Trevor was going to the pet store to get a new dog.The store had 56 animals.If 3/7 of them were dogs,how many dogs does this pet
2 answers:
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Answer:
To find all coordinates, we just need to observe the graph.
The coordinates of point C are (2c,d). From the graph, we notice that the x-coordinate of C is the same x-coordinate of V, because they are in the same vertical lines.
The coordinates of point D are (c,0). The problem states that D is a mid point, so basically its coordinate is half of point's V, which is c.
The slope of both AB and DC is d/c. The slope is the fraction between y-coordinate and x-coordinate. If you we calculate the slope of DC, we would have d as vertical coordinate and c as horizontal coordinate.
The slop of both AD and BC is -b/c-a. The slope between the points A(a,b) and D(c,0) is
Answer:
72 feet from the shorter pole
Step-by-step explanation:
The anchor point that minimizes the total wire length is one that divides the distance between the poles in the same proportion as the pole heights. That is, the two created triangles will be similar.
The shorter pole height as a fraction of the total pole height is ...
18/(18+24) = 3/7
so the anchor distance from the shorter pole as a fraction of the total distance between poles will be the same:
d/168 = 3/7
d = 168·(3/7) = 72
The wire should be anchored 72 feet from the 18 ft pole.
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<em>Comment on the problem</em>
This is equivalent to asking, "where do I place a mirror on the ground so I can see the top of the other pole by looking in the mirror from the top of one pole?" Such a question is answered by reflecting one pole across the plane of the ground and drawing a straight line from its image location to the top of the other pole. Where the line intersects the plane of the ground is where the mirror (or anchor point) should be placed. The "similar triangle" description above is essentially the same approach.
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Alternatively, you can write an equation for the length (L) of the wire as a function of the location of the anchor point:
L = √(18²+x²) + √(24² +(168-x)²)
and then differentiate with respect to x and find the value that makes the derivative zero. That seems much more complicated and error-prone, but it gives the same answer.
