Variations

Question 5: It is given that R varies directly as the square root of S and inversely as the square of T. Find the relation between R, S and T. Solution: R α S T 2 Question 6: It is given that P varies directly as the square of Q and inversely as the square … Read more

Question 1: It is given that y varies directly as the cube of x and y = 192 when x = 4. Calculate the value of x when y = – 24. Solution: y α x³ y = kx³ 192 = k (4)³ 192 = 64 k k = 3   y = 3 x³ when y = – 24  – 24 … Read more

1.3 Joint Variation   1.3a Representing a Joint Variation using the symbol ‘α’. 1. If one quantity is proportional to two or more other quantities, this relationship is known as joint variation. 2. ‘y varies directly as x and z’ is written as y α xz. 3. ‘y varies directly as x and inversely z’ is … Read more

1.2 Inverse Variation If a quantity y  varies inversely as another quantity x, then (a) y increases when x decreases, (b) y decreases when x increases 1.2b Expressing an inverse variation in the form of an equation An inverse variation can be written in the form of an equation, y = k x where k is a constant which … Read more

Example: Given that p varies directly as square root of q and p = 12 when q = 36, find (a) The value of p when q = 16 (b) The value of q when p = 18 Solution: p ∝ q , p = k q 12 = k 36 12 = k(6) k = 2 p = … Read more

(D) Solving problems involving direct variations 1. If   y∝ x n , where n= 1 2 , 2, 3,  then the equation is y = k x n where k is a constant. 2. The graph of y against xn is a straight line passing through the origin. 3.  If   y ∝ x n and sufficient information … Read more

(A) Determining whether a quantity varies directly as another quantity 1. If a quantity y varies directly as a quantity x, the (a) y increases when x increases (b) y decreases when x decreases   2. A quantity y varies directly as a quantity x if and only if y x = k  where k is called the constant … Read more