The minimum depth, d (in meters), of water in a harbour, t hours after midnight, can...

    

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The minimum depth, d (in meters), of water in a harbour, t hours after midnight, can be approximated by the function d(t) = 5 cos (0.5t) + 12 where 0 Q1. Determine the equation of the quartic function with rational coefficients, zeros 42 and -36 and a y-intercept of -21 Q2. The function f(x) = x(x+1)(x-2) is reflected in the x-axis, stretched horizontally from the y-axis by a factor of 2 and translated 3 units to the right. State the equation of the new function in simplest form and determine its zeros. One way to approximate the instantaneous rate of change at a is to add a very small increment, say 0.001, to the value, a, of the independent variable, and then calculate the slope of the secant line between the points (a, f(a)) and (a + 0.001, f(a + 0.001)). That is, f(a + 0.001) f(a) IROC 0.001 Radium (Ra-225) has a half-life of 15 days. For a 100 g sample, the amount of radioactive material remaining, A after time t, is given by the equation A(t) = 100(0.5), where A is measured in grams and t is measured in days. (a) Find the average rate of change from 3 days to 4 days, rounded to one decimal place. (b) Approximate the average rate of change at 3 days, rounded to one decimal place. Q1. Using appropriate double angle formulas and your knowledge of transformations, sketch the graphs of f(x) = 2 sin (x) and g(x) = 3 sin (2x) cos (2x) - 1 Q2. Prove that (c csc (6) sec : (0) - (1-tan (0)) tan (8) =4 for all permissible values of x The minimum depth, d (in meters), of water in a harbour, t hours after midnight, can be approximated by the function d(t) = 5 cos (0.5t) + 12 where 0 Q1. Determine the equation of the quartic function with rational coefficients, zeros 42 and -36 and a y-intercept of -21 Q2. The function f(x) = x(x+1)(x-2) is reflected in the x-axis, stretched horizontally from the y-axis by a factor of 2 and translated 3 units to the right. State the equation of the new function in simplest form and determine its zeros. One way to approximate the instantaneous rate of change at a is to add a very small increment, say 0.001, to the value, a, of the independent variable, and then calculate the slope of the secant line between the points (a, f(a)) and (a + 0.001, f(a + 0.001)). That is, f(a + 0.001) f(a) IROC 0.001 Radium (Ra-225) has a half-life of 15 days. For a 100 g sample, the amount of radioactive material remaining, A after time t, is given by the equation A(t) = 100(0.5), where A is measured in grams and t is measured in days. (a) Find the average rate of change from 3 days to 4 days, rounded to one decimal place. (b) Approximate the average rate of change at 3 days, rounded to one decimal place. Q1. Using appropriate double angle formulas and your knowledge of transformations, sketch the graphs of f(x) = 2 sin (x) and g(x) = 3 sin (2x) cos (2x) - 1 Q2. Prove that (c csc (6) sec : (0) - (1-tan (0)) tan (8) =4 for all permissible values of x