ft2ft2ft2ft2ft2ft22cm3cm3cm3cm3cm3cm331 Find two positive numbers whose product is 144 and whose sum is a minimum.a. 12, 12b. 2, 72c. 4, 362 Consider the following problem: A farmer with 760 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencingparallel to one side of the rectangle. What is the largest possible total area of the four pens?a. 14540 b. 14440 c. 14460 d. 14429 e. 14463 f. 14439 3 If 2600 cm of material is available to make a box with a square base and an open top, find the largest possible volume of the box.a. 12746 b. 12857 c. 12756 d. 12777 e. 12757 f. 12780 4 A rectangular storage container with an open top is to have a volume of 7 m . The length of its base is twice the width. Material for the base costs$15 per square meter. Material for the sides costs $5 per square meter. Find the cost of materials for the cheapest such container.a. $130.72b. $130.7c. $129.7d. $129.2e. $128.4f. $134.9PAGE 1Name: __________________ Class: Date: _____________ (copy A)y = 8x + 6 4864,764 4765,665 5065,765 4864,665 4865,865 4865,665cm2cm2cm2cm2cm2cm25 Find the point on the line that is closest to the origin.a. b. c. d. e. f. 6 Find the dimensions of the rectangle of largest area that can be inscribed in an equilateral triangle of side L = 3 cm if one side of the rectangle lieson the base of the triangle. Round the result to the nearest tenth.a. 2.5 cm, 1.8 cmb. 1.5 cm, 1.4 cmc. 4.5 cm, 0.3 cmd. 1 cm, 1.31 cme. 1.5 cm, 1.3 cmf. 6.5 cm, 1.3 cm7 A right circular cylinder is inscribed in a sphere of radius r = 3 cm. Find the largest possible surface area of such a cylinder. Round the result to thenearest hundredth.a. 96.5 b. 90.39 c. 91.5 d. 91.52 e. 92 f. 91.4 PAGE 2Name: __________________ Class: Date: _____________ (copy A)8 A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of therectangle.) If the perimeter of the window is 45 ft, find the dimensions of the window so that the greatest possible amount of light is admitted. Roundthe result to the nearest hundredth.a. base = 12.58 ft, height = 7.3 ftb. base = 12.6 ft, height = 6.3 ftc. base = 13.6 ft, height = 6.27 ftd. base = 12.6 ft, height = 5.8 fte. base = 12.71 ft, height = 6.3 ftf. base = 12.7 ft, height = 6.5 ft9 A piece of wire 19 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should thewire be cut for the square so that the total area enclosed is a minimum? Round the result to the nearest hundredth.a. 9.26 mb. 7.16 mc. 19 md. 8.31 me. 0 mf. 8.26 m10 A fence 5 ft tall runs parallel to a tall building at a distance of 4 ft from the building. What is the length of the shortest ladder that will reach from theground over the fence to the wall of the building? Round the result to the nearest hundredth.a. 12.90 ftb. 11.60 ftc. 12.69 ftd. 13.70 fte. 14.73 ftf. 12.70 ftPAGE 3Name: __________________ Class: Date: _____________ (copy A)33333311 A conical drinking cup is made from a circular piece of paper of radius R = 7 cm by cutting out a sector and joining the edges CA and CB. Find themaximum capacity of such a cup. Round the result to the nearest hundredth. a. 138.35 cm b. 138.27 cm c. 138.3 cm d. 137.24 cm e. 137.25 cm f. 138.25 cm PAGE 4Name: __________________ Class: Date: _____________ (copy A)y = 3x + 24y = 2x + 24y = 2x + 25y = 2x + 24y = 3x + 2512 A woman at a point A on the shore of a circular lake with radius 4 mi wants to arrive at the point C diametrically opposite on the other side of thelake in the shortest possible time. She can walk at the rate of 7 mi/h and row a boat at 3 mi/h. How should she proceed? (Find ). Round theresult, if necessary, to the nearest hundredth. a. 0.65 radiansb. 0.49 radiansc. She should walk around the lake from point A to point C.d. She should row from point A to point C radianse. 0.44 radiansf. 0.77 radians13 Find an equation of the line through the point (6, 12) that cuts off the least area from the first quadrant.a. b. c. d. e. PAGE 5Name: __________________ Class: Date: _____________ (copy A)14 Consider the figure below , where a = 8, b = 1 and l = 6. How far from the point A should the point P be chosen on the line segment AB so as tomaximize the angle ? Round the result to the nearest hundredth. a. 3.83b. 4.14c. 3.17d. 4.43e. 3.13f. 3.315 A painting in an art gallery has height h = 79 cm and is hung so that its lower edge is a distance d = 12 cm above the eye of an observer (as seenin the figure below). How far from the wall should the observer stand to get the best view? (In other words, where should the observer stand so asto maximize the angle subtended at his eye by the painting?) Round the result to the nearest hundredth. a. 31.69 cmb. 35.57 cmc. 36.4 cmd. 33.05 cme. 31.93 cmf. 33.14 cmPAGE 6Name: __________________ Class: Date: _____________ (copy A) 16 A steel pipe is being carried down a hallway 11 ft wide. At the end of the hall there is a right angled turn into a narrower hallway 9 ft wide. What isthe length of the longest pipe that can be carried horizontally around the corner? Round the result to the nearest hundredth. a. 27.04 ftb. 28.27 ftc. 27.21 ftd. 28.94 fte. 28.24 ftf. 28.29 ft17 Find the maximum area of a rectangle that can be circumscribed about a given rectangle with length L = 3 and width W = 7. a. 47b. 49c. 50d. 60e. 53f. 50.5PAGE 7Name: __________________ Class: Date: _____________ (copy A)x2 11.9x2 11x2 7x2 6.1 x1x2x2=78x2=98x2= 7818 The graph of a function f(x) is given below. Suppose that Newton's method is used to approximate the roots r and s of the equation f(x) = 0. Theblue (1) and red (2) lines are the tangent lines corresponding to initial approximations for finding these roots. In the approximation of the value of r, what is x2? a. b. c. d. 19 Suppose the line y = 8 x 7 is tangent to the curve y = f(x) when x = 1. If Newton's method is used to locate a root of the equation f(x) = 0 and theinitial approximation is = 1, find the second approximation .a. b. c. PAGE 8Name: __________________ Class: Date: _____________ (copy A)x1x1x1x1x1x4x3+ x2 9 = 0, x1= 3x4x4x4x4x1x3x4 29 =0,