HELP ASAP GIVING BRAINLIST!!!!!!!!!!!!
2 answers:
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I did the work, and basically i solved for the area of the faces and then multiplied that by two to get the total surface area of the faces. Then I added in the areas of the sides connecting the two faces:
just as a referral: the formulas to find the faces are as follows:
rectangle: length times width
circle: pi x r^2
trapezoid: h(base1 + base2)
and triangle: (b x h)/2
(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,