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V  =  2(3.14)r^2h

Soving for r^2  

V = 6.28 r^2 h     divide both sides by   6.28h

V / [ 6.28h]  = r^2

Solving for h

v = 6.28r^2h     divide both sides by 6.28r^2

V / [ 6.28r^2 ]  =  h

1)

Area of a trapezoid =1/2[ a + b] x h

A =1/2[25 + 33] x 30

A =1/2[58] x 30

A =870 yards^2 - area of the park.

Area of the fountain =4^2 x 3.14

A. of fountain = 50.24 - yards^2

Area of the park minus the area of the fountain:

870 - 50.24 =819.76 yards^2.

The face forms a triangle.....Area of triangle  =    (1/2) base * height

The slant height is the height of the triangle....so....

75  = (1/2) base *(30)

75 = 15 * base        divide both sides by  15

5 m  =   base 

So.....a side of  the base  = 5m 

V = 2 * π * r^2 * h

r^2 = V ÷ 2 * π * h

h = V ÷ 2 * π * r^2

(36+37)/100

73/100=0.73

0.73*100=73%

A 73%

We can choose  any 2  of the 5....so....the number of possible groups  is

C(5,.2)   =    10 different groups

2.

Volume of cone = π * r^2 * h/3

volume of cone = π * 8^2 * 1.95/3

volume of cone = 131cm^3 (nearest whole number)

(36/45)*100=80%

D 80%; they are dependent

125 ^ (-4/3)

Note that we can write this as

( 125^1/3)^(-4)        the value in the first parentheses is just the cube root of 125  = 5

So we have

(5)^(-4)          {    remember that  a^(-m)  =   1 / a^m  }

1 / 5^4   =    1 / (5^2 * 5^2)  =   1 / (25 * 25)   =  1 / 625

              Truck   Car   Total

Female    9         36     45

Male        18       31     49

Total        27       67     94

3(x + 1) (x + 7)  - (2x + 5)^2  simplify

3 (x^2 + 8x + 7) - (2x + 5)(2x + 5)

3x^2 + 24x + 21 - [ 4x^2 + 20x + 25 ]

-x^2 + 4x - 4

The x coordinate of vertex of this function  is given by :

-4/ (2 (-1) )   =  4/2  = 2

And the max value of this function  is  :

-(-2)^2 + 4(2) - 4   =  -4 + 8 - 4  =   0

So....this function is never positive

$20,000*0.7^5=$3361.40

                 Plasma TVLCD TVProjection TVTotal

54 inches     20           8                  2           30

68 inches      9           22                 2           33   

86 inches      6           16                 5           27 

Total             35          46                 9           90
 

(16/46) * 100 = 35%

A 35%

              Team Jersey    No Team Jersey   Total

Female        5                      17                    22

Male           35                      3                     38 

Total           40                      20                   60

(17/22)*100=77%

B 77%, they are independent

The base is 3......since this is > 1,  then his represents exponential growth

                             Passion Fruit     Not Passion Fruit    Total

Tropical Grape         25                          11                     36

Not Tropical Grape  54                          35                     89

Total                         79                          46                    125

(54/125)*100=43%

A 43%

jo momma

Melody,

First I want to say thank you very much, you have helped me see the numerators as powers of 3.

I did some aditional study on the net, and came to this conclusion:

The numerators change to:

\(3^0;3^1;3^2;3^3\)

so this has to be :

\(3^{n-1}\) = NOMINATOR

which I understand...THEN:

you subtracted the denominators and found:

                            \(5;8;13;20\)

becomes:            \(3;5;7;9\)

which becomes:  \(2;2;2\)

From this we see that: 2a=2, therefore, a=1

                                     3a+b = 3, therefore "b" calculates to 0

                              and a+b+c=T1=5, so "c" calculates to 4

The general equation is: \(an^2+bn+c\)

So substitute everything above into this equation, and it calculates to \(n^2+4\) = DENOMINATOR

So that is then \({Nominator \over Denominator}={3^{n-1} \over n^2+4}\)

thank you kindly for your help Melody!!

MELODY!!, My Hero!!..How are you these days????..okay, heroine...

I am going to write down on a piece of paper all you said, and see if I can work my way towards the answer...will let you know if I get stuck. Thanx for the personal invite to a personal message...

Prove algebraically that the straight line with equation x=2y+5 is a tangent to the circle with equation x²+y²=5.

x=2y+5

x²+y²=5.

substitute

\((2y+5)^2+y^2=5\\ (4y^2+20y+25)+y^2=5\\ 5y^2+20y+20=0\\ y^2+4y+4=0\\ (y+2)^2=0\\ y=-2\\ x=2*-2+5\\ x=1\\ \text{Pt of interesction is }(1,-2) \)

Since there is only one point of intersection of the line and the circle, the line must be a tangent to the circle. 

This should help answer your question.

No Guest, you have not interpreted Juriemagic's question properly.

He has the answer but he wants to know how he could have seen it, or worked it out by himself.

Lets look at the numerators seperately from the denominators

numerator - I notice straight off that these are powers of 3

denominator

5        8       13          20

now I am going to subtract the preceding term from each of these.

8-5=3   13-8=5      20-13=7   

    3             5               7         If these had all been the same then it could have been expresed as polynomial of degree 1

Now I wll subtract again

   5-3=2           7-5=2             

       2                  2                  These are the same so I can express this sequence as a polynomial of degree 2

So putting this altogether I have found the sequence to be.

\(T_n=\dfrac{3^{n-1}}{n^2+4}\)

If you have any questions Juriemagic just ask. If you want to be sure that I see it, send me a personal message and include the address of the question.  :)

Hi Juri: But it is quite clear how to derive it from the sequence as I edited it in the last 2 lines.

No guest,

The question is not to use the formula to calculate terms, etc for example, the sequence is given and the question is: Calculate the formula for the nth Term.

the formula I gave is the ANSWER the question has. use the sequence to get to that formula as answer.

What is it that you don't understand? You are given the formula to calculate any term of the sequence: T(n) =1*3^(n-1) / n^2+4. All you have to do is substitute the "term number" for n in your formula!  So, first term, or 1, goes like this: T(1)=1*3^(1-1) / 1^2+4 =1/5. For the 2nd term, or 2, you get this: T(2) =1*3^(2-1) / 2^2+4=3/8. Third term, or 3, you have: T(3) =1*3^(3-1) / 3^2+4=9/13. The 4th term, or 4, would be:T(4)=1*3^(4-1) / 4^2+4 =27/20........ and so on. So, the 10th term, or 10, would be:

T(10) =1*3^(10 - 1) / 10^2 + 4 =19,683 / 104 ..........etc. Do you get it now?.

So, to derive their formula, the numerator is 3 raised to to the power of term number -1, or 3^n - 1. The denominator is the term number, n squared + 4.