5th Posting

by silfia yulianis 11.01 0 komentar

PART 1

1. Explain how to prove that the square root of two is irrational number!

First, suppose that square root of two is rational number, that is square root of two is equal to a over b, a and b is relatively prime. We can say that a is equal to square root of two times b. So, a square is equal to two times b square.

a square and a are an even number because a square is twice an integer number.

Let say that a is equal to two times c. Then, we get four times c square is equal to two times b square. It is same with two c square is equal to b square. We see that b square is an even. So, b is an even too.

This is impossible to say that a and b is relatively prime. So, square root of two is not a rational number. Square root of two is irrational number.

2. Explain to show that sum angle of triangle is equal to one hundred and eighty degree!

First, we should make a triangle. Then, cut every angle. Arrange the angle, so the points coincide. We see that the angles of triangles make a straight angle. We just learn that the straight angle is equal to one hundred and eighty degree. So, sum angle of triangle is equal to one hundred and eighty degree.

3. Explain how you are able to get phi!

First, we can make many circles with different diameters. Then, we have to measure the circumference in every circle. Now, we have diameters and circumferences. Then, we divide every circumference by its diameters. So, we get the value is approach to three point one four. So we can find phi.

4. Explain how you are able to find out the area of region bounded by the graph of y = x² and y = x + 2

First, we must find the intersect point of y equals x square and y equals x plus two. We can substitute y. It become x square equals x plus two. We can subtract both sides by negative x minus two and we get x square minus x minus two is equal to nought. And we get x roots is two or negative one. Two and negative one is the intersect point in x.

The graph of y equals x plus two is above graph y equals x square. So, to find out the area, we can use integral with lower boundary x equals negative one to upper boundary x equals two, of x plus two minus x square in brackets dx.

So we get the area is equal to x square over two, plus two x, minus x cube over three, with lower boundary x equals negative one to upper boundary x equals two. We substitute the value of x. Then, we get two square over two, plus two times two, minus two cube over three, minus open bracket negative one square, plus negative one times two, minus negative one cube over three close bracket. So, the area of region is twenty seven over six.



5. Explain how to determine the intersection points between the circle x² + y² = 20 and y = x + 1!

First, we substitute x plus two in circle's variable y. So, we get x square plus open bracket x plus one close bracket square is equal to twenty. Then we get x square plus x square plus two x plus one is equal to twenty. Now, we add both sides by negative twenty. We get two x square, plus two x minus nineteen.
Now, we can get value of x. x is equal to a half plus a half of square root of thirty nine and x is equals to negative a half minus a half of square root of thirty nine. To get the value of y, we can substitute value of x in the equation of y equals x plus one.