MY LAST TASK

TRAPEZOID

I explain this topic to Ratna Yunitasari as my partner in my University at Friday, January 9, 2009. First I explain the definition of trapezoid. In order to easy to explain this topic I use the graph.

A Trapezoid is a quadrilateral (a closed plane shape with four linear sides) that’s has at least one pair of parallel line for sides.

The parallel sides of a trapezoid are called the bases, here symbolized by b₁ and b₂. If b1 and b2 are also parallel, then they are congruent, and the trapezoid is also a parallelogram. The trapezoid has central median. The height of the trapezoid is the perpendicular distance between the bases, here symbolized by h.

If the two sides which are not parallel have equal lengths, then the trapezoid is called an isosceles trapezoid. Two opposite sides are parallel, the two other sides are of equal length. The diagonals of an isosceles trapezoid are congruent. Since segment AB is parallel to segment CD, segment AC is congruent to segment BD. Also, the diagonals of an isosceles trapezoid are congruent and intersect at equal positions. An isosceles trapezoid has two pairs of congruent angles. The top two would be congruent (same) to one another, and the same for the bottom two angles.

Any quadrilateral with one axis of symmetry must be either an isosceles trapezoid or a kite. The base angles in an isosceles trapezoid are equal in measurement.

For example of Isosceles Trapezoid

The area of an isosceles (or any trapezoid) is equal to the average of the bases times the height. In the diagram to the right, b₁ = segment AB, b₂ = segment CD and h is the length of a line segment between AB and CB and perpendicular to them. The area is given as follows A= (h (b1+b2)/ 2

Example:

A trapezoid has a height of 6. The length of parallel sides are 2 and b 4.h0w is the area that’s trapezoid?

Answers: a=2 b = 4 h= 6 So the area would be 18 from

A= (h (b1+b2)/ 2

=(6(2+4))/2

=18

I think topic about trapezoid is not difficult because is have learned at elementary school. I feel happy when she understand what I explain to her. The vocabulary that I used is easy because we often listen and use it. The exercise that I given, she done better. Then she explain me about square. So we changing over each other topic so that the understanding of about mathematics and vocabulary increase.

Source:

http://en.wikipedia.org/wiki/Trapezoid

ttp://id.mind.net/~zona/mmts/geometrySection/commonShapes/trapezoid/trapezoid.html

http://en.wikipedia.org/wiki/Isosceles_trapezoid

.

BLOG AS MEDIA INFORMATION

In era globalization the Science & Technology developing rapidly. Along with the era of human development are required to communicate quickly without requiring the time and cost that much. One of the communication media that is using the blog. Along with the era of human development are required to communicate quickly without requiring the time and cost that much. One of the media communication that is blog. Through the blog we can get information from different countries without the limit of space and time. Blog can be said as the media information that is either formal or informal, and does not require special expertise to do so. A blog can be used as a medium for interactive learning between teachers with students in a community. Blog can also become a media to reveal a proposal, comment. Other benefit that is functioning blog as promotion media a institution.. For student blog can improve the ability to write, can stimulate the brain and can express ideas, to the idea in a creation .For faculty can benefit to develop the learning process that varying , and can develop professionalism among teachers.

ENGLISH TASK

International Communication

Human being as social creature require others to fulfill its requirement. Is for that needed by communications. Communications divided to become three formal communications, informal communications and spiritual communications. Formal communications use formal Ianguage or standard Ianguage, for example lecturer moment explain Iesson, writing blog etc. Informal Communications use colloquial or ordinary Ianguage, for example conversation with friend etc. Communications of spiritual used to deal with God, like praying. Though that communications represent activity of fundamental but there is existing resistance. Difference of culture, Ianguage also difference of pronunciation become communications resistance. Hence from that needed international language that is English

English expand very quickly so we have to always improve the quality of have our Ianguage. Learn English not only moment in its its his formal institute or campus but can also in everyday activity. Learn most effective that is practice, is always used and sharpening.

Name : EVRI KURNIAWATI

NIM : 07305144026

Prodi : Math NR 07

E – mail : ev_nye@yahoo.com

Day, date :Monday, Des 01, 2008

English task on Tuesday, November 25, 2008

Class E room 204

VIDEO 1

PRE CALCULUS

Graph of a rational function

Can have discontinuities has a polynomial in the denominator

Example:

F(x)=x-3/x-2. Is called Off Limit if x=1 subtituted in equations F(x)=x-3/x-2 so denominator is equal to zero.

If equations above substituted to x=0 so get:

F(x)=x-3/x-2

F(x)=0-3/0-2

=3/2

the function above is break function if insert 1.

not all rational function will give 0 in denominator and can be 0

Break 2 ways in rational function:

1) Missing point is a loophole

Example:

Y=x^2-2x+1/x-1 if x=1 subtituted in equations beside so denominator is equal to zero

Y=1^2(x)+1/1-1

=0/0 That’s not allowed, missing removable singularity when x leads to 0/0

Y=x^2-2x+1/x-1

=(x-1)(x-1)/(x-1) (using the way to factor)

=x-1

Subtituted x=1

Y=x-1

=1-1

=0

2) Denominator of rasional functions equal to zero

Example : f(x)=x-3/x-2

Video 2

LIMIT by INSPECTION

1. x goes to positive or negative infinity

2. Limit involved a polynomial devided by a polynomial

Example 1:

Lim x^3+7/x^2-x-6

x--~

(polynominer by polynomial with limit x approach infinity )

To solving limit above :

a. looking the power of x in the numerator and denominator

b. must be dividing f by polynomial if power of x in numerator highest than in denominator, limit can be positive or negative infinity

example above power of x in numerator highest than in denominator.

Example 2:

Lim x+3/x^2+1

x--~

Its mean power of x in denominator highest than in numerator, that limit will equal to 0

Example 3 :

Lim x^2-x/2x^2+1

x--~

=Lim ((x^2-x)*1/x^2)/((2x^2)*1/x^2)

x--~

=Lim 1-(x/x^2)/2+(1/x^2)

x--~

=1/2

We get solutions Lim x^2-x/2x^2+1=1/2

x--~

Video 3

PROBLEM SOLVING ABOUT GRAPH MATH

1. The graph y=g(x), if the function is difined by h(x)=g(2x)+2.What is the value of h(1/2)?

Solution:

The fungtions is h(x)=g(2x)+2. If h(1/2) is mean when x =1/2, we substituted this to the functions h(x)=g(2x)+2

H(1/2)=g(2*1/2)+2

= g (1) + 2

g(1) is mean g when x=-2,if we look the graph of y=g(x) we get g(1)=-2

So

h(1/2)+1=g(1)+2

= -2 + 2

= 0

We get the value of h(1/2) is 0.

2. Let the function f be defined by f(x)=x+4. If f(p)= 16,What is the value of f(2p)?

Solution:

The function is f(x)=x+4

The value of f(2p) is mean f when x=2p,we have 2f(p)=16 because each space between have factors 2

So we can over by 2 and get f(p)=8

its mean f when x=p equal to 8 we can substituted this value to the function f(x)=x+4

we getf(p)=2p+4=8

p = 2

So we can get f(2p) If p=2 so 2p=4 is mean f when x=4 we subtitued this value to the function

f(x)=x+4

f(4)=4+4

= 8

We get the value of f(2p) is 8

3. In the xy coordinate x=y^2-25 intersects line at (p,-5) and (7,t).What is the greatest possible value of the slope of l?

The function x=y^2-25 intersects line at (p,-5) and(7,t). .

The formula of slope is m=y2-y1/x2-x1 the coordinate of l are (p,-5) and (7,t)..

thats mean x1=p,y1=5,x2=7,y2=t, we subtitued thus to the m

m=y2-y1/x2-x1

= t-(-5)/7-p

= t+5/7-p

We get the greatest possible value of the slope l is t+5/7-p

Video 4

INVERS FUNCTION

Notation by : F(x,y) = 0

Function y = f (x) is called VLT and x = g (y) is called HLT

• Function x = g(y) : invertible

Example:

1. Line function y=3x-6and y=x

y=3x-6

y=3x-6

-2x=-6

x=-6/-2

x=3

Subtuted x=3 in y=3x-6

y = 6 - 6

= 0

So, line function y=3x-6 and y = x intersect in (3,0).

y=3x-6

y+6=3x

x= y+6/3

x=1/3+2 and y=1/3+2

in invers function the line be write:

f(x) = 3x-6

g(x) = 1/3x+2

f(g(x)) = 3(1/3x+2)-6

= x+6-6

= x

g(f(x)) = 1/3(3x-6)+2

=x-2+2

= x

From the operation above will get the conclusion :

g = f ^-1

f(g(x)) = g(f^-1(x)) = x

g(x) = f^-1(f(x)) = x