Find the equation of the tangent line to the curve at the given point. 12x - xy + y" = 48 at (4,4) The equation of the tangent line is y = - 2x + 12. (Type an equation. Type an exact answer.)A night club has approximated the demand for their Thursday night drink special by p + 200q = 198, where p is the price (in dollars) and q is the quantity demanded (in thousands). Find and interpret - dq dp - when the price is $6 and the demand is 900 drinks. When the price is $6 and the demand is 900 drinks, da dp = - 0.033 (Round to three decimal places as needed.) If the price is increased by $1, the quantity demanded decreases by 33 drinks. (Round to the nearest integer as needed.)For a certain company, the relationship between revenue R (in billions of dollars) and the number of full-time employees n (in thousands) can be approximated by 6000R = n (a) Would- dn dR be expected to be positive, negative or zero? Why? (b) Find dn dR What are the units? dn (c) Find - when R= 117 and n = 322, and interpret the answer. (a) Would- dn dR be expected to be positive, negative or zero? Why? dn The value - is expected to be positive because if revenue grows it would be expected that more employees would be hired compared to last time. (b) Find- dn dn dR . Select appropriate units for - dR dn 4000R dR thousand employees per billion dollars Type an exact answer.)