geno3141

|   √2/2    -√2/2   |    x  | 2 |

|   V2/2       √2/2  |        | 5 |

Take the elements of the first row of the first matrix and multiply them, term by term, to the elements of the first (and, in this case, only) row of the second matrix:   (√2/2 x 2)  +  (-√2/2 x 5)  =  -3√2/2

Take the elements of the second row of the first matrix and multiply them, term by term, to the elements of the first (and, in this case, only) row of the second matrix:    (√2/2 x 2)  +  (√2/2 x 5)  =  7√2/2

Your final matrix is:  | -3√2/2 |

                               |  7√2/2 |

which states that R' is ( -3√2/2, 7√2/2 )

Is thisVaught's conjecture; which is so far unsolved?

Here is a location that describes how to find volume by using the shell method.

0.83log69  =  log(69^.83)    (multipliers go into logs as exponents)

log(0.33H)  = log(69^.83)

If the log is base b:                          (It doesn't make any diference if the base is 10 or e.}

b^log(0.33H)  =  b^log(69^.83)

0.33H  =  69^.83

H  =  (69^.83) / 0.33

Well; it really doesn't.

Speed in air = 332 + 0.6(20)  = 338 m/s

Time for stone to drop:

s = -4.9t²

-180 = -4.9t²

t = 6.06 sec

Time for sound to come back:

D = R x T

180m = 338m/s x T

0.53 sec  =  T

Total time:  6.06 + 0.53  =  6/59 sec

If you solve this by matrices, the rotational maxtrix for counter-clockwise is:  |  cosθ    -sinθ  |                                                                                                                                         |   sinθ     cosθ  |

(I know those bars don't look like matrix notation; but I don't know how to do better. Sorry.)

Rotational Matrix X Point Matrix:

|  cos45    -sin45  |    X    | 2 |

|  sin45     cos45  |          | 5 |

(Remember; those aren't absolute value bars; they're supposed to indicate 2 matrices.)

To calculate what's in teh first row of the third column, take the first row of E times the third column of G.

If by "6sqrt(x)", you mean the sixth root of x:    (The sixth root of x can be written as x ^ (1/6).)

(x^3) · (x^(1/6) )

When multiplying numbers with the same base, you add exponents:  x^(3 + 1/6)  or x^(19/3)

The compound interest formula is:    A  =  P( 1 + r/n ) ^ ( n · t )

where  A  is the final amount                 r is the rate, written as a decimal (.11)       t is the number of years (3)

           P is the initial amount (3500)     n is the number of times compounded per year (12)

A  =  3500( 1 + .11/12) ^ (12 · 3)

That will be your answer.