Given is the equation dy dx = xy + ax + by + 1; a, b > 0. For every value of a > 0, find a value for b such that the equation becomes sepa- rable. Specify functions ga(x) and ha(y) to prove that the equation is separable. (b) Show that the equation dy dx = sin(x) + y 2 is not separable. Hint: Assume that there exist functions g(x) and h(y) such that g(x)h(y) = sin(x) + y 2 . Then insert values (0, 0), (1, 0), and (0, 1) into this equation.

the 8 in 8,420 is in the thousands place so it's value is 8 thousand.

the 8 in 6,870 is in the hundreds place so it's value is 8 hundred.

divide 8000 by 800 to find the answer:

8000 / 800 = 10

the 8 in 8,420 is 10 times greater than the 8 in 6,870

the height of the surface increases from the center out to the sides of the road.

step-by-step explanation:

as we move out we move away from the x-axis.

and as mentioned in the problem statement that height of a road increases when we move away from the center x.

hence proved that 3rd option

the height of the surface increases from the center out to the sides of the road.

is the correct option.

step-by-step explanation:

d would equal 12