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# The formula h = 0,02d^2 - 0,6d + 1 applies to one of the three situations.

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3 In the harbor a ferry boat is being pulled from one side to the other with a heavy cable. If another boat has to pass, the captain of the ferry lets the cable drop to the bottom of the canal. The cable hangs in the form of a parabola. The formula h = 0,02d^2 - 0,6d + 1 applies to one of the three situations above. In this formula d is the horizontal distance in metres from the left side of the quay h is the height in metres of the cable from the waterline.

a. Explain to which situation the formula h = 0,02d^2 - 0,6d + 1 applies.

b. Answer the same question for the formula h = 1/225 a^2 and - 30/225 a + 1 .

Feb 28, 2019

#1
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In the first scenario, h will be a positive number

in the second drawing h = 0

in the third scenario h will be some negative number

.02 d^2 - 0.6 d +1     will have a nadir (a low point) at  -b/2a   =  -  -0.6/(2*.02) = 15 m = d

SUstitute this value in for d    .02(15^2) - 0.6(15) + 1 = h  = = -3.5    so this applies to the third picture.

DO the same thing for this equation   a (low point) = - b/ 2a = 15  (again)

now substitute this value into the equation and find   h   to see what scenario this second equation fits....... you can do it! Feb 28, 2019

#1
0

In the first scenario, h will be a positive number

in the second drawing h = 0

in the third scenario h will be some negative number

.02 d^2 - 0.6 d +1     will have a nadir (a low point) at  -b/2a   =  -  -0.6/(2*.02) = 15 m = d

SUstitute this value in for d    .02(15^2) - 0.6(15) + 1 = h  = = -3.5    so this applies to the third picture.

DO the same thing for this equation   a (low point) = - b/ 2a = 15  (again)

now substitute this value into the equation and find   h   to see what scenario this second equation fits....... you can do it! ElectricPavlov Feb 28, 2019
#3
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I do kinda get what you're doing, just not how you get the low point. I'm not the greatest at math :/ Thanks for the answer! So:

h = 1/225 a^2

h = 1/225 * 15^2

1/225 * 15^2 = 1/225 * 225 = 1

h = 1

and

- 30/225 * a + 1

- 30/225 * 15 + 1

- 2 + 1 = -1

h = -1

HeyxJacq  Mar 1, 2019
#2
+1

Nice, EP  !!!   Feb 28, 2019