Math Is Fun Forum

Hey everybody, please help!

My take home final for geometry is due on thursday and i dont know how to do this, and on top of this, i have 9 other classes to worry about.

could anyone please help???!!!!?????

in desperated need....please help

how would you solve

log(2x+2) + log x - log(12)=0

and

log½ gives the same answer as -log2

true or false?

explain why?

any help would be much appreciated!!!

Could someone help me solve this... I already solved parts a) and b) ( the work is below) but i need to solve part c) but im not really sure how to do that.

1.
a)
Values of r
1. r=2   
2.r=3   
3.r=4   
4.r=5   
5.r=6   

Sum 

             10 Terms    50 Terms                   100 Terms
1.    2046    2.25 x 10^15    2.53 x 10^30
2.    59048    7.17 x 10^23    5.15 x 10^47
2.    699050    8.45 x 10^29    1.07 x 10^60
4.    4882812    4.44 x 10^34    3.94 x 10^69
5.    24186470    3.23 x 10^38    2.61 x 10^77

Work

1.    Sn=2(1-2^10 )/(1-2) = 2046
    Sn=2(1-2^50 )/(1-2) = 2.25 x 10^15
    Sn=2(1-2^100 )/(1-2) = 2.53 x 10^30

2.    Sn=2(1-3^10 )/(1-3) = 59048
    Sn=2(1-3^50 )/(1-3) = 7.17 x 10^23
    Sn=2(1-3^100 )/(1-3) = 5.15 x 10^47

3.    Sn=2(1-4^10 )/(1-4) = 699050
    Sn=2(1-4^50 )/(1-4) = 8.45 x 10^29
    Sn=2(1-4^100 )/(1-4) = 1.07 x 10^60

4.    Sn=2(1-5^10 )/(1-5) = 4882812

    Sn=2(1-5^50 )/(1-5) = 4.44 x 10^34

                  Sn=2(1-5^100 )/(1-5) =3.94 x 10^69

5.    Sn=2(1-6^10 )/(1-6) = 24186470
    Sn=2(1-6^50 )/(1-6) = 3.23 x 10^38
                   Sn=2(1-6^100 )/(1-6)= 2.61 x 10^77

b)
Values of r
1. r=.9
2.r=.8
3.r=.7
4.r=.6
5.r=.5

Sum
               10 Terms               50 Terms         100 Terms
1.    13.03             19.89         19.99
2.    8.92             9.999857275        9.999999998
3.    6.4783498            6.6666665        6.666666667
4.    4.969766912      5       5
5.    3.99609375    4         4

Work

1.    Sn=2(1-〖.9〗^10 )/(1-.9) = 13.03
    Sn=2(1-〖.9〗^50 )/(1-.9) = 19.89
    Sn=2(1-〖.9〗^100 )/(1-.9) =19.99

2.    Sn=2(1-〖.8〗^10 )/(1-.8) = 8.9262581
    Sn=2(1-.8)/(1-.8) = 9.999857275
    Sn=2(1-〖.8〗^100 )/(1-.8) = 9.999999998

3.    Sn=2(1-〖.7〗^10 )/(1-.7) = 6.4783498   
                Sn=2(1-.7)/(1-.7) = 6.6666665
    Sn=2(1-〖.7〗^100 )/(1-.7) = 6.666666667

4.    Sn=2(1-〖.6〗^10 )/(1-.6) = 4.969766912

    Sn=2(1-〖.6〗^50 )/(1-.6) = 5
                  Sn=2(1-〖.6〗^100 )/(1-.6) =5

5.    Sn=2(1-〖.5〗^10 )/(1-.5) = 3.99609375
    Sn=2(1-〖.5〗^50 )/(1-.5) = 4
                   Sn=2(1-〖.5〗^100 )/(1-.5)= 4

a)  Chose 5 different values for r such that |r|> 1. For each of these geometric series, let the first term g1 = 2. Determine the sum of each of these geometric series for 10 terms, 50 terms, and 100 terms. Organize your data into a chart. (10 points)

b) Chose 5 different values for r such that
|r| <1 For each of these geometric series, let the first term g1 = 2. Determine the sum of each of these geometric series for 10 terms, 50 terms, and 100 terms. Organize your data into a chart. (10 points)

c) The word converge means to approach or draw near to a particular value. For
example, as x gets very large, converges to zero. The word diverge means
does not converge. For example as x gets very large, x^2 diverges; as x gets large, x^2 does not approach any particular value. Make a conjecture about the conditions under which a geometric series will converge. Test your conjecture using g1 (not equals) 2 and some of the values of r. Think about the formulas for geometric series. Write a mathematical argument to support your conjecture. (30 points)

Hi everybody,

I really need help figuring this out, any help or feedback would be highly appreciated

" You purchased a car for $25,000. Its value depreciates at an average rate of 10% per year."

find an equation for the value of the car after n years

would i have to use the explicit or recursive formula....I have tried pluging in the values but the answers it gave me made no sense at all....

I know its value for the first 10 years:

after the 1st year its worth: 22,500
2nd: 20,250
3rd:18,225
4th:16,403
5th: 14,762
6th: 13,286
7th: 11, 957
8th: 10, 762
9th: 9, 686
10th: 8, 717

finding a formula for this seems very easy and obvious....but i just can't figure it out....its driving me crazy....i'm sure that after i see it i will realize how obvious it was....

so if someone could please please please help me find a formula, and explain to me how it works....I would highly appreciate that....

Thanks in advance,

Dennis Sachik