Goal: To isolate for the value of $$ R P M $$ $$ 2500=11.18 imes 10 imes \frac{R P M}{1,000}^{2} $$ $$ 2500=111.8 imes \frac{R P M^{2}}{\square} $$

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Goal: To isolate for the value of $$ R P M $$ $$ 2500=11.18 	imes 10 	imes \frac{R P M}{1,000}^{2} $$ $$ 2500=111.8 	imes \frac{R P M^{2}}{\square} $$

UpStudy AI · Accepted Answer

1. Start with the given equation:
   $$
   2500 = 11.18 \times 10 \times \left(\frac{RPM}{1000}\right)^2
   $$

2. Multiply $$11.18 \times 10$$ to simplify the equation:
   $$
   2500 = 111.8 \times \left(\frac{RPM}{1000}\right)^2
   $$

3. Divide both sides by $$111.8$$ to isolate the squared term:
   $$
   \frac{2500}{111.8} = \left(\frac{RPM}{1000}\right)^2
   $$

4. Take the square root of both sides:
   $$
   \sqrt{\frac{2500}{111.8}} = \frac{RPM}{1000}
   $$

5. Multiply both sides by $$1000$$ to solve for $$RPM$$:
   $$
   RPM = 1000 \times \sqrt{\frac{2500}{111.8}}
   $$

Thus, the value of $$RPM$$ is isolated as:
$$
RPM = 1000 \sqrt{\frac{2500}{111.8}}
$$
$$ RPM = 1000 \times \sqrt{\frac{2500}{111.8}} $$

Goal: To isolate for the value of

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