Question 16
$a ) 55 ^{\circ}$ alcohol means $55$ ml pure alcohol per $100$ ml mixture. It can be reduced to the same $T ^{\circ}$ either by adding $v$ units of water or removing $v$ units of pure alcohol. Find $T$. $b$) How many primes $p$ make $p^{2} + 59$ have exactly six positive divisors?