John (whose line of sight is 6 feet above horizontal) is trying to estimate the height of a tall oak tree. he first measures the angle of elevation from where he is standing as 35 degrees. he walks 30 feet closer to the tree and finds that the angle of elevation has increased by 12 degrees. find the height of the tree.

draw the diagram if you can, because i can't visualize it

Determine whether the following statements are true and give an explanation or counterexample. bold a. when using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. bold b. if a region is revolved about the y-axis, then the shell method must be used. bold c. if a region is revolved about the x-axis, then in principle it is possible to use the disk/washer method and integrate with respect to x or the shell method and integrate with respect to y.

If cos(2x) = tan^2(y), show that cos(2y) = tan^2(x).

The graph of f(x) = |x| is transformed to g(x) = |x + 11| - 7. on which interval is the function decreasing?