Extra Credit: 8 congruent spheres are packed into a cube with
edge length x so that each sphere is tangent to 3
faces of the cube and 3 other spheres as shown.
what is the ratio of the total volume of the
spheres of the volume of the cube?

Ratio of the volumes of the spheres and cube = 0.523

Step-by-step explanation:

From the figure attached,

Diameter of one sphere = Half of the measure of one side of the cube

                                        =

Radius of the sphere =

                                   =

Volume of a cube is given by the formula,

V =

Therefore, volume of one sphere =

                                                        =

Volume of 8 spheres =

                                   =

Volume of a cube = (side)³

                              =

Ratio of the volumes of the sphere and cube =

                                                                              =

                                                                              ≈ 0.523

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

he earned 78.75 in interest.

step-by-step explanation: