Lise jogs along the curve defined by from to Steve jogs along the straight line connecting those two points. Steve and Lise both start from at the same time and Lise jogs at a speed of . What is the speed at which Steve must run (in ) so that he arrives at at the same time as Lise?
的coordinates of a dot moving in the plane at time are given by: and . Let be the distance traveled by in the interval . If , what is the value of ?
A delivery drone flying at constant speed and constant height toward a destination drops its goods. If the trajectory of the falling goods until it hits the ground can be described by the equation where is the horizontal distance it travels and 离地面的高度,是什么distance(not horizontal displacement) traveled by the goods until it hits the ground?
Note:You can use
的re exists a unique, positive-valued, non-constant, continuous and differentiable function such that
(i) over any specified interval, the area between and the -axis is equal to the arclength of the curve, and
(ii) .
If , then find .
Consider the curve in the first quadrant. Now it's rotated about the to obtain a solid of revolution. What is its surface area to 4 decimal places?