Complete the square and write the given equation in standard form. Then give the center and radius of the circle and graph the equation.
\(x ^ { 2 } + y ^ { 2 } + 4 x - 2 y - 31 = 0\)
The equation of the circle in standard form is (Simplify your answer.)
\((x+ 2)^{2}+ (y- 1)^{2} = 36\)
Center is \((- 2,1)\)
Radius is 6
Find the inverse for each of the following functions.
\(f ( x ) = 3 x + 1\)
\(g ( x ) = 1 x ^ { 3 } - 5\)
\(h ( x ) = \frac { 3 } { x + 5 }\)
\(j ( x ) = \sqrt[ 3 ] { x + 1 }\)
The total revenue from the sale of a popular book is approximated by the rational function \( R ( x ) = \frac { 1700 x ^ { 2 } } { x ^ { 2 } + 4 } \) , where \( x \) is the number of years since publication and \( R ( x ) \)
is the total revenue in millions of dollars.
(a) Find the total revenue at the end of the first year.
(b) Find the total revenue at the end of the second year.
