Question
Solve the equation for g . \[ \frac{\theta}{\pi}=\frac{9 \mathrm{M}}{\mathrm{g}} \]
Ask by Donnelly Bernard. in the United States
Feb 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( g = \frac{9\pi M}{\theta} \)
Solution
To solve the equation
θ/π = 9M/g
for g, follow these steps:
1. Multiply both sides of the equation by g to eliminate the fraction on the right side:
g · (θ/π) = 9M
2. Now, solve for g by isolating it. To do this, multiply both sides by π/θ:
g = (9M) · (π/θ)
So the solution for g is:
g = (9πM)/θ
This answer assumes that θ is not equal to zero.
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Simplify this solution Extra Insights
To isolate \( g \) in the equation \( \frac{\theta}{\pi}=\frac{9 \mathrm{M}}{\mathrm{g}} \), you can start by cross-multiplying. This gives you: \[ \theta \cdot g = 9 \mathrm{M} \cdot \pi. \] Now, divide both sides by \( \theta \): \[ g = \frac{9 \mathrm{M} \cdot \pi}{\theta}. \] And there you have it, \( g \) expressed in terms of \( M \), \( \theta \), and \( \pi \). So, the final answer is: \[ g = \frac{9 \mathrm{M} \pi}{\theta}. \]
