(a) This part of the question concerns the graph of the function: f(x) = (x − 3)^2 – 2
(i) Explain how the graph of f can be obtained from the graph of y = x^2 by using appropriate translations.
(ii) Write down the image set of the function f, in interval notation.
b) This part of the question concerns the function: g(x) = (x − 3)^2 − 2 (3 ≤ x ≤ 6). The function g has the same rule as the function f in part (a), but a smaller domain.
(i) Sketch the graph of g, using equal scales on the axes. (You should draw this by hand, rather than using any software.) Mark the coordinates of the endpoints of the graph. What is the image set of g?
(ii) Find the inverse function g^−1 , specifying its rule, domain and image set.
(iii) Add a sketch of y = g^−1 (x) to the graph that you produced in part (b)(i). Mark the coordinates of the endpoints of the graph of g^−1 .
Drones or UAVs (unmanned aerial vehicles) are aircraft without a human pilot aboard, and they are increasingly being used in many civilian applications, including aerial surveys of pipelines, crops or geology, and even for delivery of goods ordered online. A particular small drone has a speed in still air of 20 m/s^−1 . It is pointed in the direction of the bearing 125◦, but there is a wind blowing at a speed of 7 m/s^−1 from the south-west. Take unit vectors i to point east and j to point north.
(a) Express the velocity d of the drone relative to the air and the velocity w of the wind in component form, giving numerical values in m/s^−1 to two decimal places.
(b) Express the resultant velocity v of the drone in component form, giving numerical values to two decimal places.
(c) Hence find the magnitude and direction of the resultant velocity v of the drone, giving the magnitude in m s^−1 to two decimal places and the direction as a bearing to the nearest degree
Posted on May 15, 2017, by Lulukitten |