15 m/s = 4π rad/s × r × sin(15°)

Write Equation: Write down the given equation. We are given the equation 15 m/s = 4π rad/s × r × sin(15°). We need to solve for r.Isolate r: Isolate r in the equation. To find r, we need to divide both sides of the equation by 4π rad/s and sin(15°). r = (15 m/s) / (4π rad/s × sin(15°))Calculate sin(15°): Calculate sin(15°). Using a calculator or trigonometric tables, we find that sin(15°) is approximately 0.2588.Substitute sin(15°): Substitute sin(15°) into the equation. r = (15 m/s) / (4π rad/s × 0.2588)Perform Calculation: Perform the calculation. r = (15 m/s) / (4π × 0.2588 rad/s) r ≈ (15 m/s) / (3.1416 × 0.2588 rad/s) r ≈ (15 m/s) / (0.8135 rad/s) r ≈ 18.44 m

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Calculus

Find derivatives using the quotient rule I

Full solution

15\,\text{m/s} = 4\pi\,\text{rad/s} \times r \times \sin(15^\circ)

Write Equation: Write down the given equation. $\newline$ We are given the equation $15 \, \text{m/s} = 4\pi \, \text{rad/s} \times r \times \sin(15°)$ . We need to solve for $r$ .
Isolate r: Isolate r in the equation. $\newline$ To find r, we need to divide both sides of the equation by $4\pi \, \text{rad/s}$ and $\sin(15°)$ . $\newline$ $r = \frac{15 \, \text{m/s}}{4\pi \, \text{rad/s} \times \sin(15°)}$
Calculate $\sin(15^\circ)$ : Calculate $\sin(15^\circ)$ . Using a calculator or trigonometric tables, we find that $\sin(15^\circ)$ is approximately $0.2588$ .
Substitute $\sin(15°)$ : Substitute $\sin(15°)$ into the equation. $r = \frac{15 \, \text{m/s}}{4\pi \, \text{rad/s} \times 0.2588}$
Perform Calculation: Perform the calculation. $\newline$ $r = \frac{15 \, \text{m/s}}{4\pi \times 0.2588 \, \text{rad/s}}$ $\newline$ $r \approx \frac{15 \, \text{m/s}}{3.1416 \times 0.2588 \, \text{rad/s}}$ $\newline$ $r \approx \frac{15 \, \text{m/s}}{0.8135 \, \text{rad/s}}$ $\newline$ $r \approx 18.44 \, \text{m}$