(a) If there is a scalar function f(x, y) such that ∇ f(x, y) = x² i + y² j, then
∂f/∂x = x²
∂f/∂y = y²
Integrating both of these equations with respect to x and y (respectively) gives
f(x, y) = 1/3 x³ + g(y)
f(x, y) = 1/3 y³ + h(x)
Differentiating with respect to the other variable gives
∂f/∂y = g'(y) = y²
∂f/∂x = h'(x) = x²
so it follows that
f(x, y) = 1/3 x³ + 1/3 y³ + C
for some constant C.
(b) By the gradient theorem,

Answer:
i think it is length hopefully that's correct
Here. Remember to get the correct units. If you need extra help, I am more than willing to help!
Answer:
2/11
Step-by-step explanation:
6 = 2 x 3
6/11 x 1/3
= ( 6 x 1 )/( 11 x 3 )
= ( 2 x 3 x 1 )/( 11 x 3 )
Cancel 3 in both numerator and denominator.
= ( 2 x 1 )/( 11 )
= 2/11
Answer:
65%
Step-by-step explanation: