Answer:
Step-by-step explanation:
we know that
To find out the probability of hitting a ball into the circular hole, divide the area of the hole by the area of the playing area
Let
x ----> the area of the hole
y ----> the area of the playing game
so
we have
<em>Find the area of the hole</em>
The area of the circle (hole) is equal to
we have
----> the radius is half the diameter
assume
substitute
<em>Find the probability</em>
we have
substitute
Convert to percentage
Round to the nearest tenth
If -3+5i is a solution, then by the conjugate root theorem, -3-5i is also a solution. We find the polynomial by multiplying together the factors. If x = -4, then x + 4 is the factor. If x = -3+5i, then (x-(-3+5i)) is a factor, and so is (x-(-3-5i)). Simplifying those down gives us as the first factor as (x+3-5i) and the second as (x+3+5i). We can FOIL those 2 together to get their product, and then FOIL in x+4. FOILing the 2 complex factors together gives us . If we combine like terms and cross out things that cancel it's much easier than what it looks like there! It simplifies down to
. Since i^2 = -1, it simplifies further to
and finally, to
. Now we will FOIL in x+4.
. Our final simplified third degree polynomial is