Given that \( f(x)=x^{2}-1 \) and \( g(x)=x-6 \), calculate (a) \( f \circ g(x)=f(g(x))= \) (b) \( g \circ f(x)=g(f(x))= \)

Write the equation of the hyperbola \( 36 x^{2}-16 y^{2}+360 x-128 y+68=0 \) in standard form \[ \frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1 \] Where: \( \mathrm{h}=\square \) \( \mathrm{k}=\square \) \( \mathrm{a}=\square \)

Given the geometric sequence: \[ a_{1}=3, a_{2}=\frac{7}{3}, a_{3}=\frac{49}{27}, \ldots \] find a formula for the \( n \)-th term: \[ a_{n}=\square \]

Write the arithmetic sequence \( 23,19,15,11, \ldots \) in the standard form: \( a_{n}=\square \)

2. Use the order of operations to solve. You MUST SHOW WORK to get the credit. \[ 13-5+18 \div 3 \]

The partial sum \( -3+(-9)+(-27)+\cdots+(-6561) \) equals \( \square \)