Eliminating Arbitrary Constant, 2

Category: Differential Equations

"Published in Newark, California, USA"

Eliminate the arbitrary constant for

Solution:

Consider the given equation above

Take the derivative on both sides of the equation with respect to x, we have

Multiply both sides of the equation by dx and therefore, the final answer is

Circular Cylinder Problems, 8

Category: Solid Geometry

"Published in Newark, California, USA"

The plumb-line distance from the lowest point of the top of the Leaning Tower of Pisa to the ground is 179 ft. The tower leans so that this plumb line strikes the ground 14 ft. from the nearest point of the base as shown. (a) At what angle is its axis now inclined from the vertical? (b) At what angle would its axis have to be inclined from the vertical before it would topple over?

Photo by Math Principles in Everyday Life

Solution:

(a) To understand more the problem, let's label further the figure as follows

Photo by Math Principles in Everyday Life

By Pythagorean Theorem, the length of the Leaning Tower of Pisa is

Therefore, the angle of inclination with respect to vertical axis for the Leaning Tower of Pisa is

                              or

(b) If the Leaning Tower of Pisa is inclined from the vertical before it would topple over, then the figure will be like this
 

Photo by Math Principles in Everyday Life

Therefore, the angle of inclination with respect to vertical axis for the Leaning Tower of Pisa before it would topple over is

                              or