8mathematics - 368 A=r2 . areaA.Whatisitsradius A Answer r=...

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General Chemistry
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Chapter 1 / Exercise 1.108
General Chemistry
Ebbing/Gammon
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Unformatted text preview: 368) A = πr2 is the formula for the area A of a circle with radius r. A circular tablecloth has an area A. What is its radius? A π Answer: r = 369) S = 6l2 is the formula for the surface area S of a cube with sides of length l. You have wrapping paper with surface area S. What is the length of the side of the largest cube the wrapping paper can cover? 369) S 6 Answer: l = 370) Solve: 368) 2x - 3 = 3 x 370) Answer: x = -3 371) Solve: x 2 + 8 - x = 3 x Answer: x = 371) 8 3 4 3 7 372) Solve: - = x x - 2 x 372) Answer: x = 1 373) Solve: 1 1 8 = - x + 1 x - 1 2 x - 1 373) Answer: no solution 374) Solve: 1 + 3x = 2x + 6 374) Answer: x = 5 375) Solve: x 2 - 9 = x - 1 375) Answer: x = 5 376) Solve: x - 1 = x - 1 376) Answer: x = 1 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 377) Solve for x: A) 5 6 6x - 5 3x + 5 = 4x - 5 2x+ 5 B) 3 377) D) - C) 0 Answer: C 43 5 3 E) 2 378) Solve for x: 2x 1 + = 1 x - 4 3 B) -8 A) 2 378) C) 8 D) 0 E) -2 Answer: E SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 379) Solve: 2x + 3 = 4 1 - 3x Answer: x = 379) 1 14 380) Solve: 2x + 3 - 2x - 3 = 1 Answer: x = 380) 37 8 381) Solve: 4x 2 + 5 - 1 = 2(x + 2) Answer: x = - 381) 3 4 382) Suppose the ratio of the number of hours a coffee shop is opened to the number of daily customers it gets is constant. When it is opened 3 hours, the number of customers is 180 less than the maximum number of customers. When it is opened 11 hours, the number of customers is 20 less than the maximum number of customers. Write an equation describing this situation and find the maximum number of daily customers. Answer: 3 11 = ; 240 x - 180 x - 20 383) A boat with a speed of 12 mph travels 8 miles downstream in a current of c miles an hour in the same time a boat going the same speed travels 4 miles upstream. Write an equation describing this situation and find the speed of the current. Answer: 382) 383) 8 4 = ; 4 mph 12 + c 12 - c 384) The time it takes a boat to travel a given distance downstream (with the current) can be calculated by dividing the distance by the sum of the speed of the boat and the speed of the current. Write an equation which calculates the time t it takes a boat moving at a speed r against a current c to travel a distance d. Solve your equation for r. Answer: t = d d ; r = - c r + c t 385) The time it takes an airplane to travel a given distance with a headwind (against the wind) can be calculated by dividing the distance by the difference of the speed of the airplane and the speed of the wind. Write an equation which calculates the time t it takes an airplane traveling at a speed r against a wind w to cover a distance d. Solve your equation for w. Answer: t = 384) d d ; w = r r - w t 44 385) 386) The difference between the length of a ramp and the length of the horizontal distance it covers is 4 feet. The square of the vertical distance it covers is 56 feet. What is the length of the ramp? 386) Answer: 9 feet 387) The difference between the length of a ramp and the length of the horizontal distance it covers is 1 foot. The square of the vertical distance it covers is 9 feet. What is the length of the ramp? 387) Answer: 5 feet 388) The miles a person can see to the horizon from a point above the surface of Earth is 0.85 of the square root of the personʹs distance in feet above the surface. Talia is 13 feet higher and sees 0.85 farther than John. How high are Talia and John above the surface? 388) Answer: John is 36 feet above the surface; Talia is 49 feet above the surface. 389) The miles a person can see to the horizon from a point above the surface of Earth is 0.85 of the square root of the personʹs distance in feet above the surface. Karen is 39 feet higher and sees 2.55 miles farther than Sharon. How high are Karen and Sharon above the surface? 389) Answer: Sharon is 25 feet above the surface; Karen is 64 feet above the surface. 390) The miles a person can see to the horizon from a point above the surface of Earth is 0.85 of the square root of the personʹs distance in feet above the surface. Sean is 65 feet higher and sees 4.25 miles farther than Craig. How high are Sean and Craig above the surface? 390) Answer: Craig is 16 feet above the surface; Sean is 81 feet above the surface. 391) At a certain mall in Ohio, the sales tax is 7%. If the total receipt for a food processor was $160.50, what was the price of the food processor? 391) Answer: $150.00 392) What is the sales tax paid on an item whose total receipt was $100.75 and whose sales tax rate was 5.5%? 392) Answer: $95.50 393) Solve: x 2 - 7x - 8 = 0 393) Answer: x = -1, 8 394) Solve: t2 + 8t + 7 = 0 394) Answer: t = -7, -1 395) Solve: 9x 2 - 4 = 0 Answer: x = ± 395) 2 3 396) Solve: 2x 2 - 9x + 4 = 0 Answer: x = 4, 396) 1 2 45 397) Solve: 3y 2 - 9y - 12 = 0 397) Answer: y = 4, -1 398) Solve: x 2 = 5x 398) Answer: x = 0, 5 399) Solve: 4x 2 - 4x + 1 = 0 Answer: x = 399) 1 2 400) Solve: x(4 - 2x) = -16 400) Answer: x = -2, 4 401) Solve: (x + 5)2 = 16 401) Answer: x = -1, -9 402) Solve: x 2 - 3x = 0 402) Answer: x = 0, 3 403) Solve: 3x 2 + x - 2 = 0 Answer: x = -1, 403) 2 3 404) Solve: x 2 - 6x + 9 = 0 404) Answer: x = 3 405) Solve: (10 - 2x)(5 - x) = 50 405) Answer: x = 0, 10 406) Solve: y + 1 y + 5 + = 1 2y y2 406) Answer: y = 5, -2 407) Solve: 3x = x x + 1 407) Answer: x = 0, 2 9 2 = 4 408) Solve: + x + 1 x Answer: x = 2, - 408) 1 4 2 15 409) Solve: - = 4 x x - 1 Answer: x = -2, - 409) 1 4 46 410) Solve: 6 x 2 - 1 = 3 + 1 x + 1 410) Answer: x = -5, 2 x 6 411) Solve: + = 2 6 x 411) Answer: x = 6 412) Solve: x 4 - 7x 3 - 30x 2 = 0 412) Answer: x = -3, 0, 10 413) Solve: 7(2y - 1) y y + 4 + = y + 2 y - 3 y 2 - y - 6 Answer: y = 413) 5 2 414) Solve: x + 2 = x - 4 414) Answer: x = 7 415) Solve: 2x + 5 = x -5 415) Answer: x = 10 416) Solve: 2x + 7 = x - 4 416) Answer: x = 9 417) Solve: 2 x - 1 = 2x + 7 417) Answer: x = 9 418) Solve: 3 = x 2 - 8x 418) Answer: x = 9, -1 419) Solve: x 4 - 2x 2 + 1 = 0 419) Answer: x = ±1 420) Solve: x 2 - 3x - 2 = 0 Answer: x = 420) 3 ± 17 2 421) Solve: 2x 2 + x - 4 = 0 Answer: x = 421) -1 ± 33 4 422) Solve: 2x 2 - 2x - 1 = 0 Answer: x = 422) 1 ± 3 2 47 423) Solve: x2 1 - x = 3 2 Answer: x = 1± 423) 15 3 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 424) The roots of (x - 1)(x + 2) = 10 are A) -4 and 3 only B) -4 and 8 only C) -1 and 2 only D) 1 and -2 only E) 8 and 11 only 424) Answer: A 425) Find the sum of the roots of 3x 2 + 7x - 6 = 0. 7 7 5 B) - C) A) 3 6 3 425) D) -7 E) 0 Answer: B 426) The roots of 13 + x - x = 7 are A) -4 and -9 only B) -4 and 9 only C) -4 only D) -9 only E) 4 only 426) Answer: C 427) The roots of x + 2 = x - 4 are A) 0 only B) 7 and 2 only C) 7 only D) 2 only E) -7 only 427) Answer: C 428) The equation 2x + x - 4 = 2 has exactly how many roots? A) none B) one C) two 428) D) three E) four Answer: A 429) Solve for x: 1 - 4x - 4x 2 = 0 1 1 2 B) ± A) 2 ± 2 2 2 2 429) C) 1 2 D) -2 ± 2 2 Answer: E 48 1 2 E) - ± 2 2 ...
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