Solution 4.1:7a - Revision history

Tek at 11:19, 8 October 2008

Tek — Wed, 08 Oct 2008 11:19:41 GMT

←Older revision		Revision as of 11:19, 8 October 2008
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-	As the equation stands, it is difficult directly to know anything about the circle, but if we complete the square and combine	+	As the equation stands, it is difficult directly to know anything about the circle, but if we complete the square and combine ''x''- and ''y''-terms together in their own respective square terms, then we will have the equation in the standard form
-	~~<math>~~x~~</math>~~	+
-	- and	+
-	~~<math>~~y~~</math>~~	+
-	- terms together in their own respective square terms, then we will have the equation in the standard form,	+
-		+
-		+
-	~~<math>\left( x-a \right)^{2}+\left( y-b \right)^{2}=r^{2}</math>~~	+

		+	{{Displayed math\|\|<math>(x-a)^2 + (y-b)^2 = r^2\,,</math>}}

	and we will then be able to read off the circle's centre and radius.		and we will then be able to read off the circle's centre and radius.

-	If we take the	+	If we take the ''x''- and ''y''-terms on the left-hand side and complete the square, we get
-	~~<math>~~x~~</math>~~	+
-	- and	+
-	~~<math>~~y~~</math>~~	+
-	- terms on the left-hand side and complete the square, we get	+

-		+	{{Displayed math\|\|<math>\begin{align}
-	<math>x^{2}+2x=~~\left~~( x+1 ~~\right~~)^{2}-1^{2~~}</math>~~	+	x^2 + 2x &= (x+1)^2-1^2\,,\\[5pt]
-		+	y^2 - 2y &= (y-1)^2-1^2\,,
-		+	\end{align}</math>}}
-	~~<math>~~y^{2}-2y=~~\left~~( y-1 ~~\right~~)^{2}-1^{2}</math>	+

	and then the whole equation can be written as		and then the whole equation can be written as

-		+	{{Displayed math\|\|<math>(x+1)^2 - 1^2 + (y-1)^2 - 1^2 = 1\,,</math>}}
-	<math>~~\left~~( x+1 ~~\right~~)^{2}-1^{2}+~~\left~~( y-1 ~~\right~~)^{2}-1^{2}=1</math>	+
-		+

	or, with the constants moved to the right-hand side,		or, with the constants moved to the right-hand side,

		+	{{Displayed math\|\|<math>(x+1)^2 + (y-1)^2 = 3\,\textrm{.}</math>}}

-	<math>\~~left( x+1 \right)^~~{2}+\~~left( y-1 \right)^{2}=3~~</math>	+	This is a circle having its centre at (-1,1) and radius <math>\sqrt{3}\,</math>.
-		+

-	This is a circle having its centre at
-	<math>\left( -1 \right.,\left. 1 \right)</math>
-	and radius
-	<math>\sqrt{3}</math>.

-	{{NAVCONTENT_START}}
	<center> [[Image:4_1_7a-2(2).gif]] </center>		<center> [[Image:4_1_7a-2(2).gif]] </center>
-	{{NAVCONTENT_STOP}}

Ian at 11:52, 27 September 2008

Ian — Sat, 27 Sep 2008 11:52:39 GMT

←Older revision		Revision as of 11:52, 27 September 2008
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-	{{~~NAVCONTENT_START~~}}	+	As the equation stands, it is difficult directly to know anything about the circle, but if we complete the square and combine
-	<~~center~~> ~~[[Image:4_1_7a~~-1(2)~~.gif]]~~ </~~center~~>	+	<math>x</math>
-	{{~~NAVCONTENT_STOP~~}}	+	- and
		+	<math>y</math>
		+	- terms together in their own respective square terms, then we will have the equation in the standard form,
		+
		+
		+	<math>\left( x-a \right)^{2}+\left( y-b \right)^{2}=r^{2}</math>
		+
		+
		+	and we will then be able to read off the circle's centre and radius.
		+
		+	If we take the
		+	<math>x</math>
		+	- and
		+	<math>y</math>
		+	- terms on the left-hand side and complete the square, we get
		+
		+
		+	<math>x^{2}+2x=\left( x+1 \right)^{2}-1^{2}</math>
		+
		+
		+	<math>y^{2}-2y=\left( y-1 \right)^{2}-1^{2}</math>
		+
		+	and then the whole equation can be written as
		+
		+
		+	<math>\left( x+1 \right)^{2}-1^{2}+\left( y-1 \right)^{2}-1^{2}=1</math>
		+
		+
		+	or, with the constants moved to the right-hand side,
		+
		+
		+	<math>\left( x+1 \right)^{2}+\left( y-1 \right)^{2}=3</math>
		+
		+
		+	This is a circle having its centre at
		+	<math>\left( -1 \right.,\left. 1 \right)</math>
		+	and radius
		+	<math>\sqrt{3}</math>.
		+
	{{NAVCONTENT_START}}		{{NAVCONTENT_START}}
	<center> [[Image:4_1_7a-2(2).gif]] </center>		<center> [[Image:4_1_7a-2(2).gif]] </center>
	{{NAVCONTENT_STOP}}		{{NAVCONTENT_STOP}}

Tekbot: Lösning 4.1:7a moved to Solution 4.1:7a: Robot: moved page

Tekbot — Tue, 09 Sep 2008 09:37:43 GMT

Lösning 4.1:7a moved to Solution 4.1:7a: Robot: moved page

←Older revision

Revision as of 09:37, 9 September 2008

Tekbot: Robot: Automated text replacement (-[[Bild: +[[Image:)

Tekbot — Thu, 21 Aug 2008 07:05:59 GMT

Robot: Automated text replacement (-[[Bild: +[[Image:)

←Older revision		Revision as of 07:05, 21 August 2008
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-	<center> [[~~Bild~~:4_1_7a-2(2).gif]] </center>	+	<center> [[Image:4_1_7a-2(2).gif]] </center>
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Oskar: Ny sida: {{NAVCONTENT_START}} Bild:4_1_7a-1(2).gif {{NAVCONTENT_STOP}} {{NAVCONTENT_START}} Bild:4_1_7a-2(2).gif {{NAVCONTENT_STOP}}

Oskar — Wed, 02 Apr 2008 13:29:44 GMT

Ny sida: {{NAVCONTENT_START}} <center> Bild:4_1_7a-1(2).gif </center> {{NAVCONTENT_STOP}} {{NAVCONTENT_START}} <center> Bild:4_1_7a-2(2).gif </center> {{NAVCONTENT_STOP}}

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