Answer:
1. 194
2. 189
Step-by-step explanation:
1. 991 - 797 = 194
2. 826 - 637 = 189
We want to evaluate
First we note that the integrand is even (replacing x with -x doesn't fundamentally alter the function being integrated), so this is equal to
The radicand reduces significantly to
so that taking the square root, we simplify the integral to
which is trivially computed with a substitution of 
and 
:
From the fraction solved, the distance that the rabbit should be behind the turtle will be 400 meters.
<h3>How to solve the distance</h3>
From the information, it was stated that a rabbit and a turtle run 100 meters and that when the rabbit finished, the turtle was behind by 80 meters. Therefore, the distance covered by the turtle will be:
= 100 - 80
= 20 meters
Therefore, the fraction of their distance will be:
= 20/100 = 1/5
Therefore, the number of meters behind the turtle that the rabbit should start will be:
= 80 × 5
= 400 meters.
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