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Mark Dugopolski, College Algebra, 4th Edition

201. Celsius to Fahrenheit. Fahrenheit temperature F is a linear function of Celsius temperature C. When C = 0, F = 32. When C = 100, F = 212. Use the point-slope form to write F as a linear function of C. What is the Fahrenheit temperature when C = 45?

202. Velocity of a projectile. The velocity v of a projectile is a linear function of the time t that it is in the air. A ball is thrown downward from the top of a tall building. Its velocity is 42 feet per second after 1 second and 74 feet per second after 2 seconds. Write v as a linear function of t. What is the velocity when t = 3.5 seconds?

203. Natural gas. The cost C of natural gas is a linear function of the number n of cubic feet of gas used. The cost of 1000 cubic feet of gas is $39, and the cost of 3000 cubic feet of gas is $99. Express C as a linear function of n. What is the cost of 2400 cubic feet of gas?

204. Expansion joint. The width of an expansion joint on the Carl T. Hull bridge is a linear function of the temperature of the roadway. When the temperature is 90 °F, the width is 0.75 inch. When the temperature is 30 °F, the width is 1.25 inches. Express w as a linear function of t. What is the width of the joint when the temperature is 80 °F?

205. Perimeter of a rectangle. The perimeter P of a rectangle with a fixed width is a linear function of its length. The perimeter is 28 inches when the length is 6.5 inches, and the perimeter is 36 inches when the length is 10.5 inches. Write P as a linear function of L. What is the perimeter when L = 40 feet? What is the fixed width of the rectangle?

206. Stretching a spring. The amount A that a spring stretches beyond its natural length is a linear function of the weight w placed on the spring. A weight of 3 pounds stretches a certain spring 1.8 inches and a weight of 5 pounds stretches the same spring 3 inches. Express A as a linear function of w. How much will the spring stretch with a weight of 6 pounds?

207. Velocity of a bullet. If a gun is fired straight upward, then the velocity v of the bullet is a linear function of the time t that has elapsed since the gun was fired. Suppose that the bullet leaves the gun at 100 feet per second (time t = 0) and that after 2 seconds its velocity is 36 feet per second. Express v as a linear function of t. What is the velocity after 3 seconds?

208. Enzyme concentration. The amount of light absorbed by a certain liquid is a linear function of the concentration of an enzyme in the liquid. A concentration of 2 mg/ml (milligrams per milliliter) produces an absorption of 0.16 and a concentration of 5 mg/ml produces an absorption of 0.40. Express the absorption a as a linear function of the concentration c. What should the absorption be if the concentration is 3 mg/ml? Use the accompanying graph to estimate the concentration when the absorption is 0.50.

209. Basal energy requirement. The basal energy requirement B is the number of calories that a person needs to maintain the life processes. B depends on the height, weight, and age of the person. For a 28-year-old female with a height of 160 cm, B is a linear function of the person’s weight w (in kilograms). For a weight of 45 kg, B is 1300 calories. For a weight of 50 kg, B is 1365 calories. Express B as a linear function of w. What is B for a 28-year-old 160-cm female who weighs 53.2 kg?

210. Threshold weight. The threshold weight for an individual is the weight beyond which the risk of death increases significantly. For middle-aged males the function W(h) = 0.000534h3 expresses the threshold weight in pounds as a function of the height h in inches. Find W(70). Find the threshold weight for a 6¢ 2² middle-aged male.

211. Pole vaulting. The height a pole vaulter attains is a function of the vaulter’s velocity on the runway. The function h(v) = v2/64 gives the height in feet as a function of the velocity v in feet per second. a) Find h(35) to the nearest tenth of an inch. b) Who gains more height from an increase of 1 ft/sec in velocity: a fast runner or a slow runner?

212. Credit card fees. A certain credit card company gets 4% of each charge, and the retailer receives the rest. At the end of a billing period the retailer receives a statement showing only the retailer’s portion of each transaction. Express the original amount charged C as a function of the retailer’s portion r.

213. More credit card fees. Suppose that the amount charged on the credit card in the previous exercise includes 8% sales tax. The credit card company does not get any of the sales tax. In this case the retailer’s portion of each transaction includes sales tax on the original cost of the goods. Express the original amount charged C as a function of the retailer’s portion.

214. Profitable pumps. Walter Waterman, of Walter’s Water Pumps in Winnipeg has found that when he produces x water pumps per month, his revenue is x2 + 400x + 300 dollars. His cost for producing x water pumps per month is x2 + 300x – 200 dollars. Write a polynomial that represents his monthly profit for x water pumps. Evaluate this profit polynomial for x = 50.

215. Manufacturing costs. Ace manufacturing has determined that the cost of labor for producing x transmissions is 0.3x2 + 400x + 550 dollars, while the cost of materials is 0.1x2 + 50x + 800 dollars. a) Write a polynomial that represents the total cost of materials and labor for producing x transmissions.
b) Evaluate the total cost polynomial for x = 500. c) Find the cost of labor for 500 transmissions and the cost of materials for 500 transmissions

216. Perimeter of a triangle. The shortest side of a triangle is x meters, and the other two sides are 3x + 1 and 2x + 4 meters. Write a polynomial that represents the perimeter and then evaluate the perimeter polynomial if x is 4 meters.

217. Perimeter of a rectangle. The width of a rectangular playground is 2x – 5 feet, and the length is 3x + 9 feet. Write a polynomial that represents the perimeter and then evaluate this perimeter polynomial if x is 4 feet.

218. Before and after. Jessica traveled 2x + 50 miles in the morning and 3x – 10 miles in the afternoon. Write a polynomial that represents the total distance that she traveled. Find the total distance if x = 20.

219. Total distance. Hanson drove his rig at x mph for 3 hours, then increased his speed to x + 15 mph and drove for 2 more hours. Write a polynomial that represents the total distance that he traveled. Find the total distance if x = 45 mph.

220. Sky divers. Bob and Betty simultaneously jump from two airplanes at different altitudes. Bob’s altitude t seconds after leaving the plane is –16t2 + 6600 feet. Betty’s altitude t seconds after leaving the plane is –16t2 + 7400 feet. Write a polynomial that represents the difference between their altitudes t seconds after leaving the planes. What is the difference between their altitudes 3 seconds after leaving the planes?

221. Height difference. A red ball and a green ball are simultaneously tossed into the air. The red ball is given an initial velocity of 96 feet per second, and its height t seconds after it is tossed is 16t2 - 96t feet. The green ball is given an initial velocity of 30 feet per second, and its height t seconds after it is tossed is –16t2 + 80t feet. a) Find a polynomial that represents the difference in the heights of the two balls. b) How much higher is the red ball 2 seconds after the balls are tossed? c) In reality, when does the difference in the heights stop increasing?

222. Total interest. Donald received 0.08(x + 554) dollars interest on one investment and 0.09(x + 335) interest on another investment. Write a polynomial that represents the total interest he received. What is the total interest if x = 1000?

223. Total acid. Deborah figured that the amount of acid in one bottle of solution is 0.12x milliliters and the amount of acid in another bottle of solution is 0.22(75 – x) milliliters. Find a polynomial that represents the total amount of acid. What is the total amount of acid if x = 50?

224. Harris-Benedict for females. The Harris-Benedict polynomial 655.1 + 9.56w + 1.85h – 4.68a represents the number of calories needed to maintain a female at rest for 24 hours, where w is her weight in kilograms, h is her height in centimeters, and a is her age. Find the number of calories needed by a 30-year old 54-kilogram female who is 157 centimeters tall.

225. Harris-Benedict for males. The Harris-Benedict polynomial 66.5 + 13.75w + 5.0h + 6.78a represents the number of calories needed to maintain a male at rest for 24 hours, where w is his weight in kilograms, h is his height in centimeters, and a is his age. Find the number of calories needed by a 40-year-old 90-kilogram male who is 185 centimeters tall.

226. Office space. The length of a professor’s office is x feet, and the width is x + 4 feet. Write a polynomial that represents the area. Find the area if x = 10 ft.

227. Swimming space. The length of a rectangular swimming pool is 2x – 1 meters, and the width is x = 2 meters. Write a polynomial that represents the area. Find the area if x is 5 meters.

228. Area of a truss. A roof truss is in the shape of a triangle with a height of x feet and a base of 2x + 1 feet. Write a polynomial that represents the area of the triangle. What is the area if x is 5 feet?

229. Volume of a box. The length, width, and height of a box are x, 2x, and 3x – 5 inches, respectively. Write a polynomial that represents its volume.

230. Number pairs. If two numbers differ by 5, then what polynomial represents their product? Number pairs. If two numbers have a sum of 9, then what polynomial represents their product?

231. Area of a rectangle. The length of a rectangle is 2.3x + 1.2 meters, and its width is 3.5x + 5.1 meters. What polynomial represents its area?

232. Patchwork. A quilt patch cut in the shape of a triangle has a base of 5x inches and a height of  1.732x inches. What polynomial represents its area?

233. Total revenue. If a promoter charges p dollars per ticket for a concert in Tulsa, then she expects to sell 40,000 – 1000p tickets to the concert. How many tickets will she sell if the tickets are $10 each? Find the total revenue when the tickets are $10 each. What polynomial represents the total revenue expected for the concert when the tickets are p dollars each?

234. Manufacturing shirts. If a manufacturer charges p dollars each for rugby shirts, then he expects to sell 2000 – 100p shirts per week. What polynomial represents the total revenue expected for a week? How many shirts will be sold if the manufacturer charges $20 each for the shirts? Find the total revenue when the shirts are sold for $20 each. Use the bar graph to determine the price that will give the maximum total revenue.

235. Periodic deposits. At the beginning of each year for 5 years, an investor invests $10 in a mutual fund with an average annual return of r. If we let x = 1 + r, then at the end of the first year (just before the next investment) the value is 10x dollars. Because $10 is then added to the 10x dollars, the amount at the end of the second year is (10x + 10)x dollars. Find a polynomial that represents the value of the investment at the end of the fifth year. Evaluate this polynomial if r = 10%.

236. Increasing deposits. At the beginning of each year for 5 years, an investor invests in a mutual fund with an average annual return of r. The first year, she invests $10; the second year, she invests $20; the third year, she invests $30; the fourth year, she invests $40; the fifth year, she invests $50. Let x = 1 + r as in Exercise 101 and write a polynomial in x that represents the value of the investment at the end of the fifth year. Evaluate this polynomial for r = 8%.

237. Area of a rug. Find a trinomial that represents the area of a rectangular rug whose sides are x + 3 feet and 2x – 1 feet.

238. Area of a parallelogram. Find a trinomial that represents the area of a parallelogram whose base is 3x + 2 meters and whose height is 2x + 3 meters.

239. Area of a sail. The sail of a tall ship is triangular in shape with a base of 4.57x + 3 meters and a height of 2.3x – 1.33 meters. Find a polynomial that represents the area of the triangle.

240. Area of a square. A square has a side of length 1.732x + 1.414 meters. Find a polynomial that represents its area.

241. Exploration. Find the area of each of the four regions shown in the figure. What is the total area of the four regions? What does this exercise illustrate?

242. Shrinking garden. Rose’s garden is a square with sides of length x feet. Next spring she plans to make it rectangular by lengthening one side 5 feet and shortening the other side by 5 feet. What polynomial represents the new area? By how much will the area of the new garden differ from that of the old garden?

243. Square lot. Sam lives on a lot that he thought was a square, 157 feet by 157 feet. When he had it surveyed, he discovered that one side was actually 2 feet longer than he thought and the other was actually 2 feet shorter than he thought. How much less area does he have than he thought he had?

244. Area of a circle. Find a polynomial that represents the area of a circle whose radius is b + 1 meters. Use the value 3.14 for π.

245. Comparing dartboards. A toy store sells two sizes of circular dartboards. The larger of the two has a radius that is 3 inches greater than that of the other. The radius of the smaller dartboard is t inches. Find a polynomial that represents the difference in area between the two dartboards.

246. Poiseuille’s law. According to the nineteenth-century physician Poiseuille, the velocity (in centimeters per second) of blood r centimeters from the center of an artery of radius R centimeters is given by v = k(R – r)(R + r) where k is a constant. Rewrite the formula using a special product rule.

247. Going in circles. A promoter is planning a circular race track with an inside radius of r feet and a width of w feet. The cost in dollars for paving the track is given by the formula C = 1.2π[(r + w)2 – r2] Use a special product rule to simplify this formula. What is the cost of paving the track if the inside radius is 1000 feet and the width of the track is 40 feet?

248. Compounded annually. P dollars is invested at annual interest rate r for 2 years. If the interest is compounded annually, then the polynomial P(1 + r)2 represents the value of the investment after 2 years. Rewrite this expression without parentheses. Evaluate the polynomial if P = $200 and r = 10%.

249. Compounded semiannually. P dollars is invested at annual interest rate r for 1 year. If the interest is compounded semiannually, then the polynomial P(1 + r/2)2 represents the value of the investment after 1 year. Rewrite this expression without parentheses. Evaluate the polynomial if P = $200 and r = 10%.

250. Investing in treasury bills. An investment advisor uses the polynomial P(1 + r)10 to predict the value in 10 years of a client’s investment of P dollars with an average annual return r. The  accompanying graph shows historic average annual returns for the last 20 years for various asset classes. Use the historical average return to predict the value in 10 years of an investment of $10,000 in U.S. treasury bills?

251. Comparing investments. How much more would the investment in Exercise 89 be worth in 10 years if the client invests in large company stocks rather than U.S. treasury bills?

252. Find the quotient and remainder for each division. Check by using the fact that dividend = (divisor)(quotient) +remainder. See Example 4.
(x2 + 5x + 13) ¸ (x + 3)

253. Area of a rectangle. The area of a rectangular billboard is x2 + x – 30 square meters. If the length is x + 6 meters, find a binomial that represents the width.

254. Perimeter of a rectangle. The perimeter of a rectangular backyard is 6x + 6 yards. If the width is x yards, find a binomial that represents the length.

255. Long-term investing. Sheila invested P dollars at annual rate r for 10 years. At the end of 10 years her investment was worth P(1 + r)10 dollars. She then reinvested this money for another 5 years at annual rate r. At the end of the second time period her investment was worth P(1 + r)10(1 + r)5 dollars. Which law of exponents can be used to simplify the last expression? Simplify it.

256. CD rollover. Ronnie invested P dollars in a 2-year CD with an annual rate of return of r. After the CD rolled over two times, its value was P((1 + r)2)3. Which law of exponents can be used to simplify the expression? Simplify it.

257. Distance to the sun. The distance from the earth to the sun is 93 million miles. Express this distance in feet. (1 mile = 5280 feet.)

258. Speed of light. The speed of light is 9.83569 × 108 feet per second. How long does it take light to travel from the sun to the earth? See Exercise 99.

259. Warp drive, Scotty. How long does it take a spacecraft traveling at 2 × 1035 miles per hour (warp factor 4) to travel 93 million miles.

260. Area of a dot. If the radius of a very small circle is 2.35 × 10–8 centimeters, then what is the circle’s area?

261. Circumference of a circle. If the circumference of a circle is 5.68 × 109 feet, then what is its radius?

262. Diameter of a circle. If the diameter of a circle is 1.3 × 10–12 meters, then what is its radius?

263. Extracting metals from ore. Thomas Sherwood studied the relationship between the concentration of a metal in commercial ore and the price of the metal. The accompanying graph shows the Sherwood plot with the locations of several metals marked. Even though the scales on this graph are not typical, the graph can be read in the same manner as other graphs. Note also that a concentration of 100 is 100%. a) Use the figure to estimate the price of copper (Cu) and its concentration in commercial ore. b) Use the figure to estimate the price of a metal that has a concentration of 10-6 percent in commercial ore. c) Would the four points shown in the graph lie along a straight line if they were plotted in our usual coordinate system?

264. Recycling metals. The accompanying graph shows the prices of various metals that are being recycled and the minimum concentration in waste required for recycling. The straight line is the line from the figure for Exercise 105. Points above the line correspond to metals for which it is economically feasible to increase recycling efforts. a) Use the figure to estimate the price of mercury (Hg) and the minimum concentration in waste required for recycling mercury. b) Use the figure to estimate the price of silver (Ag) and the minimum concentration in waste required for recycling silver.

265. Present value. The present value P that will amount to A dollars in n years with interest compounded annually at annual interest rate r, is given by P = A(1 + r)-n Find the present value that will amount to $50,000 in 20 years at 8% compounded annually.

266. Investing in stocks. U.S. small company stocks have returned an average of 14.9% annually for the last 50 years (T. Rowe Price, www.troweprice.com). Use the present value formula from the previous exercise to find the amount invested today in small company stocks that would be worth $1 million in 50 years, assuming that small company stocks continue to return 14.9% annually for the next 50 years.

267. Find the prime factorization of each integer. See Examples 1 and 2.

268. Find the greatest common factor (GCF) for each group of integers. See Example 3.

269. Uniform motion. Helen traveled a distance of 20x + 40 miles at 20 miles per hour on the Yellowhead Highway. Find a binomial that represents the time that she traveled.

270. Area of a painting. A rectangular painting with a width of x centimeters has an area of x2 + 50x square centimeters. Find a binomial that represents the length.

271. Tomato soup. The amount of metal S (in square inches) that it takes to make a can for tomato soup is a function of the radius r and height h:
S = 2pr2 + 2prh a) Rewrite this formula by factoring out the greatest common factor on the right-hand side. b) If h = 5 in., then S is a function of r. Write a formula for that function. c) The accompanying graph shows S for r between 1 in. and 3 in. (with h = 5 in.). Which of these r-values gives the maximum surface area?

272. Amount of an investment. The amount of an investment of P dollars for t years at simple interest rate r is given by A = P + Prt. a) Rewrite this formula by factoring out the greatest common factor on the right-hand side. b) Find A if $8300 is invested for 3 years at a simple interest rate of 15%.

273. Skydiving. The height (in feet) above the earth for a sky diver t seconds after jumping from an airplane at 6400 ft is approximated by the formula h = –16t2 + 6400, provided that t < 5. Rewrite the formula with the right-hand side factored completely. Use your revised formula to find h when t = 2.

274. Demand for pools. Tropical Pools sells an aboveground model for p dollars each. The monthly revenue from the sale of this model is a function of the price, given by R = –0.08p2 + 300p.

275. Revenue is the product of the price p and the demand (quantity sold). a) Factor out the price on the right-hand side of the formula. b) What is an expression for the monthly demand? c) What is the monthly demand for this pool when the price is $3000? d) Use the graph on page 290 to estimate the price at which the revenue is maximized. Approximately how many pools will be sold monthly at this price? e) What is the approximate maximum revenue? f) Use the accompanying graph to estimate the price at which the revenue is zero.

275. Volume of a tank. The volume of a fish tank with a square base and height y is y3 – 6y2 + 9y cubic inches. Find the length of a side of the square base.

276. Area of a deck. A rectangular deck has an area of x2 + 6x + 8 square feet and a width of x + 2 feet. Find the length of the deck.

277. Area of a sail. A triangular sail has an area of x2 + 5x + 6 square meters and a height of x + 3 meters. Find the length of the sail’s base.

278. Volume of a cube. Hector designed a cubic box with volume x3 cubic feet. After increasing the dimensions of the bottom, the box has a volume of x3 + 8x2 + 15x cubic feet. If each of the dimensions of the bottom was increased by a whole number of feet, then how much was each increase?

279. Volume of a container. A cubic shipping container had a volume of a3 cubic meters. The height was decreased by a whole number of meters and the width was increased by a whole number of meters so that the volume of the container is now a3 + 2a2 – 3a cubic meters. By how many meters were the height and width changed?

280. Height of a ball. If a ball is thrown upward at 40 feet per second from a rooftop 24 feet above the ground, then its height above the ground t seconds after it is thrown is given by h = –16t2 + 40t + 24. Rewrite this formula with the polynomial on the right-hand side factored completely. Use the factored version of the formula to find h when t = 3.

281. Worker efficiency. In a study of worker efficiency at Wong Laboratories it was found that the number of components assembled per hour by the average worker t hours after starting work could be modeled by the function N(t) = –3t3 + 23t2 + 8t. a) Rewrite the formula by factoring the right-hand side completely.
b) Use the factored version of the formula to find N(3). c) Use the accompanying graph to estimate the time at which the workers are most efficient. d) Use the accompanying graph to estimate the maximum number of components assembled per hour during an 8-hour shift.

282. Increasing cube. Each of the three dimensions of a cube with a volume of x3 cubic centimeters is increased by a whole number of centimeters. If the new volume is x3 + 10x2 + 31x + 30 cubic centimeters and the new height is x + 2 centimeters, then what are the new length and width?

283. Decreasing cube. Each of the three dimensions of a cube with a volume of y3 cubic centimeters is decreased by a whole number of centimeters. If the new volume is y3 – 13y2 + 54y – 72 cubic centimeters and the new width is y – 6 centimeters, then what are the new length and height?

284. Dimensions of a rectangle. The perimeter of a rectangle is 34 feet, and the diagonal is 13 feet long. What are the length and width of the rectangle?

285. Address book. The perimeter of the cover of an address book is 14 inches, and the diagonal measures 5 inches. What are the length and width of the cover?

286. Violla’s bathroom. The length of Violla’s bathroom is 2 feet longer than twice the width. If the diagonal measures 13 feet, then what are the length and width?

287. Rectangular stage. One side of a rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters, then what are the lengths of the sides?

288. Consecutive integers. The sum of the squares of two consecutive integers is 13. Find the integers.

289. Consecutive integers. The sum of the squares of two consecutive even integers is 52. Find the integers.

290. Two numbers. The sum of two numbers is 11, and their product is 30. Find the numbers.

291. Missing ages. Molly’s age is twice Anita’s. If the sum of the squares of their ages is 80, then what are their ages?

292. Skydiving. If there were no air resistance, then the height (in feet) above the earth for a sky diver t seconds after jumping from an airplane at 10,000 feet would be given by h(t) = –16t2 + 10,000. a) Find the time that it would take to fall to earth with no air resistance, that is, find t for which h(t) = 0.  A sky diver actually gets about twice as much free fall time due to air resistance. b) Use the accompanying graph to determine whether the sky diver (with no air resistance) falls farther in the first 5 seconds or the last 5 seconds of the fall. c) Is the sky diver’s velocity increasing or decreasing as she falls?

293. Skydiving. If a sky diver jumps from an airplane at a height of 8256 feet, then for the first 5 seconds, her height above the earth is approximated by the formula h = –16t2 + 8256. How many seconds does it take her to reach 8000 feet.

294. Throwing a sandbag. If a balloonist throws a sandbag downward at 24 feet per second from an altitude of 720 feet, then its height (in feet) above the ground after t seconds is given by S = –16t2 – 24t + 720. How long does it take for the sandbag to reach the earth? (On the ground, S = 0.)

295. Throwing a sandbag. If the balloonist of the previous exercise throws his sandbag downward from an altitude of 128 feet with an initial velocity of 32 feet per second, then its altitude after t seconds is given by the formula S = –16t2 – 32t + 128. How long does it take for the sandbag to reach the earth?

296. Glass prism. One end of a glass prism is in the shape of a triangle with a height that is 1 inch longer than twice the base. If the area of the triangle is 39 square inches, then how long are the base and height?

297. Areas of two circles. The radius of a circle is 1 meter longer than the radius of another circle. If their areas differ by 5p square meters, then what is the radius of each?

298. Changing area. Last year Otto’s garden was square. This year he plans to make it smaller by shortening one side 5 feet and the other 8 feet. If the area of the smaller garden will be 180 square feet, then what was the size of Otto’s garden last year?

299. Dimensions of a box. Rosita’s Christmas present from Carlos is in a box that has a width that is 3 inches shorter than the height. The length of the base is 5 inches longer than the height. If the area of the base is 84 square inches, then what is the height of the package?

300. Flying a kite. Imelda and Gordon have designed a new kite. While Imelda is flying the kite, Gordon is standing directly below it. The kite is designed so that its altitude is always 20 feet larger than the distance between Imelda and Gordon. What is the altitude of the kite when it is 100 feet from Imelda?

301. Avoiding a collision. A car is traveling on a road that is perpendicular to a railroad track. When the car is 30 meters from the crossing, the car’s new collision detector warns the driver that there is a train 50 meters from the car and heading toward the same crossing. How far is the train from the crossing?

302. Carpeting two rooms. Virginia is buying carpet for two square rooms. One room is 3 yards wider than the other. If she needs 45 square yards of carpet, then what are the dimensions of each room?

303. Winter wheat. While finding the amount of seed needed to plant his three square wheat fields, Hank observed that the side of one field was 1 kilometer longer than the side of the smallest field and that the side of the largest field was 3 kilometers longer than the side of the smallest field. If the total area of the three fields is 38 square kilometers, then what is the area of each field?

304. Sailing to Miami. At point A the captain of a ship determined that the distance to Miami was 13 miles. If she sailed north to point B and then west to Miami, the distance would be 17 miles. If the distance from point A to point B is greater than the distance from point B to Miami, then how far is it from point A to point B?

305. Buried treasure. Ahmed has half of a treasure map, which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map. Her half indicates that to find the treasure, one must get to Castle Rock, walk x paces to the north, and then walk 2x + 4 paces to the east. If they share their information, then they can find x and save a lot of digging. What is x?

306. Emerging markets. Catarina’s investment of $16,000 in an emerging market fund grew to $25,000 in 2 years. Find the average annual rate of return by solving the equation 16,000(1 + r)2 = 25,000.

307. Venture capital. Henry invested $12,000 in a new restaurant. When the restaurant was sold 2 years later, he received $27,000. Find his average annual return by solving the equation 12,000(1 + r)2 = 27,000.

308. If Sergio drove 300 miles at x + 10 miles per hour, then how many hours did he drive?

309. If Carrie walked 40 miles in x hours, then how fast did she walk?

310. If x + 4 pounds of peaches cost $4.50, then what is the cost per pound?

311. If 9 pounds of pears cost x dollars, then what is the price per pound?

312. If Ayesha can clean the entire swimming pool in x hours, then how much of the pool does she clean per hour?

313. If Ramon can mow the entire lawn in x – 3 hours, then how much of the lawn does he mow per hour?

314. Annual reports. The Crest Meat Company found that the cost per report for printing x annual reports at Peppy Printing is given by the formula C(x) = (150 + 0.60x)/x where C(x) is in dollars. a) Use the accompanying graph to estimate the cost per report for printing 1000 reports. b) Use the formula to find the cost per report for printing 1000, 5000, and 10,000 reports. c) What happens to the cost per report as the number of reports gets very large?

315. Toxic pollutants. The annual cost in dollars for removing p% of the toxic chemicals from a town’s water supply is given by the formula C(p) = 500000/(100 – P) a) Use the accompanying graph to estimate the cost for removing 90% and 95% of the toxic chemicals. b) Use the formula to determine the cost for removing 99.5% of the toxic chemicals. c) What happens to the cost as the percentage of pollutants removed approaches 100%?

316. Distance. Florence averaged 26.2/x mph for the x hours in which she ran the Boston Marathon. If she ran at that same rate for ½ hour in the Manchac Fun Run, then how many miles did she run at Manchac?

317. Work. Henry sold 120 magazine subscriptions in x + 2 days. If he sold at the same rate for another week, then how many magazines did he sell in the extra week?

318. Area of a rectangle. If the length of a rectangular flag is x meters and its width is 5/x meters, then what is the area of the rectangle?

319. Area of a triangle. If the base of a triangle is 8x + 16 yards and its height is 1/(x + 2) yards, then what is the area of the triangle?

320. Build each rational expression into an equivalent rational expression with the indicated denominator.

321. Find the LCD for the given rational expressions, and convert each rational expression into an equivalent rational expression with the LCD as the denominator.

322. Perimeter of a rectangle. Suppose that the length of a rectangle is 3/x feet and its width is 5/2xfeet. Find a rational expression for the perimeter of the rectangle.

321. Perimeter of a triangle. The lengths of the sides of a triangle are 1/x, 1/2x, and 2/3x meters. Find a rational expression for the perimeter of the triangle.

322. Traveling time. Janet drove 120 miles at x mph before 6:00 A.M. After 6:00 A.M., she increased her speed by 5 mph and drove 195 additional miles. Use the fact that T=D/R to complete the following table. Write a rational expression for her total traveling time. Evaluate the expression for x = 60.

323.Traveling time. After leaving Moose Jaw, Hanson drove 200 kilometers at x km/hr and then decreased his speed by 20 km/hr and drove 240 additional kilometers. Make a table like the one in Exercise 61. Write a rational expression for his total traveling time. Evaluate the expression for
x = 100.

324. House painting. Kent can paint a certain house by himself in x days. His helper Keith can paint the same house by himself in x + 3 days. Suppose that they work together on the job for 2 days. To  complete the table, use the fact that the work completed is the product of the rate and the time. Write a rational expression for the fraction of the house that they complete by working together for 2 days. Evaluate the expression for x = 6.

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