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A body’s weight varies inversely with the square of its distance from the center of the earth; if a chicken weighs 20 pounds when it is 5000 miles from the earth’s center, how much will the chicken weigh when it is 10000 miles from the earth’s center?

Answer 1

Jace Anderson

The chicken will weigh 5 pounds when it is 10000 miles from the earth's center.

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Answer 2

Eva Adamson

5 pounds

The inverse relationship means that

#W_1/W_2 = r_2^2/r_1^2#

#W_1 r_1^2 = W_2 r_2^2 = "constant"#

where #W_1# is the weight when the distance is #r_1#, and #W_2# is the weight when the distance is #r_2#.

Now, we know that

We want to find #W_2#.

#W_1/W_2 = r_2^2/r_1^2#

#(20 "pound")/W_2 = (10000 "mile")^2/(5000 "mile")^2#

#= 4#

#W_2 = (20 "pound")/4#

#= 5 "pound"#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.