Michaela spent a total of 12 1/2 hours doing her online learning work this week. If she spent 5 3/4 of those hours working on Monday, how much time did she work the rest of the week?

6 3/4 hours

Step-by-step explanation:

12 1/2 turned into an improper fraction is 25/2. 5 3/4 turned to an improper fraction is 23/4. The common denominator for these fractions is 4. So you have 50/4 -23/4 which is 27/4. The proper fraction form would be 6 3/4.

Diverges

Step-by-step explanation:

We have been given a definite integral . We are asked to determine whether the given integral converges or diverges.

We will use integral by parts formula to solve our given definite integral.

Let and .

Now we need to find du and v using above values.

Apply chain rule:

Substitute back these values in parts by integration formula.

Let us compute the boundaries.

Since is not a finite value, therefore, the integral diverges.