Answer:
Step-by-step explanation:
<u>Given function:</u>
- f(x) = -x² + bx - 65 with maximum value of 35
<u>To find </u>
<u>Solution:</u>
Maximum value is obtained at vertex as a < 0
<u>Vertex coordinate of x is:</u>
- x = -b/2a = -b / -2 = 1/2b
<u>Solving for b:</u>
- 35 = - (1/2b)² + b(1/2b) - 65
- - 1/4b² + 1/2b² = 100
- 1/4b² = 100
- b² = 400
- b = √400
- b = ± 20
See attached
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Answer: 11 and 12
Step-by-step explanation:
Answer: 42804 people per square mile
Step-by-step explanation:
As we know Population density = 
Given, population of New York City = 8.55 million
Area of New York City = 300 square miles
Then, population density of New York City = 
[1 million = 1,000,000]
Population of Manhattan = 1.64 million = 1640000
Area of Manhattan = 23 square miles
population density of Manhattan = 
Difference = 71304 - 28500 =42804
Hence, population density of Manhattan is 42804 people per square mile greater than that of New York City.
