A particle travels along the x-axis such that its position is given by x(t)=t^(1.7)sin(3t). What is the velocity of the particle at time t=3.5 ? You may use a calculator and round your answer to the nearest thousandth. Answer:

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A particle travels along the  x-axis such that its position is given by  x(t)=t^(1.7)sin(3t). What is the velocity of the particle at time  t=3.5 ? You may use a calculator and round your answer to the nearest thousandth. Answer:

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Differentiation Process: To find the velocity of the particle, we need to differentiate the position function x(t) with respect to time t. The velocity function v(t) is the derivative of the position function x(t).Product Rule Application: Differentiate x(t)=t^(1.7)sin(3t) using the product rule for differentiation, which states that the derivative of two functions multiplied together is the derivative of the first function times the second function plus the first function times the derivative of the second function.Derivatives Calculation: Let's denote u=t^(1.7) and v=sin(3t). The derivatives of u and v with respect to t are u'=1.7t^(0.7) and v'=3cos(3t), respectively.Velocity Function Evaluation: Applying the product rule, we get v(t) = u'v + uv'. Substituting the derivatives we found, we get v(t) = (1.7t^(0.7))sin(3t) + (t^(1.7))(3cos(3t)).Expression Calculation: Now we need to evaluate the velocity function v(t) at t=3.5. Plugging in t=3.5 into the velocity function, we get v(3.5) = (1.7*(3.5)^(0.7))sin(3*3.5) + (3.5^(1.7))(3cos(3*3.5)).Final Velocity Calculation: Using a calculator to evaluate the expression, we find v(3.5) ≈ (1.7*(3.5)^(0.7))sin(10.5) + (3.5^(1.7))(3cos(10.5)). Make sure to use the correct trigonometric functions and to round to the nearest thousandth as instructed.After calculating, we find that v(3.5) ≈ (1.7*(3.5)^(0.7)) * sin(10.5) + (3.5^(1.7)) * 3 * cos(10.5) ≈ (1.7*2.218) * (-0.883) + (5.958) * 3 * (-0.970) ≈ -3.345 + -17.345 ≈ -20.690.

A particle travels along the $x$ -axis such that its position is given by $x(t)=t^{1.7} \sin (3 t)$ . What is the velocity of the particle at time $t=3.5$ ? You may use a calculator and round your answer to the nearest thousandth. $\newline$ Answer:

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A particle travels along the x x x-axis such that its position is given by x(t)=t1.7sin⁡(3t) x(t)=t^{1.7} \sin (3 t) x(t)=t1.7sin(3t). What is the velocity of the particle at time t=3.5 t=3.5 t=3.5 ? You may use a calculator and round your answer to the nearest thousandth.\newlineAnswer:

A particle travels along the $x$ -axis such that its position is given by $x(t)=t^{1.7} \sin (3 t)$ . What is the velocity of the particle at time $t=3.5$ ? You may use a calculator and round your answer to the nearest thousandth. $\newline$ Answer: