Solve {l}{t=3/4}{u=3t-2t^2}{text{Solvefor}vtext{where}}{v=u}

$$\left. \begin{array} { l } { t = \frac{3}{4} }\\ { u = 3 t - 2 t ^ {2} }\\ { \text{Solve for } v \text{ where} } \\ { v = u } \end{array} \right.$$

Solve for t, u, v

$$v = \frac{9}{8} = 1\frac{1}{8} = 1.125$$

Solution Steps

Consider the second equation. Insert the known values of variables into the equation.

$$u=3\times \frac{3}{4}-2\times \left(\frac{3}{4}\right)^{2}$$

Multiply 3 and \frac{3}{4} to get \frac{9}{4}.

$$u=\frac{9}{4}-2\times \left(\frac{3}{4}\right)^{2}$$

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$u=\frac{9}{4}-2\times \frac{9}{16}$$

Multiply -2 and \frac{9}{16} to get -\frac{9}{8}.

$$u=\frac{9}{4}-\frac{9}{8}$$

Subtract \frac{9}{8} from \frac{9}{4} to get \frac{9}{8}.

$$u=\frac{9}{8}$$

Consider the third equation. Insert the known values of variables into the equation.

$$v=\frac{9}{8}$$

The system is now solved.

$$t=\frac{3}{4} u=\frac{9}{8} v=\frac{9}{8}$$