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

Studdy Solution

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

Studdy Solution

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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Question Find the value of qqq given the equation k=4pq2k=4pq^2k=4pq2.

Studdy Solution

STEP 1

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

STEP 2

First, we need to isolate qqq on one side of the equation. We can do this by dividing both sides of the equation by 4p4p4p.k4p=q2\frac{k}{4p} = q^24pk​=q2

STEP 3

Now, we have q2q^2q2 on one side of the equation. To solve for qqq, we need to take the square root of both sides.q=kpq = \sqrt{\frac{k}{p}}q=pk​​

STEP 4

We can simplify the square root by taking the square root of the numerator and the denominator separately.q=k4pq = \frac{\sqrt{k}}{\sqrt{4p}}q=4p​k​​

STEP 5

The square root of 4p4p4p can be simplified further as 2p2\sqrt{p}2p​.q=k2pq = \frac{\sqrt{k}}{2\sqrt{p}}q=2p​k​​So, the solution for qqq isq=k2pq = \frac{\sqrt{k}}{2\sqrt{p}}q=2p​k​​

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

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

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

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.
$q = \sqrt{\frac{k}{p}}$

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

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 $q = \frac{\sqrt{k}}{2\sqrt{p}}$