The equation gives the position s = f(t) of a body moving on a coordinate line (s in meters, t in seconds).

1) s = 1 + 9(cos t)
Find the body's speed at time t=pi/3 sec.

2) s = 12(sin t) - (cos t)
Find the body's velocity at time t=pi/4 sec.

1) The velocity at this time is of meters per second.

2) The velocity at this time is of meters per second.

Step-by-step explanation:

This question involves concepts of derivatives.

The velocity is the derivative of the position.

We use these following derivatives:

1) s = 1 + 9(cos t)

Find the body's speed at time t=pi/3 sec.

We have to find the derivative at . So

is a common angle, which has a sine of . So

The velocity at this time is of meters per second.

2) s = 12(sin t) - (cos t)

Find the body's velocity at time t=pi/4 sec.

We have to find the derivative at . So

is a common angle, which has both sine and cosine of . So

The velocity at this time is of meters per second.

34

step-by-step explanation:

7.25

step-by-step explanation:

we know that 7 equals to 7.0. we also know that 1/4=0.25. so we can add the two together and we get 7.25