Suppose a wealthy entrepreneur commissions the design of a spherical spaceship to house a small group for a week in orbit around the earth. the designer allocates 1000ft^3 for each person, plus additional 4073.5ft^3 for various necessary machines. the diameter of the ship is 26.8ft.

a. what is the volume of the spaceship?

b. for approximately how many people is the ship designed?

A. The volume of the spaceship is calculated through the equation,
                                 V = 4πr³/3
Dividing the given diameter by 2 to get the radius will give us 13.4 ft. Substituting the known values to the equation,
                                 V = 4π(13.4 ft)³/3 = 10078.64 ft³

b. If we let x be the number of people allowable in the spaceship, the equation that would best represent the scenario is,
                                      1000x + 4073.5 = 10078.64
The value of x from the equation is 6. 

the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.