Sentence examples for substituting the expression from inspiring English sources

Substituting the expression in step 5 into step 4 and factoring out common terms, L1 + L2 = π/8(a2 + b2 − c2) + ΔABC.

By substituting the expression of,,, and into (17), we have.

Now, substituting the expression of into, we get.

By substituting the expression of in (B.19) we find (B.20).

Substituting the expression of f into (1.2), we arrive at a contradiction.

Substituting the expression for into and applying (3.11), we obtain (3.39).

Substituting the expressions in Eq. (9) into Eqs.

Hence substituting the expressions for, and into the above equation yields (4.10).

By substituting the expressions (24) for the into (30), we get after some manipulations the following inequality: (31).

Substituting the expressions in Equation 12 into the governing Equations 9-11, we obtain the following transformed equations: (13) (14) (14).

By substituting the expressions for the functions and in (1.1), it can be shown that (1.11) holds.