geno3141

I'm assuming that you mean this:  ₄C₀·(0.12)⁰·(0.88)⁴  =  0.600

Number 2)  The circle has radius = 14, so its diameter = 28. The chord = 12

Draw the chord and the diameter of the circle which is perpendicular to the chord.

The chord divides the diameter into two parts, a short part from the chord to the circle (call this "x") 

and a longer part from the chord through the center of the circle to the other end of the circle (this is 28 - x).

The chord is divided into two equal parts, each part = 6.

There is a theorem that says that if you multiply the two parts of one chord you will get the same answer when

you multiply the two parts of the other chord (the diameter).  Thus:  x·(28 - x)  =  6·6

Solving:  28x - x²  =  36

               x² - 28x + 36  =  0

Using the quadratic formula:  x  =  1,351  (approximately)

The distance from the chord to the center of the circle is 14 - 1.351  =  12.649   (approximately)

After doing this, I realize that there is a much easier way --

-- draw the chord and the perpendicular bisector (the same as above)

-- draw the radius from the center of the circle to an end of the chord, creating a right triangle.

-- the hypotenuse of the triangle is the radius of the circle (14)

-- one leg of the right triangle is one-half the chord (6)

-- use the Pythagorean Theorem to find the distance ...

Number 1:

Point M divides BC into two equal segments; call each segment "x".

Point N divides AC into two equal segments; call each segment "y".

Triangle(BCN) is a right triangle with BC = 2x, CN = y, and hypotenuse BN = 13.

--->   (2x)² + (y)²  =  (13)²   --->   4x² + y²  =  169          [Pythagorean Theorem]

Triangle(AMC) is a right triangle, with AC = 2y, CM = x, and hypotenuse AM = 19.

--->   (2y)² + (x)²  =  (19)²   --->   4y² + x²  =  361          [Pythagorean Theorem]

Combining these two equations:

     4x² +   y²  =  169   --->   x 4    --->   16x² + 4y²  =   676

       x² + 4y²  =  361   --->   x -1   --->      -x² - 4y²  =  -361

Adding down:                                        15x²           =   315

                                                                          x²   =  21

                                                                           x   =  sqrt(21)

Substituting:   4x² +   y²  =  169   --->   4( sqrt(21) )² + y²  =  169

                                                                           84    + y²  =  169

                                                                                      y²  =  85

                                                                                      y   =  sqrt(85)

This means that one side of triangle(ABC)  =  2·sqrt(21)  while the other side  =  2·sqrt(85).

You can now use the Pythagorean Theorem to find the hypotenuse ...

I graphed it and found that the two answers are  105  and  -105.

I haven't been able to figure out a way to do it algebraicly.

32 people ate chicken and the four symbols for chicken represent the 32 persons, so each symbol

represents  32 / 4  =  8 persons.

There are 10 complete symbols and 2 half-symbols, making a total of 11 symbols.

Since each symbol represents 8 persons, 11 symbols will represent  8 x 11  =  88 persons.

If  f(x)  were a function like:  f(x)  =  (5x² + 2x + 8) / (x - 1)  it would have an oblique asymptote of  y  = 5x + 7.

This would make the final function:  y  =  [ (5x² + 2x + 8) / (x - 1) ] / (x - 2)

and would simplify to:                       y  =  (5x² + 2x + 8) / [ (x - 1)(x - 2) ]

or:                                                     y  =  (5x² + 2x + 8) / (x² - 3x + 2)

which would have an horizontal asymptote of  y  =  5.

Now, this is just an example, but I believe that this would be true for all examples, so the equation of the horizontal

asymptote woulld always be:  y  =  5.

The left-hand behavior asks the question: 

  As x goes to negative infinity (off to the far left of the graph), do the y-values increase (go upward to positive infinity)

  or decrease (go downward to negative infinity)?

Similarly, the right-hand behavior asks the question:

  As x goes to positive infinity (off to the far right of the graph), do the y-values increase (go upward to positive infinity)

  or decrease (go downward to negative infinity)?

For the function  f(x)  =  -4(x-1)⁴(x + 3):

  as x gets smaller (more and more negative), the graph goes higher and higher up the y-axis (the y-values go

      to positive infinity)  

  as x gets larger (off to the right), the graph dips lower and lower down the y-axis (the y-values go to negative infinity).

I messed up the other answer because I found the volume, not the area.

There's a problem with the drawing. If this is a regular octagon and each edge is 2 cm, the diameter will be close to,

but not quite equal to, 4.5 cm.

There is a formula for the area of a regular octagon:  Area  = 2 · ( 1 + sqrt(2) ) · (edge)² 

When the edge = 2:      Area  =  2 · ( 1 + sqrt(2) ) · (2)²   =  8 · ( 1 + sqrt(2) )  =  19.314 cm²   (approx)

To find the total area, we need two of the regular octagons (38.638 cm²), plus the 8 sides.

Each side has an area of  2 x 6.5 =  13 cm².

Multiplying this by 8, we get  104 cm²

Final amount:  (38.638 cm²) + (104 cm²)  =  142.6 cm²

1)  The Rational Zero Test says that any possible rational zero is a fraction whose numerator is a divisor of the constant term

      (in this case, a divisor of 16) and the denominator is a divisor of the coefficient of the first term (in this case, 2).

      Also, all the negative must also be considered.

      The divisors of 16 are 16, 8, 4, 2, 1.  

      The divisors of 2 are 2, 1.    

      So, for this problem the possibilities are:  16/1, -16/1, 8/1, -8/1, 4/1, -4/1, 2/1, -2/1, 1/1, -1/1

                                                               and:  16/2, -16/2, 8/2, -8/2, 4/2, -4/2, 2/2, -2/2, 1/2, -1/2

      Of course, some of these are repeats.

      Try these one at a time until you find one that makes the function zero. If it makes the function zero, it will be a root; if

       it doesn't make the function zero, it isn't a root.

       For example:  f(x)  =  2x³ + 2x² - x + 16     --->     f(16)  =  2(16)³ + 2(16)² - (16) + 16  =  8704

       This didn't make the function zero, so it isn't a root.

       So, you get to try the next number.

       Keep trying until you get one that works or until they all fail.

       Once you get one that works, divide the function by that root (for instance, if 5 works, divide by (x - 5)).

       If you can factor the result, do so; that's easier than using the RZT.    

       If you can't factor the result, use the RZT on this new function.

2)  Every factor that has an even exponent bounces; every factor that has an odd exponent passes through.

3)  f(x)  =  -3x² + 12x - 2

     Bring the constant term to the other side:            f(x) + 2  =  -3x² + 12x

     Factor out the coefficient of the squared term:    f(x) + 2  =  -3(x² - 4x)

     Complete the square by dividing the coefficient of the x-term by 2 and squaring that answer:

         -4 / 2  =  -2   --->   (-2)²  =  4

     Add that inside the parentheses -- note that you really are adding a value of -3 x 4  =  -12, so you'll have

     to add that to the other side as well:            f(x) + 2 - 12  =  -3(x² - 4x + 4)

                                                                                 f(x) -10  =  -3(x - 2)²

                                                                                        f(x)  =  -3(x - 2)² + 10

The Guest just mis-typed the final result:  (2/3)³  +  3·(2/3)³·(1/3)  +  6·(2/3)³·(1/3)²  =  64/81

Winning in three games:   BBB

Winning in four games:     BBTB, BTBB, TBBB

Winning in five games:     BBTTB, BTTBB, BTBTB, TBBTB, TBTBB, TTBBB