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

Mathematics Assignment final - Essay Example(ii). denounce that the resultant vector is 145 degrees from the positive x-axis, thus using the Sine Law, After finding the order of the resultant vector, r, becauseThus, 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 judgment of conviction t will be (600-1.3705t, -300 + 0.9596t). (iv). When the boat is directly in the south of the position (200, 100), then its x coordinate must be equal to 200, soThus, 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 slant that intercepted the arc. Hence, the length of the wire crumb be expressed as Manipulating the equation and solving for l, we will have(ii) s car that the rural bea A can be expressed as the difference between the area of the ii sectors with radius 6 and with radius (6-l) both intercepted by angle x. ThusIn terms of x only, substituting the evaluate of l, (iv) Notice that the conventionalism 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 slight than 0, so the area becomes less than 0 which is not sensible. Also, if we garnish x to be less than 0, we are assuming that the angle that intercept the arc PS is less than 0 which also doesnt make sense. (b) The graph of f follows. (ii). victimisation the trace facility as shown, As seen, the graph of f has its maximum value at (0.62, 5.30). (iii)The radical 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 grap h 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 doesnt 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 valu e of y decreases without bounds, thus f has a minimum when x is equal to -.