1. A man is climbing up a mountain which is inclined. He has to travel 100 km to reach the top of the mountain. Every day He climbs up 2 km forward in the day time. Exhausted, he then takes rest there at night time. At night, while he is asleep, he slips down 1 km backwards because the mountain is inclined. Then how many days does it take him to reach the mountain top?  I'm in the dire need of <a href=" Homework Help</a>.

A steep mountain is inclined  to the horizontal and rises  above the surrounding plain. A cable car is to be installed from a point  from the base to the top of the mountain, as shown in the figure below. What is the shortest length of the cable needed?

A Tibetan monk leaves the monastery at 7:00 AM and takes his usual path to the top of the mountain, arriving at 7:00 PM. The following morning, he starts at 7:00 AM at the top and takes the same path back; arriving at the monastery at 7:00 PM. Use the Intermediate Value Theorem to show that there is a point on the path that the monk will cross at exactly the same time of day on both days.

All of the students at mountain range foreign language. 5/8 students take Spanish. 3/10 of the students take french. The remaining students take Mandarin. What fraction of the students take Mandarin?