Mathematics Assignment final Essay Example | Topics and Well Written Essays - 750 words

Mathematics Assignment final - Essay Example (ii). Note that the resultant vector is 145 degrees from the positive x-axis, thus using the Sine Law, After finding the magnitude of the resultant vector, r, then Thus, v = -1.3705i + 0.9596j. (iii). Fore a period of one second, the boat moves 0.9596m upward and 1.3705 westward. Thus, starting from (600, -300). The position of the boat at time t will be (600-1.3705t, -300 + 0.9596t). (iv). When the boat is directly south of the position (200, 100), then its x coordinate must be equal to 200, so Thus, at time 291.8711, the boat is directly south of (200, 100) and its position is (200, -19.92). Therefore it is about (100-(-20)) m away from that position or it is 120m away. Question 2 (a) (i) The length of the arc is equal to rX where X is the radian measure of the angle that intercepted the arc. Hence, the length of the wire can be expressed as Manipulating the equation and solving for l, we will have (ii) Note that the area A can be expressed as the difference between the area of the two sectors with radius 6 and with radius (6-l) both intercepted by angle x. Thus In terms of x only, substituting the value of l, (iv) Notice that the formula for A includes a factor (1-x) in the numerator, if we select a value of x greater than 1, then this factor will become less than 0, so the area becomes less than 0 which is not sensible. Also, if we set x to be less than 0, we are assuming that the angle that intercept the arc PS is less than 0 which also doesn't make sense. (b) The graph of f follows. (ii). Using the trace facility as shown, As seen, the graph of f has its maximum value at (0.62, 5.30). (iii) The solution of the equation f(x)=3 is 0.25 and 0.89. (c) (i) The terms of the recurrence relation are...Also, by this method, at (320, 260), t = 280. Thus, the man can see the boat from time 200 sec to 280 sec or for the duration equal to 80 sec. (i) The graph above shows vb in blue, vc in yellow and the resultant vector v in black. Their magnitudes are given for a one-second span, i.e., vb has magnitude 2, vc has magnitude 0.5. Note that the direction of the line of the boat is N 40 degrees W, or equivalently, it is 130 degrees from the positive x-axis. We want to find the coordinate of the head of the vector, so (iv) Notice that the formula for A includes a factor (1-x) in the numerator, if we select a value of x greater than 1, then this factor will become less than 0, so the area becomes less than 0 which is not sensible. Also, if we set x to be less than 0, we are assuming that the angle that intercept the arc PS is less than 0 which also doesn't make sense. (iv). Note that the maximum of the function is given by the function value when x is --/3, therefore, the maximum value of f is 3.067. However, when x is equal to 2/3, the value of f is not the minimum. If we graph f, we will notice that at x approaches negative infinity, the value of y decreases without bounds, thus f has a minimum when x is equal to -.