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ivann1987 [24]
3 years ago
7

9. The approximate circumferences of Earth

Mathematics
1 answer:
Molodets [167]3 years ago
8 0

Answer and explanation:

1) Given : Circumference of Earth C_E= 365,882\ km

Circumference of Saturn C_S= 4.01\times 10^4\ km

To find : How many times  greater is the circumference of Saturn than  the circumference of Earth?

Solution :

Let x be the number of times greater is the circumference of Saturn than  the circumference of Earth.

According to question,

x=\frac{C_E}{C_S}

x=\frac{365882}{4.01\times 10^4}

x=\frac{365882}{40100}

x=9.124

Therefore, 9.124 times  greater is the circumference of Saturn than  the circumference of Earth.

2) Number  0.037854921

Estimate to the nearest hundredth.

The hundredth number is 3 and thousandth number is 7.

As thousandth number 7 is greater than 5.

So, hundredth number is added by 1 and rest became zero.

i.e. 0.037854921\approx 0.04

3) Compare the numbers 6 \times 10{-6} and 2\times 10{-8}

6 \times 10{-6}=\frac{6}{1000000}

2\times 10{-8}=\frac{2}{100000000}=\frac{0.02}{1000000}

As the denominator is same compare the numerator,

0.02<6 or 6>0.02

So, 6 \times 10{-6}>2\times 10{-8}

Therefore, 6 \times 10{-6} is greater than 2\times 10{-8}

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Sindrei [870]

The angle of elevation of 61° and 72° with the height of the tower being 553.3 m. gives Vic's distance from Dan as approximately 356 meters.

<h3>How can the distance between Vic and Dan be calculated?</h3>

Location of Vic relative to the tower = South

Vic's sight angle of elevation to the top of the tower = 61°

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Dan's angle of elevation in order to see the top of the tower = 72°

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tan( \theta) =  \frac{opposite}{adjacent}

tan( 61 ^{ \circ}) =  \frac{553.3}{ Vic' s\: distance \: to \: tower}

distance  =  \frac{553.3}{tan ( {61}^{ \circ} )}  = 306.7

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Similarly, we have;

Dan's distance  =  \frac{553.3}{tan ( {72}^{ \circ} )}  = 179.8

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Given that Vic and Dan are at right angles relative to the tower (Vic is on the south of the tower while Dan is at the west), by Pythagorean theorem, the distance between Vic and Dan <em>d </em>is found as follows;

  • d = √(306.7² + 179.8²) ≈ 356

Therefore;

  • Vic is approximately 356 meters from Dan

Learn more about Pythagorean theorem here:

brainly.com/question/343682

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