Line passing through point (-2, -3) with a slope of -6 is (y - (-3)) = -6(x - (-2)) => y + 3 = -6(x + 2)
See attachment for one such shell. The volume is given by the sum of infinitely many thin shells like this, each with radius

and height determined by the vertical distance between the upper blue curve and the lower orange curve for any given

, i.e.

.
The volume is then
Answer:
The solutions are linearly independent because the Wronskian is not equal to 0 for all x.
The value of the Wronskian is 
Step-by-step explanation:
We can calculate the Wronskian using the fundamental solutions that we are provided and their corresponding the derivatives, since the Wroskian is defined as the following determinant.

Thus replacing the functions of the exercise we get:

Working with the determinant we get

Thus we have found that the Wronskian is not 0, so the solutions are linearly independent.
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Answer:

Step-by-step explanation:
Always proceed by first extracting all common factors to all terms:
Notice that the factors: 5, x, and y are present in all terms, so we can extract them from the trinomial:

Now, the trinomial left (-x+2-3y) cannot be factored out, so then factoring is complete.