Verify the first special case of the chain rule for the composition f∘c in each of the cases: (a) f(x, y)=xy, c(t)=(et, cost)

(b) f(x, y)=exy, c(t)=(3t2,t3)

(c) f(x, y)=(x2+y2)log√x2+y2,c(t)=(et, e−t)

(d) f(x, y)=xexp(x2+y2),c(t)=(t,−t)

The ratio pv to nrt is plotted against pressure for ch4 at 0°c and 200°c. why does the curve for 0°c drop below the horizontal line for an ideal gas whereas the curve for 200°c does not?

The tuition costs, c, for a local community college are modeled by c(h) = 250 + 200h, where h represents the number of credit hours taken. the local state university has tuition costs, s, modeled by the function s(h) = 300 + 180h. how many credit hours will a student have to take for the two tuition costs to be equal? round the answer to the nearest tenth of an hour.

What value of x is in the solution set of 4x – 12 s 16 + 8x?