Answer :
To solve for [tex]\( e \)[/tex] in the equation [tex]\( 9e^2 f = 49 \)[/tex], we can follow these steps:
1. Isolate [tex]\( e^2 \)[/tex]:
[tex]\[
e^2 = \frac{49}{9f}
\][/tex]
We achieved this by dividing both sides of the equation by [tex]\( 9f \)[/tex].
2. Solve for [tex]\( e \)[/tex]:
To solve for [tex]\( e \)[/tex], we need to take the square root of both sides. Remember, taking the square root introduces a [tex]\( \pm \)[/tex] sign.
[tex]\[
e = \pm \sqrt{\frac{49}{9f}}
\][/tex]
3. Simplify the square root:
We can separate the terms inside the square root:
[tex]\[
e = \pm \frac{\sqrt{49}}{3} \times \frac{1}{\sqrt{f}}
\][/tex]
The square root of 49 is 7, so:
[tex]\[
e = \pm \frac{7}{3} \times \frac{1}{\sqrt{f}}
\][/tex]
4. Combine the terms:
[tex]\[
e = \pm \frac{7 \sqrt{f}}{3f}
\][/tex]
Simplifying further:
[tex]\[
e = \pm \frac{7}{3} \times \frac{1}{\sqrt{f}} = \pm \frac{\sqrt{7f}}{3f}
\][/tex]
5. Another equivalent form:
If you express it differently (if the value for [tex]\( f \)[/tex] does not equal zero), and consider standard approaches, you could find:
[tex]\[
e = \pm \frac{\sqrt{7f}}{3}
\][/tex]
Hence, the three potential forms of the solution for [tex]\( e \)[/tex] are:
1. [tex]\( e = \pm \frac{7 \sqrt{f}}{3} \)[/tex]
2. [tex]\( e = \pm \frac{\sqrt{7f}}{3f} \)[/tex]
3. [tex]\( e = \pm \frac{\sqrt{7f}}{3} \)[/tex]
These represent variations depending on how you choose to simplify the equation, reflecting equivalent expressions for the solution.
1. Isolate [tex]\( e^2 \)[/tex]:
[tex]\[
e^2 = \frac{49}{9f}
\][/tex]
We achieved this by dividing both sides of the equation by [tex]\( 9f \)[/tex].
2. Solve for [tex]\( e \)[/tex]:
To solve for [tex]\( e \)[/tex], we need to take the square root of both sides. Remember, taking the square root introduces a [tex]\( \pm \)[/tex] sign.
[tex]\[
e = \pm \sqrt{\frac{49}{9f}}
\][/tex]
3. Simplify the square root:
We can separate the terms inside the square root:
[tex]\[
e = \pm \frac{\sqrt{49}}{3} \times \frac{1}{\sqrt{f}}
\][/tex]
The square root of 49 is 7, so:
[tex]\[
e = \pm \frac{7}{3} \times \frac{1}{\sqrt{f}}
\][/tex]
4. Combine the terms:
[tex]\[
e = \pm \frac{7 \sqrt{f}}{3f}
\][/tex]
Simplifying further:
[tex]\[
e = \pm \frac{7}{3} \times \frac{1}{\sqrt{f}} = \pm \frac{\sqrt{7f}}{3f}
\][/tex]
5. Another equivalent form:
If you express it differently (if the value for [tex]\( f \)[/tex] does not equal zero), and consider standard approaches, you could find:
[tex]\[
e = \pm \frac{\sqrt{7f}}{3}
\][/tex]
Hence, the three potential forms of the solution for [tex]\( e \)[/tex] are:
1. [tex]\( e = \pm \frac{7 \sqrt{f}}{3} \)[/tex]
2. [tex]\( e = \pm \frac{\sqrt{7f}}{3f} \)[/tex]
3. [tex]\( e = \pm \frac{\sqrt{7f}}{3} \)[/tex]
These represent variations depending on how you choose to simplify the equation, reflecting equivalent expressions for the solution.
