DSE 數學公式 (Maths Formula): Variations 變分公式

Variations

• Direct variations (unknown 寫分子)

If y varies directly as x, then y = kx for some non-zero constant k. 

• Inverse variations (unknown 寫分母)

If y varies inversely as x, then y = \frac{k}{x} for some non-zero constant k. 

• Joint variations 

If z varies as x and y, then z = kxy for some non-zero constant k. 

• Partial variations 

If z is partly constant and partly varies directly as x, then z = k_{1} + k_{2}x for some non-zero constant k. 

If z partly varies directly as x and partly varies inversely as y, then z = k_{1}x + \frac{k_{2}}{y} for some non-zero constant k. 

變分

• 正變 (未知數寫分子)

若y 隨x而正變，則y = kx，其中k為非零常數。

• 反變 (未知數寫分母)

若 y 隨 x反變，則y = \frac{k}{x} ，其中k為非零常數。

• 聯變

若z 隨x 及y聯變, 則z = kxy，其中k為非零常數。

• 部分變

若z 部分為常數及部分隨x正變, 則z = k_{1} + k_{2}x，其中k為非零常數。

若z 部分隨x 正變及部分隨y反變, 則z = k_{1} + \frac{k_{2}}{y}，其中k為非零常數。