A curve with polar equation \( r=\frac{12}{8 \sin \theta+65 \cos \theta} \) represents a line. This line has a Cartesian equation of the form \( y=m x+b \), where \( m \) and \( b \) are constants. Give the formula for \( y \) in terms of \( x \). For example, if the line had equation \( y=2 x+3 \) then the answer would be \( 2 \cdot x+3 \). \( y=\square \)

Evaluate the function. If the value is not a rational number, round your answer to three decimal places. (a) \( \operatorname{csch}^{-1}(3) \) (b) \( \operatorname{coth}^{-1}(6) \)

Use the value of the given hyperbolic function to find the values of the other hyperbolic functions. \( \sinh (x)=\frac{5}{4} \) \( \tanh (x)= \) \( \operatorname{csch}(x)= \) \( \operatorname{sech}(x)= \) \( \operatorname{coth}(x)= \)

Evaluate the function. If the value is not a rational number, round your answer to three decimal places. (a) \( \sinh (1)=\square \) (b) \( \tanh (-8)=\square \)

Find any vertical asymptotes. \( h(x)=\frac{(x-3)(x+6)}{x^{2}-4} \)

Graph the rational function. \( f(x)=\frac{-4 x^{2}+12 x+12}{6 x+9} \) Start by drawing the asymptotes. Then plot two points on each piece of the grap