A study was performed to investigate the shear strength of soil (y) as it related to depth in feet (x1) and moisture content (x). Ten observations were collected, and the following summary quantities obtained: n = 10, Ex = 223, Ex2 = 553, Ey, = 1,916, Ex = 5,200.9, Ex = 31,729, Ex2 = 12,352, Exy; = 43,550.8, x2y; = 104,736.8, and Ey = 371,595.6. Set up the least squares normal equations for the model y= B, + B,x, + Bx2 + e.
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- 5) The length of the side of a square floor tile is 15 cm, with a possible error of 0.05 cm. Using differentials, estimate the possible propagated error in the computed area of the tile.The length and width of a rectangle are measured with errors of at most 3% and 5%, respectively. Use differentials to approximate the maximum percentage error in the calculated area.The length and width of a rectangle are measured as 38 cm and 34 cm, respectively, with an error in measurement of at most 0.1 cm in each. Use differentials to estimate the maximum error in the calculated area of the rectangle. cm2
- The measurement of the edge of a cube is found to be 15 inches, with a possible error of 0.03 inch. (a) Use differentials to approximate the possible propagated error in computing the volume of the cube. (b) Use differentials to approximate the possible propagated error in computing the surface area of the cube. (c) Approximate the percent errors in parts (a) and (b)A mass of 1 kgkg is attached to the end of a spring whose restoring force is 180 NmNm. The mass is in a medium that exerts a viscous resistance of 156 NN when the mass has a velocity of 6 msms. The viscous resistance is proportional to the speed of the object. Suppose the spring is stretched 0.07 mm beyond the its natural position and released. Let positive displacements indicate a stretched spring, and suppose that external vibrations act on the mass with a force of 7sin(3t)7sin(3t) NN at time tt seconds. Find an function to express the steady-state component of the object's displacement from the spring's natural position, in mm after tt seconds. (Note: This spring-mass system is not "hanging", so there is no gravitational force included in the model.)The radius of a sphere is measured as 9 centimeters, with a possible error of 0.025 centimeter. (a) Use differentials to approximate the possible propagated error in computing the volume of the sphere. (b) Use differentials to approximate the possible propagated error in computing the surface area of the sphere. (c) Approximate the percent errors in parts (a) and (b)
- Express the mathematical relationship between stress and strain in case of elastic material.The edge of a cube was found to be 30 cm with a possible error in measurement of 0.1 cm. Use differentials to estimate the maximum possible error in computing the surface area of the cube.The inter-arrival time X between faults in a network is exponential with parameter λ = 5.Hence, X has the pdf
- Use a linear approximation (or differentials) to estimate the given number.Solve for average value of the function within interval [0,20]the measurement of the radius of the end of a log is found to be 20 inches, with a possible error of1/8 inch. Use differentials to approximate the possible propagated error in computing the area of the end of the log.