Wednesday, 19 May 2010
Kepada Alam
Wednesday, 12 May 2010
tak ada judul
Tuesday, 11 May 2010
Disaat Daku Tua
Disaat daku tua, bukan lagi diriku yang dulu
Maklumilah diriku,bersabarlah dalam menghadapiku
Disaat daku menumpahkan kuah sayuran di bajuku
Disaat daku tidak lagi mengingat cara mengikatkan tali sepatu
Ingatlah saat-saat bagaimana daku mengajarimu,
membimbingmu untuk melakukannya
Disaat daku dengan pikunnya mengulang terus menerus ucapan yang membosankanmu
Bersabarlah mendengarkanku, jangan memotong ucapanku.
Di masa kecilmu, daku harus mengulang dan mengulang terus
sebuah cerita yang telah saya ceritakan ribuan kali
hingga dirimu terbuai dalam mimpi
Disaat daku membutuhkanmu untuk memandikanku,
Janganlah menyalahkanku, Ingatkah di masa kecilmu,
bagaimana daku dengan berbagai cara membujukmu untuk mandi?
Disaat daku kebingungan menghadapi hal-hal baru dan teknologi modern
Janganlah menertawaiku
Renungkanlah bagaimana daku dengan sabarnya menjawab
setiap 'mengapa' yang engkau ajukan saat itu
Disaat kedua kakiku terlalu lemah untuk berjalan,
Ulurkanlah tanganlu yang muda dan kuat untuk memapahku
Bagaikan di masa kecilmu daku menuntunmu melangkahkan kaki
untuk belajar berjalan
Disaat daku melupakan topik pembicaraan kita,
Berilah sedikit waktu padaku untuk mengingatnya
Sebenarnya topik pembicaraan bukanlah hal yang penting bagiku
Asalkan engkau berada di sisiku untuk mendengarkanku
Daku telah bahagia
Disaat engkau melihat diriku menua,
Janganlah bersedih
Maklumilah diriku,dukunglah daku
bagaikan daku terhadapmu
disaat engkau mulai belajar tentang kehidupan
Dulu daku menuntunmu menapaki jalan kehidupan ini
kini temanilah daku hingga akhir jalan hidupku
Berilah daku cinta kasih dan kesabaran
Daku akan menerimanya dengan senyuman penuh syukur
Di dalam senyumanku ini, tertanam kasihku yang tak terhingga padamu.
ku temukan untaian kata indah ini dalam sebuah kardus sepatu
Membacanya membuatku tersadar...betapa banyak dosa-dosaku pada ayah dan ibu
Allohumagfirli wali walidayya warhamhuma kama rabbayani shogiro..Amin
Friday, 7 May 2010
ALGEBRA
Algebraic Expressions
An algebraic expression is one or more algebraic terms in a phrase. It can include variables, constants, and operating symbols, such as plus and minus signs. It's only a phrase, not the whole sentence, so it doesn't include an equal sign.
Algebraic expression:
3x2 + 2y + 7xy + 5
In an algebraic expression, terms are the elements separated by the plus or minus signs. This example has four terms, 3x2, 2y,7xy, and 5. Terms may consist of variables and coefficients, or constants.
Variables
In algebraic expressions, letters represent variables. These letters are actually numbers in disguise. In this expression, the variables are x and y. We call these letters "variables" because the numbers they represent can vary—that is, we can substitute one or more numbers for the letters in the expression.
Coefficients
Coefficients are the number part of the terms with variables. In3x2 + 2y + 7xy + 5, the coefficient of the first term is 3. The coefficient of the second term is 2, and the coefficient of the third term is 7.
If a term consists of only variables, its coefficient is 1.
Constants
Constants are the terms in the algebraic expression that contain only numbers. That is, they're the terms without variables. We call them constants because their value never changes, since there are no variables in the term that can change its value. In the expression 7x2 + 3xy + 8 the constant term is "8."
Real Numbers
In algebra, we work with the set of real numbers, which we can model using a number line.
Real numbers describe real-world quantities such as amounts, distances, age, temperature, and so on. A real number can be an integer, a fraction, or a decimal. They can also be either rational or irrational. Numbers that are not "real" are called imaginary. Imaginary numbers are used by mathematicians to describe numbers that cannot be found on the number line. They are a more complex subject than we will work with here.
Rational Numbers
We call the set of real integers and fractions "rational numbers."Rational comes from the word "ratio" because a rational number can always be written as the ratio, or quotient, of two integers.
Examples of rational numbers
The fraction ½ is the ratio of 1 to 2.
Since three can be expressed as three over one, or the ratio of 3 to one, it is also a rational number.
The number "0.57" is also a rational number, as it can be written as a fraction.
Irrational Numbers
Some real numbers can't be expressed as a quotient of two integers. We call these numbers "irrational numbers". The decimal form of an irrational number is a non-repeating and non-terminating decimal number. For example, you are probably familiar with the number called "pi". This irrational number is so important that we give it a name and a special symbol!
Pi cannot be written as a quotient of two integers, and its decimal form goes on forever and never repeats.
Translating Words into Algebra Language
Here are some statements in English. Just below each statement is its translation in algebra.
the sum of three times a number and eight
3x + 8
The words "the sum of" tell us we need a plus sign because we're going to add three times a number to eight. The words "three times" tell us the first term is a number multiplied by three.
In this expression, we don't need a multiplication sign or parenthesis. Phrases like "a number" or "the number" tell us our expression has an unknown quantity, called a variable. In algebra, we use letters to represent variables.
the product of a number and the same number less 3
x(x – 3)
The words "the product of" tell us we're going to multiply a number times the number less 3. In this case, we'll use parentheses to represent the multiplication. The words "less 3" tell us to subtract three from the unknown number.
a number divided by the same number less five
The words "divided by" tell us we're going to divide a number by the difference of the number and 5. In this case, we'll use a fraction to represent the division. The words "less 5" tell us we need a minus sign because we're going to subtract five.
When an expression contains more than one operation, you can get different answers depending on the order in which you solve the expression. Mathematicians have agreed on a certain order for evaluating expressions, so we all arrive at the same answers. We often use grouping symbols, like parentheses, to help us organize complicated expressions into simpler ones. Here's the order we use:
- First, do all operations that lie inside parentheses.
- Next, do any work with exponents or roots.
- Working from left to right, do all multiplication and division.
- Finally, working from left to right, do all addition and subtraction.
In Example 1, without any parentheses, the problem is solved by working from left to right and performing all the addition and subtraction. When parentheses are used, you first perform the operations inside the parentheses, and you'll get a different answer!
Example 1 - Parenthesis
Without Parenthesis | With Parenthesis |
8 - 7 + 3 = | 8 - (7 + 3) = |
Example 2
Order of Operations | Explanation |
22 x 20/4 - 7 x 3 + 55 = | Calculate the exponent |
4 x 20/4 - 7 x 3 + 55 = 4 x 5 - 21 + 55 = OR 80/4 - 21 + 55 = (4 x 5 and 80/4 both = 20) | Working from left to right, do all multiplications and divisions. When there are several of these operations in the same term, the order within the term doesn't matter |
20 - 21 + 55 = | Add and subtract from left to right |
54 | The correct answer! |
source : www.math.com