The price $p($in dollars$)$ and demand $x$ for wireless headphones are related by

$x=6,000-0\mathrm{.}15p^2$

a$.$ If the current price of $$110$ is decreasing at a rate of $$5$ per week, find the rate of change $($in headphones per week$)$ of the demand.

b$.$ Find the associated revenue function $R(p)$ and the rate of change $($in dollars per week$)$ of the revenue.

$7.$ The price $p($in dollars$)$ and demand $x$ for a product are related by

$2x^2+5xp+50p^2=80,000$

a$.$ If the price is increasing at a rate of $$2$ per month when the price is $$30,$ find the rate of change of the demand.

b$.$ If the demand is decreasing at a rate of $6$ units per month when the demand is $150$ units, find the rate of change of the price.