anonymous
  • anonymous
A 30ft cable is suspended between the tops of two 20ft poles on the level ground. The lowest point of the cable is 5ft above the ground.What is the distance between the two poles?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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mathmate
  • mathmate
Draw a diagram: |dw:1437334323698:dw| If the cable is 30' long, what distance separates the two poles?
campbell_st
  • campbell_st
I would do it this way |dw:1437334277446:dw| the x axis is the directrix, so the focal length is 5 units a standard form of the parabola that uses focal length and directrix is \[(x - h) = 4a(y - k)\] where (h, k) is the vertex and a is the focal length so you have h = 0, k = 5 and a = 20 so the equation becomes \[(x - 0)^2 = 4 \times 5 \times (y - 5)\] or \[x^2 = 20(y- 5)\] so substitute the height of the pole, y = 20 into the equation and solve for x. this distance will be the perpendicular from the y-axis to the pole when you get the answer, double it to get the distance between the poles
anonymous
  • anonymous
wow

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campbell_st
  • campbell_st
oops a couple of mistakes the standard form is \[(x - h)^2 + 4a(y - k)\] h = 0, k = 5 and a = 5 |dw:1437335137953:dw| substituting \[x^2 = 4 \times 5 \times (y - 5)\] or \[x^2 = 20(y - 5)\] now substitute y = 20 and solve for x don't forget to double it
anonymous
  • anonymous
oh
mathmate
  • mathmate
|dw:1437335569990:dw|
anonymous
  • anonymous
im confuse @campbell_st
campbell_st
  • campbell_st
Well I'd say f you hang a wire between 2 pole, then you would have a parabola and I then when about finding the equation of the parabola which I gave you as \[x^2 = 20(y - 5)\] if the height of the pole is 20 then let y = 20 and substitute it into the equation
anonymous
  • anonymous
i did 20-5=15*20=300
anonymous
  • anonymous
do i have to find the square root of 300
campbell_st
  • campbell_st
that's correct, the distance from the y-axis to the pole is \[x = \sqrt{300} ~~or~~x = 10\sqrt{3}\] since the y axis is in the middle of the poles, double it to find the total distance
anonymous
  • anonymous
i got 17.3
campbell_st
  • campbell_st
that makes sense
anonymous
  • anonymous
cool
campbell_st
  • campbell_st
so that's how I'd do the question, I have no idea what you have been taught or what topic the question is from. So I don't know if this solution is something you'd be expected to show
anonymous
  • anonymous
its a summer packet for the intro of geometry
campbell_st
  • campbell_st
ok, I solved it using algebra and assumes the wire forms a parabola when hung between the poles
anonymous
  • anonymous
cool

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