with an open top is to be constructed from a square piece of cardboard that is 3 m wide, by cutting out a square from each from each of the four corners and bending up the sides Find the largest volume that such a box can have. A farmerwants to fence an area of 350 000 m3 in a rectangular field and divide it in half with a fence parallel to one ofthe sides ofthe rectangle. How can this be done so as to minimize the cost ofthe fence? Find the point on the line y = 5x+ 4, that is closesttothe origin. Find the point on the parabola 2y = x' that is closest to the point ( 4,l]. A can is to be made to hold a litre ofoil. Find the radius ofthe can that will minimize the cost of the metal to make the can. (:LL = 1ooo cm') A piece of wire co cm long is cut into two pieces. One piece is bent into the shape of a square and the other is bent into the shape ofa circle. How should the wire be cut so that the total area enclosed is a) a maximum? b} a minimum? A rectangle is inscribed in a semicircle of radius 2 cm. Find the largest area of such a rectangle