All Answers 358087 Answers

1.   Let the  radius of te circle with center D  = x

    Let the radius  of the circle with center E  = y

    Let the radius  of the circle with the center F  = z

So we have these equations

x + y  = 5

x + z = 6

y + z  = 7

Subtract thesecond equation from the  first  and we have that  y - z  =  -1

Add this to equation to the third equation  and we have that

2y  = 6

y = 3  

x = 2

z = 4

So...the total area of the circles  are   pi ( 2^2 + 3^2 +4^2)  =  pi  ( 29)  =   29 pi units^2  ≈

91.1 units^2

For #3 you can just set up ratios.

Let PC = x.

Now you can set up the ratio.

(x/(x+8)=3/5

now you just solve the ratio and the answer should be 12.

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You are a life saver!

2  EXPERIMENTAL probability =   6  H's drawn out of 20 draws      6/20 = 3/10

1. If the chance of rolling a 2 on a dice is 1/6, what is the chance of not rolling a 2?

Chance  of  not rolling a 2  =   1  - P(2)  =     1  -  1/6    =   5/6

The total number  of  sets  of 3 people that can be selected from P  people  =  C(P, 3)

And the total number of sets  of 3 people that can be selected from (P - 1)  persons   (which will not include Marie)  = C(P-1 , 3)

So....we want to solve this

C(P-1, 3)

________  =   1/2

C (P, 3)

C(P - 1, 3)  = (1/2)  * C(P, 3)

Using the combinations formula, we have that

(P -1)!                                     P!

____________  =   (1/2) *   ________

(P - 1 - 3)!    3!                      (P - 3)! 3!

(P - 1)!                                P!

______       =    (1/2)       _____

(P - 4)!                             (P - 3)!

(P - 1)! (P - 3)!              1

____________  =       ____

 P! (P - 4)!                     2

  P - 3                      1

______    =          ____        cross-multiply

      P                       2

2(P - 3) =  P

2P - 6  =  P

P  =  6  =   the number of students  on the council 

Nice, Gadfly and heureka    !!!

x^2 + y^2 + 4x + 6y = 12 and 5y = 4x + 13 

Rearrange as the second equation as

y  = [ 4x + 13 ] / 5

Sub this into the second equation

x^2  +  ( [ 4x + 13]/ 5)^2 + 4x + 6 ( [ 4x + 13' / 5)  =  12    simplify

x^2  +  [ 16x^2 + 104x + 169 ] / 25  + 4x  + [ 24x + 78 ] / 5   =  12     multiply through by 25

25x^2 + 16x^2 + 104x + 169  + 100x  + 120x + 390  =  300

41x^2 + 324x + 259  =  0        factor as

(41x  + 37)  ( x + 7)   =  0

Set each factor to 0  and   solve for x   and we get that

x = -37/41        and   x   = -7

This indicates that there are two  intersection points

now u have 7 ur score dropped down!!!!!!

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1)    3 circles area = 91.10618695 n²

2)     Circle's diameter =  8.062257748 

3)     The pathway area = 10.14159265 u²

4)      Radius  r = 4.5 units    

They can be split in:

[ 8 - 1] C [3 -1] =7 C 2 =21 ways

On the 19th day !!!.

Because it "double" in size every day!. So if it is 1/2 the size on the 19th it will double on the 20th day to its full size.

x memebers on the council:

50% * x = 3

x =3 / 50% =6 students on the council.

Quadrilateral ABCD is a parallelogram. The midpoints of AB and AD  are M and N, respectively. Let P be the intersection of DB and CM and let Q be the intersection of  DB and  CN. Compute PQ/DB.

There are 3 groups of skaters as follows:

4 x 11 x 10 =440 ways. But 1st,  2nd and 3rd prizes can be awarded in 3! =6 ways.

Therefore, there are: 440 x 6 =2,640 ways.

Look under the first post !.

Thanks that helps alot.

Let's make the solution super-formal!  We can write -4 in exponential notation as 4e^(pi*i), so the equation is z^4 = 4e^(pi*i).

By Hamilton's Theorem, the solutions are z = 4^{1/4}*e^(pi*i/4), 4^{1/4}*e^(pi*i/4 + pi/4), 4^{1/4}*e^(pi*i/4 + 2*pi/4), and 4^{1/4}*e^(pi*i/4 + 3*pi/4).  Since 4^{1/4} = sqrt(2) and e^(pi*i/4) = (1 + i)/sqrt(2), the first solution is 1 + i.  Then the other roots work out as

4^{1/4}*e^(pi*i/4 + pi/4) = 1 - i,

4^{1/4}*e^(pi*i/4 + 2*pi/4) = -1 - i, and

4^{1/4}*e^(pi*i/4 + 3*pi/4) = -1 + i.