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 #2
avatar+26400 
+15

How many numbers between 1000 and 2000 leave a remainder of 3 when divided by 11 ?

 

$$\small{
\begin{array}{rcl}
1. & 1004 & \text{remainder~} 3 \\
2. & 1015 & \text{remainder~} 3\\
3. & 1026 & \text{remainder~} 3\\
4. & 1037 & \text{remainder~} 3\\
5. & 1048 & \text{remainder~} 3\\
6. & 1059 & \text{remainder~} 3\\
7. & 1070 & \text{remainder~} 3 \\
8. & 1081 & \text{remainder~} 3\\
9. & 1092 & \text{remainder~} 3\\
10. & 1103 & \text{remainder~} 3\\
11. & 1114 & \text{remainder~} 3\\
12. & 1125 & \text{remainder~} 3\\
13. & 1136 & \text{remainder~} 3\\
14. & 1147 & \text{remainder~} 3\\
15. & 1158 & \text{remainder~} 3\\
16. & 1169 & \text{remainder~} 3\\
17. & 1180 & \text{remainder~} 3\\
18. & 1191 & \text{remainder~} 3\\
19. & 1202 & \text{remainder~} 3\\
20. & 1213 & \text{remainder~} 3\\
21. & 1224 & \text{remainder~} 3\\
22. & 1235 & \text{remainder~} 3\\
23. & 1246 & \text{remainder~} 3\\
24. & 1257 & \text{remainder~} 3\\
25. & 1268 & \text{remainder~} 3\\
26. & 1279 & \text{remainder~} 3\\
27. & 1290 & \text{remainder~} 3\\
28. & 1301 & \text{remainder~} 3\\
29. & 1312 & \text{remainder~} 3\\
30. & 1323 & \text{remainder~} 3\\
31. & 1334 & \text{remainder~} 3\\
32. & 1345 & \text{remainder~} 3\\
33. & 1356 & \text{remainder~} 3\\
34. & 1367 & \text{remainder~} 3\\
35. & 1378 & \text{remainder~} 3\\
36. & 1389 & \text{remainder~} 3\\
37. & 1400 & \text{remainder~} 3\\
38. & 1411 & \text{remainder~} 3\\
39. & 1422 & \text{remainder~} 3\\
40. & 1433 & \text{remainder~} 3\\
41. & 1444 & \text{remainder~} 3\\
42. & 1455 & \text{remainder~} 3\\
43. & 1466 & \text{remainder~} 3\\
44. & 1477 & \text{remainder~} 3\\
45. & 1488 & \text{remainder~} 3\\
46. & 1499 & \text{remainder~} 3\\
47. & 1510 & \text{remainder~} 3\\
48. & 1521 & \text{remainder~} 3\\
49. & 1532 & \text{remainder~} 3\\
50. & 1543 & \text{remainder~} 3\\
51. & 1554 & \text{remainder~} 3\\
52. & 1565 & \text{remainder~} 3\\
53. & 1576 & \text{remainder~} 3\\
54. & 1587 & \text{remainder~} 3\\
55. & 1598 & \text{remainder~} 3\\
56. & 1609 & \text{remainder~} 3\\
57. & 1620 & \text{remainder~} 3\\
58. & 1631 & \text{remainder~} 3\\
59. & 1642 & \text{remainder~} 3\\
60. & 1653 & \text{remainder~} 3\\
61. & 1664 & \text{remainder~} 3\\
62. & 1675 & \text{remainder~} 3\\
63. & 1686 & \text{remainder~} 3\\
64. & 1697 & \text{remainder~} 3\\
65. & 1708 & \text{remainder~} 3\\
66. & 1719 & \text{remainder~} 3\\
67. & 1730 & \text{remainder~} 3\\
68. & 1741 & \text{remainder~} 3\\
69. & 1752 & \text{remainder~} 3\\
70. & 1763 & \text{remainder~} 3\\
71. & 1774 & \text{remainder~} 3\\
72. & 1785 & \text{remainder~} 3\\
73. & 1796 & \text{remainder~} 3\\
74. & 1807 & \text{remainder~} 3\\
75. & 1818 & \text{remainder~} 3\\
76. & 1829 & \text{remainder~} 3\\
77. & 1840 & \text{remainder~} 3\\
78. & 1851 & \text{remainder~} 3\\
79. & 1862 & \text{remainder~} 3\\
80. & 1873 & \text{remainder~} 3\\
81. & 1884 & \text{remainder~} 3\\
82. & 1895 & \text{remainder~} 3\\
83. & 1906 & \text{remainder~} 3\\
84. & 1917 & \text{remainder~} 3\\
85. & 1928 & \text{remainder~} 3\\
86. & 1939 & \text{remainder~} 3\\
87. & 1950 & \text{remainder~} 3\\
88. & 1961 & \text{remainder~} 3\\
89. & 1972 & \text{remainder~} 3\\
90. & 1983 & \text{remainder~} 3\\
91. & 1994 & \text{remainder~} 3\\
\end{array}
}$$

 

Jun 23, 2015
 #1
avatar+33661 
+13

Differentiation 1;

Differentiation 2.

.

Jun 23, 2015
 #2
avatar+118723 
+8

 

Now it is right     I had just made a careless error right at the beginning.

Thanks for spotting it Alan     [ I do have a question at the bottom though]

 

the correct answer is   

I have not found my errors  :(

 

---------------------------------------------------------------------------------

 

$$\\\int\frac{(2cos3x + 3sinx) }{sin^3x }dx\\\\
=\int\frac{2(cos2xcosx-sin2xsinx) + 3sinx }{sin^3x }dx\\\\
=\int\frac{2cos2xcosx - 2sin2xsinx) + 3sinx }{sin^3x }dx\\\\
=\int\frac{2(cos^2x-sin^2x)cosx - 2(2sinxcosx)sinx) + 3sinx }{sin^3x }dx\\\\
=\int\frac{2cosxcos^2x-2cosxsin^2x - 4sin^2xcosx + 3sinx }{sin^3x }dx\\\\
=\int\frac{2cos^3x-2cosxsin^2x - 4sin^2xcosx + 3sinx }{sin^3x }dx\\\\
=\int\frac{2cos^3x - 6sin^2xcosx + 3sinx }{sin^3x }dx\\\\
=\int\;2cot^3x-\frac{6cosx}{sinx} + 3csc^2x \;dx\\\\
=\int\;2cot^3x\;dx -\int\;\frac{6cosx}{sinx}\;dx +\int\; 3csc^2x \;dx\\\\
=\int\;2cot^3x\;dx -6ln(sinx) +\int\; 3csc^2x \;dx\\\\
=-6ln(sinx)\;+\;\int\;2cot^3x\;dx -3cotx\\\\
=-6ln(sinx)\;-3cotx\;+\;\int\;2cot^3x\;dx$$

 

$$\\$NOW I'll use the reduction formula$\\\\
\int\;2cot^3x\;dx\\\\
=2[\frac{-Cot^{3-1}x}{3-1}-\int\;cot^{-2+3}x\;dx]\\\\
=2[\frac{-Cot^{2}x}{2}-\int\;cotx\;dx]\\\\
=-Cot^{2}x-2\;ln(sinx)\\\\$$

 

$$\\$So - continuing from before$\\\\
=-6ln(sinx)\;-3cotx\;+\;\int\;2cot^3x\;dx \\\\
=-6ln(sinx)\;-3cotx\;+\; -Cot^{2}x-2\;ln(sinx) +c \\\\
=-8ln(sinx)\;-3Cotx-Cot^{2}x \;+c \\\\$$

-------------------------------------------------------------

Now this is correct but Wolfram Alpha is telling me that  $$cot^2x=csc^2x$$   for the restricted values involed here.

WHY IS THAT ?

Jun 23, 2015
 #33
avatar+1038 
+8

Rosala, do what you need to do to make a good grade. However, if you want to be a good writer, you will have to study and understand all manner of ancient and modern literature.

It’s part of the troll’s toll. :)

Jun 23, 2015
 #32
avatar+1038 
+5

11. What sound does Lucie often hear echoing off the street when she is in her home?

Footsteps

 

12. Which of the following characters is related to the Marquis, whose carriage runs down a small child?

Charles Darnay

 

13. Who does Miss Pross believe is the ideal suitor for Lucie Manette?

Her brother, Solomon

 

14. What does Mr. Lorry try to persuade Mr. Stryver not to do?

Propose to Lucie Manette

 

15. Who promises Lucie Manette that he would, if necessary, die for her?

Sydney Carton

 

16. What does Jerry Cruncher frequently go out to do at night?

Dig up bodies in the cemetery

 

17. Who informs the Defarges that Lucie Manette has married Charles Darnay?

John Barsad

 

18. On the night after Lucie and Charles are married, what does Doctor Manette do?

He reverts to his prison pastime of making shoes.

 

19. During the storming of the Bastille, who decapitates the fortress’s guard?

Madame Defarge

 

20. Why does the Paris mob k**l Foulon?

Because he suggested that starving people should eat grass

 

21. What is the duration of Manette’s psychological relapse after Lucie leaves for her honeymoon?

Nine days

 

22. Who develops a habit of watching and speaking to Lucie as she waits on a Paris street corner each day, hoping that Darnay will be able to see her from his prison window?

wood-sawyer

Jun 23, 2015
 #31
avatar+1038 
+5

. . .   I think you took a wrong turn and stumbled into the wrong forum :/

 

I might have thought so, but this forum is one of the few where I am not banned. I know because I can log on. Which begs the question: why do I want to be a member of a forum that would allow me as a member?

 

It’s not troll-like; it antithetical to our character --It’s a paradox. :)

Jun 23, 2015

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