problem n solution

Problem solving

1. Thermometer reading 75^oF is taken out where temperature is 20^oF. The reading is 30^oF 4 minutes later. Find:

a.)Thermometer reading 7 minutes after the thermometer was brought outside. b.)The time taken for the reading to drop from 75^oF to within a half degree of the air temperature

2. Proved the identity of trigonometry

3. Determine the differential equation in behind

4. If y=x²-4x and x=

, find when t=√2

5. Find the solution

Solution:

1. Known :

75^oF 30^oF

u is the thermometer temperature (^oF)

t is time (minutes)

when t=0 temperature is 75^o (u=75^o)

when t=4 temperature is 30^o (u=30^o)

-k = decrease of temperature in thermometer

(u-20)=difference of temperature

Differential equation

Substitution t=0 and u=75 in formula where we get it.

u=20+ce^-kt

75=20+ce^-k.0

75-20=ce⁰

55=c.1

c=55

the equation become u=20+55e^-kt

to find k, substitution t=4 and u=30^o

30=20+55e^-kt

10=55 e^-kt

e^4t=5,5

ln e^4k=ln5,5

4k lne=ln 5,5

k=

so u=20+55exp(-0,43t)

a) If t=7

And you input t in the formula so

u=20+55exp(-0,43.7)

=20+55.0,5

=22,7

So the thermometer reading 22,7^oF

b) If u=75/2=37,5

And you input u in the formula so

u=20+55exp(-0,43t)

37,5=20+55exp(-0,43t)

17,5=55exp(-0,43t)

17,5:55=exp(-0,43t)

So the time taken for the reading to drop from 75^oF whiting a half degree of the air temperature is 2,66 minutes

2.

Answer:

We choose left segment to prove it

So the equation proven

3.

we can write the differential equation

From that:

Integration factor :

The general solution differential equation is:

So the solution is

4. If

and

find






when t=√2

Answer:

If t=√2, x=√5 and

So the solution dy/dx is

5. Find the solution

Answer: Choose u=secx, dv=sec²xdx, so dv=secxtanxdx, v=tanx

so

So the solution

PREFACE

Firstly, we be grateful to Allah SWT because we still ability and given easily to review Mathematics for Junior High School year VIII. We would like to give thanks to Mr. Marsigit who give us opportunity to review this books.
We also to find some benefit that we have got while review Mathematics for Junior High School year VIII such as be knew more about the different between curriculum mathematics now with three years ago, we also remember t.o grammar and pronounsation.
\ We hope this review book useful. It is important to students and teachers of Junior High School as an opinion before buy mathematics book.
To release of this review book has been made possible due to the assistance and cooperation of team. So, we would to give thanks to all, which to help us to work this review task.
Comments and suggestions to improve this review book are always welcome and approved by us.

CONTENT

This books have 7 chapter. Each of the chapter different of discussion, but all of them are used to learn mathematics for Junior High School year VIII.
The materials divided into 2 unit
UNIT I ALGEBRA
Chapter 1. Algebra and Its Applications
2. The Relation and Functions
3. The Equations of a Straight Line
4. The System of Linear Equations in two variables
UNIT II GEOMETRY and Measurement
Chapter 5. The Pythagorean Theorem
6. A Circle
7. Polyhedral
The content of this book is very well, because this have some any surplus. We can looks, in every chapter are aranged by some subtitle. Subtitle can help the readers to make easier to learn. It is complete with the introduction,definitions,examples (and its problem solving), and some exercise. To remember some formula and teory which interest there is an “be remember” in some page in every chapter. This formula or material is briefly. So, it can help the students to remember this formula with study easily.
In addition, this books have exercise in every subitle and ending of the chapter.. exercise in the end of every chapter content of mathematics problems suitable to the material of every chapter. There are 20 multiple choices problem and 5 essays. At the end of every unit,there is an evaluation. This books also be completed with “final evaluation” at the last part. There are 30 multiple choices problems and10 essays. There are as more than understanding on material or teory for students.
This books is very well to students, because this books more than to go progress. This time, education in Indonesian to be experience development. Education system in Indonesia using KTSP system. So, this books to match with situation in our country.
Language this books composed by two languages. The are Indonesian language and English language in one book. Every Indonesian page translate to English language directly. This very useful, because with reading and learning this book, students not only can improve their mathematics skill and knowledge but also development their English language. This book is suitable to some school that pioneer their school to be world class school in Indonesia, school with international school standardization.
Finally, in ending this books given description about figure of mathematicians. This book is very useful and interesting so all students can learn very well. This my appraiser about this book. I hope we have to increase attention to learn and reading.

TECHNOLOGY

Technology used to create the book is very high, because:
1. Many use the graphic design. Graphic design software from a computer that is used to design the image. eg: corel draw, photo shop, etc..
Definition of Graphic Design: is a form of painting (picture) is applied to give freedom to the designer (the designer) to select, create, or set the form elements such as illustrations, photographs, writing, and a line on the surface with the goal to produce and communicated as a message. Images and signs that can be used typography or other media such as pictures or photographs.
Graphic design is generally applied in the world of advertising, packaging, film, and others.
Graphic Design is also a science to learn about the media to convey information, ideas, concepts, and so a call to the audience by using visual language. Whether it be any posts, images, illustrations, and so forth.
Graphic design is a solution that bridge the communication between the donor information with the public, either individuals, groups, institutions and communities that are widely expressed in the form of visual communication.
2. Mold is very good, and when viewed, the color printing is very clear, giving rise to the kemenarikan readers to read the book to complete. Ink used in the paper is also good and not faded.
3. Paper used is also very good not like a normal paper is used. Paper is thick and smooth. Paper that is used is also good because the more canggihnya technology that is used to make the paper.
So, the book can be very modern and very good quality.
By using the book, we can easily learn, because the book is very interesting for young readers, especially middle-school level first seen from the sophistication of technology. But also quite expensive when the book market, because more advanced technology used to create the book.

QUALITY

The quality of the book is very good and attract attention and interest of the readers . Quality can be seen for example in terms of a cover so it is very interesting to make people interested to read.To order any posts that are on the cover very neat and organized. Paper used in the making of the book is a paper that has good quality and good, is not easily torn and not easily damaged.
Ink used for writing also has a good quality that makes posts can be read with very clear, so you can ease the readers can understand and comprehend the contents of the book.
In addition, given the quality of color and light is very interesting, so the book has a charm for the readers who want to read and readers can see a basic summary of the discussion that has been dibacanya that can understand and be understood .
In the bindery is chosen so that the quality of a good book to make it look neat and organized and does not fall apart in it . Bindery also done very carefully so that the quality of the book looks good and more interesting.
Quality is a printing also have good quality because it is also printed with a very neat and organized so that the posts which are very neatly printed and does not fall apart. Printing is also require more attention in order not to reduce the quality of the book in order to obtain satisfactory results

.