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Novay_Z [31]
3 years ago
10

One rule of thumb for estimating crowds is that each person occupies 2.3 square feet. Use this value to estimate the size of a c

rowd that is 8 feet wide on both sides of the street standing along a 4.1-mile section of a parade route.
Mathematics
1 answer:
dybincka [34]3 years ago
7 0

Answer:

150,595

Step-by-step explanation:

First, convert miles to feet:

4.1 mi × (5280 ft/mi) = 21648 ft

The area that the crowd takes up is:

2 × 8 ft × 21648 ft = 346368 ft²

The number of people is:

346368 ft² × (1 person / 2.3 ft²) = 150594.8

Rounding to the nearest integer, there are approximately 150,595 people in the crowd.

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The graphs of g(x) = x³- ax² + 6 and h(x) = 2x² + bx + 3 touch when x = 1. Therefore, the tangent to
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Answer:

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Step-by-step explanation:

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The question states that the graphs of g(x) and h(x) touch at x = 1, such that g^\prime(1) = h^\prime(1). Therefore:

3 - 2\, a = 4 + b.

On the other hand, since the graph of g(x) and h(x) coincide at x = 1, g(1) = h(1) (otherwise, the two graphs would not even touch at that point.) Therefore:

1 - a + 6 = 2 + b + 3.

Solve this system of two equations for a and b:

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g(x) = x^3 + 3\, x^2 + 6.

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Evaluate either expression at x = 1 to find the y-coordinate of the intersection. For example, g(1) = 1 + 3 + 6 = 10. Similarly, h(1) = 2 + 5 + 3 = 10.

Therefore, the intersection of these two graphs would be at (1,\, 10).

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