Answer:
b or c
Step-by-step explanation:
Answer:

Step-by-step explanation:

The answer is 24.62. Hope this help

Suppose the ODE has a solution of the form
, with total differential

This ODE is exact if the mixed partial derivatives are equal, i.e.

We have


so the ODE is indeed exact.
Integrating both sides of

with respect to
gives

Differentiating both sides with respect to
gives





so the general solution to the ODE is

Given that
, we find

so that the solution to the IVP is


Answer:
The third answer. ( John's boat was farther from the deck at the beginning but Roberta's boat traveled more quickly)
Step-by-step explanation:
You already know that in the beginning John's boat begins 20 miles from the dock. Now you need to find Roberta! When each boat begins from the dock, it means when x=0. So lets insert that! y= 6(0)+15. You get 15. Now you know that its either the 3rd or 4th answer. The second piece of info you have for John is that it is 45 miles from the dock after 5 hours. Again, in the beginning it started with 20 miles. 45-20= 25 miles TRAVELED in 5 hours. For Roberta, we need to insert 5 in the equation for x. y=6(5)+15. You get: 45 again! But... Roberta started at 15 miles. So 45-15 is 30 miles. She traveled 30 miles in 5 hours. The only answer that is matching to our problem solving is the third answer. Hope this helps!