geno3141

a₁  =  1          a₄  =  1            a₇  =  1         a₁₀  =  1

a₂  =  2          a₅  =  ½           a₈  =  2         a₁₁  =  ½

a₃  =  2          a₆ =   ½           a₉  =  2           a_{12  =}  ½

If this pattern holds, if you divide the index (the subscript) by 3 and get a remainder of 1, the value will be 1.

2011  =  670 x 3 + 1, so  a₂₀₁₁  =  1

-2 - 2i  in  r·cis(theta) form:

r  =  sqrt( (-2)² + (-2)² )  =  sqrt(8)

theta  =  tan^-1( -2/-2 )  =  5pi/4

x³  =  sqrt(8) · cis ( 5pi/4 )     --->     x  =  [ sqrt(8) · cis ( 5pi/4 )  ]^1/3

To find the principal cube root, take the cube root of  sqrt(8)  =  (8^1/2)^1/3  =  (8^1/3)^1/2  =  sqrt(2)

and divide 5pi/4 by 3  =  5p/12.

So, the principal cube root is:          sqrt(2)·cis( 5pi/12 )

Adding 2p/3, the second root is:     sqrt(2)·cis( 13pi/12 )

and another 2p/3, the third root is:  sqrt(2)·cis( 21pi/12 )

So, I don't get any of the answers ... 

If these towns are in a straight East-West line, then, from West to East are:

   A  -- 30 miles  -- B  -- 85 miles --  C  -- 100 miles --  D

If you must connect each of these by a separate calbe to a power station (at $1000 per mile),

--  if you place the power station at B or C or anywhere between B and C, the total cost will be $300,000.

--  if you place the power station either west of B or east of C, the total cost will be higher.

So, if I am reading the question correctly, I can't solve the problem.

I am interested to see anyone else's solution.

The area of a parallelogram is the product of its base and its height.

DC = 27 = base.

EG = 16 = height.

Area  =  27 x 16

To strike six o'clock, there are 5 intervals.

So, under the assumption that each strike is instantaneous, it will take 30 seconds / 5 intervals, or 6 seconds per interval.

To strike twelve o'clock, there are 11 intervals.

A 6 seconds per interval, this will take 11 x 6 = 66 seconds.

There are patterns that can be used to make a 5 x 5 magic square (not only are the sums of all the rows and all the columns the same, but also the sums of the two diagonals).

Using one of these patterns, I constructed a magic square that used the first 25 numbers, omitting 169.

Then, using the same pattern, I constructed a magic square that used the last 25 numbers, omitting 144.

So, there are at least two answers to your question: either 169 or 144.

I'm going to change each of these into rectangular coordinates.

x  =  42 + (2/3)t   --->   solve for t   --->   x - 42  =  (2/3)t    --->    3x - 126  =  2t   --->   t  =  (3x - 126)/2

y  =  8 + (1/6)t   --->   substitute   --->   y  =  8  +  (1/6)(3x - 126)/2   --->   y  =  (1/4)x - 15/6

x  =  12 + t   --->   solve for t   --->   t  =  x - 12

y  =  5 + (1/4)t   --->   substitute   --->   y  =  5 + (1/4)(x - 12)   --->   y  =  (1/4)x + 2

Since they have the same slope, they don't intersect  --  they do not collide!

Please graph this ....

You'll find that you have a rectangle.

One point of intersection of the two graphs is the point (-2.5, 2.5).

Use the distance formula to find the distance from the origin to this point. This will be one of the sides of the rectangle.

Another point of intersection is the point (1.5, 1.5).

Use the distance formula to find the distance from the origin to this point. This will be another side of the rectangle.

Knowing the two sides of the rectangle, you can find the area ...

The sum of the numbers is 540.

The median is 61.

No number is larger than 179.

There is only one mode.

Try this:  179, 178, 61, 61, 61.

In a circle, equal central angles create equal chords.

Angle(BEC) = angle(AED) because they are vertical angles; therefore, their chords are congruent.