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56 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Direct and Inverse Proportion If y x2 and y = 4 when x = 4, find the value of y when x = 12. y = kx' and y = 200 when x = 5. a) Find the value of k. b) Find the value of y when x = 8. c) Find the value of x when y = 2433.4. Given that y varies inversely as the square of x, complete the following table of values, given that x is always positive. MOM IIII 4 Two cylindrical containers are filled to the same depth, d cm, with water. The mass of the water in each container is proportional to the square of the radius of each container. The first container has a radius of 16 cm and the water has a mass of 16 kg. If the second container has a radius of 8 cm, find the mass of the water inside it. d cm x EMI 24 6 8 r = 16 cm Given that r varies inversely as the square of s, and r = 24 when s = 10, find the values of: a) r when s = 5 b) s when r = 150, given that s is positive c) r when s = 2 d) s when r = 374-, given that s is negative \\ 1 \\111111/1 l //// Don't forget about that little joker, the "inverse square" variation — they'll — expect you to know that, too. // /1 / \ 1 1 \ The gravitational pull of the Earth is inversely proportional to the square of the distance from the centre of the Earth. At the Earth's surface (approx. 6370 km from the centre) the gravitational pull is around 9.8 N kg-'. When launching a satellite into space, the gravitational pull helps determine the orbit. What would be the gravitational pull on a satellite at a height of 100 km above the Earth's surface (to 1 d.p.)? By considering the values in the table, decide whether y oc x, y oc —1 or y ccT1 a) Write down the equation which shows how y varies with x. b) Find the value of y when x = 6.4. c) Find the value of x when y = 16. X 1.2 2.5 3.2 4.8 166 i 80 62.5 413 SECTION THREE — ALGEBRA




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