QuestionExpress $p$ as a function of $q$ and $r$ from the equation $q \sqrt{p} = r^{2} - \sqrt{p}$ .

Studdy Solution

STEP 1

Assumptions1. We are given the equation $q \sqrt{p}=r^{}-\sqrt{p}$ . We need to express $p$ in terms of $q$ and $r$

STEP 2

First, we need to isolate terms involving $\sqrt{p}$ on one side of the equation. We can do this by adding $\sqrt{p}$ to both sides of the equation.
$q \sqrt{p} + \sqrt{p} = r^{2}$

STEP 3

Next, we can factor out $\sqrt{p}$ from the left side of the equation.
$(q+1) \sqrt{p} = r^{2}$

STEP 4

Now, we can solve for $\sqrt{p}$ by dividing both sides of the equation by $(q+1)$ .
$\sqrt{p} = \frac{r^{2}}{q+1}$

STEP 5

Finally, to find $p$ , we square both sides of the equation.
$p = \left(\frac{r^{2}}{q+1}\right)^{2}$

STEP 6

implify the right side of the equation.
$p = \frac{r^{4}}{(q+1)^{2}}$ So, $p$ in terms of $q$ and $r$ is $\frac{r^{4}}{(q+1)^{2}}$ .

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QuestionExpress $p$ as a function of $q$ and $r$ from the equation $q \sqrt{p} = r^{2} - \sqrt{p}$ .

Studdy Solution

STEP 1

Assumptions1. We are given the equation $q \sqrt{p}=r^{}-\sqrt{p}$ . We need to express $p$ in terms of $q$ and $r$

STEP 2

First, we need to isolate terms involving $\sqrt{p}$ on one side of the equation. We can do this by adding $\sqrt{p}$ to both sides of the equation.
$q \sqrt{p} + \sqrt{p} = r^{2}$

STEP 3

Next, we can factor out $\sqrt{p}$ from the left side of the equation.
$(q+1) \sqrt{p} = r^{2}$

STEP 4

Now, we can solve for $\sqrt{p}$ by dividing both sides of the equation by $(q+1)$ .
$\sqrt{p} = \frac{r^{2}}{q+1}$

STEP 5

Finally, to find $p$ , we square both sides of the equation.
$p = \left(\frac{r^{2}}{q+1}\right)^{2}$

STEP 6

implify the right side of the equation.
$p = \frac{r^{4}}{(q+1)^{2}}$ So, $p$ in terms of $q$ and $r$ is $\frac{r^{4}}{(q+1)^{2}}$ .

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QuestionExpress ppp as a function of qqq and rrr from the equation qp=r2−pq \sqrt{p} = r^{2} - \sqrt{p}qp​=r2−p​.

Studdy Solution

STEP 1

Assumptions1. We are given the equation qp=r−pq \sqrt{p}=r^{}-\sqrt{p}qp​=r−p​ . We need to express ppp in terms of qqq and rrr

STEP 2

First, we need to isolate terms involving p\sqrt{p}p​ on one side of the equation. We can do this by adding p\sqrt{p}p​ to both sides of the equation.qp+p=r2q \sqrt{p} + \sqrt{p} = r^{2}qp​+p​=r2

STEP 3

Next, we can factor out p\sqrt{p}p​ from the left side of the equation.(q+1)p=r2(q+1) \sqrt{p} = r^{2}(q+1)p​=r2

STEP 4

Now, we can solve for p\sqrt{p}p​ by dividing both sides of the equation by (q+1)(q+1)(q+1).p=r2q+1\sqrt{p} = \frac{r^{2}}{q+1}p​=q+1r2​

STEP 5

Finally, to find ppp, we square both sides of the equation.p=(r2q+1)2p = \left(\frac{r^{2}}{q+1}\right)^{2}p=(q+1r2​)2

STEP 6

implify the right side of the equation.p=r4(q+1)2p = \frac{r^{4}}{(q+1)^{2}}p=(q+1)2r4​So, ppp in terms of qqq and rrr is r4(q+1)2\frac{r^{4}}{(q+1)^{2}}(q+1)2r4​.

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QuestionExpress $p$ as a function of $q$ and $r$ from the equation $q \sqrt{p} = r^{2} - \sqrt{p}$ .

Assumptions1. We are given the equation $q \sqrt{p}=r^{}-\sqrt{p}$ . We need to express $p$ in terms of $q$ and $r$

First, we need to isolate terms involving $\sqrt{p}$ on one side of the equation. We can do this by adding $\sqrt{p}$ to both sides of the equation.
$q \sqrt{p} + \sqrt{p} = r^{2}$

Next, we can factor out $\sqrt{p}$ from the left side of the equation.
$(q+1) \sqrt{p} = r^{2}$

Now, we can solve for $\sqrt{p}$ by dividing both sides of the equation by $(q+1)$ .
$\sqrt{p} = \frac{r^{2}}{q+1}$

Finally, to find $p$ , we square both sides of the equation.
$p = \left(\frac{r^{2}}{q+1}\right)^{2}$

implify the right side of the equation.
$p = \frac{r^{4}}{(q+1)^{2}}$ So, $p$ in terms of $q$ and $r$ is $\frac{r^{4}}{(q+1)^{2}}$ .