1. anonymous

do you know how to do this?

2. anonymous

First Flip bottom fraction and Multiply Then factor and things will cancel $2z-8 = 2(z-4)$ $z^{2}-4 = (z+2)(z-2)$ $z^{2}+6z+8=(z+4)(z+2)$

3. anonymous

wow i forgot that the things cancelled.... okay what did you get for your answer?

4. anonymous

im not sure how you did that can you show me?

5. anonymous

$=\frac{2(z-4)(z-4)}{(z+2)(z+2)(z-2)(z+4)}$ hmm maybe they dont cancel in this case..haha

6. anonymous

yea and i think you factored wrong.....

7. anonymous

wait how did you factor that?

8. anonymous

no everything is factored correctly

9. anonymous

which one

10. anonymous

how did you do it then? i got something completly different but i thrust what you got....

11. anonymous

are you sure its division and not multiplying the 2 fractions ??

12. anonymous

you flip the second one and change to multi.

13. anonymous

correct

14. anonymous

and then can you show me what you did im completly lost

15. anonymous

oh for the factoring part. well for 2z -8 i just pulled out a 2 from each term 2(z-4) = 2z - 8

16. anonymous

ok

17. anonymous

For z^2 - 4, find factors of -4 that add up to 0 since there is no "z" term -2*2 = -4 and -2+2=0 (z-2)(z+2)

18. anonymous

wow thats sooo much easier now thanks :) can you help me with a couple more?

19. anonymous

z^2 +6z +8 same thing, look for factors of 8 that add up to 6 4*2 =8 and 4+2 =6 (z+4)(z+2)

20. anonymous

ok

21. anonymous

okay....... ((4)/(2x+1))-((3)/(2x))=

22. anonymous

can you show me step by step please?

23. anonymous

adding/subtracting fractions you need to get common denominator 2x+1 cannot be factored 2x cannot be factored common denominator is 2x(2x+1) just like adding 1/2 + 1/3, common denominator is 2*3=6

24. anonymous

now change numerators $\frac{4}{2x+1} = \frac{(2x)(4)}{2x(2x+1)}$ $\frac{3}{2x} = \frac{3(2x+1)}{2x(2x+1)}$ combine into 1 fraction $\frac{(2x)(4) - 3(2x+1)}{2x(2x+1)}$

25. anonymous

ok

26. anonymous

multiply and add like terms on top $\frac{8x -6x -3}{2x(2x+1)} = \frac{2x-3}{2x(2x+1)}$

27. anonymous

can you help me with this one? ((m+5)/(2m^2-2))+((3)/(1-m))+((5)/(2m+2))

28. anonymous

factor all the denominators 2m^2 -2 = 2(m-1)(m+1) 1-m = -(m-1) 2m+2 = 2(m+1) common denominator will include everything w/out repeats -2(m-1)(m+1)

29. anonymous

okay i can do it from there can you help me with this one? ((n+1)-(2/n))/((n+4)+(4/n))

30. anonymous

$=\frac{-(m+5)+(2(m+1))(3) + (-(m-1))(5)}{-2(m+1)(m-1)}$

31. anonymous

can you help me with this one? please???? ((n+1)-(2/n))/((n+4)+(4/n))

32. anonymous

ok combine fractions on top and bottom, then flip and multiply

33. anonymous

common denominator will just be n

34. anonymous

ok

35. anonymous

36. anonymous

yup that what i got are you good with summation notation and geometric means/sequences?

37. anonymous

sure

38. anonymous

okay.... wellthe question is... insert four geometirc means between -7 and -224

39. anonymous

hmm dont understand?

40. anonymous

nevermind i figured that one out......

41. anonymous

42. anonymous

$\sum_{n=1}^{50}(1/4)(n+2)$

43. anonymous

$=\frac{1}{4}\sum_{n=1}^{50}n+2 = \frac{1}{4}(\sum_{n=1}^{50}n +\sum_{n=1}^{50}2)$

44. anonymous

im stuck on this one.. which term of the geometric sequence 243, -81, 27, . . . is (-1/9)?

45. anonymous

8 th term

46. anonymous

how did you figure that out?

47. anonymous

haha tried proving it using geometric sequence formula but got stuck when taking log anyway just continue the sequence of dividing by 3 and flipping the sign

48. anonymous

o so you flip the sign every other time? could you help me with this one? there are seven houses; in each are seven cats. each cat kills seven mice. each mouse would hvae eaten seven ears of wheat. each ear of wheat prodece seven measures of grain. how much grain is saved? i got 16807 grains saved

49. anonymous

correct 7^3 mice 7^4 ears 7^5 grain

50. anonymous

ok that equals 16807 which is what i got:)

51. anonymous

okay change the repeating decimal .25 (sopposto have the bar above the 25) to an equivlant common fraction

52. anonymous

?? why do you need to know that some fraction close to proportional of 1/4

53. anonymous

i dontk know its on my homework though ydo you know what it'd be?

54. anonymous

haha i just guessed and put it in my calculator 25/99

55. anonymous

wow your good.... do you know how i would show that? just say guess and check? we turn this in for a grade thats why im asking

56. anonymous

actually any n/99 = .nnnnnn

57. anonymous

in a certain credit union, money left on deposit for one year earns 4% intrest at the end ot the year. if you invested \$100 at the beginning of each year in this credit union and did NOT withdraw the intrest due at the end of the year, how much would you hvae on deposit at the end of the tenth year?

58. anonymous

=100(1.04 + 1.04^2+... +1.04^10) need sum of geometric sequence sum = a(1-r^n)/(1-r) sum = 1.04(1-1.04^10)/(1-1.04)

59. anonymous

i get 1248.64

60. anonymous

so when you get your answer are you sopposto multiply it by 100?

61. anonymous

yes

62. anonymous

okay just stay right there i have a couple more i just have to go and get another pencil mine just broke

63. anonymous

ok im back i dont know what formula you used

64. anonymous

for finding sum of geometric sequence

65. anonymous

yea but can you tell me it with all of the variable in it please? i need to look and see if i have that one

66. anonymous

$s _{n} = \frac{a _{1}(1-r ^{n})}{1-r}$

67. anonymous

i only have SofN=(Asub1-Asub1R^n)/(1-R) and... SofN=(Asub1-AsubnR)/(1-R) sooo.. which one should i use, and what numbers?

68. anonymous

ues the first one, only difference is mine has factored out the a1 on top

69. anonymous

a1 = first term r = common ratio

70. anonymous

ummmm... i should get the same answer right? i think im doing someting wrong im getting 1200.610712

71. anonymous

1-(1.04)^10 = -.4802 1.04(-.4802) = -.49945 -.49945/(1-1.04) = 12.48635

72. anonymous

wait shouldnt it be..... (100-100(1.04)^10)/(1-1.04)

73. anonymous

no im leaving the 100 on outside of sequence then we multiply the sum by 100

74. anonymous

but when i do it shouldnt i be getting the same thing? and i dont understand how your doing it

75. anonymous

ok if you include the 100 then sequence will look like this =100(1.04) + 100(1.04^2) +...+100(1.04^10) a1 = 100(1.04) r = 1.04 sn = 100(1.04)(1-1.04^10)/(1-1.04)

76. anonymous

but my equation is Sn=(A1-A1R^n)/(1-R)

77. anonymous

same thing factor out the A1

78. anonymous

can you do it my way when you factor out the A1 it confuses me

79. anonymous

....^because when you factor....

80. anonymous

ok Sn = 100(1.04) -100(1.04)(1.04^10) / (1-1.04)

81. anonymous

ok ... a ball which rolls off a penthouse terrace falls 16 feet the first second, 48 feet the next second, and 80 feet the third second. if it continues to fall in this mannor, how far does it fall in the seventh second?

82. anonymous

i believe this models a parabola of y=-16x^2 the change in y from 6 to 7 is how far it falls in 7th second 16(7^2) - 16(6^2) = 16(49-36) = 16(13) = 208

83. anonymous

a rubber ball dropped 40 feet rebounds on each bounce 2/5 of the distance from which it fell. how far will it travel before comming to a rest?

84. anonymous

geometric sequence 40+40(2/5)+ 40(2/5)^2 +... looks like an infinite sequence before you get 0 lim n->inf (2/5)^n = 0 so in formula r^n = 0 a1=40 r=2/5 sum = 40 - 40(0) / 1-(2/5) sum = 40 /3/5 = 200/3 = 66.666

85. anonymous

what formula is that?

86. anonymous

same as before sum of geometric sequence

87. anonymous

no but which one of mine because yours confuse me

88. anonymous

$s _{n}=\frac{a _{1}-a _{1}r^{n}}{1-r}$

89. anonymous

what would i put for n?

90. anonymous

infinity

91. anonymous

hu?

92. anonymous

just substitute r^n=0

93. anonymous

would my answer be iin feet?

94. anonymous

yes

95. anonymous

what does the graph for ..... look like? -cubic with one real solution and two complex solutions look like? -cubic with no real solutions? -quartic with no real solutions? -a quadratic with one real solution and one complex solution? -a quartic with two real solutions and two complex solutions? -a quadratic with no real solutions? -a quartic with no real solutions? -a cubic with 3 real solutions, but one is a double root? -a quartic with for real roots, but both are double roots?

96. anonymous

umm number of real solutions represents number of x_intercepts cubic with no real solutions does not exist i believe