[Q1] For the floating ball problem shown in the Figure below; Water The floating ball has a specific gravity of 0.6 and has a radius of 5.5 cm. The equation that gives the depth x in meters to which the ball is submerged under water is given by x'-0.165x +3.993 x10 = 0 Let us assume the initial guess of the root of f (x) = 0 is Xo = 0.50. Use the Newton- Raphson method of finding roots of equations to find a) the depth x to which the ball is submerged under water. Conduct three iterations to estimate the root of the above equation. b) the absolute relative approximate error at the end of each iteration,

The intensity I of light (in lumens) at a distance x meters below the surface is given by I = I0 k x, where I0 is the intensity at the surface and k depends on the clarity of the water. At one location in the Atlantic Ocean, I0 = 14 and k = 0.7. Find the intensity of light at a depth of 11 meters. (Round your answer to three decimal places.)

The position of an object moving along a straight path is given by s(t) = 1.8t – 3.1t + 6.7. Find formulas for the velocity and acceleration functions. %3D velocity v(t) %D acceleration a(t)