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Task 5 The velocity of a car at one second interval is given by the following table Time (s) 1 2 3 4 5 Velocity 2.3 5.2 8.6 17.4 28.5 (v) Determine the distance travelled in 5 seconds. Using a)Trapezoidal rule b) mid-ordinate rule c) Simpson Rule Using Microsoft Exccl. Task 6 Determine the positive root of x2 - Sinx -3correct to 3 decimal places using the bisection method Task 7 Determine the magnitude and direction of the direction of the resultant of the three coplanar forces given below, when they act on a point. Force 1: 5N acting at 40 degrees from the positive horizontal axis. Force 2: 20N acting at 100 degrees from the positive horizontal axis. Force 3: 15N acting at 120 degrees from the positive horizontal axis. Task 8 Solve the Differential Equation using separation of variable. 2 given y=1 when x=0 dx Solve the Differential Equation d² dx dx - oWhen x=1,y=2 and d5-0 Ois an equation representing current i in an electric circuit .If inductance di dt C L is 0.25 henry, capacitance Cis .00006641 farads and R is 150 ohms Solve the equation for given the boundary conditions that when t=0 ,i=0 and Find the general solution of the given differential equations. 87+4y-58" Find the general solution of the given differential equations. dt Kirchoffs law are used to determine the current equations in an electrical network and show that i1+2i2+4=0 5i1+3i2-1=0 Find i1,i2 using matrices.

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Advanced Mathematics Equations and Their Solutions
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