(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:
communicative, you can remember this by saying (the rule for the communicative property, is as easy as can be, just remember a+b is the same as b+a )
Answer:
4 × 5 × 6 × 1012 = 121440
= 1.2 × 10⁵
Answer:
1. D y = 8
2. C y = −8
Step-by-step explanation:
1.Both points have y-coordinate 8, so the line is horizontal.
A horizontal line has equation y = k
where k is the y-coordinate of all of its points.
The y-coordinate of all points on this line is 8.
Answer: y = 8
2.A line with 0 slope is a horizontal line. All points on a horizontal line have the same y-coordinate.
A horizontal line has equation
y = k
where k is the y-coordinate of all of its points.
The y-coordinate of the given point is -8, so all points must have -8 as the y-coordinate.
Answer: y = -8
Answer:
B. $1,400
Step-by-step explanation:
8.75 x 20 x 8 =
8.75 x 160 = $1400
B
Hope that helps!
