Mathematics, 24.10.2020 09:50 kassidyopry15

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?

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Answer from: vickye146

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 = 2πr

Thus, radius is;

r = C/(2πr)

r = 132,000,000/(2π)

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, $C_{new}$ = 132000003 ft

Let's find the radius of this circumference;

$r_{new}$ = 132000003/(2π)

$r_{new}$ = 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 = $r_{new}$ - 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.

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Answer from: kamand10

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.

Work Shown:

1 mile = 5280 ft

25000(1 mile) = 25000(5280 ft)

25,000 miles = 132,000,000 ft

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.

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

Subtract the two radius values

(larger radius) - (smaller radius)

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

0.47746489569544

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.

Answer from: Quest

i think ur answer is (3,-1)

Answer from: Quest

The first one, i believe, would be correct. all the others have one thing in common, and that's that they have repeating numbers. in the second one, x and y have repeating 6's and 3's, and in the third, x and y have repeating 6's as well. in the last one, there are repeating 3's. the first one has no repeating numbers.
Which table shows a proportional relationship between x and y

Which table shows a proportional relationship between x and y

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Imagine a cable fastened snug around the earth along the equator (circumference is about 25,000 mil...