Solve all Q47, 48 explaining detailly each step 40. The table shows corresponding values of x and y obtained experimentally. It is given that xand y are connected by a relation of the form y = ax", where a and b are constants. Bydrawing a suitable linear graph, estimate the values of a and b to one decimal place.X1.72.33.24.35.9Y28.7115.0525.02100.08800.041. Solve the differential equationdy- xy – X = 0, given that y = 0 when x = 0.%3dx42. i) Sketch the curve y = 3x² – 12x and hence find the area of the region bounded by the curveand the lines y = 0, x = 0 and x =5.ii) Find the volume generated by rotating completely the area bounded by the curve x = 3(y"%3D21) and the lines x = 0 and x = 6 about the x-axis. 'Find also the x-coordinate of the centroidof the solid generated.43. The table shows corresponding values of x and y obtained experimentally. By drawing asuitable graph relating log10x and log10y, show that these values support the hypothesis that xand y are connected by a relationship of the form: y =px", where p and q are constants. Useyour graph to estimate the values of p and q to one decimal place. Hence estimate the valueof , ydx dx. Use the trapezium rule to obtain anóther estimate for J, ydx9-2456.61280.03493.97963.3350.7dyY44. Solve the differential equation xy 1+y, given that x = 2, y = 045. The table shows corresponding values of x and y obtained experimentally.dx0.500.250.170.130.100.0830.070.380.250.190.150.130.110.09VIt is given that x and y are related by an equation of the formwhere a and b areconstants.By drawing a suitable linear graph relating - and- estimate the value of a and b correct toytwo decimal places.46. Two quantities x and y are known to be connected by a law of the form y = a (x+2)", where aand n are constants. Using the given table of values below, plot log y, against log(x+2) andhence find, to one decimal place the approximate values ofn and a.1Y1.060.580.380.270.2047. Find the area of the finite region bounded by the curve: y=xlnx, the x-axis and the lines x2.48. Solve the differential equation y(1+x*)-2(1+y*) = 0, given that y = 0 and x = 0.dydx49. The variable x and y tabulated below were obtained in an experiment and are thought to obeya law of the form:y = a(x – 1)n.5.6.139.162025Y6.57.07.157.561

Question

Solve all Q47, 48 explaining detailly each step 40. The table shows corresponding values of x and y obtained experimentally. It is given that xand y are connected by a relation of the form y = ax&#34;, where a and b are constants. Bydrawing a suitable linear graph, estimate the values of a and b to one decimal place.X1.72.33.24.35.9Y28.7115.0525.02100.08800.041. Solve the differential equationdy- xy – X = 0, given that y = 0 when x = 0.%3dx42. i) Sketch the curve y = 3x² – 12x and hence find the area of the region bounded by the curveand the lines y = 0, x = 0 and x =5.ii) Find the volume generated by rotating completely the area bounded by the curve x = 3(y&#34;%3D21) and the lines x = 0 and x = 6 about the x-axis. 'Find also the x-coordinate of the centroidof the solid generated.43. The table shows corresponding values of x and y obtained experimentally. By drawing asuitable graph relating log10x and log10y, show that these values support the hypothesis that xand y are connected by a relationship of the form: y =px&#34;, where p and q are constants. Useyour graph to estimate the values of p and q to one decimal place. Hence estimate the valueof , ydx dx. Use the trapezium rule to obtain anóther estimate for J, ydx9-2456.61280.03493.97963.3350.7dyY44. Solve the differential equation xy 1+y, given that x = 2, y = 045. The table shows corresponding values of x and y obtained experimentally.dx0.500.250.170.130.100.0830.070.380.250.190.150.130.110.09VIt is given that x and y are related by an equation of the formwhere a and b areconstants.By drawing a suitable linear graph relating - and- estimate the value of a and b correct toytwo decimal places.46. Two quantities x and y are known to be connected by a law of the form y = a (x+2)&#34;, where aand n are constants. Using the given table of values below, plot log y, against log(x+2) andhence find, to one decimal place the approximate values ofn and a.1Y1.060.580.380.270.2047. Find the area of the finite region bounded by the curve: y=xlnx, the x-axis and the lines x2.48. Solve the differential equation y(1+x*)-2(1+y*) = 0, given that y = 0 and x = 0.dydx49. The variable x and y tabulated below were obtained in an experiment and are thought to obeya law of the form:y = a(x – 1)n.5.6.139.162025Y6.57.07.157.561

Accepted Answer

In the given question we have to solve question (47) and (48)in question (47) we have to find the…

47.Find the area of the finite region bounded by the curve: y=xlnx, the x-axis and the lines x = 2. 48. Solve the differential equation y(1+x*)-2(1+y) = 0, given that y 0 and x 0. dy %3D dx