Question Number 45122 by MrW3 last updated on 09/Oct/18
Commented by MrW3 last updated on 09/Oct/18
$${A}\:{mountain}\:{has}\:{the}\:{shape}\:{of}\:{a}\:{semi} \\ $$$${sphere}\:{with}\:{radius}\:{R}.\:{From}\:{a}\:{point}\:{A} \\ $$$${at}\:{the}\:{foot}\:{of}\:{mountain}\:{to}\:{a}\:{point}\:{B}\: \\ $$$${over}\:{point}\:{A}\:{two}\:{paths}\:{will}\:{be}\:{built}. \\ $$$${One}\:{path}\:{should}\:{have}\:{the}\:{shortest} \\ $$$${length}.\:{The}\:{other}\:{one}\:{should}\:{have} \\ $$$${an}\:{uniform}\:{slope}.\:{Find}\:{the}\:{lengthes} \\ $$$${of}\:{both}\:{paths}\:{in}\:{terms}\:{of}\:{R}\:{and}\:\theta. \\ $$