Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Nov 02, 2023

Find the value of $q$ given the equation $k=4pq^2$ .

STEP 1

Assumptions1. The equation given is k=4pq^ . We are solving for $q$

STEP 2

First, we need to isolate $q$ on one side of the equation. We can do this by dividing both sides of the equation by $4p$ .
$\frac{k}{4p} = q^2$

STEP 3

Now, we have $q^2$ on one side of the equation. To solve for $q$ , we need to take the square root of both sides.
$q = \sqrt{\frac{k}{p}}$

STEP 4

We can simplify the square root by taking the square root of the numerator and the denominator separately.
$q = \frac{\sqrt{k}}{\sqrt{4p}}$

STEP 5

The square root of $4p$ can be simplified further as $2\sqrt{p}$ .
$q = \frac{\sqrt{k}}{2\sqrt{p}}$ So, the solution for $q$ is $q = \frac{\sqrt{k}}{2\sqrt{p}}$

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