Question
Jesus Henderson \begin{tabular}{|l|} Directions: Solve for \( x \). Round to the nearest tenth. \\ 4.\end{tabular} \( \sin (28)=\left.\frac{x}{4}\right|^{5 .} \)
Ask by Ward Bates. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x \approx 3.4 \)
Solution
To solve the equation for \( x \):
\[
\sin(28^\circ) = \left(\frac{x}{4}\right)^5
\]
**Step 1: Calculate \(\sin(28^\circ)\)**
\[
\sin(28^\circ) \approx 0.4695
\]
**Step 2: Solve for \(\frac{x}{4}\)**
\[
\left(\frac{x}{4}\right)^5 = 0.4695 \\
\frac{x}{4} = \sqrt[5]{0.4695}
\]
**Step 3: Calculate the 5th root**
\[
\sqrt[5]{0.4695} \approx 0.86
\]
**Step 4: Solve for \( x \)**
\[
x = 4 \times 0.86 = 3.44
\]
**Rounding to the nearest tenth:**
\[
x \approx \boxed{3.4}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To solve for \( x \) in the equation \( \sin(28^\circ) = \frac{x}{4} \), first, we can rearrange the equation to find \( x \): \[ x = 4 \cdot \sin(28^\circ) \] Next, we need to calculate \( \sin(28^\circ) \). Using a scientific calculator or trigonometric tables, we find that \( \sin(28^\circ) \approx 0.4695 \). Now, multiplying by 4 gives: \[ x \approx 4 \cdot 0.4695 \approx 1.878 \] Finally, rounding to the nearest tenth, we have: \[ x \approx 1.9 \]
