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cupoosta [38]
3 years ago
14

A mobile base station (BS) in an urban environment has a power measurement of 8µW at 225m. Assuming the propagation follows an i

nverse cube power law (Section 3.2.2), what is a reasonable value to assume at a distance 675m from the BS?
Give your answer in scientific notation, to 2 decimal places.
Mathematics
1 answer:
nata0808 [166]3 years ago
8 0

Answer:

The reasonable value = 2.96 × 10^(-1) µW

Step-by-step explanation:

* Lets explain how to solve the problem

- A mobile base station in an urban environment has a power

 measurement of 8 µW at 225 m

- The propagation follows an inverse cube power law

- We need to find the reasonable value to assume at a distance

  678 m from the base station

∵ The propagation follows an inverse cube power law

- <em>The power would have been decreased by a factor 1/n³ </em>

<em>   times the power as a distance increasing</em>

∵ n = the ratio between the distances

∵ The distance are 675 m and 225

∴ n = 675/225 = 3

∴ 1/n³ = 1/3³ = 1/27

- The reasonable value is the product of the power measurement of

  8 µW and 1/27

∴ The reasonable value = 8 × 1/27 = 8/27 µW = 0.296296

∴ The reasonable value = 2.96 × 10^(-1) µW

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n200080 [17]
A=43°
B=82°
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1) A+B+C=180°
Replacing A=43° and B=82° in the equation above:
43°+82°+C=180°
125°+C=180°
Solving for C. Subtracting 125° both sides of the equation:
125°+C-125°=180°-125°
C=55° (option B or C)

2) Law of sines
a/sin A=b/sin B=c/sin C
Replacing A=43°, B=82°, C=55°, and c=28 in the equation above:
a/sin 43°=b/sin 82°=28/sin 55°

2.1) a/sin 43°=28/sin 55°
Solving for a. Multiplying both sides of the equation by sin 43°:
sin 43°(a/sin 43°)=sin 43°(28/sin 55°)
a=28 sin 43° / sin 55°
Using the calculator: sin 43°=0.681998360, sin 55°=0.819152044
a=28(0.681998360)/0.819152044
a=23.31185549
Rounded to one decimal place
a=23.3

 2.2) b/sin 82°=28/sin 55°
Solving for a. Multiplying both sides of the equation by sin 82°:
sin 82°(b/sin 82°)=sin 82°(28/sin 55°)
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Using the calculator: sin 82°=0.990268069, sin 55°=0.819152044
b=28(0.990268069)/0.819152044
b=33.84903466
Rounded to one decimal place
b=33.8

Answer: Option B) C=55°, b=33.8, a=23.3
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