olesya6398
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Imagine a cable fastened snug around the earth along the equator (circumference is
about 25,000 miles). Now loosen the cable so that it is 3 feet longer and thus not so perfectly snug anymore. How high off the ground will the cable be?

Respuesta :

Answer: about 5.73 inches off the ground

Note: the cable will need to be held up with vertical poles of this height so that a taut wire rope ring forms around the earth.

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Work Shown:

1 mile = 5280 ft

25000(1 mile) = 25000(5280 ft)

25,000 miles = 132,000,000 ft

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Let's find the radius of a circle that has circumference 132,000,000 ft

C = 2*pi*r

r = C/(2pi)

r = (132,000,000)/(2pi)

r = 21,008,452.4881301

The radius of the earth is approximately 21,008,452.4881301 ft

A more simplified view is that the radius is little over 21 million feet.

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Increase the value of C by 3 ft, so C = 132,000,003 now. Repeat the steps to get the larger radius to be...

r = C/(2pi)

r = (132,000,003)/(2pi)

r = 21,008,452.965595

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Subtract the two radius values

(larger radius) - (smaller radius)

(21,008,452.965595) - (21,008,452.4881301)

0.47746489569544

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This is less than a foot, so let's convert this to inches to see what comes up

Multiply by 12 to convert from feet to inches

0.47746489569544*12 = 5.72957874834529

This rounds to about 5.73 inches. Round the answer however you need to. Also, if you need me to convert to some other measurement, then let me know.

The height of the cable off the ground will be 5.73 inches high.

  • We are given;

Circumference; C = 25,000 miles

From Conversion tables, we know that;

1 mile = 5280 ft

Thus;

25000 miles = 25000 × 5280

⇒ 132,000,000 ft

 

  • We know that formula for circumference is;

C = 2Ï€r

Thus, radius is;

r = C/(2πr)  

r = 132,000,000/(2Ï€)

r = 21,008,452.48813 ft  

  • We are told that the cable is loosened so that it is 3 ft longer. This means that the circumference increases by 3 ft.

Thus, [tex]C_{new}[/tex] = 132000003 ft

  • Let's find the radius of this circumference;

[tex]r_{new}[/tex] = 132000003/(2Ï€)

[tex]r_{new}[/tex] = 21,008,452.965560

  • To find how high the cable will be off the ground, we will find the difference between the two radius;

Thus;

Height of cable above the ground = [tex]r_{new}[/tex] - r

Height of cable above the ground = 21,008,452.96556 - 21,008,452.48813

 Height of cable above the ground = 0.47743 ft

Converting to inches gives us;

Height of cable above the ground ≈ 5.73 inches.

Read more at; https://brainly.com/question/21837338

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