$4\mathrm{.}5$ a$.$ Consider an L$1$ cache with an access time of $5ns$ and a hit ratio of $H=0\mathrm{.}9.$ Suppose that the memory access time is $100ns$ and we can increase the cache access time to $6ns.$ What must be the hit ratio, $H,$ for this change to result in improved performance?

b$.$ Repeat the above question for a cache access time of $10ns.$