Pre Calculus

User Generated

fxjgf

Mathematics

Description

On page 129, do problems # 1, 3, 7, 9, 11, 13, 17, 21, 23, 27, 39

On page 130, do # 45

NOTE: Please provide detailed steps (show all the work).

Unformatted Attachment Preview

SECTION 2.1 Quadratic Equations 129 Spreadsheet Note To solve f(x) = ax + bx + c = 0 with Excel if it has two solutions: 1. Graph y = f(x) to find x-values close to the x-intercepts, and enter those values in Column A. 2. Use the Goal Seek menu, selecting a cell in column B containing a value at or near 0, setting it to 0, and entering the changing cell in column A that corresponds to the cell in column B. 3. Click OK, and an exact or approximate solution appears in Column A. 4. Repeat the process with a second function value at or near 0 to find a second solution. For example, to solve the equation 0 = -7x + 16x – 4, we use its graph to find x-values close to the x-intercepts (use 2 and 0). The following screens illustrate how Excel works to solve the equation 0 = -7x? + 16x - 4. The first screen shows how we input the formula with val- and 2, and the second screen shows the approximate solutions (in column A). The solutions are x = 0 and x = 0.2857. See Appendix B, Section 2.1, for details. ues near A A B 1 1 x 7x2 + 16x 4 B -7x2 + 16x 4 = -7*A2^2 + 16*A2 - 4 = -7*A3^2 + 16A3 - 4 2 2 2 2 0 3 0 3 0.285688 -0.00032 ✓ CHECKPOINT ANSWERS 1. Zero; zero 2. (a) x= 20; x = -1 (b)x=0; x = 3 3. If ax? + bx+c= 0 and a = 0, then -b + b2 - 4ac 2a 5+ V97 4. x= 4 V97 5 x= = 3.712 or - 1.212. 4 | EXERCISES | 2.1 In Problems 1-4, write the equations in general form. 1. 2x + 3 = x2 - 2x + 4 2. x? - 2x + 5 = 2 - 2x 3. (y + 1)(y + 2) = 4 4. (z - 1)(2-3) = 1 In Problems 5-12, solve each equation by factoring. 5. x - 4x = 12 6. X = 11x - 10 7. 9- 4x = 0 8. 25x - 16 = 0 9. x= x 10. - 4t = 31 11. 41 – 4t + 1 = 0 12. 49z2 + 14z + 1 = 0 In Problems 23-32, use any method to find the exact real solutions, if they exist. 23. x2 + 5x = 21 + x 24. x + 17x = 8x - 14 w W y 11 25. -4 = 0 26. + 1 = 0 8 2 2 6 27. 162? + 162 - 21 = 0 28. 10y - y - 65 = 0 29. (x - 1)(x + 5) = 7 30. (x - 3)(1 – x) = 1 31. 5x = 2x + 6 32. 3x = -6x - 2 In Problems 13-16, solve each equation by using the quadratic formula. Give real answers (a) exactly and (b) rounded to two decimal places. 13. x2 - 4x = 4 14. x + 7 = 6x 15. 2w2 + w +1 = 0 16. 22 + 2z +4= 0 In Problems 33-38, solve each equation by using a graph- ing utility. 33. 21x + 70 = 7x? 34. 3x? + 6 = 11x 35. 300 - 2x -0.01x = 0 36. -9.6 + 2x – 0.1x = 0 37. 25.6x2 - 16.1x - 1.1 = 0 38. 6.8z2 – 4.9z - 2.6 = 0 In Problems 17-22, find the exact real solutions to each equation, if they exist. 17. y2 = 7 18. z = 12 19. 5x = 80 20. 3x2 = 75 21. (x + 4)2 = 25 22. (x + 1)2 = 2 In Problems 39-42, multiply both sides of the equation by the LCD and solve the resulting quadratic equation. 8 39. X + -= 9 40. 1= x + 1 130 CHAPTER 2 Quadratic and Other Special Functions 5 3 41. X = 2x + x-1 X 42. 1 z + 4 2- 2 In Problems 43 and 44, solve using quadratic methods. 43. (X + 8)2 + 3(x + 8) + 2 = 0 44. (s - 2)2 – 5(s - 2) - 24 = 0 53. Corvette acceleration The time t, in seconds, that it takes a Corvette to accelerate to x mph can be described by = 0.001(0.732x2 + 15.417x + 607.738) (Source: Motor Trend). How fast is the Corvette going after 8.99 seconds? Give your answer to the nearest tenth. 54. Social Security trust fund Social Security benefits are paid from a trust fund. As mentioned in the Application Preview, the trust fund balance, B, in trillions of 2012 dollars, t years past the year 2000 is described by APPLICATIONS B= -0.0046 - 0.033t + 6.05 45. Profit If the profit from the sale of x units of a prod- uct is P = 90x - 200 - x?, what level(s) of production will yield a profit of $1200? 46. Profit If the profit from the sale of x units of a prod- uct is P = 16x – 0.1x? – 100, what level(s) of produc- tion will yield a profit of $180? 47. Profit Suppose the profit from the sale of x units of a product is P = 6400x 18x - 400. (a) What level(s) of production will yield a profit of $61,800? (b) Can a profit of more than $61,800 be made? 48. Profit Suppose the profit from the sale of x units of a product is P = 50x - 300 -0.01x? (a) What level(s) of production will yield a profit of $250? (b) Can a profit of more than $250 be made? 49. Flight of a ball If a ball is thrown upward at 96 feet per second from the top of a building that is 100 feet high, the height of the ball is given by S = 100+ 96t – 16tfeet where t is the number of seconds after the ball is thrown. How long after it is thrown is the height 100 feet? 50. Flight of a ball A tennis ball is thrown into the air from the top of a hotel that is 350 feet above the ground. The height of the ball from the ground is given by D(t) = -167 + 10t + 350 feet where t is the time, in seconds, after the ball is thrown. How long after the ball is thrown does it hit the ground? 51. Wind and pollution The amount of airborne particulate pollution p from a power plant depends on the wind speeds, among other things, with the relationship between p and s approximated by p=25 – 0.01 (a) Find the value(s) of s that will make p = 0. (b) What value of s from part (a) makes sense in the context of this application? What does p = 0 mean in this application? 52. Drug sensitivity The sensitivity S to a drug is related to the dosage size by S= 100x - x where x is the dosage size in milliliters. (a) What dosage(s) will yield 0 sensitivity? (b) Explain what your answer in part (a) might (Source: Social Security Administration). Find in what year the trust fund balance is projected to be $5 trillion in the red-that is, when B=-5. 55. Marijuana use For the years from 2001 to 2012, the percent of high school seniors who have tried marijuana can be considered as a function of time according to p= f(t) = 0.177 - 2.611 + 52.64 where t is the number of years past 2000 (Source: National Institute on Drug Abuse). In what year after 2000 is the percent predicted to reach 55%, if this function remains valid? 56. Projectile motion Two projectiles are shot into the air over a lake. The paths of the projectiles are given by (a) y = -0.0013x + x + 10 and (b) y = : + 10 81 31 where y is the height and x is the horizontal dis- tance traveled (both in feet). Determine which pro- jectile travels farther by substituting y = 0 in each equation and finding 57. Percent profit The Ace Jewelry Store sold a necklace for $144. If the percent profit (based on cost) equals the cost of the necklace to the store, how much did the store pay for it? Use + P= (160). с where Pis profit and C is cost. 58. Tourism spending The global spending on travel and tourism (in billions of dollars) can be described by the equation y = 0.787x? - 11.0x + 290 where x equals the number of years past 1990 (Source: World Tourism Organization). Find the year after 1990 in which spending is projected to reach $1000 billion. 59. National health care Using data from 2006 and with projections to 2021, total annual expenditures mean.
Purchase answer to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Explanation & Answer

Attached. Let me know ...


Anonymous
Awesome! Made my life easier.

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4

Related Tags