Test 21 SHOW YOUR WORK Write three cube roots of -216i in rectangular coordinates. Give exact answers. Name: The number of dolphins varied linearly with the number of fish. When 400 fish were present, 250 dolphins appeared, and when 300 fish were present, 200 dolphins appeared. How many dolphins will appear if 250 fish are present? 3. Given the hyperbola 25y2 - 9x2 = 225, write the equation in standard form and find the coordinates of the vertices and the equations of the asymptotes. Graph the hyperbola. 4. If c children could pick 8 flowers in 10 minutes, how many minutes would it take 4 more children to pick y flowers? Graph the solution to the system of inequalities: ( x2 + 32 + 2x - 6y - 26 5 0 y 2 x 2 + 2 6. Write the equation in standard form and graph the ellipse: 16y2 + 25x2 = 400. 7. The perimeter of a 10-sided regular polygon is 120 meters. Find the area of the polygon in square meters. 8. Evaluate: sin Arccos (-,) 9. Solve: 54142 = 42x+3 10. Show: sin' x + sin x cos"x + cot2x = csc2x sin x 11. Write all seven terms of (c + d) 6. 12. Use De Moivre's theorem to find cis 30 ) . Write the answer in rectangular coordinates. Give an exact answer. 13. The urn contained twelve marbles. Seven were blue and five were green. Two marbles were randomly drawn. What is the probability that both were green (a) with replacement and (b) without replacement? 14. A fair coin is tossed 5 times. What is the probability that it will come up heads every time? 15. Two wires are attached to a vertical pole from a point on the ground. The angle between the wires is 32. The longer wire is 108 meters long and is attached to the top of the pole. The shorter wire is attached to a point 60 meters below the top of the pole. Find the length of the shorter wire. 16. The horticulturist observes several patches of strawberries and records the number of strawberries in each patch. The horticulturist then decides that the population counts are normally distributed with a mean of 500 strawberries and a standard deviation of 75 strawberries. If the horticulturist is correct, what percent of strawberry patches would have at least 560 strawberries? Use the Standard Normal Table. 17. Solve 2 csc2 0 - 3 csc 0 - 2 = 0 given that 0 5 0