(MAT200 -PreCalclus) Final Exam

(MAT200 -PreCalclus) Final Exam - Student Shanna Hawxhurst...

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Unformatted text preview: Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Final Exam Submitted: 03324! 09 12:49pm Course: 903 CURLEY C, MAT 200 004 016 Book: Strayer University Math 200: Precalculus 1_ Find the slope, if it exists, of the line containing the pair of points. (9,4) and (10, - 9) The slope m = - 13 . (Simplify your answer. Type an integer or a fraction. Type N if the slope is undefined.) 2_ During one year, $13.8 billion was spent on copies of films for home viewing. About $0.8 billion of this amount was spent on laserdiscs. What percent of the spending for films went for laserdiscs? About 5.8 % of spending went for laserdiscs. (Round to the nearest tenth.) 3_ Divide. 8 5 + i 8 n 4 . 5 + i _ 13 _ 1—3I (Simplify your answer. Type an integer or a fraction. Type your answer in the form a +b 1'.) 4_ Solve for it using the quadratic formula. x2-10x=39 The solution set is { - 3,13 }. (Simplify your answers. Type exact answers, using radicals as needed. Use commas to separate answers.) Page 1 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Final Exam Submitted: 0315241509 12:49pm Course: 903 CURLEY C, MAT 200 004 016 Book: Strayer University Math 200: Precalculus 5_ Find the vertex, the maximum or minimum value of the quadratic fimction, the range, and the intervals where the function increases and decreases. t‘(x)=2x2-12x+l4 The x-coordinate of the vertex is 3 . The y-coordinatc of the vertex is — 4 . The maximumfminimum of f(x) is -4 . What is the range of f(x)? [— 4,00) (Type your answer in interval notation.) On what interval is the function increasing? (3,00) (Type your answer in interval notation.) On what interval is the function decreasing? ( — 00,3). (Type your answer in interval notation.) 6. 501V?" The solution(s) isfare x = — 1‘. (Use a comma to separate answers. i + x = L Type N if there is no solution.) x x+3 x2+3x YOU ANSWERED: 3? -l I Solve and write interval notation for the solution set. Then graph the solution set. 3x5 —9 or x-6>0 Choose the correct solution set below. M. (—00,—3] u (6,00) 21.3. (-00:25) u [6,00) -:.:.uc. (—3,6] -ILi'-D- [-3,6) Choose the correct graph below. agg'fA. 2i}- B. 4-1—1—1—1—14 1—1—1—1» fi—l—l—l—l-l 1—1—1—1» —12 —1D —8 —6 —4 —2 [2- 2 4 6 8 1D 12 42—10 —8 —6 —4 —2 E} 2 4 6 8 1E} 12 if» c. if .- D. 4-1—1—1—1—h) H—l—h» (-1—1—1—1—H H—l—h) —12 —1D —8 —6 —4 —2 [2- 2 4 6 8 1D 12 42—10 —8 —6 —4 —2 E} 2 4 6 8 1E} 12 Page 2 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Final Exam Submitted: 03324! 09 12:49pm Course: 903 CURLEY C, MAT 200 004 016 Book: Strayer University Math 200: Precalculus 8. A hot-air balloon rises at a rate of Balloon 140 fifmin. The balloon is tracked from point P, d which is 350 ft from release point Q. Let 140t d = distance from the balloon to point P and t = time, P in minutes, since the balloon was released. Express d as a fimction oft. What is d expressed as a filnction of t? "I ‘A- d(t) = V 140:2 + 3502 "TB- d(t} = (14m) 2 + (350) 2 ‘5?" ‘3' do) = W 50- do = W 9_ For the given functions, find the domain of f, g, and f - g, and find (f - g)(x). f(x)= Vx-9,g(x)= Itlx+9 What is the domain of t? 13A. [999) -::j.'= B. (— 00,9) u (9,oo) c1]- (2. [—9,oo) -‘.‘_"-D. (-9990) What is the domain of g? Iii " C. (— 00,90) 1-15" D. [_ 99°) What is the domain of f — g? {#‘A. [990) B. [— 9,9] C- [_ 9,00) I D- (_ “3900) (f—g)(x)= Vx—fli' — Vx-l-Q. Page 3 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Final Exam Submitted: 03i24i09 12:49pm Course: 903 CURLEY C, MAT 200 004 016 Book: Strayer University Math 200: Precalculus 10. _ 1 _ l Descnbe how the graph of h(x) = ; + 4 can be obtained from the graph of fix) = ; Then graph the function h(x). l 1 How can the graph of h(x) = E + 4 be obtained item the graph of f(x) = ;? ejjuA. Shift the graph 4 units down. B. Shift the graph 4 units right. C. Shift the graph 4 units left. A“ D. Shift the graph 4 units up. 1 What is the graph of h(x) = — + 4? x Page 4 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Final Exam Submitted: 03324! 09 12:49pm Course: 903 CURLEY C, MAT 200 004 016 Book: Strayer University Math 200: Precalculus 11_ Find the center, the vertices, the foci, and the asymptotes of the hyperbola. Then draw the graph. x2 —y2+4x-6y- 6:0 The center is ( - 2-,.- 3) . (Type an ordered pair.) The vertices are (2— 3.,-— 3) ,_(-— 1, —-'3) . (Use a comma to separate answers. Type an ordered pair.) The fociare (—2—W,.—'3),(—2+’V._,—.3). (Use a comma to separate answers. Type an ordered pair. Type an exact answer.) The asymptotes arey= x- 1 andy= —x-_5. (Write in slope-intercept form. Type the equation that has a positive slope in the first input box.) Choose the correct graph of the hyperbola. 10' {I ._1Q_.I a? 12. Find the center and the radius of the circle. xz—Sx +y2+6y= —21 The center is (.4,— 3) . (Type an ordered pair.) The radius is 2 . Page 5 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Final Exam Submitted: 03I'24I' 09 12:49pm Course: 903 CURLEY C, MAT 200 004 016 Book: Strayer University Math 200: Precalculus 13_ Determine whether the function is one-to-one. If it is, find a formula for its inverse. fl ) 5 + 5 x = —x 7 5 . Is f(x) = “7—K + 5 a one-to-one filnctlon? ‘ No A“ Yes . _ 1 _ 5 chl the formula for f (x), the mverse of f(x) = :3: + 5. 'A. _ 7 Us. _ 7' t‘ I(x)=—x—l i" f '(x)=—x—7 5 5 'c. _ 5 o. _ 7 t‘ '(x)=—y+5 f '(x)=—x+7 7 5 14. , r ‘1‘ . . Use the compound 1nterest formula A = p l + — to compute the total amount after $2500 IS mvested at n 6% over 5 years compounded daily. (Use 11 = 360.) Then compute the interest eamed. The total amount is $ 33'?4.56 . (Round to the nearest cent.) The interest earned is $ 874.56 . (Round to the nearest cent.) 15_ Walking speed. The average walking speed R of a person living in a city of population P in thousands is modeled by the fimction, R(P) = 0.3? - In P + 0.05, where R is in feet per second. The population of Wheeling is 40,000. Find the average walking speed of people living in Wheeling. . . ft The average walking speed 1s 1.4 Q' (Round to the nearest tenth.) 16_ Express as a single logarithm. ' log t( 2) + log K30) = log ta) '03 t( 2) + 103130) Page 6 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Final Exam Submitted: 03324! 09 12:49pm Course: 903 CURLEY C, MAT 200 004 016 Book: Strayer University Math 200: Precalculus 17. Solve for x. log x+log (x - 15) =2 x = 20‘ (Type an integer or a simplified fraction. Use a comma to separate answers as needed. Type N if there is no solution.) YOU ANSWERED: 20, - 5 18_ Country A has a growth rate of 4.7% per year. The population is currently 5,401,000, and the land area of Country A is 16,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land? This will happen in 170' years. (Round to the nearest integer.) 19- Solve by the elimination method. What is the solution of the system? (2,7) Also, determine whether the system is consistent or T e anordered air. inconsistent and dependent or independent. ( W p ) Is the system consistent or inconsistent? 7 7 70 , —x +3), = —3 is" con51stent - :1 inconsistent 1 l 17 _X + _Y = — . 3 6 Is the system dependent or 1ndependent? .- :3 dependent 4.!“ independent 20_ Solve this system of equations. I The solution is ( _ 3 a -_ -] , _ 4 )_ 4a + 7b = - 19 83 + 30 = - 36 613 + 30 = - 18 Page 7 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Final Exam Submitted: 03324! 09 12:49pm Course: 903 CURLEY C, MAT 200 004 016 21. Book: Strayer University Math 200: Precalculus Solve the system. 1 m x+y +z—w— | ._. _. 4x +y —z +w ‘ x—3y-t-4z +w — —x -y +z+3w *" | l u a: The solution set is { (2,2,25) }. (Type an ordered quadruple.) 22. A dietician works in a hospital and prepares meals under the guidance of a physician. Suppose that for a particular patient, a physician prescribes a meal to have 800 calories, 55 g of protein, and 220 mg of vitamin C. The dietician decides to prepare the meal using steak (each 3-oz serving contains 300 Cal, 20 g of protein, and no vitamin C), baked potatoes (one baked potato contains 100 Cal, 5 g of protein, and 20 mg of vitamin C), and Brussels sprouts (one 156-g serving contains 50 Cal, 5 g of protein, and IOU mg of vitamin C). How many servings of each food are required to satisfy the physician's requirements? How many servings of steak are required? 2 How many baked potatoes are required? 1 How many servings of Brussels sprouts are required? 2. 23. Solve the following system of equations using Gaussian or Gauss~Jordan elimination. z=—8 -2x— 3y— -4x— 2y— 22: -12 331+ 3y+ z=10 Find the solution to the system of equations. (2, 1 ,‘1 ) (Type an exact answer in simplified form. If there is no solution, type N for each coordinate. If there are infinitely many solutions, type an expression involving 2 for each coordinate where 2 represents all real numbers.) Page 8 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Final Exam Submitted: 03I'24I' 09 12:49pm Course: 903 CURLEY C, MAT 200 004 016 Book: Strayer University Math 200: Precalculus 24_ Find the product of the following matrices, if possible. — 6 — 4 2 7 — 8 — 1 0 9 '3' — 9 — 3 3 3 - 7 8 - l - 3 - 2 Find the product. e 8. 5.4 -— 1.0 — .83 — 48 1 3 3'6 — 2'? — 40 25_ Find the inverse of the matrix A, if possible. 2 0 — l A = 0 - l 0 3 — 2 - 2 2 2 - I A ‘ ' = 0 — 1 0 3 4 — 2 26. Find the determinant. 6 4 l 0 A = 4 - l 0 3 5 8 det A = '54 Page 9 Student: Shanna Hawxhurst Instructor: Christine Carley Assignment: Final Exam Submitted: 03324/09 12:49pm Course: '903 CURLEY C, MAT 200 004 016 Book: Strayer University Math 200: Precalculus 27_ Graph the system of inequalities. Then, find the coordinates of the vertex. x+ySl,x-y22 Choose the correct graph for the system. Find the coordinates of the vertex. (Simplify your answer. Type an ordered pair. Type integers or fractions.) Page 1 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Final Exam Submitted: 03I'24I' 09 12:49pm Course: 903 CURLEY C, MAT 200 004 016 Book: Strayer University Math 200: Precalculus 28. Find the exact values of sin 45°, cos 45°, and tan 45°. . a V2 s1n 45 = .— 2 (Simplify your answer. Type an integer or a fraction. Type an exact answer, using radicals as needed. Rationalize any denominators.) V2— cos 45° = — 2 (Simplify your answer. Type an integer or a fraction. Type an exact answer, using radicals as needed. Rationalize any denominators.) tan 45° = '1 (Simplify your answer. Type an integer or a fraction. Type an exact answer, using radicals as needed. Rationalize any denominators.) Page 1 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Final Exam Submitted: 03324! 09 12:49pm Course: 903 CURLEY C, MAT 200 004 016 Book: Strayer University Math 200: Precalculus 29. A baseball diamond is a square 90 ft on a side. If a line is drawn from third base to a runner between home plate and first base, then a right triangle QPH P h is formed where (QPH is 29°. Q Using a trigonometric function, find the distance 90 fl from third base to the runner. The runner is 102.9 H feet from third base. (Round to 2 decimal places.) Page 1 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Final Exam Submitted: 03324! 09 12:49pm Course: 903 CURLEY C, MAT 200 004 016 Book: Strayer University Math 200: Precalculus 30. A raft 24 feet from the shore is tied by a rope that runs perpendicular to the shore line. Madison wants to tie a second line from point B to the raft, where the angle from B to the corner of the raft is 41°. If 5 feet at each end are required to tie the line down, how long must the line he? The line must be 47‘ feet long. (Round to the nearest integer.) YOU ANSWERED: 37 Page 1 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Final Exam Submitted: 03/24/09 12:49pm Course: 903 CURLEY C, MAT 200 004 016 Book: Strayer University Math 200: Precalculus 31_ Find the exact value of the following expression. cos 360° cos 360° = l Page 1 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Final Exam Submitted: 03324! 09 12:49pm Course: 903 CURLEY C, MAT 200 004 016 Book: Strayer University Math 200: Precalculus 3 2_ An airplane flies 170 kilometers from an airport in a direction of 220°. How far west of the airport is the airplane then? How far south? In navigation, directions are given in degrees measured clockwise from north. The airplane is 109 kilometers west. (Round to the nearest integer.) The airplane is 130 kilometers south. (Round to the nearest integer.) Page 1 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Final Exam Submitted: 03/24/09 12:49pm Course: 903 CURLEY C, MAT 200 004 016 Book: Strayer University Math 200: Precalculus 33_ The planet Venus has a radius of 4000 miles and rotates one revolution every 5800 hours. What is the linear speed of a point on its equator, in miles per hour? The linear speed is approximately 4 miles per hour. (Round to the nearest integer as needed.) Page 1 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Final Exam Submitted: 03/24/09 12:49pm Course: 903 CURLEY C, MAT 200 004 016 Book: Strayer University Math 200: Precalculus 34_ Use a calculator to approximate the following. sin 0.9 it cos 0.9 II: Use a calculator. sin 0.9 1'! = .3090 cos 0.9 1t= - .9511 (Round to four decimal places.) Page 1 Student: Shanna Hawxhurst Instructor: Christine Curley Assignment: Final Exam Submitted: 03I'24I' 09 12:49pm Course: 903 CURLEY C, MAT 200 004 016 Book: Strayer University Math 200: Precalculus 35. Determine the period, phase shift, and range of y = cos( 3 x) + 2. Also, choose its graph. 2-7: The period is 3—. . The phase shift is Q . The range is [ 1‘, 3‘] Choose the correct graph below. '-.:.-'A. '.:-'B. are. ILL-D. _ _3_Ay|_ ‘_I_3_A1._‘ —J 35y— _ i__3_Ay ' x I ' Ix WWNWX NWWMX W —.—'—) ,—.——.—'—) ~13 _ 6 «95:59.5. 3W5 «B. .. 3 ~8 _ B a | | a. | I; I a _ YOU ANSWERED: - l Page 1 ...
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