h 4.1.2 Homogeneous Equations In Problems 15-22 determine whether the given set of functions is linearly independent on the interval (-∞, ∞). 15. f(x)=x, f(x) = x², f(x)=4x-3x² 16. f(x) = 0, f(x) = x, f(x) = ex

Solve all parts !

Q1 / Reduce the block diagram to the simple form R(s) S 13 S 0. S 1 S C(s)

Points for stress vs strain (in image) Assume the compressive concrete strength (f’c) is 3,000 lb/in2 (psi)Calculate a cubic function (3rd order polynomial – Ax3+Bx2+Cx+Constant)Use this function to create a function that describes the slope of the cubic function (the derivative of thecubic function). This new function allows you to calculate the tangent to any point along the curve. Thetangent is the modulus of elasticity (E).   The concrete code provides a formula to calculate E for concrete. That formula is:E = 57,000√??′, where f’c is in units of psi, and E is in units of psi.Use the derivative function you calculated to locate the point on the curve where the slope of the curvematches E using the concrete code formula. Express that stress point on the curve as a percentage ofthe compressive strength of the concrete. Now, calculate the secant modulus for the test case using 1,500 psi (50% f’c) as the arbitrary point onthe curve.Assume fracture occurs at the last point…