Find the distance (in ft) traveled in 10 seconds by an object traveling at a velocity of
v(t) = 20 + 5 cos(t)
feet per second.

To find the distance traveled by an object over a given time interval when its velocity \(v(t)\) is known, we need to compute the definite integral of the velocity function over that time interval.

Given the velocity function:
\[
v(t) = 20 + 5 \cos(t)
\]

We want to find the distance traveled over the time interval from \(t = 0\) to \(t = 10\) seconds. The distance traveled is given by:

\[
\text{Distance} = \int_{0}^{10} v(t) \, dt = \int_{0}^{10} (20 + 5 \cos(t)) \, dt
\]

### Step-by-Step Solution

1. **Separate the Integral:**

\[
\int_{0}^{10} (20 + 5 \cos(t)) \, dt = \int_{0}^{10} 20 \, dt + \int_{0}^{10} 5 \cos(t) \, dt
\]

2. **Compute Each Integral:**

- The first integral is straightforward:

\[
\int_{0}^{10} 20 \, dt = 20t \Big|_{0}^{10} = 20

Learn how to calculate the distance traveled by an object with the velocity function v(t) = 20 + 5 cos(t) over a time interval of 10 seconds. This problem involves computing a definite integral and covers concepts in integral calculus. Suitable for advanced high school students and above.

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