أرجو المساعدة أسئلة باللغة الإنجليزية [الأرشيف]

مشاهدة النسخة كاملة : أرجو المساعدة أسئلة باللغة الإنجليزية

amk

11-11-2003, 10:19 PM

بحثت كثيرا وقرات كثرا الأجد حل لهده المسائل فلم اجد ارجو مساعدتي فأنا خارج الوطن ولا يوجد من يساعدني في حلهاا ارجو مساعدتي مشكورين

َQ1 FIND THE EQUATION OF THE LINE PASSING THROGH THE POINT (-1,2)AND IS PARALLEL TO THE LINE 2X-3Y=1

Q2FIND THE EQUATION OF THE CIRCLE AT (3,-2)AND PASSES THROUGH (-1<,2) ???ANS

Q3 FIND THE CENTER AND RADUIS OF THE CIRCLE WHOSE EQUATION IS X^2+Y^2+2X-4Y-4=0 AND OBTAIN THE POINTS OF INTERSECTION OF THIS CIRCLE AND THE
LINE Y=X-1

uaemath

12-11-2003, 12:57 AM

أهلا بك ،تفضل الحل:
إذا لم تستطع رؤية اللرموز عليك تحميل Java sun environment :

http://java.com/en/download/manual.jsp

َQ1 FIND THE EQUATION OF THE LINE PASSING THROGH THE POINT (-1,2)AND IS PARALLEL TO THE LINE 2X-3Y=1:

The equation of any straight line in general is:
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "100" height = "25" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "y-SUB(y;0)=m(x-SUB(x;0))"></applet></html>
where m is the slope and
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "59" height = "25" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "(SUB(x;0),SUB(y;0))"></applet></html>
is any point on the straight line.
We have the point which is (-1,2
that is:
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "81" height = "25" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "SUB(x;0)=-1,SUB(y;0)=2"></applet></html>
We need the slope m
since it is parallel to the straight line
2X-3Y=1
It has the same slope:Two parallel straight line have the same slope
therefore
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "73" height = "40" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "m = DIV(-2;-3)=DIV(2;3)"></applet></html>
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "90" height = "40" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "DIV(-coefficient of X;Coefficient of y)"></applet></html>
Hence:
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "103" height = "25" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "y -SUB(y;0)=m(x-SUB(x;0))"></applet></html>
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "104" height = "40" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "y -2 =DIV(2;3)(x-(-1))"></applet></html>
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "85" height = "40" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "y -2 =DIV(2;3)(x+1)"></applet></html>
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "85" height = "40" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "y -2 =DIV(2;3)(x+1)"></applet></html>
3Y -2X=8

uaemath

12-11-2003, 01:19 AM

Q2FIND THE EQUATION OF THE CIRCLE AT (3,-2)AND PASSES THROUGH (-1,2) ???ANS
the equation of a circle of center (a,b
and passing throuh the point
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "59" height = "25" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "(SUB(x;0),SUB(y;0))"></applet></html>
is:
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "133" height = "30" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "SUP((x-a);2)+SUP((y-b);2)=SUP(R;2)"></applet></html>
where R is the radius of the circle
which is the distance from the center to any point on the circle Therefore the radius R here is the distance between the points
(3,-2)AND
(-1,2)
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "191" height = "34" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "R = ROOT(SUP((SUB(x;2)-SUB(x;1));2)+SUP((SUB(y;2)-SUB(y;1));2);)"></applet></html>
Substituting ,you will get:
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "48" height = "30" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "SUP(R;2)=32"></applet></html>
Now:
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "133" height = "30" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "SUP((x-a);2)+SUP((y-b);2)=SUP(R;2)"></applet></html>

<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "127" height = "30" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "SUP((x-3);2)+SUP((y+2);2)=32"></applet></html>

uaemath

12-11-2003, 01:38 AM

Q3 FIND THE CENTER AND RADUIS OF THE CIRCLE WHOSE EQUATION IS X^2+Y^2+2X-4Y-4=0 AND OBTAIN THE POINTS OF INTERSECTION OF THIS CIRCLE AND THE
LINE Y=X-1
The general equation of the circle is:

<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "118" height = "30" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "SUP(x;2)+SUP(y;2)+ax+by+c=0"></applet></html>
The center is given by :

<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "197" height = "40" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "(DIV(-coefficient of x;2),DIV(-coefficient of y;2))"></applet></html>
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "105" height = "40" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "(DIV(-2;2),DIV(4;2))=(-1,2)"></applet></html>
the radius is given by:
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "101" height = "30" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "SUP(R;2)=SUP(a;2)+SUP(b;2)-c"></applet></html>
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "160" height = "30" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "SUP(R;2)=SUP((-1);2)+SUP(2;2)-(-4)=9"></applet></html>
that is R= 3
To find the intersection ,Substitute the equation f the straight line in the equation of the circle:
Y = X-1
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "113" height = "30" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "SUP(x;2)+SUP(y;2)+2x-4y-4=0"></applet></html>
Replace Y by X - 1
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "171" height = "30" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "SUP(x;2)+SUP((x-1);2)+2x-4(x-1)-4=0"></applet></html>
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "78" height = "30" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "2SUP(x;2)-4x+1=0"></applet></html>
Solving,you get:
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "75" height = "54" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "x = DIV(2SYMBOL_32ROOT(2);2)"></applet></html>
Subsitute these in Y=X-1
The points of intersection are:
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "124" height = "54" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "(DIV(2-ROOT(2);2),DIV(2-ROOT(2);2)-1)"></applet></html>
and
<html><applet archive = "formula.jar" codebase = "." code = "formula.FormulaViewApplet.class" name = "FormulaViewApplet" width = "130" height = "54" hspace = "0" vspace = "0" align = "middle"><param name = "FORMULA_CODE" value = "(DIV(2+ROOT(2);2),DIV(2+ROOT(2);2)-1)"></applet></html>

amk

12-11-2003, 02:42 AM

جزااك الله خير على هدا الرد المميز والسريع ووفقك الله
اخوك عبدالله

uaemath

16-11-2003, 02:41 AM

عذرا على شكل آخر معادلتين
تم إصلاحهما