If a spring is oscillating (moving) according to the velocity equation v(t) = 2sin(t) (in ft/s), then what is its displacement over its first π seconds of travel?

ANSWER

4 ft

EXPLANATION

The velocity equation of the oscillating spring is given by the function.

To find the displacement function, we need to to Integrate the velocity function.

At time t=0, there was no displacement.

This implies that,

The displacement function then becomes,

To find the displacement over the first π seconds, we put

into the equation for the displacement to get,

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500