csZachariah Greaves
June 11, 2014
MAT 220
40. In an equation, y=kx, when you multiply x by a fixed amount, y is also multiplied by the same amount. If x doubles, then y would also double. As long as x is always as twice as much as y, then they vary directly.
41. The first thing you would do is start with the equation y=kx. Next you would take the given values, plug them in, and solve to find k. Then you would substitute that answer for k into the equation. Finally, you would solve whatever the question is asking.
42. In an equation, y=k/x, y would vary inversely as x. If y increases, then x would decrease, and vice versa.
43. Combined variation is when direct and inverse variation occur at the same time. An example would be; Y=kA, this being a direct variation equation, and Y=k/Z, this being an inverse variation equation. The combined variation equation would be Y=kA/Z.
44. Joint variation is when a variable varies directly as the product of two or more other variables. The equation would be y=kxz, and it would be defined as y varies jointly as x and z.
45. This equation is a combined variation equation.
46. This equation is a joint variation equation.
47. The name is appropriate, because as with the gravitation formula, the two bodies are the two cities, and they vary jointly as their population, which is their masses like the gravitation formula. They also vary inversely as the square of the distance between them, which is the exact same as the gravitation formula. So with this problem, a similar version of F=G m1m2/d^2 would work