## anonymous one year ago 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?

1. mathmate

Draw a diagram: |dw:1437334323698:dw| If the cable is 30' long, what distance separates the two poles?

2. 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

3. anonymous

wow

4. 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

5. anonymous

oh

6. mathmate

|dw:1437335569990:dw|

7. anonymous

im confuse @campbell_st

8. 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

9. anonymous

i did 20-5=15*20=300

10. anonymous

do i have to find the square root of 300

11. 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

12. anonymous

i got 17.3

13. campbell_st

that makes sense

14. anonymous

cool

15. 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

16. anonymous

its a summer packet for the intro of geometry

17. campbell_st

ok, I solved it using algebra and assumes the wire forms a parabola when hung between the poles

18. anonymous

cool