Create a 3 pages page paper that discusses mathematics assignment final. (ii). Note that the resultant vector is 145 degrees from the positive x-axis, thus using the Sine Law, After finding the magnit

Create a 3 pages page paper that discusses mathematics assignment final. (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.