Assignment 5.
Square Equation ( translate book )
Reference: Erlangga, page 182 – 193
7.1 Definition of square equation
Look at some equation below
a) P^2-4 = 0
b) q^2 – 9q = 0
Every equation above only have one variable, and the highest power of variable is two. Equation
a) 2x^2 + 3x -2 = 0; a=2, b=3, c=-2
b) x^2-6x+9=0; a=1 b=-6 c=9
solving or roots of square equation of x are changer of x such that equation become correct.
Example 7.1
I equation x square minus 16 times equals zero
If x change by 4 so 4^2-16=0,
16 – 16=0 ( is correct )
If x change by -4 so -4^2-16=0,
16 – 16=0 ( is correct )
And so roots of equation x^2 – 16=0 is correct for 4 or -4
If x change by 2 so (2^2)-16=0,
4-16=-12(wrong)
If x change by 2 so (2^2)-16=0,
4-16=-12(wrong)
So 2 or (-2) are not roots of equation x^2-16=0. Actually roots of equation x^2-16=0 onli 4 or (-4). Lets try to other value of x!
There are three ways to solve square equation, there are by factoring , by complete the perfect square, and by using formula.
7.2 Solve Square equation by Factoring
We have known that multiply by zero will be product zero. On the contrary, a multiply if product zero, surely one its number that multiplied is zero.
Example:
If 3x=0 so that x=0
If 5(x-4)=0 so x-4=0
If pq=0 so p=0 or q=0
Example 7.2
1. Solve the square equation below :
a. x^2 +2x -3 =0
b. 3x^2=5x+2
c. 2x^2+6x=0
answers :
a. . x^2 +2x -3 =0
(x-1) (x+3)=0
X=1 or x=-3
b. 3x^2=5x+2
3x^2-5x-2=0
(3x+1)(x-2)=0
X=-1/3 or x=2
c. 2x^2+6x=0
2x(x+3)=0
2x=0 or x+3=0
X=0 or x=-3
2.Determine solving set of 9x^2 -4 =0
ANSWERS :
(3x-2)(3x+2)=0
X=-2/3 or x=2/3
Exercise 1
1. determine changer variable at every equation !
a. 3(3x-2)=0
b. p(p-4)=0
c. 2p(p+3)=0
d. (t-3)(t+1)=0
e. 5(t-2)(t+3)=0
f. (3n-4)^2=0
g. (-7n+1)(6n-5)=0
h. –(2m-5)(2m+5)=0
2. Solve equations by factoring!
a. 2x^2-x=0
b. 4x-6x^2=0
c. 9y^2-25=0
d. 16t^2-49=0
e. 3x^2-17x-6=0
3. Determine the solving sets of these equations
a. x^2+x=0
b. x^2-25=0
c. 9x^2-1=0
d. x^2+12x+35=0
4. Known 4 is one of solving roots of equation x^2+5=a(3x-a-2). Determine value of a.
5. Determine value of b if 5 is one of solving of equation 2x^2+x+b=0. Determine also the other solving.
7.2.1 Square equation in form of fraction
Oftentimes square equation writes by fraction form. To making to come easy, solve the equation, initially we must omit the denominator, by multiply by LCM (Least Common Multiply) of denominator.
Conclusion.
Steps to solving the square equation by complete prefect square are:
1. Place coefficient that have variable at left side and constant at right side.
2. Coefficient of x^2 must one
3. Add two side by square of half coefficient of x so that left side come perfect square
Kamis, 15 Januari 2009
Sabtu, 10 Januari 2009
final assignment( How difficult to explain math )
On Friday, 9th 2009 at 10.30pm, I try to explain about trigonometry to riza Aritara ( my lovely classmate) I explain about trigonometry function, and abot table trigonometry. First I explain about trigonometry function. This is my explanation:
> Trigonometry is study of right triangle
to remember you can use:
SOH is defined by sine equals opposite over hypotenuse
CAH is defined by cosine equals adjacent over hypotenuse
TOA is defined by tangent equals opposite over adjacent
Trigonometry function is only needed to know the values of side to find measure of an angle, figure out figure of all part of triangle.
Riza can understand may explanation very fast, and I give her a problem like this :
There is a right-triangle, with the length of opposite is 3, the length of adjacent is 4, and the length of hypotenuse is 5. And there is angle-x in front of the right-angle, and there is angle-m above the right-angle. What is the value of sinus of x, cosines of x, and tangent of x?
Riza can answer it correctly, although sometimes she is wrong to use the function of basic trigonometry, this is her correct answers :
SOH is defined by “Sinus is Opposite over Hypotenuse”, CAH is defined by “Cosine is Adjacent over Hypotenuse”, and TOA is defined by “Tangent is Opposite over Adjacent”.
So we get,
Sin x = Opp/Hyp = 4/5
Cos x = Adj/Hyp = 3/5
Tan x = Opp/Adj = 4/3
second, I explain about table trigonometry, there is:
sin 0=0, sin30=half, sin 45=half square root of two, sin 60=half square root of three and sin 90=1
cos 0=1, cos30=half square root of three, sin 45=half square root of two, cos 60=half and cos 90=0
for this table, riza has any problem to remember the table, I teach riza to remember faster by using our fingers. To sinus table, we start from thumb finger to little finger, there are sin 0=0, sin30=half, sin 45=half square root of two, sin 60=half square root of three and sin 90=1
To cosine table, we start from little finger to thumb finger.
for conclusion my problem to explain math to Riza aritara are: its very difficult to remember the table, second the function trigonometry has difficult to remember.
> Trigonometry is study of right triangle
to remember you can use:
SOH is defined by sine equals opposite over hypotenuse
CAH is defined by cosine equals adjacent over hypotenuse
TOA is defined by tangent equals opposite over adjacent
Trigonometry function is only needed to know the values of side to find measure of an angle, figure out figure of all part of triangle.
Riza can understand may explanation very fast, and I give her a problem like this :
There is a right-triangle, with the length of opposite is 3, the length of adjacent is 4, and the length of hypotenuse is 5. And there is angle-x in front of the right-angle, and there is angle-m above the right-angle. What is the value of sinus of x, cosines of x, and tangent of x?
Riza can answer it correctly, although sometimes she is wrong to use the function of basic trigonometry, this is her correct answers :
SOH is defined by “Sinus is Opposite over Hypotenuse”, CAH is defined by “Cosine is Adjacent over Hypotenuse”, and TOA is defined by “Tangent is Opposite over Adjacent”.
So we get,
Sin x = Opp/Hyp = 4/5
Cos x = Adj/Hyp = 3/5
Tan x = Opp/Adj = 4/3
second, I explain about table trigonometry, there is:
sin 0=0, sin30=half, sin 45=half square root of two, sin 60=half square root of three and sin 90=1
cos 0=1, cos30=half square root of three, sin 45=half square root of two, cos 60=half and cos 90=0
for this table, riza has any problem to remember the table, I teach riza to remember faster by using our fingers. To sinus table, we start from thumb finger to little finger, there are sin 0=0, sin30=half, sin 45=half square root of two, sin 60=half square root of three and sin 90=1
To cosine table, we start from little finger to thumb finger.
for conclusion my problem to explain math to Riza aritara are: its very difficult to remember the table, second the function trigonometry has difficult to remember.
tugas 4( explain the 8 video )
grammar
Tata bahasa adalah bagaimana bagian-bagian dari bahasa dihubungkan untuk membemtuk sebuah kalimat. Tipe kalimat yang paling dasar adalah simple sentence (kalimat sederhana). Dikatakan sederhana karena semua elemen di dalam kalimat tersebut terdiri dari subjek dan predikat. Subjek menunjukkan kegiatan dari kata kerja utama. Subjek utama adalah kata benda khusus yang menunjukkan sebuah kegiatan.
Contoh:
The happy litle child kicked the gnome over fence.
The happy litle child merupakan subjek.
Happy litle menghubungkan subjek sederhana child.
Child menunjukkan kata kerja “kick”
Predikat dari sebuah kalimat terdiri dari:
Main verb (kata kerja utama) + apapun yang mengikutinya.
Gabungan keduanya disebut predikat yang lengkap. Pada kalimat “The happy litle child kicked the gnome over fence” kita dapat mengidentifikasikan kata “kicked” sebagai kata kerja (predikat sederhana). Karena “the gnome” dan “over the fence” menunjukkan lebih jauh lagi tentang apa yang ditendang dan bagaimana tendangan itu. “Kicked the gnome over fence” merupakan predikat yang lengkap.
Kalimat sederhana dapat diperoleh tanpa subjek dan predikat. Kalimat perintah merupakan kalimat yang ditunjukkan langsung pada orang kedua yang adalah “kamu” atau memerintahkan seseorang untuk melakukan sesuatu.
Contoh:
Kicked the gnome over fence.
Kalimat diatas merupakan pedikat yang lengkap, tidak memiliki subjek. Dan siapa sebenarnya yang melakukan kegiatan tersebut? Jawabannya adlah “kamu”. Kalimat tersebut dapat ditulis menjadi “hey you, kick the gnome over fence!”. Dalam kalimat tersebut kata “you” tidak perlu ada karena sudah tersirat.
Kata kerja
Kata keja menunjukkan sebuah kegiatan atau untuk menjelaskan sebuah kegiatan atau menunjukkan apa yang sedang dilakukan oleh suatu benda atau seseorang. Kata kerja sangat penting ada dalam suatu kalimat.
Contoh:
Dave runs
“Run” adalah kata kerja yang menunjukkan apa yang sedang dilakukan oleh Dave.
Dalam bahasa inggris, kata kerja berubah bentuk untuk menunjukkan suatu kegiatan.
Misalnya:
I do, you do, we do, he does, she does, they do, it does.
Contoh:
Dave runs
Jika subjeknya diganti menjadi “i”, maka kalimatnya akan berubah menjadi “i run”. Kata kerja berubah karena perbedaan subjek. Dalam hal ini, subjek “i, you, we, they” menggunakan kata kerja “run”, sedangkan subjek “he, she, it” menggunakan kata keja “runs”.
Kata kerja dalam bentuk “to be” adalah:
“I am, you are, she is, he is, it is” merupakan singular subjek atau kata ganti tunggal. Sedangkan “we are, they are” merupakan plural subjek atau kata ganti jamak. Kata gan6ti tunggal diikuti oleh akta kerja tunggal, dan kata ganti jamak diikuti oleh kata kerja jamak.
Contoh:
Ms. Midori yodels
“Ms. Midori” merupakan kata ganti tunggal, dan “yodels” merupakan kata kerja tunggal.
Ms. Midori’s sister: Else, Gretel, Heidi.
“Else, Gretel, Heidi” merupakan kata ganti jamak
Else, Gretel, Heidi yodel
“yodel” merupakan kata kerja jamak
Dengan kata lain kita dapat menuliskannya sebagai berikut:
I yodel, you yodel, we yodel, they yodel, she yodels, he yodels, it yodels.
Kata keterangan
Adverb (kata keterangan) adalah kata yang menjelaskan verb (kata kerja), adjective (kata sifat), and adverb-adverb lainnya. Adverb digunakan untuk menjawab pertanyaan dengan kata Tanya “how?, how often?, when?, to what extend?”.
Sangat mudah untuk membentuk sebuah adverb. Caranya adalah adjective (kata sifat) dan diakhiri dengan akhiran –ly.
Contoh:
Simon might be ‘slow”, but he talks ‘slowly”.
Kata “slow” menjelaskan Simon. “Slow” = adjective.
Kata “slowly” menjawab pertanyaan “how does Simon talk? (bagaimana Simon berbicara)”. “Slowly” = adverb.
The color of these mushrooms is slightly different.
Slightly = slight + (-ly)
Sekarang mari kita pelajari tentang adverb yang diikuti oleh adverb-adverb lainnya.
Contoh:
This mushroom is very definitely poisonous.
“Poisonous” (adjective) dimodifikasikan oleh kata “definitely” (adverb).
Sedangkan “definitely” dijelaskan oleh adverb lain, yaitu kata “very”.
Pada umumnya kata “very” adalah adverb yang digunakan untuk menjelaskan adverb lainnya. “very” digunakan sebagai adverb dan tidak diakhiri dengan akhiran (-ly).
Sekarang kita akan mempelajari tenteng pengecualian dalam penggunaan akhiran “-ly” dalam adverb. Misal, untuk kata sifat (adjective) “ good” dan “fast” bila diubah dalam bentuk adverb, maka kita tidak boleh sembarang mengubahnya menjadi “goodly” dan “fastly” karena kedua kata itu salah.
Untuk kata “good”, bila kita akan menjawab pertanyaan “how?” maka kita menggunakan kata “well” sebagai adverb.
Contoh:
Candace can play the accordion very well.
Kata “well” adalah adverb yang dibentuk dari “good” (adjective).
Dan untuk pertanyaan “how Candace can play?” maka jawabannya adalah “candace’s playing is good”. Sedangkan good adalah kata sifat (adjective) yang menjelaskan gerund “playing”.
Ingat, gerund dapat dibentuk dari “verb (kata keja) + (-ing)”, dan digunakan sebagai kata benda (noun).
Basic trigonometry
Trigonometry comes from greek, they are trigon and metron. Trigonometry is really study of rectangle and the relationship between the side and the angle of rectangle. There is a right-triangle, with the length of opposite is 3, the length of adjacent is 4, and the length of hypotenuse is 5. And there is angle-x in front of the right-angle, and there is angle-m above the right-angle. What is the value of sinus of x, cosines of x, and tangent of x?
To solve them, use the simple trigonometry, they are SOH CAH TOA.
SOH is defined by “Sinus is Opposite over Hypotenuse”, CAH is defined by “Cosine is Adjacent over Hypotenuse”, and TOA is defined by “Tangent is Opposite over Adjacent”.
So we get,
Sin x = Opp/Hyp = 4/5
Cos x = Adj/Hyp = 3/5
Tan x = Opp/Adj = 4/3
If the angle is m, so we get tan m = ¾, the inverse of tangent x.
Kalimat majemuk
“it is the end of the world as we know it and I feel fine”. Dalam kalimat tersebut terdapat 2 klausa yang dihubungkan dengan 1 kata penghubung, yaitu “and”. Ketika suatu kalimat digunakan sebagai bagian-bagian dalam kalimat yang lebih besar, maka kalimat yang lebih kecil disebut klausa. Ketika sebuah klausa dapat berdiri sendiri dalam sebuah kalimat, maka klausa tersebut disebut “ndependent clause”. Dan jika kita memiliki 2 klausa dalam sebuah kalimat, maka kalimat tersebut disebut kalimat majemuk.
Untuk menggabungkan 2 independent clause, kita dapat menggunakan:
Tanda titik dua (:), ketika klausa ke-2 menjelaskan klausa ke-1.
Contoh:
I love my two sisters, they bake me pie
Untuk menggabungkan kalimat menjadi kalimat majemuk kita gunakan titik dua (:).
Kalimat di atas menjadi: “I love my two sisters: they bake me pie”
Titik koma (;), untuk menggantikan konjungsi.
Contoh:
“it is the end of the world as we know it and I feel fine”
Kalimat di atas dapat dipersingkat menjadi:
“it is the end of the world; I feel fine”
Garis penghubung (-)
Menggunakan garis penghubung karena klausa ke-2 dihubungkan dengan klausa ke-1.
Dengan demikian, dapat disimpulkan bahwa untuk menggabungkan kalimat ada 4 cara, yaitu:
Kata penghubung
Tanda titik dua (:)
Tanda titik koma (;)
Garis penghubung
Kalimat fragmen dapat didefinisikian jika kita mendapat porsi dalam suatu kalimat yang tidak dapat berdiri sendiri sebagai kalimat lengkap.
Contoh:
“My pet komodo dragon is as gentle as a lamb” merupakan kalimat lengkap.
“because he has no teeth” merupakan kalimat fragmen.
Dependent clause adalah klausa yang tidak dapat berdiri sendiri, terdapat pada klausa independent, dan bukan merupakan kalimat lengkap.
Kalimat kompleks terdiri dari:
Klausa dependent + klausa independent
Contoh:
Although Tom sleeps regulery, he is constantly tired.
“Although Tom sleeps regulery” merupakan klausa dependen.
“He is constantly tired” merupakan klausa independent.
“Although Tom sleeps regulary, he is constantly tired” merupakan kalimat kompleks.
Limit by inspection
There are two conditions, they are:
X goes to positive or negative infinity
Limit involves a polynomial divided by a polynomial
For example:
Limit of the function x cube plus four divided by x square plus x plus one as x approaches infinity. This problem is caused of two conditions, they are:
Polynomial over polynomial
X approaches infinity
The key to determine the limits by inspection is in looking at powers of x in the numerator and the denominator.
Remember!
To apply this rules, the things which must we do are:
We must be dividing by polynomials
X has to be approaching infinity
The first shortcut rule
If the highest power of x is greater in numerator, then limit is positive or negative infinity. X cube plus four divided by x square plus x plus one as x approaches infinity equals infinity equals positive or negative infinity. From that function we get three at x cube is the highest power of x in numerator. Two at x square is the highest power of x in denominator. Limit of function x cube plus four divided by x square plus x plus one as x approaches infinity equals infinity equals positive or negative infinity. It can be happened Since all the number are positive and x is going to positive infinity.
If you cannot tell it, the answer is positive or negative. And the rule is:
Substitute a large number for x
See if you end up with a positive or negative number
Whatever sign you get is the sign of infinitive for the limit
The second shortcut rule
If the highest power of x is in the denominator, then the limit is zero let limit of x square plus three divided by x cube plus one as x approaches infinitive equals zero. To at x square is highest power of x in numerator, and three x cube is the highest power of x in denominator
The third shortcut rule
This rule is used when the highest power of x in numerator is same as highest power of x in denominator. Limit of a function as x approach positive or negative infinity has the quotient on the coefficients at the two highest powers.
Remember!
Coefficient is the number that goes with a variable.
Example : two is the coefficient of two times x square, seventy five is the coefficient of seventy five times x fourth
The last shortcut rule
Limit of four time x cube plus x square plus one divided by three times x cube plus four as x approaches infinity has three as highest power at numerator and denominator
According to this rule, with conclude that the coefficient of x cube is over each other for example :
Limit of four time x cube plus x square plus one divided by three times x cube plus four as x approaches infinity equals four over three.
Pre-calculus
Graph of a rational function can be discontinuities because it has polynomial in the denominator. Is possible value x divide by zero?
Example: there is a function f, it is f of x equals x plus two divided by x minus one. If we insert x equals one, we get the value of f of one equals one plus two divided by one minus one equals three divided by zero. We know that three divided by zero is bad idea and the graph f of x equals x plus two divided by x minus one will break in function graph. If we insert x equals zero, we will get the function f of zero equals zero plus two divided by zero minus one equals negative two.
We will draw graph f of x equals x plus two divided by x minus one in the x y-coordinate plane. First we draw x y-coordinate plane, then we draw the graph f of x equals x plus two divided by x minus one as we know that this graph intersects axis y at point (0, -2), then we can draw the graph which through point (0, -2) and approach axis x in axis positive y. So we can say that graph f of x equals x plus two divided by x minus one is break. On the contrary, if there is line x equals one, so the graph approaches this line and axis positive x is discontinue.
Rational function does not always work this way!
Not all rational functions will give zero in denominator. Take the graph f of x equals one over x square plus one, it’s denominator never zero because of plus one and of course this graph is not break in function graph.
Do not forget!
Rational function denominator can be zero if the polynomial have smooth and unbroken curve and for rational function x equals zero in denominator, because that is impossible situation. It is impossible because there is not value for the function, so make break in function graph.
The break is showed up by two ways!
First, it can break in graph function because of the missing point in the graph. For example the graph f of x equals x square minus x minus six over x minus three has missing point at line x equals three. It can be happened because if we insert x equals three to the graph, so we get f of three equals three square minus three minus three over three minus three equals zero over zero. It can break because the value zero over zero is not possible, not feasible and not allowed. Typical f of three equals three square minus three minus three over three minus three equals zero over zero named missing point syndrome. If the result is zero over zero, to solve this problem we can make the factor top and button to be simplify. For example, y equals x square minus x minus six over x minus three. We get the top factor are x minus three and x plus two, the button factor is x minus three. So we can write y equals (x minus three) times (x plus two) over x minus three, and we can divide numerator and nominator with x minus three so we get y equals x plus two. Now, it is not problem if we insert x equals three to the new function y equals x plus two.
Trigonometry function
Now we will describe aright-triangle. Take x as the angle in front of the right-angle. The length of opposite is four, the length of adjacent is three and the length of hypotenuse is five.
To remember it you can see:
SOH is defined by sine equals opposite over hypotenuse
CAH is defined by cosine equals adjacent over hypotenuse
TOA is defined by tangent equals opposite over adjacent
Trigonometry function is only needed to know the values of side to find measure of an angle, figure out figure of all part of triangle. Things is included in trigonometry function are sine, cosine, tangent, cosecant , secant, cotangent. There are six basic of trigonometry function :
Sides of a triangle
Angel being measured
So we conclude that opposite equals side opposite to x, adjacent equals side adjacent to x.
Sin x equals opposite over hypotenuse, cosine x equals over hypotenuse, tangent x equals opposite over adjacent, cosecant x equal hypotenuse over opposite, secant x equals hypotenuse over adjacent, cotangent adjacent over opposite.
Tata bahasa adalah bagaimana bagian-bagian dari bahasa dihubungkan untuk membemtuk sebuah kalimat. Tipe kalimat yang paling dasar adalah simple sentence (kalimat sederhana). Dikatakan sederhana karena semua elemen di dalam kalimat tersebut terdiri dari subjek dan predikat. Subjek menunjukkan kegiatan dari kata kerja utama. Subjek utama adalah kata benda khusus yang menunjukkan sebuah kegiatan.
Contoh:
The happy litle child kicked the gnome over fence.
The happy litle child merupakan subjek.
Happy litle menghubungkan subjek sederhana child.
Child menunjukkan kata kerja “kick”
Predikat dari sebuah kalimat terdiri dari:
Main verb (kata kerja utama) + apapun yang mengikutinya.
Gabungan keduanya disebut predikat yang lengkap. Pada kalimat “The happy litle child kicked the gnome over fence” kita dapat mengidentifikasikan kata “kicked” sebagai kata kerja (predikat sederhana). Karena “the gnome” dan “over the fence” menunjukkan lebih jauh lagi tentang apa yang ditendang dan bagaimana tendangan itu. “Kicked the gnome over fence” merupakan predikat yang lengkap.
Kalimat sederhana dapat diperoleh tanpa subjek dan predikat. Kalimat perintah merupakan kalimat yang ditunjukkan langsung pada orang kedua yang adalah “kamu” atau memerintahkan seseorang untuk melakukan sesuatu.
Contoh:
Kicked the gnome over fence.
Kalimat diatas merupakan pedikat yang lengkap, tidak memiliki subjek. Dan siapa sebenarnya yang melakukan kegiatan tersebut? Jawabannya adlah “kamu”. Kalimat tersebut dapat ditulis menjadi “hey you, kick the gnome over fence!”. Dalam kalimat tersebut kata “you” tidak perlu ada karena sudah tersirat.
Kata kerja
Kata keja menunjukkan sebuah kegiatan atau untuk menjelaskan sebuah kegiatan atau menunjukkan apa yang sedang dilakukan oleh suatu benda atau seseorang. Kata kerja sangat penting ada dalam suatu kalimat.
Contoh:
Dave runs
“Run” adalah kata kerja yang menunjukkan apa yang sedang dilakukan oleh Dave.
Dalam bahasa inggris, kata kerja berubah bentuk untuk menunjukkan suatu kegiatan.
Misalnya:
I do, you do, we do, he does, she does, they do, it does.
Contoh:
Dave runs
Jika subjeknya diganti menjadi “i”, maka kalimatnya akan berubah menjadi “i run”. Kata kerja berubah karena perbedaan subjek. Dalam hal ini, subjek “i, you, we, they” menggunakan kata kerja “run”, sedangkan subjek “he, she, it” menggunakan kata keja “runs”.
Kata kerja dalam bentuk “to be” adalah:
“I am, you are, she is, he is, it is” merupakan singular subjek atau kata ganti tunggal. Sedangkan “we are, they are” merupakan plural subjek atau kata ganti jamak. Kata gan6ti tunggal diikuti oleh akta kerja tunggal, dan kata ganti jamak diikuti oleh kata kerja jamak.
Contoh:
Ms. Midori yodels
“Ms. Midori” merupakan kata ganti tunggal, dan “yodels” merupakan kata kerja tunggal.
Ms. Midori’s sister: Else, Gretel, Heidi.
“Else, Gretel, Heidi” merupakan kata ganti jamak
Else, Gretel, Heidi yodel
“yodel” merupakan kata kerja jamak
Dengan kata lain kita dapat menuliskannya sebagai berikut:
I yodel, you yodel, we yodel, they yodel, she yodels, he yodels, it yodels.
Kata keterangan
Adverb (kata keterangan) adalah kata yang menjelaskan verb (kata kerja), adjective (kata sifat), and adverb-adverb lainnya. Adverb digunakan untuk menjawab pertanyaan dengan kata Tanya “how?, how often?, when?, to what extend?”.
Sangat mudah untuk membentuk sebuah adverb. Caranya adalah adjective (kata sifat) dan diakhiri dengan akhiran –ly.
Contoh:
Simon might be ‘slow”, but he talks ‘slowly”.
Kata “slow” menjelaskan Simon. “Slow” = adjective.
Kata “slowly” menjawab pertanyaan “how does Simon talk? (bagaimana Simon berbicara)”. “Slowly” = adverb.
The color of these mushrooms is slightly different.
Slightly = slight + (-ly)
Sekarang mari kita pelajari tentang adverb yang diikuti oleh adverb-adverb lainnya.
Contoh:
This mushroom is very definitely poisonous.
“Poisonous” (adjective) dimodifikasikan oleh kata “definitely” (adverb).
Sedangkan “definitely” dijelaskan oleh adverb lain, yaitu kata “very”.
Pada umumnya kata “very” adalah adverb yang digunakan untuk menjelaskan adverb lainnya. “very” digunakan sebagai adverb dan tidak diakhiri dengan akhiran (-ly).
Sekarang kita akan mempelajari tenteng pengecualian dalam penggunaan akhiran “-ly” dalam adverb. Misal, untuk kata sifat (adjective) “ good” dan “fast” bila diubah dalam bentuk adverb, maka kita tidak boleh sembarang mengubahnya menjadi “goodly” dan “fastly” karena kedua kata itu salah.
Untuk kata “good”, bila kita akan menjawab pertanyaan “how?” maka kita menggunakan kata “well” sebagai adverb.
Contoh:
Candace can play the accordion very well.
Kata “well” adalah adverb yang dibentuk dari “good” (adjective).
Dan untuk pertanyaan “how Candace can play?” maka jawabannya adalah “candace’s playing is good”. Sedangkan good adalah kata sifat (adjective) yang menjelaskan gerund “playing”.
Ingat, gerund dapat dibentuk dari “verb (kata keja) + (-ing)”, dan digunakan sebagai kata benda (noun).
Basic trigonometry
Trigonometry comes from greek, they are trigon and metron. Trigonometry is really study of rectangle and the relationship between the side and the angle of rectangle. There is a right-triangle, with the length of opposite is 3, the length of adjacent is 4, and the length of hypotenuse is 5. And there is angle-x in front of the right-angle, and there is angle-m above the right-angle. What is the value of sinus of x, cosines of x, and tangent of x?
To solve them, use the simple trigonometry, they are SOH CAH TOA.
SOH is defined by “Sinus is Opposite over Hypotenuse”, CAH is defined by “Cosine is Adjacent over Hypotenuse”, and TOA is defined by “Tangent is Opposite over Adjacent”.
So we get,
Sin x = Opp/Hyp = 4/5
Cos x = Adj/Hyp = 3/5
Tan x = Opp/Adj = 4/3
If the angle is m, so we get tan m = ¾, the inverse of tangent x.
Kalimat majemuk
“it is the end of the world as we know it and I feel fine”. Dalam kalimat tersebut terdapat 2 klausa yang dihubungkan dengan 1 kata penghubung, yaitu “and”. Ketika suatu kalimat digunakan sebagai bagian-bagian dalam kalimat yang lebih besar, maka kalimat yang lebih kecil disebut klausa. Ketika sebuah klausa dapat berdiri sendiri dalam sebuah kalimat, maka klausa tersebut disebut “ndependent clause”. Dan jika kita memiliki 2 klausa dalam sebuah kalimat, maka kalimat tersebut disebut kalimat majemuk.
Untuk menggabungkan 2 independent clause, kita dapat menggunakan:
Tanda titik dua (:), ketika klausa ke-2 menjelaskan klausa ke-1.
Contoh:
I love my two sisters, they bake me pie
Untuk menggabungkan kalimat menjadi kalimat majemuk kita gunakan titik dua (:).
Kalimat di atas menjadi: “I love my two sisters: they bake me pie”
Titik koma (;), untuk menggantikan konjungsi.
Contoh:
“it is the end of the world as we know it and I feel fine”
Kalimat di atas dapat dipersingkat menjadi:
“it is the end of the world; I feel fine”
Garis penghubung (-)
Menggunakan garis penghubung karena klausa ke-2 dihubungkan dengan klausa ke-1.
Dengan demikian, dapat disimpulkan bahwa untuk menggabungkan kalimat ada 4 cara, yaitu:
Kata penghubung
Tanda titik dua (:)
Tanda titik koma (;)
Garis penghubung
Kalimat fragmen dapat didefinisikian jika kita mendapat porsi dalam suatu kalimat yang tidak dapat berdiri sendiri sebagai kalimat lengkap.
Contoh:
“My pet komodo dragon is as gentle as a lamb” merupakan kalimat lengkap.
“because he has no teeth” merupakan kalimat fragmen.
Dependent clause adalah klausa yang tidak dapat berdiri sendiri, terdapat pada klausa independent, dan bukan merupakan kalimat lengkap.
Kalimat kompleks terdiri dari:
Klausa dependent + klausa independent
Contoh:
Although Tom sleeps regulery, he is constantly tired.
“Although Tom sleeps regulery” merupakan klausa dependen.
“He is constantly tired” merupakan klausa independent.
“Although Tom sleeps regulary, he is constantly tired” merupakan kalimat kompleks.
Limit by inspection
There are two conditions, they are:
X goes to positive or negative infinity
Limit involves a polynomial divided by a polynomial
For example:
Limit of the function x cube plus four divided by x square plus x plus one as x approaches infinity. This problem is caused of two conditions, they are:
Polynomial over polynomial
X approaches infinity
The key to determine the limits by inspection is in looking at powers of x in the numerator and the denominator.
Remember!
To apply this rules, the things which must we do are:
We must be dividing by polynomials
X has to be approaching infinity
The first shortcut rule
If the highest power of x is greater in numerator, then limit is positive or negative infinity. X cube plus four divided by x square plus x plus one as x approaches infinity equals infinity equals positive or negative infinity. From that function we get three at x cube is the highest power of x in numerator. Two at x square is the highest power of x in denominator. Limit of function x cube plus four divided by x square plus x plus one as x approaches infinity equals infinity equals positive or negative infinity. It can be happened Since all the number are positive and x is going to positive infinity.
If you cannot tell it, the answer is positive or negative. And the rule is:
Substitute a large number for x
See if you end up with a positive or negative number
Whatever sign you get is the sign of infinitive for the limit
The second shortcut rule
If the highest power of x is in the denominator, then the limit is zero let limit of x square plus three divided by x cube plus one as x approaches infinitive equals zero. To at x square is highest power of x in numerator, and three x cube is the highest power of x in denominator
The third shortcut rule
This rule is used when the highest power of x in numerator is same as highest power of x in denominator. Limit of a function as x approach positive or negative infinity has the quotient on the coefficients at the two highest powers.
Remember!
Coefficient is the number that goes with a variable.
Example : two is the coefficient of two times x square, seventy five is the coefficient of seventy five times x fourth
The last shortcut rule
Limit of four time x cube plus x square plus one divided by three times x cube plus four as x approaches infinity has three as highest power at numerator and denominator
According to this rule, with conclude that the coefficient of x cube is over each other for example :
Limit of four time x cube plus x square plus one divided by three times x cube plus four as x approaches infinity equals four over three.
Pre-calculus
Graph of a rational function can be discontinuities because it has polynomial in the denominator. Is possible value x divide by zero?
Example: there is a function f, it is f of x equals x plus two divided by x minus one. If we insert x equals one, we get the value of f of one equals one plus two divided by one minus one equals three divided by zero. We know that three divided by zero is bad idea and the graph f of x equals x plus two divided by x minus one will break in function graph. If we insert x equals zero, we will get the function f of zero equals zero plus two divided by zero minus one equals negative two.
We will draw graph f of x equals x plus two divided by x minus one in the x y-coordinate plane. First we draw x y-coordinate plane, then we draw the graph f of x equals x plus two divided by x minus one as we know that this graph intersects axis y at point (0, -2), then we can draw the graph which through point (0, -2) and approach axis x in axis positive y. So we can say that graph f of x equals x plus two divided by x minus one is break. On the contrary, if there is line x equals one, so the graph approaches this line and axis positive x is discontinue.
Rational function does not always work this way!
Not all rational functions will give zero in denominator. Take the graph f of x equals one over x square plus one, it’s denominator never zero because of plus one and of course this graph is not break in function graph.
Do not forget!
Rational function denominator can be zero if the polynomial have smooth and unbroken curve and for rational function x equals zero in denominator, because that is impossible situation. It is impossible because there is not value for the function, so make break in function graph.
The break is showed up by two ways!
First, it can break in graph function because of the missing point in the graph. For example the graph f of x equals x square minus x minus six over x minus three has missing point at line x equals three. It can be happened because if we insert x equals three to the graph, so we get f of three equals three square minus three minus three over three minus three equals zero over zero. It can break because the value zero over zero is not possible, not feasible and not allowed. Typical f of three equals three square minus three minus three over three minus three equals zero over zero named missing point syndrome. If the result is zero over zero, to solve this problem we can make the factor top and button to be simplify. For example, y equals x square minus x minus six over x minus three. We get the top factor are x minus three and x plus two, the button factor is x minus three. So we can write y equals (x minus three) times (x plus two) over x minus three, and we can divide numerator and nominator with x minus three so we get y equals x plus two. Now, it is not problem if we insert x equals three to the new function y equals x plus two.
Trigonometry function
Now we will describe aright-triangle. Take x as the angle in front of the right-angle. The length of opposite is four, the length of adjacent is three and the length of hypotenuse is five.
To remember it you can see:
SOH is defined by sine equals opposite over hypotenuse
CAH is defined by cosine equals adjacent over hypotenuse
TOA is defined by tangent equals opposite over adjacent
Trigonometry function is only needed to know the values of side to find measure of an angle, figure out figure of all part of triangle. Things is included in trigonometry function are sine, cosine, tangent, cosecant , secant, cotangent. There are six basic of trigonometry function :
Sides of a triangle
Angel being measured
So we conclude that opposite equals side opposite to x, adjacent equals side adjacent to x.
Sin x equals opposite over hypotenuse, cosine x equals over hypotenuse, tangent x equals opposite over adjacent, cosecant x equal hypotenuse over opposite, secant x equals hypotenuse over adjacent, cotangent adjacent over opposite.
explain video Do You Believe in Me
Assignment 2.
Do You Believe in Me
A boy stand on the stage. He is a student from Dallas. He say all of his friends, and all of his friends, and all of people in that room. He ask them about himself. He can do anything, be anything, create anything, become anything. His name is Dalton Sherman. He very brave and confident, He enthusiasm to tell it.
Although Dallas has many student from some region, but Dallas can do anything. Dallas can produced useful to the city. He say that every single one of us can be graduate, ready for college, and can get workplace. We are ( Charles Rice Learning Center ) all showing up in their school. He ask the to believe him about we can reach a highest potential.
Whether they are a counselor, on librarian, a teacher assistant or work in the front office, whether you serve up meals in the cafeteria, Dalton needs themselves. What they doing is most important job in the city today. There’s probably easier ways to make a living. They must believe that Dallas student can achieve. He trust that all of people in Dallas can become a success people.
Do You Believe in Me
A boy stand on the stage. He is a student from Dallas. He say all of his friends, and all of his friends, and all of people in that room. He ask them about himself. He can do anything, be anything, create anything, become anything. His name is Dalton Sherman. He very brave and confident, He enthusiasm to tell it.
Although Dallas has many student from some region, but Dallas can do anything. Dallas can produced useful to the city. He say that every single one of us can be graduate, ready for college, and can get workplace. We are ( Charles Rice Learning Center ) all showing up in their school. He ask the to believe him about we can reach a highest potential.
Whether they are a counselor, on librarian, a teacher assistant or work in the front office, whether you serve up meals in the cafeteria, Dalton needs themselves. What they doing is most important job in the city today. There’s probably easier ways to make a living. They must believe that Dallas student can achieve. He trust that all of people in Dallas can become a success people.
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