(a) Evaluate : (2 div (frac{64}{125})^{-frac{2}{3}})
(b) The lines (y = 3x + 5) and (y = – 4x – 1) intersect at a point k. Find the coordinates of k.
Explanation
(a) ((frac{64}{125})^{-frac{2}{3}} = (frac{125}{64})^{frac{2}{3}})
= ((frac{5}{4})^{3})^{frac{2}{3}} )
= ((frac{5}{4})^{2})
= (frac{25}{16})
(therefore 2 div (frac{64}{125})^{-frac{2}{3}} = 2 div frac{25}{16})
= (2 times frac{16}{25})
= (frac{32}{25})
(b) (3x + 5 = – 4x – 1)
(3x + 4x = – 1 – 5)
(7x = – 6)
(x = -frac{6}{7})
(y = 3x + 5) ( You can use any of the given equations to get y)
(y = 3(-frac{6}{7}) + 5 = -frac{18}{7} + frac{35}{7})
= (frac{17}{7})
(k = (x, y) = (-frac{6}{7}, frac{17}{7}))