Then in the entire integrand, set , so that . The integral is then equivalent to
Note that by letting , we are enforcing an invertible substitution which would make it so that requires or . However, is positive over this first interval and negative over the second, so we can't ignore the absolute value.
So let's just assume the integral is being taken over a domain on which so that . This allows us to write
We can show pretty easily that
which means the integral above becomes
Back-substituting to get this in terms of is a bit of a nightmare, but you'll find that, since , we get
To find her unit rate, we need to find how many problems she can do in 1 minute. Our current fraction is . We need to divide the top and bottom by 2.5 to get the rate per minute
<u>The correct answer is A. The distance traveled depends on the number of hours traveled. </u>
Step-by-step explanation:
Let's recall that:
1. The formula of the speed is distance/time
2. If the speed is constant, like the train in our problem, which is 45 miles per hour, then we can assume it as a value of 1 and a we can confirm a direct relation between the distance traveled and the number of hours traveled, this way:
Speed = Distance/Time
Distance = Speed * Time
Distance = 1 * Time
Distance = Time
This means the longer you stay in the train, the more miles you will travel or the more hours you travel by the train, the more distance you will cover.
<u>The correct answer is A. The distance traveled depends on the number of hours traveled. </u>