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Nombre de usuariohectictar
Puntuación7543
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Preguntas 8
Respuestas 2448

 #1
avatar+7543 
+1

The scale drawing of a rectangular yard measures (2x2 + 2) by (x + 4). If the area of the scale drawing and the

area of the actual yard are in the ratio 12:140, find an expression for the area of the actual yard in expanded form.

 

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area of scale drawing  =  ( length )( width )  =  (2x2 + 2)(x + 4)

 

area of scale drawing / area of actual yard  =  12 / 140

                                                                                        Substitute  (2x2 + 2)(x + 4)  for  area of scale drawing

(2x2 + 2)(x + 4) / area of actual yard  =  12 / 140            Now we just have to solve for  area of actual yard

                                                                                        Cross multiply

(140)(2x2 + 2)(x + 4)  =  12(area of actual yard)

                                                                                        Divide both sides of the equation by  12

(140)(2x2 + 2)(x + 4) / 12  =  area of actual yard

 

area of actual yard  =  (140)(2x2 + 2)(x + 4) / 12

                                                                                        Expand the right side of the equation

area of actual yard  =  (140)(2x3 + 8x2 + 2x + 8) / 12

 

area of actual yard  =  (280x3 + 1120x2 + 280x + 1120) / 12

                                                                                                 Divide the numerator and denominator by  4

area of actual yard  =  (70x3 + 280x2 + 70x + 280) / 3

18-may-2019
 #1
avatar+7543 
+1

I think you’re pretty much on the right track smiley

 

Assuming:   \(x^2 + y^2 - 6x + py + q = 0\)

 

\(x^2 + y^2 - 6x + py + q = 0\)
                                                    Subtract  q  from both sides of the equation
\(x^2 + y^2 - 6x + py = -q\)
                                                    Rearrange the terms on the left side of the equation.
\(x^2 - 6x + y^2 + py = -q\)
                                                                                          Add  9  and add  \((\frac{p}{2})^2\)  to both sides of the equation.

\(x^2 - 6x + 9 + y^2 + py + (\frac{p}{2})^2 = -q + 9 + (\frac{p}{2})^2\)
                                                                                           Factor both perfect square trinomials on the left side.
\((x - 3)^2 + (y + \frac{p}{2})^2 = -q + 9 + (\frac{p}{2})^2\)

 

Now we can see that the center of the circle is the point  (3, -\(\frac{p}{2}\))

 

Because the circle is tangent to the y-axis,

 

radius  =  distance between center and y-axis

radius  =  distance between  (3, -\(\frac{p}{2}\))  and  (0, -\(\frac{p}{2}\))

radius  =  3

 

area  =  π · radius2

area  =  π · 32

area  =  9π     sq. units

 

You can play around with the sliders on this graph to check:

https://www.desmos.com/calculator/zvm1f8xhaf

 

Notice that the distance between the center and the y-axis stays  3 .

18-may-2019