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A parabolic arch has a height of 25 feet and a span of 40 feet. How high is the arch 8 feet from each side of the center?

Llana [10]

Answer:

The correct option is;

21 ft

Step-by-step explanation:

The equation of the parabolic arc is as follows;

y = a(x - h)² + k

Where the height is 25 ft and the span is 40 ft, the coordinates of the vertex (h, k) is then (20, 25)

We therefore have;

y = a(x - 20)² + 25

Whereby the parabola starts from the origin (0, 0), we have;

0 = a(0 - 20)² + 25

0 = 20²a + 25 → 0 = 400·a + 25

∴a = -25/400 = -1/16

The equation of the parabola is therefore;

$y = (-\frac{1}{16})(x-20)^2 + 25$

To find the height 8 ft from the center, where the center is at x = 20 we have 8 ft from center = x = 20 - 8 = 12 or x = 20 + 8 = 28

Therefore, plugging the value of x = 12 or 28 in the equation for the parabola gives;

$y = (-\frac{1}{16})(12-20)^2 + 25 = (-\frac{1}{16})(-8)^2 + 25 = 21 \ ft$ .

4 0

2 years ago

What mathematical sentence is represented by the diagram?

cricket20 [7]

My only guess is a^2 + b^2 = c^2

7 0

2 years ago

A projectile is launched upward from a height of 704 feet with an initial velocity of 112 ft/s. The equation gives the height h

Feliz [49]

We are given the data ho equal to 704 feet and vo equal to 112 feet per second. We apply then kinematics equation: h = ho + vot - 1/2 gt2. Substituting to the given equation,
h = 704 + 112t - 1/2 * 32*t2when h is equal to zero,0 = 704 + 112t - 1/2 * 32*t2t is equal to 11 seconds

4 0

2 years ago

Suppose that in a random sample of 300 employed Americans, there are 57 individuals who say that they would fire their boss if t

otez555 [7]

Answer:

The 95% confidence interval for the population proportion is (0.1456, 0.2344). This means that we are 95% sure that the true proportion of employed American who say that they would fire their boss if they could is between 0.1456 and 0.2344.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

$n = 300, \pi = \frac{57}{300} = 0.19$

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.19 - 1.96\sqrt{\frac{0.19*0.81}{300}} = 0.1456$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.19 + 1.96\sqrt{\frac{0.19*0.81}{300}} = 0.2344$

The 95% confidence interval for the population proportion is (0.1456, 0.2344). This means that we are 95% sure that the true proportion of employed American who say that they would fire their boss if they could is between 0.1456 and 0.2344.

4 0

2 years ago

1.) -12/6 is a natural, whole, integer, rational or irrational

Norma-Jean [14]

Answer:

Rational

Step-by-step explanation:

6 0

2 years ago

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