Questions: Solve for (q). [ k=4 p q^2 ] (q= pm sqrtk p/2) (q= pm 2 sqrtk p/p) (q= pm 2 sqrtk p) (q= pm sqrtk p/(2 p))

Transcript text: Solve for $q$. \[ k=4 p q^{2} \] $q= \pm \frac{\sqrt{k p}}{2}$ $q= \pm \frac{2 \sqrt{k p}}{p}$ $q= \pm 2 \sqrt{k p}$ $q= \pm \frac{\sqrt{k p}}{2 p}$

Solution

Solution Steps

To solve for $ q $ in the equation $ k = 4pq^2 $, we need to isolate $ q $. Start by dividing both sides by $ 4p $ to get $ q^2 = \frac{k}{4p} $. Then, take the square root of both sides to solve for $ q $, which gives $ q = \pm \sqrt{\frac{k}{4p}} $.

Step 1: Isolate $ q^2 $

Starting from the equation: \[ k = 4pq^2 \] we divide both sides by $ 4p $: \[ q^2 = \frac{k}{4p} \]

Step 2: Solve for $ q $

Next, we take the square root of both sides to find $ q $: \[ q = \pm \sqrt{\frac{k}{4p}} \]

Step 3: Simplify the Expression

We can simplify the expression further: \[ q = \pm \frac{\sqrt{k}}{2\sqrt{p}} \]