"Published in Newark, California, USA"
Evaluate
Solution:
Since there's a double angle involved in the integration, we have to convert it into it's equivalent single angle as follows
Consider
Consider
Consider
Therefore
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)
Friday, January 25, 2013
More Integration Procedures
Category: Integral Calculus, Trigonometry
"Published in Newark, California, USA"
Evaluate
Solution:
Since there's a double angle involved in the integration, we have to convert it into it's equivalent single angle as follows
Consider
Consider
Consider
Therefore
"Published in Newark, California, USA"
Evaluate
Solution:
Since there's a double angle involved in the integration, we have to convert it into it's equivalent single angle as follows
Consider
Consider
Consider
Therefore
Thursday, January 24, 2013
Right Circular Cylinder - Cube
Category: Solid Geometry
"Published in Newark, California, USA"
Find the volume and total area of the largest cube of wood that can be cut from a log of circular cross section whose radius is 12.7 in.
Solution:
Since the radius of a wood log is given, we have to consider the cross section of a wood log as follows
As you notice that a square is inscribed in a circle. There are 6 equal squares in a cube and so all the sides of a cube are equal. The radius of a wood log or a circle is equal to ½ of its diagonal. The diagonals of a square bisect each other at a right angle. A right triangle that has two equal sides and two equal angles is called an isosceles right triangle. In this figure, there are four isosceles right triangles in a square. By Pythagorean Theorem,
The length of a side of a cube is 17.9605 in.
The total area of a cube is
The volume of a cube is
"Published in Newark, California, USA"
Find the volume and total area of the largest cube of wood that can be cut from a log of circular cross section whose radius is 12.7 in.
 |
| Photo by Math Principles in Everyday Life |
Solution:
Since the radius of a wood log is given, we have to consider the cross section of a wood log as follows
 |
| Photo by Math Principles in Everyday Life |
As you notice that a square is inscribed in a circle. There are 6 equal squares in a cube and so all the sides of a cube are equal. The radius of a wood log or a circle is equal to ½ of its diagonal. The diagonals of a square bisect each other at a right angle. A right triangle that has two equal sides and two equal angles is called an isosceles right triangle. In this figure, there are four isosceles right triangles in a square. By Pythagorean Theorem,
The length of a side of a cube is 17.9605 in.
The total area of a cube is
The volume of a cube is
Wednesday, January 23, 2013
Approximate Value - Cube Root
Category: Differential Calculus, Arithmetic
"Published in Newark, California, USA"
Find the approximate value of ∛200 without using a calculator.
Solution:
Well, we know that
13 = 1
23 = 8
33 = 27
43 = 64
53 = 125
63 = 216 and so on.
Since 200 is between 125 and 216, the ∛200 is between 5 and 6. We can get the approximate value of ∛200 without using a calculator as follows
Let
then
If x = 216 (please choose this number because it is close to 200)
dx = 200 - 216 = -16
then dy will be
Therefore
using a calculator
and using a scientific calculator
which is close to the final answer.
"Published in Newark, California, USA"
Find the approximate value of ∛200 without using a calculator.
Solution:
Well, we know that
13 = 1
23 = 8
33 = 27
43 = 64
53 = 125
63 = 216 and so on.
Since 200 is between 125 and 216, the ∛200 is between 5 and 6. We can get the approximate value of ∛200 without using a calculator as follows
Let
If x = 216 (please choose this number because it is close to 200)
dx = 200 - 216 = -16
then dy will be
Therefore
using a calculator
and using a scientific calculator
which is close to the final answer.
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