This is a really interesting question! One thing that we can notice right off the bat is that each of the circles has the same amount of area swept out of it - namely, the amount swept out by one of the interior angles of the hexagon. Let’s call that interior angle θ. We know that the amount of area swept out in the circle is proportional to the angle swept out - mathematically
θ/360 = a/A
Where “a” is the area swept out by θ, and A is the area of the whole circle, which, given a radius of r, is πr^2. Substituting this in, we have
θ/360 = a/(πr^2)
Solving for “a”:
a = π(r^2)θ/360
So, we have the formula for the area of one of those sectors; all we need to do now is find θ and multiply our result by 6, since we have 6 circles. We can preempt this but just multiplying both sides of the formula by 6:
6a = 6π(r^2)θ/360
Which simplifies to
6a = π(r^2)θ/60
Now, how do we find θ? Let’s look first at the exterior angles of a hexagon. Imagine if you were taking a walk around a hexagon. At each corner, you turn some angle and keep walking. You make 6 turns in all, and in the end, you find yourself right back at the same place you started; you turned 360 degrees in total. On a regular hexagon, you’d turn by the same angle at each corner, which means that each of the six turns is 360/6 = 60 degrees. Since each interior and exterior angle pair up to make 180 degrees (a straight line), we can simply subtract that exterior angle from 180 to find θ, obtaining an angle of 180 - 60 = 120 degrees.
Finally, we substitute θ into our earlier formula to find that
6a = π(r^2)120/60
Or
6a = 2πr^2
So, the area of all six sectors is 2πr^2, or the area of two circles with radii r.
Answer: The complex conjugate has a very special property. Consider what happens when we multiply a complex number by its complex conjugate. We find that the answer is a purely real number it has no imaginary part. This always happens when a complex number is multiplied by its conjugate the result is real number.
Real numbers can be positive or negative, and include the number zero. They are called real numbers because they are not imaginary, which is a different system of numbers
Step-by-step explanation: Every complex number has a complex conjugate. The complex conjugate of a + bi is a - bi. For example, the conjugate of 3 + 15i is 3 - 15i, and the conjugate of 5 - 6i is 5 + 6i.
The average between 12.00 and 15.00 seconds
can be defined in a few different ways.
Way #1: (speed)
Average speed =
(1/2) (the speed at 12 seconds + the speed at 15 seconds) .
Way #2: (speed)
Average speed =
(1/3) (the distance covered between 12.00 and 15.00 seconds)
Way #3: (velocity)
Average velocity =
(1/3) (distance between location at 12 sec and location at 15 sec)
in the direction from location at 12 sec to location at 15 sec.
That's the best we can do with the combination of given and
not given information in the question.
Answer:
0.09375 tons
Step-by-step explanation:
In this problem, it is given that Samuel has 3/4 tons of mulch i.e. 0.75 tons of mulch.
Again it is given that Samuel has to spread equally this amount of mulch in 8 square yards of the plot.
Since the mulch is spread uniformly, then we can say that in each square yard of the plot (0.75/8) = 0.09375 tons of mulch is been spread.
Therefore, 0.09375 tons of mulch will be spread in each square yard. (Answer)
Answer:
52%
Step-by-step explanation:
