Consider the vector field f=(x2+y2,4xy). compute the line integrals ∫c1f⋅ds and ∫c2f⋅ds, where c1(t)=(t, t2) and c2(t)=(t, t) for 0≤t≤1. can you decide from your answers whether or not f is a gradient vector field? why or why not?

The value of the line integral depends on the path, so is not a gradient vector field.

distance covered by pamela in 9 l of fuel = 99km

let us apply unitary method here.

distance covered by pamela in 1 l of fuel =99/9 =11 km

now let us find distance covered by pamela if she has 12 l of fuel.

distance covered in 12 l = distance covered in 1 l of fuel * 12

we know that distance covered by here in 1 l is 11 km.

so distance covered in 12 l of fuel = 11*12 = 132 km.

it has the same slope and a different y-intercept

hope this : )