Express the edge length of a cube as a function of the cube's diagonal length d. Then express the surface area and volume of the cube as a function of the diagonal length. a. A function for the edge length of a cube is L(d) =
b. A function for the surface area of a cube is Ald) =
c. A function for the volume of a cube is V(d) =

Step-by-step explanation:

If L is the length of a side, the longest diagonal in the cube is

d = √(L² + L² + L²) = √(3L²) = L√3

meaning

a) L(d) = d/√3 = ⅓d√3

b) A(d) = 6(L(d))² = 6(⅓d√3)² = 6(⅟₉d²(3)) = 2d²

c) V(d) = (L(d))³ = (⅓d√3)³ = ⅟₂₇d³3√3 = ⅟₉d³√3

step-by-step explanation:

; fx

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.