Solve for the indicated variable. Assume the variable you are solving for must be greater than 0.
-$$r m = t ^ { 2 } - m t , \quad \text { for } t$$
A) $$\mathrm { t } = \frac { \mathrm { m } + \sqrt { \mathrm { m } ^ { 2 } - 4 \mathrm { mr } } } { 4 }$$
B) $$\mathrm { t } = \frac { \mathrm { m } + \sqrt { \mathrm { m } ^ { 2 } + 4 \mathrm { rm } } } { 2 }$$
C) $$\mathrm { t } = \frac { \mathrm { m } + \sqrt { \mathrm { m } ^ { 2 } + 4 \mathrm { mr } } } { 2 \mathrm {~m} }$$
D) $$\mathrm { t } = \sqrt { \mathrm { mr } - \mathrm { m } }$$

Question

Quizplus · Accepted Answer

To solve for $t$, we first rearrange the equation to standard quadratic form: $t^2 - mt - rm = 0$. Applying the quadratic formula, $t = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, with $a = 1$, $b = -m$, and $c = -rm$, we get $t = \frac{m \pm \sqrt{m^2 + 4rm}}{2}$. Since $t > 0$ and we're solving for $t$, we choose the positive root, leading to choice B.

Solve for the Indicated Variable rm=t2−mt, for tr m = t ^ { 2 } - m t , \quad \text { for } trm=t2−mt, for t

Solve for the Indicated Variable $r m = t ^ { 2 } - m t , \quad \text { for } t$