Answer with Step-by-step explanation:
The given differential equation is
Now the above differential equation can be re-written as
Checking for exactness we should have
As we see that the 2 values are equal thus we conclude that the given differential equation is exact
The solution of exact differential equation is given by
The value of can be obtained by differentiating u(x,y) partially with respect to 'y' and equating the result with P(x,y)
Answer:
4:18 8:36 1:4.5
Step-by-step explanation:
8 x 7 x 6 x 5 x4 x3 = 20,160 ways
When we connect the ends of the poles and the project the horizontal line from the end of the 10-ft pole to the other pole, we form a right triangle with the legs equal to 12 ft and difference of the lengths of the pole. Using the Pythagorean theorem,
h² = sqrt ((12 ft)² + (15 - 10)²)
h = 13 ft
Thus, the distance between the tops of the poles is equal to 13 ft.