My Mathematics

It is about my mathematics writing. In this time I will share about sphere, parallelogram, and integral.

SPHERE
A sphere is a set of all points that are given distance from a point called center. Sphere has diameter, radius, and tangent. Sphere is one of three dimensional shape.
Diameter of sphere is a chord of the sphere that dividing the area of sphere in two similar parts. The radius of sphere is line from the center to on the sphere. The length of radius is half of the diameter. Tangent of a sphere is a line that has intersection point exactly one point at the sphere.
Application the sphere in our life is a ball. The form of ball is similar with sphere.

A sphere has surface area and volume.
The surface formula of sphere is four time phi time radius square. It can be wrote,
S (surface ) equal 4phi time r square.
The volume formula of sphere is four-third phi time radius cube.
V (volume ) equal 4/3 phi time r cube.

Problem solving,
Find the surface area and volume of the sphere since the diameter fourteen centimeters, the radius is seven centimeters.
Solution ,
Volume ( V) equal four-third phi time radius cube.
V equal four-third time seven cube time twenty two-seventh
V equal one thousand four hundreds thirty seven point three three.


PARALLELOGRAM
Parallelogram is quadrilateral with two pairs of parallel sides. For example parallelogram ABCD. It has two pairs of parallel sides, they are AB parallel with CD and AD parallel with BC. Parallelogram ABCD also have two pairs of congruent angles. The opposite angels of parallelogram are congruent ( < A with < C and < C with < D ). The consecutive angles of parallelogram are supplementary 180 degree.
Parallelogram have two diagonals. The diagonals of parallelogram bisect each other. A diagonal of parallelogram separate it into two congruent triangles.

Problem,
In quadrilateral ABCD, with diagonal BD, AB parallel with CD, AB congruent CD. Show that ABCD is parallelogram!
Solution ,
One way to show that ABCD is a parallelogram is to show AD congruent CB. It can do by showing ABC triangle congruent CDB triangle.
-ABD angle congruent CDB angle. If two parallel lines are cut by transversal, then each pair of alternate interior angle is congruent.
-BC congruent CB
-AB congruent CD
-ABD triangle congruent CDB triangle.
-AD congruent CB
For the conclusion, ABCD is a parallelogram.




DIFFERENTIAL
The differential f function ( f’ ) is other function f’ that the value in any number c, is
F’ ( c ) equal limit h approach 0 of f ( c plus h ) minus f ( c ) over h,

The rule to look for differential,

A theorem,( the rule of constant function )
If f(x) equal k, with k is constant
Then to any x f(x) equal 0. Is Dx (k) equal zero.

B theorem, ( the rule of identity function )
If f(x) equal x, then f’(x) equal one.
Is Dx (x) equal one.

C theorem, ( the rule of power )
If f(x) equal x to be n, with n is positive integers, so f’(x) equal n time x to be n minus 1.
Dx ( x to be n ) equal n time x tobe n minus one.

D theorem ( the rule of constant multiply )
If k is constant n function can be differential, so
(kf’) (x) equal k time f(x) is
Dx [ k tme f(x)] equal k time Dx f(x).

E theorem (the sum / dispute rule)
If f and g are functions that can be differentiated, so
( f plus or minus g )’ (x) equal f’(x) plus or minus g’(x)
Is Dx [f(x) plus or minus g(x)]’ (x) equal Dx f(x) plus or minus Dx g(x).

Application,
Andi run in street. His position S suitable with S equal two t square plus twelve t plus eight, ( S in meters, t in second ).
When two second, he run with velocity twenty meters/hours.
Proof,
V ( velocity ) equal Ds ( two t square plus twelve t plus eight )
V equal Dt (two time t square) plus Dt ( twelve t) plus Dx eight
V equal four time t plus twelve.
To get his velocity at four second, we substitute t equal in equation above.
We get V equal twenty meters/hours.

It is all about sphere, parallelogram, and diferential. My posting not complete,my knowledge about it still low, so I need advice from readers. Thankyou..