Sindbad~EG File Manager

Current Path : /usr/home/beeson/MathXpert/bin/ProblemLibrary/
Upload File :
Current File : /usr/home/beeson/MathXpert/bin/ProblemLibrary/problems41-61.o

ELF	>��@@1. z = xy2. z = cos x cos y1. z = r^2       @This is called the \it paraboloid.\rm @It is obtained by revolving a parabola about its axis of symmetry.2. z = r^2 cos 2 theta       @The real part of the complex function $z^2$.3. z = ln(cos(x)/cos(y))       @This is Scherk's surface.  It is a \it minimal surface \rm, @which means that its area cannot be decreased by small perturbations.4. z = theta       @This is called the \it helicoid \rm.  It is a minimal surface.5. z = arccosh r       @One part of the \it catenoid.\rm  This surface @is obtained by rotating $r = cosh z$ about the $z$-axis, @but to write it in the form $z = f(x,y)$, we use @only the upper half.1. x = (cos theta) ( 1 + 0.4 cos r), y = (sin theta) (1 + 0.4 cos r), z = 0.4 sin r | -pi <= r <= pi, 0<=theta<=2pi       @This is called a \it torus.2. x = r cos theta, y = r sin theta, z = 0.2 * a theta | -2pi  <= theta <= 2pi, 0 <= r <= 1.5       @This is called the \it helicoid.  \rm Try changing the range of $theta$ @or the parameter $a$.3. x = r cos theta - (1/3) r^3 cos(3 theta), y = -r sin theta - (1/3) r^3 sin(3 theta), z = r^2 cos(2 theta)       @Enneper's surface, discovered in 1846.4. x = cos theta, y = sin theta, z = r | 0 <= theta <= 2pi, -1 <= r <= 1       @This is a cylinder, because $x$ and $y$ describe a circle.5. x = cosh r cos theta, y = cosh r sin theta, z = r | -1 <= r <= 1, 0 <= theta <= 2 pi       @This is the \it catenoid, \rm obtained by revolving $x = cosh z$ about the $z$-axis.  It is a minimal surface.6. x = cosh r cos theta cos(pi b/2) + sinh r sin theta sin(pi b/2), y = cosh r sin theta cos(pi b/2) - sinh r cos theta sin(pi b/2), z = r cos (pi b/2) + theta sin(pi b/2) | -1 <= r <= 1, 0 <= theta <= 2 pi       @As b changes from 0 to 1, this surfaces changes from the helicoid to the catenoid. @This is an example of an \it isometric deformation.1. (x+1)(x+2)2. (x-1)^23. (x+2)(x+3)4. (2x-1)(x+1)5. x(x-y-1)6. (x+1) (x^2 - x + 1)7. (x-y)(x^2 + xy - y^2)8. (x^3 + x + 1)(x^3 - x + 1)9. (x-1)(x-2)(x-3)(x-4)10. (x^2-1)(x^2 + 1)11. (5x+2) + (7x-1) + (-4x-3)12. (12x-9) - (-3x+4) - (7x+1)13. 3x - (5x-(x+6))14. 2x^2 - (-2x^2 - (x^2-4))15. (4t^2 -(2t+1)+3)-(3t^2 + (2t-1)-5)16. (4x^3)(9x)17. (6x^3)(7x^2)18. (-2x^2)(6x^3)19. (3x)(-2x^2)(-5x ^3)20. (-2x)(-6x^3)(x^2)21. (-6x^2)(3x^3)x^422. (-7x^2)(3x)(4x^3)23. (4x^3 - (2x^2-x-1)) - (-x^3 + (7x^2 -x + 10))24. (-3y^2)(-2y^2)(-4y^5)25. (-y^3)(-6y)(-8y^4)26. (3xy^2)^327. (4x^2y^3)^328. (-2x^2y)^529. (-3xy^4)^330. (-x^4y^5)^431. (-x^5y^2)^432. (9xy^4)^233. (8x^2y^5)^234. (2xy)(-4x^2y)35. (5xy)(-6y^3)36. (-7xy)(4x^4)37. (-x^3y^2)(xy^3)38. ((2/5) xy^2)((3/4)x^2y^4)39. ((1/2) x^2y^6)((2/3)xy)40. (-(1/2)xy)((1/3)x^2y^3)41. ((3/4)x^4y^5)(-x^2y)42. (x^2y)(-3xy^2)(x^3y^3)43. (xy^2)(-5xy)(x^2y^4)44. ((2/3)xy)(-3x^2yy)(5x^4y^5)45. ((3/4)x)(-4x^2y^2)(9y^3)46. (12y)(-5x)(-(5/6)x^4y)47. (-12x)(3y)(-(3/4)xy^6)48. 9x^4/y^5/(3xy^2)49. 12x^2y^7/(6x^2y^3)50. 25x^5y^6/(-5x^2y^4)1. (x^2 + y^2)(x- y)(x+y) - x^4 = -y^42. (x^2x^2 + x^4)x^4 + x^8= 3x^83. (x-1)(x-2)+(x-3)(x-4)= 2(x^2-5x+7)4. (x^2-1)(x^2 + 1) + (x^2-3)(x^2 + 3)= 2(x^4-5)5. (6x+4) - (4x-2) + (-x^2 -1)= -x^2 +2x+56. (x^2x^2 + x^4)x^4 - x^8 = x^87. (x-1)(x+1)+(x+1)(x-1)= 2(x^2-1)8. (2x(a+bx^2)-2bx^3)(a+bx^2)^2 = 2ax(bx^2 +a)^29. ((a^2-x^2) + x^2)(a^2-x^2)= a^2(a-x)(a+x)10. (x+a)^2 - (x-a)^2  = 4ax11. (x+a)^2 + (x-a)^2 = 2x^2 + 2a^212. x(2a-x) + 2x^2 + a^2 = (x-a)^2 + 4ax13. (1-x)(1 + x + x^2 + x^3 + x^4) = 1-x^514. (1+x)(1 - x + x^2 - x^3 + x^4) = 1+x^515. (1-x^2)(1+x^2)(1+x)(1-x+x^2)=(1+x^3)(1-x)(1+x+x^2+x^3)16. (a^2-b^2)(a^2+b^2) + 2b^4+2a^2b^2 = (a^2 +b^2)^217. u^2(u^2 + u^3) - u^3(u -u^2) = 2u^518. (x^3 x^2 + x^5)x^2 - (x^2 -x)x^5 = x^6(x + 1)19. x(x+y)y + x(x-y)y = 2x^2 y20. x(x+y)y - x(x-y)y = 2xy^221. x(x+y)^2 - x(x-y)^2 = y(x+y)^2 - y(x-y)^2 +4x^2y -4xy^222. x(x+y+z) + y(x+y+z) + z(x+y+z) = (x+y+z)^223. (x+y)^3 + (x-y)^3 = 2x^3 + 6xy^224. (x+y)^3 - (x-y)^3 = 6x^2y + 2y^325. x(x^2-y) - y(y^2-x) = (x-y)(x^2+xy+y^2)26. x^2(x-y) + y(x^2+y^2) = x^3 + y^327. x(x^2 + x + 1) - x^2(x + 1) = x28. x^2(x+2) - x(x+1)^2 = -x29. x(x+1) + x^2(x+2) + x^3(x+3) = x + 3x^2 + 4x^3 + x^430. (x+1)(x+2) + (x-1)(x+2) = 2x^2 + 4x31. (x+1)(x+2) + (x+3)(x+4) = 2x^2 + 10x + 1432. x(x-1)(x-2)-1 = (x-1)^3 -x1. 4x+2 = 112. 7x+4 = -33. 5y-3 = 214. 3x-4 = 5x5. -14 = 3a-26. -8y-2 = 8y7. 7x+4 = -318. 4x - x = 3x9. 7(2x - 1) = 5x + 210. 8x/7 = 56x/911. 5y+2 = 2y-1412. 3x+4 = 5x+213. -6a -4 = -7a + 1114. 2(3x-7) + 4x=1215. 4x-2-x = 5x+116. 4x-1 - 2x = 8x-3+x17. 4x -2=x+818. x+7=3x+319. 6n-4-3n = 3n + 10 + 4n20. 3(x-2) = -15021. 6x +1=2x/322. 5x/2 -5= 3x-1523. -5(x-1) = 1024. 5x-4(x+6) = -1025. -2(3x-1) - 3 = -1426. 2x-1 = 5(2x-9)27. 2(1-x)= 2x -1+1028. 4(x-2) + 3(x-1) = x+629. 3(2a-1) + 2(5a+1) = 3a+430. 3(2x-(x-2))=-6(3-2x)31. -2(n-4) -(3n-1) = -2 + (2n-1)32. 4-3x=3(4-x)33. 1-12x =7(1+2x)2. (x+3)(x-1)3. (x+2)(x-1)4. (x-1)^25. (x+1)^26. (x+2)^27. (x+2)(x+3)8. (x+2)(x-3)9. (2x+1)(x+1)10. (2x-1)(x+1)11. (x-y)(x+y)12. (x-y)(x-1)13. x(x-y-1)14. (x+y)(x+y-1)15. (x-1) (x^2 + x + 1)16. (x+1) (x^2 - x + 1)17. (1+x)(1-x-x^2)18. (x+y)(x^2 - xy + y^2)19. (x-y)(x^2 + xy - y^2)20. (x+y+1)(x+y-1)21. (x^2 + x + 1)(x^2 - x + 1)22. (x^3 + x + 1)(x^3 - x + 1)23. (x-1)(x^2-1)(x^3-1)24. (x-1)(x-2)(x-3)25. (x-1)(x-2)(x-3)(x-4)26. (x^2-1)(x^2 + 1)27. x (3x^2y+7xy^2)28. c t^2 (3c - 2t+4)29. (x - 2y) (y - 2x)30. (9x+y) (9x - y)31. (2x+4) (4+x - x^2)32. (x^3 - 3) (x^2 - x - 12)33. (x^n - 3) (x^n - 1)34. (10 x^2 - 15)^235. (2x+y)^336. (1+x^3)^337. (3 - x) (x^2+x - 1)38. 2x (x - y)^2 (1+y)39. 3 (x+6) (x+5) (x+4)40. (16+25x^4) (16 - 25x^4)41. (x^3+2x^2 - 5x) (3x^2 - 3x - 10)42. x^3 (x - 1) (1 - x^2)43. 2 (x - 1) (3x+1) (2x+4)44. (x^2 - x+a) (-5x^3 - x+4)45. xy^2 (16 x^2 y^3 - 12 x^3 y^4+x^5 y^5)46. (4x^2+5) (16x^4 - 20 x^2+10)47. (2x - 9)^2 (2x+1)48. (x^2 - 9) (x - 3)^249. (4+x)^2 (16+x^2)50. (x^2 - y^2) (x - y)^251. (4a^4b - b^2) (4b^4a+a^2)1. abs x < 22. abs x < 33. abs x <= 104. abs x <= 45. abs x > 56. abs x > 37. abs (x+1) < 28. abs (x-2) < 49. abs (x+2) <= 410. abs (x+1) <= 111. abs(x-2) > 1112. abs(x+1) > 613. abs(x-3) >= 214. abs(x-2) >= 115. abs(x-1)=916. abs(x+2)=1317. abs(x-2) > 518. abs(x-3) > 719. abs(x+3) < 820. abs(x+1) < 2021. abs(2x-4) = 1622. abs(3x-4) = 1823. abs(2x-1) <=1224. abs(3x+1) <= 925. abs(4x-2) >= 1026. abs(5x-2) >= 1227. abs(6x-4) = 1128. abs(5x-3) = 1529. abs(4-8x) = 530. abs(3-4x) = 1031. abs(2-x) > 432. abs(3-x) > 333. abs(4-2x) < 234. abs(8-3x) < 535. abs(5x+8) <= 836. abs(7x-6) >= 2237. abs(x-3/4) = 2/538. abs(x-1/2) = 3/539. abs(-2x+7) <= 1340. abs(-3x+4) <= 1541. abs((x-3)/4) < 842. abs((x+2)/3) < 1043. abs((2x+1)/2) > 1044. abs((3x-1)/4) > 1345. abs(2x-3) - 2 = 5046. abs(3x-1) +1 = 1947. abs(x-7) - 3 >= 1448. abs(x-2) - 4 >= 149. abs(2x+1) + 1 <= 650. abs(5x+3) - 2 <= 51. 2^3 2^52. 2^2 3^23. 2^3 2^4 3^24. 2^3 2^5 3^2 3^55. 2^3 3^3 2^46. 2^3 3^3 2^4 3^47. 2^(2^3)8. (2^2)^39. 2^(2^2^2)10. (2^2)^(2^2)11. (2^2^2)^212. 2^(3^2)13. 2^2^3 2^214. 2^2^3 (2^2)^315. 2^(2^3) - (2^2)^316. 12(3^3) 317. (2^3)4(3^2)18. (-4^2)(-4) 2^319. 3^2 4^2 2 2^2 3^320. (6 2 3)^3(-6 2^3)21. (4 3 5)(4 3^4)22. (3 3^3 3)( 9 2^2^2)23. (-2^3 5^2)(2 5^3)24. (3/7) 3 7 (1/3)3^2^325. 5 (-2^3)(-5 2^2)26. (-3 5)(-5 3^3)( 5^2)27. (-2^2)(3^3)2^528. (5^2 3)(-5 5 3^2)(5^3 3^5)29. (8 7^2)(-4 7)(2^2 7^3)30. (3)(-2 3^2)^231. (3/4)(-2 3^2 5^2)(3 3^4)32. (-8)(3 3^5)(-(3/4) 2^5)33. (-2 3^2 2)^334. (-3 2^4)^435. (-2^5 3^2)^536. (3^2 4^3 2^5)^337. (2 3^3 2^2)^538. (2^2^2 2^5)^439. ((-2 3)^2 3^3)^240. -(-5 (-3)^3^2  5)^341. ((3^2 2^3)^2 6^2)^542. -(5 6^2  2^3)^743. ((-3)^3 3^3 2^2)^444. ((-4^2) 2^4^2)^545. 6 (3^2 2^6)/(6 3^2 2^4)46. 2^6^4/(2^2^3)47. (-3 (2 3)^4 2^5 3^7)/(4^2 (3 2)^3)48. ((-5)^4 2^5 3)/(5^2 2^4 9)49. 17 5 3^3/(-51)( 5^3 3^2)^350. -48 (3^2 2^3)^2 /(2 2^2^3 6)1. (x^3)(8x)2. (3x^3)(4x^2)3. (-a^2b)(-4ab ^3)4. (-8a^2b^2)(-3ab^3)5. (x^2yz^2)(-8xyz^3)6. (6xy)(-6y^3)7. (-4xy)(4x^4)8. (3a^3b)(9a^2b^2)9. (-8a^2b^3)(-12ab^4)10. (-x^3y^2)(xy^3)11. (-(3/7)ab)((1/7)a^2b^3)12. (-(2/5)a^2)((3/5)ab^2)13. x (-2x^3)(-5x ^2)14. (-3x)(-5x^3)(x^2)15. (-x^2)(3x^3)x^516. (x^2y)(-5xy^2)(x^3y^5)17. (xy^2)(-4xy)(x^2y^3)18. (4ab)(-2a^2b)(7a)19. (3b)(-2ab^2)(7a)20. (-5a^2b)(-ab^2)(-3a)21. ((3/4)x)(-2x^2y^2)(3y^4)22. (-8x)(3y)(-(3/4)xy^5)23. (-2x^2y)^624. (-3xy^4)^525. (-x^5y^2)^726. (a^2b^3c^5)^327. (2a^3b^2)^828. (x^2y^5)^429. (-2a^2b^3)^230. -(5ab)^431. -(xy^2z^2)^732. -(xy^2z^3)^733. (-xy^3z^2)^834. (-x^2y^4z^5)^535. 6x^2y^6/(6x^2y^4)36. 56x^6y^4/(-7x^2y^3)37. (-8a^3bc^4)/(-6a^2c^3)38. (-32x^4y^5z^7)/(x^2yz^3)39. (-a^4b^5c)/(a^2b^4c)40. 7ab^3/(-7ab)41. (-12abc^2)/(3bc)42. (-48xyz^2)/(2xz)43. (2x^n)(7x^(2n))44. a^(2n-1) a^(3n+5)45. x^(3n+2) x^(n+1)46. a^(10n-2) a^347. (2x^n)(-5x^n)48. (-3a^2)(-4a^(n-2))49. x^n(2x^(2n))(3x^2)50. (6x^(n+1))x^(n-1)(4x^(2+n))1. 5x^2 + 6x2. 7xy-3y3. x^5 - 8 x^24. 7a^2b - 4ab^25. 4a^3b^2 + 36a^2b6. x^2-167. x^2-49y^28. 4x^2-649. 3 b^2+6xb10. x^3-25x11. 8+x^312. 4x^3 + 9 x13. 5y^2 - 8014. x^3-2715. (x - 1)^3+116. x^4 - 4x^217. (x+2)^2 - 9x^218. 9x^4 - 121 x^219. 8x^3 - 27y^320. 125x^3 + 64y^321. r^3 - t^322. 7x^3+7a^323. a^2x^2 - y^224. 49 - 9y^225. (2x - 1)^2 - (x+3)^226. (a+2)^3+827. (x-5)^2 - y^228. 25s^2 - (3t+1)^229. 8x^2-7230. 9y^2-81x^231. (x+1) (x^2 - 5)^2+4x (x+1)^2 (x^2 - 5)32. x(y+1) + 5(y+1)33. x(x-1) +8(x-1)34. 4x (x - 2)^2 (x - 1)+8 (x - 2) (x - 1)35. x (x - 2)^2+2 (x - 2)36. x^4 (x - 7)^2 - 4x^3 (x - 7)^337. 6x^5 - 18x^3 + 24x38. 16 x^5y^2+8x^3y^339. 4x^5y^3 - 3x^4y^5 + 6x^2y^340. x^6-25y^241. 81 - y^442. 81 x^4 - 256y^443. x^4 - y^444. x^4 - 1645. x^6 - 27y^346. 64 x^3 - y^647. x^4-8148. 16 - x^449. x^6-y^650. x^6+y^651. 3 x^6 - 24y^652. x^8 - y^81. x^2+7x+62. a^2+5a-363. x^2-3x-544. x^2+3x-45. 6x^2+7x - 206. a^2+a - 207. 9x^2+30x+168. x^2+11x+189. 12n^2-43n-2010. 9x^2+6x+111. 2x^2 - 7x - 1512. 12x^2 - x - 613. 20y^2+31y-914. 6x^2+12x+615. 6x^2+48x+7216. 21x^2+41x+1017. 3x^3 - 3x^2 - 6x18. 3m^3 - 6m^2+15m19. 7n^2+31n +1220. t^2+3t -18021. 12x^2+10x - 1222. 8x^2 - 9x+123. 3x^2 - 11x - 2024. 10x^2 - 8x - 225. 7x^2 - 13x+626. 2x^2+3x - 2027. 6x^2 - 5x - 628. 14x^2+37x+529. x^4 - 4x^230. 3x^4 + 7x^2 - 631. 2x^4+8x^2 - 4232. x^4 - 10x^2+2433. y^4 - 3y^2 - 434. x^4-17x^2 + 1635. x^4+2x^2 - 3536. x^4 - 2x^2+137. 2(x - 1)^2+3(x - 1)+138. 16x^2+8xy+y^239. x^3 - 4x^2 - 5x40. x^3+x^2+2x41. 45 x^2+38 xy+8y^242. y^6+7y^3 - 843. y^6 - 6y^3 - 1644. x^8 - 17x^4+1645. 25x^2 - 20 xy+4y^246. 63 x^2 - 46 xy+8y^247. 9x^2 + 15x - 1448. 6x^2 - x - 3549. 48 x^2 + 22 x - 550. x^4+2x^2y - 3y^21. x+1+y+xy2. 2 - y^2+2x - xy^23. 2a(a+3) -(3+a)4. -y - x+1+xy5. (5x - 2) (x - 2)+(3x+8) (5x - 2)6. a^2 (x - 1)+ b^2 (1 - x)7. 9 (x - 5) + x^2 (5 - x)8. 5x^4 (x+7)^2+ 4x^3 (x+7)^39. x^2 - 2x+3x - 610. (x-3)^2 - x^2 +911. x^2y - 3+3x^2 - y12. 5x^2 - 40x - x+813. a^5 - a^3 - a^2+114. x^2(x-y) + y^2(y-x)15. x^2 +4x+4 - 9y^216. x^2+y^2-2xy -117. x^2 - y - x+xy18. y^2 - 2xy+x^2 - y+x19. y^2+9 - 6y - 4x^220. x^2y - 2z^2 - 2xyz+xz21. 2ax+bx - 4a - 2b22. a^5 - a^3 - a^2+123. x^4 + 2x^3 - x - 224. (12x^2-8xy) - 5(3xz-2yz)25. 2ax - 2ay+x - y26. 2xy - 3y+2xz - 3z27. p^2-2pq + pr - 2qr28. xy - zy - xw+zw29. 4z^3 - 6z^2 - 6z + 930. 4x^2+y^2+4xy - 131. h^2-4k^2-4h + 432. 2ax -6bx +ay -3by33. 8ac+3bd - 6bc - 4ad34. x^4+x^3y-xy^3-y^435. p^2 + q^2 - r^2 -2pq + 2r - 136. a^4+ab^3-a^3b -b^437. 2x^3 -50x +2x^2 -5038. y^3 - 3y^2 - 4y+1239. x^3 - 5x - 3x^2+1540. x^3 - y^3+xy^2 - yx^241. a^3+1+3a+3a^242. 15x^3 y^5 - 25 x^4 y^2+10 x^6 y^443. x^5 - x^2 - 4x^3+444. u^2-v^2 + 2v-145. u^2 - 2uv - 15v^246. 63 u^2 - 46 uv + 8v^247. (h^2k^2 + 4k^2) + (h^2k + 4k)48. 70a -84b +20ab -24b^249. 21bc^2 -6c-3c^3 +42b50. 12y-9x^2+36-3x^2y51. 30a^3 -18a^2b -72b +120a52. x^3+y^3+2x^2-2xy+2y^253. a^3-b^3+3a^2 +3ab+3b^254. a^4+ab^3-a^3b -b^455. 3 ay^2 - a x y + 9 xy - 3 x^21. x^2 + 2x -1 = 02. y^2+8y = 103. 3x^2 -2x-2=04. -y^2 = -9y + 55. z^2-6z-307=86. 2x^2 -4x+1=07. 2x^2 + x-4 = 08. w^2 + w = 39. 2x^2 -4x +3=010. 2y^2/3 - y - 3 = 011. x^2 -x/2 +1=012. 3a^2 - 8a+2 = 013. -x^2 +3x -4=014. y^2/2 - y/4 = 315. x^2 -3x+4=016. 4x^2 +20x +13=017. n^2+5n-3= 018. -2x^2 -6x -5=019. a^2-8a = 420. x^2 +4x+4=021. n^2+5n+8 = 022. 3x^2 -4x-2=023. x^2-18x+80 = 024. x^2 -2x+2=025. 4x^2+7x+2=026. x^2 -6x +1 =027. 4x^2 -12x -11=028. -2n^2 + 3n+5 = 029. 2x^2 +6x+8=030. 3x^2 + 19x + 20 = 031. x^2 -6x +1 =032. x^2 -8x+11=033. 36n^2 - 60n + 25 = 034. x^2 +2x-4=035. x^2 +6x +7=036. 4x^2 - 2x = 337. x^2 +x-1=038. 3x^2 -6x +5=039. 5x^2 - 13x = 040. x^2 +2x -2=041. 2x^2 +4x-3=042. 2x^2 +8x+1=043. 6t^2  +t - 3 = 044. x^2 +2x -4=045. n^2+32n+252 = 046. 3x^2 -10x -1=047. 12x^2-73x+110=048. 7x +10 =3x^249. -3x^2+6x+4=050. x^2 = 3x-551. -6x^2+2x+1=052. x^2 -4x+2=053. x^2 +5x-10=054. x^2 +mx +n =01. 2 < 3x2. 1 + 3x < 43. x < x+14. x < x - 15. 1+x > 36. 1+x >= 37. 1 + 4x < 5x8. 3(x+1) < 99. 2(x+2) < 3610. 2(x-1) <= x+311. 4 <= 2x - 112. (2 - x) / 5 >= 013. 2x+9 > 014. -5x > 5015. 2x +4 <= 716. - 9x < - 4517. 3 - x/2 <= 818. 3x - 8 <= 13x - 919. x - 8 < 5x + 820. 3/4 x + 4 > 421. 3x+5 <= - 1722. 6x + 13 <= 6 (x+1)23. 5x - 4 < 6+4x24. x - 6 < 5x+425. 6x - 13 <= 6 (x+1)26. 4 (x+5) < 5x+327. 6x - 1 <= 2/3 x +128. (x - 1) / 2 < (x+1)/329. 4 - 6x <= -7+9x30. x/2 - 4 > 8 - x31. 2 (x+3) <= 6(x+1)32. 3 (x - 1) >= 2 (x - 1)33. 100 + 5x <= - 4x +1034. 2 (1 - x) >= 5x35. 1/2 x - 5 <= 1/4 x - 336. (9x - 5) / 7 > (2x+4) / 337. (3x+2) / (- 3) >= (5x+1) / 438. x + 3(x - 7) >= 3x + 2 (x - 1)39. x/3 +7/2 >= 3/2x - 1/340. 3 (7x +11) < 4 (3x - 7) - 3 (5 - 3x)41. 0 < x+7 < 342. 1 < 2x - 1 < 643. -1 <= 3x+4 < 1644. -4 < 3x - 2 <= 445. -2 <= 1 - x < 546. 0 <= 1+x <147. -3/2 < 1/3 - x < 748. 15 < 7 - 3x < 1749. -1 < (5 - x) / 3 < 350. -10 < 4+2x <= 1651. 0 < 4+x/2 < 252. -2 < (4x - 1) /3 <= 053. -5 <= 2 - x <= 554. 2 <= (6 - 5x) / 3 < 555. 0 < (2 - x) / 5 <= 1/21. y = x, y=3x - 12. y= - 3 - x, y = 2x+33. y = x - 2, y = 5x+64. - 2x - y = - 5, 5x - 7y = 05. 2x - y = 0, 3x+y = 56. 3x-2y =1, 5x+y = 67. 2x+7y = 3, x-14y = -18. 5x-3y=2, 15x-9y = -49. 8x+6y = 24, 4x+3y=1210. y = 1/3x - 5, x - y - 15 = 011. 3 x - y = 4, 3y = x - 412. 5x+2y = 1, 2x - 3y = - 1113. 4y = 3x+2, 2x = 3y - 314. 2x+3y = 2, x - 2y = 815. 4x+2y = 2, 6x - 5y = 2716. 4x - y = 13, x+2y = 117. 4x = 7y - 6, 9y = - 12x+1218. x - 2y = 1, 2x - y = 519. 3x+y = 7, x - y = 120. - x+2y = - 4, x - y = 321. x - 2y = 3, y - 3x = - 1422. x - 3y = 10, 3x+2y = 223. x+7y = -1, 3x+21y = - 324. 2x - y = 3, x+2y = 1425. 2x+8y = 7, 3x - 5y = 426. 2x+y = 1, - 3x+2y = 927. 2x - 4y = - 2, 3x+6y = 328. 2x - 2y = 12, - 2x+3y = 1029. 3x - y = - 6, 2y = 4x+1230. 3x - y = - 5, x+3y = 531. 3x+y = 11, 2x - 5y = 1332. 3x+8y = 4, 12y+6x = - 133. 3x - 2y = 15, 2x+y = 1034. 5x - 4y = 0, x = y-135. 5x - y = 12, 3x+2y = 1536. 5x - 2y = 1, x - 5y = - 3237. 7x - 2y - 19 = 0, 3x+5y+14 = 038. 9x - 3y = 1, 6x - 2y = - 539. 9/2 x - 4y = - 3, 4/3x - 1/2y = 7/640. 1/2x - 1/3y = 2, 3/4x+2/5y = - 141. x/5 +y/3 = 2, x/4 +y/3 = 242. 2/3x+8y = 6/7, 3/4x+9y =343. (sqrt 3)x - (sqrt 2)y = 2 sqrt 3, (2 sqrt 2)x+(sqrt 3)y = sqrt 244. (x - y)/4+(x+y)/3 = 1, (x+2y)/3+(3x - y)/2 = - 245. (x+y)/4 - (x - y)/3 = 1, (x+y)/4+(x - y)/2 = 946. (x+3)/2+(y - 4)/3 = 10/6, (x - 2)/3+(x - 2)/2 = 21. (a^2b^2)/(ab) (a^3)/(ab^3)2. (4x^2y)/(xy^3)/(33x^4/(x^2y^2))3. (1-x^2)/(x^3-1)4. x/(x-1)- 1/(x^2-x)5. ((3x+9)/(2x)) (11x^2)/(x^2 - 9)6. (x/(x+1) + 2/x) / (2/x+1 / (x+1))7. x^2/(x+3) - 9/(x+3)8. 3x/(x+2)-1/x9. ((xy)^3 - 8) / (xy - 2)10. (x - y) (3 - (2x - y) / (x - y))11. (9x^2-4)/(6x-9x^2)12. (xy-1)/(x^3 y^3 -1)13. 1 /(x^2 - 1) - 2 / (x^2 - 2x+1)14. x/(x^2+x - 2) - 3 / (x^2 - 5x+4)15. (x+ 5/x)/(1+ 5/x^2)16. (x/2-2/x)/(x/2+2/x)17. 4/(5 (x - 1)(x - 2)^2) + x / (2(x - 1)^2 (x - 2))18. (3x+8) / (x^2) - (2x - 1)/ x^3 - 12/(8x)19. (2x+3)/(x-3) -(x-1)/(x+3)20. 1/(x+1)^2 - 1/(x+1)^321. (2x) / (x+2) - 6/(x^2+2x) - 3/x22. x/(2x+3) - 6/(2x^2+3x) -1/x23. 1/x^2 + 4/x - 5/x^324. (1/x + 6/y)/(1/x^2 - 36/y^2)25. 2y/(y+3) - 1/(y - 3) + y/(y^2 - 9)26. 1/(x+1) + 3/(x+1)^2 + 1/(x^2 - 1)27. ((3+x)/(4+x) -3/4)/x28. 8/(x+1) -4/(x-1) (x^2-1)/(2x^3)29. 3/(x+2) + 1/(x^2 - 4) +8/(x^2 - x - 2)30. 10/(x+1 + x/(1 + 1/x))31. (2/(x-3) +8/(x+3) x/(x-3)) (9-x^2)/1432. (x+2)/(x^2 +8x-9) (2x+18)/(x^2-4)33. ((x-y) / (x+2y)) / ((x-y) / (xy))^234. (y^2 / x^2 - 1) / (y / x + 1)35. (x+4)/(x^2-x-2) (x-2)/(3x^2 -4x+1)36. ( 2x^2/(x^2+3x+9))/((2x^3-18x)/(x^3-27))37. ((x+1)/(x - 4)) / ((x+1)/(x+2) - x/(x - 4))38. (9x - 1/x) / (3+1/x)39. ((x-1)/(x^2-1) (2x+2)/(x^2-4))/((5x+5)/(x^2+4x+4))40. ( 2/(x-2) +3)/(1/(x^3-8))41. 5x / (x+1 /(5+4/x))42. 3 - 2/(2-2/(2-2/(2-x)))43. ((2x-1)/(3x+1) + 3x/(9x^2-1))/( 2/(3x-1) +2)44. x/(4x-4) + 5/(x^2-1)45. (x^2-1)/(3x) - 3x/(x^2-1) + 3/246. (x+4)/(x+1) - (x+2)/(x+3)47. 1/(x+4) + 3/(x-4)-(3x+8)/(x^2-16)48. 11/(x^2-4) +(x+3)/(2-x)-(2x-3)/(x+2)49. (x+2)/(x+3) -(x^2)/(x^2-9)-(x-1)/(3-x)50. 2x/(x+2) + 15/(x^2-7x+10) - 3/(x+5)1. 1/2 + 1/32. 1/3 + 1/43. 1/4 + 1/54. 2/3 + 1/45. 2/3 + 3/46. 3/8 + 1/57. 2/7 + 1/98. 1/5 + 1/79. 1/4 + 1/1010. 1/3 + 1/911. 1/6 + 1/312. 3/5 + 6/713. 2/7 - 1/914. 7/11 + 11/715. 1/10 + 1/10016. 1/10 + 1/100 + 1/100017. 1/2 + 1/3 + 1/418. 1/3 + 1/4 + 1/519. 3/4 - 1/2 + 8/1120. 1/2 + 1/4 + 1/821. 5/8 - 6/7 + 6/522. -4/5 + 5/4 +123. 3/4 - 2/3 + 1/224. 45/3 - 45/9 - (- 54/6)25. 2/7 - 45/11 + 34/926. 5 + 1/10 + 3/10027. 1 + 3/10+4/100+7/100028. 1/10+10(1/100)+100(1/1000)29. (2/3)(- 5/8) +3/430. (2/3)(9/5) - (4/5)(10/8)31. 2 (1/2) - 4 (1/4) + 5 (1/2)32. 3/5 (- 2/3) + 1/233. 4 (3/8) - 10 (1/5)34. 2 - 3 (1/3) + 4 (5/6)35. 3 (- 1/2) - 2/3 - 5 (1/6)36. 12 (3/8) - 5 (-1/4) + 7(1/2)37. - 5(- 4/9) + 3(- 5/6)38. 8 (1/3) - 6(1/2) - 3(5/6)39. 2(5/6) - (1/5) (1/9) + (5/7) (1/7)40. 1/2 + 2(1/4) + 4(1/8) +8(1/16)41. 1/3 +3(1/6) - 6(1/12)42. 7/8 - 3(1/4) - 2(1/16)43. 21/7+21/3 - (1/2) (1/3)- 1044. (- 3/4) - (2/3)^245. (- 2/5)^2 - 3/446. -3 +(2/3)(1/2)^2 - 3(1/6) (1/2)47. 3 (- 1/2)^2 - 2(1/2) +1148. 2 (- 1/4)^2 - 3(- 1/4) +649. 7/72 + 11 / 5450. 4/63 - 5/4251. 3/50 + 7/301. x^2/x^32. x^3/x^23. 3x^2/x^34. pi r^2/ (2 pi r)5. x^2y/(yx^2)6. x^2 y/(xy^2)7. x^(k+1)/x8. x^(k+1)/x^k9. ((2x)/(5y))( (5y^2)/(8x^4))10. ((20x)/(10y))( (15y)/(30x))11. (x^2 + x)/x12. (6-3x)/(x^2-4)13. 10(x^2-1)/(x+1)14. (x^2 + x - 2)/(x +2)15. (x^2 + x)/(x + 1)16. (x^2 -1)/(x+1)17. (x^2 - 3x+ 2)/(x-1)18. (x^2 - x - 2)/(x+1)19. (x^3+y^3)(x^2-y^2)20. (x-y)/(ax(y-x))21. ((xy)^3-1)/(xy-1)22. (x^3-y^3)/(x^2-y^2)23. (x-y)(2-(2x-y)/(x-y))24. (x^3-(x-1)3x^2)/x^625. (x^4-y^4)/(x-y)26. (x^3-x^2+x-1)/(x-1)27. (a^3+8)/(a^2-4)28. (x+4)^2 x/(16-x^2)29. (x^2-xy)/(xy+y^2)30. (x^2-y^2)/(x^2+2xy+y^2)31. (x^2-y^2)/(x^2-2xy+y^2)32. ((x+1)^2-2x(x+1))/(x+1)^433. (x^2-4)/(x^2-4x-12)34. (x^2-25)/(x^3-125)35. (x^2-9)/(x^2+2x+1)36. (x^3-3x^2+9x-27)/(x^4-81)37. (t^2+t+1)/(t^3-1)38. (x^2+4x+4)/(x^2-4)39. (10+3x-x^2)/(x^4+2x^3)40. (6x^2-5x-6)/(2x^2-3x)41. (x^2+4x+4)/(2x+x^2)42. x(x^2-x-6)/(x^2+2x)43. (3x^2+6x-24)/(3x^2+4x)44. (9x^2-4)/(27x^4+8x)45. (6x^2-7x-5)/(4x^2+4x+1)46. (x^2-2x-15)/(x^3-3x^2-10x)47. ((2-x)/(2x+x^2)) ((x^2+4x+4)/(x^2-4))48. ((x^3-y^3)/(x-y)^3) ((x^2-2xy+y^2)/(x^2+xy+y^2))49. ((2x^2-7x+6)/(x^2-x-6)) ((5x-15)/(x^2-4))50. ((2x^2-2ax+2a^2)/(ax)^3) (ax^3/(a^3+x^3))1. (3+3/5)/(5-1/8)2. (2/3-1/2)/(1/8+2/5)3. (1/2)/(2/3-1/2)4. (3/5-1/2)/(7/10 +2)5. (4-2/3)/(2/5-6)6. (1/8)/(-1/4)^37. (1/3+1/9)/(1/9)8. (1/2-1/4)/(3(3/4)+2/3)9. (4-2(1/2)(3/5))/(3(1/3)-1/3)10. (3(2/15)-2/5)/(1/3-2(1/5))11. (2+5/7)/(3-2/7)12. (1/2 - 1/4)/ (5/8 + 3/4)13. (3/8 + 3/4)/(5/8 - 7/12)14. (3/28 - 5/14)/(5/7 + 1/4)15. (5/9 + 7/36)/(3/18 - 5/12)16. (3 + 1/4) / (5 - 2/5)17. (2+5/7)/(3-2/7)18. (1/2 - 1/4)/ (5/8 + 3/4)19. (5/18+11/12) / (7/6 - 2/9)20. (3/8 + 1/4)/(5/8 + 7/12)21. (3/28 + 5/14)/(5/7 + 1/4)22. (1/9 + 7/36)/(3/18 - 3/12)23. (1/2 - 1/4) / (2 - 4)24. 1 / (1/2+1/5)25. (3/2)/(1/(3/2)+4) + 126. (1/16 - 1/3^2) / (3+4)27. (1 - 1/3^2) / ((3 - 1)/3)28. (5/2 + 7/2^2)/(5/3 + 1/3^2)29. 7/3 - 2/7 + 3 (3/7^2)30. (1 / (1/4 - 3) - 1/3) / (1/4)31. [1/3-2/(1/3+1)]/[1/3+(1/3-3)/(1/3+1)]32. (1 / (2/3+2) - 3) / (4/(2/3) - 2/3)33. (1/(5/2)+1/(2/3)) / (1 / (5/2+2/3))34. (1/3+1/5) / (1/3^2 - 1/5^2)35. 6/(1/7) - 3/(2(1/7)^2)36. (3/5) / (3/5 - 2 / (3 - 1/(3/5)))37. (1/3+1/11) / (1/(33))38. ((1/2)/(1/7)^2 + (1/7) / (1/2)^2) / (1 / (1/7)^2 - 1/(1/2)^2)39. (3/(2(1/5)-1) - 1/(1+2(1/5))) /( (5-4(1/5))/(1-4(1/5)^2))40. (2/(1/3) - 2/(1/3+2))/(3/((1/3)^2+2(1/3)) - 3/(1/3))41. 1/2 - (3/7) / ((1/2)/(3/7) + (3/7)/(1/2))42. (5 / (3/5+1) + (2(3/5)) / (3/5+3)) / ((3/5) / (3/5+1) - 7 / (3/5+3))43. (1/(2/3-3/5) - 3/(2/3+3/5))/(3/(2/3+3/5) + 1/((2/3)^2-(3/5)^2))44. 1 / (7/8+1/(7/8) - (7/8) / (1 - 1/(7/8)))45. (1+1/(5/8+4)) / ((5/8+5) / ((5/8)^2 - 16))46. 1+1 / (1+1/(1+3/5))47. 1 - 1/(1 - 1/(1 - 1/(7/5)))48. (2+1/(2 - 1/2)) / (1 - 2/(2-1/2))49. (3/(3/7)+(3/7)/3+1) / ((3/7+1)/3+(3/7+1)/(3/7))50. (1/2+1/3+1/5) / (1/(6)+1/(15))51. (3 + 1/4) / (5 - 2/5)52. (2+5/7)/(3-2/7)53. (1/2 - 1/4)/ (5/8 + 3/4)54. (5/18+11/12) / (7/6 - 2/9)55. (3/8 + 1/4)/(5/8 + 7/12)56. (3/28 + 5/14)/(5/7 + 1/4)57. (1/9 + 7/36)/(3/18 - 3/12)�5..;	5f.
V	5�.z	5�.2"�	5�. X�	5�.!|�	5.3�
	؞	�	D�	5|.4zl	��	5�.7��	5�.6#�	]�	5..�	��	
	7�	5y.9mi	I!I/4:!;9!I?4:!;9!I?$>%I6.�
problems58GNU C17 13.2.0 -mtune=generic -march=x86-64 -glong unsigned intproblems41problems42problems43problems44problems45problems46problems47problems48problems49problems55problems50problems57problems51problems59problems52problems56problems53problems54charproblems60/home/beeson/MathXpertProblemLibrary/problems41-61.c/home/beeson/MathXpertProblemLibraryproblems41-61.cproblems41-61.cGCC: (FreeBSD Ports Collection) 13.2.0�
 X'�H2��=�H�S��^`�i�t�	�@��
�����`�� ���x�`�������@�problems41-61.cproblems41problems42problems43problems44problems45problems46problems47problems48problems49problems50problems51problems52problems53problems54problems55problems56problems57problems58problems59problems60
  (X0�8�@PH�P�X8`xh�p���`�
�(���X�(�X������������ (60K8p@�H�P�X�`�h	p	x1	�G	�\	�x	��	��	��	��	��	�
�
�'
�7
�E
�U
�g
�x
�
�
�
�
 �
(0'8@@`H}P�X�`�h�p��� �H�p�����
�(
�`
��
��
��
��8�h���@_ �(�0�8@@HpP�X�`�h pHxx��������������������+�<Lbv� �(�0�8�@�H�P	X`.hEpXxm����������������!�,�7�B�P^m}� �(�0�8�@�H�PX0`Hhhp�x�����������!�5�L�i��������������=Ws �(�0�8�@H,PFX`dhqp~x������������������1�C�R�b�s�������� �(08.@AHSPfXw`�h�p�x���������'�<�R�i�������������- @(O0b8m@xH�P�X�`�h�p�x������,�B�U�m��������������,�I	e	v	�	� 	�(	�0	�8	�@	�H	P	'X	>`	Sh	op	�x	��	��	��	�	 �	 �	. �	B �	X �	n �	~ �	� �	� �	� �	� �	� 
!
!
0!
D! 
_!(
x!0
�!8
�!@
�!H
�!P
�!X
"`
"h
!"p
3"x
C"�
R"�
c"�
p"�
�"�
�"�
�"�
�"�
�"�
�"�
�"�
#�
5#�
F#�
[#�
p#�
�#�#�#�#�# �#($0@($H5$P?$XN$`_$hs$p}$x�$��$��$��$��$��$��$��$��$��$�%�%%�6%�I%�W%�e%�v%�%�%�%�% �%(�%0�%8&@/&HH&Ps&X�&`�&h�&p�&x'�'�'�/'�='�J'�Z'�k'�v'��'��'��'��'�
�'
�'
�'
�' 
�'(
�'0
(8
(@
((H
8(P
F(X
Y(`
k(h
{(p
�(x
�(�
�(�
�(�
�(�
�(�
�(�
)�
)�
,)�
?)�
P)�
a)�
s)�
�)�
�)�
�)�
�)�)�)�)* *(/*0A*8U*@d*Hz*P�*X�*`�*h�*p�*x�*�+�+��2+�>+�S+�e+�x+��+��+��+��+�,�,�/,D,Z,r,�, �,(�,0�,8�,@�,H
-P -X7-`T-hh-p~-x�-��-��-��-��-�.�.�0.�R.�i.��.��.��.��.��.�/�/0/F/`/�/ �/(�/0�/8�/@0H0P80X`Z0hm0p|0x�0��0��0��0��0��0��0�1�1�-1�?1�S1�c1�w1��1��1��1�1�1�1�1 �1(20 2842@I2HZ2Pr2X�2`�2h�2p�2x�2��2��2�3�3�&3�73�H3�]3�n3��3��3��3��3��3��3��3�34 4((40648A4@N4HY4Pe4Xt4`�4h�4p�4x�4��4��4��4��4�5�5�(5�;5�M5�^5�u5��5��5��5��5��5�56616 L6(e60y68�6@�6H�6P7X 7`I7hY7pl7x�7��7��7��7��7��7��7�8�%8�?8�T8�n8���8��8��8��8�89969 N9(h90�98�9@�9H�9P�9X:`0:hO:pj:x�:��:��:��:��:�
;�(;�B;�`;�;��;��;��;��;�<�$<�@<`<�<�<�< �<(=08=8�=@�=H�=P`&>hH>pk>x~>��>��>��>��>�?�(?�M?�d?��?��?��?��?�@�8@�e@��@�@�@�@A (A(PA0vA8�A@�AH�APBX0B`XBh�Bp�Bx�B�C�0C�PC��C��C��C��C�D�0D�TD�xD��D��D�E�(E5EBEOE \E(iE0vE8�E@�EH�EP�EX�E`�Eh�Ep�Ex�E�F�%F�9F�NF�bF�vF��F��F��F��F��F�G�G�5G�XG�xG�G�G�G�G H(H0@H8hH@�HH�HP�HX�H`�HhIp4IxQI�oI��I��I���I��I��I��I��I��I��I�J�J�8J�XJ�hJ{J�J�J�J �J(�J0K8K@,KHBKPZKXtK`�Kh�Kp�Kx�K��K��K�L�1L�OL�gL�~L��L��L��L��L��L�M�-M�EM�`MxM�M�M�M  N(PN0@~NH�NP�NX�N`�Nh�Np�Nx
O�(O�HO�gO�{O��O��O��O��O�P�%P�HP�gP��P��P��P��P�P
Q(QHQ hQ(�Q0�Q8�Q@RH0RPPRXpR`�Rh�Rp�Rx8S�xS��S��S�@T�pT��T��T��T�U�8U�[U�uU��U��U��U��UV





1
:>
C
LNg
Wr	�
b�
�
m��
x��
�

�&/
�:C
�OX
�d}
���
���
���
��
��
�"+
�7@
LU
�az
�
"
6&
M0
\5
l.symtab.strtab.shstrtab.text.rela.data.bss.rodata.rela.debug_info.debug_abbrev.rela.debug_aranges.rela.debug_line.debug_str.debug_line_str.comment.note.GNU-stack@&@ !@{ R,P1P'V>wr�9@8�hJu`]fu X@��	q�u:l@��`}0�u"�0�v|�0^w(��w�w�	(z���

Sindbad File Manager Version 1.0, Coded By Sindbad EG ~ The Terrorists