QuestionSolve for $r_{2}$ in the equation $R(r_{1}+r_{2})=r_{1} r_{2}$ .

Studdy Solution

STEP 1

Assumptions1. The formula given is $R(r_{1}+r_{})=r_{1}r_{}$ . We need to solve this formula for $r_{}$

STEP 2

First, we need to isolate the terms containing $r_{2}$ on one side of the equation. We can start by distributing $R$ on the left side of the equation.
$Rr_{1} + Rr_{2} = r_{1}r_{2}$

STEP 3

Next, we move the term $Rr_{1}$ to the right side of the equation to isolate terms containing $r_{2}$ .
$Rr_{2} = r_{1}r_{2} - Rr_{1}$

STEP 4

Now, we can factor out $r_{2}$ from the right side of the equation.
$Rr_{2} = r_{2}(r_{1} - R)$

STEP 5

Finally, we can solve for $r_{2}$ by dividing both sides of the equation by $(r_{1} - R)$ .
$r_{2} = \frac{R}{r_{1} - R}$ So, the solution for $r_{2}$ is $\frac{R}{r_{1} - R}$ .

Was this helpful?

QuestionSolve for $r_{2}$ in the equation $R(r_{1}+r_{2})=r_{1} r_{2}$ .

Studdy Solution

STEP 1

Assumptions1. The formula given is $R(r_{1}+r_{})=r_{1}r_{}$ . We need to solve this formula for $r_{}$

STEP 2

First, we need to isolate the terms containing $r_{2}$ on one side of the equation. We can start by distributing $R$ on the left side of the equation.
$Rr_{1} + Rr_{2} = r_{1}r_{2}$

STEP 3

Next, we move the term $Rr_{1}$ to the right side of the equation to isolate terms containing $r_{2}$ .
$Rr_{2} = r_{1}r_{2} - Rr_{1}$

STEP 4

Now, we can factor out $r_{2}$ from the right side of the equation.
$Rr_{2} = r_{2}(r_{1} - R)$

STEP 5

Finally, we can solve for $r_{2}$ by dividing both sides of the equation by $(r_{1} - R)$ .
$r_{2} = \frac{R}{r_{1} - R}$ So, the solution for $r_{2}$ is $\frac{R}{r_{1} - R}$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve for r2r_{2}r2​ in the equation R(r1+r2)=r1r2R(r_{1}+r_{2})=r_{1} r_{2}R(r1​+r2​)=r1​r2​.

Studdy Solution

STEP 1

Assumptions1. The formula given is R(r1+r)=r1rR(r_{1}+r_{})=r_{1}r_{}R(r1​+r​)=r1​r​ . We need to solve this formula for rr_{}r​

STEP 2

First, we need to isolate the terms containing r2r_{2}r2​ on one side of the equation. We can start by distributing RRR on the left side of the equation.Rr1+Rr2=r1r2Rr_{1} + Rr_{2} = r_{1}r_{2}Rr1​+Rr2​=r1​r2​

STEP 3

Next, we move the term Rr1Rr_{1}Rr1​ to the right side of the equation to isolate terms containing r2r_{2}r2​.Rr2=r1r2−Rr1Rr_{2} = r_{1}r_{2} - Rr_{1}Rr2​=r1​r2​−Rr1​

STEP 4

Now, we can factor out r2r_{2}r2​ from the right side of the equation.Rr2=r2(r1−R)Rr_{2} = r_{2}(r_{1} - R)Rr2​=r2​(r1​−R)

STEP 5

Finally, we can solve for r2r_{2}r2​ by dividing both sides of the equation by (r1−R)(r_{1} - R)(r1​−R).r2=Rr1−Rr_{2} = \frac{R}{r_{1} - R}r2​=r1​−RR​So, the solution for r2r_{2}r2​ is Rr1−R\frac{R}{r_{1} - R}r1​−RR​.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSolve for $r_{2}$ in the equation $R(r_{1}+r_{2})=r_{1} r_{2}$ .

Assumptions1. The formula given is $R(r_{1}+r_{})=r_{1}r_{}$ . We need to solve this formula for $r_{}$

First, we need to isolate the terms containing $r_{2}$ on one side of the equation. We can start by distributing $R$ on the left side of the equation.
$Rr_{1} + Rr_{2} = r_{1}r_{2}$

Next, we move the term $Rr_{1}$ to the right side of the equation to isolate terms containing $r_{2}$ .
$Rr_{2} = r_{1}r_{2} - Rr_{1}$

Now, we can factor out $r_{2}$ from the right side of the equation.
$Rr_{2} = r_{2}(r_{1} - R)$

Finally, we can solve for $r_{2}$ by dividing both sides of the equation by $(r_{1} - R)$ .
$r_{2} = \frac{R}{r_{1} - R}$ So, the solution for $r_{2}$ is $\frac{R}{r_{1} - R}$ .