b) A container is lifted off a boat at point by crane The arm of the crane is rotated D AG. AB through an angle of to The container is then lowered onto the quay from to The AC. E F. angle of elevation of from is. The length of is metres. D F AB r 1) Prove that (3) 2) Determine the distance the container was lowered onto the quay. (The (2) length of EF.) QUESTION 7 13 Marks A dartboard consists of three concentric circles with diameters dividing it into 12 equal sectors as shown. The radii of the circles are 10cm, 8cm, and 6cm respectively. The diameter AB is parallel to the x-axis. Diagonals CD and EF have equations and respectively. a) Determine the co-ordinates of the centre P of the dartboard. (Leave (5) your answer in surd form if necessary). b) Hence find the equation of the second circle (2) c) Write down the equation of the diameter AB (1) d) Scores for a particular sector are shown on the outer ring of the dartboard. If a dart lands on the inner ring of that sector, the score remains unchanged. If a dart lands between the first and second rings of that sector, the score is doubled, and if a dart lands in the outer ring of that sector, the score is halved. For example, the dart shown in the
b) A container is lifted off a boat at point D by crane AG. The arm of the crane AB is rotated through an angle of to AC. The container is then lowered onto the quay from E to F. The angle of elevation of D from F is. The length of AB is r metres. 1) Prove that (3) 2) Determine the distance the container was lowered onto the quay. (The length of EF.) (2) QUESTION 7 13 Marks A dartboard consists of three concentric circles with diameters dividing it into 12 equal sectors as shown. The radii of the circles are 10cm, 8cm, and 6cm respectively. The diameter AB is parallel to the x-axis. Diagonals CD and EF have equations and respectively. a) Determine the co-ordinates of the centre P of the dartboard. (Leave your answer in surd form if necessary). (5) b) Hence find the equation of the second circle (2) c) Write down the equation of the diameter AB (1) d) Scores for a particular sector are shown on the outer ring of the dartboard. If a dart lands on the inner ring of that sector, the score remains unchanged. If a dart lands between the first and second rings of that sector, the score is doubled, and if a dart lands in the outer ring of that sector, the score is halved. For example, the dart shown in the