Question 1 5 Points A farmer wants to fence an area of 570 000 m- in a rectangular field and divide it in half with a fence parallel to one of the sides of the rectangle. What dimensions of the field will minimize the cost of the fence? Quantity to be minimized: P =4x + 3y ap 855000 A dx therefore A field 150,/ 38 m x 100./ 38 m will minimize the cost of the fence . Quantity to be minimized: P=4x + 3y ap 1125000 B dx therefore A field 375,/ 2 m x 1000./ 2 m will minimize the cost of the fence . C None of the above Quantity to be minimized: P=4x + 3y ap 855000 D =4- dx therefore A field 75,/ 38 m x 200,/ 38 m will minimize the cost of the fence . Quantity to be minimized: P=4x + 3y ap 1125000 E dx x2 therefore A field 500./2 mx 750/2 m will minimize the cost of the fence .Question 2 5 Points A cylindrical can is to be made to hold - Liter of paint. determine the radius and height of the can that will minimize the cost of material required. (that is surface area). ( The can is covered from the Top and the bottom, Im = = 1000 Liter). 500 -3 =5.4 cm A h=10.8 cm 500 - 3 B =5.4 cm h=5.4 cm 250 3 C =4.3 cm h=4.3 cm 500 D r=2x 3 =10.8 cm h =10.8 cm 250 3/ E =4.3 cm h =8.6 cmQuestion 3 5 Points An inverted conical tank is 3 m high with diameter at the top of 1.2 m. Water runs into the tank at a rate of 1.5 m/ min . How fast is the level in the tank rising when the depth at the centre is 2 m? (Round your answer to THREE DECIMAL PLACES, DO NOT ENTER UNITS) Blank 1 Blank 1 Add your answer Question 4 5 Points Helium is blown into a spherical balloon that increases steadily in radius at the rate of 7.00 cm/ Find the rate of increase of the volume of the balloon when the radius is - m. (1 m = 100 cm) - (Round your answer to Two Decimal Places, DO NOT ENTER UNITS). Blank 1 Blank 1 Add your answerQuestion 5 5 Points A rectangular box with open top is to be made from a rectangular sheet of metal 18 cm x 12 cm by cutting out of each corner and turning up the four sides. Find the expression of the volume (Quantity to be maximized), Find the maximum volume in cmof the box and the size of the squares at the corners in cm. V=4r2- 60x + 216 A x=2.4 cm V =228 cm V=12x2- 120x+ 216 B x=2.4 cm V =228 cm C All of the above V=4x3- 60x2+ 216x D x=2.4 cm V =228 cm V=4x- - 60r + 216x E x=2.4 cm V =228 cm=Question 6 5 Points A rocket is launched and is tracked by a radar station, which is located on the ground 4 :/ 3 km from the launch site. What is the vertical speed of the rocket at the instant when its distance from the radar is 8 am and this distance is increasing at the rate of 6250 km/h . (Give your answer in Decimal form DO NOT INTER UNITS) . Blank 1 Blank 1 Add your answer Question 7 5 Points A spotlight on the ground shines on a wall 15m away. A man 1.8 m tall walks from the spotlight towards the wall at a speed of 1.25 /1 . How fast is the shadow on the wall decreasing when he is 3 m from the wall? (Round your answer to Three Decimal Places, DO NOT ENTER UNITS). Blank 1 Blank 1 Add your answerQuestion 8 2 Points The motion of an object (in meters) is given by the parametric equations x(1) =60 / t+1 and y(1)=> Find the magnitude and direction of the instantaneous velocity at 1=3.5 seconds . A V=15.4 m/ @ 69.0 B V =14.1 1/ @ 69.0 C V =39.4 m/ @ 69.0" D V=36.8 m/ @ 69.0 E V =36.9 m/ @ 69.0: Question 9 5 Points A cylindrical tank has a radius of 3 m and a depth of 10 m . water pours out through a crack at rate of 7.50 m/ min. How fast is the level of the water falling? (Round your answer to Three Decimal places DO NOT ENTER UNITS). Blank 1 Blank 1 Add your