Question

The main cable of a suspension bridge forms a parabola described by the equation y = a(x - 50)2 + 6. What is the value of a?

Answer 1

Answer:

Which quadratic equation models the main cable of the bridge correctly?

y = 0.048x2 – 2494

y = 0.048x2 – 6

y = 0.0048(x – 50)2 + 6 (This is correct)

y = 0.0048(x – 6)2 + 50

Answer 2

The value of a is 0.0048.

Given that,

The main cable of a suspension bridge forms a parabola described by the equation,

$\rm y = a(x-50)^2+6$

We have to find,

The value of a.

According to the question,

The given relationship between the variables x and y is,

$\rm y = a(x-50)^2+6$

In the given graph the points of the parabola are (30, 7.92), (50, 6), and (70, 7.92)

1. The value of an at the point (30, 7.92) is,

$\rm y = a(x-50)^2+6\\\\7.92 = a (30-50)^2 +6\\\\7.92 = a(-20)^2 + 6\\\\7.92 = 400a +6\\\\7.92 -6 = 400a\\\\1.92 = 400a\\\\a = \dfrac{1.92}{400}\\\\a = 0.0048$

2. The value of an at the point (70, 7.92) is,

$\rm y = a(x-50)^2+6\\\\7.92 = a (70-50)^2 +6\\\\7.92 = a(20)^2 + 6\\\\7.92 = 400a +6\\\\7.92 -6 = 400a\\\\1.92 = 400a\\\\a = \dfrac{1.92}{400}\\\\a = 0.0048$

3.  The value of an at the point (50, 6) is an infinite solution the value of a is not defined at the points.

Hence, The value of a is 0.0048.

For more details refer to the link given below.

https://brainly.com/question/25996776