geno3141

The guy has  x  apples.

The girl has 2 more than that guy; she has  x + 2  apples.

Another girl has three times as many as the guy; she has  3x  apples

Since they have 32 apples (total):

     (x)  +  (x + 2)  +  (3x)  =  32

                 x + x + 2 + 3x  =  32

                              5x + 2  =  32

                                     5x  =  30

                                       x  =  6

Guy has  6  apples.

First girl has 6 + 2  =  8  apples.

Othr girl has 3(6)  =  18 apples.

To find the difference subtract the values:

    31.6 - -34.1  =  31.6 + 34.1  =  65.7 degrees

     3³ + 4( 21( 7 + 2·3 ) )

=  27 + 4( 21( 7 + 2·3 ) )

=  27 + 4( 21( 7 + 6 ) )

=  27 + 4( 21( 13 ) )

=  27 + 4( 273 )

=  27 + 1092

=  1119

Are you sure that you copied the problem correctly?

12 inches in four days:  12 inches / 4 days  =  3 inches / 1 day  =  3 inches per day

The first series:  18 - 9 + 4.5 - ...

appears to be a geometric series with common ratio -1/2.

Since the common ratio is a fraction between -1 and 1, there is an infinite sum:

Sum  =  a / (1 - r)  =  18 / (1 - -1/2)  =  18 / ( 1 + 1/2)  =  18 / (3/2)  =  12.

The second series:  1.2 + 1.8 + 2.7 + ...

appears to be a geometric series with common ratio 1.5.

Since the common ratio is not a fraction between -1 and 1, there is no infinite sum.

To find when the finite sum exceeds 100, use the formula:  Sum  =  a(1 - rⁿ) / (1 - r):

100 =  1.2(1 - 1.5ⁿ) / (1 - 1.5)

100 =  1.2(1 - 1.5ⁿ) / (-0.5)

-50  =  1.2(1 - 1.5ⁿ)

-125/3  =  1 - 1.5ⁿ

-128/3  =  -1.5ⁿ

128/3  =  1.5ⁿ

log(128/3)  =  log1(.5ⁿ)

log(128/3)  =  n·log(1.5)

n  =  9.3   --->   10 terms

f(x)  =  x² - 2x - 5

When x = 1:  f(1))  =  1² - 2(1) - 5  =  1 - 2 - 5  =  -6   --->  one endpoint is (1, -6).

When x = 4:  f(4))  =  4² - 2(4) - 5  =  16 - 8 - 5  =  3   --->  one endpoint is (4, 3).

The line through the endpoints  (1, -6)  and  (4, 3)  has slope:  m  =  (3 - -6) / (4 - 1)  =  9/3  =  3.

The Mean Value Theorem states that there is at least one point on the function  f(x)  =  x² - 2x - 5  in the open interval  (1, 4)  that has the same slope (m = 3).

The first derivative of  1  is  0.

The first derivative of  sin(x)  is  cos(x).

The first derivative of  1 - sin(x)  =  0 - cos(x)  =  -cos(x).

Working with only the numerator:  (factoring out  3^{2012 )}

3²⁰¹²·3³ + 3²⁰¹²·3² + 3²⁰¹²·3  =  3²⁰¹²·(3³ + 3² + 3)  =   3²⁰¹²·(27 + 9 + 3)  =  3²⁰¹²·(39)

Working with only the denominator:

3²⁰¹²·3² - 3²⁰¹²·3¹ - 3²⁰¹²  =  3²⁰¹²·(3² - 3¹ - 1)  =   3²⁰¹²·(9 - 3 - 1)  =  3²⁰¹²·(5)

Combining:  3²⁰¹²·(39)  /  3²⁰¹²·(5)  =  39 / 5

To solve:     9x - 13  <  -22     or     -8x + 7  <  -25

                            9x  <  -9       or            -8x  <  -32

                              x  <  -1       or                x  >  4

All real numbers less than -1 or greater than 4.

               ( - infinity, -1 )     union     ( 4, infinity )

To place an equation into slope-intercept form, solve the equation for y.

                                          -3x - 2y  =  30

Add 3x to both sides:             -2y  =  3x + 30

Divide both sides by -2:             y  =  (-3/2)x - 15