geno3141

The distance from the chord to the center of the circle is the distance from the center of the chord to the center of the circle.

Drawing a triangle from the center of the circle to the center of the chord (x), then from the center of the chord to the end of the chord (6), and finally from the end ot the chord to the center of the circle (14), we have a right triangle with the Pyhagorian Theorem:  x² + 6²  =  14².

Solving this, we get  x²  =  160  and  x  =  sqrt(160).

If a  1  or a  6  is showing, the product will be  6.

If a  2  or a  5  is showing, the product will be 10.

If a  3  or a  4  is showing, the product will be 12.

The greatest product will be  12  x  12.

Of the three positive values:  a + 1,  6a,  and  6a + 1,  6a + 1  must be the largest.

Using the Pythagorean Theorem:  (a + 1)² + (6a)²  =  (6a + 1)²

                                                  a² + 2a + 1 + 36a²  =  36a² + 12a + 1

                                                                    a² + 2a  =  12a

                                                                   a² - 10a  =  0

                                                                  a(a - 10)  =  0

                               Either  a = 0 (impossible)  or  a = 10

I can get nine --

Consider the vertices A and B; there are two squares that share the side AB (say ABXY with X and Y on one side of AB and X and Y on the other side of AB) and there is also the square that has A and B being opposite vertices of the square (square AXBY). 

So, that gives 3 squares using A and B; there will also be 3 squares using B and C and 3 squares using A and C.

Since he must divide the number of coins into six groups, the number of coins must be both a multiple of 2 and a multiple of three.

Since you know that there are an even number of coints, you already know that the number of coins is a multiple of two.

Therefore, for the number of coins to also be a multiple of three, there is a 1/3 probability that Jack survives.

f(x)  =  (x - 1) / (x + 1)

f(2)  =  (2 - x1 / (2 + 1)  =  1/3

f( f(2) )  =  f( 1/3 )  =  (1/3 - 1) /(1/3 + 1)  =  -2/3 / 4/3  =  -1/2

f( f ( f(2) ) )  =  f( f( 1/3) )  =  f( -1/2 )  =  (-1/2 - 1) / (-1/2 + 1)  =  (-3/2) / (1/2)  =  -3

The first term of the geometric progression is  3,  the next term is  3r,  and the third term is  3r².

What are the possible r-values if the sum of these three terms is 9?

3 + 3r + 3r²  =  9

    1 + r + r²  =  3         [divide by 3]

      r²+ r - 2  =  0         [subtract 3 from both sides and rearrange] 

(r - 1)(r + 2)  =  0

Either  r = 1  or  r = -2

Divide the quadrilateral into two triangles by drawing YW.

Triangle(ZYW):  

Area(ZYW)  =  ½·32·24  =  __________

Since triangle(ZYW) is a right triangle, we can find YW by the Pythagorean Theorem:

YW²  =  32²  +  24²   --->   YW  =  40

Triangle(XYW:

We know the values of the three sides, so we can use Heron's formula to find the area.

s  =  (a + b + c) / 2   --->   s  =  (32 + 24 + 40) / 2  =  48

Area  =  sqrt[ s · (s - a) · (s - b) · (s - c) ]

          = sqrt[ 48 · (48 - 32) · (48 - 24) · (48 - 40) ]  =  ____________

The area of the quadrilateral will be these two areas added together.

You can either use the Pythagorean Theorem or the distance formula (which is just the 

Pythagorean Theorem adapted for coordinates:

d  =  sqrt( (x₂ - x₁)² + (y₂ - y_1)² )  =  sqrt( (4 - -4)² + (3 - -2)² )

                                                     =  sqrt( 8² + 5²  =  sqrt( 89 )  =  .... 

Sim, ele é.