Question and Answers Forum
GeometryQuestion and Answers: Page 72
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Question and Answers Forum |
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GeometryQuestion and Answers: Page 72 |
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| given a,ar,ar^2 ,ar^3 ,... is a GPwith n→∞ ,r < 1 if : a,x_1 ,x_2 ,ar,x_3 , x_4 ,x_5 ,x_6 ,ar^2 , x_7 ,x_8 ,x_9 ,x_(10) ,x_(11) ,x_(12) , ar^3 ,... . where : a,x_1 ,x_2 ,ar ⇒AP ar,x_3 ,x_4 ,x_5 ,x_6 ,ar^2 ⇒AP ar^2 ,x_7 ,x_8 ,x_9 ,x_(10) ,x_(11) ,x_(12) ,ar^3 ⇒AP ...etc if lim_(n→∞) (x_1 +x_2 +x_3 +...)= ((21)/(16))×(a/(1−r)) what is r ? |
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| common equation of conic sections ax^2 +bxy+cy^2 +dx+ey+f=0 if b≠0 we rotate tan 2α =(b/(a−c)) [if a=c ⇒ α=45°] { ((x=x′cos α −y′sin α)),((y=x′sin α +y′cos α)) :} we now have [using x, y again instead of x′, y′] Ax^2 +Cy^2 +Dx+Ey+F=0 now complete the squares A(x+(D/(2A)))^2 +C(y+(E/(2C)))^2 +(F−(D^2 /(4A^2 ))−(E^2 /(4C^2 )))=0 { ((x=x′−(D/(2A)))),((y=y′−(E/(2C)))) :} we now have [using x, y again instead of x′, y′] one of these { ((Ax^2 +By^2 +C=0)),((Ax+By^2 +C=0)),((Ax^2 +By+C=0)) :} a, c, A, C, A, B, C ≠0 in all other cases use your brain to interprete which kind of curve (if any) we have |
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