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Answer:
Explanation:
[tex]\theta = 0.3t^3 - 1.6t + 3[/tex]
1. Substitute ( t = 2 ) into the equation:
[tex]\theta = 0.3(2)^3 - 1.6(2) + 3[/tex]
2. Calculate each term separately:
[tex]( (2)^3 = 8 )[/tex]
[tex]( 0.3 \times 8 = 2.4 )[/tex]
[tex]( 1.6 \times 2 = 3.2 )[/tex]
[tex]\theta = 2.4 - 3.2 + 3[/tex]
[tex]{\theta = 2.4 - 3.2 + 3 = 2.4 - 3.2 + 3 = -0.8 + 3 = 2.2}
[/tex]
[tex]{ (\theta) \text when ( t = 2 ) seconds is ( 2.2 ) radians.}[/tex]
To convert the angle from radians to degrees, use the conversion factor
[tex]( 180^\circ / \pi ):[/tex]
[tex]\theta_{\text{degrees}} = 2.2 \times \left( \frac{180^\circ}{\pi} \right)[/tex]
[tex]using \ (\pi \approx 3.14159):[/tex]
[tex]{\theta_{\text{degrees}} = 2.2 \times \left( \frac{180^\circ}{3.14159} \right) \approx 2.2 \times 57.2958 \approx 126.05^\circ}[/tex]