Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and sodium chlorate to evaporate slowly. If v is the volume of such a cube with side length x, calculate the derivative when x = 4 mm.

48 mm ^ 2

Step-by-step explanation:

We know we have a cube of side x, therefore the volume of that cube will be equal to:

V = x ^ 3, because it is a cube and each side is the same.

Now the derivative of the volume with respect to the length (that is, x) would be:

dV / dx = 3 * (x ^ 2)

They tell us that x takes a value of 4, replacing we have:

dV / dx = 3 * (4 ^ 2) = 48

That is, 48 mm ^ 2 would be the value of dV / dx when x is equal to 4 mm.

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)