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frez [133]
3 years ago
14

(Photo attached) Trig question. I partially understand it, but not completely. Please explain! :) Thanks in advance.

Mathematics
1 answer:
aliya0001 [1]3 years ago
5 0

Answer:

  • A = 2
  • B = 3

Step-by-step explanation:

You can start by recognizing 19/12π = π +7/12π, so the desired sine is ...

  sin(19/12π) = -sin(7/12π) = -(sin(3/12π +4/12π)) = -sin(π/4 +π/3)

  -sin(π/4 +π/3) = -sin(π/4)cos(π/3) -cos(π/4)sin(π/3)

Of course, you know that ...

  sin(π/4) = cos(π/4) = (√2)/2

  cos(π/3) = 1/2

  sin(π/3) = (√3)/2

So, the desired value is ...

  sin(19π/12) = -(√2)/2×1/2 -(√2)/2×(√3/2) = -(√2)/4×(1 +√3)

Comparing this form to the desired answer form, we see ...

  A = 2

  B = 3

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Answer:

Greatest population density: Denmark

Smallest population density: The U.S.

Step-by-step explanation:

Population density = population / area

So let's find the population density of each country

For U.S

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Area: 9,364,520 sq km

Population density: 272,648,000/9,364,520=29.1 ( rounded to the nearest tenth )

So the population density of the U.S is 29.1 people per sq km

For Denmark

Population: 5,248,000

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Population density: 5,248,000/42,077=124.7 ( rounded to the nearest tenth )

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Area: 237,533

Population density: 18,339,000/237,533=77.2 ( rounded to the nearest tenth ).

So the population density of Ghana is 77.2 people per sq km

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Looking at the population densities we can conclude that Denmark has the largest population density at 124.7 people per sq km and the U.S. has the smallest population density at 29.1 people per sq km

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