Definition, Theorem, Rules, Example, Application, and It's problem

ROM I

1. To proof that the square roots of two is an irrational number, first we must assume that the square roots of two is a rational number.
2. To show/indicate that the sum angle’s of triangle is equal to one hundred and eighty degree, first, we can make a straight line. Then, sketch a parallel line that equivalent with one of triangle side above that straight line. The next step, sketch the other side at the line and make sure that the line intersect both of the line. From this sketch, we can see that this picture build up angles that equal to the vertex of triangle. As we know that the sum angle of straight line always one hundred and eighty degree, so we can conclude that the sum angle of triangle is one hundred and eighty degree.
3. How we are able to get phi????

To proof how we get the value of phi, we can use the perimeter of a circle. As we know that the formula to find the perimeter of the circle is two times phi times the radius of the circle.

Prepare a wire with then makes a circle shape with define radius. Stretch that wire and observe the length. From this problem, we got the length as the perimeter of circle and that radius, so we can easily get the value of phi by dividing the perimeter by two times that radius.

4. To find the area of region bounded by the graph of y equal x square and y equal to x plus two:

The first step is sketch the graph. Then find the intersection points both of the graph. That intersection point can be the bound of the area. Use integration to solve this problem.

We get the intersection point by combine both of the equation, x square equal to w plus two and we get the bound that x equal negative one and x equal two. So, the integration is define integral of x plus two minus x square dx from x equal negative one to x equal two. From the integration, we get the value of nine second or four point five, so the area of the region is four point five unit of region.

5. How we are able to determine the intersection point between the circle x square plus y square equal to twenty and y equal to x plus one.

To make us more easy, we can sketch the graph before. So, we can see that the line intersect the circle at two points.

The next step is combine both of the equation by substitution methode. And at the last, we have an equation two x square plus two x minus nineteen equal to oh. Find the value of x and then substitute at the equation and we’ll get the value of y too. So, the intersection points, is x point y.

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ROM II

• A Kite

Everybody have ever seen a kite. But, what do you know about mathematics kite?

Based on definition, a kite is a four-sided which one of its diagonal joining to the other diagonal axis. A theorem said that if a quadrangular ABCD is a kite and diagonal AC joining to the axis of diagonal BD, then the line AB congruent with AD and the line CB congruent with CD.This theorem shows that the diagonals of a kite have perpendicular intersection. The line AC cutting the segmebt BD and make the right angel. It’s shows that a kite has one folded-simetry and the line AC as the axis.

The other theorem said that if a kite which the close angels are straightly, then it’s called a rhombus. From this theorem, we know that to find the region of a kite has the same rules to find rhombus area. We must times a half with the length of the first diagonal and then times with the second diagonal.

• Factorisation

When we talk bout factorisation, it’ll remind us with the prime numbers, the least common multiple, and the great common multiple.

A theorem said that every whole numbers which more than one are devided by a prime number, so every positive whole number which more than one is a prime number or those number are multiplication from some prime numbers.

The singular factorisation theorem said that factorisation of a positive whole numbers which more than one from the prime number is singular, except the rotation of that factors. This theorem become the base theorem at arithmatics.

An interesting theorem from Euclid said if the quantity of the prime number unlimited. The interesting point which located at the proof of this theorem is the forming of N positive whole number as the result of multiplication all prime numbers plus one.

• Permutation

One problem which have to thoght and evaluated by statisticians is the influence of probable factor which connected to some cases. This problem included to the branch of mathematics called as probability theory.

Sometimes we have a population which has a sample. For exampler, if we’ll find how many formation that probable formed by six persons to seat round a rond table or how probable if we take two lottery-tickets from twenty tickets. The different formation is called permutation.

Permutation is a formation which formed by all or a part from gathering things. The sum of permutation ‘n’ different things is n factorial. The sum of permutation caused by the take ‘r’ things from ‘n’ different things is n factorial over n minus r in bracket factorial. And the sum of permutation ‘n’ different things formed at a round is n minus one in bracket factorial. This kind called round permutation. It’s usually used at the bridge games.