step by step math solutions solving for projects

The following are the steps to solve a system of linear equations using Cramer's rule. Step 1: Find the value of the determinant Step 2: If D 0, then the system has unique solution, given by Where D 1 , D 2 and D 3 are the determinants obtained from..

If (x 1 , y 1 ) is the point found in step 4, then x = x 1 , y = y 1 , is the optimal solution of the LPP and Z = ax 1 + by 1 is the optimal value. The above method of solving an LPP is more clear with the following exampl..

So far we have learnt how to construct a mathematical model for a linear programming problem. If we can find the values of the decision variables x 1 , x 2 , x 3 , ..... x n , which can optimise (maximize or minimize) the objective function Z, then we say that these values of x i are the ..

If log (sin C) comes out as positive, sin C would have to be greater than 1 and there is no solution..

For a differentiable function f (x), find f '(x). Equate it to zero. Solve the equation f '(x) = 0 to get the Critical values of f (x..

To maximise Z draw a line parallel to ax + by = k and farthest from the origin. This line should contain at least one point of the feasible region. Find the coordinates of this point by solving the equations of the lines on which it lies. To minimise Z draw a line parallel to ax + by = ..

Check if f (a) = f (b) If all the above condition are satisfied, then Rolle's theorem is applicable else the Rolle's theorem is not applicable. If Rolle's theorem is applicable, solve f '(c) = 0. Show that one of these roots lie in the open interval (a, b..

Solution is obtained by integrating both sides and substituting ..

Solution is obtained from ..

If Mean value theorem is applicable, solve the equation Show that one of the roots lie in the open interval (a, b). This verifies the Mean Value Theore..