Regents Review # In the accompanying diagram, PC is tangent to circle at C and PAB is a secant. If PC = 8 and PA = 4, find AB.

Transcription

1 Regents Review # 6 Name: Date: 1. In the accompanying diagram, PC is tangent to circle at C and PA is a secant. If PC = 8 and PA = 4, find A. 3. In the accompanying diagram, DCFG is tangent to circle O at F, ECH is a secant intersecting the circle at A and, ma = 140 and maf = 160. If FC = 10, find AF to the nearest tenth. 2. In the diagram below, chords A and CD intersect at E. If m AEC = 4x, mac = 120, and md = 2x, what is the value of x? A In the accompanying diagram, CD is tangent to circle O at. AO and O are radii, and chord A is drawn. If m AO = 108, find m AD. C. 30 D. 60 page 1

2 5. A sprinkler system is set up to water the sector shown in the accompanying diagram, with angle AC measuring 1 radian and radius A = 20 feet. 7. In the accompanying diagram, PA is tangent to circle O and PC is a secant. If PA = 4 and C = 6, find P. What is the length of arc AC, in feet? A C. 20 D In the accompanying diagram of circle F, FN bisects HJ and m NJ = 68. Find mhg. 8. In the accompanying diagram, PA is tangent to circle O at A, chord AC and secant PCED are drawn, and chords AO and CD intersect at E. If mad = 130 and mac = 50, find m P, m EC, and m PCA. page 2 Regents Review # 6

3 9. Which figure can have the same cross section as a sphere? 11. Which expression is always equivalent to sin x when 0 < x < 90? A. A. cos90 x). cos45 x) C. cos2x) D. cos x. C. D. 12. As shown in the diagram below, a ship is heading directly toward a lighthouse whose beacon is 125 feet above sea level. At the first sighting, point A, the angle of elevation from the ship to the light was 7. A short time later, at point D, the angle of elevation was The equation of a circle is x 2 + y 2 + 6y = 7. What are the coordinates of the center and the length of the radius of the circle? To the nearest foot, determine and state how far the ship traveled from point A to point D. A. center 0, 3) and radius 4. center 0, 3) and radius 4 C. center 0, 3) and radius 16 D. center 0, 3) and radius 16 page 3 Regents Review # 6

4 13. During an experiment, the same type of bacteria is grown in two petri dishes. Petri dish A has a diameter of 51 mm and has approximately 40,000 bacteria after 1 hour. Petri dish has a diameter of 75 mm and has approximately 72,000 bacteria after 1 hour. 15. A hemispherical water tank has an inside diameter of 10 feet. If water has a density of 62.4 pounds per cubic foot, what is the weight of the water in a full tank, to the nearest pound? A. 16, ,673 C. 130,690 D. 261,381 Determine and state which petri dish has the greater population density of bacteria at the end of the first hour. 16. Given: Circle O, chords A and CD intersect at E 14. Line segment EA is the perpendicular bisector of ZT, and ZE and TE are drawn. Theorem: If two chords intersect in a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord. Which conclusion can not be proven? Prove this theorem by proving AE E = CE ED. A. EA bisects angle ZET.. Triangle EZT is equilateral. C. EA is a median of triangle EZT. D. Angle Z is congruent to angle T. page 4 Regents Review # 6

5 17. A snow cone consists of a paper cone completely filled with shaved ice and topped with a hemisphere of shaved ice, as shown in the diagram below. The inside diameter of both the cone and the hemisphere is 8.3 centimeters. The height of the cone is 10.2 centimeters. 18. New streetlights will be installed along a section of the highway. The posts for the streetlights will be 7.5 m tall and made of aluminum. The city can choose to buy the posts shaped like cylinders or the posts shaped like rectangular prisms. The cylindrical posts have a hollow core, with aluminum 2.5 cm thick, and an outer diameter of 53.4 cm. The rectangular-prism posts have a hollow core, with aluminum 2.5 cm thick, and a square base that measures 40 cm on each side. The density of aluminum is 2.7 g/cm 3, and the cost of aluminum is $0.38 per kilogram. If all posts must be the same shape, which post design will cost the town less? How much money will be saved per streetlight post with the less expensive design? The desired density of the shaved ice is g/cm 3, and the cost, per kilogram, of ice is $3.83. Determine and state the cost of the ice needed to make 50 snow cones. page 5 Regents Review # 6

6 Problem-Attic format version c EducAide Software Licensed for use by Jen Calderon Terms of Use at Regents Review # 6 5/20/ , C m P = 25, m EC = 115, and m PCA = 115 A A A [proof] $19.06