A joint is moving at an angular velocity of 0.2e^(0.2 t) radians per second (where t is the time in seconds since the joint was at rest). Through how many radians does the joint move between t=1 and t=3 ? Choose 1 answer: (A) e^(0.4) (B) e^(0.6)-e^(0.2) (C) 0.2(e^(0.6)-e^(0.2)) (D) 0.2e^(0.4)

Integrate angular velocity function: The angular displacement of the joint can be found by integrating the angular velocity function with respect to time over the interval from t=1 to t=3.Given angular velocity function: The angular velocity function is given by ω(t) = 0.2e^(0.2t). To find the angular displacement, we integrate this function from t=1 to t=3.Evaluate integral with constant: The integral of ω(t) = 0.2e^(0.2t) with respect to t is (0.2/0.2)e^(0.2t) = e^(0.2t) + C, where C is the constant of integration.Evaluate integral from t=1 to t=3: We evaluate the integral from t=1 to t=3, which gives us e^(0.2*3) - e^(0.2*1) = e^(0.6) - e^(0.2).Final angular displacement calculation: We multiply the result by the coefficient 0.2 to get the final angular displacement: 0.2(e^(0.6) - e^(0.2)).

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A joint is moving at an angular velocity of
0.2e^(0.2 t) radians per second (where
t is the time in seconds since the joint was at rest).
Through how many radians does the joint move between
t=1 and
t=3 ?
Choose 1 answer:
(A)
e^(0.4)
(B)
e^(0.6)-e^(0.2)
(C)
0.2(e^(0.6)-e^(0.2))
(D)
0.2e^(0.4)

A joint is moving at an angular velocity of $0.2 e^{0.2 t}$ radians per second (where $t$ is the time in seconds since the joint was at rest). $\newline$ Through how many radians does the joint move between $t=1$ and $t=3$ ? $\newline$ Choose $1$ answer: $\newline$ (A) $e^{0.4}$ $\newline$ (B) $e^{0.6}-e^{0.2}$ $\newline$ (C) $0.2\left(e^{0.6}-e^{0.2}\right)$ $\newline$ (D) $0.2 e^{0.4}$

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Algebra 2

Write equations of cosine functions using properties

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Q. A joint is moving at an angular velocity of

0.2 e^{0.2 t}

radians per second (where

t

is the time in seconds since the joint was at rest).

\newline

Through how many radians does the joint move between

t=1

and

t=3

\newline

Choose

1

answer:

\newline

(A)

e^{0.4}

\newline

(B)

e^{0.6}-e^{0.2}

\newline

(C)

0.2\left(e^{0.6}-e^{0.2}\right)

\newline

(D)

0.2 e^{0.4}

Integrate angular velocity function: The angular displacement of the joint can be found by integrating the angular velocity function with respect to time over the interval from $t=1$ to $t=3$ .
Given angular velocity function: The angular velocity function is given by $\omega(t) = 0.2e^{0.2t}$ . To find the angular displacement, we integrate this function from $t=1$ to $t=3$ .
Evaluate integral with constant: The integral of $\omega(t) = 0.2e^{0.2t}$ with respect to $t$ is $(\frac{0.2}{0.2})e^{0.2t} = e^{0.2t} + C$ , where $C$ is the constant of integration.
Evaluate integral from $t=1$ to $t=3$ : We evaluate the integral from $t=1$ to $t=3$ , which gives us $e^{(0.2\cdot 3)} - e^{(0.2\cdot 1)} = e^{0.6} - e^{0.2}$ .
Final angular displacement calculation: We multiply the result by the coefficient $0.2$ to get the final angular displacement: $0.2(e^{0.6} - e^{0.2})$ .