Answer:
B. x(x) + (−6)(−3)
NOT equivalent to (x − 6)(x − 3)
Step-by-step explanation:
(x − 6)(x − 3)
= x^2 - 3x - 6x + 18
= x^2 - 9x + 18
A. (6 − x)(3 − x)
= 18 - 6x - 3x + x^2
= 18 - 9x + x^2
= x^2 - 9x + 18 ---->equivalent to (x − 6)(x − 3)
B. x(x) + (−6)(−3) = x^2 + 18 ----> NOT equivalent to (x − 6)(x − 3)
C. x2 − 3x − 6x + 18 = x^2 - 9x + 18 --> equivalent to (x − 6)(x − 3)
D. x(x − 6) − 3(x − 6)
= x^2 - 6x - 3x + 18
= x^2 - 9x + 18 ---->equivalent to (x − 6)(x − 3)
(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: Choice A
Step-by-step explanation:
53 + 9x < 115
THE LESS THAN SYMBOL SHOULD HAVE A LINE UNDER IT!