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

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.