Answer:
Radius of the circle is <em>15 inches.</em>
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Step-by-step explanation:
Relation between length of arc, radius and the angle subtended by the arc on center is:

where
is the central angle in radians subtended by arc
is the length of arc
is the radius of arc
We are Given the following details:


We know that 
Converting
to radians:
radians
Putting the values of
and
to find the value of 

Hence, Radius of the circle is <em>15 inches.</em>
If you think about it, a hexagon can be cut into 6 equilateral triangles. Because of this, all you need to do is find the area of one triangle and multiply it by 6. Since the side length of one triangle is 12, we know that is the base. Since the triangles that are created when cutting the equilateral triangle in half are both 30 60 90, the height must be 6(3)^1/3. We can then multiply 12 • 6 radical 3 •1/2 to get 36 radical 3. Multiply this by 6 and get 216 radical 3 units squared.
Answer:

Step-by-step explanation:
Look at the component form of each vector.
Note that vector c is <4,4> and vector d is <-2,-2>
If one imagined the line that contained each vector, the line for both would have a slope of 1, because 
Since they have the same slope they are parallel, but since they are in opposite directions, we often call them "anti-parallel" (simply meaning parallel, but in opposite directions).
If two vectors are parallel, one vector can be multiplied by a scalar to result in the other vector. This means that there is some number "k", such that
, or equivalently,
and
.
If
and
, we just need to substitute known values and solve for k:

Double checking that k works for the y-coordinates as well:

? 

So, 