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pogonyaev
3 years ago
5

The height h of a thrown object as a function of horizontal distance d that it has traveled is a quadratic function. An object i

s thrown from ground​ level, 57 m away from the base of a tower 17 m high and just barely clears the top of the tower. It then lands 57 m away on the other side. Find​ h(d), the quadratic function that represents this.

Mathematics
1 answer:
omeli [17]3 years ago
5 0

Answer:

  h(d) = (17/3249)(-d² +114d)

Step-by-step explanation:

For this purpose, it is convenient to translate and scale a quadratic parent function so it has the desired characteristics. We can start with the function ...

  f(x) = 1 -x² . . . . . . . has zeros at x = ±1 and a vertex at (0, 1)

We want to horizontally expand this function by a factor of 57, so we can replace x by x/57. We want to vertically scale it by a factor of 17, so the vertex is at (0, 17). Finally, we want to translate the function 57 m to the right, which requires replacing x with x-57. After these transformations, we have ...

  f(x) = 17(1 -((x-57)/57)²) = (17/3249)(-x²+114x)

Using the appropriate function name and variable, we have ...

  h(d) = (17/3249)(-d² +114d)

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At Burnt Mesa Pueblo, archaeological studies have used the method of tree-ring dating in an effort to determine when prehistoric
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a) (1215, 1297)

b) (1174,  1338)

c) (1133, 1379)      

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 1256

Standard Deviation, σ = 41

Empirical Rule:

  • Also known as 68-95-99.7 rule.
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a) range of years centered about the mean in which about 68% of the data lies

\mu \pm 1(\sigma)\\=1256 \pm 41\\=(1215, 1297)

68% of data will be found between 1215 years and 1297 years.

b) range of years centered about the mean in which about 95% of the data lies

\mu \pm 2(\sigma)\\=1256 \pm 2(41)\\=1256 \pm 82\\=(1174, 1338)

95% of data will be found between 1174 years and 1338 years.

c) range of years centered about the mean in which about all of the data lies

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All of data will be found between 1133 years and 1379 years.

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3 years ago
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