"Published in Vacaville, 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
This website will show the principles of solving Math problems in Arithmetic, Algebra, Plane Geometry, Solid Geometry, Analytic Geometry, Trigonometry, Differential Calculus, Integral Calculus, Statistics, Differential Equations, Physics, Mechanics, Strength of Materials, and Chemical Engineering Math that we are using anywhere in everyday life. This website is also about the derivation of common formulas and equations. (Founded on September 28, 2012 in Newark, California, USA)
Tuesday, March 3, 2015
Eliminating Arbitrary Constant,3
Category: Differential Equations
"Published in Vacaville, 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
"Published in Vacaville, 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
Monday, March 2, 2015
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
"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
Sunday, March 1, 2015
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?
Solution:
(a) To understand more the problem, let's label further the figure as follows
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
Therefore, the angle of inclination with respect to vertical axis for the Leaning Tower of Pisa before it would topple over is
or
"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
(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
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