(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:
{x,y}={-8,-2}
Step-by-step explanation:
[1] x = 2y - 4
Plug this in for variable x in equation [2]
[2] 7•(2y-4) + 5y = -66
[2] 19y = -38
Solve equation [2] for the variable y
[2] 19y = - 38
[2] y = - 2
By now we know this much :
x = 2y-4
y = -2
Use the y value to solve for x
x = 2(-2)-4 = -8
Answer:
91 why you need to know this late
Step-by-step explanation:
Answer:
Step-by-step explanation:
The answer would be 0.375 as a decimal and 37.5% as a percentage
Answer:
x=-1, -6
Step-by-step explanation:
x^2+7x+6=0
factor
(x+1)(x+6)=0
x+1=0, x+6=0
x=0-1=-1
x=0-6=-6
