(b-a)(c-a)(c-b)=1 1 1
a b c
a^2 b^2 c^2
prove this matrix
(b-a)(c-a)(c-b)=what matrix?
Ideas: Subtract the values of the first column from the second column and the third column, respectively.
So, the determinant
= (b-a)(c^2 - a^2) - (c-a)(b^2 - a^2)
= (b-a)(c-a)(c+a - b-a)
= (b-a)(c-a)(c-b)
Reply:I do not understand the question.
b-a=1
b=a
c-a=1
c=a
c-b=1
c=b
a=b=c=1
a b c = 1 1 1
a^2 b^2 c^2 = 1 1 1
So the Matrix is
1 1 1
1 1 1
1 1 1
Is this what you wanted to prove? The matrix should have 3 rows and 3 columns.
Monday, May 24, 2010
The Circle C has the equation x^2 + y^2 - 12x + 8y +16 = 0?
a) Find the coordinates of the centre of C
b) Find the radius of C
c) Sketch C
Given that C crosses the x-axis at the points A and B
d) Find the length AB, giving your answer in the form K√5
Its the last question i'm stuck on for my homework, any help would be great :)
The Circle C has the equation x^2 + y^2 - 12x + 8y +16 = 0?
a) General equation of a circle can be expressed in
x^2 +y^2 +2gx+2fy +c = 0 with (-g,-f) as centre and
SQRT(g^2 + f^2 -c)
=%26gt; Hence the above equation can be transformed to
x^2 + y^2 + 2(-6)x + 2(4)y + 16 = 0 ,
i.e g = -6 , f = 4 , hence the centre of the above circle is (6,-4) .
b) Radius = SQRT(6^2 + (-4)^2 - 16)) = SQRT(36) = 6 Units
c) You can draw the Circle with (6,-4) as centre and 6 as radius on a coordinate axes.
d) For solving this , put y = 0 in the equation of the circle and solve for point A %26amp; B.
=%26gt; x^2 + 0^2 - 12x + 8x0 + 16 = 0
=%26gt; x^2 -12x + 16 = 0
Solving for x , you will get the coordinates for A and B as follows:A(6+2√5,0) and B(6-2√5,0). Hence the length of AB
= 4√5 units
Reply:We need to put this in the form (x-a)^2 + (b-y)^2 = r^2, and we get (x-6)^2 -36 + (y+4)^2 -16 +16 = 0. This simplifies to (x-6)^2 + (y+4)^2 = 36. This takes care of parts a and b. Substitute y = 0 in this, solve for the two values of x, take their difference, and you're done.
Reply:Perhaps this may help:
The center of a circle is defined as (h,k)
h is the x value, k is the y value
in order to find (h,k) you have to get the equation into the form
(x-h)^2 + (y-k)^2 = r^2 r here is the radius
to put your equation in to the right form you must group the x values and the y values.
so you get: x^2 -12x + y^2 + 8y= - 16
(note that the 16 was brought over to the other side)
now lets work with x and y separately
right now we have x^2 - 12X
we must complete the square. take the -12 and cut it in half.
we now have 6. square this number to get 36
[Make sure you add the 36 to the -16 on the other side of the equal sign!]
so now you have x^2-12x+36
Factor this to get (x-6)^2
now do the same for the y: cut the 8y in half, square it, add that value to the -16 on the other side, and factor.
this should lead you to (y+4)^2
now all in all you should have (x-6)^2 + (y+4)^2 = 36
(the 36 comes from [ -16+36+16]
so looking at this equation we can tell that the center of the circle is (6, -4)
to find the radius we remember that (x-h)^2+(y-k)^2=r^2
in this case r^2 = 36 so r equals the square root of 36 which equals six.
I hope this helps you with the first questions of your homework and should you need further help you might find it at http://www.analyzemath.com/CircleEq/Tuto...
Reply:(x-6)^2 + (y+4)^2 = 36+16-16 = 36
[(x-6)/6]^2 + [(y+4)/6]^2 = 1
origin (6,-4)
radious 6
Reply:center is(-a/2,-b/2)=(12/2,-8/2)=(6,-4)
Reply:As many have said,
(x - 6)^2 + (y + 4)^2 = 36.
The x-axis is y=0, so the two x-values are the solutions of
(x - 6)^2 + (0 + 4)^2 = 36;
i.e.
(x-6)^2 = 20; x = 6 ± √20 = 6 ± 2√5.
The distance between the two is
(6 + 2√5) - (6 - 2√5) = 4√5
Reply:First of all, complete the square to get the equation in the form
(x - x0)^2 + (y - y0)^2 = r^2
(x^2 - 12x) + (y^2 + 8y) = -16
(x^2 - 12x + 36) + (y^2 + 8y + 16) = -16 + 36 + 16
(x - 6)^2 + (y + 4)^2 = 6^2
a) From the equation above, x0 = 6 and y0 = -4, so the coordinates of the center are (6, -4).
b) Again, from the equation above, r = 6.
c) Simply draw a circle centered at the point (6, -4) with a radius of 6 units.
d) I'm not sure what you mean by AB. More information is needed.
Reply:x^2 - 12x + y^2 + 8y = -16.
(x - 6)^2 + (y + 4)^2 = -16 + 36 + 16
(x - 6)^2 + (y + 4)^2 = 36.
A) Center is located at (6, -4).
B) The radius is 36^.5 = 6 units.
D) I'd help you with the length of AB, but you didn't even mention A or B in your answer.
b) Find the radius of C
c) Sketch C
Given that C crosses the x-axis at the points A and B
d) Find the length AB, giving your answer in the form K√5
Its the last question i'm stuck on for my homework, any help would be great :)
The Circle C has the equation x^2 + y^2 - 12x + 8y +16 = 0?
a) General equation of a circle can be expressed in
x^2 +y^2 +2gx+2fy +c = 0 with (-g,-f) as centre and
SQRT(g^2 + f^2 -c)
=%26gt; Hence the above equation can be transformed to
x^2 + y^2 + 2(-6)x + 2(4)y + 16 = 0 ,
i.e g = -6 , f = 4 , hence the centre of the above circle is (6,-4) .
b) Radius = SQRT(6^2 + (-4)^2 - 16)) = SQRT(36) = 6 Units
c) You can draw the Circle with (6,-4) as centre and 6 as radius on a coordinate axes.
d) For solving this , put y = 0 in the equation of the circle and solve for point A %26amp; B.
=%26gt; x^2 + 0^2 - 12x + 8x0 + 16 = 0
=%26gt; x^2 -12x + 16 = 0
Solving for x , you will get the coordinates for A and B as follows:A(6+2√5,0) and B(6-2√5,0). Hence the length of AB
= 4√5 units
Reply:We need to put this in the form (x-a)^2 + (b-y)^2 = r^2, and we get (x-6)^2 -36 + (y+4)^2 -16 +16 = 0. This simplifies to (x-6)^2 + (y+4)^2 = 36. This takes care of parts a and b. Substitute y = 0 in this, solve for the two values of x, take their difference, and you're done.
Reply:Perhaps this may help:
The center of a circle is defined as (h,k)
h is the x value, k is the y value
in order to find (h,k) you have to get the equation into the form
(x-h)^2 + (y-k)^2 = r^2 r here is the radius
to put your equation in to the right form you must group the x values and the y values.
so you get: x^2 -12x + y^2 + 8y= - 16
(note that the 16 was brought over to the other side)
now lets work with x and y separately
right now we have x^2 - 12X
we must complete the square. take the -12 and cut it in half.
we now have 6. square this number to get 36
[Make sure you add the 36 to the -16 on the other side of the equal sign!]
so now you have x^2-12x+36
Factor this to get (x-6)^2
now do the same for the y: cut the 8y in half, square it, add that value to the -16 on the other side, and factor.
this should lead you to (y+4)^2
now all in all you should have (x-6)^2 + (y+4)^2 = 36
(the 36 comes from [ -16+36+16]
so looking at this equation we can tell that the center of the circle is (6, -4)
to find the radius we remember that (x-h)^2+(y-k)^2=r^2
in this case r^2 = 36 so r equals the square root of 36 which equals six.
I hope this helps you with the first questions of your homework and should you need further help you might find it at http://www.analyzemath.com/CircleEq/Tuto...
Reply:(x-6)^2 + (y+4)^2 = 36+16-16 = 36
[(x-6)/6]^2 + [(y+4)/6]^2 = 1
origin (6,-4)
radious 6
Reply:center is(-a/2,-b/2)=(12/2,-8/2)=(6,-4)
Reply:As many have said,
(x - 6)^2 + (y + 4)^2 = 36.
The x-axis is y=0, so the two x-values are the solutions of
(x - 6)^2 + (0 + 4)^2 = 36;
i.e.
(x-6)^2 = 20; x = 6 ± √20 = 6 ± 2√5.
The distance between the two is
(6 + 2√5) - (6 - 2√5) = 4√5
Reply:First of all, complete the square to get the equation in the form
(x - x0)^2 + (y - y0)^2 = r^2
(x^2 - 12x) + (y^2 + 8y) = -16
(x^2 - 12x + 36) + (y^2 + 8y + 16) = -16 + 36 + 16
(x - 6)^2 + (y + 4)^2 = 6^2
a) From the equation above, x0 = 6 and y0 = -4, so the coordinates of the center are (6, -4).
b) Again, from the equation above, r = 6.
c) Simply draw a circle centered at the point (6, -4) with a radius of 6 units.
d) I'm not sure what you mean by AB. More information is needed.
Reply:x^2 - 12x + y^2 + 8y = -16.
(x - 6)^2 + (y + 4)^2 = -16 + 36 + 16
(x - 6)^2 + (y + 4)^2 = 36.
A) Center is located at (6, -4).
B) The radius is 36^.5 = 6 units.
D) I'd help you with the length of AB, but you didn't even mention A or B in your answer.
How do i Begin to learn Visual C++?
I have read that C++ is built on C and I'm Not even sure if C++ and Visual C++ are related at all, and I don't care much for C#. If I eventually want to master Visual C++, but I don't know any C, C++, C#, or Visual C++ or Visual anything, where do I start?
How do i Begin to learn Visual C++?
I would start by doing a Yahoo search about what in C++ you want to learn.
I found this page might have some information on how to learn:
http://www.codeguru.com/Cpp/
Reply:You start by lerning programming. Learning a language does you no good at all if you don't know programming. (Try Wirth's "Algorithms + Data Structures = Programs".) Then start with an easier language - VB or php. Then move on to Javascript. Then try a dialect of C.
Reply:Here are some video tutorials to get you started with standard C++:
http://xoax.net/comp/cpp/console/index.p...
Here are some that use Visual C++ specific tecnologies:
http://xoax.net/comp/cpp/index.php
You can use all of these tutorials with Visual C++, but the technologies like Win32 and MFC are Microsoft specific. Visual C++ isn't a language, it is the compiler. However, Microsoft packages their own libraries with thier compiler, like MFC and Win32 to support thier platform.
How do i Begin to learn Visual C++?
I would start by doing a Yahoo search about what in C++ you want to learn.
I found this page might have some information on how to learn:
http://www.codeguru.com/Cpp/
Reply:You start by lerning programming. Learning a language does you no good at all if you don't know programming. (Try Wirth's "Algorithms + Data Structures = Programs".) Then start with an easier language - VB or php. Then move on to Javascript. Then try a dialect of C.
Reply:Here are some video tutorials to get you started with standard C++:
http://xoax.net/comp/cpp/console/index.p...
Here are some that use Visual C++ specific tecnologies:
http://xoax.net/comp/cpp/index.php
You can use all of these tutorials with Visual C++, but the technologies like Win32 and MFC are Microsoft specific. Visual C++ isn't a language, it is the compiler. However, Microsoft packages their own libraries with thier compiler, like MFC and Win32 to support thier platform.
How do I learn to write C++ applications?
I use Visual Studio 2005 for programming. When I was little, I used to do programming all the time with Turbo C 3.0, so I'm familiar with all the C grammars and stuffs. But, somehow I don't know how to get on the application programming. I can write console programs only run don command prompt, using C++. But when it comes to windows application programs(like MFC programmings and stuffs,) I don't know how to design window resources and everything. There are not much books on Application programming on Visual C++ 2005. Does the version matter in C++(Can I use older version books for C++ 2005?) It's hard to find the way to start these. Do you have any suggestion?
Quesiton Summary:
1) What is the most famous website/forum for C++ developers group?
2) How do I get started on Windows APP Programming?
3) Is the older version of C++ compatible with Visual C++ 2005(Can I get books for VC++ 6.0 or .NET and would it still work on 2005?)
Thx, and I always give 5 stars to the best answer.
How do I learn to write C++ applications?
You can download for free the Visual Studio Express and there are tutorials you can follow for each of the languages in it to learn.
You can write a program and then look at the final code source to see how it was developed in order to use in your other C++ work.
Download selection here:
http://msdn.microsoft.com/vstudio/expres...
Take a look here for learning materials:
http://msdn.microsoft.com/vstudio/expres...
If you need graphics programs or some other free programs you can find some more links on my webpage at http://www.tom-olsen.com/links.html
Reply:learn by doing
Reply:I took it up when I was going to school. The first 2 weeks are the basics. I was hanging in there, then that mess got advanced. I was completely lost. LOL I ended up dropping out of the class. LOL Good Luck with Computer Programming, man.
Reply:Buy book of last part or take teacher you're know his expert on C++ last Part.
Reply:Fred Wow!Your Extra News here!
★※★ http://208.109.69.157/funstuff/extra/ext...
flower garden
Quesiton Summary:
1) What is the most famous website/forum for C++ developers group?
2) How do I get started on Windows APP Programming?
3) Is the older version of C++ compatible with Visual C++ 2005(Can I get books for VC++ 6.0 or .NET and would it still work on 2005?)
Thx, and I always give 5 stars to the best answer.
How do I learn to write C++ applications?
You can download for free the Visual Studio Express and there are tutorials you can follow for each of the languages in it to learn.
You can write a program and then look at the final code source to see how it was developed in order to use in your other C++ work.
Download selection here:
http://msdn.microsoft.com/vstudio/expres...
Take a look here for learning materials:
http://msdn.microsoft.com/vstudio/expres...
If you need graphics programs or some other free programs you can find some more links on my webpage at http://www.tom-olsen.com/links.html
Reply:learn by doing
Reply:I took it up when I was going to school. The first 2 weeks are the basics. I was hanging in there, then that mess got advanced. I was completely lost. LOL I ended up dropping out of the class. LOL Good Luck with Computer Programming, man.
Reply:Buy book of last part or take teacher you're know his expert on C++ last Part.
Reply:Fred Wow!Your Extra News here!
★※★ http://208.109.69.157/funstuff/extra/ext...
flower garden
Differentiate between c nd c++?
differentiate between c nd c++
use of ::(scope resolution operator)
what kind of projects are suitable for c and c++
what is a class? example
Differentiate between c nd c++?
O_o... this sounds like a homework question. And such I won't give you clear answers. I will give you an overview and suggest that you visit www.wikipedia.org and search for C Programming and C++ Programming.
C is a procedural language thats considered C++ predecessor.
C++ was considered the extension to C by adding Object Oriented Programming/Design to the language.
:: is used When you need to access or define a part of a class.
Reply:C++ is a superset of C. It is object oriented. It has all of the capabilities of C, plus it allows you to use polymorphism and inheritance.
This link can provide you with a lot more detail
http://unthought.net/c++/c_vs_c++.html
Reply:Do your own homework.
use of ::(scope resolution operator)
what kind of projects are suitable for c and c++
what is a class? example
Differentiate between c nd c++?
O_o... this sounds like a homework question. And such I won't give you clear answers. I will give you an overview and suggest that you visit www.wikipedia.org and search for C Programming and C++ Programming.
C is a procedural language thats considered C++ predecessor.
C++ was considered the extension to C by adding Object Oriented Programming/Design to the language.
:: is used When you need to access or define a part of a class.
Reply:C++ is a superset of C. It is object oriented. It has all of the capabilities of C, plus it allows you to use polymorphism and inheritance.
This link can provide you with a lot more detail
http://unthought.net/c++/c_vs_c++.html
Reply:Do your own homework.
After 10 years C++ or C#?
Both have their own pros and cons and their market share. What I want to know is,10 yrs from now
C++ will be there for sure(they r improving it further with C++0x), but will C# loose it's glitter or will it have the same market-share
and love-and-affection(if it has any).
Or on the contrary you think C# will gain over C++.
Pros pl help with "logical reasoning" I have to choose one
After 10 years C++ or C#?
Both C++ and C# will be around for the next 10 years. However, I do see C# and .NET dorminating because it is always improving and Microsoft has some brilliant minds, fans and money behind it. Microsoft will keep updating C# with changing time. As for C++, other than C++ on .NET I do not see companies pumping brilliant minds and money to advance the language. Relying on academia to advance a language is a waste of time (just look at Pascal and it would of had died completely if not for Borland's Delphi.) That is why I am banking my money on Microsoft and .NET.
Another point; language is not that important. What is important is the engine behind the language. Object oriented programming drive C++, C#, JAVA and other dorminant languages today and the lack of it in C, Cobol (classic), Visual Basic has lead to these downfall. Just as procedural programming benefits lead to the downfall of goto-statements languages and assembly-usuage in business and Object oriented programming benefits and change in business needs lead to the downfall of procedural programming I see a new methodology on a significant rise in 10 years. It is probably aspect oriented programming or something else. Microsoft will keep updating .NET with this in mind since it has billions of dollars of market share to maintain or lose while C++ has really been the same for years other than what third-party vendors have added to it; which than MFC and .NET is not huge I believe. So Microsoft is the way!
Reply:in similar condition i chose c++
Reply:C# is tied to Microsoft's .NET, and I don't see that disappearing anytime soon. On the contrary, I see it gaining ground over Java. Rather than compare C++ to C#, I would say that both are gaining share from Java on servers. On desktops, Java is essentially nonexistent, and C++ is quite dominant. I personally would choose C++ because it would be useful on non-Windows platforms as well.
Reply:C# has great inevitable features which are not well and nicely implemented in managed (CLR) C++. Improving C++ to cover features which we take for granted in C# has turned this powerful compiler to a bunch of unreadable awkward codes which would soon looses its attention. C# has a nice look. C# surely wins.
Reply:I wouldn't go with anything that is primarily, if not only, supported by Micro$oft. (I say this as I type on my Windoze computer... lol) Has it made it to other platforms? I remember, when it was still in Beta, that it was reported that it would become an ANSI standard. Did that ever happen?
I was also unaware that C# ever gained any glitter, or wide acceptance, for that matter. But hey, I live in the embedded system trenches with C and Assembly. What do I know?
C++, if you must make a choice, is probably the way to go.
Reply:Both will be there 10 years from now. C++ is definitely going to be there because it is one of the strongest system level languages. C# and Java are application level languages.
C# won’t go away. Microsoft has exposed its Windows API through .NET, and will from now on focus on .NET only. In other words, if you want to write native windows applications, you need a .NET language, which is ideally C#. Do you think Windows will be going strong 10 years from now? Sure, so the same applies to C#.
Reply:C++ will definitely be around because a lot of code being written (or written 5-15 years ago) is in c++. People will still have to maintain this code in 10 years.
Also, many people will continue using c++ because it is platform and framework independent.
c# will be around as long as .NET is around. It was built for .NET. However, if MS goes in a different direction in, say, 5-6 years, and abandons .NET for a new framework, then c# would probably go away with it.
Reply:Wow, in ten years from now? With the major leaps and bounds technology is making I'd doubt any of the current languages will be the prevalent ones.
I predict that in ten years the great monolith Microsoft will crash, and out of the ashes rose a new software company, Phoenix, and they programmed in D and D++.
C++ will be there for sure(they r improving it further with C++0x), but will C# loose it's glitter or will it have the same market-share
and love-and-affection(if it has any).
Or on the contrary you think C# will gain over C++.
Pros pl help with "logical reasoning" I have to choose one
After 10 years C++ or C#?
Both C++ and C# will be around for the next 10 years. However, I do see C# and .NET dorminating because it is always improving and Microsoft has some brilliant minds, fans and money behind it. Microsoft will keep updating C# with changing time. As for C++, other than C++ on .NET I do not see companies pumping brilliant minds and money to advance the language. Relying on academia to advance a language is a waste of time (just look at Pascal and it would of had died completely if not for Borland's Delphi.) That is why I am banking my money on Microsoft and .NET.
Another point; language is not that important. What is important is the engine behind the language. Object oriented programming drive C++, C#, JAVA and other dorminant languages today and the lack of it in C, Cobol (classic), Visual Basic has lead to these downfall. Just as procedural programming benefits lead to the downfall of goto-statements languages and assembly-usuage in business and Object oriented programming benefits and change in business needs lead to the downfall of procedural programming I see a new methodology on a significant rise in 10 years. It is probably aspect oriented programming or something else. Microsoft will keep updating .NET with this in mind since it has billions of dollars of market share to maintain or lose while C++ has really been the same for years other than what third-party vendors have added to it; which than MFC and .NET is not huge I believe. So Microsoft is the way!
Reply:in similar condition i chose c++
Reply:C# is tied to Microsoft's .NET, and I don't see that disappearing anytime soon. On the contrary, I see it gaining ground over Java. Rather than compare C++ to C#, I would say that both are gaining share from Java on servers. On desktops, Java is essentially nonexistent, and C++ is quite dominant. I personally would choose C++ because it would be useful on non-Windows platforms as well.
Reply:C# has great inevitable features which are not well and nicely implemented in managed (CLR) C++. Improving C++ to cover features which we take for granted in C# has turned this powerful compiler to a bunch of unreadable awkward codes which would soon looses its attention. C# has a nice look. C# surely wins.
Reply:I wouldn't go with anything that is primarily, if not only, supported by Micro$oft. (I say this as I type on my Windoze computer... lol) Has it made it to other platforms? I remember, when it was still in Beta, that it was reported that it would become an ANSI standard. Did that ever happen?
I was also unaware that C# ever gained any glitter, or wide acceptance, for that matter. But hey, I live in the embedded system trenches with C and Assembly. What do I know?
C++, if you must make a choice, is probably the way to go.
Reply:Both will be there 10 years from now. C++ is definitely going to be there because it is one of the strongest system level languages. C# and Java are application level languages.
C# won’t go away. Microsoft has exposed its Windows API through .NET, and will from now on focus on .NET only. In other words, if you want to write native windows applications, you need a .NET language, which is ideally C#. Do you think Windows will be going strong 10 years from now? Sure, so the same applies to C#.
Reply:C++ will definitely be around because a lot of code being written (or written 5-15 years ago) is in c++. People will still have to maintain this code in 10 years.
Also, many people will continue using c++ because it is platform and framework independent.
c# will be around as long as .NET is around. It was built for .NET. However, if MS goes in a different direction in, say, 5-6 years, and abandons .NET for a new framework, then c# would probably go away with it.
Reply:Wow, in ten years from now? With the major leaps and bounds technology is making I'd doubt any of the current languages will be the prevalent ones.
I predict that in ten years the great monolith Microsoft will crash, and out of the ashes rose a new software company, Phoenix, and they programmed in D and D++.
Water boils at 100 degrees C and sodium chloride boils at 1415 degrees C. At what temperature will they sepera
Water boils at 100 degrees C and sodium chloride boils at 1415 degrees C. At what temperature will they seperate?
105 degrees c
1500 degrees c
1415 degrees c
80 degrees c
90 degrees c
Water boils at 100 degrees C and sodium chloride boils at 1415 degrees C. At what temperature will they sepera
If sodium chloride and water are mixed, they form a solution. The solution will boil at just over 100 degrees C and you can distill the solution ,catching the water. The salt will be left in the container. Best answer is 105 degrees C.
Reply:You're only considering the two endpoints of the solid-liquid equilibrium line. The temperature at which the single phase (NaCl dissolved in Water) will become two distinct phases will depend on the pressure as well as the composition of the solution.
105 degrees c
1500 degrees c
1415 degrees c
80 degrees c
90 degrees c
Water boils at 100 degrees C and sodium chloride boils at 1415 degrees C. At what temperature will they sepera
If sodium chloride and water are mixed, they form a solution. The solution will boil at just over 100 degrees C and you can distill the solution ,catching the water. The salt will be left in the container. Best answer is 105 degrees C.
Reply:You're only considering the two endpoints of the solid-liquid equilibrium line. The temperature at which the single phase (NaCl dissolved in Water) will become two distinct phases will depend on the pressure as well as the composition of the solution.
Subscribe to:
Posts (Atom)