## Loser66 one year ago A total x feet of fencing is to form 3 sides of a level rectangular yard. What is the maximum area of the yard in term of x? A) x^2/9 B) x^2/8 C) x^2/4 D)x^2 E)2x^2 Please, help

1. freckles

oops meant to write x

2. freckles

one sec

3. freckles

$2L+W=x \\ A=LW=L(x-2L)$

4. freckles

So we want to find A' here

5. Loser66

yes, then??

6. freckles

x is a constant I believe $A=Lx-2L^2 \\ A'=x-4L \\ A'=0 \implies x=4L \\ A=L(x-2L)=L(4L-2L)=L(2L)=2L^2 \\$ I think you can find A in terms of x now since x=4L

7. freckles

still processing?

8. Loser66

Yes. Thanks a lot. I got the right answer. It is not test, just practice exam with the answer sheet. But I want to know logic.

9. freckles

Why are you doing calculus 1 problems?

10. Loser66

oh, is it calculus problem??

11. freckles

Yes it is an optimization problem

12. Loser66

Question: why do you link to derivative?

13. freckles

because it say to maximize

14. Loser66

I assume it is an algebra problem and get no outlet

15. freckles

usually those in the cal problems I have seen they actually gave a number instead of saying x

16. Loser66

I am prepare for my GRE test for maths major students. ha!!!

17. freckles

http://tutorial.math.lamar.edu/Classes/CalcI/Optimization.aspx this example one here is pretty similar

18. Loser66

My tough one is English, not math.

19. freckles

except as I said they say 500 feet instead of x feet

20. Loser66

Any tips for GRE math practice?? I have only 1. :)

21. freckles

there was a question and I think it was on the gre it was my favorite question to give me a sec and I will remember it

22. freckles

solve for x+y $x^2+y^2+2xy+2x+2y=-1$

23. freckles

there was a similar question on the gre or it might have been on another standard test can't remember which standard test

24. Loser66

hihihi... I have time. I will study carefully before taking the test. But you know, I am old. hahaha..... I am slow!!

25. freckles

that question isn't too bad did you want me to show you how to do it or did you want to try it first

26. Loser66

27. freckles

$x^2+2xy+y^2+2x+2y+1=0 \\ (x+y)^2+2(x+y)+1=0 \\ (x+y+1)^2=0 \\ x+y+1=0 \\ x+y=-1$

28. freckles

I turned it into a quadratic in terms of (x+y)

29. Loser66

What if we let x+y =t??

30. Loser66

oh, yea, we met there

31. freckles

good luck on your gre if i could figure out anything to tell you to help you I will I probably should have studied for it back in the day more than I did

32. Loser66

Sure. Again, thanks for the help.

33. freckles

np

34. Loser66

What is the units digit in standard decimal expansion of the number 7^(25) I don't get what it mean

35. Loser66

since $$7^{25} = 1.34106862 *10^{21}$$ hence the number of digits after decimal point is 8 but it is not one of the options which are 1,3,5,7 or 9

36. Loser66

@freckles

37. Loser66

To this problem, if I don't have calculator, how can I find out the answer?

38. freckles

so you are trying to find out the length of the number 7^(25) ?

39. Loser66
40. freckles

on

41. freckles

oh*

42. freckles

the units digit is the ones digit

43. freckles

44. Loser66

total??

45. Loser66

46. freckles

wait standard notation is not scientific notation is it ?

47. Loser66

I am not sure.

48. freckles

there was need to write in scientific notation because standard notation is different from scientific notation

49. freckles

7^(25) mod 10 will give you number in 1's digit

50. freckles

or aka units digit

51. freckles

$4^2=16 \text{; 16 is standard notation for } 4^2 \\ 4^2=1.6 \times 10 \text{ is sceinfict notation }$

52. freckles

I missed the word no in there was need to write in scientific notation there was no need to write in scientific notation*

53. Loser66

to this http://mathcentral.uregina.ca/QQ/database/QQ.09.06/tyrone1.html they said that the units digit is the last digit of the number in standard form in decimal form, the unit digit of 7^25 is the last one, which is 2, not 7 : (

54. freckles

$7^{2} \mod 10=9 \\ 7^4 \mod 10 =9 \cdot 9 \mod 10=81 \mod 10=1 \\ 7^{4(6)+1} \mod 10=(7^4)^6(7) \mod 10=1^6(7) \mod 10 =7 \\ 7^{25} \mod 10=7$

55. freckles

the units digit is the first number it is the one's digit that is what that picture above says also

56. freckles

for example 61 do you call 1 the first digit because I do and 6 is the last digit 1 is in the one's place (or the units place) 6 is in the ten's palce

57. freckles

oh I think I see where you are getting confused

58. freckles

$7^{25} = 1.34106862 *10^{21}$ you think this equality is exact when it is not

59. freckles

and even if it was exact you would say the units digit is 0 but it is not the case because this equation is not exact

60. freckles

like you still need to move that decimal to the right like 21 times

61. freckles

2 is not in the one's digit

62. freckles
63. freckles

the number where it says result is the number in standard notation

64. Loser66

oooooooooooooooooh!! got you

65. freckles

a mod 10 should always give you the units digit of a

66. Loser66

modular method help me out 7^0 -----1 last digit 7^1 -----7 last digit 7^2 -----9 7^3 -----3 7^4-----1 hence the cycle is 4, 25 = 4*6 +1, hence \(7^25 = 7^24 *7 , but the last digit of 7^24 is 1 then *7 =7

67. freckles

yah

68. Loser66

Thanks a ton. :) I do appreciate.

69. freckles

np

70. freckles

interesting practice exam I think they have made changes to it seen I last took the gre I feel like that was 8 years ago or something :p

71. freckles

I don't remember linear algebra or number theory on it

72. freckles

but maybe there was some