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nata0808 [166]
3 years ago
6

How do I calculate this? Is there a formula?

Mathematics
2 answers:
alex41 [277]3 years ago
8 0

<u>Answer:</u>

Height of cables = 23.75 meters

<u>Step-by-step explanation:</u>

We are given that the road is suspended from twin towers whose cables are parabolic in shape.

For this situation, imagine a graph where the x-axis represent the road surface and the point (0,0) represents the point that is on the road surface midway between the two towers.

Then draw a parabola having vertex at (0,0) and curving upwards on either side of the vertex at a distance of x = 600 or x = -600, and y at 95.

We know that the equation of a parabola is in the form y=ax^2 and here it passes through the point (600, 95).

y=ax^2

95=a \times 600^2

a=\frac{95}{360000}

a=\frac{19}{72000}

So new equation for parabola would be y=\frac{19x^2}{72000}.

Now we have to find the height (y)of the cable when x= 300.

y=\frac{19 (300)^2}{72000}

y = 23.75 meters

lana [24]3 years ago
3 0

Answer: 23.75 meters

Step-by-step explanation:

If we assume that the origin of the coordinate axis is in the vertex of the parabola. Then the function will have the following form:

y = a (x-0) ^ 2 + 0\\\\y = ax ^ 2

We know that when the height of the cables is equal to 95 then the horizontal distance is 600 or -600.

Thus:

95 = a (600) ^ 2

a = \frac{95} {600 ^ 2}\\\\a = \frac {19} {72000}

Then the equation is:

y = \frac{19}{72000} x ^ 2

Finally the height of the cables at a point 300 meters from the center is:

y = \frac{19}{72000}(300) ^ 2

y =23.75\ meters

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