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:
This is a function, because for every x-value, there is exactly one y-value.
The domain is: {-5, -4, -3, -2}, and the range is {-2, -1, 0}
Let me know if this helps!
Answer:
0.5
Step-by-step explanation:
we see that A is 1 of 2 choices, so theoretically, P(A) = 1/2 = 0.5
Answer:
f) None of the above.
Step-by-step explanation:
When we try to adjust a curve from a scatter plot to try and predict values of the dependent variable y given known values of the independent variable x.
The curve is a function y=f(x) which usually is a line, a logarithmic, parabola, power or exponential.
In order to choose which curve adjust the best, we compute a number r called correlation coefficient.
The closer r is to -1 or +1, the better the curve adjust the scatter plot.
When r =0, we say there is no correlation between the points x and y
When -1<r<0 we say there is a negative correlation, this means that the values of y decrease as the values of x increase.
When 0<r<1 we say there is a positive correlation, this means that the values of y increase as the values of x increase.
When r =1 or r =-1, we say that there is a perfect correlation. It means that all of the points of the scatter plot lie on the curve.
So, from the possible choices of answer, f) None of the above is the right one.
