Afour-wheel-drive vehicle is transporting an injured hiker to the hospital from a point that is 30 km from the nearest point on a straight road. the hospital is 70 km down that road from that nearest point. if the vehicle can drive at 30 kph over the terrain and at 130 kph on the road, how far down the road should the vehicle aim to reach the road to minimize the time it takes to reach the hospital? (round your answer to two decimal places.)

You and a friend (alex) are at a a tree-top adventure park .. . part of the course requires you to climb up a rope. you both climb the same rope in the same amount of time. however, the tension in the rope is greater when alex climbs. who did the most work? alex did - more tension means more force - more force means more work was done you did - less tension means less force - less force means more work was done to find the work done, the force exerted and distance moved are multiplied. a couch is moved twice before you are happy with its placement. the same force was used to move the couch both times. if more work is done the first time it is moved, what do you know about the distance it was moved? when more work was done, the couch was moved less. when more work was done, the couch was moved further. when more work was done, the couch wasn't moved at all. when more work was done, the couch was moved the same distance.

Find the dimensions and area of the largest rectangle that can be inscribed in the upper half of the ellipse. (give your answers in terms of a and b. enter the dimensions as a comma-separated list.)

What is the role of lenses in microscopy?