The coefficients of the polynomial are rational, which means that any non-real roots occur alongside their complex conjugates. In this case, 6+<em>i</em> is a root, so 6-<em>i</em> is also a root.
So the simplest polynomial you can build with these roots is
(<em>x</em> - (-5)) (<em>x</em> - (6 + <em>i </em>)) (<em>x</em> - (6 - <em>i</em> )) = <em>x</em> ^3 - 7<em>x</em> ^2 - 23<em>x</em> + 185
(first choice)
g(5) means we substitute every x in the equation with a 5.
g(5) = (5)^2 - 4.
g(5) = 21.
Answer:
Step by step explanation:
The number is 6. 8*7=56, 9*7+5=68, 6860.
Answer:
b. 98.5°
Step-by-step explanation:
There are a number of ways to do this. Perhaps one of the simplest is to compute the angle associated with each vector, and find the difference.
We can compute that angle as ...
vector angle = arctan((coefficient of j)/(coefficient of i))
where the arctangent is computed in the appropriate quadrant according to the signs of i and j.
∠u = arctan(-8/√5) ≈ -74.38°
∠v = arctan(1/√5) ≈ 24.09°
The angle between these vectors is then ...
24.09° -(-74.38°) = 98.47° ≈ 98.5°
